Talk:Mass in special relativity/Archive 2

Archive 1

Archive 2

Archive 3

Erroneous statement "which change cannot be observed"

I have the impression that this article is so much affected by a one-sided POV that it even resulted in errors. The 1950 claim has been corrected to satisfaction (at least, it now looks fine to me), but more remains to be done. For example, the claim that relativistic mass change "cannot be observed". To the contrary: Feynman explained with a perfectly simple and straightforeward example how to observe relativistic mass increase, and I was similarly taught at college how to calculate the required increase of magnetic force in order to keep particles in their orbit because of mass increase - which boils down to accurately measuring relativistic mass. Of course this has to be done in motion, just as also time dilation is measured on moving clocks. Harald88 21:55, 9 May 2007 (UTC)

The phrase segment you refer to seems to be this one: "...some change in internal structure of the object, which change cannot be observed". What it says is that one cannot observe changes in the internal structure of an object as a function of the speed of an observer relative to the object (to make it clearer, as it does not matter who is considered to be at rest).

This corresponds to physical observation. If a deep-space proton flies by you at 0.999c, there will not be any change to your internal structure (or mass).

You can also read it as saying that there is no actual increase of the mass of the body, even if an observer "sees" an increase of its relativistic mass. In fact, that different observers (in different inertial frames) will see different values of the relativistic mass of the same object.

This also means that there is no change in the inertia or gravitational properties of the body, within special relativity, for different speeds of the body relative to an observer.

Calculations done with "relativistic mass" can give the right results, as a 4-coordinate transformation method, but with considerable care and pain. However, interpreting the results as an actual change in mass of the object is not warranted. That's why the phrase says ...some change in internal structure of the object, which change cannot be observed".

Hope this proves helpful. Thanks. Edgerck 22:17, 9 May 2007 (UTC)

It was indeed helpfull to see such a clear display of prejudice. To start with, it would be a misconception to think that the relativistic mass concept suggests a change in internal structure (and even more, to think that the proper mass of a body perfectly corresponds to the amount of protons and neutrons). Such a misconception must of course not be conveyed by this article.

But the sentence that follows the sentence we cite above seemed to suggest that relativistic mass can not be measured. Anyway, now I see that you have attempted to improve the text (but it's not really clear now, and it sounds more like a defence of an opinion using a circular argument than like an objective introduction of "mass").

Also, a general claim that there is no change in the inertia of a body with speed is erroneous. It might be that such a claim can be correct with certain definions of inertia, but in the ones I know inertia is resistance against acceleration, just as Wikipedia now states. By the way, calculations with relativistic mass are quite painless. :-)

Your last claim, "interpreting the results as an actual change in mass of the object is not warranted", may not be promoted in a Wikipedia article: it boils down to claiming that the opinion of Feynman and others was wrong because again other people have a different opinion about what should be meant with "mass". Instead, [WP:NPOV]] requires this article to represent the literature's different opinions fairly and accurately.

I hope that this was helpful too! I'll check the article at a later time. Harald88 18:01, 12 May 2007 (UTC)

While everyone is entitled to their opinion, of course, the article clearly states the chronology and evolution of the concept of mass in special relativity, and does so with source citations anyone can verify, from 1912 to present mainstream use in physics.

The begriff "relativistic mass" was created by Tolman in 1912 (with one definition) and then redefined by Tolman and others in 1934. While Feynman, Max Born, Schwartz, and other physics Nobel Prize winners deserve our study, the concept of science is that it is in constant progress. So, rather than being undeserving of the work of such giants and continue looking at physics on the same level they stood, we need to stand on their shoulders and look farther, higher, till we reach present day knowledge. It is not whether their "opinion" was wrong -- physics is an exact science governed by observation. No one can, or ever will, observe "relativistic mass" as mass.

Regarding your physics question, according to relativity theory: inertia provides resistance against acceleration 'and there is no change in the inertia of a body with speed relative to an observer. So, you see once again that the theory directly contradicts the idea of a relativistic mass that changes with speed.

Present day, mainstream, and verifiable knowledge is clearly given in the article. There have been a couple revisions lately. Please read the article when you have time. Thanks! Edgerck 23:34, 12 May 2007 (UTC)

Edgerick, your claim that "No one can, or ever will, observe "relativistic mass" as mass" is so erroenous that I can't understand how you could write it. It can be both calculated and measured - very different from [length contraction]] which until now could not be measured, it was the very first relativistic effect that was measured. This has also nothing to do with "progress of science" but everything with opinion and taste. Not everyone has the same taste, and Wikipedia must fairtly represent the diferent opinions.

Below I take note of the remark by count Iblis about your experiment. I will verify that strong claims in the article are backed up by reliable in-text references that are in agreement with NPOV policy.

Harald88 18:22, 3 June 2007 (UTC)

Mass of composite systems and conservation of mass in COM frame

On May 10 a number of changes were made:

<-- it is not true that mass is conserved for closed systems during chemical and nuclear reactions -->.

- :$m={\frac {E}{c^{2}}}$ (Center of Momentum frame for systems) + If a rest frame (also called center of mass frame or COM frame) can be defined for the system (which is equivalent to say that the system is not massless), then in the rest frame p = 0 and E takes on a value such that the mass is defined by:

- Since the COM frame (also called center-of-momentum frame) is chosen as the frame to measure the mass of most compound objects, Einstein's mass-energy equivalence formula E = mc² continues to apply in these circumstances. For example, if the mass of a nuclear bomb were measured by weighing it, this system mass would be a conserved invariant mass and would not change, even after the bomb exploded. However, after the explosion, this total system mass would also include the heat and light from the explosion. Only after the heat and light was removed (resulting in a non-closed system) would the mass of the constituents of the bomb show a decreased mass (in this case, a mass decrease equal to the mass of the heat and light removed). + :$m={\frac {E}{c^{2}}}$ (Center of Momentum frame for systems)

- Invariant mass is a concept widely used in particle physics, as the invariant mass of a particle's decay products is equal to its rest mass. It is this that is used to make measurements of the mass of particles such as the z particle or top quark. + This relation, which is valid only for the rest frame, is Einstein's famous mass-energy equivalence formula E = mc². <-- this relation cannot be applied to photons, so it cannot be applied to imply mass conservation in atomic explosions even if the system is considered large enough to be closed immediately after the explosion -->

The comments in the <--> bracketts are completely wrong, and I'm amazed that a physicist made them. The Einstein E = mc^2 CAN be applied to photons even if the m stands for invariant mass (all systems of photons have an invariant mass so long as not traveling in the same direction) so a nuclear or chemical reaction would NOT change total mass if confined on a scale, in a superstrong box. Blow up a nuke in such a box on a scale and the temp in the box would go up millions of degrees, but the mass of the box as seen by the scale, wouldn't budge. Only after you let the heat and radiation out, would the mass go down. And then, of course, the heat and radation carries away the missing mass, and in the COM frame, still HAS that mass, as part of a system in the old frame. Even a single photon has an invariant mass if it's part of a system in a COM frame, such as the box. In such a system the photon bouncing in the box will deliver downward momentum in any gravity field, and will contribute weight E/c^2, and thus (by the equivalence principle) also E/c^2 inertial mass. Thus, even a single photon's energy will contribute to invariant mass of that system. SBHarris 08:57, 24 May 2007 (UTC)

I agree with your comments. I'll check the history of the article and revert to the latest correct version. Count Iblis 12:57, 24 May 2007 (UTC)

I do not want to be overbearing and I feel I already discussed all clarifications on my edit and references. So, for right now, I just want to leave the matter in your hands and in the hands of the community. I'll be very happy to just watch and see how the system processes the correct information (see my talk page for definition) that I inserted, referenced according to the WP reliable sources policy, and clarified when contested. Thank you for your kind review. Edgerck 19:15, 24 May 2007 (UTC)

WP:NPOV and WP:RS violations

Richard Feynman in The Character of Physical Law wrote "The energy associated with motion appears as an extra mass, so things get heavier when they move." This POV and the associated name "relativistic mass" are outdated and not used in physics today. The opposite view, that ("things do not get heavy when they move") and that the only type of mass is invariant mass, is not the least controversial today (see WP:RS source below). This article is in violation of WP:NPOV and WP:RS. Historical references may mention the previous use of "relativistic mass", as done in the version of 03:09, 24 May 2007 (ref. below).

I am sourcing this comment under WP:NPOV and WP:RS, to (inter alia) Mass.

The last version that is not in violation is 03:09, 24 May 2007, as edited by 137.132.3.11.

I formally request the editor who reverted from 03:09, 24 May 2007 to reinstate that version in a timely manner, preventing other WP editors from working on the current version visible -- with the subsequent loss of work.

Thanks. 20:14, 25 May 2007 (UTC)Edgerck

Hi Edgerck,

The reason why I reverted your version was that you deleted a lot content, e.g. the example about the atomic bomb. The current version, like it or not, describes pretty accurately how professional physicists who use special relativity on a daily basis use this theory. Now, there are some physicists who hold minority opinions, like e.g. Okun. They prefer to define things in a slightly different way.

Although these things can be mentioned in this article, it is wrong to then delete any mention of the relativistic mass of the photon by saying that gamma times m is undefined. That's just silly. Of course, you can define the relativistic mass by declaring it to be the zeroth component of the four momentum. So, this is i.m.o. just a straw man argument.

Here on wikipedia, you have to be tolerant. I have my own POVs that go against the consensus on wikipedia which I can justify using reliable sources too. E.g. in modern physics one does not regard units and dimensions as fundamental quantities; you can use units in which h-bar = c = G = 1. This is regarded not just as a trick, but taken literally, i.e. h-bar, c and G are no more than conversion factors and the dimensions we have assigned to length time and mass are only there for historic reasons (Okun is a well known physicist who strongly disagrees with this view).

But if I were to edit wiki articles on this subject, completely rewriting them from the (correct) POV giving all the sources, then you would get an article that most other editors would not be happy with. E.g. the explanation of why dimensional analysis works would now be very difficult to follow for most people.

Now, in your edits of this article you didn't even address the examples that were given in the article, you just deleted them. Count Iblis 20:51, 25 May 2007 (UTC)

WP policy says that "Zero information is preferred to misleading or false information". Thus, what did not meet WP policy should be (as it was) deleted. Please provide a WP:NPOV and WP:RS compliant reference for every affirmation of article content that you make above (eg, example about the atomic bomb) or please do not use them in WP discussions or articles. Thanks.Edgerck 21:06, 25 May 2007 (UTC)

Don't be silly. Generally, sum of 4-momentum is conserved for all observers (all frames) in systems of interacting particles. See for example [1]. Conservation of energy and momenta as separate quantities are derivative of this, and the split between time-like and space-like quanties for energy and momentum (which cannot be defined without a frame) is what makes conservation of each of them single-frame-dependent, through time, in an interaction. Conservation of 4-momentum is much more general, and its limitations are only for volumes so large that space-like intervals need to be considered-- but then we don't have interacting systems anymore, do we? In any case, what we're talking about as "mass", and what you weigh on a scale, is the square root of the norm of 4-momentum. So obviously, it's conserved as well for small systems like fissioning nuclei and atom bombs. As for needing an RS cite for this, if I have a cite for a general case, I hardly need one for a specific one, by logic. Example: If angular momentum is conserved for all bodies, cite given, I don't need WP:RS to say it's conserved for a figure skater named Alice as she pulls in her arms, now do I? SBHarris 05:14, 26 May 2007 (UTC)

SBharris, I kindly ask you to please keep a civil tone. I did not question conservation of 4-momentum or energy, so this is off-topic. Mass is not in general conserved in SR even for closed systems, and I source this affirmation to authoritative elementary texts, including Lev Davidovich Landau and Evgenii Mikhailovich Lifshits, (1987) Elsevier, ISBN 0750627689.

BTW, your logic fails when you consider that mass must be conserved because E and p are conserved and m² = E² - p² in c=1 units. Can you see the mistake? Anyway, whether you can see it or not is irrelevant for this talk-page and WP (this is not a usenet discussion group in physics), as all the WP:NPOV verifiable sources say that mass is not conserved in SR in general, even for an isolated (free) system. Thank you. Edgerck 20:54, 26 May 2007 (UTC)

I also kindly remark that I verifiably sourced my comment about the current WP:NPOV and WP:RS violations to (inter alia) Mass -- which is linked to http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html. Thanks. Edgerck 21:43, 25 May 2007 (UTC)

Edgerck, please stop using these Straw Man arguments. This is all matter of definition. What matters is not what Okun has written or what you can find in the Landau&Lifshitz series (physics is not religion with Okun et al. the prophets). What matters is if given some definition of mass an assertion is correct. This article discusses several definitions of mass. One of these definitions is the invariant mass which is defined to be the energy in the zero-momentum frame. The fact that invariant mass is conserved (for an isolated system on which no external forces act) then follows from conservation of energy and momentum.

You can edit this article by giving the perspective of Okun, e.g. by saying that: "according to Okun, the relativistic mass of the photon cannot be defined". But just saying that it cannot be defined because Okun says so, is not allowed under the Wikipedia rules (even if the citation to Okun's article is given). This is because you can define the relativistic mass as the zeroth component of the four momentum which also works in case of the photon. Only if you demand that it must be given by a relation m times gamma does it become undefined. But that is not the standard definition. Count Iblis 21:56, 26 May 2007 (UTC)

CI: Please be respectful to others and their points of view. This means: Do not simply revert changes in a dispute. A tag calling the dispute a dispute -- see WP:NPOV and references -- should not be reverted unless there is a resolution. I disagree with its removal.

I kindly ask you to please reinstate the tags and follow WP policy.

Wikipedia relies on what reliable sources have said about the matter. By relying what sources have reported about a subject, WP limits the influence of an editor's POV. The incorrect information in this page is not accepted in the mainstream, and it is easy to find numerous sources taking the "correct", or mainstream, position.

I have made all the proper requests according to WP policy. I have no need to repeat myself, as WP has all my comments and edited pages in the archives. I am now entering a disengage phase in the hope that this will be helpful. Edgerck 23:29, 26 May 2007 (UTC)

Edgerck, there are many reliable sources that disagree with some of the points you have been making here. And you can't hold an article hostage by placing an POV tag on it, only to remove it when you get your way. Wikipedia has a very important rule that superseeds all other rules: Wikipedia:Ignore all rules. This rules says: "If the rules prevent you from improving or maintaining Wikipedia, ignore them." In this case you made edits that amounted to removal of a large amounts of content. You did not even address the issues raised in the removed content (you could have explained the removed examples differently...). Count Iblis 00:10, 27 May 2007 (UTC)

CI: WP policy says that "Zero information is preferred to misleading or false information". Thus, what did not meet WP policy should be (as it was) deleted. But (as you can see above) I said that before. You can "ignore all rules" at a price, and here the price was WP:NPOV, fairness, and maybe more.

Finally, no one can claim lack of my explanations. I used well-documented edit summary lines (that you called "chatty"), I left HTML tags in the text to call attention to incorrect text that was deleted, and I was available in multiple talk pages that you insist in revert. And, I summarized all the reasons in my user talk page, with a commented list of non-controversial answers in special relativity. Thank you.Edgerck 03:39, 27 May 2007 (UTC)

My two cents worth: I think the longer version of the article is a better starting point. I recall that the book A Guide to Introductory Physics Teaching by Arnold B. Arons has some useful comments -- I will look them up when I am back in my office. For the record, I am a professional physicist and have been teaching Special Relativity in a university physics department for the last few years. Timb66 10:56, 27 May 2007 (UTC)

All hands, including Timb66: I do not know about Timb66 qualifications but while it is easy and has no consequences for anonymous expert users to claim that invariant mass is conserved in SR, or that it is conserved in nuclear fission or fusion, this is not so for those few who use their real identities and qualifications. That's why I myself would prefer anonymous participation here, but I decided not. I want people to understand that these edits are serious and not some willy-nilly change.

As I announced about a week ago, I am conducting a public experiment to verify the trustworthiness of information in WP. Since information in WP is dynamic, I think this question cannot be answered by simply sampling at specific times. Instead, I decided to measure the lifetime of correct information (defined as correct according to WP policy) that was seeded in WP edits of selected articles. To reduce error in defining what is correct information I used topics that are not the least controversial today, even though they are widely misunderstood (to motivate editing interest).

This is not a "trap". To make sure that my justification for the edits were visible to any editor, I used several channels. I used well-documented edit summary lines, I left HTML tags in the text to call attention to incorrect text that was deleted or changed, and I was available in multiple talk pages, in addition to my own and a special talk page for this experiment. I also answered questions in other editor's talk pages.

Some changes, notwithstanding all the above, were reverted without a WP valid justification. Applying WP policy, typically results in the following steps, after a revert:

1. my statement, in the talk page, that the reverted version was correct according to NPOV and RS, with current, authoritative, mainstream, supporting references (while the current version is not), with a call for that version to be reinstated.

2. back arguments, without understanding (or, perhaps even reading) the current references, that the changes do not make sense and contradict well-known (but outdated) authors.

3. Reaffirmation of #1, with more references and with a tag for NPOV dispute placed in the article.

4. The tag is deleted under a call to the "break all rules" WP policy, stating that the article cannot be held "hostage" to a clearly incorrect edit.

While this goes on, anyone reading WP or editing it will not see correct information, where correct information means information that is not the least controversial today.

Now, how many more hoops should a voluntary WP editor have to jump in order to assure that WP reflects a viewpoint that is not controversial? Escalating the edit difference to any form of litigation does not seem to be a pleasant or fun activity, or rewarding in time.

The WP idea of "anyone can edit" finds its limits in the observation that "ignorance is bliss". Those who ignore, by definition, ignore that they ignore. Many subjects, most (but not all) of them technical, have subtleties that are important. It may be easy to read a correct phrase but it is a lot harder to write one, as anyone taking a test knows.

So, requiring a WP editor to follow NPOV and RS when the editor simply does not understand the subject (eg, is not able to ascertain the falsity of his beliefs versus what the references say), seems to be nonsensical. No one can write what they do not understand. The emphasis in WP:Verifiability goes nowhere in such context, and we can see that in WP.

WP is an encyclopedia project but the bottom of the iceberg is currently dominated by an education project for editors, which is open ended.

Looking at this as a pyramid, at the top we have well-educated, scholar editors, numbering (say) one hundred. At the bottom, we have well-meaning but clueless editors who want to edit what looks to them to be an error or lack of an example that they heard somewhere, but which is not correct (according to WP:Verifiability references that they do not have and, even if they would read, would have the same "error").

I don't have the answers. The problem is not anonymity. Academic qualifications do not always mean fairness or even competence. But it seems to me that current WP rules are somewhat in contradiction with the WP goals.

The experiment I mentioned above, hopefully, asks some of the right questions that we need to see in order to improve the quality of information found in WP. The experiment page is at Reliance on Information. Thanks. Edgerck 15:51, 27 May 2007 (UTC)

Reply by Count Iblis

You are making a big issue out of a minor point. The source of the disagreement is not the physics, but a simple matter of definitions. You seem to insist on defining invariant mass for composite systems in a clumsy way. If photons escape you will automatically re-define the system by omitting the photons. Fine, you can write that Okun et al. do this, why they do this, and that if you do this then what you get is what you wrote. But you cannot write (or suggest) that it isn't possible to define a composite system by including photons.

This article makes it very clear that the invariant mass of nuclei that are involved in nuclear reactions is not conserved, so as far as the physics is concerned, there is no disagreement at all!Count Iblis 16:33, 27 May 2007 (UTC)

This article makes it very clear that the invariant mass of nuclei that are involved in nuclear reactions is not conserved, so as far as the physics is concerned, there is no disagreement at all!Count Iblis 16:33, 27 May 2007 (UTC)

WP Policy for removing NPOV tags is resolution, not removal war. The technical content issues also affect Talk:Mass-energy_equivalence, and Talk:Introduction_to_special_relativity. The POV expressed by the editor above is not mainstream for more than 50 years in research and more than 30 years in textbooks, according to mainstream references (it is easy to find even more). , , ,, , , , , , ,

References

This dispute will never be resolved to your liking. The issue is not whether or not relativistic mass is an oudated concept. Of course, it is outdated and the current article says so. But that doesn't mean we can't write about relativistic mass in this article (or perhaps another) wiki article. Count Iblis 18:03, 27 May 2007 (UTC)

It's easy to do a diff between the current version and the version edited by 137.132.3.11 at 03:09, 24 May 2007, which is the last version I saw that complies with WP:Verifiability. Significant differences exist with the current version, for example:

CURRENT VERSION

Reactions in this special inertial frame (so long as the system remains closed) do not produce changes in mass, relativistic mass, or energy.

which is incorrect per references cited; and this section (which is correct and cites mainstream reference using current POV) was deleted:

VERIFIED VERSION

Today, following Einstein, instead of introducing the concept of relativistic mass when changing frames of reference, one uses the relativistic energy-momentum relation. In this relation, mass is always invariant. Scales and balances operate in the rest frame of objects being measured, measuring mass.

<reference/>

and also this was deleted, even though is cited almost verbatim in current POV references):

VERIFIED VERSION

This usage is less confusing because it does not appear to make the increase of energy of an object with velocity or momentum to be connected with some change in internal structure of the object that would increase its mass, which change cannot be observed. In other words, one cannot observe changes in the mass of an object as a function of the speed of an observer relative to the object (to make it clearer, as it does not matter who is considered to be at rest).

but this fringe view was added without reference (no mainstream author supports it):

CURRENT VERSION

For example, this formula states that a photon (which moves at the speed of light) has relativistic mass.

This incorrect view (rejected since 1920, mass is not conserved in SR, not even in closed systems), was also added, also without WP:RS source :

CURRENT VERSION

Note that the invariant mass of a closed system is also independent of observer or inertial frame, and is a constant, conserved quantity for closed systems and single observers, even during chemical and nuclear reactions.

And more. The differences (additions and deletions), are such that the current article should be immediately provided with the tags that I inserted, to prevent trusting users from trusting such content, and reversed as soon as possible to the last verified version.

This is not about one definition, or a historical note that became too large. It's about basic misleading and false information that was inserted while verified and correct by WP:RS information that contradicted it was simply deleted.

Thank you. Edgerck 18:29, 27 May 2007 (UTC)

You wrote: "CURRENT VERSION

Reactions in this special inertial frame (so long as the system remains closed) do not produce changes in mass, relativistic mass, or energy.

which is incorrect per references cited; and this section (which is correct and cites mainstream reference using current POV) was deleted:"

Reply: This is not incorrect at all. Okun considers something else he does not consider the invariant mass of the entire' system after the reaction. If you consider the whole system which has some total four-momentum, then the invariant mass corresponding to that total four-momentum cannot change assuming that the system is completely isolated and insulated. If you think that his is oincorrect, then just give a counterexample instead of giving the same refs over and over again (which don't prove your point).

Of course, if you just add up the (invariant, or rest) masses of the particles in the system, then that sum will decrease after the reaction. If that point is not clearly explained in this article, then that must be explained better in this article. No one is objecting to that. What we are objecting to is the notion that Okun can declare a "fatwa" on wikipedia, precluding us to consider the isolated system containing the particles as a system in its own right with its own invariant mass, which will then be conserved because the isolated system has, by asumption, no interactions with anything else. Count Iblis 20:24, 27 May 2007 (UTC)

Edgerck wrote:

"but this fringe view was added without reference (no mainstream author supports it):

CURRENT VERSION

For example, this formula states that a photon (which moves at the speed of light) has relativistic mass."

You are confusing two issues. One is the fact that the use of "relativistic mass" is fringe. There is no dispute about that, and the article does say that in the scientific community no one uses "relativistic mass" (because it is the same as the total energy).

Another issue is that if we do consider this (fringe) concept of relativistic mass, then the photon has a relativistic mass equal to E/c^2. How on Earth can that be disputed (apart from a straw man-like argument that m times gamma is undefined)? Count Iblis 20:38, 27 May 2007 (UTC)

---

Hi. I am having trouble following this discussion because I can't see the boundaries of the postings. Can you please insert lines to mark the boundaries in this section? i could do it using the history but it would be quicker for one of you two. thanks! Timb66 21:18, 27 May 2007 (UTC)

---

CI: WP policy prohibits editing other people's postings in the talk-page. I just reverted what you did with this talk-list. What you are doing is not new. This is not a show of good faith. DO NOT EDIT MY POSTS, MARK OR MOVE THEM.

It also seems to be a good guess that you are using multiple user IDs to manipulate discussions.

Please act kindly, fairly and respect the community's rules. Thank you.Edgerck 00:15, 28 May 2007 (UTC)

WP:NPOV and WP:RS violations

Richard Feynman in The Character of Physical Law wrote "The energy associated with motion appears as an extra mass, so things get heavier when they move." This POV and the associated name "relativistic mass" are outdated and not used in physics today. The opposite view, that ("things do not get heavy when they move") and that the only type of mass is invariant mass, is not the least controversial today (see WP:RS source below). This article is in violation of WP:NPOV and WP:RS. Historical references may mention the previous use of "relativistic mass", as done in the version of 03:09, 24 May 2007 (ref. below).

I am sourcing this comment under WP:NPOV and WP:RS, to (inter alia) Mass.

The last version that is not in violation is 03:09, 24 May 2007, as edited by 137.132.3.11.

I formally request the editor who reverted from 03:09, 24 May 2007 to reinstate that version in a timely manner, preventing other WP editors from working on the current version visible -- with the subsequent loss of work.

Thanks. 20:14, 25 May 2007 (UTC)Edgerck

Reply by Count Iblis

Hi Edgerck,

The reason why I reverted your version was that you deleted a lot content, e.g. the example about the atomic bomb. The current version, like it or not, describes pretty accurately how professional physicists who use special relativity on a daily basis use this theory. Now, there are some physicists who hold minority opinions, like e.g. Okun. They prefer to define things in a slightly different way.

Although these things can be mentioned in this article, it is wrong to then delete any mention of the relativistic mass of the photon by saying that gamma times m is undefined. That's just silly. Of course, you can define the relativistic mass by declaring it to be the zeroth component of the four momentum. So, this is i.m.o. just a straw man argument.

Here on wikipedia, you have to be tolerant. I have my own POVs that go against the consensus on wikipedia which I can justify using reliable sources too. E.g. in modern physics one does not regard units and dimensions as fundamental quantities; you can use units in which h-bar = c = G = 1. This is regarded not just as a trick, but taken literally, i.e. h-bar, c and G are no more than conversion factors and the dimensions we have assigned to length time and mass are only there for historic reasons (Okun is a well known physicist who strongly disagrees with this view).

But if I were to edit wiki articles on this subject, completely rewriting them from the (correct) POV giving all the sources, then you would get an article that most other editors would not be happy with. E.g. the explanation of why dimensional analysis works would now be very difficult to follow for most people.

Now, in your edits of this article you didn't even address the examples that were given in the article, you just deleted them. Count Iblis 20:51, 25 May 2007 (UTC)

Reply by Edgerck

WP policy says that "Zero information is preferred to misleading or false information". Thus, what did not meet WP policy should be (as it was) deleted. Please provide a WP:NPOV and WP:RS compliant reference for every affirmation of article content that you make above (eg, example about the atomic bomb) or please do not use them in WP discussions or articles. Thanks.Edgerck 21:06, 25 May 2007 (UTC)

Reply by Sbharris

Don't be silly. Generally, sum of 4-momentum is conserved for all observers (all frames) in systems of interacting particles. See for example[2]. Conservation of energy and momenta as separate quantities are derivative of this, and the split between time-like and space-like quanties for energy and momentum (which cannot be defined without a frame) is what makes conservation of each of them single-frame-dependent, through time, in an interaction. Conservation of 4-momentum is much more general, and its limitations are only for volumes so large that space-like intervals need to be considered-- but then we don't have interacting systems anymore, do we? In any case, what we're talking about as "mass", and what you weigh on a scale, is the norm of system total vector 4-momentum. So obviously, it's conserved as well for small systems like fissioning nuclei and atom bombs. As for needing an RS cite for this, if I have a cite for a general case, I hardly need one for a specific one, by logic. Example: If angular momentum is conserved for all bodies, cite given, I don't need WP:RS to say it's conserved for a figure-skater named Alice as she pulls in her arms, now do I? SBHarris 05:14, 26 May 2007 (UTC)

Reply by Edgerck

SBharris, I kindly ask you to please keep a civil tone. I did not question conservation of 4-momentum or energy, so this is off-topic. Mass is not in general conserved in SR even for closed systems, and I source this affirmation to authoritative elementary texts, including Lev Davidovich Landau and Evgenii Mikhailovich Lifshits, (1987) Elsevier, ISBN 0750627689.

BTW, your logic fails when you consider that mass must be conserved because E and p are conserved and m² = E² - p² in c=1 units. Can you see the mistake? Anyway, whether you can see it or not is irrelevant for this talk-page and WP (this is not a usenet discussion group in physics), as all the WP:NPOV verifiable sources say that mass is not conserved in SR in general, even for an isolated (free) system. Thank you. Edgerck 20:54, 26 May 2007 (UTC)

I also kindly remark that I verifiably sourced my comment about the current WP:NPOV and WP:RS violations to (inter alia) Mass -- which is linked to http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html. Thanks. Edgerck 21:43, 25 May 2007 (UTC)

Rebuttal by SBHarris

SBharris, I kindly ask you to please keep a civil tone. I did not question conservation of 4-momentum or energy, so this is off-topic. Mass is not in general conserved in SR even for closed systems, and I source this affirmation to authoritative elementary texts, including Lev Davidovich Landau and Evgenii Mikhailovich Lifshits, (1987) Elsevier, ISBN 0750627689.

Answer Since we're discussing what is partly a matter of controversy of modern notation in physics-- namely, how shall we define "mass" is SR-- the text you're referring to is not very useful, because it's based on lecture notes from the middle of the last century. Landau and Lifschitz are both dead. Landau died in 1968 and did no creative work after his skull fracture and coma in 1962. His lecture notes are not appropriate to the subject of modern notation in physics. If L&L say "mass" is not conserved in closed systems in SR, they must refer to some mass defined as some kind of sum of invariant masses, not the total system invariant or proper mass, which most modern relativists (included Thorne, see my own much more recent reference), and also originally and usually Einstein (see your own reference below) preferred as the definition for "msss". This quantity is directly the 4-momentum norm, so obviously it's conserved if total 4-momentum is, in systems. Which, in fact, is the case; are you really arguing otherwise? Discussion of 4-momentum of systems is hardly off topic, since most of the physics community now defines mass in SR as Mandelstam's s, a simple function of the length of the system total 4-momentum vector (the 4-momentum vector norm, in natural units). You do understand this, I hope. The Baez reference you give discusses the issue fully, and Taylor and Wheeler, as well as Thorne in the reference I gave you, all discuss it fully. Thorne is full professor of physics at Caltech, co-author of the most-used text in GR, and one of the most famous living relativists. His elementary text, which I referenced for you directly above, is available online, and is still being expanded by Thorne. If you want to know how the average modern physicist thinks of mass in SR, you must read Misner, Thorne, Taylor, Wheeler, etc. Who are all still alive. Not edited lecture notes of a man in his grave for close to half a century, now.

BTW, your logic fails when you consider that mass must be conserved because E and p are conserved and m² = E² - p² in c=1 units. Can you see the mistake? Anyway, whether you can see it or not is irrelevant for this talk-page and WP (this is not a usenet discussion group in physics), as all the WP:NPOV verifiable sources say that mass is not conserved in SR in general, even for an isolated (free) system. Thank you. Edgerck 20:54, 26 May 2007 (UTC)

Answer I see no mistake in logic. If you pick a particular frame and stick to it, so that E and p are conserved for a system interaction, then obviously total E² - p² will be conserved also in that frame. It's just a matter of picking out the E and p vector components for each particle, adding them up, then doing the square and subtraction AFTER that, then taking square root to get length of your system vector. Those are vector rules: because these are all vector quantities, so you have to add the components separately before you consider their total 4-length to get the proper mass of the system.

For individual photons moving in opposite directions, that minus sign means the momenta can cancel when added, but the energies always simply add. So even though (for example) each photon has zero proper mass (this is always the case in any frame), the sum of their masses as calculated by summed 4-momenta, is NOT zero. Instead, the system of two photons where p's cancel (eash photon has the same E) has a 4 momenta of 2E, and the length of this in natural units is the same as its relativistic mass. This is true for any frame in which total p = 0 (proper mass is the same as relativistic mass wherever total system p = 0), so obviously mass of sytems in interactions is equally conserved in all such frames (ie, on scales where you can weigh a system, so p must be zero in the system) no matter which definition of mass you use.

What isn't so obvious, is that proper mass (invariant mass) of systems is conserved in interactions, even in frames where p is not zero, simply because 4-momentum of systems is Lorentz-invariant (pick any frame you like, and even change it before and after the interaction, and it still works!), whereas E and p are not Lorentz-invariant, so are not conserved if you change frames. Nor is relativistic mass, since it's a function of E (in natural units, it IS E). That's one reason why proper mass is a more useful definition of mass: for any given interaction you can switch frames from COM to lab frame, and back, and it makes no difference in the answer. The mass of a particle is easy to calculate in its own rest frame, if that's also the summed energy of its decay produts in the COM frame of the decay products, which is the same as the norm of summed 4-momenta for them in the lab frame. Thus, it's better to define mass that way, as the norm of summed 4-momenta, and simply say THAT mass (by that definition) is conserved in all interactions. But the case for interactions in systems which you can weigh on scales (like a bomb in an unbreakable box), where total p = 0, should be especially easy to see, and I cannot fathom why you argue with it when used as an example. The sum of rest masses is not conserved, but the summed mass of a p=0 system, before and after interaction, which is Lorentz-invariant, IS conserved. Simply because system 4-momentum is, using vector addition rules. You seem to want to define mass as something other than length of a vector for systems, then also refuse to use vector rules to add system masses. Sorry, but most modern physicists would prefer to do it the 4-momentum way, and that way works. Proper mass (system total 4-momentum norm) is conserved.

I also kindly remark that I verifiably sourced my comment about the current WP:NPOV and WP:RS violations to (inter alia) Mass -- which is linked to http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html. Thanks. Edgerck 21:43, 25 May 2007 (UTC)

Answer And I kindly observe that there isn't a sentence in that essay to suggest that mass isn't conserved in an interacting system, unless (perhaps) it's some kind of sum of rest masses, or sum of proper masses, that you're talking about. But as discussed above, it's not kosher to sum proper masses-- to get system proper mass you don't sum proper masses, but rather you must sum E's and p's separately as vector quantities, and then calculate system proper mass AFTER, as the norm of the final vector. That quantity IS conserved.

For systems on scales, all types of system mass (either relativistic or proper/invariant) are conserved over time, so long as the system is closed. But change frames and now relativistic mass of the system is no longer conserved, because it's not Lorentz-invariant. However, total system invariant mass obviously still is conserved, because obviously total system summed 4-momentum still is invariant. I gave you a cite for conservation of 4-momenta in interactions in SR (see equation 1.3 in Thorne). If you go to Baez above to see that 4-momenta is the basis of the most commonly used definition of mass in SR today (no matter what Landau and Lifschitz thought 60 years ago), then there you are. It's nice that Einstein associated mass with "proper mass" (which is associated with the total 4-momentum) also. We have Baez to thank for finding those references. SBHarris 18:20, 28 May 2007 (UTC)

Reply by Count Iblis

Edgerck, please stop using these Straw Man arguments. This is all matter of definition. What matters is not what Okun has written or what you can find in the Landau&Lifshitz series (physics is not religion with Okun et al. the prophets). What matters is if given some definition of mass an assertion is correct. This article discusses several definitions of mass. One of these definitions is the invariant mass which is defined to be the energy in the zero-momentum frame. The fact that invariant mass is conserved (for an isolated system on which no external forces act) then follows from conservation of energy and momentum.

You can edit this article by giving the perspective of Okun, e.g. by saying that: "according to Okun, the relativistic mass of the photon cannot be defined". But just saying that it cannot be defined because Okun says so, is not allowed under the Wikipedia rules (even if the citation to Okun's article is given). This is because you can define the relativistic mass as the zeroth component of the four momentum which also works in case of the photon. Only if you demand that it must be given by a relation m times gamma does it become undefined. But that is not the standard definition. Count Iblis 21:56, 26 May 2007 (UTC)

Reply by Edgerck

CI: Please be respectful to others and their points of view. This means: Do not simply revert changes in a dispute. A tag calling the dispute a dispute -- see WP:NPOV and references -- should not be reverted unless there is a resolution. I disagree with its removal.

I kindly ask you to please reinstate the tags and follow WP policy.

Wikipedia relies on what reliable sources have said about the matter. By relying what sources have reported about a subject, WP limits the influence of an editor's POV. The incorrect information in this page is not accepted in the mainstream, and it is easy to find numerous sources taking the "correct", or mainstream, position.

I have made all the proper requests according to WP policy. I have no need to repeat myself, as WP has all my comments and edited pages in the archives. I am now entering a disengage phase in the hope that this will be helpful. Edgerck 23:29, 26 May 2007 (UTC)

Reply by Count Iblis

Edgerck, there are many reliable sources that disagree with some of the points you have been making here. And you can't hold an article hostage by placing an POV tag on it, only to remove it when you get your way. Wikipedia has a very important rule that superseeds all other rules: Wikipedia:Ignore all rules. This rules says: "If the rules prevent you from improving or maintaining Wikipedia, ignore them." In this case you made edits that amounted to removal of a large amounts of content. You did not even address the issues raised in the removed content (you could have explained the removed examples differently...). Count Iblis 00:10, 27 May 2007 (UTC)

Reply by Edgerck

CI: WP policy says that "Zero information is preferred to misleading or false information". Thus, what did not meet WP policy should be (as it was) deleted. But (as you can see above) I said that before. You can "ignore all rules" at a price, and here the price was WP:NPOV, fairness, and maybe more.

Finally, no one can claim lack of my explanations. I used well-documented edit summary lines (that you called "chatty"), I left HTML tags in the text to call attention to incorrect text that was deleted, and I was available in multiple talk pages that you insist in revert. And, I summarized all the reasons in my user talk page, with a commented list of non-controversial answers in special relativity. Thank you.Edgerck 03:39, 27 May 2007 (UTC)

Reply by Timb66

My two cents worth: I think the longer version of the article is a better starting point. I recall that the book A Guide to Introductory Physics Teaching by Arnold B. Arons has some useful comments -- I will look them up when I am back in my office. For the record, I am a professional physicist and have been teaching Special Relativity in a university physics department for the last few years. Timb66 10:56, 27 May 2007 (UTC)

Reply by Edgerck

All hands, including Timb66: I do not know about Timb66 qualifications but while it is easy and has no consequences for anonymous expert users to claim that invariant mass is conserved in SR, or that it is conserved in nuclear fission or fusion, this is not so for those few who use their real identities and qualifications. That's why I myself would prefer anonymous participation here, but I decided not. I want people to understand that these edits are serious and not some willy-nilly change.

As I announced about a week ago, I am conducting a public experiment to verify the trustworthiness of information in WP. Since information in WP is dynamic, I think this question cannot be answered by simply sampling at specific times. Instead, I decided to measure the lifetime of correct information (defined as correct according to WP policy) that was seeded in WP edits of selected articles. To reduce error in defining what is correct information I used topics that are not the least controversial today, even though they are widely misunderstood (to motivate editing interest).

This is not a "trap". To make sure that my justification for the edits were visible to any editor, I used several channels. I used well-documented edit summary lines, I left HTML tags in the text to call attention to incorrect text that was deleted or changed, and I was available in multiple talk pages, in addition to my own and a special talk page for this experiment. I also answered questions in other editor's talk pages.

Some changes, notwithstanding all the above, were reverted without a WP valid justification. Applying WP policy, typically results in the following steps, after a revert:

1. my statement, in the talk page, that the reverted version was correct according to NPOV and RS, with current, authoritative, mainstream, supporting references (while the current version is not), with a call for that version to be reinstated.

2. back arguments, without understanding (or, perhaps even reading) the current references, that the changes do not make sense and contradict well-known (but outdated) authors.

3. Reaffirmation of #1, with more references and with a tag for NPOV dispute placed in the article.

4. The tag is deleted under a call to the "break all rules" WP policy, stating that the article cannot be held "hostage" to a clearly incorrect edit.

While this goes on, anyone reading WP or editing it will not see correct information, where correct information means information that is not the least controversial today.

Now, how many more hoops should a voluntary WP editor have to jump in order to assure that WP reflects a viewpoint that is not controversial? Escalating the edit difference to any form of litigation does not seem to be a pleasant or fun activity, or rewarding in time.

The WP idea of "anyone can edit" finds its limits in the observation that "ignorance is bliss". Those who ignore, by definition, ignore that they ignore. Many subjects, most (but not all) of them technical, have subtleties that are important. It may be easy to read a correct phrase but it is a lot harder to write one, as anyone taking a test knows.

So, requiring a WP editor to follow NPOV and RS when the editor simply does not understand the subject (eg, is not able to ascertain the falsity of his beliefs versus what the references say), seems to be nonsensical. No one can write what they do not understand. The emphasis in WP:Verifiability goes nowhere in such context, and we can see that in WP.

WP is an encyclopedia project but the bottom of the iceberg is currently dominated by an education project for editors, which is open ended.

Looking at this as a pyramid, at the top we have well-educated, scholar editors, numbering (say) one hundred. At the bottom, we have well-meaning but clueless editors who want to edit what looks to them to be an error or lack of an example that they heard somewhere, but which is not correct (according to WP:Verifiability references that they do not have and, even if they would read, would have the same "error").

I don't have the answers. The problem is not anonymity. Academic qualifications do not always mean fairness or even competence. But it seems to me that current WP rules are somewhat in contradiction with the WP goals.

The experiment I mentioned above, hopefully, asks some of the right questions that we need to see in order to improve the quality of information found in WP. The experiment page is at Reliance on Information. Thanks. Edgerck 15:51, 27 May 2007 (UTC)

Reply by Count Iblis

You are making a big issue out of a minor point. The source of the disagreement is not the physics, but a simple matter of definitions. You seem to insist on defining invariant mass for composite systems in a clumsy way. If photons escape you will automatically re-define the system by omitting the photons. Fine, you can write that Okun et al. do this, why they do this, and that if you do this then what you get is what you wrote. But you cannot write (or suggest) that it isn't possible to define a composite system by including photons.

This article makes it very clear that the invariant mass of nuclei that are involved in nuclear reactions is not conserved, so as far as the physics is concerned, there is no disagreement at all!Count Iblis 16:33, 27 May 2007 (UTC)

Reply by Edgerck

WP Policy for removing NPOV tags is resolution, not removal war. The technical content issues also affect Talk:Mass-energy_equivalence, and Talk:Introduction_to_special_relativity. The POV expressed by the editor above is not mainstream for more than 50 years in research and more than 30 years in textbooks, according to mainstream references (it is easy to find even more). , , ,, , , , , , ,

References

Reply by Count Iblis

This dispute will never be resolved to your liking. The issue is not whether or not relativistic mass is an oudated concept. Of course, it is outdated and the current article says so. But that doesn't mean we can't write about relativistic mass in this article (or perhaps another) wiki article. Count Iblis 18:03, 27 May 2007 (UTC)

Reply by Edgerck

It's easy to do a diff between the current version and the version edited by 137.132.3.11 at 03:09, 24 May 2007, which is the last version I saw that complies with WP:Verifiability. Significant differences exist with the current version, for example:

CURRENT VERSION

Reactions in this special inertial frame (so long as the system remains closed) do not produce changes in mass, relativistic mass, or energy.

which is incorrect per references cited; and this section (which is correct and cites mainstream reference using current POV) was deleted:

VERIFIED VERSION

Today, following Einstein, instead of introducing the concept of relativistic mass when changing frames of reference, one uses the relativistic energy-momentum relation. In this relation, mass is always invariant. Scales and balances operate in the rest frame of objects being measured, measuring mass.

<reference/>

and also this was deleted, even though is cited almost verbatim in current POV references):

VERIFIED VERSION

This usage is less confusing because it does not appear to make the increase of energy of an object with velocity or momentum to be connected with some change in internal structure of the object that would increase its mass, which change cannot be observed. In other words, one cannot observe changes in the mass of an object as a function of the speed of an observer relative to the object (to make it clearer, as it does not matter who is considered to be at rest).

but this fringe view was added without reference (no mainstream author supports it):

CURRENT VERSION

For example, this formula states that a photon (which moves at the speed of light) has relativistic mass.

This incorrect view (rejected since 1920, mass is not conserved in SR, not even in closed systems), was also added, also without WP:RS source :

CURRENT VERSION

Note that the invariant mass of a closed system is also independent of observer or inertial frame, and is a constant, conserved quantity for closed systems and single observers, even during chemical and nuclear reactions.

And more. The differences (additions and deletions), are such that the current article should be immediately provided with the tags that I inserted, to prevent trusting users from trusting such content, and reversed as soon as possible to the last verified version.

This is not about one definition, or a historical note that became too large. It's about basic misleading and false information that was inserted while verified and correct by WP:RS information that contradicted it was simply deleted.

Thank you. Edgerck 18:29, 27 May 2007 (UTC)

Reply by Count Iblis

You wrote: "CURRENT VERSION Reactions in this special inertial frame (so long as the system remains closed) do not produce changes in mass, relativistic mass, or energy.

which is incorrect per references cited; and this section (which is correct and cites mainstream reference using current POV) was deleted:"

Reply: This is not incorrect at all. Okun considers something else he does not consider the invariant mass of the entire' system after the reaction. If you consider the whole system which has some total four-momentum, then the invariant mass corresponding to that total four-momentum cannot change assuming that the system is completely isolated and insulated. If you think that his is oincorrect, then just give a counterexample instead of giving the same refs over and over again (which don't prove your point).

Of course, if you just add up the (invariant, or rest) masses of the particles in the system, then that sum will decrease after the reaction. If that point is not clearly explained in this article, then that must be explained better in this article. No one is objecting to that. What we are objecting to is the notion that Okun can declare a "fatwa" on wikipedia, precluding us to consider the isolated system containing the particles as a system in its own right with its own invariant mass, which will then be conserved because the isolated system has, by asumption, no interactions with anything else. Count Iblis 20:24, 27 May 2007 (UTC)

Additional reply by Count Iblis

Edgerck wrote:

"but this fringe view was added without reference (no mainstream author supports it):

CURRENT VERSION

For example, this formula states that a photon (which moves at the speed of light) has relativistic mass."

You are confusing two issues. One is the fact that the use of "relativistic mass" is fringe. There is no dispute about that, and the article does say that in the scientific community no one uses "relativistic mass" (because it is the same as the total energy).

Another issue is that if we do consider this (fringe) concept of relativistic mass, then the photon has a relativistic mass equal to E/c^2. How on Earth can that be disputed (apart from a straw man-like argument that m times gamma is undefined)? Count Iblis 20:38, 27 May 2007 (UTC)

---

Reply by Timb66

Hi. I am having trouble following this discussion because I can't see the boundaries of the postings. Can you please insert lines to mark the boundaries in this section? i could do it using the history but it would be quicker for one of you two. thanks! Timb66 21:18, 27 May 2007 (UTC)

Reply by Count Iblis (to Timb66)

I've partitioned the discussion in sections for clarity :) Count Iblis 21:47, 27 May 2007 (UTC)

quote from Arons

Thanks for cleaning up the above discussion. By the way, I am not anonymous, my name and affiliation are on my user page.

As promised, here is the quote from A Guide to Introductory Physics Teaching by Arnold B. Arons (1990, page 263):

For many years it was conventional to enter the discussion of dynamics through derivation of the relativistic mass, that is the mass-velocity relation, and this is probably still the dominant mode in textbooks. More recently, however, it has been increasingly recognized that relativistic mass is a troublesome and dubious concept. [See, for example, Okun (1989).] Not only does it get one into the infelicities associated with longitudinal and transverse masses, but it also tempts one to associate relativistic mass (rather than just rest mass) with gravitational effects. The latter association is basically incorrect. The sound and rigorous approach to relativistic dynamics is though direct development of that expression for momentum that ensures conservation of momentum in all frames:

$p={m_{0}v \over {\sqrt {1-{\frac {v^{2}}{c^{2}}}}}}\!$

rather than through relativistic mass. Unfortunately, it is more difficult to derive the momentum expression in a simple way that it is to obtain the mass-velocity relation from the collision gedanken experiments prevalent in the literature. [See Peters (1986) for a recent effort to simplify this derivation.]

I suggest the above quote be included verbatim in the article. Timb66 01:44, 28 May 2007 (UTC)

Thanks! Count Iblis 22:07, 28 May 2007 (UTC)

Edgerck on massless photon

see here

Nonetheless, in SR, a photon has no mass. So, if an atom emits a photon, the system atom+photon has less mass, even though it has the same energy. Hope this is useful. Edgerck 22:36, 28 May 2007 (UTC)

Thanks Edgerck! I guess we can now move on!  :) Count Iblis 23:23, 28 May 2007 (UTC)

You are copying my quote from my user page. I had a minor edit on it, changing "weight" to "mass", which I changed above as well. Barring vandalism, the quote above is correctly mine. Have fun with it! Edgerck 00:00, 29 May 2007 (UTC)

BTW, I also edited the item's title, to keep it on the polite tone we should all enjoy in these discussions. Please feel free to add your opinion in your personal comment, also kindly. Thanks.Edgerck 00:05, 29 May 2007 (UTC)

Eh, you have a problem here. What do you do with a system of electron plus positron (or for that mattter, a single neutral pi-meson), which annihilates/decomposes into a pair of photons? According to you, the system mass just disappears, since the leptons or mesons have mass, but the photons do not. What do you think happens to the system's gravitational field when the mass disappears? Do you think this results in an expanding gravity wave with a hole in the middle of it, like a bubble, and a sharp boundary? If so, I assure you that GR contains no equations for what happens to G fields when source mass just disappears like that. The reason is that it doesn't have to, because it does not happen. Anymore than Maxwell's equations contain prescriptions for what happens to the EM field when charge disappears, like an electron winking out of the universe with no positron to counterbalance. That's what you're saying happens to mass (which has only one sort of "charge"), and I'm here to tell you that it doesn't. SBHarris 00:18, 29 May 2007 (UTC)

Edgerck gravity gedanken

A perfectly-mirrored evacuated sphere contains an atom at its center. It sits on a scale, which weighs atom and container. Now the atom emits a photon. While it is in flight Edgerck maintains the atom has less mass and weight, since the photon is massless and carries away energy. Presumably the system has less mass and weight while the photon is in flight? Presumably it has less of a gravity field? Now the photon bounces from the mirror and is reabsorbed by the atom. Does it now go back to its original mass, weight, and total gravitational power? If the gravitational field the atom and sphere generates, jitters like the system weight and mass are said to, now we have a gravitational wave generator. But gravitational waves carry energy. Where does the energy come from? Does this system run down, and what is the mechanism for this, in GR? Where is the changing mass-quadrupole moment, when an atom emits a photon? The student wishes to know. SBHarris 00:58, 29 May 2007 (UTC)

I will tell my opinion. I say my opinion because it may be right or wrong — you decide.

First, it's important to distinguish mass from the gravitational force acting upon a particle or body. It is not necessary to have mass in order to suffer the influence of a gravitational force!

A photon is massless; the gravitational attraction between a photon and a large mass (the Earth) is determined by their energy-momentum tensors, not just by their energies (that's why "relativistic mass" is not useful here either). The known result in GR is that the gravitational force attracting a horizontally moving photon to the Earth (ie, horizontal to the Earth's surface) is twice as large as that attracting a vertically moving photon.

So, after the photon is emitted the atom loses mass given by E/c^2 and recoils. As the photon bounces back and forth in the box, vertically and horizontally, the photon may be subject to different gravitational forces as well. Nonetheless (and this is a grave error in SR!) the photon does not change its energy in the gravitational field, so that if and when it's absorbed by the atom, the atom increases its mass by the same amount E/c^2.

Result: the photon should have lost energy, but does not in SR. In GR, the photon red-shifts and the atom (if absorption of the less energetic photon is possible) will have less mass after absorption of the red-shifted photon.

Hope this is useful. Edgerck 01:42, 29 May 2007 (UTC)

Not really. We don't really need to have an external G field for this problem to work--that's only necessary to weigh it. Let us dispense with the earth and put our atom in its mirrored sphere out in space, between stars. The problem that your system is supposed to change mass while the photon is in flight, means that this system will still radiate gravitational waves, even sitting out in space. Do you believe this? The system can also be made of two atoms trading a single photon. You believe this all has less mass while the photon is in transit. Does that mean it creates less gravity? Has a smaller gravitational field? Yes or no? The G field goes up and down as the photon is transferred back and forth? You can't escape this. SBHarris 04:48, 29 May 2007 (UTC)

Addendum: About two weeks ago, foreseeing that some readers/editors of WP might fall into this trap, I pre-empted this question in my edit of this very page Mass in special relativity. My answer to this question survived several revisions until CI simply reverted the page to the current, incorrect page. Please see the last correct (LC) version, edited by 137.132.3.11 at 03:09, 24 May 2007 and look for section "Mass and gravitation". The LC version is here.

It is interesting that the same person (Sbarris) who could not see the relevance of the reverted version, also does not know the answer that was given in the LC version.

• Huh? What answer? You still haven't come to the real basis for my question. If the mass of a thing changes as it undergoes a reversible "constant energy decrease in mass," of the sort which you claim is possible in closed systems emitting photons, then its gravitational field will change, along with its mass. (Unless you're positing a disconnect between a thing's mass and its gravitational field). But physics will not support such gravitational waves from things (closed systems) going up and down in mass, according to your ideas. Thus, you have a really big problem in your explanation. Address it, please. SBHarris 04:48, 29 May 2007 (UTC)

This question and answer then exemplifies what I observed before, that WP editing rules are nonsensical. People get angry over an impossible proposition. Truth is subjective. An editor cannot write what he does not agree on. But anyone can edit.

So, I find that WP's rules are putting us somewhat at odds, and that is not what I personally want. Thank you. Edgerck 04:01, 29 May 2007 (UTC)

I follow SB's thought experiment but not your explanation; your addendum sounds more like resignation than explication. You don't answer any of SB's questions directly. Is it because you find them invalid? If so, in what way? Robert K S 04:17, 29 May 2007 (UTC)

It's all given above. I did answer the question and I did it 2x. In case any of you lost the first answer: search for these words above: "Result: the photon should have lost energy, but does not in SR."

For the second answer (which I actually gave two weeks ago), please click here (also given above) and read the section "Mass and gravitation".

Hope this helps more. Edgerck 05:50, 29 May 2007 (UTC)

Let's try it this way. Do you agree that an object's gravitational attraction is proportional to its mass? And that therefore if its mass is reduced, so too reduces its gravitational pull? Robert K S 06:04, 29 May 2007 (UTC)

Short answers -- 1) In SR: no answer; 2) in GR: No and (by logical consequence) No. All said above. Edgerck 06:14, 29 May 2007 (UTC)

Okay, but I have the feeling I didn't ask the right question. What's your answer if, instead of framing it in terms of "attraction", I ask if GR "spacetime curvatures" are the function of an object's mass? Robert K S 06:28, 29 May 2007 (UTC)

I am sorry to have to ask this: why don't you get it that this is off-topic in SR? I sourced it according to WP:NPOV and WP:RS. Thanks. Edgerck 17:49, 29 May 2007 (UTC)

We get that it's off-topic for an SR article, but since it's physics, it's not off-topic for an SR article TALK page, if it helps to clarify the problems and subject. You claim you answered this 2-weeks ago, but your pointer just points to an article which says the same thing you're saying now: that it's off-topic for SR. Which is a cop-out. SBHarris 18:12, 29 May 2007 (UTC)

Invariant_mass

I started a discussion on Talk:Invariant_mass on whether both that page and this page are needed. Editros of this page are welcome to comment there. Timb66 09:31, 29 May 2007 (UTC)

Comments on the definition of mass

Sbharris did a good job above by pointing out the flaw. But his argument involves gravity and that allowed Edgerck some opportunities to avoid checkmate.

To recapitulate, Edgerck is saying that the (invariant) mass of a closed box is not given by the total energy in the zero momentum frame.

Be truthful: I never said that. Please do not say what I said anymore, because you don't seem to be able to do it well. Further, this is not a "I said, you said" discussion. This is a WP group that should follow WP policy in WP:verifiability. I am also editing the section title, to be more civil. Edgerck 18:12, 29 May 2007 (UTC)

You are saying exactly that in case of the "atom+photon" system on this talk page and we discussed this issue further on your own talk page. Please forgive me for trying to understand your reasoning. Anyway, in the argument below, you can just take a box containing an atom and a photon instead of a box filled with radiation. The conclusion will be the same. Count Iblis 18:42, 29 May 2007 (UTC)

The mass, he says, is given by the contribution to the total energy of the "massive degrees of freedom".

Be truthful: I never said that or used those terms within quotes.

I am going to stop commenting here. This looks like manipulation of information but is not going to go very far, as any one can verify the archives. Edgerck 18:12, 29 May 2007 (UTC)

E.g., in a closed box filled with radiation, the energy of the radiation does not contribute to the invariant mass of the box.

In principle one could define mass this way. As long as your definitions are mathematically consistent, nothing will go wrong. The only way to point out that the definition is flawed is by showing that it is not related to what you measure when measuring properties that sould be directly related to mass.

This is what Sbharris did above by looking at gravitational effects. We could, of course, look at inertia instead, thus staying firmly within the realms of Special Relativity. This will deny Edgerck any option but to capitulate.

Consider a closed box filled with radiation (Edgerck does not dispute that the radiation contributes to the internal energy of the box). Let's now look at collisions. A mass collides with the box at some velocity and is reflected. How do we compute the velocity the box gains? Of course, that's pretty trivial. Momentum and energy are conserved. You write down that the total four-momentum stays the same. Some manipulations involving inner products with the four-vectors can be used to simplify the algebra.

In the end you obtain an answer that only depends on the intitial four-momenta of the systems involved. Never will you encounter an answer that involves the contribution of the four-momentum of the box from only massive particles. So, the mass as defined by Edgerck, is not what you measure when measuring inertia.

To make the unphysical nature of Edgerck's definition even more clear, suppose that the photon does have a tiny mass of, say $10^{-100000000000}$ eV so that it is physically irrelevant. Note that the best limits are of the order of $10^{-27}$ eV. Then, according to Edgerck's definition, the mass of the box would include the energy of the black body radiation. Count Iblis 13:30, 29 May 2007 (UTC)

Invitation to fair discussions

Folks, as I said before, I need to let the group digest the information I provided in my edits.

I regret if I have unsettled any views here, but WP photon agrees with WP:NPOV and WP:RS in saying that the photon is massless, so when an atom emits a photon (the photon momentum cancels with the atom's recoil momentum), the system atom+photon must have less mass .

I am going to stop commenting here, and just observe once in a while the evolution of the special relativity pages. I refer any editor and reader to the standard, authoritative, current textbooks that I cited according toWP:NPOV and WP:RS, for any such notions as discussed here. I fully agree with those sources and don't think these issues are the least controversial today.

Looking at this list's archives, I see evidence of information manipulation. I also see that competent editors left this group, dismayed. I invite this group to become more than just a raunchy usenet discussion group and follow the WP policy. You yourselves will have much to gain, not just WP.

Finally, I personally regret that I am not able to invite you over for a cup of coffee and have a chat. I think that I would like to meet each one of you personally. Thanks for giving me so much food for thought in regard to the education process in physics and the editing process in an open environment. Edgerck 18:12, 29 May 2007 (UTC)

"so when an atom emits a photon, the system atom+photon must have less mass". This is false. You can't source this from the literature. The photon is massless? Of course! The atom has less mass in the ground state than in the excited state? Of course! But can you add up the (invariant) mass of the photon to the invariant mass of the atom in its ground state to obtain the invariant mass of the atom+photon system? No, this is contrary to the way mass is defined for composite systems. No reputable source agrees with your conclusion. Count Iblis 18:27, 29 May 2007 (UTC)

You say:

I regret if I have unsettled any views here, but WP photon agrees with WP:NPOV and WP:RS in saying that the photon is massless, so when an atom emits a photon (the photon momentum cancels with the atom's recoil momentum), the system atom+photon must have less mass.

COMMENT: Wrong! As Count Iblis notes, that doesn't follow at all, inasmuch as photons contribute mass to systems even when free within the system, just as they contribute mass when absorbed into objects (yes, Einstein was right about that, and we have not overturned this idea in any way). And if you want a cite, see Taylor and Wheeler, Spacetime Physics, p 232: "A photon has no rest energy-- that is, no mass of its own. However, a photon can contribute energy and momentum to a system of objects [contributes 4-momentum or EM 4-vector magnitude]. Hence the presense of one [emphasis added] or more photons can increase the mass of that system. More: a system consisting entirely of zero-mass photons can itself have non-zero mass!" Following are some simple single photon-plus particle interactions which are just the sort that Ed Gerck is referring to-- except the answers given (that the system mass is invariant through them all) are not the ones that Ed wants us to accept. This is an authoritative text. I've given my cite specifically by page and even quote. Ed, let's see you do that with Landau and Lifschitz on this point. It would do you a lot of good to read the entire chapter 8 of this undergrad SR text, written by physicists who were full professors at (respectively) MIT and Princeton. Wheeler invented the term "black hole" and he does know relativistic physics historically. SBHarris 18:42, 29 May 2007 (UTC)

Folks: It is clear that my quote above needs clarification, which I am letting the group process. I added the comment in parentheses, to help with the process: (the photon momentum cancels with the atom's recoil momentum). Regarding the excellent book Spacetime Physics, I cite it in one of my non-controversial points in physics, for their two-photon example with mass. I agree with Taylor and Wheeler -- please note that they rightly say "can", not that it always does. Thanks again for your verification and inquiring minds. Edgerck 19:06, 29 May 2007 (UTC)

Taylor and Wheeler only say "can" because of the one special case of the 2-photon system where the photons are going in the same direction. THAT system has no mass. But an extra photon FROM THE OUTSIDE adds mass to any other kind of system, including any with a particle that has rest mass. A photon emitted from within a system does not change the system mass, if the system boundaries are drawn to continue to include the emitted photon. In your example, when an atom emits a photon, of course momenta cancel. If we start with an atom of rest energy E and a frame in which it is at rest, the atom's energy is E. If it emits a photon of energy e in this frame, then the atom now has energy E-e, and that includes not only its (new) rest mass, but also its kinetic energy of recoil (so the actual rest mass is a bit less than this, which is why the photon e comes out less if the atom emitting it is free to recoil, as directly confirmed by Mossbauer). The system energy is the sum of 4-momentum vectors (or EM-4-vectors if you like) and since the momenta cancel, that energy remains E. The invariant mass of the system remains E/c^2. When momenta in systems cancel, as they do here, Einstein's equation E = mc^2 remains true even when m is invariant mass.

And BTW, if you think Taylor and Wheeler is such an excellent book, why don't you read chapter 8? Particularly page 249 in which they point out that the .93 kg of mass converted to heat and light in a 20 megaton hydrogen bomb, does not appear as a mass deficit until the products cool; of such a bomb they say: "Thus, part of the constituents has been converted to energy, but the system mass has not changed!" Here, Taylor and Wheeler affirm in two examples what you explicitly deny. SBHarris 19:27, 29 May 2007 (UTC)

Folks and Sbharris in particular: It's easier to calculate the atom+photon mass (after the emission) in the atom's rest frame, where the atom is at rest and there is no kinetic energy for the atom or Doppler shift for the photon (even though a Doppler shift appears in the COM frame, where the emitter is not at rest). Since mass is invariant, the same result will apply to the COM frame and the lab frame.

Using m for the mass of the system atom+photon in the atom's rest frame, m² = [(M - e) + e]² - e², where M is the atom mass before the photon is emitted and e is the photon energy (also its momentum), in c=1 units. The result is m² = M² - e². The mass of the atom+photon system is less than the atom mass before emission. Mass is not conserved in a closed system.Edgerck 13:55, 30 May 2007 (UTC)

You forgot to consider the change in kinetic energy of the atom. Whatever frame you chose, after the photon is emitted, the velocity of the atom will have to change in order to satisfy conservation of momentum. M is thus not the energy of the atom before the collision. If you "rewind the movie" of the atom emitting the photon, you'll see an atom at rest absorbing a photon and ending up in an excited state. The total energy of the atom is gamma M, which to a good approxmation will be given by M + p^2/(2M). P is the momentum of the atom, which in c = 1 units is just e. This explains the magnitude of the "missing mass error" in your calculation

m = sqrt[M² - e² ] is approximately M[1-1/2 e^2/M^2] = M - e^2/(2M)

Count Iblis 14:56, 30 May 2007 (UTC)

There's no kinetic energy in the atom's rest frame. There's no kinetic energy history component in the energy-momentum equation. An observer "waking up" on the atom can readily calculate the atom's 4-momentum and add it to the photon's 4-momentum, to calculate the system's 4-momentum, and then the resulting magnitude, which is the system's mass. The same observer can then compare that value for mass to the mass value in the atom's rest frame before the photon was emitted, resulting in a mass deficit for the system in the atom's rest frame. Since mass is an invariant, an observer in the lab frame will measure the same thing. Note that energy is conserved in the process -- the system energy does not change when the photon is emitted.

Let me give another example, this time using a result already provided in Spacetime Physics. Take a laser medium as a closed system including some photons. These photons will be copied by the stimulated emission process, resulting in a field of photons all with the same momenta and collinear (because of the stimulated emission process). According to "Spacetime Physics", these photons will have mass zero. However, they did take energy out of the laser medium, which energy resulted in a decrease in mass of each photon emitter (atom or molecule). So, at the end of the process, in the closed system, mass decreased.

You can also see that Spacetime Physics contradicts itself on the atomic bomb example, versus the 2-photon system example. Only in the case when the photons have opposing momenta they will have mass equivalent to their energy according to E=mc², but the opposing momenta case is the exception, not the rule. So, most photons will not add up to compensate the mass decrease.

Another problem with Spacetime Physics in the atomic bomb example is that it puts E=mc² in front stage, whereas E=mc² only plays second fiddle in the energy released (less than 10%). For a verifiable quote on this, please read below.

When Einstein's most famous formula E=mc2 is mentioned, the atomic bomb is usually not far behind. Indeed there is a connection between the two, but it is subtle, and sadly, some popular science texts get it wrong: they will tell you that a nuclear explosion is "caused by the transformation of matter and energy" according to Einstein's formula, and that the gigantic conversion factor c2 is responsible for the immense power of such weapons.

The strength of the nuclear bond depends on the number of neutrons and protons involved. It varies in such a way that binding energy is released both in splitting up a heavy nucleus into smaller parts and in fusing light nuclei into heavier ones. This, as well as the chain reaction phenomenon, explains the immense power of nuclear bombs.

Einstein's formula plays second fiddle in that derivation - it's all about different kinds of energy. Sure, there are some radioactive decay processes following nuclear fission, and, if so inclined, one can view the decay of a neutron decaying into a slightly lighter proton as a transformation of rest energy into other energy forms. But these additional processes contribute a mere 10 per cent of the total energy set free in nuclear fission. The main contribution is due to binding energy being converted to other forms of energy - a consequence not of Einstein's formula, but of the fact that nuclear forces are comparatively strong, and that certain lighter nuclei are much more strongly bound than certain more massive nuclei. in MPG - Atomic Bomb

This is, BTW, another point where WP needed the correction I edited in.

Thanks for your comments. Edgerck 18:17, 31 May 2007 (UTC)

I have given a detailed calculation below which shows that you are completely wrong. Of course, you can choose the frame in which the atom is at rest, but you cannot just take the energy of the photon to be the difference of the rest masses of the atom in the ground state and excited state. The energy of the photon in any frame is given by the diference in the total energy of the atom before and after the emission of the photon. But in any given frame the velocity of the atom must have changed because momentum must be conserved.

So, there is a difference in kinetic energy of the atom as well, which you did not take into account at all. And the only way to take this effect into account is by doing a fully fledged calculation, as I did below. But then the fact that the invariant mass stays the same is basically "build in" a priori. But anyway, I did also evaluate all the quantities of interest in the rest frame of the atom after emission explicitely below. Count Iblis 18:43, 31 May 2007 (UTC)

CI: In 1958 Mößbauer reported that all atoms in a solid lattice absorb the recoil energy when a single atom in the lattice emits a gamma ray. Therefore, the experiment (atom+photon) can be done in such a way that the emitting atom will move very little even in the lab frame, therefore there is not any need for us to argue about the recoil velocity. Otherwise -- when recoil is significant -- the emitted photon's energy is reduced by the kinetic energy expressed in the atom's recoil velocity in the lab frame, which is automatically taken into account when I consider the photon energy in the inertial frame on the atom. In the atom frame, the emitter is at rest.Edgerck 19:21, 1 June 2007 (UTC)

Yes, and I've tried to tell Count Iblis that recoil velocity and energy isn't an issue in this system, because you can jigger it so they are so small as to make no difference in the physics. Alas, you can't do the same with recoil momentum, which remains. The basic reasons the photon adds mass to the Mößbauer while in flight (so mass never decreases so long as the system is closed to include the photon), is that the photon's momentum cancels its energy so it individually has no mass. However, the photon's momentum in the system is cancelled by the emitting system's recoil (even if that system is huge and gets almost no energy or velocity, it still gets the entire photon momentum), and thus when you're calculating system invariant mass, emitter and photon momenta cancel, their energies thus are free to add, and so total energy and total mass is conserved. Voila. SBHarris 19:39, 1 June 2007 (UTC)

Sbharris and all: For WP purposes, I have spoken my peace for my experiment's purposes and I am happy to let the information be processed within the community. Now, if you could help me find verifiable sources that say that mass is conserved in closed systems at all times in SR, that would be useful as well.

I note again that if any topic that I selected for correct information is not entirely clear, not sufficiently referenced, or even proves to be wrong, then that topic will be eliminated from the evaluation. You can read my experimental conditions for reducing my influence on the WP experiment on reliance on information. Thank you for your kind dialogue and help.Edgerck 19:50, 1 June 2007 (UTC)

The decay: excited atom ----> ground state atom + photon

Suppose that we know the (invariant) masses of the atom in the excited state and in the ground state. Let's denote the mass of the excited atom as $M_{1}$ and the mass of the ground state atom by $M_{2}$. Consider the frame in which the excited atom is at rest. That frame is thus the center of mass (zero momentum) frame.

Now, let's calculate the energy of the photon and the velocity of the atom in terms of $M_{1}$ and $M_{2}$. We assume that the photon will be emitted in the negative x-direction and we only write out the time and x-components of four-vectors. The four-momentum of the excited atom is $p_{1}=\left(M_{1},0\right)$, the four momentum of the atom in the ground state is $p_{2}=\left(\gamma M_{2},\gamma M_{2}v\right)$ and the four-momentum of the photon is $p_{3}=\left(e,-e\right)$, where $e$ is the energy of the photon.

Conservaton of four-momentum gives: $p_{1}=p_{2}+p_{3}$. We can write this as: $p_{2}=p_{1}-p_{3}$. Square both sides: $p_{2}^{2}=p_{1}^{2}+p_{3}^{2}-2p_{1}p_{3}$. Insert in here: $p_{1}^{2}=M_{1}^{2}$, $p_{2}^{2}=M_{2}^{2}$ and $p_{3}^{2}=0$, and the inner product $p_{1}p_{3}=eM_{1}$. This yields:

$e={\frac {M_{1}^{2}-M_{2}^{2}}{2M_{1}}}$ (1)

The x-component of the equation $p_{1}=p_{2}+p_{3}$ yields:

$e=\gamma M_{2}v$ (2)

Eliminating $e$ from (1) and (2) gives:

$\gamma v={\frac {1}{2}}\left(r-r^{-1}\right)$

$\gamma ={\frac {1}{2}}\left(r+r^{-1}\right)$

$v={\frac {r-r^{-1}}{r+r^{-1}}}$

where $r\equiv {\frac {M_{1}}{M_{2}}}$

All this has been derived rigorously from four-momentum conservation: $p_{1}=p_{2}+p_{3}$, the invariant mass of the combined system is thus equal to $M_{1}$. But what the above derivaton shows is that you don't need to make any ad hoc assumptions like Edgerck did to do these calculations. Edgerck obtained incorrect results because he did not rigorously stick to four-momentum conservation. From his incorrect reasoning he found that the invariant mass of the photon atom system was less than that of the excited atom. Count Iblis 18:27, 30 May 2007 (UTC)

Perhaps it is interesting to perform a Lorentz transformation to the rest frame of the atom after the photon has been emitted. The energy of the photon is this frame is given by:

$e'=\gamma \left(e+ve\right)=\left(\gamma v+\gamma \right)e=re={\frac {M_{1}^{2}-M_{2}^{2}}{2M_{2}}}$

Here we have used the above equations for $\gamma v$ and $\gamma$. We can now do what Edgerck attempted to do above: Write down the total four-momentum of the atom-photon system in te rest frame of the atom and square it to obtain the square of the invariant mass.

The four-momentum of the atom is:

$P_{\text{atom}}=\left(M_{2},0\right)$

The four-momentum of the photon is:

$P_{\text{photon}}=\left(e',-e'\right)$

The four-momentum of the atom-photon system is:

$P_{\text{total}}=\left(M_{2}+e',-e'\right)$

And thus:

$m^{2}=P_{\text{total}}^{2}=\left(M_{2}+e'\right)^{2}-e'^{2}=M_{2}^{2}+2M_{2}e'$

Insert in here $e'={\frac {M_{1}^{2}-M_{2}^{2}}{2M_{2}}}$ which we derived above, and you get:

$m^{2}=M_{1}^{2}$

Edgerck's mistake was to assume that $M_{2}=M_{1}-e'$, or $e'=M_{2}-M_{1}$. This is clearly false, although it is approximately true:

$e'={\frac {M_{1}^{2}-M_{2}^{2}}{2M_{2}}}={\frac {\left(M_{1}-M_{2}\right)\left(M_{1}+M_{2}\right)}{2M_{2}}}$

If we define ΔM as the mass difference between exited and ground states of the atom: $\Delta M=M_{1}-M_{2}$, then this becomes (exactly):

$e'=\Delta M+{\frac {\Delta M^{2}}{2M_{2}}}$

Edgerck's mistake amounts to ignoring the second term in this equation. The second term is much smaller than the first term, so to a good approximation it is the square of the photon energy divided by twice the mass of the atom. The photon's energy is also the momentum of the photon, which in turn must be the momentum of the atom before the photon was emitted, so it is just (to a good apprximation) the kinetic energy which Edgerck didn't take into account. Count Iblis 23:47, 30 May 2007 (UTC)

Hmm, the last can't be right, and I'm confused by your new epsilon which you don't define. In any case, the kinetic energy of the recoil atom is generally WAY less than that of the photon. Here one problem is that Ed first claimed atoms changed mass in emitting a photon because the photon is massless, then blamed the disparity on the kinetic energy of the recoil atom, which is many orders of magnitude less. For example, consider Tc99m, which emits a photon of 142,683 eV, but recoils at only 0.11 eV kinetic energy, which is insignificant, and not even strong enough to break a bond (so called "hot atom chemistry" bond breaking generally requires beta and alpha emitters for this reason-- even a gamma photon usually doesn't carry enough momentum to give the parent nucleus enough recoil to do much chemically). The 0.11 eV energy of course comes out of the total available decay energy in the COM frame and results in a photon which has 0.11 eV less in that frame than it would if the atom were held still (for example in a crystal)-- the latter situation resulting in the photon getting all the energy (0.11 eV more), rather like an elastic collison between infinitely disparate masses.

It's interesting to calculate the velocity of recoil for this system (about 460 m/sec in the COM frame) and then to see what happens by Doppler shift to the photon energy from the frame of the recoil atom: for Newtonian v doppler shifts (as here) you get e' = e (v/c), so a 142 kev photon get shifted up in energy (as seen by the atom) by 142,000 eV (460 m/sec/3e8 m/sec) = 0.22 eV, which is exactly twice the atom recoil kinetic energy in the COM frame! Add energies of photon and atom, and there's more energy in the atom frame. Energy is not conserved over this process, but of course it's not expected to be, because you don't get energy conservation when you change frames. In this case to the recoil atom-- something else that Ed didn't note. That happens in Newtonian physics, too, of course. The whole system gains energy when you look at it from any frame but the COM frame (which is here the lab frame), and of course the frame of the recoil atom, which is going thataway at about the speed of sound, is not the COM frame or lab frame. So the whole system of atom+photon increases in energy when you change to the recoil atom frame, but that's just what you'd expect. What doesn't change is the invariant mass of the system, which is the same in either frame (or any frame), as you prove above. I'm trying to think of an elegant and obvious reason why for low velocities, the increase in total energy for the system works out as just twice the kinetic energy of the atom, if you change to the recoil atom frame. Hmmm. SBHarris 06:23, 31 May 2007 (UTC)

$\epsilon$ is the difference of the two rest masses of the atom (Edgerck wrongly took this quantity to be the photon energy). But I'll check the algebra later today (you are welcome to make corrections if you spot errors) :) Count Iblis 18:46, 31 May 2007 (UTC)

Okay, since I don't see it until it's introduced at the end, I've replaced it with a ΔM, if that's okay with you. And yes, I think you've got it. If you do the calculation for the recoil energy for Tc99m using your equation, you do indeed get (142,000 eV)^2/(2*9.2e10 eV) = 0.11 eV, so that checks with my result, doing it the old fashioned way by conservation of plain old 3-D momentum. Note again the odd fact that this recoil energy is same as the change in the system decay energy due to frame shifting to the recoil atom. It's not obvious that this should be so. But I don't think that was Ed's error, as noted. His was much worse, amounting to maintaining that subsystem rest mass's should be additive in systems, so that when M_2 does not equal M_1 because the photon has taken off energy which has no rest mass, that simply means rest mass is not conserved. But nobody ever said rest masses are additive in relativity. It's the system total rest mass which is conserved, and it's not the sum of the component rest masses. Ed seems to want it both ways: he wants mass to be some quantity which is additive in systems (which would make it relativistic mass, making photons massive), but at the same time he insists that photons should have zero mass, meaning he wants mass for them to be invariant mass. It has to be one way or the other. SBHarris 04:29, 1 June 2007 (UTC)

My comments are above. See Mößbauer (1958) to verify the experimental set up so that the recoil velocity can be neglected in the lab frame, allowing the same results that I report for the atom frame to be calculated in the lab frame as well. Edgerck 19:25, 1 June 2007 (UTC)

Well, no, because although the Mößbauer systems allows you to neglect recoil energy and velocity in the lab frame, and consider them to be the same as the atom frame (you basically tack the atom down), you can't by this mechanism neglect atomic recoil momentum, which remains. This doesn't change the photon's energy (because recoil energy is now nil), but that momentum does change the system's energy, because it changes the emitter's momentum, and thus invariant mass of the system is the same as the sum of emitter relativistic energy change, and emitted photon relativistic energy. Which are both nonzero, and can be (in this case) simply added (they are equal, and of opposite sign). What energy the photon gets in Mößbauer systems, the emitter looses--- as is the case in all systems, of course. But because we remain in the COM frame (even if this is also now the atom frame, which essentially does not change), the energy of the Mößbauer photon with energy E adds E/c^2 to the system mass, because the photon's momentum remains cancelled by the emitter's momentum, no matter how well the emitter is tacked down-- and thus their energies are free to simply add, in a 4-vector calculation. In a way, this is much simpler system than if we had a recoil energy. The emitter, of course, loses E energy, and looses E/c^2 mass if we don't include the photon (but then the system is open). SBHarris 19:50, 1 June 2007 (UTC)

About the kinetic energy, note the Edgerck wrote above (in the invitation to fair discussion section) :

"Using m for the mass of the system atom+photon in the atom's rest frame, m² = [(M - e) + e]² - e², where M is the atom mass before the photon is emitted and e is the photon energy (also its momentum), in c=1 units. The result is m² = M² - e². The mass of the atom+photon system is less than the atom mass before emission. Mass is not conserved in a closed system.Edgerck 13:55, 30 May 2007 (UTC)"

So, Edgerck is reasoning like this. M is the (invariant) mass of the excited atom. He subtracts the photon energy e from M where e is measured in the rest frame of the ground state atom) to obtain the mass of the ground state atom. This is, of course, not correct. He then takes the four momentum of the atom after it has emitted the photon to be (M-e,0), because in the atom is at rest. The photon has a four-momentum of (e,e). The total four momentum is then (M-e+e,e)=(M,e). And this then leads to the false conclusion that m^2 = M^2 - e^2.

So, the source of this mistake was to take e to be the difference of the two rest masses, while it should be taken to be equal to the difference in total energy. So, the error is just the kinetic energy that he ignored. Now, this is indeed small, but so is the effect he claimes:

m^2 = M^2 - e^2 --->

m = sqrt[M^2 - e^2] = M sqrt[1-e^2/M^2] = approximately

M[1-1/2e^2/M^2] = M - 1/2 e^2/M

So, Edgerck is saying: I ignored the kinetic energy because the kinetic energ due to recoil is small. Fair enough, but then he claimes that m is less than M. He didn't say by how much. As you can see it is less than M by an amount 1/2 e^2/M. Now e is the momentum of the photon (in c = 1 units), so this is just the kinetic energy of the atom he ignored.  :) Count Iblis 23:18, 1 June 2007 (UTC)

Force carriers and mass

This article is linked from the article on the Graviton, which states:

"If it exists, the graviton must be massless (because the gravitational force has unlimited range)[...]"

Note that massless links here. It might be valuable to provide some form of explanation of this property, and relate this concept to other physical forces (weak, strong, EM). --Tsuji 03:19, 2 June 2007 (UTC)

Ed Gerck is testing reliance on information in WP

See here. Count Iblis 17:17, 3 June 2007 (UTC)

Thanks for the clarification which comes just in time. For I just noticed that he repeatedly makes remarks as "Present day, mainstream, and verifiable knowledge is clearly given in the article" as if that would be satisfying. We all know that articles that promote such a biased view are in violation of WP:NPOV, and probably he also knows it. Harald88 18:30, 3 June 2007 (UTC)

You think there's no such thing as a "mainstream" POV in physics? Or is it just with this topic you're questioning it? SBHarris 19:47, 3 June 2007 (UTC)

NO. Why would you think so? Harald88 21:17, 4 June 2007 (UTC)

There was NO incorrect information inserted in my edits. My experiment rules make this absolutely clear.

Sorry but I did not claim (nor disclaim) that you inserted incorrect information in your edits. I simply noticed that you seemed to suggest that an article would be automatically of acceptable quality for Wikipedia if "Present day, mainstream, and verifiable knowledge is clearly given in the article". That is patently wrong, as is very well explained in WP:NPOV and the related NPOV manual. Harald88 21:17, 4 June 2007 (UTC)

My phrase above was a response to CI, not you. Regarding the experiment's method, it is not correctly summarized by what you quoted. Please read User:Edgerck#Correct_information and other sections on the experiment's methods, NPOV, and impartiality conditions. The correct information was defined following WP policy.Edgerck 21:37, 4 June 2007 (UTC)

Regarding WP purpose's, I edited exactly those articles that were NOT neutral. All my edits are documented and explained.

All my edits represented an honest attempt to improve neutrality of the articles, which were biased to use outdated information. If, because I am not perfect and the volume of my edits was very large, any of my edits contain material that is found to be incorrect, that can be taken into account as I explain in my experiment's conditions for impartiality.

Further, I did not take an anonymous identity exactly so people would understand that this is an honest attempt to 1) improve some WP's "eye-sore" articles; and 2) see how long that improvement would last, be improved more, or just disappear. Thank you. Edgerck 17:39, 4 June 2007 (UTC)

OK, thanks for the explanation. I tried this with Twin paradox; since I left it alone for a while, some of my improvements remain but one or more accurate citations that I provided (such as of Langevin) have been in part replaced by distorted and misleading explanations while at the same time the reference to his article has been deleted - against the Wikipedia rules - so that readers are not able to verify if the article's claims are correct (I may correct that another time when I feel like it). Thus, it's not all-together positive, but that was to be expected. Wikipedia is a jungle and no perfection should be attempted. :-(

Still, despite my partly negative experience, Wikipedia is IMHO already better than many other general information sources. :-)

Harald88 21:17, 4 June 2007 (UTC)

Thanks for sharing your experience. As I wrote in my disclaimer, my humble experiment is not a criticism of WP. How can we preserve point to view diversity, tolerance, and yet prevent the decay of trustworthy information in WP? I don't have the answer but I am presenting the question -- with a method to help measure its importance.

Of course, people may say that this whole approach is over-simplified. But to make some progress in this, I believe we need to cut to the core issue first. As a further benefit, we shall not run out of work in improving it.Edgerck 21:30, 4 June 2007 (UTC)

I don't know what's up with Ed Gerck, but I want to go on record as saying that many of his alleged "improvements" are simply wrong - at least the ones I've seen on his homepage. Pervect 08:56, 17 June 2007 (UTC)

POV

As I feared, the article is promoting the mainstream POV of particle physicists and neglecting significant minority views, even pushing them into history. For example - and as most of us know - "Today, in the scientific community, the word "mass" is exclusively reserved for invariant mass" is incorrect; and since it's a POV that people try to push, it may actually be called a propagandistic lie. I propose: "Today, in the particle physics, the word "mass" is almost exclusively reserved for invariant mass". Next a biased POV about anti-relativistic mass is exclusively cited (in the summary!), including the erroneous claim that the concepts "longitudinal" and "transverse" mass (that were outdated by 1920) have anything to do with dynamic or relativistic mass.

Thus the above-mentioned experiment of Edgerck had a highly succesful start. :-(

Harald88 18:57, 3 June 2007 (UTC)

Since "dynamic or relativistic" mass (and inertia) varies by direction of force, it's not the same longitudinally as transfersely. Two different masses in two different directions invite two different names, do they not? In fact, one of the big reasons to ditch relativistic mass was so we didn't have to talk any more about how it varied by direction, and no longer had to bother with "transverse and longitudinal mass" and inertia. These concepts are not anymore "outdated" than relativistic mass is, because they are needed if you must have it. You can't really have one concept, without inviting in the others. Face it. SBHarris 20:06, 3 June 2007 (UTC)

Thanks for presenting a live case of misinformation - you saved me the trouble of looking for an example. :-)

It is erroneous to claim that "dynamic or relativistic mass varies by direction of force"; and the use of such misinformation about it as argument against it must either be the result of lack of understanding or of dishonest propaganda (don't take it personally: I certainly don't accuse you to be the orginator of it).

However, "inertia" may be said to depend on direction; but then, "inertia" is not currently used in equations...

Now, anyone who like me learned the relativistic mass concept (and that's perhaps roughly half of the now living physicists as well as many new students) knows (or knew) that relativistic mass is not "direction dependent", as much as for example clock frequency isn't "direction dependent". The relevant textbooks that I was tought with (and that I still have) were by Alonso&Finn; similar explanations can also be found in Feynmann's physics lectures (of which our university has many copies in its library since it is still very much used by students). No doubt such textbooks are also at your disposition. So, please don't present such misinformation here!

Notes:

1. "relativisic mass" was introduced in order to replace the upto then used (but messy) concepts of "longitudinal mass" and "transverse mass".

2. As there is a never-ending POV battle between promotors of relativistic mass and promotors of invariant mass, reliable information about each can only be expected to be found in the literature that is written by the corresponding experts.

Regards, Harald88 19:23, 4 June 2007 (UTC)

[I moved the below comments ofSbharris outside of my above message] Harald88 15:38, 9 June 2007 (UTC)

Sorry, but you'll have to do better than to simply state what is not the case. Transverse mass has a wikipedia particle and two references, and what you say is simply wrong.SBHarris 01:55, 7 June 2007 (UTC)

You cannot define mass independently of inertia in any kind of relativistic physics. So your own argument just went down in flames, right there.SBHarris 01:55, 7 June 2007 (UTC)

Same, back at you. The definition of transverse mass is included in this very article. It's direction dependent. For that matter, so indeed is the ticking of a clock, which simply measures the time rate in a given inertial frame-- which isn't a constant. This quantity is rather direction dependent, because it depends on the velocity (speed and direction) of the clock observer's inertial frame. Only frame-independent quantities are not direction dependent. Length and time-rate don't qualify. They depend on the velocity of the observer. Or energy (which is your suggested definition of "mass"), or 3-momentum. Non-direction dependent quantities are those which are Lorentz invariant. Those are the familiar invariant 4-vector lengths: the space-time interval, the length of the 4-momentum, the length of the EM-4-vector (invariant mass), the length of the 4-velocity (the speed of light), etc. SBHarris 01:55, 7 June 2007 (UTC)

I referred to the fact that "relativistic mass" is a different concept from the concepts transverse mass and longitudinal mass - this is the case in all textbooks that I know of (and I mentioned two). I happen to know this by heart because special relativity with "relativistic mass" is part of my curriculum. And Wikipedia is not accepted as reliable source for Wikipedia! Please inform us where you read that relativistic mass is another word for transverse mass... and please explain why you think that gamma * m_0 == sqrt(m_0^2 + px^2 + py^2).

Note that you misunderstood my answer to your remark about "inertia": it does not appear in any equation. It is therefore not meaningful for this discussion.

"Transverse mass" is direction dependent, which means that, in a given frame of reference, at any point in space-time the related "mass" value depends on the direction in which a force would act on the object. Such is not the case with resonance frequency, nor is it the case with relativistic mass: they have at any point in space-time a unique value. BTW, energy is not identical to relativistic mass: they are not the same concept and don't have the same units.

Please don't continue to increase the strength of my argument that in Wikipedia we must not include misinformation that is spread by non-expert authors - those are not WP:reliable sources. Harald88 15:38, 9 June 2007 (UTC)

I see that again misconceptions are promoted that are based on erroneous articles, instead of providing a fair overview of the different opinions as required. Thus I reinserted the POV banner; see also below for an example of a more reliable source. Harald88 08:12, 15 June 2007 (UTC)

As an indicator for us of the evolution of popularity of the different approaches, http://arxiv.org/pdf/physics/0504110 may provide guidance. That non-reviewed paper contains a few errors, but I see little reason to doubt the graphs of Fig.1 and 2 - my only criticism concerns the choice of presentation with GREEN, UP for one concept and RED, DOWN for the other. :-) Harald88 14:19, 17 June 2007 (UTC)

Note: I will copy this to the topic below, as the discussion continues there! Harald88 21:00, 20 June 2007 (UTC)

Some references for modern use of "relativistic mass"

In order to fill the lacking knowledge about relativistic mass, I did a quick Google search for references; I think that the following link is a good starter (in addition to the abovementioned physics textbooks):

http://web.archive.org/web/20040220171942/http://www.geocities.com/physics_world/relativistic_mass.htm

Interestingly, some of the above links not also illustrate that the concept is still in use in the 21st century, but even that it is still used by particle physicists.

Regards, Harald88 20:49, 4 June 2007 (UTC)

And here are several hundred good books to check for more info.

What is the crux of the current "neutrality disputed" tag? Can we fix it? It seems to me that Edgerck and maybe some others are overly invested in one viewpoint that says that relativistic mass is an obsolete concept, to the extent that they're unwilling to admit that that concept is still in use. We ought to be able to converge on indisputable things to say if we base them of references, though. Dicklyon 21:13, 14 June 2007 (UTC)

It was not just about viewpoints but even misinformation that served to support it. Thanks for the improvements; I'll check the sumary for possible remaining errors and if I find one or two I'll weed them out. Harald88 21:40, 14 June 2007 (UTC)

I just renamed the "Summary" section to "Terminology usage" since it wasn't a summary. If you think of a better heading, feel free. Dicklyon 22:01, 14 June 2007 (UTC)

There may be some minor issues, but let's leave Edgerck out of the equation here, as he is somewhat of an anomaly  :) Count Iblis 21:44, 14 June 2007 (UTC)

OK. I did a bit, but haven't checked the whole article for POV or consistency, so more improvements are welcome. Dicklyon 22:01, 14 June 2007 (UTC)

To me it looks reasonably OK now; only, it seems a bit meager that Okun is mentioned several times while for example the alternative POV such as by Sandin ("In defense of relativistic mass, T. R. Sandin, Am. J. Phys. 59(11) 1032 (1991)") is not directly mentioned. I have not read that paper, so I plan to get it and have a look at it. Harald88 22:28, 14 June 2007 (UTC)

Sorry, I had to roll back your latest edit again. See edit summary or my response to you on my talk page. Definitely please do add refs for other points of view to balance Okun and Arons. Dicklyon 23:18, 14 June 2007 (UTC)

Sorry too: peddling patently erroneous claims that are the result of either false or mistaken propaganda is POV.

I just downloaded the paper which turns out to not just give one opinion but (apparently after a 2 year battle!) a NPOV discussion of pro-and contra - effectively it's an overview paper. It was in reaction to the debate that was started by Adler and Okun. The errors by Okun and Adler that I mentioned above are pointed out in this AJP paper as well as other errors.

Thus it would be better to cite this paper here than the misconceptions of earlier papers. If anyone can't get it, I can send you a copy for citations.

Harald88 08:13, 15 June 2007 (UTC)

If I understand what you're saying, the quote by Arons is erroneous and therefore should not be quoted. I have no opinion on how much of it is true, but I took it to represent one side of the opinions on these issues, and felt it should stay since it's very clearly attributed to Arons, not just listed as a statement with a reference. If there are alternative viewpoints, shouldn't we just add them, instead of deleting this one? In other words, I'm unclear still on why you think having this quote makes the section "POV". Or explain what about it is "patently erroneous" and maybe I'll agree we should just ditch it; but if any one editor wants it back as representing one POV, how can we object? Dicklyon 16:53, 15 June 2007 (UTC)

It is not necessarily wrong to quote erroneous sources; what is wrong is to quote only such a erroneous source without mentioning that it is not accepted to be a reliable, neutral point of view. It is sometimes useful to cite such a source together with the rebuttal, so that the fact that a dispute is/was going on is also on the table. Harald88 09:29, 17 June 2007 (UTC)

I agree. Also, if there is a real dispute in the physics (teaching) community about this issue, then that dispute itself is what we should write about, rather than editing from the POV of one of the parties. I just note that Okun and Adler are first class physicists who have published hundreds of peer reviewed articles on quantum field theory. They are not wrong about the points they make. The dispute about this issue is really a metaphysical dispute. It isn't really about "who is right or wrong". See also this recent article by Okun, in particular section 5 on page 16: "The pedagogical virus of relativistic mass".  :) Count Iblis 17:25, 15 June 2007 (UTC)

Interesting. He does certainly seem to contradict the statement even as I toned it down that "In physics teaching, relativistic mass is now less often presented to students than it was in the past," when he says, "However the number of proponents of relativistic mass seemed not to decrease." It's very clear that there's a currently ongoing "dispute" that is what we need to fairly represent. This is a good source. Sounds like Harald88 has a good source from the other side of it. Let's get the section to represent them fairly, and there should be no problem. Dicklyon 18:00, 15 June 2007 (UTC)

Yes I agree. To reiterate a point I made earlier: The argument that people are first class physicists is insufficient for accepting everything they write about other people's methods. It certainly cannot mean that they necessarily correctly describe viewpoints and methods which they dislike: usually they know them less well than the physicists who do use them. And as Count Iblis indicates, Okun is emotionally involved ("pedagogical virus") - such things do not do objectivity any good.

Also, of course on this Talk page it can be revealing to cite non-journal papers, but for the article we should preferably cite papers that were published in peer-reviewed physics journals - other sources are a justified target for deletion from physics articles. Harald88 09:48, 17 June 2007 (UTC)

I'm afraid that I don't have much time for this, I hope that someone else will take care of summarizing the different claims and opinions. Here is the official nut-shell summary of the 1991 AJP article:

"The concept of relativistic mass brings a consistency and simplicity to the teaching of special relativity to introductory students. For example, E=mc^2 then expresses the beautifully simplifying equivalence of mass and energy. Those who claim not to use relativistic mass acutally so so - if not by name - when considering systems of particles or photons. Relativistic mass does not depend on the angle between force and velocity - this supposed dependence results from incorrect use of Newton's second law of motion."

Harald88 11:46, 17 June 2007 (UTC)

Additional note: As I already mentioned above, it is evident to a careful reader that Sandin's article was heavily moderated by people with a different opinion which affected the clarity of the text. I now found his own comments https://carnot.physics.buffalo.edu/archives/2000/02_2000/msg00451.html and https://carnot.physics.buffalo.edu/archives/2000/02_2000/msg00464.html :

Let me stop "lurking" long enough to suggest that those interested read my article, "In Defense of Relativistic Mass" in the November 1991 issue of the American Journal of Physics, pages 1032-36. I apologize for the quality of its writing, but both the editor and the reviewers were anti-relativistic mass and the agony of getting something that they'd agree to publish resulted in a paper that reads like it was written by a committee.

The controversy over relativistic mass has reminded many of arguments over religion--but unless you truly believe there is only one way (your way), you will agree relativistic mass can be used or not.

However, with relativistic mass, the equation E = mc^2 beautifully unifies the previously disparate concepts of mass and energy--energy and mass are equivalent and c^2 is merely the conversion factor from mass units to energy units. Isn't this one of the great unifications of modern physics?

Without relativistic mass, energy and mass are sometimes equivalent, sometimes not. Read the article for examples and for discussions of other topics that have been mentioned such as "converting mass to energy" and mass as an additive quantity.

Tom Sandin

Harald88 15:06, 17 June 2007 (UTC)

Tom, it's not a "unification" to define mass as E/c^2, where E is relativistic total energy. There is no insight implied here-- it's like writing "1 + 1 = 2" or "Platypuses are mammals". No scientific knowledge is created. Rather, we are simply defining "2" and the meaning of the word "mammal" so as to make the statements correct.

Now the question arrises as to whether or not it's USEFUL to define mass in this fashion. Here there are pro's and con's. The major "con" is that the factor of c^2 is just a constant, and so defining mass in this fashion is redundant. We already have a quantity which does everything we want in the way of system additivity and so on, in energy. There's little to be gained in just defining mass so it's another name for relativistic energy. Whatever such a "mass" can do, energy can do for us as a concept, already.

On the other hand, there is much to be said for defining mass as the invariant mass. One is that invariant mass is a separately conserved quantity which is invariant and needs a name. There is a certain attractiveness in associating invariant mass with "mass" because one thinks of the mass of a particle as an invariant quantity, like charge. We'd like mass to be a property of the object which doesn't change willy-nilly, when seen by different observers. If we choose invariant mass to be "mass", then that become true for mass. We can then say that an electron has a certain mass and a certain charge which are characteristic of it as a particle, and which don't change for different observers. This is in accord with certain predictions of relativity, such as the idea that no matter how fast you fly by an object, it never turns into a black hole if it wasn't already one for an observer at rest. If mass is invariant, that becomes trivially obvious. But if "mass" is identified with relativistic energy, it's not so clear. Yes, it's true that without relativistic mass, mass and energy are sometimes equivalent and othertimes not. But that's okay, because we have one quantity which is Lorentz-invariant, and another which isn't. We expect them to be different, therefore, in some cases.

Finally, if we define mass as invariant mass, we get the pleasing result that particles which travel at the speed of light have no mass. That's good, because we really don't want to have in our system some massive particles which, for some reasons, always travel at speed c, and other massive particles which, for some reason, never do, and can't (which is what happens if you define mass as E/c^2-- all particles end up with a mass, which changes for every observer). It's much easier to understand all this, if you simply define mass so that the mass of photons, gravitons, and gluons is zero, and note that under this definition, that the speed of massless particles is always c, while that of particles with any mass at all, is always less than c.

Finally, as to the issue of "converting" mass to energy, neither definition of "mass" helps us, there. Both kinds of mass are conserved in reactions in closed systems for a given observer, so both remain fixed. Thus, mass never changes in closed systems for single observers, no matter which way you define it. Thus, converting energy to mass is never an issue, because unless you add or subtract something from a system, its mass doesn't change, no matter how you define it. SBHarris 07:07, 18 June 2007 (UTC)

The author is unlike to respond, since he probably does not participate to these Wikipedia discussions - I merely added it as a clarification for editors who read his paper.

I also looked diagonally through your comments here above, but I saw no citations of any paper. Our task here is not to continue already published debates on Wikipedia talk pages. Instead, we are here to discuss how to neutrally report on them. Harald88 12:28, 18 June 2007 (UTC)

The litmus test for including a POV as minority view is not whether it is cited or not. Please read WP:NPOV and here for the concept of prominent adherents.

The concept of "relativistic mass" is no longer used in physics and there are no longer prominent adherents of its use. The use of "relativistic mass" should be restricted at most to historical references in this article and not used to explain physical phenomena, according to WP:NPOV: "Views held only by a tiny minority of people should not be represented as significant minority views, and perhaps should not be represented at all.".

Since May 24, 2007 editors of this article are promoting a clear violation of WP:NPOV. The last version in compliance was on 03:09, 24 May 2007.Edgerck 19:30, 20 June 2007 (UTC)

The section above is about POV and unreliable claims about approaches by people who don't use them; here we look at reliable references for "relativistic mass" as well as evidence about how popular the different approaches are. I will copy my last contribution from the above section to here below, please add your evidence to it. Harald88 21:08, 20 June 2007 (UTC)

I understand the point about not overrepresenting minor minority views, but I don't understand why you think that applies to relativistic mass, which is still taught in numerous textbooks by reputable professionals, and is defending by at least a few research physicists as well. The writings of Okun and Arons themselves strongly imply that they are still fighting against a large opposition to their idea. How can you say that is not significant? And why do you imply that Sandin is not "prominent" in his role speaking for the other viewpoint? In any case, your POV is too strong, and the current article is more more balanced than your latest version. But if it's not balanced, please do help set it right. Dicklyon 19:48, 20 June 2007 (UTC)

Reading the 03:09, 24 May 2007 version (ref. above), I believe users will find a more balanced view of the matter, including references on relativistic mass that are missing today, than today's version.

If the concept of relativistic mass would be held by a "significant minority", as WP defines it, then it should be easy to find numerous prominent adherents, which is not the case -- and that number has been in frank decline both in quantity as well as in quality. It is not even used in physics research anymore. BTW, I already helped to set it within WP:NPOV in my revisions included in the 03:09, 24 May 2007 version. Edgerck 19:58, 20 June 2007 (UTC)

Here are a few hundred since year 2000. Are you saying that all of these writers are disqualified as not "prominent adherents", even though their editors let them write physics books? Dicklyon 20:10, 20 June 2007 (UTC)

Nobel Prize winners such as Feynman, Tollman, Schwartz and others who used the concept of relativistic mass were prominent adherents at their time. Einstein was a famous and prominent adherent to the contrary. Authors of engineering textbooks and introductory level physics books are usually not prominent in physics, so their use of relativistic mass today is most probably because they do not know better. Any physics Ph.D. student today would be ill-advised to try to use the concept of relativistic mass in his thesis or exam. Edgerck 18:10, 21 June 2007 (UTC)

As an indicator for us of the evolution of popularity of the different approaches, http://arxiv.org/pdf/physics/0504110 may also be of interest. That non-reviewed paper contains a few errors, but I see little reason to doubt the graphs of Fig.1 and 2 - my only criticism concerns the choice of presentation with GREEN, UP for one concept and RED, DOWN for the other. :-) Harald88 21:08, 20 June 2007 (UTC)

Only a small fraction of physicists do research that involves them using the concepts we are discussing (mostly high-energy physicists). Those working in other fields (optics, astrophysics, materials, quantum theory, etc.) are like me - they have not thought about it since they learned the subject, unless they have to teach it themselves, and many would still find relativistic mass to be a useful concept. Therefore, it is not a tiny minority who still use the concept of relativistic mass, as stated above. I think the article at the moment has about the right balance. This discussion page is rather passionate for what is essentially a definition debate. Apart from two or three physicists who have published on the subject, most physicists don't "adhere" to either view or have strong opinions. Timb66 22:07, 20 June 2007 (UTC)

Let me try to summ up and clarify. An encyclopedia is different from a textbook on physics, which is different from a popular science and engineering presentations. An encyclopedia may cite historical uses that are no longer found to be useful for understanding the subject. A popular science presentation, as well as an engineering textbook, may use concepts that would not pass peer review in physics. In that regard, WP policies define what to include or not.

There is no question (refs already given, including Usenet FAQ), I believe, that the concept of "relativistic mass" is not mainstream in physics today, is not used in research, and that any physics Ph.D. student (whether in optics, astrophysics, materials, quantum theory, cryogenics, etc.) would be ill-advised to try to use the concept in his thesis or exam.

Feel free to quote any source that says that, but "there is no question" is a characterization of your own take on it; most of us seem to not be buying it, even with the sources quoted. Okun makes a good case, but all the evidence shows the use of "relativistic mass" as a concept is still going strong, and is not physically contradictory or a problem even if out of favor among researchers. Dicklyon 17:48, 21 June 2007 (UTC)

Therefore, without going into the further issues below, the article should reserve main space to the current use of mass as "invariant mass" and use it for explanations of the concept of mass as well, making it clear to the reader that this is the mainstream view.

You wouldn't have much left of an article on "mass in special relativity" without saying much about relativistic mass. Dicklyon 17:48, 21 June 2007 (UTC)

Please keep reading...Edgerck 18:22, 21 June 2007 (UTC)

Regarding the citation of "relativistic mass" as a minority view, the WP concept of "prominent adherents" apply for its inclusion. Because, in my opinion, there were a large number of prominent adherents among physicists, I included text, original citations and references (citations and references which, curiously, are missing in the current purportedly "balanced" article) on relativistic mass while making it clear that the concept is of historical interest only.

The "historical interest only" is your opinion, contradicted by the evidence of large amounts of current use. I'll try to find the references that got lost; point me at a version if you care to help. Dicklyon 17:48, 21 June 2007 (UTC)

Any physics Ph.D. student today would be ill-advised to try to use the concept of relativistic mass in his thesis or exam. The refs are in 03:09, 24 May 2007.Edgerck 18:10, 21 June 2007 (UTC)

I recovered a missing Tolman ref, improved and quoted the other, and moved the un-cited FAQ ext. links to the ext. links section. Is there more you're suggesting? Dicklyon 22:42, 21 June 2007 (UTC)

Anyone wishing to use relativistic mass in this article and in teaching students today should think about the confusion they themselves went and are going through in using a concept that goes against experimental observation! Imagining that your mass would increase just because a fast particle (considered to be at rest in its own inertial frame) goes by is not just contrary to fact but false and misleading.

I don't find it confusing to have both concepts of mass, and I'm not aware of what experimental observation you believe is contradicted when using the concept of relativistic mass. Elaborate? Dicklyon 17:48, 21 June 2007 (UTC)

Any experiment, including all of those in the past that purportedly showed that relativistic mass was "real" and that mass increased with speed. Edgerck 18:22, 21 June 2007 (UTC)

You're not being clear. What experiment, and how does it contradict the use of this concept? Dicklyon 22:42, 21 June 2007 (UTC)

Reply in new item, below, to facilitate reading. Edgerck 19:12, 23 June 2007 (UTC)

Regarding the "passionate discussion", I think that the issue is very logical, not passionate. This is not about the West Bank occupation. This is about a physics article in the 21st century that is not according to physics already known in the 20th century. That the concept of "relativistic mass" is disappearing (as statistics show for more than 50 years), is not a tragedy or a "diversity loss" in the idea pool. It is the natural evolution of knowledge. Think for a moment: Why should a WP article give weight to an idea that has proven itself to be 1) not observable and 2) misleading?

Why should it ignore a concept, or pretend it's just historical, that appears in hundreds of books and articles and is part of a consistent view of physics? Dicklyon 17:48, 21 June 2007 (UTC)

Nobel Prize winners such as Feynman, Tollman, Schwartz and others used the concept of relativistic mass at their time, some 50~30 years ago. Authors of engineering textbooks and introductory level physics books are usually not prominent in physics, so their use of relativistic mass today is most probably because they do not know better. Note that Einstein, some 80 years ago, already explained why relativistic mass should not be used. There is no consistency gained in using it but there is consistency lost -- mass is a scalar and thus must not depend on the inertial frame (contrary to relativistic "mass") while energy is the time-component of the 4-momentum vector. Edgerck 18:22, 21 June 2007 (UTC)

As a historical reference, I find it useful to include relativistic mass. It should help warn the reader about its pitfalls and progressive decline in physics -- including Einstein's own words in disfavor of its use.

Regarding advocacy, and "knowledge by consensus", physicists have usually rejected them both. I believe that the main reason that Okun and other physicists went to popular science vehicles such as Physics Today is because they are also educators, who feel the pain of the intellectual trap holding their students.

This WP article, today, is confusing, self-contradictory, talks about metaphysical notions (such as in its texts of mass versus matter), is not scientific, and is not WP encyclopedic (due to its lack of balance). It is of little help to anyone wanting to read about the 2007 scoop on mass in SR. Hope this is useful.Edgerck 17:11, 21 June 2007 (UTC)

Editing others' comments

There has been some discussion on other pages about whether it is ok to break up one editor's comments by interspersing them with responses, often numerous. My reading of WP:TALK#Others.27_comments indicates that such action counts as editing another users comments and that it should generally be avoided (see the policy on Interruptions). It makes it very difficult to follow. Timb66 11:03, 22 June 2007 (UTC)

Interesting. I never heard that, and it seems to be done all the time. It allows the discussion to be multithreaded, and while complicated, also helped to follow some points; the alternative of a more linear organization is also hard to follow for other reasons, especially when some of the posts are long with many points. I've never noticed the "interrupted" template being used; do you have examples? Dicklyon 16:01, 22 June 2007 (UTC)

No, I haven't seen it used. I looked up the policy when one editor on another talk page insisted on interpersing numerous comments and breaking the flow of other peoples comments - against the request of the others. It's not a huge problem if you read the talk page every day, but it makes it hard to follow if you come back from a break! Timb66 09:53, 25 June 2007 (UTC)

Relativistic mass is not observable

(quoted and replied from item on relativistic mass references, to facilitate reading)

Anyone wishing to use relativistic mass in this article and in teaching students today should think about the confusion they themselves went and are going through in using a concept that goes against experimental observation! Imagining that your mass would increase just because a fast particle (considered to be at rest in its own inertial frame) goes by is not just contrary to fact but false and misleading. (fragment of Edgerck's comment above). Edgerck 17:11, 21 June 2007 (UTC)

I don't find it confusing to have both concepts of mass, and I'm not aware of what experimental observation you believe is contradicted when using the concept of relativistic mass. Elaborate? Dicklyon 17:48, 21 June 2007 (UTC)

Any experiment, including all of those in the past that purportedly showed that relativistic mass was "real" and that mass increased with speed. Edgerck 18:22, 21 June 2007 (UTC)

You're not being clear. What experiment, and how does it contradict the use of this concept? Dicklyon 22:42, 21 June 2007 (UTC)

Funny that you ask this. It's written in the article today: "We have, moreover, of course the experimental verification of the expression in the case of moving electrons to which we shall call attention in §29. We shall hence have no hesitation in accepting the expression as correct in general for the mass of a moving particle." -- who added it?

I added that. Unfortunately the limited preview available in Google book search doesn't let me see the description of the experiments that he refers to. So maybe you can tell us, and say what's wrong with them? Dicklyon 03:38, 24 June 2007 (UTC)

We know today that Tollman's experimental verification reference is incorrect. As I wrote above, all of those experiments in the past that purportedly showed that relativistic mass was "real" and that mass increased with speed were incorrectly interpreted. The mass of a moving particle does NOT increase with speed. WP's 2007 article on mass in SR notwithstanding. Hope this is useful. Edgerck 19:17, 23 June 2007 (UTC)

Relativistic mass of an object is, by definition, the same as the energy of that object in the lab frame. How can this not be observable? Count Iblis 19:54, 23 June 2007 (UTC)

I agree. Treat "relativistic mass" as a synonym for total energy and you have a consistent system. Why all the angst? Dicklyon 03:38, 24 June 2007 (UTC)

Hey, is that now a fourth definition of "relativistic mass"? That "relativistic mass" is a synonym for total energy? WP is really breaking new ground here. Edgerck 21:33, 24 June 2007 (UTC)

That relativistic mass should be defined as simply E/c^2, where E is total energy, is Tolman's original definition of relativistic mass! Read the article you're commenting on.SBHarris 22:05, 24 June 2007 (UTC)

My comment above is that defining m = E/c² does not mean that relativistic mass and energy are synonymous. Mass should not be confused with energy.

Moreover, m = E/c² is not the original definition by Tollman. Read the article, yourself. The WP article today includes my original quote from Tollman in 1912, when relativistic mass was defined without reference to energy as the well-known expression m = m₀(1 − v²/c²)^−1/2. Later and in 1934, as my original quote also says in the article, Tollman tried to save it from criticisms and defined it using energy as m = E/c², which definition is equivalent to the first and retains the same problems. Edgerck 21:10, 25 June 2007 (UTC)

The only real danger in having people "confuse" energy with mass, comes from unwisely defining "mass" in some fashion as to be equivalent to (relativistic) energy-- only differing by some constant dimentional dividing factor. Which of course is what Tollman does when defining m as "total-E/c^2". That's really no different than talking of photon "energy" in electron-volts or wavenumbers. As you admit when you say that E/c^2 is equivalent to defining mass as gamma*(rest mass). Really, the unit problem by itself shouldn't confuse anybody, just because the units are "wrong." We know what to do to them. The serious confusion which does the damage comes not from the dimentional problem, but from defining mass "badly" in terms of conceptualization. The definition of mass we really want to define as "mass," should be invariant. If it isn't, then there still exists in nature a certain invariant and very useful type of mass, which now must be referred to, by some other name! Perhaps "invariant mass," which sounds ridiculous, since we had the chance to call the stuff mass to begin with. Especially when "invariant mass" is really the same mass we measure, whenever we measure mass by the usual procedures, say weighing it on a scale, or by calculating what the "mass" of a new particle is, so that we can compare notes with some other scientist who may (or may not) have observed the same beastie at some different energy, in some different process, where it had a different velocity and energy.

Again, it's not total energy E which is an intrinsic property of particles, like charge, and it's not E/c^2, either. The intrinsic property we are after, a property of particles, is the norm of E^2-p^2. Suppose somebody wanted to know the mass of the electron. Would it not be dumb to define "mass" in our system, so that you had to ask the further question: "In whose inertial frame?" Isn't it rather obvious that the mass-value which makes electrons special, and identifies them as one particular particle, is one particular value, independent of all observers, and that if you make your definition of "mass" in physics to be anything else other than this, then you've chosen a really silly definitional system?

This whole thing reminds me of definitions of length and time. You can define time t by any standard you like, but once you've done so, then your way of defining length L had better make it come out that L = c*t for light in vacuum, since c is constant, so you know that your L varies from t by just a dimensional constant. Might this make people confuse length with time to write L = t?? No. In fact, if you don't, you're being silly again with your definitions, choosing them in such a way as to introduce error which doesn't need to be there. Now, this is not to say that physicists didn't historically DO just that. But they've come to their senses (as of 1983--see metre), and now that they have, articles on length standards need to note that length is no longer DEFINED as a fundamental quantity, but is now DEFINED as a derived quantity, based on time and then just fiddling with units. A meter is now basically defined as some fraction of a second. A long discussion of making marks on bars of metal, or measuring wavelengths of light from krypton lasers, is more and more irrelevant and a waste of space, as time (no pun intended) goes on. It's important as scientific history only. SBHarris 00:06, 26 June 2007 (UTC)

But why are we rehashing these arguments here? They're all in the referenced sources, aren't they? Aren't we supposed to be discussing the article, as opposed to the subject of the article? Is there a recommended action in there somewhere? Dicklyon 00:11, 26 June 2007 (UTC)

Edgerck wrote above: The mass of a moving particle does NOT increase with speed. If you define mass as total energy divided by c^2 then it does increase with speed. This definition has fallen out of fashion but that does not make it wrong. Timb66 09:58, 25 June 2007 (UTC)

Definitions are axiomatically right. But to be right in physics, definitions have to be consistent and represent observable phenomena. Mass is a measurement of inertia. The great point by Tollman was that mass (as a measurement of inertia) increases with speed. This point was purportedly proven by experiments. Later on, it was found that the experiments were incorrectly interpreted. The reasons that relativistic mass has fallen in disuse include the fact that the increase of mass with speed is NOT observable. Relativistic mass is also a misnomer, as it cannot be mass.

Again, any physics student today would be ill-advised to use the concept of relativistic mass to explain anything, in their exams or thesis. Things do not get heavier when they move. Edgerck 21:10, 25 June 2007 (UTC)

Look, there are some cases when relatistic mass is the same as invariant mass (namely, in the COM frame), and then it has all the same properties. Thus, the increase in system mass due to kinetic energy may be measureable as mass and inertia, in that frame. For example, if you heat a can of helium, putting in heat energy Q, then the can will increase in weight (according to SR theory) by an an amount Q/c^2. That entire increase in weight, in inertia, and in mass, is due to the helium atoms all flying around faster. You are thus weighing a sum total of kinetic energy when you weigh that heat. True, this kinetic energy has no location. But it is kinetic energy and it is weighable, and it does show up as increased system mass, even though it is stored nowhere but in velocity. SBHarris 00:33, 26 June 2007 (UTC)

Three comments: 1) There is no need to use "system mass" or "invariant mass" -- we can just use mass, as there is no other competing mass concept today in SR. 2) A system of Helium atoms has a mass given by the energy-momentum equation. 3) A single Helium atom has the same mass independently of its speed in any inertial reference frame. These three facts (cited by mainstream references today in SR) are in contradiction with the predictions of the "relativistic mass" model, which ignores the energy-momentum equation and the invariance of mass.Edgerck 19:47, 26 June 2007 (UTC)

Ed, you're going around in circles here. Your comments boil down to: If "mass" means "invariant mass", then "relativistic mass" isn't "mass". Well, obviously. --Trovatore 19:55, 26 June 2007 (UTC)

There is no "if". The experimental fact is that "relativistic mass" is not observable mass.

Yes, "relativistic mass" was once though by Tollman and others to be "THE mass of a moving body". It was even "proven" experimentally that an electron gets heavier when it moves. But it is not so. The mass of a moving electron does not depend on how fast it goes -- mass is invariant.

In other words, something that we call mass has physical significance as a measurement of inertia, which isn't the case for "relativistic mass". Further, because a helium atom has the same mass at any speed in any inertial reference frame, a helium atom does not get heavier when it moves --contrary to the "relativistic mass" model. Third, the mass of a system of particles depends not only on energy (as the "relativistic mass" equation E/c² says) but on energy AND momentum. Edgerck 00:19, 28 June 2007 (UTC)

Everything you write depends on accepting your definition of mass. That's unadulterated begging of the question. If you can isolate an experimental prediction of Tolman that's actually falsified, that's different. But of course you can't, because Tolman wasn't wrong; he just used language different from your preferred language. --Trovatore 00:26, 28 June 2007 (UTC)

True enough. The mass of a can of hot helium gas on a scale doesn't depend on the atom's momentum, because their momentum is zero (system momentum sums to zero). So the mass of the can depends on energy only, and is the same m = E/c^2, no matter whether you use invariant mass or Tollman's relativistic mass, as your definition of "mass." Which is good, because both definitions show that you weigh the kinetic energy of helium atoms in such a system, and thus this kinetic energy has mass. SBHarris 01:04, 28 June 2007 (UTC)

In WP, it's NOT "my" or "your" definition but what's valid according to WP:NPOV. In Physics, it's what's valid according to Nature. The definition of mass according to WP:NPOV and Physics, for more than 50 years, is very clear to anyone in the field -- there is no controversy, and it's not "relativistic mass".

Regarding Tolman, I did describe where Tolman was incorrect in his book and that was exactly the passage I copied at the beginning of this section. There are other works by Tolman that are also incorrect in this regard, as well known in Physics, including:

• The Principle of Relativity and Non-Newtonian Mechanics, R.C. Tolman and G.N. Lewis, Philosophical Magazine, 18, (1909), pg. 510-523.
• Non-Newtonian Mechanics: The mass of a moving body, R.C. Tolman, Philosophical Magazine, 23, (1912), pg. 375-380.

It is a significant to see WP editors create such confusion without even (as reported here) having actually read Tolman's book and chapter (§29) they "cite" to support their views, not to mention the lack of critical comparison with more recent sources to verify that Tolman's chapter §29 is no longer a valid WP:NPOV reference.

Further, SBharris needs to first answer what happens with a single helium atom, which mass would increase with speed according to "relativistic mass" and WP today -- but not according to WP:NPOV and Nature.

In regard to a can of helium atoms, even though the total 3-momentum is zero, the can's mass depends on the photon momentum distribution inside the can (see the two-photon result by Wheeler). The most unlikely result is that cited by SBharris and WP today, where all photons have opposing momenta, which is the only case where the energy-momentum equation for mass would have a zero momentum component and m=E/c².

The relativistic mass effect, that things get heavier when they move, is not observable -- neither for an isolated particle nor for a system. Edgerck 15:21, 29 June 2007 (UTC)

I checked the WP:NPOV page you referenced, and didn't find anything there on mass, relativity, or nature. I'm having a hard time seeing how it supports your point that only the more modern definition is "neutral". Dicklyon 15:32, 29 June 2007 (UTC)

And I testify that I was taught that "mass" is relativistic (variant) some 26 years ago - that is definitely much less than "50 years ago"; thus that disproves the claim by Edgerck above. I already gave the reference to one of my university physics textbooks. Moreover, I also provided evidence (from an opponent of relativitistic mass), that that concept and its teaching is not disappearing but is about as widespread as the invariant mass concept. Thus, whatever the situation may have been in the past, nowadays they should be given about equal space.

BTW, that you can observe relativistic mass increase with a particle accelerator (particularly with a cyclotron), is well known (also explained by Feynman).

Harald88 15:02, 14 July 2007 (UTC)

Cosmic catastrophe

Let's suppose that a toothbrush is thrown by a spaceship towards the Earth, and it travels towards it at the speed of light. When it knocks the Earth, which of the following is true: Tgeorgescu 14:31, 20 July 2007 (UTC)

- its relativistic mass is infinity, therefore it finishes off the Earth (producing a great cosmic catastrophe, and Earth ceases to exist as a planet); Tgeorgescu 14:31, 20 July 2007 (UTC) - the previous is untrue, for it only produces an impact energy of the inert mass of my toothbrush multiplied with the square of the speed of light, acting thus as a small nuclear weapon. Tgeorgescu 14:31, 20 July 2007 (UTC)

Please explain this to me! Tgeorgescu 14:31, 20 July 2007 (UTC)

Suppose that the collision is 100% inelastic. Then let's first transform to the center of mass frame using a Lorentz transformation, i.e. to that frame in which the total momentum is zero. In that frame you see the Earth and the tootbrush moving toward each other. And after the collsion both velocities are zero. The total kinetic energy in this frame is converted to heat. Unlike in Classical Mechanics, you still have conservation of energy here, because the heat energy is accounted for by the masses. You can then transform back to the original frame.

Now, we don't actually have to carry out these transformations. Instead we can reason as follows. We can just write down the total four momentum of the toothbrush-Earth system. The invariant mass of this system is the total energy in the center of mass frame. This is thus precisely the energy of the system after the inelastic collision in the center of mass frame. If you subtract from this energy the sum of the rest energies of the Earth and the tootbrush, you know how much energy is dissipated in the form of heat.

If the toothbrush has a mass of $m$ and moves with velocity $v$ then its four-momentum is (in units $c=1$ and first component is energy, second component is momentum):

$\left(\gamma m,\gamma mv\right)$

Denoting the mass of the Earth by $M$, the four momentum of the Earth is simply $\left(M,0\right)$. Total four-momentum is thus:

$\left(M+\gamma m,\gamma mv\right)$

Invariant mass of the system is:

$M_{\mbox{inv}}={\sqrt {\left(M+\gamma m\right)^{2}-\left(\gamma mv\right)^{2}}}={\sqrt {\left(M+m\right)^{2}+2\left(\gamma -1\right)Mm}}$

You can now look at the cases $M\gg \gamma m$ and $M\ll \gamma m$. In the first case you take the a factor $\left(M+m\right)^{2}$ out of the square root and expand the square root according to ${\sqrt {1+\epsilon }}\approx 1+{\frac {\epsilon }{2}}$, while in the second case you take out a factor $2\left(\gamma -1\right)Mm$ and again expand the square root. If you subtract $m+M$ you get the generated heat.

If you want to know the velocity of the Earth-toothbrush system in the lab frame after the collision, you simply use that the four momentum is of the form:

$\left(M_{\mbox{inv}}\gamma ',M_{\mbox{inv}}\gamma 'v'\right)$

where $v'$ is the velocity and $\gamma '$ the corresponding gamma factor. Total energy is conserved (despite the collising being inelastic), so we can find the gamma factor by equating:

$M_{\mbox{inv}}\gamma '=M+\gamma m$

Insert in here the expression for $M_{\mbox{inv}}$ that we found above and solve for $\gamma '$ and from that you can easily find $v'$. Count Iblis 17:09, 20 July 2007 (UTC)

Just to add that the toothbrush cannot be going at the speed of light, and so the premise of Tgeorgescu's argument is false, as is the statement that its relativistic mass is infinite. Timb66 22:59, 20 July 2007 (UTC)

True but inessential. Change the toothbrush's speed to c(1-10⁻¹⁰⁰). Its relativistic mass isn't infinite, but it's close enough for practical purposes.

What I want to know is, why a toothbrush, particularly? I mean, if it were a whelk, I'd understand.... --Trovatore 08:40, 21 July 2007 (UTC)

Now, I found amusing the idea that all one needs to destroy Earth is a toothbrush moving fast enough. Most people would say With a toothbrush, are you kidding? And then I could answer, It is a scientific fact, do the math. You know, science should be fun and exciting. Tgeorgescu 17:09, 21 July 2007 (UTC)

There was a joke of Walther Nernst's: "The proper safety match for the island of explosive whereupon we live, it has not been found yet!" Tgeorgescu 17:09, 21 July 2007 (UTC)

Reading the article, I also guessed that one has to compute for conservation of momentum (it is more or less there, in plain English); but, talking of the wolf (namely doing the math), I don't have the math skills to compute that. Tgeorgescu 17:09, 21 July 2007 (UTC)

So, I thought, even if I cannot do the math, I can still have fun thinking about theory of relativity. Tgeorgescu 17:09, 21 July 2007 (UTC)

So, having in mind the above, a toothbrush moving at a speed close to the speed of light towards the Earth, which conclusion holds true? Tgeorgescu 17:09, 21 July 2007 (UTC)

I think I figured it out: gamma is close to infinity, so gamma*m is much bigger than M, therefore we have something like (sqrt(2*close_to_infinity*M*m)*sqrt(1+(almost_nothing/2))-m-M)*v*v/2, which makes it close to infinity. Therefore, a toothbrush moving fast enough would destroy our planet, right? Tgeorgescu 17:29, 21 July 2007 (UTC)

Yes, since all of the toothbrush's kinetic energy (which can be anything) is available for planetary destruction, just as if it were an asteroid. However, it might take considerably more toothbrush energy than asteroid energy, since the toothbrush atoms would be expected to penetrate far into the ground where they might not do as much damage to the ecosystem. It's fairly easy to prove from your above equations that: 1/[1-(beta)^2] = 1 + K^2/Er^2 where beta is v/c, Er is the toothbrush rest energy = rest-mass*c^2, and K is the kinetic energy. For really high kinetic energies we can obviously forget the 1 on the right hand side. If v/c is 1-10^-100, then the left hand side is 10^200. Taking the square root gives K/Er = 10^100 (in general, if your ultra-relativistic speed is (1-x)c where x is small, then the kinetic energy of the object is 1/x times its rest mass energy). So for a 15 gram toothbrush with rest energy of 15 Nagasaki plutonium bombs, then you have 10^100 times that number of such bombs. More than a planet-killer, it's a ridiculously high amount of energy. The energy of 15 x 9e13 x 1e100 = 1.35e115 J, is equivalent to 1.5e98 kg, which is vastly more than the mass of the observable universe which is on the order of 10^52 kg.

If you want planet-wrecker energies, ie Chicxulub type dinosaur-killers, that's about 10^25 J or so, which is 10^17 kg. Divide by 0.01 kg toothbrushes and you get a needed beta of only 1-10^-19. This is your v/c. Cosmic ray protons have been observed with considerably higher betas than that-- it's a good thing they aren't as massive as toothbrushes! SBHarris 01:24, 22 July 2007 (UTC)

Actually, how much of the toothbrush's KE is "available for planetery distruction" is not so clear to me. Would all the energy be dissipated in a fireball, or would it more leave a toothbrush-shaped hole in the planet and punch out the other side, having barely slowed down? Somewhere in between the two, I imagine, but it doesn't seem that there's any simple calculation that could reliably tell us. --Trovatore 04:26, 22 July 2007 (UTC)

You have a point, I will admit, but I think it can be estimated from the behavior of Ultra-high-energy cosmic rays. The bonds between atoms, and even between nucleons are trivial compared with these energies, so basically we're talking about 15 grams of protons and neutrons hitting the Earth at c(1-10^-19). Let's just call it 16 grams of -CH2- plastic so we can have an even mole of each nucleon. Then forget the carbon (pretend it doesn't interact) and call it 2 grams of protons = 2 moles, each with 1/16th of the total energy of 10^25 J. That's 2 moles of protons, each with 10^25 J/[16*(6e23)] = 10 J per proton. That's less than the 50 J/proton of the Oh-My-God particle events from protons which are estimated to be doing (1 - (5 × 10-24))c. But these things are stopped in a few 10's of m of rock (or otherwise we couldn't know what their energy was, since these things are seen by Fly's Eye equipment as showers stopped by the atmosphere, which has an equivalent density of only 10 m of water = 3 m of rock), and the only thing which continues beyond that, are ultra-high-energy muons and neutrinos which carry only a fraction of the energy of the event. So yeah, it won't punch through. [3] And BTW, there must be something wrong with my calculation above, since I get 3e13 J for a proton traveling at [1-5e^-19]c. But even if we accept the figures in the (probably right) article, our toothbrush with a 6e23 nucleons still needs about 10 J/nucleon to be a dinosaur-killer at 10^25 J, and so [1-5e10^-24]c might be the correct v. It's in that range, somewhere, anyway.

BTW, such speeds give you funny effects. Whole galaxies are only about 10 times the distance to the moon thick, and from the viewpoint of the proton, you therefore traverse a whole galaxy in about 12 seconds. Whee. SBHarris 08:21, 22 July 2007 (UTC)

Well, if a toothbrush of 15 grams moves as fast as the Oh-My-God particle, it has five times the energy which was needed to exterminate the dinosaurs. That fast moving proton had an energy of 50 J or so. If one uses an electric toothbrush of about 100 grams, then at such a speed it gives about 33 times as much energy as the cataclysm which destroyed the dinosaurs. Tgeorgescu 12:34, 22 July 2007 (UTC)

Computing exactly, 10^25 J divided by Avogadro_s_number is about 16 J/nucleon. Considering a speed wherein a proton has 50 J, and since a neutron has more or less the same mass as a proton, it results that a diamond of 1,6 carats was enough to finish off the dinosaurs. (Assuming that a diadmond of 1 gram = 5 carats has roughly Avogadro's number of nucleons.) Tgeorgescu 16:56, 22 July 2007 (UTC)

The energy reported for Chicxulub Crater is 20 times smaller than 10^25 J. So, a diamond of 0,08 carats (or 16 milligrams) would have finished off the dinosaurs, moving at the speed of such particle. Tgeorgescu 14:07, 1 August 2007 (UTC)

statistics

Above I already cited a paper by an opponent of "relativistic mass" with statistics that shows it continued use. However, the article still claimed that it's "virtually never" used in 2007 research literature. So I now googled '"relativistic mass" 2007' and found that that is simply not true: I got hundreds of hits, most of which are to-the-point. Consequently, I corrected the phrase to "rarely".

Harald88 14:11, 22 August 2007 (UTC)

Rewrite

I tried to write a neutral version of this article, free of polemics, but the result was so much shorter than this article that a bot got rid of it automatically. The version is there in the history, I assume. Perhaps it will satisfy all parties. Likebox 22:56, 5 September 2007 (UTC)

Pre-relativistic history

I made some historical corrections in the relativistic mass concept section. First, relativistic mass was known long bevor Tolman (1912). It was JJ Thomson (1881), Searle (1896) and finally Lorentz (1899,1904) and Abraham (1902), who introduced this concept in the framework of Lorentz ether theory, and this concept evolved into the relativistic mass concept. See the references in the article. --D.H 16:29, 21 September 2007 (UTC)

That is mostly erroneous: relativistic mass should not be confused with "transverse" and "longitudinal" mass - these also increase with speed but contrary to relativistic mass and rest mass, they relate to direction of acceleration. I recall that we made sure that this article explained that issue to avoid such confusions among the readers. However, only a small precision is needed

A new problem is created, as Einstein and Lorentz used the same mass concepts and made the same relativistic prediction about "mass change" with speed. It's therefore incorrect to call that prediction and use "pre-relativistic". I'll move it to the relativistic paragraph - or better, I rephrase the whole part to "early developments": it's indeed relevant because these were the mass concepts that were used at the inception of special relativity. Harald88 17:44, 30 September 2007 (UTC)

I deleted the following quote, as I think it's not important for this article:

"Lorentz wrote in 1899 by using the term "ions" for the basic constituents of matter:

“ [...] states of motion, related to each other in the way we have indicated, will only be possible if in the transformation of S₀ into S the masses of the ions change; even this must take place in such a way that the same ion will have different masses for vibrations parallel and perpendicular to the velocity of translation. ”

"

If others think it's useful, just paste it back. Harald88 18:19, 30 September 2007 (UTC)

You say that transverse and longitudinal mass have nothing to do with relativistic mass. But some critics of rel. mass like Okun, Oas and Noack say that relativistic mass requires the introduction of direction dependent masses. Shouldn't that be included?

For example, Oas writes in his article: In regards to the antiquated concepts of longitudinal and transverse mass, they shall not be considered here. C. Adler[6] demonstrated how these must be accepted if one is to propose an inertial relativistic mass.

See also: http://www.math.ucr.edu/home/baez/physics/Relativity/SR/mass.html: So now, if we still want to maintain some meaning for relativistic mass, then we'll have to realise that it has a directional dependence--as if the object somehow has more mass in the direction of its motion, than it has sideways.

It think we should include that in the article. BTW: Except this problem I agree with your edits. --D.H 07:06, 1 October 2007 (UTC)

No I did not say so; certainly relativistic mass is an improvement of those earlier definitons. I said that it is important not to confuse such direction dependend mass concepts with relativistic mass which is not direction dependent. Note: I myself use relativistic mass and it never was direction dependent in any of my course books. ;-)

That confusion is already pointed out in the article, although without elaboration. If you search the history, you will see that it used to be more elaborated, but it was reduced to the minimum. Thus if you want to expand it, you can reinsert some of the erroneous claims by people who don't use relativistic mass as well as the debunking of those errors by people who do use it (please do not cite Arxiv sources or web sites). And I hope that with the new introduction it is now even more clear for the readers.

BTW, thanks for pointing out the blooper in the relativity faq. I'll point it out to Don Koks and will ask him to correct it (the good thing about websites such as that one and this one: they can be improved after-the-fact, if people are not too stubborn). Harald88 19:06, 2 October 2007 (UTC)

The quote on Relativistic mass is Misleading at Best

While I understand the some people don't like having redundant words for the energy, the quote which attacks relativistic mass is misleading. It says that relativistic mass leads to the "infelicities" of longitudinal and transverse mass, which isn't true, and it also says that relativistic mass is not the source of a gravitational field. But if a photon whizzes by the Earth, it deflects, and its reaction deflects the Earth right back. So the photon is acting gravitationally. The energy in relativity is the source of the gravitational field, not the rest mass.

In the pre-GR Nordstrom scalar theory of gravity, a photon indeed does not deflect off the earth and does not deflect the Earth either. In Nordstrom gravity, the rest-mass is in fact the source of gravity. But in normal tensor gravity obeying the equivalence principle, it is the energy that is the source of gravity, the "relativistic mass".Likebox (talk) 21:52, 27 January 2008 (UTC)

The energy of a single particle is not the source of gravity. That distinction, I would think, has to attach to the 4-momentum, including all its components. Melchoir (talk) 23:22, 27 January 2008 (UTC)

That's true, but the four momentum is not rest mass. The point is that the gravitational effects of a particle don't go like the scalar E^2-P^2, but like the component of the momentum E itself, like the relativistic mass. The gravitational field of a particle is proportional to P tensor P, not to P dot P.Likebox (talk) 04:19, 28 January 2008 (UTC)

Right, neither mass concept is sufficient. So I guess your beef is really with the part "...it also tempts one to associate relativistic mass (rather than just rest mass) with gravitational effects" then? If one reads that as suggesting that the gravitational field of a body is determined solely by its rest mass, I suppose it is misleading.

A more forgiving interpretation is that mentally associating the gravitational field with the relativistic mass leads ("tempts") one to make errors like assuming that any body gets a symmetric Newtonian gravitational field proportional to its energy. The quote is, after all, in the context of education. Melchoir (talk) 04:46, 28 January 2008 (UTC)

Yes, I am sure we agree on the substance. But I am unhappy with a quote that suggests the idea that the gravitational field is sourced by rest mass. Since it is a direct quote, it can't be rewritten. The idea that relativistic mass is the source of the gravitational field is not so misleading, because in situations where the average momentum is zero, it is exactly true (at distances large compared to the Schwartschild radius) that a body gets a symmetric Newtonian gravitational field propotional to its energy, which can be thought of in the linear limit as the sum of contributions from each particle, with all the energy contributions adding up and all the momentum contributions cancelling.Likebox (talk) 19:09, 28 January 2008 (UTC)

I have reservations about this. I can understand why you removed the first part about longitudinal and transverse masses, but I don't see a reason for removing the statement that "it is more difficult to derive the momentum expression in a simple way than it is to obtain the mass–velocity relation from the collision gedanken experiments". I teach SR and I understand exactly what Arons means here.

Also, just above you wrote "the four momentum is not rest mass". That could never be true, in the sense that a four vector is a different animal to a scalar, but I hope you realise that the length of the four momentum is precisely the rest mass. Timb66 (talk) 21:29, 28 January 2008 (UTC)

It's not the length of the four momentum that tells you what the gravitational pull is going to be. It's the time component. The pull on a stationary observer is determined by P_0, not by m. The pull of an object which is whizzing by fast is much bigger than the pull of an object which isn't moving. You can see that by putting reflectors to bounce the object back and forth, to make a box of relativistic gas, but it's also obvious in linearized GR. I gather that some people are saying that "the pull has to be the length, because that's the only invariant quantity", but that's just wrong. The pull is covariant, not invariant. It's only true in Nordstrom gravity, and that's why Nordstrom's gravity is wrong.

The reason I erased the part about the derivations is because it is unsupportable. It is trivial to turn any derivation of "mass dependence" from a collision analysis to an "energy dependence", because there is a mass energy relation. Another way of saying it is in the article: there precisely one four vector associated to a particle, (1,v), and so the conserved quantity is (E,Ev), which gives you E from the norm m by taking the length. I can't make any sense of the statement that one formula is inherently more difficult to arrive at than another, even pedagogically. I would like to erase the whole quote honestly.Likebox (talk) 18:50, 29 January 2008 (UTC)

The use of relativistic mass is self-consistent within special relativity

Inertial frame of reference is very important in Physics. Energy, mass, momentum and angular momentum, which are regarded as the most fundamental quantities, is only well-defined in inertial frame of reference. Before the proposal of special relativity, we used Galilean Transformation to switch from one frame (inertia) to another. It is admitted that in General Relativity, which treats all frame of reference (including non-inertial frame of reference) one cannot define mass, energy and momentum easily. (See mass in general relativity). We now use Lorentz Transformation to switch from one frame to another. Galilean Transformation implies time is universal to everyone. Lorentz Transformation which treats the speed of light in vacuum to be a fundamental constant shows that space-time is relative to observer. In fact, if the speed of light in vacuum is infinity, Lorentz Transformation is exactly identical to Galilean Transformation. We can say that certain Laws of Physics which are well-defined in Galilean Transformation may not be well-defined in Lorentz Transformation. It is known that Schrödinger equation is invariant under Galilean Transformation and plays central important role in non-relativistic quantum mechanics. It is not invariant under Lorentz Transformation. Similarly, momentum as defined under Galilean Transformation should be invariant under Lorentz Transformation. This eventually led to the redefinition of momentum. What is the main problem rose by Lorentz Transformation? Consider the following situation.

We have two inertial frame of reference, namely S frame and S' frame. They coincides at the same origin. That is when t,x,y,z=0, t',x',y',z'=0. S' frame is moving along the X-axis in the positive direction with a constant velocity of v without moving along the y-axis and z-axis. In addition, x and x', y and y', z and z' point to the same direction. We can say this is the standard configuration. A particle is moving with the velocity of u' along the y'-axis in the positive direction. This particle does not move along the x'-axis and z'-axis. In S frame, however, this particle does move along the x-axis. Lorentz Transformation shows that in S frame, the velocity of this particle along the y-axis is $u'{\sqrt {1-v^{2}/c^{2}}}$. Since this particle does not move along x'-axis and z'-axis and S' frame only moves along the x-axis, the momentum of this particle along the y-axis and y'-axis should be the same. The differences of velocity between both frame in y-axis and y'-axis may mean the violation of conservation of momentum. There are two possible resolutions to conserve momentum in both frame. One, as suggested by Okun, is to redefine momentum. It is shown that if we define momentum as

${\vec {p}}={\frac {m{\vec {v}}}{\sqrt {1-v^{2}/c^{2}}}}$,

momentum is conserved in both frame. Or, we can stick with the original definition of momentum, i.e. $m{\vec {v}}$. This will lead to a conclusion that mass changes with speed. This mass is now regarded as "Relativistic Mass". Note that Newton's Second Law in the form of ${\vec {F}}=m{a}$ come from the assumption that mass is regarded as a constant. The more general formula of Newton's Second Law is ${\vec {F}}={\frac {d{\vec {p}}}{dt}}$ One may argue that $m=\gamma m_{0}$ does not hold true for photon which travels at the constant speed in vacuum, since $\gamma$ tends to be infinity when the velocity tends to the speed of light. However, we can rearrange the formula, so that it would be,

$m_{0}={\frac {m}{\gamma }}=m{\sqrt {1-v^{2}/c^{2}}}.$

The above formula is exactly the same as $m=\gamma m_{0}$. This clearly shows that the invariant mass of a photon is zero. If one considers that a particle which is initially at rest relative to a frame gains kinetic energy as the force is done on it, after doing the integration, one will find that $dE_{k}=c^{2}dm$. This suggests the identity of relativistic mass and energy. Furthermore, by considering that a body which initially at rest emits two photo simultaneously in opposite direction, this two photons carries equal amount of momentum so that the body remains at rest after the emission of photons. We now know that the momentum of photon is $|{\vec {p}}|={\frac {h}{\lambda }}$. Assume that relativistic mass is just another name of energy, then the momentum of photon will be$|{\vec {p}}|=mc$. Einstein, 1905, predicts the packets of light energy. He personally called it light quanta. He suggested that the energy of a light quantum, according to the theory of Black-body radiation, should be $h\nu$. From $|{\vec {p}}|=mc$, this will eventually lead to the formula $|{\vec {p}}|={\frac {h}{\lambda }}$. In the case of the body which emits two photons in opposite direction in COM frame, from relativistic Doppler effect, one can easily find the magnitude of momentum of these two photons in the frame where the body itself is moving. If photons carry momentum, the only way to conserve momentum in every frame is to assume rest mass is a form of energy. I must admit that invariant mass and rest mass are useful concepts. Relativistic mass is also useful. One can completely eliminate term "Relativistic Mass" by using energy. He just doesn't use the same name but uses the same concept. Rest mass or some will just call it as mass, turns out to be a form of energy or just a special case of relativistic mass.

Some argues that relativistic mass is not the measure of inertia. Relativistic mass determines the momentum P of the body at given velocity v; it is a proportionality factor in the formula:

P = mv

The factor m is referred to as inertial mass. Original concept of inertia is a tendency to maintain momentum rather than the measure of a body's resistance to changes in momentum. mass is also defined as F/a as a measure of resistance to the change of momentum since mass was perceived to be constant. Thljcl (talk) 19:49, 22 April 2008 (UTC)

Objects moving at the speed of light

Under the Terminology section (4th paragraph), the following statement is made regarding objects moving at the speed of light: "In this case the total energy of the object becomes smaller and smaller in frames which move faster and faster in the same direction."

Doesn't that imply that the speed of light is measurably different in inertial frames moving at different speeds, which would contradict SR? - GordYoung (talk) 20:28, 28 May 2008 (UTC)

Intro had become inaccurate due to newly POV

I corrected one sentence about disuse as it had become inaccurate due to overly strong POV: - kg is not the same as Joules! - disuse is not general, as statistics show and even the sentence implied: it's really particle physicists who have no use for "relativistic mass" since they already use energies and they are interested in rest mass. - Arxiv is *not* a "reliable source".

Note that with that the intro is still unbalanced: the main argument of Okun is given as "making the case", while Sandin was merely "argued otherwise". Thus I will correct that as well.

Please obey the Wikipedia rules, thanks!

Harald88 (talk) 09:28, 30 September 2008 (UTC)

Sorry, who other than particle physicists and experts in GR uses special relativity? -- SCZenz (talk) 09:31, 30 September 2008 (UTC)

It's useful in all branches of physics, mostly because of the logical coherence it brings. It's just like Euclid's geometry, except that it includes time, and it turns into rotational invariance in imaginary time, which has been a useful spin-off unifying statistical and quantum physics. But directly, relativity is important in atomic physics, where large atoms of (Z about 100) have large relativistic corrections to their energy levels, and even small Z atoms have a relativistic spin-orbit coupling which leads to changes in electronic structure. In nuclear physics, beta decay emits relativistic electrons and positrons, and that is a common process. In astrophysics, any compact stars is relativistic.75.24.124.36 (talk) 19:10, 26 October 2008 (UTC)

Okun references this article

In his article in the May issue of AJP, Okun includes a reference to this wikipedia article. /Pieter Kuiper (talk) 22:27, 14 May 2009 (UTC)