Science desk
< October 13	<< Sep \| October \| Nov >>	October 15 >

Welcome to the Wikipedia Science Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

October 14

Does the Minkowski space (or the Min. metric) add, any empirically verifiable information, to Einstein's original Special Relativity theory?

Just as Einstein's Special Relativity theory added some empirically verifiable information, to what scientists had known about physics. HOTmag (talk) 08:01, 14 October 2024 (UTC)[reply]

No it doesn't. It is a name for the mathematical structure of the space described in Special Relativity. If you take it away you just make things cumbersome and can't talk properly to physicists. It would be like taking complex numbers away from electronics - it would make formulae bigger and annoy people. NadVolum (talk) 09:06, 14 October 2024 (UTC)[reply]

That's what I think as well, but surprisingly, your first sentence is not mentioned (nor hinted) in our article Minkowski space, although it's a very important point that should have been pointed out, IMO. HOTmag (talk) 09:47, 14 October 2024 (UTC)[reply]

The earliest empirical confirmations of ~~special~~ relativity announced by Einstein in 1905 included Arthur Eddington's photographic record of the Solar eclipse of May 29, 1919. I expect that Eddington was aware of Minkowski's lecture that presented his Spacetime diagram in 1908. Philvoids (talk) 09:17, 14 October 2024 (UTC)[reply]

AFAIK, this solar eclipse has nothing to do with special relativity. HOTmag (talk) 09:43, 14 October 2024 (UTC) Thank you for that correction. Philvoids (talk) 15:20, 17 October 2024 (UTC)[reply]

The very first sentence of Minkowski space says "In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation", and later in the lead "Minkowski space is closely associated with Einstein's theories of special relativity and general relativity and is the most common mathematical structure by which special relativity is formalized". It says it is used in formalizing special relativity, it does not say it is a theory or anything like that. That's straight in your face! No extra 'hinting' is needed! NadVolum (talk) 11:10, 14 October 2024 (UTC)[reply]

In physics, Minkowski space (or Minkowski spacetime) is the main mathematical description of spacetime in the absence of gravitation. Yes, but I can't see any relation between this fact and my question in the title.

Minkowski space is closely associated with Einstein's theories of special relativity. Of course, just as the electric force - actually expressed by Coulomb's law, is closely associated with the magnetic force - actually expressed by the Lorentz force law. Yet, the Lorentz force law, does add some empirically verifiable information to Coulomb's law. For the same reason, the sentence you've quoted from our article Minkowski space, doesn't rule out the possibility that the Minkowski space adds some empirically verifiable information to Einstein's theory of special relativity.

Minkowski space...is the most common mathematical structure by which special relativity is formalized. Of course. That's because the Minkowski space is an integral part of Special relativity. However, my question in the title didn't ask whether the Minkowski space added new information to "Special relativity", but rather whether the Minkowski space added new information to "Einstein's original Special Relativity theory".

That's why I'm still asking, if you think the article should have pointed out the very important fact (IMO), that the Minkowski space added no new information to "Einstein's original Special Relativity theory. HOTmag (talk) 11:54, 14 October 2024 (UTC)[reply]

No I see no good reason for thinking the article should say irrelevant things like that. Find a reliable source if you want to add it. NadVolum (talk) 13:20, 14 October 2024 (UTC)[reply]

Isn't your first sentence (in your first response) based on a reliable source? If it is, then what does your last sentence (in your last response) mean? HOTmag (talk) 13:24, 14 October 2024 (UTC)[reply]

No what I said is not based on a reliable source. This discussion is not an article. NadVolum (talk) 13:46, 14 October 2024 (UTC)[reply]

I'm quite surprised. You are calling - the relation between the Minkowski space and Einstein's theory of Special relativity - "irrelevant things", but you admit that your own opinion (about this relation) - that the Minkowski space adds no empirically verifiable information to Einstein's original Special Relativity theory - "is not based on a reliable source".

Anyway, we will probably remain in disagreement, about whether this relation is "irrelevant" (as you claim) or "very important" (as I claim). I wonder what other users think about this controversy between us. HOTmag (talk) 15:26, 14 October 2024 (UTC)[reply]

There are experimentally verifiable geographic facts, such as that Europa and Asia are part of a connected landmass that is not connected to the Americas. There are many ways to create flat two-dimensional maps of the surface Earth, such as the Mercator projection and the Mollweide projection. The maps are alternative ways of describing the same geographic reality; obviously, they cannot produce new verifiable geographic facts. Likewise, Minkowski space is an alternative way of mathematically describing the same physical reality; it cannot produce new verifiable physical facts. --Lambiam 17:18, 14 October 2024 (UTC)[reply]

Yes, that's what I think as well, as I have already responded to the user above you, but then I asked them a follow-up question, as you can see above. HOTmag (talk) 07:08, 15 October 2024 (UTC)[reply]

I'm not sure what the follow-up question is. In my opinion, it would be curious, to say the least, to see some statement in Wikipedia to the effect that the Molweide projection did not add any empirically verifiable information to geography. It is not different for Minkowski space and physics. --Lambiam 15:26, 16 October 2024 (UTC)[reply]

Mathematics is a symbolic system used for describing and organizing information. Like natural languages. Minkowski space is a mathematical construction, used for...describing and organizing information. This question is in essence like asking, "Did the German language (the original language Einstein wrote his big scientific papers in such as the one in which he set out special relativity) add any empirically verifiable information to sp. relativity?" It's a category error. I guess the simple answer is, "No, why would it? Does the number 17 add any?" Slowking Man (talk) 04:14, 20 October 2024 (UTC)[reply]

Yes, all agree that mathematics is a symbolic system used for describing and organizing information. Of course the Minkowski space is a mathematical construction, intended to describe and organize the information in Einstein's Special relativity. The only question is, if the Minkowski space only does what it's intended to do, or - not on purpose - does more. For example, If I try to describe and organize the finite sequence: (1,2,4,8,16,32), I may use the mathermatcal construction

a_{n+1}=2a_{n}

. But this mathematical construction does more than what it's intended to do, because it also predicts that 32 is followed by 64... I guess that's why your last sentence begins with "I guess". But my original question is about what the facts really are. HOTmag (talk) 05:40, 20 October 2024 (UTC)[reply]

If the OP's question ever find a "Yes" reply, its explanation would likely benefit the articles Tests of general relativity and Test theories of special relativity. At present neither article mentions Minkowski. Philvoids (talk) 15:20, 17 October 2024 (UTC)[reply]

There is the possibility to switch the sign in Minkowski space. Then the Minkowski space would have properties of Quaternions. That would add additional properties. 176.0.154.107 (talk) 13:27, 20 October 2024 (UTC)[reply]

Now you can ask why the sign is chosen that way it is. The possible answer is to avoid the consequences. Another answer is that a coin never falls on both sides. You can choose which answer you like most. Even by tossing a coin. 176.0.154.107 (talk) 13:34, 20 October 2024 (UTC)[reply]

That would add additional properties. Empirically verifiable ones? HOTmag (talk) 15:52, 20 October 2024 (UTC)[reply]

Violation of the conservation of energy by virtual particles, vs violation of the formula E=mc^2

Virtual particles, appearing out of the cacuum, are known to be a (theoretical) instance violating the conservation of energy.

Is there also any instance (even a theoretical one only), violating the formula $E_{0}=m_{0}c^{2}$ (while $E_{0}$ denotes a given body's rest energy and $m_{0}$ denotes the body's rest mass)? HOTmag (talk) 12:56, 14 October 2024 (UTC)[reply]

Theory says they don't. However they can for instance have negative kinetic energy which balances the equation. NadVolum (talk) 13:25, 14 October 2024 (UTC)[reply]

What do you mean by "they"? Do you mean virtual particles?

Additionally, what do you mean by "don't"? Do you mean they don't [violate the conservation of energy]? Or don't [violate the equation

E_{0}=m_{0}c^{2}]?

Additionally, could you elaborate on your second sentence? HOTmag (talk) 13:35, 14 October 2024 (UTC)[reply]

Yes they refers to a virtual particle, but really since one never comes across an actual isolated virtual particle one should be considering the whole configuration, see On shell and off shell. NadVolum (talk) 13:42, 14 October 2024 (UTC)[reply]

Thank you. HOTmag (talk) 15:28, 14 October 2024 (UTC)[reply]

I don't think they're violating conservation of energy. Yes, they "exist" and would have mass. At the same time they're entangled to have a zero sum of mass. That means, if you observe one of the particles into existence, the other particle automatically achieves negative mass equivalent to the observed particle. Such a "negative" particle is for all intents and purposes like an anti particle,but with one exception. If it encounters it's partner (entangled or not) it doesn't annihilate, it merely nihilates. That is like annihilation but without releasing energy. 2A02:3032:302:3F8E:5531:CB3D:1EB2:F4FC (talk) 02:30, 15 October 2024 (UTC)[reply]

Virtual particles essentially don't exist. They're a mathematical formalism; I think a way to express sub-terms in certain difficult calculations. (The explanation for Hawking radiation of black holes in terms of virtual particles is essentially just wrong as far as I heard, or at the least misleading).

Your question also doesn't make a lot of sense. Conservation of energy and E=mc^2 are not the same thing: one says that mass is a form of energy and energy acts as mass; the other says that energy is conserved. Virtual particles would violate the conservation of energy if they actually existed; are you asking if there are any mathematical formalisms in general relativity that would violate E=mc^2 if they actually existed? It seems unlikely to me, but I don't know. Mrfoogles (talk) 20:50, 27 October 2024 (UTC)[reply]