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What is the source of gravitational force in Newton's theory?

In sect. "sources of spacetime curvature" one reads: "In Newton's theory of gravitation, the only source of gravitational force is mass". This is not true. In Newton's theory mass is absolutely passive (first law of motion). Consequently mass cannot be a source of force. Ed Dellian2003:D2:9703:5982:E5FC:D23:1439:EA1E (talk) 19:22, 7 November 2018 (UTC)

I have never seen a law mentioning absolutely passiveness of mass, but in Newton's law of universal gravitation#Modern form we read (with a pretty reliable source): Every point mass attracts every single other point mass by a force acting along the line intersecting both points. - DVdm (talk) 22:25, 7 November 2018 (UTC)

As well as I ever knew it, Newton didn't try to explain the source, but describe the effect. I believe he was also bothered by the action at a distance not knowing about the mechanism, or possible delay. Gah4 (talk) 22:37, 7 November 2018 (UTC)

The OP may be thinking of Bondi's distinction between three types of mass: (1) active mass which acts as the source of a gravitational field; (2) passive mass which reacts to a gravitational field; and (3) inertial mass which reacts to acceleration. In Newton's theory, active mass must equal passive mass, or the third law of motion would be violated. On the other hand, the equality of passive mass and inertial mass was a mystery that bothered Newton, and which most researchers chose to ignore. Einstein resolved the mystery with his theory of general relativity. The article is very clear on this point. Prokaryotic Caspase Homolog (talk) 22:48, 7 November 2018 (UTC)

I forgot about that one. Reminds me of, what I believe came from Galileo, arguing why heavier masses shouldn't fall faster than lighter ones. If you take two small masses, and tie them together with a thin string, they are now one larger mass. Also reminds me of an undergrad experiment which is supposed to measure gravitational vs. inertial mass, but doesn't. Gah4 (talk) 01:15, 8 November 2018 (UTC)

Non-primary source needed

The Macleod reference is not cited by any secondary source, and it is thus impossible to evaluate the status of this explanation of spacetime based on the Simulation hypothesis (i.e. all of reality is an artificial simulation).

Mass-space-time, charge-space-time

A potential relationship linking both mass with space-time and charge with space-time was posited in a 2018 article that re-normalized the Planck units as geometrical objects from a (dimensionless) mathematical electron . The Planck units are defined as geometrical objects in terms of 2 dimensionless constants, fine structure constant α and Ω, and assigned a rule set uⁿ that dictates their interactions. These objects can translate from 'natural units' (geometry independent of any numbering system and of any system of units ) to the CODATA 2014 SI values by using appropriate numerical scalars ktla. These scalars overlap and cancel in ratios dictated by the formula for the mathematical electron, thus for example if we know the numerical values for Planck length and Planck time then we know the numerical values for Planck mass and the elementary charge (e = at).

Geometrical Planck units

Unit	Geometry	Scalar
mass	$M=1$	$k,\;unit=u^{15}(kg)$
time	$T=2\pi$	$t,\;unit=u^{-30}(s)$
length	$L=2\pi ^{2}\Omega ^{2}$	$l,\;unit=u^{-13}(m)$
ampere	$A={\frac {2^{6}\pi ^{3}\Omega ^{3}}{\alpha }}$	$a,\;unit=u^{3}(A)$

Scalar relationships:

${\frac {l^{15}}{k^{9}t^{11}}}={\frac {(.203...x10^{-36})^{15}}{(.217...x10^{-7})^{9}(.171...x10^{-43})^{11}}}{\frac {u^{-13*15}}{u^{15*9}u^{-30*11}}}=1$

${\frac {a^{3}l^{3}}{t}}={\frac {(.126...x10^{23})^{3}(.203...x10^{-36})^{3}}{(.171...x10^{-43})}}{\frac {u^{3*3}u^{-13*3}}{u^{-30}}}=1$

For example, from the scalars k, t;

$M=(1)k;\;k=m_{P}=.2176728175...\;10^{-7},\;u^{15}$

$T=(2\pi )t;\;t={\frac {t_{p}}{2\pi }}=.1715855128...\;10^{-43},\;u^{-30}$

$V=(2\pi \Omega ^{2})\;{\frac {k^{9/15}}{t^{4/15}}}=299792458,\;unit=u^{9/15*15-4/15*(-30)=17}$

$L=(2\pi ^{2}\Omega ^{2})\;k^{9/15}t^{11/15}=.1616036601...\;10^{-34},\;unit=u^{9/15*15+11/15*(-30)=-13}$

$A=\left({\frac {64\pi ^{3}\Omega ^{3}}{\alpha }}\right)\;{\frac {1}{k^{3/5}t^{2/5}}}=.1486106299...\;10^{25},\;unit=u^{9/15*(-15)+6/15*30=3}$

References

Description of Fig. 2-7b: spacelike vs timelike

I believe the terms "spacelike" and "timelike" should be swapped in the description of Fig. 2-7b. Griffiths (2013:530) writes, "Under Lorentz transformations, however, it is the interval I = (x^2 − c^2 t^2) that is preserved, and the locus of all points with a given value of I is a hyperbola—or, if we include the y axis, a hyperboloid of revolution. When the displacement is timelike, it’s a 'hyperboloid of two sheets' (Fig. 12.24a); when the displacement is spacelike, it’s a 'hyperboloid of one sheet' (Fig. 12.24b)." Griffiths, D. J. (2013). Introduction to Electrodynamics, 4th ed., Pearson. — Preceding unsigned comment added by 217.45.27.75 (talk) 21:16, 7 December 2020 (UTC)

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 Yep: swapped: [1]. Now the descriptions of 2-7a and 2-7b are consistent. Thanks for having noticed. - DVdm (talk) 00:33, 8 December 2020 (UTC)

• This is rather a confusing point of nomenclature, and there have been multiple good faith "corrections" going back and forth on this point.

1. In Fig 2-7a, each magenta hyperbola connects all events having some fixed spacelike separation from the origin.
2. These magenta hyperbolae are timelike curves, because they represent actual paths that can be traversed by (constantly accelerating) particles in spacetime.
3. In the expression "timelike curves", replace the word "curves" with the word "hyperbolae", which of course are a form of curve.
4. Therefore, the magenta hyperbolae should technically be called "timelike hyperbolae" since they are timelike curves.
5. However, in a rather extensive search of the literature, I have found only a single reference that would actually term the magenta hyperbolae as "timelike hyperbolae" and the green hyperbolae as "spacelike hyperbolae".
6. Given how confusing this nomenclature ("spacelike hyperbolae" vs "timelike hyperbolae") seems to be, it would be better to avoid the issue altogether with appropriate rewording following Griffiths. I will try out a possible rewording in the next few minutes.

Prokaryotic Caspase Homolog (talk) 02:25, 8 December 2020 (UTC)

I'm with you . - DVdm (talk) 09:41, 8 December 2020 (UTC)

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Discussion of BGV theorem does not belong in lede

I removed the following material from the lede. I suggest that a more appropriate location for discussion of the BGV theorem would be in the articles on Cosmology or on the Big Bang. Could somebody with more expertise on these subjects check whether incorporation of this material into those articles is appropriate? Thanks!

The BGV theorem demonstrates that classical spacetime, under a single, extremely general state, cannot be prolonged to past infinity but must arrive at a boundary at some moment in the finite past.

Prokaryotic Caspase Homolog (talk) 13:27, 28 May 2021 (UTC)

References

Addition to History of Special Relativity

time cannot be separated from the three dimensions of space except for wave particles with a velocity equal to the speed of light

Einstein's Original Paper on Special Relativity https://www.fourmilab.ch/etexts/einstein/specrel/specrel.pdf Page 22 "Thus, when v = c, W becomes infinite"

In the context of special relativity, time cannot be separated from the three dimensions of space except for wave particles with a velocity equal to the speed of light, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer. General relativity also provides an explanation of how gravitational fields can slow the passage of time for an object as seen by an observer outside the field. — Preceding unsigned comment added by AtlasDidntShrug (talk • contribs) 17:29, 11 February 2022 (UTC)

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@AtlasDidntShrug: The cited source (Einstein's 1905 article) does not mention wave–particle duality, so we cannot use that for such content. See, for instance, wp:original research and wp:synth. DVdm (talk) 18:40, 11 February 2022 (UTC)

Existing articles on (Introduction to the) mathematics of general relativity are virtually useless

The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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My recent DIFF addition to the Spacetime article was reverted by User:Zefr, justified by policies WP:SYNTH and WP:NOTTEXTBOOK.

I created this new section because, quite frankly, I find the existing articles on Introduction to the mathematics of general relativity and Mathematics of general relativity to be virtually useless for their presumably intended target audiences. These two articles are nothing but lists of mathematical concepts that provide the reader with virtually no clues as to how these concepts apply to general relativity.

The existing two Wikipedia articles on this subject provide absolutely no assistance to, say, a college student who wants a bit of guidance getting through a chapter of, say, Hartle, Wald, or Schultz.

• In regards to WP:SYNTH: I have, as much as possible, tried to avoid introducing my own original thoughts on the subject. Unfortunately, adding ALL of the citations that I could have put in to justify each and every single statement to show that I haven't been trying to show off my own thoughts on the subject would have made the text unreadable. I chose to limit my citations to the more obvious.
• In regards to WP:NOTTEXTBOOK: If, by this objection, User:Zefr means that I have provided many detailed derivations, I assert that the presence of detailed derivations does not make an article a textbook. I note that derivations are common in articles on relativistic topics. For example:
  • Relativistic_Doppler_effect#Relativistic_longitudinal_Doppler_effect
  • Michelson–Morley_experiment#Light_path_analysis_and_consequences
  • Kennedy–Thorndike_experiment#Basic_theory_of_the_experiment
  • Special_relativity#Invariant_interval
  • and so on and so forth...

The only thing that I have done here that is different from the above, is that I have strung together a series of related derivations together in logical, coherent order, following as guide a classic semi-popular book on the subject by Lillian Lieber, whom many of you might recognize as the author of The Education of T.C. Mits.

• Do we want Wikipedia to be a useful resource?
• Or do we insist that Wikipedia adhere rigidly to general guidelines that result in the articles becoming useless for their supposedly intended purpose?

Prokaryotic Caspase Homolog (talk) 17:59, 27 March 2022 (UTC)

Understanding derivations, rather than merely knowing abstract definitions, is an important part of physics and mathematics. I note that many mathematical articles, especially those of an introductory nature (directed towards K-12 students), include derivations as an integral part of their presentation. Articles covering upper-level topics tend to be more abstract. Here are some examples of mathematics articles that use derivations, interpretative segments, "how to" segments, and detailed discussion of specific use cases as part of their presentation.

• Quadratic equation
• Solving quadratic equations with continued fractions
• Linear equation
• Cubic function
• and so forth

Prokaryotic Caspase Homolog (talk) 08:11, 30 March 2022 (UTC)

Notes

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.