I want a good reference to a discussion of the meaning of "the speed of light is constant"

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Discussion Overview

The discussion revolves around the meaning of the statement "the speed of light is constant," particularly in the context of general relativity (GR) and special relativity (SR). Participants explore the implications of this statement, the definitions of speed in various contexts, and the challenges of measuring light speed in curved spacetime versus flat spacetime.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses the need for a precise understanding of the speed of light and questions the common assertion of its constancy, suggesting that it may not hold in an expanding universe.
  • Another participant notes that in GR, light follows null worldlines, making the locally measured speed of light invariant, while globally it is coordinate dependent.
  • Some participants clarify that the coordinate speed of light is constant only in local inertial frames, and that curvature effects can complicate this understanding.
  • It is proposed that the invariance of light cones is more significant than the numerical value of the speed of light itself, which can vary with coordinate transformations.
  • Participants discuss the two-way speed of light in SR, emphasizing that it is invariant and measurable, but caution that defining distance can affect the calculated speed.
  • There is a discussion about the tautological nature of the calculated two-way speed of light being constant in flat spacetime under specific conditions.
  • One participant asserts that in general curved spacetime, there are no two timelike geodesics with constant distance as defined by round-trip light travel time.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the implications of the speed of light being constant or invariant. Multiple competing views are presented regarding the definitions and conditions under which the speed of light can be considered constant or invariant.

Contextual Notes

The discussion highlights limitations in defining speed across different contexts, particularly in curved spacetime, and the dependence on coordinate choices. There are unresolved mathematical steps regarding the implications of these definitions.

  • #61
pervect said:
Consider the Milne universe, if you're aware of it. https://en.wikipedia.org/wiki/Milne_model

It expands, but in the region of validity of the Milne universe, t>0, there is a diffeomorphism to the standard "Minkowskii" flat space-time of special relativity which does not expand.

My not-very precise resolution of this issue is to conclude that expansion, per se, does not cause physical effects. It's basically the result of a coordinate choice, though the expanding coordinates are lacking in complete coverage of the space-time.

However, acceleration or deacceleratio of the expansion DOES have physical effects. But these effects can be analyzed in terms of the effects of the matter, dark matter, energy, or dark energy that is causing the rate of expansion to accelerate or deaccelerate in the first place. The cause can ultimately be traced back to normal and dark matter/energy distributions.

Fore example, without dark energy, "gravity" causes the expansion of the universe to de-accelerate (slow down), this gravity has physical effects. Dark energy is the only one of the four that causes an accelerating expansion.

Orodruin wrote an article on some of this recently, with much more precision than what I wrote above, but I wasn't able to locate it.
Thanks, very helpful.
 

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