Could a Variable Speed of Light Theory Challenge the FLRW Metric in Cosmology?

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SUMMARY

The discussion centers on the implications of a variable speed of light theory on the Friedmann–Lemaître–Robertson–Walker (FLRW) metric in cosmology. It asserts that postulating a decreasing speed of light instead of an expanding universe leads to significant challenges, including the redefinition of fundamental measurements like the meter. The conversation highlights that such theories conflict with established principles, including Lorentz invariance and energy conservation, and suggests that they would necessitate a reevaluation of gravity and its propagation. Ultimately, while theoretically possible, these ideas would disrupt the foundations of General Relativity and broader physics.

PREREQUISITES
  • Understanding of the Friedmann–Lemaître–Robertson–Walker (FLRW) metric
  • Familiarity with General Relativity (GR) principles
  • Knowledge of Lorentz invariance and its implications
  • Basic concepts of gravitational theory and energy conservation
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  • Research the implications of variable speed of light theories on General Relativity
  • Study the Friedmann equations and their derivation from GR
  • Examine the role of Lorentz invariance in modern physics
  • Explore the relationship between the speed of light and the nuclear fine structure constant
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Cosmologists, theoretical physicists, and students of advanced physics interested in the foundational principles of cosmology and the implications of altering fundamental constants.

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Suppose we postulate that instead of the universe expanding, the speed of light was decreasing? Now we try to derive the Friedmann–Lemaître–Robertson–Walker (FLRW) metric from Newtonian conservation of energy. Would we get the same result?
 
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You would need some way to contract gravitationally bound objects at the same time, otherwise we could measure this slowed speed of light.
And if you do that, you just redefine the length of a meter. This is possible, of course, but you get nothing new. I don't see how you plan to use Newtonian conservation of energy.
 
Variable speed of light theories are plagued by a number of issues. It does not play well with any number of theories that incorporate c in their formulation - like the nuclear fine structure constant. It unavoidably breaks Lorentz, diffeomorphism and time translational invariance, implying a violation of energy conservation. And plays strangely with gravity, suggesting both gravity and its propagation speed must also vary to avoid conflicts with well established observational evidence. It's not that such a thing is not possible, but, would have far reaching consequences for GR and much of physics.
 

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