Special & General Relativity Questions and Answers
Do the different estimates for the age of the universe imply that the speed of light may have changed?
No. At least not directly. The ages for globular cluster stars do not depend on the speed of light except via the propagation speed of light within the stars, and other atomic quantities. The expansion speed of the universe is determined by the redshifts measured for galaxies and their distances.
The 'expansion age' is just 2/3 of the reciprocal of the expansion rate called Hubble's constant. This calculation does involve the speed of light, and also depends on which method was used to determine the distance to the galaxy which might depend in various ways on the value of the speed of light. In converting from a redshift to an expansion speed, you use
velocity = speed of light x Zwhere Z = the change in the wavelength divided by the reference wavelength. The value for Hubble's Constant, H = expansion velocity / distance, and the expansion age = 2/3 x 1/H. If the speed of light were to have been different long ago, the expansion speed could have been greater or less than what we currently measure and so the age would be different due to this 'acceleration or deceleration' effect. A 10 percent change in the speed of light would produce about a 10 percent change in the expansion speed, but to get the kind of change needed to solve the current age paradox would require at least a factor of 2 change in the speed of light over 10 billion years or so. Such a large change would have serious repercussions for stellar evolution and other physical phenomena.
There have been cosmological models proposed in the past that assume that 'light gets tired' only as it travels across intergalactic space, however, there should be other measurable effects that could be detected locally that would indicate a change in the speed of light over billions of years. These models are not seriously considered today because they lead to so many undesirable side effects that are not compatible with observational evidence. As I mentioned in a previous question, there is no evidence that the speed of light changes.
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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.