The special theory of relativity is one of the most strongly corroborated theories that humanity has ever developed. It’s central to everything from space travel to GPS to our power grid. Central to the theory of relativity is the fact that the speed of light in a vacuum is an absolute constant. The problem is, that fact has never been proven.
When Einstein proposed the theory of relativity, it was intended to explain why light always had the same speed. In the late 1800s, it was believed that as light spreads as a wave, it must be carried by some type of invisible material known as luminous ether. The reasoning was that waves require a medium, like sound in air or water waves in water. If the aether exists, the observed speed of light must change as the earth moves through the aether. However, the measurements for observing the ether drift were zero. The speed of light seemed constant.
Einstein found that the problem was assuming that space and time were absolute and that the speed of light could vary. If instead you assumed that the speed of light is absolute, then space and time must be affected by relative motion. It’s a radical idea, but it is supported by any measurement of the constant speed of light.
How to measure the speed of rotation of light. Photo credit: Wikipedia user Krishnavedala
However, several physicists have pointed out that while the theory of relativity assumes that the vacuum speed of light is a universal constant, it also shows that speed can never be measured. In particular, the theory of relativity forbids you to measure the time it takes light to get from point A to point B. To measure the speed of light in one direction you will need a synchronized stopwatch at each end, but the relative movement affects the speed of your watches relative to the speed of light. You cannot sync them without knowing the speed of light which you cannot know without measurement. You can use a single stopwatch to measure the cycle time from A to B back to A. This happens with every measurement of the speed of light.
Since all orbital speeds of light measurements provide a constant result, you can simply divide the time by two and call it a day. That is exactly what Einstein did. He assumed the time there and back was the same. Our experiments agree with this assumption, but they also agree with the idea that the speed of light approaching us is ten times faster than the speed leaving us. Light does not have to have a constant speed in all directions, just a constant “average” speed to and from the place. The theory of relativity persists when the speed of light is anisotropic.
A Milne universe with anisotropic light would look uniform. Photo credit: Wikipedia user BenRG
If the speed of light varied with its direction of movement, we would see the universe differently. When we look at distant galaxies, we look back in time because light takes time to reach us. If distant light reached us quickly in one direction, we would see the universe as older and expanded in that direction. The faster the light reaches us, the less we would see “back in time”. Since we observe a unified cosmos in all directions, this certainly shows that the speed of light is constant.
Well, not exactly, as a new study shows. It turns out that as the speed of light varies with direction, the contraction in length and dilation in time also vary. The team studied the effects of anisotropic light on a simple relativistic model known as the Milne Universe. It’s basically a toy universe whose structure is similar to observation, but without all of the matter and energy. They found that the anisotropy of light would cause anisotropic relativity effects in time dilation and cosmic expansion. These effects would cancel out the observable aspects of varying the speed of light. In other words, even if the universe were anisotropic due to a different speed of light, it would still appear homogeneous.
So it seems that simple cosmology cannot prove Einstein’s assumption about the speed of light either. Sometimes the most basic ideas in science are the hardest to prove.
Reference: Lewis, Geraint F., and Luke A. Barnes. “The one-way speed of light and the Milne Universe.” arXiv preprint arXiv: 2012.12037 (2020).
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