Two photons (experiment) and light speed. Why? [closed]

Question

I found a part of a popular-science film on YouTube:

https://www.youtube.com/watch?v=-vrJxRCf4-E

(Please see around 24:10 on this video)

I have a small question.

An example with two photons is shown in the film.

At the moment of the gamma-ray burst, two photons (at the same time) are emitted.

If after ten billion years one photon reaches Earth faster than another, it means that not everywhere in the Universe the speed of light is the same.

Why can it be?

Can you tell more about this?

I will be very grateful for your help.

Answer 1

That would be exactly what they are testing. In science, you don't go out to prove what is already believed to be true, you go out and challenge existing models.

In this storyline, the experimenter is hypothesizing that the speed of light might not be a constant. Indeed, they're hypothesizing that it might change over time, according to some mathematical equation (which was not actually shown in the video). They predict that if the speed of light is changing over time, they would see high energy photons fall behind the low energy photons. Why? Because that's what the model they're hypothesizing suggests.

They can't go around and announce "the speed of light isn't constant because I built a model which says it changes." That'd be silly. But if you can make a good enough argument to get funding, you can run an experiment to test your hypothesis, which is exactly what they are doing. If, for a gamma ray burst, they detect that high energy photons arrive later than low energy ones, that is substantial evidence that the speed of light is not constant. This would force us to re-evaluate our existing models (which assume the speed of light is constant). If, however, their experiment shows no such difference in timing between high and low energy photons, then they "fail to reject the null hypothesis," which is to say that they found no evidence to suggest the speed of light is variable. The status quo will remain.

I believe the challenge you are facing is one which is very typical of the way we teach science these days. We tell students "the speed of light is constant," with the same sincerity as Moses descending from Sinai with the laws of the universe etched in stone. What would be more accurate is to say that we've done literally thousands upon thousands of experiments on light, and every single experiment is consistent with the assertion that "the speed of light is constant." If you want to predict what's going to happen to some light beam, that is the best advice science can give you. However, it's still just a scientific model.

After finding, say, 10000 experiments that all are consistent with "the speed of light is a constant," we find the 10001th experiment shows that it's variable in some way, then we repeat and reproduce that result until we're confident that it's legit, and then we reject the claim that "the speed of light is constant," and develop a new model which accounts for this discrepancy.

In this case, the experimenters are positing that the speed of light changed over time. 100% of our direct measurements of the speed of light have occurred in the last 400 years. The experimenters are theorizing that perhaps the rules were different 13,772,000,000 years ago. They argue that if the rules were different, we would be able to see indirect evidence from these gamma ray bursts. And thus, they go out looking at these bursts for evidence.

Answer 2

The video is referring to a property called optical dispersion. This happens when different wavelengths of light travel at different speeds.

If you shine light through glass, ordinary window glass, then you'll find that different wavelengths (i.e. different colours) of light do indeed travel at different speeds, and that is why prisms split white light into different colours. This happens because the electric field in the light interacts with the glass, and the strength of the interaction depends on the wavelength of the light. We say that glass is a dispersive material.

But if you shine light through a vacuum there should be no dispersion - all wavelengths of light should travel at the same speed. That's because a vacuum is empty so unlike light travelling through glass there is nothing in the vacuum for the electric field of the light to interact with.

Now this is where the fun starts, because in a number of the more speculative theories the vacuum is not simply empty but contains things the light can interactive with, and this interaction can be wavelength dependent. That means if these theories are correct the vacuum, i.e. empty space, could be dispersive - much like glass is, but to a much, much smaller extent.

And this is the point of the video. There could be a very small difference between the speed of red light and the speed of blue light. The difference is so small that we'd never measure it in the lab, but if the light has travelled billions of light years from a gamma ray burst there might be a detectable difference.

And experimentally detecting a difference in the speed of light coming from a gamma ray burst would be a very big deal. It's the sort of thing that would win you a Nobel prize. That's because our current theory for how light travels (the Standard Model) predicts there should be no dispersion. Detecting dispersion in light from a gamma ray burst would be the first incontrovertible experimental evidence that our current theories are incomplete.

As it happens we have an existing question asking what experimental evidence there is for dispersion: Experimental bounds on Lorentz-violating dispersion relation. You may be interest to read the answers to it.