# Have we measured the speed of light coming from galaxies?

• I
Usually we measure the speed of light using light generated here on Earth or coming from the Sun or other stars, but have we ever tried to measure the speed of the light coming from distant galaxies? As in directing that light into an apparatus and measure its average velocity over a round-trip.

And do you know if any experiment that measured the Shapiro time delay also attempted to measure whether the light that came back was also slightly redshifted?

Regarding the first question I know that general relativity predicts the result would be c, but I wonder whether any experiment has actually checked that.

Regarding the second question I'm guessing general relativity would predict no redshift but I'm not sure?

## Answers and Replies

mfb
Mentor
There are gravitational lenses that lead to multiple images of more distant stars/galaxies, often with a time-delay. This time delay fits to the speed of light.

Radio astronomy often connects different telescopes distributed over Earth, with variable distances to the source. The time delay observed there fits to the speed of light.
On a smaller scale (100 m) this is also done with visible light, with the same result.

The motion of Earth around the sun leads to aberration, which depends on the speed of light. Again, same result.

As in directing that light into an apparatus and measure its average velocity over a round-trip.
I'm not aware of that, but where would be the point?
And do you know if any experiment that measured the Shapiro time delay also attempted to measure whether the light that came back was also slightly redshifted?
The Shapiro delay is not associated to any redshift. Also, come back from what? There can be redshift and Shapiro delay at the same time, but the effects are independent.

There are gravitational lenses that lead to multiple images of more distant stars/galaxies, often with a time-delay. This time delay fits to the speed of light.

Radio astronomy often connects different telescopes distributed over Earth, with variable distances to the source. The time delay observed there fits to the speed of light.

How precise is this fit to the speed of light? What's the margin of error and how far would be the most distant galaxies tested in this way?

I'm not aware of that, but where would be the point?
To test whether a part of the redshift of distant galaxies might be due to their light traveling slower when it reaches us. I know it sounds crazy from the point of view of general relativity, but if it has never been checked that would be an experiment worth doing.

The Shapiro delay is not associated to any redshift. Also, come back from what? There can be redshift and Shapiro delay at the same time, but the effects are independent.
How do you prove in the framework of general relativity that the Shapiro delay is not associated to any redshift?

Come back from wherever the signals in the Shapiro experiments are reflected off, Mercury, Venus, Mars, ...

mfb
Mentor
How precise is this fit to the speed of light? What's the margin of error and how far would be the most distant galaxies tested in this way?
I don't know. Read the publications.

VLBI (radio waves) reaches microarcsecond resolution, that suggests a precision better than 10-10.
And it works at high redshift: VLBI observations of hot spots in the lobes of distant radio sources.
To test whether a part of the redshift of distant galaxies might be due to their light traveling slower when it reaches us.
Please give a peer-reviewed publication discussing that.
Also, the very first publication I found with my first google search disproved this by about 10 orders of magnitude...

How do you prove in the framework of general relativity that the Shapiro delay is not associated to any redshift?
It is called delay for a good reason. Everything that is not a delay is not called Shapiro delay. This is an arbitrary splitting, you can ignore all names and just calculate what GR predicts.
Come back from wherever the signals in the Shapiro experiments are reflected off, Mercury, Venus, Mars, ...
What? All Shapiro delay experiments are done between Earth and space probes.

VLBI (radio waves) reaches microarcsecond resolution, that suggests a precision better than 10-10.
And it works at high redshift: VLBI observations of hot spots in the lobes of distant radio sources.

What would be interesting to know is whether that microarcsecond resolution applies to high-redshift galaxies. The resolution achieved in the paper you linked seems to be on the order of 0.1 arcsecond. Also we would still need to determine how that angular resolution translates to a speed of light resolution.

Especially considering this statement from the VLBI page on wikipedia:

"At the location of the correlator the data are played back. The timing of the playback is adjusted according to the atomic clock signals on the (tapes/disk drives/fibre optic signal), and the estimated times of arrival of the radio signal at each of the telescopes. A range of playback timings over a range of nanoseconds are usually tested until the correct timing is found."

"A range of nanoseconds". In the paper you linked the interferometers are separated by less than 300 km, which in the line of sight would translate to a much smaller difference, and then the resolution would not be inconsistent with a slower speed of light.

Please give a peer-reviewed publication discussing that.
Are we allowed to ask whether an experiment has been done only if this experiment has been discussed in a peer-reviewed publication? I can content myself with the answer that no such experiment has been done, if that's indeed the case.

Look I'm not trying to prove that light coming from distant galaxies is traveling slower, I just want to know if experiments have directly shown that the speed of light we receive from distant galaxies is traveling at c to high accuracy when it reaches us.

mfb
Mentor
What would be interesting to know is whether that microarcsecond resolution applies to high-redshift galaxies. The resolution achieved in the paper you linked seems to be on the order of 0.1 arcsecond.
Still orders of magnitude better than necessary. A speed of light changed by just 10% would appear like a source at a completely different location in the sky. Telescope orientation and time delay would have to correspond to completely different locations to see the source.
Are we allowed to ask whether an experiment has been done only if this experiment has been discussed in a peer-reviewed publication?
You can ask if an experiment has been performed, but not speculate about ideas that are not in peer-reviewed publications. And ideally the experiment still makes sense, because it tests something worth a test. It's like asking if anyone ever checked the speed of light of the light bulb in my room. No, no one did - but would it worth doing so?

Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
2021 Award
This is all in the FAQ. c.f "Optical extinction"

pervect
Staff Emeritus
Science Advisor
This is all in the FAQ. c.f "Optical extinction"

Specifically, start here: https://www.physicsforums.com/threads/faq-experimental-basis-of-special-relativity.229034/
Take the link to here: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#moving-source_tests
and here: http://www.edu-observatory.org/physics-faq/Relativity/SR/experiments.html#Optical_Extinction

There are several tests there using cosmological sources, a simple test, due to DeSitter, simply involves observing binary stars, and is widely described (for instance in WIkipedia). The results from these cosmological tests are consistent with special relativity.

The extinction theorom mentioned by Vanadium suggests however, that while the OP asked about cosmological tests, terrestrial tests of the speed of light of moving sources may be superior in some regards. For an example of terrestrial tests, ee for instance the tests where the speed of gamma rays from the decay of fast π0 (~0.99975 c) were measured.

However, both cosmological and terrestial measurements of the speed of light from moving sources have results that are consistent with special relativity as should be expected, and this is described in the aforementioned FAQ.

BTW, I interpret both the FAQ and the question about "measuring the speed of light" to use the old platinum bar standard for the meter In the interests of intelligibility it's probably best to not over-stress this point. Lots of old textbooks, popular articles, and even the above FAQ talk about the speed of light as something that can be measured - the most sensible way to interpret such remarks in my opinion is to assume that one is using older definition of the meter which makes the speed of light something that CAN be measured (rather than a predefined constant, an approach that also makes sense, but is probably less familiar to the reader).

Vanadium 50
Staff Emeritus
Science Advisor
Education Advisor
2021 Award
Optical extinction is an important complication. The OP's assumption is that starlight that moves through a lens or is reflected by a mirror is still starlight. That is at the very least questionable.