# Proof: Velocity of Light can't depend on velocity of body emitting the light

• haitham1984
In summary, the author discusses an experiment that DeSitter performed to show that the velocity of light is not affected by the velocity of the emitting body.
haitham1984
Hello All,

I am reading a book about relativity and early on in the book I read the following:

"...By means of similar considerations based on observations of double stars, the Dutch
astronomer De Sitter was also able to show that the velocity of propagation of light
cannot depend on the velocity of motion of the body emitting the light..."

1) The experiment mentioned in the quotation above with some detail.

2) Or, explain the idea above using a different experiment (assuming one was made) which leads us to the same conclusion.

Hi, Haitham,

Welcome to PF!

It's always helpful if you can tell us the source you're quoting from. I found the source by googling: http://www.marxists.org/reference/archive/einstein/works/1910s/relative/ch07.htm I think the preceding sentence pretty much describes the idea. If c wasn't independent of the velocity of the source, then we'd see strange time-lags in observations of an eclipsing binary, since one star is approaching us while the other is receding.

Hello bcrowell,

That's the correct quotation. The book is simply called Albert Einstein: Relativity. You are referring to the sentence:

"At all events we know with great exactness that this velocity is the same for all colours, because if this were not the case, the minimum of emission would not be observed simultaneously for different colours during the eclipse of a fixed star by its dark neighbour"

I guess I am a little confused with this concept. I understand the part that if the colours had different velocities we should seem the colours arrive at different times (which is not the case obviously), but how does the eclipse of a fixed star by its dark neighbour have to do with explaining this concept?

haitham1984 said:
I guess I am a little confused with this concept. I understand the part that if the colours had different velocities we should seem the colours arrive at different times (which is not the case obviously), but how does the eclipse of a fixed star by its dark neighbour have to do with explaining this concept?

Take a look at the graph and animation here:
http://en.wikipedia.org/wiki/Eclipsing_binary_star#Eclipsing_binaries

If different photons had different velocities, then they would all take different amounts of time to reach us. The graph would get scrambled and distorted.

Yes, I know see it. Truly amazing. The graph simplified everything for me.

Thank you bcrowell. Please let me know if there is anything you need. You helped me a lot. :)

PS: I wonder if an experiment could be done in the lab to show students.

Last edited:
The earliest experiment of that sort, I guess, should be Michelson-Morley, stating that though sources are moving with the earth, speed of light doesn't change.

ZealScience said:
The earliest experiment of that sort, I guess, should be Michelson-Morley, stating that though sources are moving with the earth, speed of light doesn't change.

But in the MM experiment, the source and the receiver are at rest relative to one another.

haitham1984 said:
"...By means of similar considerations based on observations of double stars, the Dutch
astronomer De Sitter was also able to show that the velocity of propagation of light
cannot depend on the velocity of motion of the body emitting the light..."

1) The experiment mentioned in the quotation above with some detail.

That's the DeSitter-double-star-experiment, which rule out the emission (or ballistic) theory of light, in which the speed of light depends on the velocity of the source, and in which light acts like a cannon ball:

http://en.wikipedia.org/wiki/De_Sitter_double_star_experiment
http://en.wikipedia.org/wiki/Emission_theory

2) Or, explain the idea above using a different experiment (assuming one was made) which leads us to the same conclusion.

While the Michelson-Morley experiment is compatible with Emission theories, there are many other experiments refuting this model, for example the Sagnac effect. It shows, that the speed of light is independent of the motion of the Sagnac interferometer, that is, while the source/receiver is moving, the light path becomes longer for one beam, and shorter for the counter-propagating beam. According to emission theory, this effect shouldn't exist.

So all of those experiments confirm special relativity, and refute emission theories. See also
http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html
http://en.wikipedia.org/wiki/Tests_of_special_relativity

Regards,

## What is the proof that the velocity of light cannot depend on the velocity of the body emitting the light?

The proof for this is based on the principle of relativity, which states that the laws of physics should be the same for all observers regardless of their relative velocity. Since the speed of light is constant in all inertial frames, it cannot depend on the velocity of the body emitting it.

This proof was first theorized by Albert Einstein in his theory of special relativity. He proposed that the speed of light is a fundamental constant and does not change based on the velocity of the source.

## Can the velocity of light change in any situation?

No, according to this proof, the speed of light remains constant in all situations, regardless of the velocity of the body emitting it or the observer's frame of reference. This has been experimentally proven and is a fundamental principle of modern physics.

## Is there any evidence to support this proof?

Yes, there is a significant amount of evidence to support this proof. Numerous experiments, such as the Michelson-Morley experiment and the Kennedy-Thorndike experiment, have consistently shown that the speed of light is constant, regardless of the observer's velocity.

## What implications does this proof have for our understanding of the universe?

This proof has profound implications for our understanding of the universe. It is the basis for Einstein's theory of special relativity, which has revolutionized our understanding of space and time. It also has practical applications in modern technology, such as GPS systems, which rely on the constant speed of light to function accurately.

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