# The speed of light and the mass of a photon

• JollyOlly
In summary, the theory of Relativity uses a constant c which has the approximate value of 3x108 ms-1. The measured speed of light in a vacuum vl has apparently the same value. What is the experimental evidence for this equivalence? As far as I know, the only way to measure c is to measure the speed of light. Of course, if c was slightly larger than vl, photons would have a small mass. Does this have consequences? It would make sense of the recent suggestion that neutrinos can travel faster than light. One of Einsteins postulates is that all observers measure the same speed for light in a vacuum. Speed "c" is the speed of light - therefore, measuringf

#### JollyOlly

The theory of Relativity uses a constant c which has the approximate value of 3x108 ms-1

The measured speed of light in a vacuum vl has apparently the same value.

What is the experimental evidence for this equivalence? As far as I know, the only way to measure c is to measure the speed of light.

Of course, if c was slightly larger than vl, photons would have a small mass. Does this have consequences?

It would make sense of the recent suggestion that neutrinos can travel faster than light.

One of Einsteins postulates is that all observers measure the same speed for light in a vacuum. Speed "c" is the speed of light - therefore, measuring the speed of light is the only way to measure c.

It follows, also, that light does not have mass. It is not merely "very small", it is zero.

By comparison, neutrinos have a very small mass - which allows them to decay into each other. It also means that they travel slightly slower than the speed of light. As it stands, there are several ways the FTL neutrino result could have been obtained. It's best not to get too carried away by the result - any explanation also needs to account for neutrino's apparent failure to be FTL in the past.

Have a look at:
http://blogs.discovermagazine.com/b...up-ftl-neutrinos-explained-not-so-fast-folks/

I agree that one of Einsteins postulates is that the speed of light is the same for all observers but what is the evidence for this? A postulate is not evidence.

If c (the constant in Einstein's equations) was just a fraction of a % larger than the speed of light - would it make any significant difference to our GPS devices or predictions of the orbit of Mercury for example? I think not.

So I repeat, what experiments have been carried out to check this important equivalence between c and the speed of light?

There is no evidence and there can be no evidence for Einstein's second postulate, that light propagates at the speed of light for all inertial observers. We can measure to great accuracy the two-way speed of light, but we cannot identfy an absolute rest state for a medium that propagates light but we could if there were anything that could propagate faster than light.

Philosophically there is no such thing as an empirical proof of anything.
The strength of Special Relativity and the validity of Einstein's postulates rests on the variety and cunning of the experiments that could have found them mistaken.

Y.Z. Zhang, Special Relativity and its Experimental Foundations, [World Scientific (1997)].
... it's especially comprehensive. However, a bit long. For an overiew, try this website

The observations cover quantum through cosmological scales.

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Thanks Simon for that link. It would appear that measurements have been made that put an upper limit on the rest-mass of a photon of the order of10-17 eV/c2.

This raises the important question - If a photon had this rest-mass, how fast would a typical photon actually travel in a vacuum?

My gut feeling is that a 1 eV photon would travel at a speed of (1 - 10-17)c. Am I right?

Surely the speed would become energy dependent which is not what is observed.

My gut feeling is that a 1 eV photon would travel at a speed of (1 - 10-17)c. Am I right?

What is your basis for that? guessing is not a rationale.

The theory of Relativity uses a constant c which has the approximate value of 3x108 ms-1

The measured speed of light in a vacuum vl has apparently the same value.

What is the experimental evidence for this equivalence? As far as I know, the only way to measure c is to measure the speed of light.

Of course, if c was slightly larger than vl, photons would have a small mass. Does this have consequences?

It would make sense of the recent suggestion that neutrinos can travel faster than light.

c is not measured, its value in the SI is defined exactly. You can measure the time needed for a light signal to travel from A to B and obtain its speed. Then compare with c. If photons have mass then electrodynamics would be modified (Proca equations). Today, there is none experimental evidence of mass for photons.

About neutrinos, I think that OPERA guys did something wrong.

Surely the speed would become energy dependent which is not what is observed.
I am talking about an extremely small variation in speed but it would imply for example that visible light and gamma rays from a distant supernova would arrive at different times. I think this would be extremely difficult to prove or disprove however.
What is your basis for that? guessing is not a rationale.
My guess is based on a 'back of the envelope' calculation but I would like it confirmed by someone with more knowledge of SR than I possess

My gut feeling is that a 1 eV photon would travel at a speed of (1 - 10-17)c. Am I right?

Why use a gut feeling when you can calculate it?

$$\frac{v}{c} = \frac{pc}{E} = \frac{\sqrt{E^2 - (mc^2)^2}}{E} = \sqrt{1 - \left( \frac{mc^2}{E} \right)^2 }$$

Use mc^2 = 10^{-17} eV and E = 1 eV and see what you get.

If your calculator barfs on this, try the binomial approximation: $(1 - x)^n \approx 1 - nx$ when x << 1.

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One interesting development is called "Doubly Special Relativity", (the only person I recognize who was a part of it is Lee Smolin). Where they expand on Einstein's Second Postulate about the absolute nature of the speed of light, and replace it with an upper energy bound. This doesn't really answer your question but I think its cool and kind of relevant.

http://arxiv.org/PS_cache/hep-th/pdf/0405/0405273v1.pdf

One interesting development is called "Doubly Special Relativity", (the only person I recognize who was a part of it is Lee Smolin). Where they expand on Einstein's Second Postulate about the absolute nature of the speed of light, and replace it with an upper energy bound. This doesn't really answer your question but I think its cool and kind of relevant.

http://arxiv.org/PS_cache/hep-th/pdf/0405/0405273v1.pdf

I would not call it «interesting»,

http://arxiv.org/abs/0912.0090

c is not measured, its value in the SI is defined exactly.
The standards organization didn't make c a defined value until 1983, almost 100 years after the Michelson Morley experiment. A century of ever refined measurements of c (and they were measuring c back then) demonstrated an ever improving agreement between theory and reality.

Today, there is none experimental evidence of mass for photons.
Absolutely correct. While there is no way to measure an exact value of zero, what can be done experimentally is to (a) put an upper bound on the mass of a photon and (b) test whether the theoretical rest mass of zero is consistent with experimental results. The margin of error has shrunk drastically with improvements to experiment techniques and technologies. However, even with these ever shrinking margins of error, the theoretical mass of zero remains well within those margins.

Since this was partly my fault: the take-away lesson here is that you cannot just take a single result (in this case the upper-bound for the mass of a photon) and draw general conclusions from it.

You need to check if the conclusions you draw by accepting a non-zero photon mass is consistent with the other experiments. For instance, if the speed of a photon was not the same as the listed speed of light, relativistic doppler shifts wouldn't work ... and there are a host of "moving source" measurements in the list.

Take your time, read through the papers. You need the earlier ones to understand the later ones.

There is no evidence and there can be no evidence for Einstein's second postulate, that light propagates at the speed of light for all inertial observers. We can measure to great accuracy the two-way speed of light, but we cannot identfy an absolute rest state for a medium that propagates light but we could if there were anything that could propagate faster than light.

Being somewhat ignorant in this field, I'm reluctant to chime in. However, it seems to me that the second postulate is more about information than EM waves in particular. Imagine all humans are blind and we detect moving objects through other methods (gravitational waves?). Whatever that method happens to be would also be limited to c. So everything Einstein did could be recreated with no references to EM waves if such a detection method existed.

So if true, the real question is how we know light moves at c. I'm not educated in this area enough to answer this, but if you experimentally show that photons have no mass, than relativity would still require light to move at c, no?

I'm just spewing ignorant speculation here, so take this post as more of a request for discussion/explanation.

However, it seems to me that the second postulate is more about information than EM waves in particular.
The title alone of Einstein's 1905 paper says otherwise: "On the Electrodynamics of Moving Bodies." Look inside and you will find that the paper is indeed very much about EM waves. The second half of the paper is a relativistic formulation of Maxwell's equations.

c is not measured, its value in the SI is defined exactly.
The standards organization didn't make c a defined value until 1983, almost 100 years after the Michelson Morley experiment. A century of ever refined measurements of c (and they were measuring c back then) demonstrated an ever improving agreement between theory and reality.

Right and the SI was established only 50 years ago. I would have been more accurate and emphasize that c is not measured today in the SI and that its value is taken to be, by definition, c = 299 792 458 ms−1.

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The title alone of Einstein's 1905 paper says otherwise: "On the Electrodynamics of Moving Bodies." Look inside and you will find that the paper is indeed very much about EM waves. The second half of the paper is a relativistic formulation of Maxwell's equations.

Well, of course Einstein was talking about light. He says that pretty plainly and it's obviously the most straightforward analogy. However, the universe does not just preserve c as the speed of light, but rather information in general, correct? That's why I gave the example of a group of blind train riders that can only detect gravity. If relativity really defines the true nature of spacetime, than surely the type of energy wouldn't matter, no?

I guess it would be easier if I just rephrase this into a question: Is there anything in Einstein's paper or subsequent interpretations that says the universal c comes from the fact that EM radiation has a speed limit rather than information in general has a speed limit? It seems like all of the arguments could be made by postulating another type of energy transfer medium with no mass.

However, the universe does not just preserve c as the speed of light, but rather information in general, correct?
Some physicists prefer to hold that a constant speed of light (better said: speed of any massless particle) as axiomatic, others prefer a geometric set of axioms, yet others that information has a speed limit. There is no one axiomatization of physics. (There isn't even a consistent, unified description of all of physics.)

Which interpretation is "best" is getting into metaphysics rather than physics. They are either indistinguishable (interpretations of quantum mechanics) or incommensurate (quantum vs. relativistic physics). I'd rather not have this thread become yet another discussion of which is the right way to go. Such discussions on interpretations of physics have a marked tendency to devolve into a shouting match and then get locked.

Re the question about blind men and gravity waves:

It is predicted by GR that gravity waves travel at 'c' in a vacuum, just as light waves do. Of course the experimental evidence for this is not as good as the experimental evidence that light waves travel at 'c', because we have yet to detect our first gravity wave.

While it is not about gravity waves, experiments such as the detection of muons at the Earth's surface shows that relativity isn't just an electromagnetic phenomenon. If muons didn't respect the laws of special relativity, they would decay before they reached the Earth's surface.

Why use a gut feeling when you can calculate it?

Use mc^2 = 10^{-17} eV and E = 1 eV and see what you get.

My thanks to jtbell for this timely rebuke. What you get is the amazing result that v differs from c by only 1 part in 10-34. Even over a distance of 700km this would slow a photon down by totally negliible amount. Not nearly enough to explain the OPERA results.

This http://permalink.lanl.gov/object/tr?what=info:lanl-repo/lareport/LA-UR-08-05197" [Broken] gives some interesting information about experiments to measure the mass of a photon. Apparently the most sensitive experiments involve measuring the deviations from Coulombs inverse square law. It also transpires that if photons had significant mass, charge would not be conserved either. (Thanks again to Simon for pointing me in the right direction)

On balance, I think we had better stick with a zero rest mass for now and look for another explanation of the OPERA results.

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It is predicted by GR that gravity waves travel at 'c' in a vacuum, just as light waves do.
When you say travel at c do you mean locally or in the large?

Of course the experimental evidence for this is not as good as the experimental evidence that light waves travel at 'c', because we have yet to detect our first gravity wave.
What do you mean by 'not as good', I thought there was no evidence whatsoever.

Of course, if c was slightly larger than vl, photons would have a small mass. Does this have consequences?

It would make sense of the recent suggestion that neutrinos can travel faster than light.

Photon mass limits are in http://arxiv.org/abs/0809.1003

Photon mass is a quantum concept. The corresponding classical concept is "wavelength dispersion" in which different wavelengths or frequencies of light travel at different speeds.

https://www.physicsforums.com/showpost.php?p=3517099&postcount=46" says that the photon mass limits are tight enough that if the OPERA neutrino result were true, then Lorentz invariance would probably be violated.

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I agree that one of Einsteins postulates is that the speed of light is the same for all observers but what is the evidence for this? A postulate is not evidence.

If c (the constant in Einstein's equations) was just a fraction of a % larger than the speed of light - would it make any significant difference to our GPS devices or predictions of the orbit of Mercury for example? I think not.

So I repeat, what experiments have been carried out to check this important equivalence between c and the speed of light?

Einstein's postulation of a constant speed of light was based on Maxwell's 1860's derivation of the speed of light as :
$$c= \sqrt {\frac 1 {\mu_0 \epsilon_0}}$$

This was known, in the day, as Maxwell's conundrum and was the root of the great schism in physics which lasted from publication of Maxwell's work to publication of Einstein's Theory of Relativtiy.