# Insights The Speed of Light and of Galilean Relativity - Comments

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#### haushofer

A clear way for me to look upon this stuff, is the idea that the speed of light c is not 'just' the speed of E.M-waves, but determines the causal structure of spacetime. Also, the Poincare symmetries and dynamics of special relativity can be 'contracted' by sending c to infinity (for the underlying Lie algebras this procedure is known as Inönü-Wigner contraction). This opens up the lightcones of spacetime and gives you absolute time and a Galilean spacetime structure (i.e. the Galilei-group).

Why is this a nice view? Well, it shows that Galilean relativity and Special Relativity differ in only one (!) single aspect. They both say inertial observers are equivalent and the speed of light is the same for all inertial observers. For Galilean Relativity however, c is infinite, while for Special Relativity c is finite. This is the only difference. Kind of amazing.

#### Greg Bernhardt

Nice Insight! @klotza

#### robphy

Homework Helper
Gold Member
A clear way for me to look upon this stuff, is the idea that the speed of light c is not 'just' the speed of E.M-waves, but determines the causal structure of spacetime. Also, the Poincare symmetries and dynamics of special relativity can be 'contracted' by sending c to infinity (for the underlying Lie algebras this procedure is known as Inönü-Wigner contraction). This opens up the lightcones of spacetime and gives you absolute time and a Galilean spacetime structure (i.e. the Galilei-group).

Why is this a nice view? Well, it shows that Galilean relativity and Special Relativity differ in only one (!) single aspect. They both say inertial observers are equivalent and the speed of light is the same for all inertial observers. For Galilean Relativity however, c is infinite, while for Special Relativity c is finite. This is the only difference. Kind of amazing.
In my opinion, it is best to leave the "speed of light" ' c ' as 3e8 m/s always [since light's speed is finite, even in Galilean relativity].
For this relativity-selecting speed-parameter, call it "maximum signal speed" ' c_max or "invariant speed" c_invariant. The dimensionless ratio c/c_max can then take the value of 1 for special-relativity and 0 for galilean-relativity. (In the Galilean case, the speed of light is finite, and nothing particularly special.)

#### Drakkith

Staff Emeritus
2018 Award
Nice insight! I thoroughly enjoyed it!

Gold Member

#### haushofer

A clear way for me to look upon this stuff, is the idea that the speed of light c is not 'just' the speed of E.M-waves, but determines the causal structure of spacetime. Also, the Poincare symmetries and dynamics of special relativity can be 'contracted' by sending c to infinity (for the underlying Lie algebras this procedure is known as Inönü-Wigner contraction). This opens up the lightcones of spacetime and gives you absolute time and a Galilean spacetime structure (i.e. the Galilei-group).

Why is this a nice view? Well, it shows that Galilean relativity and Special Relativity differ in only one (!) single aspect. They both say inertial observers are equivalent and the speed of light is the same for all inertial observers. For Galilean Relativity however, c is infinite, while for Special Relativity c is finite. This is the only difference. Kind of amazing.
In my opinion, it is best to leave the "speed of light" ' c ' as 3e8 m/s always [since light's speed is finite, even in Galilean relativity].
For this relativity-selecting speed-parameter, call it "maximum signal speed" ' c_max or "invariant speed" c_invariant. The dimensionless ratio c/c_max can then take the value of 1 for special-relativity and 0 for galilean-relativity. (In the Galilean case, the speed of light is finite, and nothing particularly special.)
Well, what's the speed of an electromagnetic wave which obeys Galilean symmetries? :)

#### haushofer

Hmm, quoting is not going right. So let me repeat. Writing down a Galilei-covariant form of the Maxwell's equations gives eqn.'s similar to Newton's grav.eqn's. Hence instanteneous propagation, hence an infinite speed of light.

@klotza Nice article by the way, haven't said that yet!

#### resurgance2001

Hi

I was reading your article and you mentioned Fizeau's experiment to measure the speed of light using a cog wheel.

I believe it said that he shone a light some 15 km to a mirror and then it was reflected back.

I have tried to find more details about how he actually achieved this. For example, what did he use as a light source and what did he use the drive the cog wheel? Any ideas?

I have not yet been able to track down any proper diagrams/drawing of the actuall apparatus he used. A French university tried a while back to reproduce the experiment using a modern laser and hi-tech brushless motor and simply were not able to do the experiment.

#### eltodesukane

see this video
near 0:56

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#### exmarine

Nice write-up. But it repeats my pet peeve that is in all the textbooks. That is some version of: “The velocity of light is c in all inertial reference frames”. It takes a really generous reading of that sentence to have it be correct. Yes, the speed of light is independent of the emitter’s speed. But the speed of a photon is not c in all inertial reference frames. In fact, it is c in only one inertial reference frame, and that is the frame of its eventual absorber / detector. That fact is right there in Einstein’s brilliant derivation of the Lorentz Transform. It just seems to me that it should be explicitly stated.

#### Ygggdrasil

Gold Member
Really nice article. It's always fun to read about some of the elegant experiments that scientists designed long ago.

Maxwell's equations showing that the speed of light propagates with a constant velocity is usually used as the motivation for replacing Galilean relativity with Einstein's relativity. Where do Maxwell's equations fit into this picture? Were the scientists motivated by testing his prediction of a constant velocity of light or were they just trying to measure the speed of light as a experimental challenge?

#### Buzz Bloom

Gold Member
"By considering these experiments, I think one could discount the idea that light’s speed simply adds to the speed of its source, as is required by Galilean relativity."
Hi @klotza:

I very much liked your article, but the sentence above confuses me. In the article
Wikipedia says
"Galilean relativity states that the laws of motion are the same in all inertial frames."​
Other Internet sources say the same thing in different words. For example
says
"Generalizing these observations Galileo postulated his relativity hypothesis: any two observers moving at constant speed and direction with respect to one another will obtain the same results for all mechanical experiments."​
What confuses me is that these definitions of Galilean relativity do not seem to imply what the quote above from your article says. Were you perhaps thinking of some other Galileo writings in which he said that light’s speed adds to the speed of its source?

Regards,
Buzz

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#### robphy

Homework Helper
Gold Member
Hmm, quoting is not going right. So let me repeat. Writing down a Galilei-covariant form of the Maxwell's equations gives eqn.'s similar to Newton's grav.eqn's. Hence instanteneous propagation, hence an infinite speed of light.
I guess my point of view is that we already have something called "light" which we have experimentally measured its speed to be 3e8 m/s (say, in the frame of the source).

We write down a theory [on electricity and magnetism] yielding a set of PDEs, which satisfies some symmetries under (say) Galilean or Lorentz transformations.
If those PDEs have an invariant-propagation-speed that is infinite or finite but not equal to 3e8 m/s,
then why would one associate the finitely-measured-speed of light with that invariant propagation-speed?
That is to say, one would likely look elsewhere to explain "light".... There would still be the finite "speed of light" at 3e8 m/s (which wouldn't be invariant under that PDE's transformations) and an invariant-speed associated with that PDE.

If those PDEs have an invariant-propagation-speed that is finite and equal to 3e8 m/s,
then one would look further to try to associate light with that PDE.

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#### PeterDonis

Mentor
Writing down a Galilei-covariant form of the Maxwell's equations
Can you be more explicit? I wasn't aware that there was such a thing. Maxwell's equations are Maxwell's equations; they are Lorentz invariant, not Galilean invariant.

#### Orodruin

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But the speed of a photon is not c in all inertial reference frames. In fact, it is c in only one inertial reference frame, and that is the frame of its eventual absorber / detector.
Your pet peeve seems to be wrong. There is nothing special about any particular inertial frame and the speed of light is going to be the same in any inertial frame. In fact, the special relativity "inertial frame" is generally just a substitute for a particular type of coordinate system on Minkowski space. In general, you can use any coordinate system and get the same results. The propagation of light is not tied into any particular coordinate system, it is a property of space-time.

#### haushofer

I guess my point of view is that we already have something called "light" which we have experimentally measured its speed to be 3e8 m/s (say, in the frame of the source).

We write down a theory [on electricity and magnetism] yielding a set of PDEs, which satisfies some symmetries under (say) Galilean or Lorentz transformations.
If those PDEs have an invariant-propagation-speed that is infinite or finite but not equal to 3e8 m/s,
then why would one associate the finitely-measured-speed of light with that invariant propagation-speed?
That is to say, one would likely look elsewhere to explain "light".... There would still be the finite "speed of light" at 3e8 m/s (which wouldn't be invariant under that PDE's transformations) and an invariant-speed associated with that PDE.

If those PDEs have an invariant-propagation-speed that is finite and equal to 3e8 m/s,
then one would look further to try to associate light with that PDE.
I'm looking at these issues from the Correspondence Principle point of view.

#### robphy

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I'm looking at these issues from the Correspondence Principle point of view.
I understand. In my backburner project, I am also interested in a correspondence. However, I prefer to disentangle (or at least distinguish) the many roles of "c" in relativity: Speed of light (experimental value), speed of Maxwell-type equations, invariant-speed of relativity theories, unit-conversion factor, etc... Then, when one examines a particular limit... possibly interesting features about the structure of physical theories may be better revealed.

It's along the lines of ... If we discover that the photon has a tiny but nonzero rest-mass (so that its speed is not Lorentz invariant), does special relativity fall apart? I would argue "no".

#### exmarine

Your pet peeve seems to be wrong. There is nothing special about any particular inertial frame and the speed of light is going to be the same in any inertial frame. In fact, the special relativity "inertial frame" is generally just a substitute for a particular type of coordinate system on Minkowski space. In general, you can use any coordinate system and get the same results. The propagation of light is not tied into any particular coordinate system, it is a property of space-time.
Thank you for your response. But please note carefully what I said. I did NOT say that LIGHT has speed c in only one reference frame. I said that A PHOTON has speed c in only one inertial frame, that of the eventual observer. The two observers in relative motion in Einstein's derivation of the Lorentz Transform did not / could not observe the same photon - they must observe at least two different photons. Any photon that one sees apparently arrives with velocity c relative one's own frame and not relative to any other's frame. That is right there in his derivation. I think that is also true for all the experimental verifications of SRT. I don't think one can detect a photon destined to be observed in some other reference frame. If I am wrong please let me know. But if this is correct, then it removes some of the strange and mysterious aspects of SRT for me. Thanks.

#### Orodruin

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But please note carefully what I said. I did NOT say that LIGHT has speed c in only one reference frame. I said that A PHOTON has speed c in only one inertial frame, that of the eventual observer. The two observers in relative motion in Einstein's derivation of the Lorentz Transform did not / could not observe the same photon - they must observe at least two different photons. Any photon that one sees apparently arrives with velocity c relative one's own frame and not relative to any other's frame.
There is no need to even talk about photons in special relativity, photons are not present. You need to quantise the EM field to have photons and this is one of the most involved processes in quantum field theory. Photons are not small billiard balls. Regardless, the events of emission and detection exist in all frames - they are not coordinate dependent. Any other statement borders on misinformation.

I don't think one can detect a photon destined to be observed in some other reference frame. If I am wrong please let me know. But if this is correct, then it removes some of the strange and mysterious aspects of SRT for me. Thanks.
Photons are not observed "in a frame". Frames are only different ways of putting different coordinates on the same events in space-time.

#### klotza

Gold Member
Some interesting points of discussion have been brought up, some of which you are discussing amongst yourselves. I will attempt to address the questions asked to me directly.

Regarding Fizeau's experiment with the cogwheel, I do not have the original source unfortunately.

"Maxwell's equations showing that the speed of light propagates with a constant velocity is usually used as the motivation for replacing Galilean relativity with Einstein's relativity. Where do Maxwell's equations fit into this picture? Were the scientists motivated by testing his prediction of a constant velocity of light or were they just trying to measure the speed of light as a experimental challenge?"

I think this is where a bit of historical rearrangement comes into it for pedagogical purposes. Many of these experiments took place before Maxwell's electromagnetic wave equation was derived. The derivation of the speed of light from Maxwell's equations shows that its speed is related to the magnetic and electric properties of the vacuum, which is interesting, especially so in the 19th century I imagine, but by themselves I don't see how they imply special relativity unless you already assume that the Lorentz transform is the right way to go between reference frames. To show that the speed is the same in all reference frames you'd have to know that, let's say, the electric attraction between two charges didn't depend on how fast they were moving with respect to some fixed frame. We now know that's true, but that information would have to be input into Maxwell's derivation somehow, which it normally isn't.

Regarding the definition of Galilean invariance, I was going with the idea that considering dynamics of ball throwers on a riverboat in the rest frame of the shore by subtracting the speed of the river would also work for people playing laser tag. I guess technically this means that Galilean relativity assumes that the Galilean transformation is the correct way to go between frames, which is an equivalent statement to the ones you pasted.

I am not familiar with Schulenberger's work.

#### JSBailey

I also very much enjoyed Alex' article.

#### create14all

Nice write-up. But it repeats my pet peeve that is in all the textbooks. That is some version of: “The velocity of light is c in all inertial reference frames”. It takes a really generous reading of that sentence to have it be correct. Yes, the speed of light is independent of the emitter’s speed. But the speed of a photon is not c in all inertial reference frames. In fact, it is c in only one inertial reference frame, and that is the frame of its eventual absorber / detector. That fact is right there in Einstein’s brilliant derivation of the Lorentz Transform. It just seems to me that it should be explicitly stated.
How do you explain the The Fizeau Water Experiment which demonstrates 3 inertial frames being observed having 3 different speeds relative to each other?

#### nettleton

I am puzzled why c is defined as the velocity of light in presumably a perfect vacuum. I have read a couple of papers, which have been subject to criticisms, that c may vary via its interactions with virtual particles in space. Is there an accepted theory dealing with the effect of variation in the number densities in space through which light propagates?

#### PeterDonis

Mentor
I have read a couple of papers, which have been subject to criticisms, that c may vary via its interactions with virtual particles in space.
Please give a specific reference. We can't answer your question without knowing what specific papers you have looked at.

"The Speed of Light and of Galilean Relativity - Comments"

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