# The Speed of Light and Galilean Relativity

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Introduction

In this article I will discuss some experiments in the 19th and early 20th centuries that looked how the velocity of a light source affects the speed of the light emitted from it. In particular, the Fizeau water experiment, the de Sitter double star experiment, and the Michelson-Morley experiment, which is the most well known. These experiments cast significant observational doubt on the Galilean idea of relativity as it applies to light, that the velocities of the emitted light and the source simply add together. We know now that this is wrong and that special relativity must be taken into account, but that was not always the case and had to be inferred from observation.

I will not discuss experiments devised with the hindsight of special relativity (such as measurements of time dilation), although they are interesting. I will also not go into the details of ether theory, because I’m not too familiar with it.

Early Determination of the Speed of Light

The first attempted measurement of the speed of light that I know of was by Galileo himself and an assistant, who stood on opposing hilltops and attempted to communicate by opening a lantern shutter and waiting for the lantern on the opposing hill to be opened in the response. They did not notice a delay, and concluded that the speed of light must be much faster than the speed of sound. Although this experiment was inconclusive, it was one of the first examples of a negative result being used to constrain the bound of an unknown quantity, an analytical technique so common in physics today.

Diagram of Romer’s observations. The timing of Io’s eclipses is different if the Earth is at H or at E.

The first partially successful measurement was by Ole Rømer who was making careful observations of eclipses of the moon Io by Jupiter’s shadow. He noticed that the eclipses did not appear on a regular schedule as expected, but varied by a few minutes depending on where Earth was with respect to Jupiter in its orbit. He reasoned that this variation was due to the time taken for the light to reach the Earth, and took an extra 22 minutes to cross the diameter of Earth’s orbit, if it was farther from Jupiter. This isn’t too far off from the 16 minutes we now know it takes. With an accurate knowledge of the astronomical unit, this puts his speed of light at 222,000 km/s. This is significant because it was the first piece of evidence that the speed of light is finite.

In the 18th century, James Bradley made a measurement of stellar aberration, the apparent change in position of a star due to the velocity of Earth relative the star (not to be confused with parallax, which is a change in apparent position due to the changing position of Earth). Based on the 20 arcsecond change in a star’s position due to aberration over a year, he concluded that light must travel about 10,000 times as fast as Earth does around the sun, and was able to conclude that light takes eight minutes to reach the Earth from the sun, even though he didn’t know the speed of light or the astronomical unit.

The first “modern” measurement of the speed of light was in the 1840s by Hippolyte Fizeau. He shone light through the teeth of a quickly rotating cog, off a distant mirror, and back through the cog. If the cog rotated slowly, the light would pass through the same gap. If it was going sufficiently fast, it would be blocked as the tooth would rotate into its path. If it were going even faster, the next gap would rotate into its path and it would get through again. By measuring the amount of light getting through as a function of the cog’s rotational speed, he could measure the speed of light by finding the cog speed that would allow it to get through the next gap. He measured about 313,000 km/s, within 5% of the actual value.

Diagram of the Fizeau’s experiment. He presumably did not use a lightbulb, and the mirror was eight kilometers away.

The Fizeau Water Experiment

In addition to his cogwheel experiment, Fizeau did an experiment measuring the speed of light through moving water. Light through water is slower than light in a vacuum, and if the light is “dragged” along with the water then one could naively expect that its velocity would just be the sum of the velocity of the water and the speed of light in the water. To test this, Fizeau designed an experiment where two parallel beams of light were sent through two columns of counter-flowing water, reflected off a mirror, and sent back through the other column of water. One beam of light would always be travelling with the current, and one always against it. The beams were then projected onto the same spot, so that an interference pattern could be seen. The magnitude of the interference depends on the relative velocity of the two beams.

Set up from the Fizeau experiment. Light emitted at S is split into two beams at G, through two slits at E, and through tubes of water in A where it flows in the directions of the arrow. After being reflected at m, the light goes back through the opposite tube of water, and the two beams meet again at G and interfere. One beam is always going with the flow of water, while one is always going against the flow.

The result was not null. But it did not verify the Galilean dragged light hypothesis. The size of the interference fringe he observed was about half of what was expected. Taking special relativity into account, we can apply relativistic velocity addition to find that the two beams actually differ in speed by a  factor ##1-\frac{1}{n^2}\approx 0.43## times the speed of the water (n is the index of refraction), so the special relativistic effect is roughly half of the Galilean effect. Fizeau wasn’t aware of this derivation, but he could see that the Galilean prediction was wrong by a factor of two.

Looking at an English translation of his initial report, he comments that the observed interference effect is half that of the his expectation, but quite close to the “ether drag” theory that the medium of light propagation was dragged along with the water. Again, hindsight is 20/20 but this was a step in the right direction.

The de Sitter Double Star Experiment

This analysis actually took place in the 1910s, after special relativity had been formulated, but conceptually it could have been understood centuries earlier. It was proposed by Willem de Sitter, better known for the eponymous space-time and its arch-nemesis, de Sitter space and anti-de Sitter space.

A diagram of the “experiment,” an observation of an orbiting star at two phases of its orbit, with the assumption that the speed of light is additive.

Consider the light being emitted by one member of a binary star system, with the Earthward velocity of the star oscillating periodically with the orbit. If the speed of the light adds to the speed of the star, it could eventually catch up with the light emitted by the star as it moves away from us in its orbit. If the stars are sufficiently far from Earth, we would observe some strange things as the blue shifted light caught up with the red shifted light, including spontaneous duplications of spectral lines, multiple appearances of the same star at a given time, and violations of Kepler’s laws, all of which would be more extreme for more distance stars, as there would be more time for the fast light to catch up with the slow light.

An animation of faster blueshifted light catching up with slower redshifted light from a member of a binary star system. If both pulses reach Earth at the same time, the image of the star briefly doubles.

Fortunately, we live in a galaxy full of binary star systems, so we can test this. In 1913, none of these effects had been observed (although de Sitter’s paper is a little skimpy on the data), and they still haven’t. If the simple velocity addition of light were true, then to be consistent with observations the laws of orbital mechanics would have to depend on their distance from Earth.

The Michelson-Morley Experiment

This experiment is typically mentioned when introducing special relativity, sort of as an experimental nail of the coffin for ether theory. There’s a lot of mixing and mashing of historical timelines that are rearranged to introduce concepts in a pseudo-chronological order, and it’s not actually known to what extent Einstein was influenced by it 1905, as he only credits the Fizeau experiment.

A Michelson interferometer, where light from a is split at b, bounces off the mirrors at d and c, us recombined at q and then observed at e.

The experiment was not so much a refutation of Galilean relativity per se, but rather the idea that there is a fixed reference frame through which light propagates. This experiment was basically the most sensitive interferometer of its time, spitting two beams of light, sending them along different perpendicular paths, and then re-uniting to form an interference fringe. If the speed of light were different in different directions due to the motion of the Earth relative to rest frame of light propagation, the interference pattern would change. By rotating the entire experiment, they close probe the relative velocities of light in the two arms relative to Earth’s movement, and they found nothing. Any potential signal that could observe was less than a fortieth that of the theoretical prediction.

The Michelson-Morley experiment with a preferred light frame. If the entire apparatus, on the orbiting Earth, moves with respect to light’s reference frame, the beams going in perpendicular directions would arrive at different times.

These results, according to my 21st century physics education, really made people think about a potential rest frame for light and the existence of luminiferous ether. Lorentz developed his transformations in order to explain this experiment, which fit nicely into special relativity.

Conclusion

All  of these experiments probe a fairly simple idea, that the velocity of light is additive with its source. Each of them is fairly straightforward to understand on a conceptual level, and doesn’t require special relativity to understand (although it certainly helps in interpreting their results). 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, and would force the physicists of the day to dig deeper to uncover the nature of light, which is indeed what happened. Physics students have been told for generations that the speed of light is constant in all rest frames and that that leads to Lorentz transformations, but it’s important to remember how we know that is the case.

43 replies
1. R
resurgance2001 says:

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.
[QUOTE=”klotza, post: 5324912, member: 569939″]klotza submitted a new PF Insights post

[URL=’https://www.physicsforums.com/insights/speed-light-galilean-relativity/’]The Speed of Light and of Galilean Relativity[/URL]

[URL=’https://www.physicsforums.com/insights/speed-light-galilean-relativity/’]Continue reading the Original PF Insights Post.[/URL][/QUOTE]

2. E
exmarine says:

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.

3. Ygggdrasil says:

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?

4. B
Buzz Bloom says:

“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 [USER=569939]@klotza[/USER]:

I very much liked your article, but the sentence above confuses me. In the article
[INDENT][URL]https://en.wikipedia.org/wiki/Galilean_invariance[/URL][/INDENT]
Wikipedia says
[INDENT]”Galilean relativity states that the laws of motion are the same in all [URL=’https://en.wikipedia.org/wiki/Inertial_frame’]inertial frames[/URL].”[/INDENT]
Other Internet sources say the same thing in different words. For example
[INDENT][URL]http://physics.ucr.edu/~wudka/Physics7/Notes_www/node47.html[/URL][/INDENT]
says
[INDENT]”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.”[/INDENT]
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

5. robphy says:

[QUOTE=”haushofer, post: 5325538, member: 20128″]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.
[/QUOTE]

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.

6. PeterDonis says:

[QUOTE=”haushofer, post: 5325538, member: 20128″]Writing down a Galilei-covariant form of the Maxwell’s equations[/QUOTE]

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.

7. G
Greylorn says:

[QUOTE=”klotza, post: 5324912, member: 569939″]klotza submitted a new PF Insights post

[URL=’https://www.physicsforums.com/insights/speed-light-galilean-relativity/’]The Speed of Light and of Galilean Relativity[/URL]

[URL=’https://www.physicsforums.com/insights/speed-light-galilean-relativity/’]Continue reading the Original PF Insights Post.[/URL][/QUOTE]
Alex Klotza,

Excellent post, thank you! I’m delighted to know that there is someone out there who is taking an honest look at physics fundamentals.

You’ve probably not heard of John R Schulenberger. This link, [URL]http://www.tandfonline.com/doi/abs/10.1080/03605308008820135[/URL]
might get you to some references to his paper, “Isomorphisms of hyperbolic systems and the aether.” At the level of deeply fundamental physics you may find it interesting, because he shows that the M-M experiment could not have detected the aether.

Thus, while the old “aether” concept has been left by the wayside, because relativistic concepts bypassed it like a Texas driver ignores roadkill, however unusual it might be, the aether has not yet been mathematically discredited.

Schulenberger was not the ordinary physicist. He obtained his first university level degree in Electrical Engineering by merely testing for it, without taking or auditing courses. He remained on the fringes of academia throughout his life, living simply and economically, making conventional income by bicycling to Idaho and building a house every year with a brother. He made beer and cigar money in Tucson by translating Russian math and physics papers for the University of Arizona. His life’s focus was the investigation of fundamental physics concepts. You might find him to be a kindred spirit. Or, you might not.

8. Orodruin says:

[QUOTE=”exmarine, post: 5325734, member: 106947″]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.[/QUOTE]
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.

9. haushofer says:

[QUOTE=”robphy, post: 5325874, member: 9587″]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.[/QUOTE]
I’m looking at these issues from the Correspondence Principle point of view.