# Galilean relativity vs special relativity

1. Oct 12, 2012

### TrickyDicky

I was told in another thread that saying that the Galilean relativity of Newtonian and classical mechanics could be thought of as light speed having the possibility of being infinite was nonsense. Since it was true that a discussion there of these points was off-topic, I use this new thread to offer this for debate.

From wikipedia "Inertial frame of reference" entry:
"In Newtonian mechanics, which can be viewed as a limiting case of special relativity in which the speed of light is infinite, inertial frames of reference are related by the Galilean group of symmetries."
This other quote is from John Hawley's professor of the virginia university page on questions about relativity: http://www.astro.virginia.edu/~jh8h/Foundations/Foundations_1/quest7.html

"Interestingly, these things are true even in Galilean relativity, except that in Galilean relativity the speed of light is infinite."
Fortunately I'm not alone in saying this kind of "nonsense". What do you folks think?

Last edited: Oct 12, 2012
2. Oct 12, 2012

### A.T.

I think it is an odd way to put it. I would rather say that Newtonian mechanics is the limiting case where:

v/c → 0

Because:

v << c

Not because:

c → ∞

What the quotes mean to say, is that if c was infinite then there would be no difference between Galilean and Lorenz transformations. The sentence "in Galilean relativity the speed of light is infinite" should rather say:

"in Galilean relativity the invariant speed is infinite, while in Special relativity the invariant speed is finite".

Your are just comparing transformations here. No need to talk about light. You can then bring physics into it, and say: Observation shows that the speed of light is finite and invariant. Therefore we need a transformation where the invariant speed is finite.

Last edited: Oct 12, 2012
3. Oct 12, 2012

### TrickyDicky

Hmmm...except I don't think in galilean relativity it can be considered invariant, since it assumes absolute time, depending on the different frames it could range from >0 to infinity.

4. Oct 12, 2012

### Simon Bridge

I think you also need to present the argument as to why the idea was thought "nonsense".

Note that Newton did conceive of light having a speed and the classical construction of a refractive index requires a finite speed for light in a vacuum. This did not affect relativity.

It is probably more helpful to think of Galilean relativity as being for the limiting case where relative speeds are small compared with the speed of light. Historically, it can be thought of as the case where light-speed has no special status: it is different for different observers.

When people like Hawley talk about infinite c then don't mean "the speed of light in a vacuum" c. They are considering that, classically, the c of the Lorentz factor has a value other than the speed of light ... a very big value. This has the same effect as making v<<c. This is what A.T. is saying when he talks about the invariant speed - classically this is infinite, but in SR it is finite and equal to the speed of light in a vacuum.

This simple confusion is one reason why it is not a very useful way to think about it.

Aside: Charles Fort wrote (in New Lands) that it was nonsense to conceive of light as having a speed: why, you turn on the light and the room is "illuminated" ... how can it have a speed. All this rotating wheels stuff was just so much confusing mumbo jumbo designed to mislead ... a simple experiment such as carried out by Galileo shows that light just switches on and off and that should be good enough for anybody! (Quality trollage.) :D

Last edited: Oct 12, 2012
5. Oct 12, 2012

### A.T.

Infinite speed doesn't change under Galilean transformations, so it is the invariant speed for Galilean transformations.

Last edited: Oct 12, 2012
6. Oct 12, 2012

### Simon Bridge

I think he's mixing up "invariant speed" with "speed of light".

In Galilean relativity, the speed of light in a vacuum is not invariant.
But you never made that claim.

7. Oct 12, 2012

### A.T.

Yes, I realized that and edited my post. He quoted my entire post, so it was not clear what he means by "it".

8. Oct 12, 2012

### TrickyDicky

Right, that was my point at the other thread("twin paradox problem"). I maybe should have said c intead of speed of light, but I thought the context was clear after having clarified I was not saying Newton or anyone using classical mechanics thought the speed of light was infinite, as it was clear at least since the Romer experiments it wasn't. I was clearly talking about the difference between the galilean transformations and the Lorentz transformations.
Just like the quotes I brought.

9. Oct 12, 2012

### TrickyDicky

Maybe this is more clarifying

http://en.wikipedia.org/wiki/Invariant_speed

"The invariant speed or observer invariant speed is the speed an object or particle must be traveling at for its speed to have the same measure in all reference frames. The invariance of the speed of light is one of the postulates of special relativity, and the terms speed of light and invariant speed are often considered synonymous. In non-relativistic classical mechanics, or Newtonian mechanics, finite invariant speed does not exist (the only invariant speed predicted by Newtonian mechanics is infinity)."

10. Oct 12, 2012

### Simon Bridge

The quotes, as presented, were ambiguous on that point.
So perhaps the trouble is just one of communication in a text-only environment?

You need to be explicit to avoid these kinds of confusions - which is why A.T. chose different actual words to distinguish the speed invariant under transformation from the speed of light. (It is not a good idea to consider the terms synonymous in all contexts - like when you want to discuss a situation where the speed if light is not invariant.)

Better yet - just don't use "infinite invariant speed" as a description of Galilean relativity ... use v<<c or deny special status to any speed.
OK I can see why you would feel that it is something you can safely do - but you should not use wikipedia as a source of subtle insights.
See if you can find a peer-review journal article using the terms synonymously.

Probably others will weigh in soon enough.
Have fun.

11. Oct 12, 2012

### TrickyDicky

Thanks

12. Oct 12, 2012

### A.T.

No, don't say "c", because that is a symbol often used for the speed of light in vacuum. Just say "invariant speed". Or: "speed invariant under transformations". It is a purely mathematical property of the transformations, that as such has nothing to do with physical phenomena like light.

13. Oct 12, 2012

### TrickyDicky

Fair enough. As I said I thought by the context it was understood that by lightspeed in vacuum I was meaning "invariant speed" (since we are in the relativity forum and in SR the two terms are synonimous), but you are right it is alway better to use the most rigorous term to avoid confusion.
I'm not sure in any case if using the most accurate term saves the statement from being considered nonsensical by some.
Otherwise the logical thing to say would have been: "by lightspeed you must be meaning invariant speed, no?".

14. Oct 12, 2012

### TrickyDicky

And here an instance where the c→infinity view is found intructive

http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

"For electromagnetic radiation, the limit to classical mechanics, c→infinity, is instructive. The Doppler effect formula simply becomes f = f'. This is the correct result for classical mechanics, although it is clearly in disagreement with experiment. It is correct since classical mechanics regards the maximum speed of interaction — for electrodynamics, the speed of light — to be infinite."

15. Oct 12, 2012

### TrickyDicky

This "odd" behaviour of infinite maximum speed of transmission of signals and information also leads to a very important property of classical mechanics: it's time invariance.

16. Oct 12, 2012

### D H

Staff Emeritus
I think that it's wikipedia being what it is (free; you get what you pay for) and a physics professor who doesn't know his history of science.

The latter is the more troubling of the two. What does this physics professor think the Michelson Morley experiment was about? The intent was not to prove that the speed of light is the same to all observers. If that was the intent, the MM experiment would be called one of the most famous successful experiments in physics. It's not called that. It's called one of the most famous failed experiments in all of physics. The intent of the experiment was to detect the variations in the speed of light due to the Earth moving at different velocities through the luminiferous aether. It failed to find those variations.

Even Maxwell thought that there must be a luminferous aether, that his electrodynamics equations strictly applied only in the rest frame of this aether. Almost all physicists of the time thought this was the case. Many continued to think this was the case for over a decade after Einstein's miracle year. Einstein's brilliance was to take Maxwell's equations at their word: The speed of light truly is the same to all observers. Einstein went on to answer "So what does this mean?" Even Poincare couldn't quite make that final step. Poincare did manage to arrive at the speed of light appearing to be the same to all observers. But that appearance was just an illusion to Poincare. He clung to the idea of an ether of some sort to the end.

No. Light speed means one thing, the speed of light in vacuum, Maxwell's c.

Physicists from Newton's time on knew that the speed of light was finite. The concept of an invariant speed didn't even make sense in a Newtonian context (better: is ridiculously trivial). The concept of an invariant speed is a relatively new addition to relativity theory. Einstein spoke specifically of the speed of light being the same to all observers. It was Maxwell's equations that motivated Einstein, and Maxwell's equations about electromagnetic phenomena. He did not speak of some random speed that was the same to all observers, and just happens to be equal to the speed of light.

The concept of an invariant speed only makes sense in the context of relativity plus quantum mechanics, or quantum electrodynamics (QED). This postdates Einstein by 40 years or so. QED dictates that all particles with zero rest mass, not just photons, must move at the same speed. Now an invariant speed does make sense. It's not just some random finite speed that is the same to all observers and happens to be equal to the speed of light. Since the photon has zero rest mass, the speed of light is just a special case of this concept of an invariant speed that applies to all massless particles.

17. Oct 12, 2012

### TrickyDicky

Your ideas about the hystory of relativity may be debatable but certainly all you mention here is not even remotely related to what is discussed here that is much more related to classical physics. Especially the MM experiment has nothing to do with my point.

18. Oct 12, 2012

### robphy

I describe Galilean relativity by saying that
it has a maximum signal speed that is infinite.
Light speed is still finite, but not invariant under Galilean boosts.
An infinite speed is invariant under Galilean boosts.

Special relativity has a maximal signal speed that is finite,
and that light's speed is equal to that maximal signal speed.

In their respective geometries/relativities,
these maximum signal speeds correspond to eigenvectors of the boosts.

A useful way to encode this is to define a dimensionless quantity (I call the indicator)
$$\epsilon^2=\frac{c_{light}}{c_{max\ signal}}$$
where $c_{light}=3\times 10^8\ m/s$.

$\epsilon^2$ has the value 0 for the Galilean spacetime, and 1 for Minkowski space.

With this, one can formulate special relativity with this indicator
so that one can clearly obtain the Galilean limits by having this indicator tend to zero.

19. Oct 12, 2012

### TrickyDicky

Interesting. That leaves open the question what kind of signals if not EM signals would be those since there aren't any known signals that can travel faster than EM signals also in classical mechanics.

20. Oct 12, 2012

### robphy

That issue is about the dynamics of particles and fields that you might have live in the Galilean spacetime... and not so much about the "arena" that the Galilean spacetime provides.

The above formulation distinguishes the maximum-signal speed of the spacetime from the speed of a particular field (the electromagnetic field).