Galilean relativity vs special relativity

[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?

 

[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.

 

[TrickyDicky]

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 c".

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.

 

[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

 

[A.T.]

Hmmm...except I don't think in galilean relativity it can be considered invariant

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

 

[Simon Bridge]

What you mean by "depending on the different frames"? What are talking about frame invariance, meaning that it doesn't depend on the frame.

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.

 

[A.T.]

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

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

 

[TrickyDicky]

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

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.

 

[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)."

 

[Simon Bridge]

Just like the quotes I brought.

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.

You asked: "what do we think" - you have your answer.
Probably others will weigh in soon enough.
Have fun.

 

[TrickyDicky]

You asked: "what do we think" - you have your answer.
Probably others will weigh in soon enough.
Have fun.

Thanks

 

[A.T.]

I maybe should have said c intead of speed of light

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.

 

[TrickyDicky]

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.

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?".

 

[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."

 

[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.

 

[D H]

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?

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.

Otherwise the logical thing to say would have been: "by lightspeed you must be meaning invariant speed, no?".

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.

 

[TrickyDicky]

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.

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.

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.

 

[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.

 

[TrickyDicky]

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.

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.

 

[robphy]

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.

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).

 

[harrylin]

I think that most has been said already, so just a few loose ends:

[..] 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.

If you had formulated it there as "could be thought of as", and without adding more to it, probably you would have received less strong reactions. The problem was a total confusion, as follows (here I compress it to the worst of several posts, sorry to "rub it in"):

Classical Newtonian mechanics assumed infinite light-speed, it wasn't until Maxwell eq. that a finite constant c came to dispute that to Newton [..]
classical mechanics assumed galileo relativity in which light speed is treated as infinite. [..] This is basic classical mechanics. In which [..] there is no relativity of simultaneity, it takes no time for light signals to travel [..] Is this so hard to understand? Ask anyone versed on classical mechanics if you don't believe me.

Hopefully, thanks the disambiguations of the earlier replies in this thread, it is now clear that, instead, Newtonian mechanics assumed a finite light-speed (ballistic theory of light), while Maxwell introduced a wave propagation constant c; and that was certainly in dispute with Newton, but nothing about the level of speed, and nothing related to modifying the transformation equations. Moreover, with ballistic light theory (at 3E8 m/s), the Galilean transformations are no doubt perfectly relativistic.

The confusion, which certainly does not originate with you, is due to the fact that with SR the speed of light c became equal to the limiting speed. Thus the symbol for the speed of light also acquired the meaning of limiting speed, because the two are equal. However, it goes wrong when one confounds the two in classical mechanics, in which the limiting speed is infinite and the speed of light is finite.

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?

It looks to me more like a "slip of the pen":
"The principle of causality would be violated if things could go faster than light. Interestingly, these things are true even in Galilean relativity, except that in Galilean relativity the speed of light is infinite. "

He probably simply makes a straightforward substitution error: the label "the speed of light" was attached in his discussion to the invariant speed. He took that out of the context of SR in which it is right, into the context of Galilean relativity, in which it is wrong. I can understand that, as such errors also happen to me now and then, due to the "stickiness" that labels can have in a discussion.

I don't think that when asked if in classical mechanics light speed was assumed to be infinite, he would have agreed.

 

[TrickyDicky]

how would imposing an infinite light speed change the equations of Newtonian mechanics?

 

[TrickyDicky]

Let's see if I can find a statement that can be fully agreed with. The idea that I was trying to reflect was that special relativity reduces to classical mechanics (that is its results are recovered) in the limit of an infinite speed of light. Anyone against this statement?

 

[haushofer]

Perhaps it is nice to note that the c to infinity limit of GR can be taken in way such that it reproduces Newton- Cartan theory, although it is rather artificial in the sense that the answer seems to depend on when you take the limit. See e.g. the papers of Dautcourt. From a group contraction point of view, see e.g. Arxiv: 1011.1145.

 

[harrylin]

Let's see if I can find a statement that can be fully agreed with. The idea that I was trying to reflect was that special relativity reduces to classical mechanics (that is its results are recovered) in the limit of an infinite speed of light. Anyone against this statement?

Yes of course - because of the mislabelling that I elaborated on in my posts (as did most others), and which you despite all that still reproduce. Instead, probably everyone would agree with the following variant (because, different from SR, in classical mechanics the limit speed is not equal to the speed of light):

Special relativity reduces to classical mechanics (that is its results are recovered) with an infinite limit speed (or, without a limit speed).

 

[TrickyDicky]

Yes of course - because of the mislabelling that I elaborated on in my posts (as did most others), and which you despite all that still reproduce. Instead, probably everyone would agree with the following variant (because, different from SR, in classical mechanics the limit speed is not equal to the speed of light):

Special relativity reduces to classical mechanics (that is its results are recovered) with an infinite limit speed (or, without a limit speed).

The "mislabelling" was already clarified by several posters including me. The infinite invariant speed doesn't necessarily have to be that of EM wave signals in classical mechanics, we all know that, but that doesn't mean that EM signals are not allowed to have infinite speed in classical mechanics. Hopefully you can see that subtle distinction.
When you mention infinite speed that speed must be of some kind of signal or information, I'm simply proposing in my example that since I'm comparing relativistic mechanics with classical mechanics instead of talking about an infinite invariant speed abstractly we use light signals as example. Can you give any reason to forbid light signals from being used as example of infinite invariant speed once is clarified that light speed and invariant speed are not the same thing in classical mechanics?

 

[Simon Bridge]

The "mislabelling" was already clarified by several posters including me. The infinite invariant speed doesn't necessarily have to be that of EM wave signals in classical mechanics, we all know that, but that doesn't mean that EM signals are not allowed to have infinite speed in classical mechanics. Hopefully you can see that subtle distinction.

When you say "infinite speed of light", since "light" is "EM Waves", that wording means infinite speed for all EM waves ... what is the problem with using the term "invariant speed" in your statements when you don't mean the literal speed that EM-waves travel at?

Here you seem to want to clarify that some EM waves may, in classical mechanics, travel faster than light does in a vacuum. Perhaps the speed of propagation of an EM wave is somehow frequency dependent? In which case, you would need to specify which EM wave you are calling "light".

But I'd be more interested in how you support that assertion: since when could EM waves have infinite speed in classical mechanics? Please provide examples so it is clear what you are talking about.

When you mention infinite speed that speed must be of some kind of signal or information,

Not exactly. Do you believe that for every speed imaginable there must be a physical entity traveling at that speed in order for us to consider it in our math?

Surely the point of a limit is that things need not actually be at the limit. It can be like the absolute zero of temperature: the limit of a trend. In classical mechanics it would take an infinite energy (and time) to accelerate to the infinite speed (and there is the issue of how you'd measure it).

A there need be no object traveling at a particular speed for that speed to still exist in our models. In the particular case of a limit - there need be no entity with a property at that limit for the limit to exist for that property.

I'm simply proposing in my example that since I'm comparing relativistic mechanics with classical mechanics instead of talking about an infinite invariant speed abstractly we use light signals as example.

The problem with this approach as a description for classical mechanics vs special relativity is that light (meaning all EM waves) have a finite speed in classical mechanics which has, as a top limit, it's speed in a vacuum.

Can you give any reason to forbid light signals from being used as example of infinite invariant speed once is clarified that light speed and invariant speed are not the same thing in classical mechanics?

If the speed of EM-signals in a vacuum is infinite, then all materials would have, in classical physics, infinite refractive index.

Why is it useful to posit an infinite speed for anything?
For practical purposes, the classical limit is always when v<<c ... it tells us when we can stop using SR. How does taking c → ∞ help things?

Why must you choose light as having a special status - why not posit an infinite speed for some hypothetical signal or object, if you must have a something to have a speed, and have done with it? Especially considering the infinite limiting speed is, itself, incorrect anyway. Why so invested in some signal, particularly a light signal, being infinite? What brought this on?

----------------

Hopefuly you begin to see that the wording you have chosen carries more baggage than is needed to discuss the distinctions you want to talk about in a clearly understood way. This is a well known problem. The established solution is to adopt a different wording which you have been provided with. To avoid further problems it is strongly recommended that you adopt that wording.

 

[TrickyDicky]

Simin, so if classical mechanics already had a limit finite speed of light c in vacuum, why did Einstein have to introduce his second postulate?(the first being already present in galilean relativity). If there was already a limit speed, by the principle of relativity already present in galilean relativity it would have made that speed limit invariant.
Your are totally blurring any distinction between SR and classical mechanics. It was considered a revolution back in 1905, though.

 

[TrickyDicky]

My point is that one difference between classical mechanics and SR is that the former admits an infinite light speed (since it has infinite invariant speed of signalling we can choose any kind of signal, even make up one, but since I'm choosing to make a pedagogical comparison with SR it makes sense to choose light). Also I'm not making any historical point nor implying anything about what people in the last centuries before SR thought or knew about the speed of light. This is obviously a comparison from the perspectibe of what we know now about SR with purely pedagogical purposes.

 

[Simon Bridge]

Simin, so if classical mechanics already had a limit finite speed of light c in vacuum, why did Einstein have to introduce his second postulate?

Because classical mechanics did not have an invariant speed c for light - I have not made that claim.

I was attempting to clarify two assertions from your post:
1. different EM waves may have different speeds
2. (some) EM waves may have an infinite speed

I have asserted that classical mechanics predicts that different observers will measure a different speed for light depending on the relative speed of observer and source.

AND all EM waves whose source has the same relative speed will, classically, be measured to have the same speed in a vacuum

AND that speed will be finite.

i.e. gamma waves and radio waves have the same finite c, though different observers measure different values for c (always finite).

I provided justification for these assertions within the classical model - i.e. refractive index.

Then I challenged you to produce any result from classical mechanics that contradicts these statements... which also explains finite refractive index.

I'm also interested in the answers to the questions I posed in my previous post because, judging from your other threads, this is not like you man. What's up?

 

[Simon Bridge]

My point is that one difference between classical mechanics and SR is that the former admits an infinite light speed (since it has infinite invariant speed of signalling we can choose any kind of signal, even make up one, but since I'm choosing to make a pedagogical comparison with SR it makes sense to choose light).

In what sense?
EM waves were known to have a measurable finite speed before Einstein, so it does not make historical sense.
From a teaching perspective, "pedagogical", don't you need the models to be consistent or risk confusing students?

This is obviously a comparison from the perspectibe of what we know now about SR with purely pedagogical purposes.

Positing light for the thing with an infinite speed would be inconsistent with classical optics so it is not very useful from a pedagogical perspective.
(Note: saying the infinite-speed signal must be EM in nature has extra implications beyond the speed thing - eg. it also has to obey Maxwel's equations... what do you have to do to those to let some EM wave have an infinite speed? But why do you need to postulate an infinite-speed particle anyway - merely having infinity as the invarient speed does not require that one exist.)

On top of that - that is not how it is used.
If you use this idea in teaching, you risk, needlessly, seeding misconceptions others will have to tidy up later. That could be you - why make extra work for yourself?

Relativity replaces the classical theory - it is best practice to encourage students to see the classical regime as the limiting case where v<<c since it is the classical theory that is the approximation and that is the nature of the approximation.

 

[TrickyDicky]

Because classical mechanics did not have an invariant speed c for light - I have not made that claim.

Why did you ignore in the quote my second sentence?

I have asserted that classical mechanics predicts that different observers will measure a different speed for light depending on the relative speed of observer and source.

Aha, and that is the Galilean addition of velocities for light, precisely this is the kind of addition law that contrary to the addition law of SR one gets when one admits infinite light speed instead of finite c. Do you not see this difference?

For more detailed explnation consult this: http://en.wikiversity.org/wiki/Special_relativity
Under the first heading "Speed limit".

 

[TrickyDicky]

Also the more i insist that I'm not making any historical point, the more you act as if you were trying to convince me that in the 19th century they knew light speed was finite. I know that, thanks, I'm not talking about that at all. That smells of a strawman argument.

 

[TrickyDicky]

I never suspected that explaining why in classical mechanics a finite speed of light was not an invariant would be so tough.

 

[TrickyDicky]

Not to mention that the usually accepted limit for classical mechanics of considering v being negligible wrt c (v<<c) is mathematically equivalent to taking arbitrary v at the limit where c→∞.