Galilean relativity vs special relativity

[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→∞.

 

[D H]

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).

Classical mechanics did not have a "limit finite speed of light c in vacuum". Classical mechanics, like Montana's highways pre-1974, did not have a speed limit. There was no top speed. You are still confusing the speed of light with the universally agreed upon speed.

Einstein's second postulate had nothing to do with a speed limit. It didn't even say that the speed of light was the same in all inertial frames. As written by Einstein, all that his second postulate claims is that light (electromagnetic radiation) moves at a specific speed c through vacuum in some inertial frame of reference, and that this speed is independent of the speed of the source. Einstein developed a definition of simultaneity in his 1905 paper prior to introducing these two numbered postulates. This definition is really just another postulate, an unnumbered one.

That the speed of light is c in all inertial frames is a derived result in Einstein's 1905 paper. It falls out from of his definition of simultaneity and his two postulates. Most physicists teach relativity by making the constancy of the speed of light in all inertial frames a postulate; concepts of simultaneity fall out as a derived result. Einstein did it the other way around because his statement of the second postulate is a direct consequence of Maxwell's equations.

This revised way of teaching remains true to Einstein's 1905 paper in the sense that it is uses the speed of electromagnetic radiation (aka, the speed of light) as a central concept, not some arbitrary finite speed that is the same to all observers. Einstein's 1905 paper was ultimately about Maxwell's equations. The subject of the second half of that paper is Maxwell's equations. After all, it was the apparent conflict between Maxwell's equations and Newtonian mechanics that was the key problem in physics in the latter part of the 19th century.

This concept of basing relativity on some finite universally agreed upon (but unspecified speed) is a relative newcomer, 1960s or so, maybe later. This new point of view was motivated by mathematicians. Mathematicians and physicists think differently. To a mathematician, starting with the assumption that there exists some finite speed c that is the same to all observers is a vastly superior to starting with assumption that the speed of light in vacuum c is the same to all observers. Physicists are tied to reality; there's nothing wrong with making the speed of light a magic number. Mathematicians aren't tied to reality; starting with a specific assumption based on reality is a foreign and perhaps repugnant concept. Starting with a non-specific assumption is the way to go. That said, most texts that cover relativity still start with the speed of light (the speed at which light travels) rather than some random finite speed as being special. Physicists are still bound by reality.

 

[TrickyDicky]

I still feel the arguments being thrown at me don't address what I'm saying, which is very simple.
Consider this:By the Galilean addition of velocities law and the infinite invariant speed, that is the non existence of a limiting speed for signals or observers, an observer in classical mechanics could ideally build a spaceship that travels at infinite speed and that astronaut would see light at infinite speed just by using the Gallilean velocities addition.

 

[TrickyDicky]

Classical mechanics did not have a "limit finite speed of light c in vacuum". Classical mechanics, like Montana's highways pre-1974, did not have a speed limit. There was no top speed. You are still confusing the speed of light with the universally agreed upon speed.

There I was quoting Simon Bridge, so nothing to do with me.

 

[TrickyDicky]

I really don't understand the insistence on arguments about the history of science or relativity after all the times I explained my point has nothing to do with it and that this is a purely conceptual thing as it is explained in the SR learning project of the wikiversity.

 

[D H]

Thread locked pending moderation.