Galilean relativity vs special relativity

[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.