Hi: Einstein's second postulate states that the speed of light is constant as viewed from any frame of reference. Most of the books on relativity that I have been reading usually ask the reader to accept that fact because proving it is behind the scope of the book. Can anyone help me understand the actual reason behind the second postulate? thanks
Moneer81, a "postulate" is something that you assume to be true at first for the sake of argument. In this case, the whole special theory of relativity follows from the postulates that the laws of nature are the same in all inertial frames, and that the speed of light is the same in all inertial frames. So, the acutal reason behind the second postulate is this: special relativity follows from it + the other potulate. That does not mean that you could ever prove that it is true by doing experiments, and as it turns out you can't. On the other hand: nobody has ever proved that it is not true either, but they could.
hmm....that's interesting. I thought it was experimentally proven that the speed of light is constant from all frames of reference. I could swear that Brian Greene said that too in this book "The Elegant Universe".
I can't speak as to exactly what it was that Brian Greene said in his book, but nope, that could never be proven. However, as a postulate, it is simply true by definition within the framework of special relativity. However, don't let me give you the wrong idea: accepting that postulate for the sake of argument is usually a safe bet so long as you keep in mind that it's a postulate and not something that you could ever prove by making measurements.
It has been proven that the speed of light has been the same from all refference frames in which the speed of light has ever been measured. That doesn't meab that it couldn't be different in some instance that we simply haven't measured, or it may even be different in every instance when we are not looking. Maybe we're like a cop sitting at the side of the road with a radar-gun, who concludes at the end of the day that "all drivers everywhere in the universe travell at or below the posted speed limit", not realising that all those drivers are just waiting untill he;s not looking so they can floor it! Maybe light travells at all different speeds depending on what mood it's in, and only regulates itself to c when we're watching. But it seems unlikely to me.
It has been. Aether (as his name would imply) is incorrect. Every attempt to measure the speed of light has always come up with the same answer, to within the margin for error of the experiment. Based on that, it is reasonable to theorize (and for the sake of further theories, postulate) that the speed of light is, in fact, always constant in inertial reference frames. While Aether is correct that postulates are assumptions for the purpose of the theory, they are based on experimental evidence - and in this case, also the math of Maxwell's equations. It is important to note that theories require postulates. While it is theory that the speed of light is constant, for the sake of logical consistency, it is necessary to assume it to be universallly true for the sake of building other theories on it. Postulates aren't just some random assumption you pull out of your a- er, um air.... They have to be grounded in reality to actually be useful.
Special relativity is empirically equivalent to "...an ether theory taking into account time dilation and length contraction but maintaining absolute simultaneity..." R. Mansouri & R.U. Sexl, A Test Theory of Special Relativity: I. Simultaneity and Clock Synchronization, General Relativity and Gravitation, Vol. 8, No. 7 (1977), pp. 497-513. In such an empirically equivalent ether theory, the speed of light varies with direction. This is not just some cherry-picked statement from an article that I pulled out of thin a- er, um air, it is the very crux of a famous paper referenced by most if not all of the experiments published over the past 30 years which measure local Lorentz invariance.
This is not correct. A postulate does not mean one cannot verify it with experiment. One can and this is continually done on SR's postulates. A postulate on the other hand cannot be derived from First Principles! If it can, one doesn't need a postulate in the first place! Zz.
This postulate has so far proven to be consistent with experiment, but so too has "...an ether theory taking into account time dilation and length contraction but maintaining absolute simultaneity...". No experiment has ever been able to distinguish between these two points of view, and if one ever does it could only favor the ether view.
Of course the speed of light postulate can be verified. Just measure the speed of light from any moving source. In fact this has been done: Alvaeger F.J.M. Farley, J. Kjellman and I Wallin, Physics Letters 12, 260 (1964).
Perhaps we could at least agree that it is possible to experimentally test the statement that the speed of light will be measured to be the same by all observers, assuming these observers all use the same type of procedure to make their own measurements (ie if one observer uses rulers and clocks which are at rest relative to himself to make his measurements, then all observers must do so).
The second postulate is an immediate consequence of Newton's first law of motion and the homogeneity of time. http://www.everythingimportant.org/relativity/ http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000043000005000434000001 http://arxiv.org/PS_cache/physics/pdf/0302/0302045.pdf
No it isn't--it may be that you can use those assumptions to show that coordinate transformations must have the same general form as the Lorentz transformation equations, except with the constant c having the option of being infinite (and if you plug infinite c into the Lorentz transform you get the Galilei transform), as is suggested on that paper from arxiv.org that you linked to. But the c in this equation has no necessary connection to the speed of electromagnetic waves--it is perfectly compatible with Newton's first law and the homogeneity of time that there would be no time dilation so you could synchronize clocks just by setting them to the same time in one location and moving them apart (in which case, assuming there's no Lorentz contraction you'll be using the Galilei transform to convert between different observer's measurements), and yet light would only have a constant speed in one preferred frame, while in other frames it would be measured to go faster in one direction than the other.
It is the convention used for the synchronization of clocks which determines the outcome of a one-way speed of light measurement. If you postulate that the speed of light is isotropic, then clocks are synchronized by Einstein's convention, and...voila...all subsequent experiments measure a constant speed of light. That does not constitute experimental proof that the speed of light is constant; it is not possible to ever prove that by experiment. It is possible to disprove it upon the identification of a locally preferred frame, but that hasn't been done yet, and maybe it never will be. To prove that the speed of light is constant, you would have to prove a negative: e.g., "there is no locally preferred frame".
You have missed my objection. You said: "So, the acutal reason behind the second postulate is this: special relativity follows from it + the other potulate. That does not mean that you could ever prove that it is true by doing experiments, and as it turns out you can't." A postulate does not mean you can't verify it with experiments. Read this again. This has nothing to do with SR. And I'd like to see you come up with "time dilation" and "length contraction" based on your ether postulate, make just JUST fit together that they happen to cancel any variation to make it agree with the tons of experimental observations, and then publish it. Till then, you'll understand if I don't buy this. Zz.
Merriam-Webster's dictionary defines postulate as: to assume or claim as true, existent, or necessary : depend upon or start from the postulate of b : to assume as a postulate or axiom (as in logic or mathematics) I guess the whole jargon is getting me a little confused, but what I know is that if we're gonna have believe a theory like SR then it better be based on something that makes sense, and for those of us that don't believe in faith, it better be something we can convince ourselves that it is valid.
I agree that "a postulate does not mean that you can't verify it with experiments", but I don't see where I implied otherwise. I haven't suggested that you should buy an ether theory, yet. What I recommend that you should buy today is that the possibility has not been, and never will be, ruled out by experiment.
There is a difference between a "postulate" in mathematics and a "postulate" in physics. In fact those blasted physicists should know better than to use the word "postulate" at all. I suspect that those who use it in a physics book are really saying "I don't want to bother to explain how this has be shown". The fact that the speed of light is constant in all frames goes back to the Michaelson-Morley experiment- it and versions of it are probably one of the most "repeated" experiments in the history of science.
The round-trip speed of light, such as in MM experiments, is a constant in all frames because the issue of clock synchronization doesn't arise. However, that does not allow one to distinguish between special relativity and "...an ether theory taking into account time dilation and length contraction but maintaining absolute simultaneity...".