Solving the Mystery of Relativity: What Postulates Say?

[Sampad Saha]

In this above image you can see that, The Galilean transformation for t=t' was rejected by Einstein and then again in Einstein 2nd postulates it was written"Velocity of Light is independent on inertial frame i.e it could be the same from all inertial frame"
So how can something is rejected and then written in postulates...please tell me if I'm going wrong..

[Mentor's note: Duplicate and redundant attachments have been removed]

 

[Fredrik]

He rejected $t'=t$ but didn't reject $\frac{\sqrt{x'^2+y'^2+z'^2}}{t'}=\frac{\sqrt{x^2+y^2+z^2}}{t}$. (Here (t,x,y,z) and (t',x',y',z') are the coordinates in two different inertial coordinate systems, of an event where an object can get hit but a pulse of light that was emitted at (0,0,0,0).

You posted three identical attachments, plus an irrelevant one. If edit feature allows you to delete three of your attachments, I suggest that you do so.
[Mentor edit: Thanks for pointing that out. We've taken care of it]

Edit: In the special case where the x and x' axes are in the same direction as the relative velocity, and the position coordinates are positive, the above simplifies to x'/t'=x/t.

 

[Nugatory]

If you could tell us which book you're using we will be able to give you better answers and maybe suggest some others.

 

[harrylin]

In this above image you can see that, The Galilean transformation for t=t' was rejected by Einstein and then again in Einstein 2nd postulates it was written"Velocity of Light is independent on inertial frame i.e it could be the same from all inertial frame"
So how can something is rejected and then written in postulates...please tell me if I'm going wrong..

I'm not sure what you mean, but I can clarify more. I already mentioned to you in #3 of the other thread, in Einstein's second postulate does not state that the speed of light is independent on inertial frame. Probably you had not yet seen my answer there.

The speed of light according to SR is constant, independent of the motion of the source. Perhaps you misunderstood what that means; the physical meaning of that postulate is that light propagates like a wave - which is a basic assumption of Maxwell's theory. Based on that assumption (Einstein's "second postulate"), people had been trying to detect in vain their velocity relative to the light medium: the laws of Maxwell were found to be the same, independent of the velocity of the used inertial frame. In other words, the principle of relativity (Einstein's "first postulate") was found to also hold for optics.

At first sight that is a hopeless contradiction. However, Lorentz as well as Einstein found that the problem came from the use of the Galilean transformations with Maxwell's laws. And they came up with transformations that removed the contradiction - the Lorentz transformations.

Does that help?

Also, I strongly recommend to read Einstein's introduction - I gave you the link.

 

[wabbit]

There is at times some confusion as to what "postulate" means in this context. The fact the the speed of light is constant was an established experimental result by the time Einstein elaborated his theory. It's consequences such as the changing length of a moving object were also known, though puzzling. A physical contraction in the ditection of motion had been proposed, but without a satisfactory explanation as to what was causing the contraction.

What Einstein did was build an alternative explanation (the contraction is not a physical transformation but a matter of perspective) that was far more natural. But to do that he had to question the relation between times and distance measured by two observers. He added the hypothesis (postulate) that the law of physics should be the same for both observers, which, when combined the the observed constancy of light speed (also raised to a postulate), forced him to drop the Newtonian assumption (postulate) that $t'=t,x'=x$. The rest follows.

 

[harrylin]

There is at times some confusion as to what "postulate" means in this context.
[..] the changing length of a moving object were also known, though puzzling. A physical contraction in the ditection of motion [..] is not a physical transformation but a matter of perspective. [..]

I'm not sure what confusion about "postulate" there is in this context according to you; if you simply mean that Einstein did not pretend to postulate something new, then I fully agree with that. Einstein showed how to derive from those postulates new transformations to replace the Galilean transformations. But note that Einstein had not seen the paper by Lorentz of a year earlier; it was not about philosophy but about finding a solution to solve the apparent contradiction in physics.

Also, your following statement concerning changing length was apparently debunked by Bell (who nevertheless had no disagreement with Einstein on that topic!); but perhaps we just mean something else with "physical".
Einstein: §4 of http://www.fourmilab.ch/etexts/einstein/specrel/www/
See also the parallel thread https://www.physicsforums.com/threads/clocks-within-each-ship-in-bell-spaceship-paradox.804582/