E=mc2 and Postulates to prove it

[Hallale]

As we know very famous equation E= mc2
While deriving this equation there are two postulates

Postulate I:
The laws of physics are the same in same in all inertial frames.

Postulate II:
The speed of light (in a vacuum) has the same constant value c in all inertial frames.

If we prove by experiment that postulate II that is "The speed of light (in vacuum) has the same constant value c in all inertial frame" is not correct, then what will be change in E = mc2

 

[Passionflower]

If we prove by experiment that postulate II that is "The speed of light (in vacuum) has the same constant value c in all inertial frame" is not correct, then what will be change in E = mc2

If, hypothetically, an experiment would prove that that postulate is wrong then obviously the whole theory collapses.

 

[starthaus]

If we prove by experiment that postulate II that is "The speed of light (in vacuum) has the same constant value c in all inertial frame" is not correct, then what will be change in E = mc2

Nothing since there is ample experimental proof that $$\Delta(E)=c^2 \Delta(m)$$
Experiment trumps theory.

 

[DrGreg]

Postulate II says that the speed of light is "invariant", to use the jargon: all observers agree its value. But the point of the postulate is simply that a finite invariant speed exists, not whether or not light travels at that speed. In fact it turns out that you can use Postulate I to show that either there is a finite invariant speed, or else the "invariant speed is infinite", which would give you Newtonian physics.

If we later discover that light doesn't travel at the invariant speed c (e.g. that it travels at 0.99999999999999c relative to its emitter), that wouldn't affect the theory. There is overwhelming evidence to support the theory of relativity even without measuring the speed of light.

 

[Hallale]

If that is the case then why we always state second postulate before writing E=mc2.
Secondly because of this second postulate we are further proving time dilation, lengh contraction ... So now my qeustion is can we still prove Time dilation theory (if second postulate is wrong).

 

[russ_watters]

If it is wrong it is wrong...but it is not wrong...so where is this going?

 

[starthaus]

If that is the case then why we always state second postulate before writing E=mc2.
Secondly because of this second postulate we are further proving time dilation, lengh contraction ... So now my qeustion is can we still prove Time dilation theory (if second postulate is wrong).

Same answer as I gave you before, there is ample experimental confirmation of relativistic time dilation. Experiment trumps theory. Every time.
So, where are you trying to go with your questions?

 

[bcrowell]

It's not enough to imagine that postulate II fails. You need to state how it fails. Possibilities: (a) We're talking about an alternate universe where the laws of physics are different, and therefore it can fail in ways that contradict past experiments in our universe. (b) Photons have nonvanishing mass. (c) Something else...?

An example of (a) is a universe in which Galilean relativity is valid. Such a universe is equivalent to taking the limit of special relativity when $c\rightarrow\infty$.

If, hypothetically, an experiment would prove that that postulate is wrong then obviously the whole theory collapses.

Not true. For example in case (b), nothing fundamental changes at all about relativity, but you just have to stop referring to c as the speed of light. For an example of an experiment setting an upper limit on the photon mass: R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters , 1998, 80, 1826-1829, http://silver.neep.wisc.edu/~lakes/mu.html

If we later discover that light doesn't travel at the invariant speed c (e.g. that it travels at 0.99999999999999c relative to its emitter), that wouldn't affect the theory.

Not quite. A fixed speed not equal to c is not compatible with SR. Massless particles have to travel at the invariant speed c. Massless particles don't have fixed speeds.

If it is wrong it is wrong...but it is not wrong...so where is this going?

There are ways for it to be wrong without contradicting previous experiments. A small but nonvanishing photon mass is one of them.

This is essentially a question about the axiomatic foundations of SR. To get more insight, it really helps to look at an alternative axiomatization. For derivations of the Lorentz transformation that don't take a constant c as a postulate, see Morin or Rindler.

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51
Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008

By comparing the Rindler axiomatization with Einstein's 1905 axiomatization, we can see that there are only three ways for Einstein's postulate II to fail: (1) Rindler's postulates all hold, but Galilean relativity is valid. (2) Rindler's postulates fail, because spacetime lacks the symmetry properties that everyone expected. E.g., rotational or translational symmetry is violated. (3) Einstein's postulate II fails, but Rindler's postulates all hold. The way that this can happen is if light doesn't travel at c (which presumably means that photons have mass).

Case 1 is inconsistent with experiment, so we can rule it out.

Case 2 is possible, but experiment shows that if these symmetries are broken, they're broken extremely weakly, so SR is a fantastically good approximation in almost all situations.

Case 3 is possible, but the upper limit on the photon mass is incredibly small, so again SR is a fantastic approximation.

 

[Troponin]

As we know very famous equation E= mc2
While deriving this equation there are two postulates

Postulate I:
The laws of physics are the same in same in all inertial frames.

Postulate II:
The speed of light (in a vacuum) has the same constant value c in all inertial frames.

If we prove by experiment that postulate II that is "The speed of light (in vacuum) has the same constant value c in all inertial frame" is not correct, then what will be change in E = mc2

If it is wrong, then Postulate II is no longer valid. I don't think it will affect the theory much though. There is more than enough experimental data to show that the equation is correct (as others have said). If experiment proves the equation, it doesn't really matter if the postulates that were used as the starting point for its development weren't perfect.

To quote Richard Feynman "If it isn't verified by experiment...it's wrong. It doesn't matter how beautiful the theory is, it doesn't matter what your name is, none of that matters. If the theory isn't verified by experiment...it's wrong. It's as simple as that."

Taking that quote in reverse, if experiment verifies the theory...whatever late night thoughts that may have raced through your mind to get you to start developing the theory don't matter.

What matters is that $$E=mc^{2}$$ has been experimentally verified by many experiments (In some form or other, by just about every physics major on Earth during one of their first "modern physics" labs), and appears to be a valid expression. If you don't like the second postulate, you can give your future lectures with the preface;

"Let me start by saying that I don't like the fact that we have to include the second postulate. It's never been proven to be wrong, but if it is proven to be wrong at some point in the future, it won't really affect things because the theory has been validated by extensive experimentation. Of course, for now it also appears to be completely true, and no experiments have been able to show otherwise, but I still don't like to include it.
Now that you all know how I feel...here are the two postulates..."