Exploring the Relationship between SR Postulates 1 & 2

[ivan]

Hi all
I was recently told that certain postulates of SR are equivalent or one can be derived from the other. Namely 1) The speed of light in vacuum is constant and is independent of the speed of emitting body; 2) The speed of light is impassable limit;

I did some search and found quite different statements though. I found that postulate #1 was first postulated by Einstein in his "ON THE ELECTRODYNAMICS OF MOVING BODIES". One article said even that Einstein did not say light speed is impassable limit. Postulate #2 was first proposed by Poincare.

My question is: Can #1 be derived from #2 or vice versa?

Thank you all.

 

[Janus]

The two postulate of SR are (paraphrased):

1. The speed of light in a vacuum is a constant for all inertial observers.
2. The laws of Physics are the same for all inertial observers.

The speed of light limit for massive objects is a conclusion arrived at from these postulates, not a postulate itself.

The "in a vacuum" part is important, as the apparent speed of light changes through different mediums. In fact, it is given a special symbol, "c". And it is c that the limit refers to.

Thus it is possible to travel faster than the speed of light in a medium in which the speed of light is less than c, for example, water. All relativistic effects however would be calculated in reference to c, not the speed of light through the medium.

It can also be said that velocities greater than c are not strictly forbidden by Relativity. There are hypothetical particles called tachyons, which travel at speeds greater than c. Tachyons, however, can only travel at velocities greater than c. The speed of light barrier is still in force. Objects that travel at less than c can not be accelerated to c or greater than c, and tachyons can not be slowed to c or less than c.

Also, no one has ever detected a tachyon, and we don't know if they really exist.

 

[ivan]

The two postulate of SR are (paraphrased):

1. The speed of light in a vacuum is a constant for all inertial observers.
2. The laws of Physics are the same for all inertial observers.

The speed of light limit for massive objects is a conclusion arrived at from these postulates, not a postulate itself.

Thank you. That was a very clear explanation.

 

[pmb_phy]

The two postulate of SR are (paraphrased):

1. The speed of light in a vacuum is a constant for all inertial observers.
2. The laws of Physics are the same for all inertial observers.

The speed of light limit for massive objects is a conclusion arrived at from these postulates, not a postulate itself.

First off Einstein did call the constancy of light a postulate in that paper, i.e. after stating the principle of relativity Einstein went on to say

..., and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light always propagated with a definite velocity c which is independant of the motion of the emitting body.

Einstein knew quite well that if Maxewell's equations hold then the second postulate follows. However this assumes the correctness of Maxwell's equation. If, for example, the proper mass of the photon was non-zero then Maxwell's equations are no longer valid and must be replaced by the equations derivable from the Proca Lagrangian which has a photon proper mass term in it. A decent relativity textbook will explain this. This is stated quite nicely in Special Relativity; A Modern Introduction, by Hans C. Ohanian, Physics Curriculum & Instruction, (2001). In the footnote (to the second postulate) on page 41 Ohanian writes

^*Although Einstein stated the invariance of the speed of of light as a second principle, the two principles are not entirely independant. If Maxwell's equations are valid laws of physics, then one can deduce the value of the speed of light from Maxwell's equations, and then the first principle implies the second. Hence the second principle is to be regarded as "insurance" in case Maxwell's equations are not valid laws of physics.

There was a time when I agreed with you Janus. About 5 years ago I think. So I wrote this up in a letter to the Editor of the Am. J. Phys.. The letter was rejected for the exact reasons given above by Ohanian and myself.
The reason Einstein

The "in a vacuum" part is important, as the apparent speed of light changes through different mediums. In fact, it is given a special symbol, "c". And it is c that the limit refers to.

It can also be said that velocities greater than c are not strictly forbidden by Relativity.

As you mention below, what is strictly forbidden is that a particle which is originally at rest in the inertial frame S could be accelerated past the speed of light. However it may be possible that a hypothetical a particle, known as a tachyon, could be created and for which is already moving faster than light. This would not violate special relativity and it could be done with a finite amount of energy. It was for that reason that the article

Possibility of Faster-Than-Light Particles, G. Feinberg, Phys. Rev. 159(5), 25 July 1967, was written. As the author says in the abstract

We consider the possibility of describing, within the special theory of relativity, particles with spacelike four-momentum, which therefore have velocities greater than that of light in vacuum. The usual objections to such particles are discussed, and they are found to be unconvincing within the framework of relativistic quantum theory. A quantum field theory of noninteracting, spinless, faster-than-light particles is described. The field theory is Lorentz invariant, but must be quantized with Fermi statistics. The associated particle theory has the property that the particle number is not Lorentz-invariant, and the no-particle state is not Lorentz-invariant either. Never the less, the principle of relativity is satisfied. The Lorentz invariance implies a relation between emission and absorption processes, in contradiction to the usual case. Some comments are made about the problem of introducing interactions into the field theory. The limiting velocity is c, but a limit has two sides.

Pete

 

[bernhard.rothenstein]

The two postulate of SR are (paraphrased):

1. The speed of light in a vacuum is a constant for all inertial observers.
2. The laws of Physics are the same for all inertial observers.

The speed of light limit for massive objects is a conclusion arrived at from these postulates, not a postulate itself.

The "in a vacuum" part is important, as the apparent speed of light changes through different mediums. In fact, it is given a special symbol, "c". And it is c that the limit refers to.

Thus it is possible to travel faster than the speed of light in a medium in which the speed of light is less than c, for example, water. All relativistic effects however would be calculated in reference to c, not the speed of light through the medium.

It can also be said that velocities greater than c are not strictly forbidden by Relativity. There are hypothetical particles called tachyons, which travel at speeds greater than c. Tachyons, however, can only travel at velocities greater than c. The speed of light barrier is still in force. Objects that travel at less than c can not be accelerated to c or greater than c, and tachyons can not be slowed to c or less than c.

Also, no one has ever detected a tachyon, and we don't know if they really exist.

Please explain me in more detail your statement in boild. I know many papers where the problems are studied in the rest frame of the medium where the light signals propagate with c/n.

 

[pmb_phy]

The speed of light limit for massive objects is a conclusion arrived at from these postulates, not a postulate itself.

What do you mean "the speed of light for a massive object"? Do you mean a object that has non-zero proper mass? If so then that violates conclusions reached with the postulates of relativity.

Pete

 

[neutrino]

What do you mean "the speed of light for a massive object"? Do you mean a object that has non-zero proper mass? If so then that violates conclusions reached with the postulates of relativity.

Pete

Janus said, "The speed of light limit for a massive object...".

 

[pmb_phy]

Janus said, "The speed of light limit for a massive object...".

Thank you very much for the correction neutrino. I am much obliged. I was sure Janus wouldn't make sure a mistake. Hence my confusion!

Darn dyslexia! :rofl:

Best wishes

Pete