Is the first postulate necessary?

[CPL.Luke]

you can derive the lorentz transformation by just assuming that the speed of light is constant, so why is the first postulate of special relativity necessary?

 

[robphy]

you can derive the lorentz transformation by just assuming that the speed of light is constant, so why is the first postulate of special relativity necessary?

The first postulate is based on "Galileo's Principle of Relativity", essentially a claim of something being invariant among inertial frames.

To make a claim like yours, there are lots of implicit assumptions that you must be making. Do you have a reference for your claim?

 

[CPL.Luke]

well every textbook on special relativity I've ever seen (I've seen quite a few at this point) derives the transformation based off of the constancy of the speed of light without reference to the first postulate. however you do make a point that another frame could see things happen differently without the first postulate put into the theory.

 

[robphy]

well every textbook on special relativity I've ever seen (I've seen quite a few at this point) derives the transformation based off of the constancy of the speed of light without reference to the first postulate.

Really?
What would (say) t' and x' in the Lorentz Transformations refer to, without reference to the first postulate or its equivalent? Without the first postulate (or an equivalent set of postulates), there is nothing that distinguishes the set of inertial frames in this context.

 

[pmb_phy]

well every textbook on special relativity I've ever seen (I've seen quite a few at this point) derives the transformation based off of the constancy of the speed of light without reference to the first postulate. however you do make a point that another frame could see things happen differently without the first postulate put into the theory.

Then this one must be one of the ones you missed. From Classical Electrodynamics - Second Edition, Hans C. Ohanian, page 172

The principle of the universality of the speed of light is sometimes regarded as a corollary of the Principle of Relativity, because the validity of Maxwell's equation's in all inertial frames implies that light waves propagate in the same way in all such reference frames. However, such a deduction hinges on the assumption that Maxwell's equations are valid laws of physics. Althought it is true that Einstein was led to relativity by thinking about
Maxwell's equations, the theory of relativity is more fundamental than Maxwell's theory. It is therefore undesireable to make relativity logically dependant on Maxwell's equations, and it is preferable to adopt a second postulate for the universality of the speed of light.

Best regards

Pete

 

[yogi]

Einstein's second postulate does not say the speed of light is constant - it says it is independent of the velocity of the source - it is simply a repudiation of the ballistic theory of light, which was really nothing new. The constancy of the speed of light is consequent to Einstein's method of synchonization of two clocks - this forces the one way speed to be constant in all inertial frames.

 

[pmb_phy]

Einstein's second postulate does not say the speed of light is constant - it says it is independent of the velocity of the source - it is simply a repudiation of the ballistic theory of light, which was really nothing new. The constancy of the speed of light is consequent to Einstein's method of synchonization of two clocks - this forces the one way speed to be constant in all inertial frames.

That is the way that Einstein first stated that postulate, sure. However the speed of light being independant of the source is identical to saying that the speed of light is invariant. That's why Einstein reffered to the second postulte as the "constancy of light" in his book The Meaning of Life.

Pete

 

[yogi]

Pete - this is an academic thing but I do not see how you arrive at your conclusion. The speed of all known waves depend upon the properties of the medium and not the velocity of the source; the measured speed of waves in all cases other than em depend upon the motion of the receiver relative to the medium

One-way light isotropy was not necessary to explain the experimental results (MMx) but Einstein was predisposed to the notion that the velocity of an object relative to space could not be measured. What was needed at the time was "over-and-back" isotropy, so Einstein accomplishes his objective via synchronization. Repudiation of the ballistic theory does not guarantee "one-way" isotropy - but "one-way" isotropy does guarantee
"over-and-back" isotropy, and that was what was needed to comport with the experiments.

Just my opinion, but I think Einstein was sensitive to the fact that too bold a hypothesis at the outset would have resulted in ridicule and summary rejection (It certainly would not have survived modern peer review) so ..Einstein eases into the synchronization process by selling his readers on the logic of the idea that he is free to do this w/o conflicting with existing physics - this is the only real new postulate of his 1905 paper, but it is buried in the synchronization method.

 

[pmb_phy]

Pete - this is an academic thing but I do not see how you arrive at your conclusion. The speed of all known waves depend upon the properties of the medium and not the velocity of the source; the measured speed of waves in all cases other than em depend upon the motion of the receiver relative to the medium

I think you took what I said in a vacuum, i.e. you didn't consider what else Einstein said in that second posulate. That's most likely my fault. Sorry.

In 1905 Einstein wrote in his famous SR paper On The Electrodynamics of Moving Bodies

...and also introduce another postulate, which only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independant of the velocity of the source.

I think he could have left that last part out since it is implied in the first part, i.e. in "light is always propagated in empty space with a definite velocity c"

That quite literally means that the speed of light is the same in all frames.

Pete

 

[yogi]

OK - I see what you are saying - apparently most folks see it that way also - I had always given a different interpretation to the words:

"the same laws of electrodynamics and optics will be valid for all frames
of reference for which the equations of mechanics hold good. 1) We will raise this conjecture (the purport of
which will hereafter be called the ``Principle of Relativity'') to the status of a postulate, and also introduce
another postulate, which is only apparently irreconcilable with the former, namely, that light is always
propagated in empty space with a definite velocity c which is independent of the state of motion of the
emitting body."

Specifically, the first postulate covers the situation involving both mechanical and optical equivalence for all frames of reference - and the second appears as Einstein says, to contradict the first - so I have always interpreted this
2nd to refer to the idea that c is a velocity determined by global attributes and as such it would "apparently" be inconsistent with constant c in relative moving local frames

Obviously my interpretation is not the majority view - thanks for the clarification

Yogi

 

[pmb_phy]

Obviously my interpretation is not the majority view - thanks for the clarification

Yogi

You're welcome Sir. Anytime.

Best regards

Pete