Re: SR fundamental contradiction

mluttgens@xxxxxxxxxx wrote:
Let x = ct.
Then x' = g(x - vt), where gamma = 1/sqrt(1-v^2/c^2), becomes
x' = g(c-v)t
What represents the length (c-v)t?

It is merely a mathematical artifact, and is not really the "length" of anything. <shrug>

You are manipulating symbols without understanding what they represent or mean. And you obtain nonsense. <shrug>

If you write down what you are trying to do more precisely, defining each and every one of your symbols, you will see that the above is nonsense because it intermixes symbols of different types.

For instance, when you said "Let x = ct", I imagine that you might have meant:
Let us construct inertial coordinates {x,y,z,t} and ignore y and z.
In those coordinates let us consider a light pulse emitted from
the point (x=0,t=0) moving in the +x direction, so with x=f(t)
being the trajectory of this pulse parameterized by the time
coordinate t of this frame, the pulse has position x=f(t) = ct
for t>=0.

So your x refers to a specific light pulse and your t refers to a path parameter of its trajectory.

On the other hand, when you wrote "x' = g(x - vt)" you really meant a COORDINATE TRANSFORM between two inertial frames. That is, those symbols DO NOT REFER TO THE LIGHT PULSE ABOVE, and t is NOT a path parameter, it is a coordinate of an arbitrary point in the manifold.

If you spend the effort to fix up your overly loose terminology and symbols, you will be able to answer your own question, and you will find there is no "contradiction". If you don't bother to do that, you will remain mystified. <shrug>

Yes, physicists are notoriously loose; but if you claim
to display a "contradiction", _YOU_ must be precise.


Tom Roberts
.

Relevant Pages

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  • Re: SR fundamental contradiction
    ... at rest in the S' frame. ... So your x refers to a specific light pulse and your t refers to a path ...
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  • Re: SR fundamental contradiction
    ... at rest in the S' frame. ... So your x refers to a specific light pulse and your t refers to a path ...
    (sci.physics.relativity)
  • Re: SR fundamental contradiction
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    (sci.physics.relativity)
  • Re: SR fundamental contradiction
    ... at rest in the S' frame. ... Notice that Vdm implicitely recognized that the length t ... So your x refers to a specific light pulse and your t refers to a path ...
    (sci.physics.relativity)