Re: SR fundamental contradiction
- From: "Ajay Sharma" <ajay2244@xxxxxxxxxxx>
- Date: 27 Sep 2006 21:29:41 -0700
Tom Roberts wrote:
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
.
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