Re: SR fundamental contradiction


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>

Vdm wrote:

"Now imagine a stick with this particular length
x' = g (c-v) t
at rest in the S' frame.
What is the length of such a stick in the S-frame?
If you apply length contraction, you find that this length
would be
x' / g = (c - v) t
in the S frame."

Notice that Vdm implicitely recognized that the length (c-v)t
is *dilated* in the S'-frame, according to the LT x' = g(c-v)t.
Such length *dilation* is of course false, a *contraction* being
expected.

I used exactly the same scenario:

Imagine a stick with the particular length
x = (c-v) t
at rest in the S frame.
What is the length of such a stick in the S'-frame?
If you apply length contraction, you find that this length
would be
x' = (c - v) t / g
in the S frame.

Such length corresponds to the solution given by the correct
transform x' = (c-v)t / g.

The rest of your post is mere quibbling.

Marcel Luttgens


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

  • 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)
  • Re: SR fundamental contradiction
    ... at rest in the S' frame. ... If you apply length contraction, ... So your x refers to a specific light pulse and your t refers to a path ...
    (sci.physics.relativity)
  • Re: SR fundamental contradiction
    ... 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. ... So your x refers to a specific light pulse and your t refers to a path parameter of its trajectory. ...
    (sci.physics.relativity)
  • Re: SR fundamental contradiction
    ... So your x refers to a specific light pulse and your t refers to a path ... If you spend the effort to fix up your overly loose terminology and ...
    (sci.physics.relativity)
  • 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)