Re: SR fundamental contradiction

mluttgens@xxxxxxxxxx wrote:
Brian Kennelly wrote:
mluttgens@xxxxxxxxxx wrote:
Brian Kennelly wrote:
Dirk Van de moortel wrote:
But t was fixed in the beginning of the thread:
| Consider the event E on the light signal with x = c t for some
| chosen value of t.
Remember, this is Marcel Luttgens you are dealing with.
I was attempting to demonstrate the source of the error by
taking his equations at face value. If we do so, the source of
the dilation is found in the variable length, not in the LT
equations. The endpoints in S', determined at the same time t',
are at two different S times, t1 and t2. By his definition of
the length, the stick is longer when S' measures it, because it
is longer when S measures it. [If t2>t1, then (c-v)t2 > (c-v(t1)].
The origin of the *dilation* lies in the LT x' = g(x-vt).
When, for instance, x = ct, x' = g(c-v)t.
For a given value of t, (c-v)t is of course the distance, as seen by S,
between
the point reached by a light signal and the origin of S'.

Of course the distance between any point and an out-going light
signal is increasing with time. That increase leads to the
dilation.

I was not referring to that obvious expansion, but to the fact that
the ratio between a distance measured in S' and the corresponding
distance measured in S is always g, according to the LT (see below).

In the S'-frame, such distance becomes g(c-v)t, meaning that it is
dilated.
If you wish to calculate the S' length of a stick at rest in S,
with endpoints at vT and cT [so that L=(c-v)T], we can use the
LT as follows:

vT=g(x1'+vt')
cT=g(x2'+vt')

Subtracting we get:
(c-v)T=g(x2'-x1')

The length is:
x2'-x1'=(c-v)T/g
= L/g
It is contracted.

Here is an exemple given by the tracking guru, which
indirectly proves the dilation:

"Now imagine a stick with this particular length
x' = g (c-v) t
at rest in the S' frame.
Note this ^^^^^^^^^^^^^^^^. You switched the rest 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."

So, when the stick is at rest in the S' frame, it is contracted in the S frame. When the stick is at rest in the S frame, it is contracted in the S' frame, as I showed above.



The length (c - v)t represents the distance in S between the
endpoints ct and vt (for a given value of t).

The particular length x' = g (c-v)t corresponds of course
to the dilated length obtained by applying the LT x' = g(x - vt)
to that case where x = ct in S.
The case <x=ct> is a light signal, and increases with time. If you do not want it expanding, choose a fixed time T, or simply call the length L.
.

Relevant Pages

  • Re: SR fundamental contradiction
    ... the dilation is found in the variable length, ... The endpoints in S', determined at the same time t', ... at rest in the S' frame. ... If you apply length contraction, ...
    (sci.physics.relativity)
  • Re: SR fundamental contradiction
    ... possible only if you know the endpoints of the stick in S': ... at rest in the S' frame. ... If you apply length contraction, ... Setting t1'=t2' in the LT equations above and subtracting we get ...
    (sci.physics.relativity)
  • Re: SR fundamental contradiction
    ... calculate the endpoints in S' from the fixed values in S, ... at rest in the S' frame. ... If you apply length contraction, ... Setting t1'=t2' in the LT equations above and subtracting we get ...
    (sci.physics.relativity)
  • Re: There is no physical length contraction
    ... points) are not simultaneous in the observers frame. ... accelerating rod as measured in the frame where the rod started out at ... that the contraction was an artifact of how we measure things. ...
    (sci.physics.relativity)
  • Re: Time dilation requires physical contraction
    ... If there is no physical contraction, ... will cover the full 100m length of the spaceship from emitter to ... accept time dilation. ... the frame of the spaceship, I agree but then neither does time ...
    (sci.physics.relativity)
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