Re: SR fundamental contradiction

mluttgens@xxxxxxxxxx wrote:
mluttgens@xxxxxxxxxx wrote:
Brian Kennelly wrote:
mluttgens@xxxxxxxxxx wrote:

Derivation of the correct transformation:
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Let's consider two frames of reference, S and S', each in uniform
translatory motion relative to the other, the velocity of S' relative
to S being v.

Basis relations:

x' = ax + bt
t' = ex + kt

At the origin of S', x' = 0 and x = vt.
Hence, 0 = (av+b)t, whence b = -av

The basis relations are now

(1) x' = a(x - vt)
(2) t' = ex + kt

Now, let's suppose that a light signal, starting from the coincident

origins of frames S and S' at t = t' = 0, travels toward positive x.
After a time t, it will be at
x = ct, and also at
x' = (c-v)t'
(Notice that Einstein postulated here that x' = ct')
It appears that, again, you are assuming a vector sum for the
velocity vector.
Not at all, the factor (c-v) doesn't mean that light speed
is not c anymore. According to S, light is at ct and S' at vt,
hence in S', after a time t, light has travelled a distance
(c-v)t. To express such distance in S', one has to use t', thus
x' = (c-v)t'.
I don't follow.
You state that:
x'=(c-v)t
and
x'=(c-v)t'

From these two equations, we find that t'=t.

I thought that my sentence was clear enough: According to S, etc...
Thus, I stated that x = (c-v)t and x' = (c-v)t'.

I would like to make clearer why, after a time t, the light signal will
be at
x' = (c-v)t' in S'.
Indeed, according to S, the distance between the endpoint of the signal
and the origin of S' is ct - vt after a time t. In S', the
corresponding distance
is (c-v)t',
I don't follow this step. The distance between the light signal and the origin of S' is (c-v)t in S. How do you get from there to the distance in S' having a distance (c-v)t'.

Are you assuming, a priori, that the relative velocity is invariant?


hence the S'-coordinate of the endpoint is x' = (c-v)t'.
In S, the endpoint is of course at x = ct.
But I am convinced that you already grasped what I meant.
Yes, but I did not follow the leap to x'=(c-v)t'.
.

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