Re: SR fundamental contradiction


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

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'.
If you look at the text quoted above, you stated > in S', after
a time t, light has travelled a distance
(c-v)t.
Does that not say that x'=(c-v)t?

The answer is given in mine (and your) almost simultaneous post.

As far as I can see, you answered in the affirmative, that
x'=(c-v)t. From that and your postulated x'=(c-v)t', we derive
t'=t when x=ct.

Yes, x'=(c-v)t *according* to S, but *in S'* -as S' is moving at v
relative to S-, its time should be t'<>t, hence x'=(c-v)t'.
Notice that x' represents the difference between the endpoint of
the light signal and the origin of S', the same endpoint having
the coordinate x=ct in S.
At this point of my derivation, the link between t' and t
is not yet known.

You found yourself such relations in your demonstration
"If you prefer, we can do it the long way:
Setting t1'=t2', choosing t1=T, so that x1'=0, etc.
x2 = cT
x2'=(c-v)T/g",
where T/g represents T'.


Einstein got that equation from his light postulate. Because of
that postulate, a light signal travelling along the y' access
must have speed 'c'.

You reject that postulate, so you cannot use it here.
I don't reject the hypothesis that the speed of light is independent
of the motion of its source.

That part of the postulate was not used to derive y'=ct'. The
primary assertion of the postulate is that the speed of light is
a universal constant; it has the same value for every observer,
in every direction.

I agree that you accurately quoted the fanciful Einstein's postulate.
I disagree with your first sentence.

You have not explained how you derived y'=ct'.


y' = ct' is a direct consequence of the hypothesis that c is
independent
of the motion of S'.
Then why do you reject x'=ct'? If c is independent of the
motion of S', it follows as directly as y'=ct'.

If you disagree, please explain how y'=ct' is a direct
consequence, but x'=ct' is not.

As shown above, one has x'=(c-v)t', not x'=ct'.
The case of y' is wholly different, because the light signal
follows the y' axis, which is moving at v wrt the y axis.
Iow, the vector v is perpendicular to the vector c, not
parallel as in the case of x,x'.

You should closely follow the reasoning:

"Let us see how the length now measure in S, relative to which the
stick is moving with a velocity v.
It seems reasonable to define the length as the distance between
two points fixed in S, which are occupied by the ends of the stick
simultaneously, i.e., at the same time t.
If the coordinates of these points are x1 and x2, the length is
then L = x2 - x1."

We agreed to call the length of the stick at rest in S, Lo(S).
Now, it is called L. Iow, L = Lo(S).

Don't lose track of the fact that you are looking for the length
of the stick in motion in S. This is not Lo(S), according to
your definition.

You are right, it should be called Lo(S)'.


"Since the stick is at rest in S', its ends have fixed coordinates
x1', x2' such as Lo = x2' - x1'."

We also agreed to call Lo(S') the length of the stick at rest in S'.
Hence, Lo = x2' - x1' sould be written Lo(S') = x2' - x1'.

This is correct.


"If one substitutes in this last equation values of x2' and x1'
calculated from the LT x' = g(x - vt), one obtains, for a given
value of t,

x2' = g(x2 - vt)
x1' = g(x1 - vt)

Lo = g(x2 - x1) = gL, or L = Lo/g"

Logically, as Lo represents in fact Lo(S') and (x2-x1) represents
Lo(S),

No, according to your definition, Lo(S) is the length of the
stick, if it were at rest in S. You cannot assume that it is
the same as L, the length of the stick in motion.

So, we have Lo = Lo(S'), which is the length of the stick at rest in
S',
and L = Lo(S)', which is its length in S when S is moving wrt S'.
L = Lo/g could thus be written
Lo(S)' = Lo(S')/g.
As Lo(S) = Lo(S'), this relation means that the length of a moving
stick
is shortenend by 1/g relative to a stick at rest.


Lo = g(x2 - x1) = gL should be written Lo(S') = gLo(S), meaning, as I
said,
that the length of a moving stick is *dilated* relative to the length
of the
same stick at rest.
You cannot use that equation, because we did not agree that
L=Lo(S). In fact, you just demonstrated that it is not equal.


Yes.

Marcel Luttgens


Are you an Einstein's integrist? I hope not.

I am not familiar with that term.

.

Relevant Pages

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  • Re: SR fundamental contradiction
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  • Re: SR fundamental contradiction
    ... (Notice that Einstein postulated here that x' = ct') ... To express such distance in S', one has to use t', thus ... Einstein got that equation from his light postulate. ... Let the stick be set moving relative to S at such velocity that it is ...
    (sci.physics.relativity)