Re: SR fundamental contradiction

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

I reject the POR.
On what basis? The principle of relativity has been a fundamental part of physics since at least the time of Newton. It is consistent with all observations.


Your equations can be used, but they single out one system as
preferred, and you lose the POR.

It is also a problem that your equations lead to the prediction
of *dilation* of moving objects.

Assume a stick of length L' at rest in S'. Let the left end be
at the S' origin. Then your equations give:
0=(x1-vt)/g
:: x1=vt
L'=(x2-vt)/g
:: x2=gL'+vt

Subtracting, we find the that length in S is L=gL'. The length
is expanded compared to its length at rest.


What my transformation predicts is that a moving stick is contracted
wrt a
stick at rest, i.e. L'=L/g.
Knowing the length L' of the moving stick, it is clear that the length
of the
stick at rest is L = gL', Iow, it is dilated in S.
Calling the moving stick a stick at rest, because it is at rest in the
moving frame S',
but forgetting that the rest frame remains S, is the type of logical
error systematically
made by SRists.
I am afraid you just lost a lot of ground. The rest length is the length measured from a reference frame moving with the stick (IOW, in which the stick is at rest).

But, let's do it your way. A stick of length L in S is moving with speed v to the right. The left end is x1=vt, and the right end is x2=L+vt
The length of the moving stick is x2-x1=L. There is no change in length for a moving stick.




That is because they are not. The LT are internally consistent.

Ha! Ha!
You have yet to demonstrate a single inconsistency.



Not until you explain how you calculated these numbers.

One has g=1/sqrt(1-v^2/c^2) and t1'=t1/g, thus g corresponds to t1/t1'.
Similarly, g(LT) corresponds to t2/t2', with t2'= T/g.
We can calculate g(LT) from t2 = T(1 + v/c - v^2/c^2)
g(LT) = t2/(T/g) = g(1 + v/c - v^2/c^2)
Now we can compare the ratio g(LT) for different values of v.
Your g(LT) cannot be compared to g, because it was computed from a different S time interval.

You computed g from the interval from 0 to T, but you computed g(LT) from the S interval from 0 to T(1+v/c-v^2/c^2), then divided it by T. Your numbers are meaningless.


As far as I can see, g depends only on the velocity, and is the
same at every point.

Both g and g(LT) depend only on velocity.
No, you demonstrated a difference due to position. Your error introduced a dependence on position.



To calculate the time dilation factor, you need to compare time
intervals between the systems.

Let us look at a stick of length L', at rest in S', and
calculate the S times when t' is 0 and T'.


You make again the same logical mistake, because S' remains the moving
frame.
Iow, the stick continue to move wrt the S-frame, even if one considers
it at rest
in the S'-frame.
I fully agree that a stick at rest in S' is moving in S. If I made a logical mistake, then we made it together.



No, you do not have an alternate theory. You have a set of
ad-hoc equations, and they predict length expansion for moving
objects.

They are not ad hoc and they predict time 'dilation' and length
contraction,
not length expansion.
When you tried to derive your equations, you had to put in the g factor by hand. You made an ad-hoc assumption about light speed along y', without physical justification.

You obtained a result that is inconsistent with the results we can obtain from considering the x direction alone (which requires that a=1).


Perhaps don't you realize that, when a moving clock shows a time
interval of
1 second when a clock at rest shows a time interval of 2 seconds, the
observer moving with the clock and reading 1 second will rightly claim
that
the observer at rest will read 2 seconds, even if the moving observer
considers himself at rest.

You must be careful about your use of 'when', because they may disagree about its meaning. I will make the disambiguating assumption that the clocks are adjacent at the moment designated by when for each of them.

Assuming the clocks are adjacent, they will agree about each other's readings, but that does not allow them to compare intervals. You must add to your example comparison of readings at another time, if you want to compare intervals.
.

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