Re: A twin contraction paradox


"tomtom" <Carmam1534@xxxxxxx> wrote in message news:1168353438.959110.175460@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


Dirk Van de moortel wrote:

> Yet your first
> 2 calculations are calculating how far apart the scratch marks on B are
> as seen from A.

That is not what I calculated.
Dirk Vdm

Maybe it is not what you intended to calculate, but that is what you
did.

You can use the constant L and leave it at L for as long as you like.
What you must not do is to lose sight of what it represents, or the
fact that it cannot be changed. In this thought experiment it
represents 1, and is a fixed value. You still cannot see your error in
your calculation (1)
You wrote :-
Calculation of how far B's prongs are apart according to A
dx' = g ( dx - v dt )
giving
L = g ( dx - v 0)
Giving
dx(actually dx') = L / g

Constants :- dx = L = 1 : v = 0.5 : dt = 0 : gamma =
1.155

No, not dx = L.
see below.


Now put the values in
1. dx' = g ( dx - v dt ) = 1.155 * (1 - ( 0.5 * 0 )) = 1.155
giving
2. L = g ( dx - v 0) = 1.155 * (1 - 0.5 * 0)) = 1.155 Which
is 1 = 1.155 ??!!
giving (as dx' now has the value 1.155)
3. dx' = L / g = 1 / 1.155 = 0.866 Which is 1.155 = 0.866
??!!

The above three equations are clearly nonsense when put together.

Of course. You can't put them together. part of these equations
talk about two events on A's prongs and another part talks
about B's prongs. That is the heart of your confusion. We'll
pull them apart again.

I will repeat a part and add a new calculation at the end.
Try to follow carefully now. Read the text. It is much more important
than the equations.

A measures his own prongs to be a distance L apart.
B measures his own prongs to be a distance L apart.
A uses coordinates x and t to specify events.
B uses coordinates x' and t' to specify events.

(1) Physical statement: We calculate how far B's prongs are
apart according to A.
We translate this physical statement into coordinates language now:
If A wants to measure the distance dx between the prongs, he
must must measure the coordinates of the prongs simultaneously
(dt = 0), and we know the distance between the prongs
according to B, namely dx' = L.
So we use an equation that contains dx, dt and dx' and we don't
care about dt' because if B wants to measure the distance between
*his* prongs, he can measure the x'-coordinates at *any* time.
So we use
dx' = g ( dx - v dt )
giving
L = g ( dx - v 0 )
giving
dx = L/g (your 0.866m)
This was coordinate language.
Now we translate to physical language:
If B measures his own B-prongs to have distance L between them,
then A measures these B-prongs to have a distance L/g between
them.

Now, since you have seen a physical statement, you can FORGET
all the coordinate equations above and only remember the physical
statements.
Here comes a new calculation of something entirely different.
In (1) we talked about B's prongs. Now in (1') we are going to talk
about A's prongs.

(1') Physical statement: We calculate how far A's prongs are
apart according to B.
We translate this physical statement into coordinates language now:
If B wants to measure the distance dx between the prongs, he
must must measure the coordinates of the prongs simultaneously
(dt; = 0), and we know the distance between the prongs
according to A, namely dx = L.
So we use an equation that contains dx', dt' and dx and we don't
care about dt because if A wants to measure the distance between
*his* prongs, he can measure the x-coordinates at *any* time.
So we use
dx = g ( dx' + v dt' )
giving
L = g ( dx' + v 0 )
giving
dx' = L/g (your 0.866m)
This was coordinate language.
Now we translate to physical language:
If A measures his own A-prongs to have distance L between them,
then B measures these A-prongs to have a distance L/g between
them.

So we conclude:
If A measures his own A-prongs to have distance L between them,
then B measures these A-prongs to have a distance L/g between
them.
If B measures his own B-prongs to have distance L between them,
then A measures these B-prongs to have a distance L/g between
them.

*This* is how special relativity works. It is how length contractions
are rigorously calculated.
Are you with me on this for a 100%?

If yes, maybe I will continue with yet another calculation.
If no, just quote following the standards quoting system, and
interrupt where you don't follow me or where you don't undertand.
Explain what you mean or what you think I should have written
in stead of what I have written. And stop there. We take one
step at a time.

Dirk Vdm
.

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