Re: Time Dilation achieves isotropic Speed

On Feb 2, 1:49 pm, "Jeckyl" <no...@xxxxxxxxxxx> wrote:
"Peri of Pera" <rie...@xxxxxxxxxxx> wrote in messagenews:bb01e949-a208-4aa8-a317-e490b88dffd3@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Time Dilation achieves isotropic Speed

When Lorentz invented time dilation as part of his contraction
hypothesis he did so to allow the speed of light to remain constant.
He thought that if  the length  of a moving object contracted, its
time  had to slow down or the speed of light would not be constant.

And there also has to be a change in simultaneity as well

However, Lorentz achieved the opposite effect with his thought
process.

This should be good for a laugh again...

Example:
An object of 100m length traveling with a speed of 200000km/sec  would
according to the Lorentz transformation

gamma = 1/sqrt(1-200000km/sec^2/300000km/sec^2)  = 1.3416408

shrink to 74.535599m (100/gamma).

If you mean that a stationary obserer would measure as the distance between
the endpoint of the moving rod at a given instance of time in the stationary
system .. then yes

At rest, light will cover 100m in
100m/300000000m/sec = 0.000000333333sec.

OK

Time dilation will expand
this fraction of  time to 0.00000044721360 seconds
(0.000000333333secs*1.3416408) for an object with the speed of
200000km/sec.

If you mean that at the location of the stationary observer, an interval
that is 0.000000333333 on the moving clock will take 0.00000044721360 on the
observers clock .. then yes.

In the dilated time of 0.00000044721360 seconds, light at 300000000m/
sec will transit a distance of 134.16408m (300000000m/
sec*0.000000044721360sec) but if light had slowed down to 223607021m/
sec, light would exactly cover the original 100m in the dilated time
of  0.000000044721360sec (223607021m/sec*0.00000044721360sec=100m).
Clearly, if the speed of light had not been reduced, the law of
physics d=v*t would have been violated.

You are clearly confused about relativity.

Let's look at this more clearly...

Let us assume our coordinates are such that at x=0,t=0 we also have x'=0,
t'=0
Let us assume that we have a moving rod of length L travelling at speed v
Let us assume the light is shining along the rod in the direction of travel
Let us assume the light is emitted at t=t'=0, when the rear end of the rod
is at x=x'=0

In the stationary frame of reference, the rod is moving while the light is
travelling at c
So the light gets to the other end of the rod, as seen by the stationary
observer, at x, t where
t = L / (c - v)
x = c . t ... because x / t = c

That corresponds in the rods frame of reference to a point (x',t')

x' = gamma . ( x - v.t ) ... Lorentz
x' = gamma . ( c.t - v.t ) ... subs for x
x' = gamma . ( c - v ) . t ... factorise
x' = gamma . ( c - v ) . L / (c - v) ... subs for t
x' = gamma . L ... cancel

t' = gamma . ( t - v.x / c^2 ) ... Lorentz
t' = gamma . ( t - v.t / c ) ... subs for x
t' = gamma . (1 - v/c ) . t ... factorise
t' = gamma . (c - v) / c . L / (c - v) ... subs for t
t' = gamma . L / c ... cancel

so the speed of light as seen in the moving rods frame is

c' = x' / t'
c' = gamma . L / ( gamma . L / c )
c' = c

So you can see that the speed of light as measuring in the frame of the
moving frame is c as well


Jecko,
The questions are: If time slows down and there is more time to do
things will light go a longer distance or is the speed of light
reduced? Either must occur to preserve the law of physics d=v/t.
Peter Riedt






.

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