Subject: Re: Special Relativity Paradox
From: Cees Roos
Date: Fri, 06 Dec 1996 08:15:36 +0000 (GMT)
In article <57qnfk$b0e@sjx-ixn6.ix.netcom.com>, Allen Meisner
wrote:
>
> I have a thought experiment for special relativity that leads to a
> paradox. Could anyone solve it for me? A person is traveling in a
> spaceship at .5c. The spaceship crosses directly in front of a
> stationary observer. The observer in the spaceship has a laser, located
> at the midpoint of the ship. As the spaceship crosses in front of the
> stationary observer, the observer in the spaceship shines the laser in
> the direction of the ship's motion. The stationary observer sees the
> light travel a longer distance than the observer in the spaceship, so
> for him time dilates and for the observer in the spaceship the time
> slows. Now the same process is repeated, except
> this time the laser is
> rotated 180 degrees and points toward the back of the plane, opposite
> the direction of motion. The spaceship crosses in front of the
> stationary observer, in exactly the same way as previously and the
> observer inside the ship shines the laser toward the back of the ship.
> This time the stationary observer sees the light travel a shorter
> distance, so for him times slows and for the observer inside the
> spaceship time dilates. How can time both slow down and speed up at the
> same time for both observers?
>
>
> Edward Meisner
Time dilation relates to the flow of time in a frame which is moving
relative to the frame of the observer. An observer will never observe
a time dilation in his own frame.
You assume two inertial frames, i.e.:
The 'stationary' frame of the observer, let's call this frame A, and
the observer obsA.
The 'moving' frame, let's call this one B, and the observer obsB.
Let's assume the spaceship moves in the +x direction, relative to A.
The first event is when the two frames synchronize, i.e. when they
both start their clocks at zero, and the spaceship launches two light
pulses, one ahead, and one backwards. (I have combined both passes to
one).
After that, there are two events of interest, i.e one where the
light pulse which was launched ahead is a certain distance from the
spaceship, and one where the lightpulse which was launched backwards
is a fixed distance from the spaceship. Let's fix these distances at
1 lightsecond.
First, lets study the case of the lightpulse which was launched ahead.
What obsA sees is a pulse of light, outspeeding the spaceship with
0.5 c. So, after 2 seconds, obsA sees a spaceship, preceded by a
lightpulse at one lightsecond distance.
At that moment, the clock of obsB, shows, according to the Lorentz
transformation:
1/SQRT(1-0.5^2)*(2-0.5*2)seconds,
and the distance of the lightpulse, as measured in frame B, is
1/SQRT(1-0.5^2)*(2-0.5*2) lightseconds.
So, if we devide the distance by te time, we get 1 lightsecond per
second, which is called c.
Analoguously, we can write out the transformations for the backwards
lightpulse:
What obsA sees is a pulse of light, heading backwards, relative to the
spaceship, with 1.5 c. So, after 0.6667 seconds, obsA sees a spaceship, speeding away from a lightpulse at minus one lightsecond distance.
Again we do the Lorentz transformations:
t' = 1/SQRT(1-0.5^2)*(0.6667+0.5*0.6667)seconds,
x' = 1/SQRT(1-0.5^2)*(-0.6667-0.5*0.6667)lightseconds.
Again, division yields -1 light second per second, again c (in the
negative x direction).
So, no paradox at any moment.
--
Regards, Cees Roos.
I think it's much more interesting to live not knowing than
to have answers which might be wrong. Richard Feynman 1981
Subject: Re: Energy, a spacial dimension?
From: Hernan Altman
Date: Fri, 6 Dec 1996 15:13:08 GMT
On Wed, 4 Dec 1996, Jeffrey O'Callaghan wrote:
> Is it possible that energy could be a separate dimension on it's own.
> It would seem logical to assume this because the dimensions of length,
> width, and height give the position of something in our three
> dimensional coordinate plain. However each position in three
> dimensional space is associated with a unique relative energy value
> for that position. This would indicate that to define a position of a
> object in space and time that you should also included a reference to
> it's relative energy position. This energydepth would to be
> parallel and co-terminal to all three of the dimensions of spacial
> dimensions of length width and height.
>
> In other words is it possible that our universe consists of four
> spacial dimensions plus time. These four spacial dimensions would be
> length, width, height and theenergydepth.
>
> Your coments would be appreciated.
>
> Jeff
>
> IMAGINATION ILLUMINATES REALITY Links to the Future
> http://www2.pcix.com/~jeffocal/shadlink.htm
> The Virtual Reader for the vision impaired
> http://shell.idt.net/~jeffocal/frank.htm
>
>
>
Well, I think energy isn't another dimension. In the same way momentum
is complementary to space dimensions, energy is complementary to time (the
fourth dimension according to relativity).
Bye,
Hernan.
