Natural Science Forum / Physics / Relativity / February 2005

I posted this message last night at about 11:30 PM local.  Now at 9:04 AM
the next day it is not visible to be so I am re-posting.  If this is a
double post I appologize and ask that someone please let me know.
Thanks, BK

To All,
About a week or so ago I posted a question about Double Observation and
asked for an equation about how clocks will run slower as they move faster.
I have thought about that and extended my observation scenario.  My
conclusion appears to contradict  the concept that one cannot determine
their speed in an absolute sense, only in a relative sense.

I ask that someone tell me my error.  Please note that I claim to be an
intelligent person, but clearly not knowledgable in the concepts of
relativity.  I have tried to read some books on the general relativity and
come up with questions that I cannot answer on my own.  Now with a bit more
information I can ask a question and provide some numbers (theoretical
measurements if you will) to demonstrate my thoughts.  Can someone give me a
response in layman's terms?

Thank you,
Bryan

********************************

Double Observation

Sally put Tom on a very long flat car (similar to a rail road flat car) so
that she could watch him and everything that happened on the flat car. She
positioned Tom on the flat car so that he was facing away from her. When Tom
observed something moving to his left, Sally saw it moving to her left.

Sally placed a clock in front of Tom that moved with Tom at all times. For
clarity, this clock was painted red. To the far side of Tom's flat car Sally
placed a long fence. The fence was stationary with respect to Sally. When
Tom and his flat car passed in front of Sally, a pair of paint spray cans
discharged a very short burst of red paint onto the fence such that, if Tom
had been stationary with respect to Sally, the distance between the inner
edges of the marks would be exactly on meter apart.

Tom had a second clock in front of him, painted blue, that he could move
left and
right at high speeds. This clock also had a pair of paint cans that when
stationary in front of Sally, would make two marks on the fence, exactly one
meter apart, but with blue paint.

Sally started the experiment by having Tom move from her right to her left
at 50% the speed of light. While Sally was watching Tom's every move, Tom
had no awareness of Sally, nor of his velocity with respect to her.

While he was moving Tom conducted an experiment. Tom started his blue clock
moving
from his left to right at what he perceived was 50% of the speed of light.
The timing was such that just as Tom passed right in front of Sally, Tom's
blue clock pass right in front of Tom, and of course, Sally. The paint cans
on
Tom's car and on Tom's moving clock put their marks on the fence just as
each pass right in front of Sally.

An equation I was given to calculate how fast Toms clock would be running
was

gamma = 1/sqrt(1-X^2/100^2)

Y = 100 / gamma "percent slower than my clock"

I decided to use gamma to determine the width between the paint marks. Since
Tom was moving at 50% the speed of light, I calculated gamma to be 1.155.
Dividing this into the 1 meter between the stationary paint marks I conclude
that Tom's marks on the fence would be 1 / 1.155 or 0.866 meters apart.
Sally saw that the red paint marks were 0.866 meters apart. Tom saw them to
be 1 meter apart, while he was moving that is.

Tom's blue clock was moving at 50 % the speed of light from Tom's
perspective. So as Tom watched his moving clock go by, he saw that blue
paint marks it left behind were 0.866 meters apart.

Now I attempt to determine what Sally found when she measured the blue paint
marks. To do this I make reference to

URL:http://hermes.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/velocity.html

w = ( u + v ) / ( 1 + uv / c^2 )

As u and v are both 50% c or 150,000,000 meters per second I get w =
240,000,000 or 80% the speed of light. Plugging this back into my equation
for gamma I get 1.7. From this I calculate that the blue paint marks are 0.6
meters apart.

Sally brings Tom back to rest in front of her and they both look at the
paint marks. Not they both agree that the red marks are .866 meters apart
and the blue marks are 0.6 meters apart.

Sally changes the paint cans substituting Tom's red paint with green and
changes the paint on his clock from blue to black. She them puts Tom and his
two clocks back on the flat car and starts another test.

Sally starts Tom moving from her left to her right at 50% the speed of
light. Tom repeats his test without change, and his clock moves from his
right to his left at 50% the speed of light, from Tom's perspective that is.
Everything else is the same and at Toms red clock (she did not repaint his
clock and the red clock is stationary with respect to Tom) puts its two
green marks on the fence at the same time Toms blue clock puts its black
marks on the fence. Now I calculate the distances.

Tom's clock was moving at 50% the speed of light with respect to Sally in
both experiments. The green paint marks are the same distance apart as the
blue paint marks, 0.866 meters apart.

Now I calculate the black marks. From Tom's perspective, while moving, the
black marks should be the same as before, 0.866 meters apart. Let calculate
from Sally's perspective. Using the same equation for w as above, I now have
u = 150,000,000 but v is now negative 150,000,000. Running this through the
equation I now get the velocity of Toms blue clock to be 0. From Sally's
perspective, the paint marks should be 1 meter apart.

Now Sally brings Tom back to rest in front of her and they evaluate the
paint marks. The now examine all the marks. Tom looks at the red and blue
marks and the distance between them. The red marks are 0.866 meters apart
and the blue ones are 0.6 meters apart. With no help from Sally, he can
determine that he had been moving at 50% the speed of light with respect to
Sally.

Now they look at the green and black marks. The green marks are 0.866 meters
apart and Tom determines that he had been moving at 50% the speed of light
with respect to Sally. When they look at the black marks, they both see that
the marks are 1.0 meters apart.

Now Tom determines that his blue clock that he had observed as moving at 50%
the speed of light had been really stationary with respect to Sally. Since
Tom moved his clock in the same direction from his perspective in both
experiments, and he now sees that the black marks are not the same distance
apart in the two experiments, Tom can now deduct that in the first
experiment he was moving from Sally's right to her left, and in the second
experiment he was moving from her left to her right. He does this with no
assistance from Sally. This tells Tom that he was moving past Sally and that
Sally was not moving.

Now if Sally had been moving with respect to Richard (who was watching both
Sally and Tome), then Tom's green and
black marks would be different distances apart with respect to the blue and
red marks.

If I understand this correctly, Tom and Sally are now able to determine
their absolute speed within existence.

I will attempt to summarize this as I understand it. If Tom accelerates to
his left and runs his experiment, the red and blue marks will be some pair
of distances apart. If he them accelerates to this right and does the same
test, the marks green and black marks should be the same distance apart. If
not, he was moving with respect to Sally, or absolute space, and now Tom can
determine in which direction he was moving and how fast.

Now I relate this to "The Elegant Universe" by Brian Greene, chapter 2,
"Space, Time, and the Eye of the Beholder", section "The Principle of
Relativity." In this section Brian used George and Gracie and says that they
cannot determine if one or both is moving. In the above scenario, it seems
that Tom can verify that he was moving and Sally was not. This seems to
contradict the theory.

So what are your thoughts