"Edwards" <edwards@nouce.trurl.bsd.uchicago.edu> wrote in message
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On 2006-03-30, Spaceman <Realspace@comcast.not> wrote:

"PD" <TheDraperFamily@gmail.com> wrote in message
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Spaceman wrote:

"PD" <TheDraperFamily@gmail.com> wrote in message
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Spaceman wrote:

"PD" <TheDraperFamily@gmail.com> wrote in message
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Spaceman wrote:

Lets add another observer to different conditions now.
Three cars are on the highway.
2 cars are heading north, 1 car is heading south
Car (u) is moving at 100 mph northbound.
Car (w) is moving at 50 mph northbound.
Car (y) is moving at 100 mph southbound

Can you show the paradox?

What paradox?

The different answers for different observers.
2 observers will not agree on the third observers
relative velocity if you are using a transform.

I'm sorry, you'll have to be more concrete. Which two observers will
not agree on what?

Any 2 observers will not figure the same relative velocity wrt
the other of the third observer if you use a transform.

Car (u) will measure car (w) to have a relative velocity of 50 mph,
according to you.
Car (y) will measure car (w) to have a relative velocity of 150 mph,
according to you.
Is that what you meant?

Why don't you use a transform for each case and see where
the actual paradox exists.

I'm sorry, I still don't understand. The two observers already don't
agree, using your methods. What paradox?

Using basic math.
Observer w agrees that observer v will measure the same relative
velocity of y (to v) that observer y would measure of v (to y).
Using a transform, w will not do such.

Depends on the transform, maybe, but for the SR velocity "transform",
w will indeed "do such".

Can you show that he would by using a transform for all of them?

Okay, your setup was:

Car (u) is moving at 100 mph northbound
Car (w) is moving at 50 mph northbound
Car (y) is moving at 100 mph southbound

in what I'll call the "road frame". The frame with "Car (u)" at rest
will be called the "u frame", and similarly for frames w and y.

Velocity of u in the w frame (in the north-south direction, with north
being +), c is in units of mph:

u_w = ( 100 - 50) / (1 - 5000/c^2)

y_w = (-100 - 50) / (1 + 5000/c^2)

w (i.e. an observer at rest in frame w) can immediately determine that
the "relative velocity" (ie. closing velocity) between u and y is u_w
- y_w (or y_w - u_w, depeding on which orientation you want). Of
course, w is also aware that even under Galilean relativity, this
"relative velocity" (or closing velocity or whatever you want to call
it) has no particular physical significance.

Now w calculates the velocity of (car) y from the point of view of an
observer at rest in u:

y_{u_w} = (y_w - u_w) / [1 - (y_w * u_w) / c^2]

And similarly, the velocity of u from the point of view of y is
calculated to be:

u_{y_w} = (u_w - y_w) / [1 - (u_w * y_w) / c^2]

= -y_{u_w}

Tada, they are indeed equal in magnitude. Of course, they are not
_exactly_ equal to what w calls the closing velocity, but since
closing velocity has no particular physical significance, nobody
(including w) cares. (Of course, since they differ in this case from
closing velocity by less than 2 x 10^(-7), nobody _really_ cares.

Science would care flies completley above your head huh?
The use of the transform conflicts with itself mathematically.
sheesh!
The paradox remains or like real life, the transform is *****.

"Edwards" <edwards@nouce.trurl.bsd.uchicago.edu> wrote in message
news:slrne2p0ni.tps.edwards@trurl.bsd.uchicago.edu...

Tada, they are indeed equal in magnitude.

Of course, they are not _exactly_ equal to what w calls the closing
velocity, but since closing velocity has no particular physical
significance, nobody (including w) cares. (Of course, since they
differ in this case from closing velocity by less than 2 x 10^(-7),
nobody _really_ cares.

How can you measure the speed of a car going about 100mph to within
about 6 microns per second?)

Science would care flies completley above your head huh?

The use of the transform conflicts with itself mathematically.
sheesh!
The paradox remains or like real life, the transform is *****.