Suppose you have an observer looking at two moving masses, A and B. A
is seen to move vertically up (+y) with speed u and B to left (-x)
with speed v.

How does B see A moving? We apply SR velocity addition formulae to
get:
x velocity: +v, y velocity: u*sqrt(1-v^2/c^2)

A sees B moving:
x velocity: -v*srqt(1-u^2/c^2), y velocity: -u.

What is going on? Should they not see each other going opposite?
If it were 1-D velocity addition we would have them going opposite
when we applied SR.

Can we arrange another paradox out of this, Ha, Ha!

"John Tapper" skrev i melding om...
Suppose you have an observer looking at two moving masses, A and B. A
is seen to move vertically up (+y) with speed u and B to left (-x)
with speed v.

How does B see A moving? We apply SR velocity addition formulae to
get:
x velocity: +v, y velocity: u*sqrt(1-v^2/c^2)

A sees B moving:
x velocity: -v*srqt(1-u^2/c^2), y velocity: -u.

What is going on?

What's going on is that you are demonstrating that
you don't know how to transform velocities.

Paul

John Tapper wrote:
Suppose you have an observer looking at two moving masses, A and B. A
is seen to move vertically up (+y) with speed u and B to left (-x)
with speed v.

How does B see A moving? We apply SR velocity addition formulae to
get:
x velocity: +v, y velocity: u*sqrt(1-v^2/c^2)

A sees B moving:
x velocity: -v*srqt(1-u^2/c^2), y velocity: -u.

What is going on? Should they not see each other going opposite?
If it were 1-D velocity addition we would have them going opposite
when we applied SR.

Can we arrange another paradox out of this, Ha, Ha!

This paradox is already known as "The Paradox No Relativist Can Weasel
Out Of": news:XUJZATNT38251.8705787037@anonymous

Theo Wollenleben wrote:
John Tapper wrote:

Suppose you have an observer looking at two moving masses, A and B. A
is seen to move vertically up (+y) with speed u and B to left (-x)
with speed v.

How does B see A moving? We apply SR velocity addition formulae to
get:
x velocity: +v, y velocity: u*sqrt(1-v^2/c^2)

The formula you used is valid ONLY for collinear velocitites. For
non-collinear velocities the composition is much more complicated. It's
given in any intermediate or advanced textbookon relativity, but is
usually omitted from elementary textbooks.


This paradox is already known as "The Paradox No Relativist Can Weasel
Out Of"

That may be the Subject of the thread in this newsgroup, but its
sentiment is completely wrong -- it's merely your lack of understanding
of the Lorentz group that prompted you to initiate that thread. There's
no problem in SR, and no need to "weasel".


Tom Roberts

"Tom Roberts" wrote in message ...
Theo Wollenleben wrote:
John Tapper wrote:

Suppose you have an observer looking at two moving masses, A and B. A
is seen to move vertically up (+y) with speed u and B to left (-x)
with speed v.

How does B see A moving? We apply SR velocity addition formulae to
get:
x velocity: +v, y velocity: u*sqrt(1-v^2/c^2)

The formula you used is valid ONLY for collinear velocitites. For
non-collinear velocities the composition is much more complicated. It's
given in any intermediate or advanced textbookon relativity, but is
usually omitted from elementary textbooks.


This paradox is already known as "The Paradox No Relativist Can Weasel
Out Of"

That may be the Subject of the thread in this newsgroup, but its
sentiment is completely wrong -- it's merely your lack of understanding
of the Lorentz group that prompted you to initiate that thread. There's
no problem in SR, and no need to "weasel".

Just for the record, Theo was talking ironically ;-)

Dirk Vdm

Tom Roberts wrote in message ...
Theo Wollenleben wrote:
John Tapper wrote:

The formula you used is valid ONLY for collinear velocitites. For
non-collinear velocities the composition is much more complicated. It's
given in any intermediate or advanced textbookon relativity, but is
usually omitted from elementary textbooks.
...
Tom Roberts

You, of course, have no idea what you are talking about!

(BTW, who would admit to working for Lucent? :-) )

"Eli Botkin" wrote in message news:1096055108.c46DejH1WszbkV/i7QWXPA@teranews...
"John Tapper" wrote in message
om...
Suppose you have an observer looking at two moving masses, A and B. A
is seen to move vertically up (+y) with speed u and B to left (-x)
with speed v.
...
What is going on? Should they not see each other going opposite?

Can we arrange another paradox out of this, Ha, Ha!

Sorry John, can't arrange a paradox here since each sees the other moving at
the same speed, namely
sqrt(u^2+v^2-(uv/c)^2).

Eli

Eli, I explicitly stated that velocity direction and not magnitude was the issue!