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[Phys-L] Re: [BULK] frame independence



I think Joel is correct saying that V dot Xhat as defined by John,
is a frame-dependent quantity. It becomes obvious in the Alice's frame,
where V dot Xhat = 0 simply because V = 0 in this frame, whereas
V dot Xhat may be non-zero in other frames.
In the end of his definition of the quantity V dot Hhat, John wrote:
"Everything above applies equally well to Galilean relativity and to
Einsteinian relativity."
If V is regular 3-velocity, than V dot Xhat would be invariant only
under 3-rotations of a reference frame. It is not invariant under either
Galilean or Lorentz transformations.
The only condition when V dot Xhat would be Lorentz-invariant, is if
V were meant to be 4-velocity, and x - a unit vector in spacetime, and
this should have been explicitly stated.

Moses Fayngold,
NJIT


-----Original Message-----
From: Forum for Physics Educators [mailto:PHYS-L@list1.ucc.nau.edu]On
Behalf Of Rauber, Joel
Sent: Thursday, November 17, 2005 11:39 AM
To: PHYS-L@LISTS.NAU.EDU
Subject: Re: [BULK] frame independence


Warning: mostly semantics & perhaps a bit of metaphysics

John D. clarified in part with:

| Rather than asking
| -- What is the X-component of Alice's velocity in Bob's frame?
| it would be conceptually preferable to ask
| -- What is V dot Xhat?
| where V is Alice's velocity and Xhat is a unit vector aligned
| with Bob's X-axis.
|
| The point is that V dot Xhat is manifestly invariant.

No argument that V dot Xhat is the invariant way to express the quantity
so that a person can calculate that quantity using any inertial frame to
perform the calculation; but I wonder if the quantity itself isn't a
frame-dependent quantity? Afterall, if I ask what is Alice's
x-component of velocity in Moe's frame I may get a different answer.
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