I guess what I strongly object to is the abuse of language, eg:
JD wrote:
| THEREFORE, perhaps it would be better to say something like:
| The fact that that object's 3-velocity *appears* to another observer
| to asymptotically approach the speed of light is not a property of
| the object, and it's not a property of the observer, either. It is
| a property of the projective geometry of spacetime ... and of the
| definition of 3-velocity.
Yes, the behavior of quantities depends on our definitions! By our
definition of 3 velocity, the above 3 velocity doesn't "APPEAR to another
observer to asymptotically approach the speed of light" it is measured to
do so, and DOES so. du/dt is a useful and easily measured quantity. Of
what more use is du/dtau of Betelgeuse? What would improve if we ceased
calling du/dt "velocity" and reserved that name for du/dtau?
It is not unusual to find a certain set of concepts to be more useful for
"philosophical appreciations" and a different, operational set for
calculational and practical use . We need both (and more!).
Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "John Denker" <jsd@av8n.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Wednesday, February 22, 2006 11:54 AM
Subject: Re: [Phys-l] geometry of spacetime (was: relativisitic mass ...)
| John M wrote:
| > | The fact that that object *appears* to another observer to
| > | asymptotically approach the speed of light is the *observer's*
| > | problem!
|
| Bob Sciamanda wrote:
|
| > Whatever this means, is it not in the same way the "object's" problem
that
| > the left behind observer "appears" to asymptotically approach the speed
of
| > light?
| >
| > We understand that speed is a relative quantity and that the idea of an
| > "intrinsic" speed is without meaning or use. So what's the point?
|
|
| 1) I understood what John M. meant, and I agree with it in spirit.
|
| 2) However Bob raises a valid objection; the original statement is
| perhaps a bit glib and/or open to misinterpretation.
|
| First of all, let's get some facts on the table. I hope we all agree
that:
|
| A) As JM said, a particle can undergo uniform acceleration forever
| (uniform in the particle's own frame). WLoG let this be an
acceleration
| in the X direction.
|
| B) The X-component (in the lab frame) of the particle's 4-momentum (p)
| increases uniformly, and increases without bound.
|
| C) The X-component (in the lab frame) of the particle's 4-velocity (u)
| increases uniformly, and increases without bound.
|
| D) In all generality, frame-independently, we can say p = m u.
|
| E) The 3-velocity is !!not!! the spatial part of the 4-velocity:
| 4-velocity is d(position)/d(tau), whereas 3-velocity is
d(position)/d(t).
| They differ by a factor of gamma.
|
| THEREFORE, perhaps it would be better to say something like:
| The fact that that object's 3-velocity *appears* to another observer
| to asymptotically approach the speed of light is not a property of
| the object, and it's not a property of the observer, either. It is
| a property of the projective geometry of spacetime ... and of the
| definition of 3-velocity.
|
| To repeat, it's not a problem with the object, it's not a problem
| at all, and it's not even a _property_ of the object or observer.
| It's just geometry.
|
| The geometrical situation is discussed on page 10 of the odometer
paper:
| http://www.av8n.com/draft/odometer.pdf
|
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