Bob Sciamanda
Physics, Edinboro Univ of PA (Em) http://www.winbeam.com/~trebor/
trebor@winbeam.com
----- Original Message -----
From: "Bob Sciamanda" <trebor@winbeam.com>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Wednesday, February 22, 2006 1:42 PM
Subject: Re: [Phys-l] geometry of spacetime (was: relativisitic mass ...)
|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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|
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