Re: SR's velocity addition -- ANY Experimental Evidence?
From: Timo Nieminen (timo_at_physics.uq.edu.au)
Date: 07/15/04
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Date: Thu, 15 Jul 2004 16:43:52 +1000
On Thu, 14 Jul 2004, Jim Greenfield wrote:
> Timo Nieminen <timo@physics.uq.edu.au> wrote:
> > On Wed, 14 Jul 2004, Androcles wrote:
> >
> > > "Timo Nieminen" <timo@physics.uq.edu.au> wrote:
> > > | On Tue, 13 Jul 2004, Sam Wormley wrote:
> > > |
> > > | > Jim Greenfield wrote:
> > > | > >
> > > | > > Like the man said: 1c+1c=2c if this formula doesn't hold in
> > > | > > standard math (classical mechanics), then please put me right. :-)
> > > | >
> > > | > [Physics FAQ]
> > > | > How Do You Add Velocities in Special Relativity?
> > > | >
> > > http://hermes.physics.adelaide.edu.au/~dkoks/Faq/Relativity/SR/velocity.html
> > >
> > > yeah, it says:
> > > Suppose an object A is moving with a velocity v relative to an object B and
> > > B is moving with a velocity u (in the same direction) relative to an object
> > > C. What is the velocity of A relative to C?
>
> In case T N (deliberately) missed it:
> see here that A, B & C are all in the same frame?
In case J G (deliberately) missed it:
See here that A is measured to have velocity v in a coordinate system in
which B is at rest, and B is measured to have velocity u in a coordinate
system in which C is at rest.
Whatever do you mean by "A, B & C are all in the same frame"? A, B, and C
are physical objects, and exist independently of any coordinate system.
> > > w = (u + v)/(1 + uv/c2)
> > >
> > > Let object A be the "tip of the ray" moving relative to B, the initial point
> > > of k.
> > > Let object B be moving relative to C, the "stationary" frame. What is the
> > > velocity of A relative to C?
> > > Einstein can do it, he says c = (c+v)/(1+v/c), right?
> > >
> > > Quote:
> > > "It follows, further, that the velocity of light c cannot be altered by
> > > composition with a velocity less than that of light. For this case we obtain
> > > V = (c+w)/(1+w/c) = c."
> >
> > Straightforward use of Lorentz transformations to determine what the
> > measured value of the velocity would be in a second coordinate system,
> > given the measured value in the first coordinate system.
>
> .......and now they are not! How is that, for sleight of hand? (and
> brain)
??? Translation, please!
> > > So how in the blue blazes does he come up with
> > > "But the ray [call it A] moves relatively to the initial point of k [call it
> > > B], when measured in the stationary system [call it C], with the velocity
> > > c-v ..."
> > > Reference :
> > > http://www.fourmilab.ch/etexts/einstein/specrel/www/
> > >
> > > Seems to me that someone can't think straight, and it sure ain't me.
> >
> > This actually well illustrates the difference between (1) the addition of
> > velocities, and (2) the transformation of velocities when changing
> > coordinate systems.
> >
> > In coordinate system C, the ray of light moves at a velocity c, the
> > original moving point from which the ray of light was emitted is moving at
> > v in the same direction. So, as measured by coordinate system C, the
> > velocity of light relative to the moving point is c - v. What's so
> > mysterious about that? It's simple Galilean physics. Lorentz
> > transformations only required when changing coordinate systems.
>
> (from faq "adding velocities in Relativity")
> ***Notice that the only case with velocities less than or equal to c
> which is singular is w = u = c which gives the indeterminate zero
> divided by zero. In other words it is meaningless to ask the relative
> velocity of two photons going in the same direction.
A simple consequence of there being no inertial coordinate system in which
either of the two photons is at rest.
The FAQ is using "relative velocity" restricted to the special case of
"relative velocity of A relative to B as measured in an inertial
coordinate system where B is at rest." Without this restriction, it is no
longer meaningless to ask the relative velocity of two photons going in
the same direction (and the relative velocity is zero).
> No worries! I just happen to have here a mirror which lets one photon
> through, and reverses the other. Now what is the problem?
There still isn't any inertial coordinate system where either photon is at
rest. So, with the restricted defintion as above, there is still exactly
the same problem. Without the restriction, there is no problem, and this
situation was already addressed in the following paragraph:
> > In exactly the same way, the relative speed between two pulses of light
> > emitted in opposite directions in coordinate system C is 2c. Simple
> > vector addition. Do you think that calculations of relative speed in
> > coordinate system C, using velocities measured in coordinate system C,
> > should use something other than straightforward vector addition?
>
> Choosy, choosy! You wish to add light pulses using "ordinary" vector
> addition, but refuse to allow it for the sources of the photons.
> Please play fair :-(
Exactly the same rules apply to both. Use Lorentz transformations when
changing coordinate systems, and use vector addition when adding
velocities within a coordinate system.
Compare with classical mechanics: use Galilean transformations when
changing coordinate systems, and use vector addition when adding
velocities within a coordinate system.
-- Timo Nieminen
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