reference frames question

tony.hartin@gmail.com

Hi,

My question probably has a simple answer, but I've been scratching my
head over it a little too long so I thought I would ask it here. I
have three initial photons involved in a collision with 4-momenta k1,
k2 and k3. I have two reference frames:
frame 1: the centre of mass frame of photons k1 and k2 (so that 3-
momenta k1+k2=0)
frame 2: the centre of mass frame of all photons k1, k2 and k3 (so
that 3-momenta k1+k2+k3=0)

I want to find out what the relativistic beta v/c and gamma 1/Sqrt(1-
(v/c)^2 are. So there seems no way to directly find the relative
velocity of the two frames is as only photons are involved. I thought
to use the expression for the relativistic doppler shift, but that
doesn't seem appropriate.

Can anyone help me out here?

cheers.

Jim Black

On Thu, 27 Sep 2007 11:04:05 +0000 (UTC), tony.hartin@gmail.com wrote:

> Hi,
>
> My question probably has a simple answer, but I've been scratching my
> head over it a little too long so I thought I would ask it here. I
> have three initial photons involved in a collision with 4-momenta k1,
> k2 and k3. I have two reference frames:
> frame 1: the centre of mass frame of photons k1 and k2 (so that 3-
> momenta k1+k2=0)
> frame 2: the centre of mass frame of all photons k1, k2 and k3 (so
> that 3-momenta k1+k2+k3=0)
>
> I want to find out what the relativistic beta v/c and gamma 1/Sqrt(1-
> (v/c)^2 are. So there seems no way to directly find the relative
> velocity of the two frames is as only photons are involved. I thought
> to use the expression for the relativistic doppler shift, but that
> doesn't seem appropriate.
>
> Can anyone help me out here?
>
> cheers.

First, although each photon is travelling at the speed of light, the center
of mass of a group of photons need not be travelling at the speed of light.

Second, use 4-vectors! They make relativity problems like this much
easier. An analogous 3-dimensional problem would be to find the tangent
and cosine of the angle between two 3-vectors. How would you solve that?
Not by doing an ugly coordinate transformation, I hope! Take advantage of
the fact that

(E1+E2) (E1+E2+E3) - (p1+p2) dot (p1+p2+p3) c^2

has the same value in all reference frames.

--
Jim E. Black

jwill@BasicISP.net

Hi.

You are calling it a "frame", but the full name is "inertial frame".
Only particles with nonzero mass can be referenced to an inertial
frame.

If photons could have a frame, the speed of light would not be c in
all frames.

Photons have no inertial frame, and no proper time.

Jim Black wrote:
> On Thu, 27 Sep 2007 11:04:05 +0000 (UTC), tony.hartin@gmail.com wrote:
>
> > Hi,
> >
> > My question probably has a simple answer, but I've been scratching my
> > head over it a little too long ...