## reference frames question

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.

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 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
 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 ...
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