# A positronium atom decays into two photons c+c=c

1. Feb 24, 2006

### Loren Booda

A positronium "atom" decays into two photons c+c=c

A positronium "atom" decays into two photons travelling antiparallel to each other, both at the speed c away from the origin of decay. How can one appreciate the fact that they are also travelling away from one another at the speed c?

2. Feb 24, 2006

### robphy

Here is a [possibly unfamiliar] way to appreciate this... using rapidity, the additive parameter akin to an angle. In 1+1 Minkowski spacetime, as measure of separation between [future-pointing causal] "rays" from the origin, a light ray is infinitely far away from every other ray.... in the sense, one would have to boost by an infinite amount to get to or from that light ray. [It is along these lines that one can explain why one can never get a massive object to travel at the speed of light.]

So, the left-traveling photon is infinitely far away (in rapidity) from the origin of decay... as well as infinitely far away (in rapidity) from the right-traveling photon.

For a formula, one can write down the usual "relative velocity formula" in terms of the identity for the hyperbolic tangent of a difference of two rapidities [angles]. I'm too lazy to do this now.

3. Feb 24, 2006

### clj4

Suggestion:

In the relativistic speed composition formula:

w=(u+v)/(1+uv/c^2) make u=v=c

It appears that this comes up all the time because "it offends our senses".
What can you do, the laws of physics may be counterintuitive sometimes. :!!)

4. Feb 25, 2006

### Loren Booda

Can any of you construct a schematic which demonstrates this addition of light speeds relative to the origin, resulting in light speed correlative to the photons themselves? That is, show the situation in picture form.

5. Feb 25, 2006

### clj4

The formula is a nonlinear function, (a type of hyperbolic surface) so, try using Mathematica :

w(u,v)=(u+v)/....

6. Feb 25, 2006

### Staff: Mentor

In relativity, there is no inertial reference frame in which a photon is at rest. Therefore one cannot talk about the speed of a photon relative to another photon, in the same sense that one can talk about the speed of a photon relative to you or any other massive object (which speed is always c, of course).

7. Feb 25, 2006

### clj4

True. Despite this the formulas STILL hold.
I can see what the author of this thread wanted: does the formula still hold for u=c and v=-c? The answer is "yes". (it will disappoint a lot of antirelativists). Here is why:

w(u,-c)=(u-c)/(1-uc/c^2)=c! for ANY u (including u=c)