SR problem in book seems to be faulty

1. The problem statement, all variables and given/known data
The problem in question is 11.10 of "A traveler's guide to spacetime" by Moore. It goes as follows (by the way, the unit of distance that is used in the book is the lightsecond):

"A neutral boson of mass m traveling with v=4/5 in the +x direction strikes a snoozon of mass M=3m at rest. The interaction of these particles produces a previously undiscovered particle (which we will call a "rayon") and a photon with energy 2m. Assume that the photon is emitted in the -x direction.
a. What is the four-momentum of the rayon?"

2. Relevant equations
[tex]E=\frac{m}{\sqrt{1-v^2}}[/tex]
[tex]p_x=v_xE[/tex]
[tex]p_y=v_yE[/tex]
[tex]p_y=v_yE[/tex]

3. The attempt at a solution
I calculate the following values:
[tex]E_{boson}=5m/3[/tex]
[tex]p_{x, boson}=4m/3[/tex]
[tex]E_{snoozon}=3m[/tex]
[tex]p_{x, snoozon}=0[/tex]
[tex]E_{foton}=2m[/tex]
[tex]p_{x, foton}=-2m[/tex]
All the y- and z-components of p are 0.

With this I calculate the components of the four-momentum of the rayon, using the fact that the four-momentum of the system of particles is conserved:
[tex]E_{rayon}=E_{boson}+E_{snoozon}-E_{foton}=5m/3+3m-2m=8m/3[/tex]
[tex]p_{x, rayon}=p_{x, boson}+p_{x, snoozon}-p_{x, foton}=4m/3+0+2m=10m/3[/tex]
And again, the y- and z-components are 0.

The four-momentum then, is [tex]\left[ \begin{array}{cccc} 8m/3 \\ 10m/3 \\ 0 \\ 0 \end{array} \right][/tex]
But this doesn't make any sense, since E should always be qreater or equal to p.

Have I made a mistake somewhere or is the question just not right?
 
Last edited:
Should I, perhaps, explain my solution in more detail?
 

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