In an experiment at CERN in 1964, a neutral pion moving at a speed of 0.99975c with respect to the laboratory decayed into two photons. The speed of each photon was measured with respect to the laboratory.

Describe how the result of this experiment provided support for special relativity.

In another experiment, a neutral pion moving at 0.80c relative to a laboratory decayed into two photons as shown in the diagram.

Photon R moved in the direction of the pion and photon L in the opposite direction. The rest mass of the pion is 135 MeVc^–2.

According to a laboratory observer,

(i) determine the total energy of the pion in MeV.

(ii) determine the momentum of the pion, in MeVc^–1.

(iii) state and explain which photon, R or L, has the greater energy.

special relativity rests on the postulate that the speed of light (c) is independent of the speed of its source / speed of light is constant;
both photons were measured to have a speed equal to c with respect to the lab thus verifying the postulate;

(i) the gamma factor is \(\gamma  = \frac{1}{{\sqrt {1 - {{0.80}^2}} }} = \frac{5}{3} = 1.67\);
so the total energy of the pion is \(\left( {\frac{5}{3} \times 135} \right) = 225{\rm{MeV}}\);

(ii) \(p = \left( {\gamma mv} \right) = \frac{5}{3} \times 135 \times 0.80c\);
=180MeVc^-1;

or

use of E²=p²c²+m²c⁴
\(p = \sqrt {\left( {{{225}^2} - {{135}^2}} \right)} \);
=180MeVc^-1;

(iii) (since the momentum of a photon is \(\frac{E}{c}\)) by momentum conservation
\(\frac{{{E_R}}}{c} - \frac{{{E_L}}}{c} = 180{\rm{MeV}}{{\rm{c}}^{ - 1}}\);
hence the right photon has the greater energy;

or

the total momentum before the decay is directed towards the right;
by momentum conservation the momentum after the decay is also to the right, hence the right photon has the greater energy;
Award [1] for “right photon has greater energy” with wrong or missing explanation.