The Basic Forces and Messenger Particles — Question 10

Question 10

An interference term can make a small force amplitude visible

Two interactions connect the same initial and final states. In common units $A_1=2$ and $A_2=.30e^{i\phi}$. Rate is proportional to $|A_1+A_2|^2$.

1. Expand the rate and calculate its value for phases zero, pi/2 and pi.

2. Compare the interference term maximum magnitude with the isolated second-interaction rate and explain the sensitivity gain.

Question 10 - Solution

An interference term can make a small force amplitude visible

(a) Method and calculation

$$R=4+.09+1.20\cos\phi.$$$$\boxed{R(0)=5.29,\quad R(\pi/2)=4.09,\quad R(\pi)=2.89}.$$

(b) Interpretation and further calculation

$$\boxed{|R_{\mathrm{int}}|_{\max}=1.20,\quad R_2=.09}.$$$$\boxed{|R_{\mathrm{int}}|_{\max}/R_2=13.3333}.$$

Physical check

Interference needs coherent amplitudes for indistinguishable states; adding rates instead is appropriate for distinguishable or incoherent channels.