Yes, the b's are raising/lowering operators, and index m does run through positive and negative integers. The latter is a matter of choice since we can label our "sites" as we wish.
Suppose, there is an electro-optical modulator that can couple the neighboring modes in an optical ring resonator. The Hamiltonian for the system
looks something like this^^ (see the attached image). Here we sum over all modes m and 𝜙0 is a parameter. What will be a good set of basis for the...
So, by drawing analogy with EM, I can easily find the eqn of field of a moving mass, the power radiated or other quantities ?
And, as this is highly negligible, is that the reason why it took so long to detect it?
A moving charge that starts or stops generates a spherical wave-front of EM wave, can the same analogy be drawn for a moving mass?
Reference: Electricity & Magnetism by EM Purcell