Identity crisis : a new principle

There is indeed yet another principle, about the peculiar listing of states, which occurs for an assembly of quanta. This principle was first proposed by S. N. Bose as the the fundamental indistinguishability of photons. The uncanniness of this principle is best brought out by considering a simple heads-or-tails experiment with two Quantum coins. Classical indistinguishability will imply that the HH and the TT possibilities have weightage 1/4 each, while the HT (indistinguishable from TH) has the weightage 1/2 because it can be arrived at in two different ways. But this is where quanta differ. They are so strictly indistinguishable that there is no point even conceiving of two different configurations. Thus two bosonic coins will have the three possibilities, each with weightage exactly 1/3. It gets even more mysterious with fermions. Pauli exclusion principle will insist that there is only one possible state for the two coin system, viz., HT, being completely equivalent to what we may have called TH, and it has weightage exactly 1. No other states are possible.

We see that this ``identity crisis'' - absence of any ``individual'' identity of quanta - should actually be understood as a property of the space of eigenstates available to a set of quanta. We should avoid first introducing distinct particles and then insisting they are indistinguishable. Quanta are therefore not ``particles'' at all. ``Number of quanta'' is however an approximate observable of many systems. Or more correctly put, only those systems have a classical analogue of being a collection of ``particles'' that permit an approximately conserved number operator. Indeed photons are the most familiar quanta that have no conserved number. Their states are superpositions of states with different values of the number. Only under special conditions do we observe states with a few or a definite number of photons.

Fermions obey the Exclusion Principle. As a result far fewer number of states are available to them than to similar number of classical particles. In most practical applications this is expressed as the presence of ``exchange coupling'' or ``degeneracy pressure''. But experts know that there is no force involved. This is simply the kinematics of fermions, not their dynamics.

In summary it is not Uncertainty or Wave-Particle Duality that are so important. It is the Superposition Principle and the different listing of states. Furthermore, exactly identical quanta is a feature of the microscopic world. Quantum Mechanics is not seen in its full glory until it is stated for assemblies of identical quanta.