A recent preprint on Time in Quantum Theory(adsbygoogle = window.adsbygoogle || []).push({});

( http://www.rzuser.uni-heidelberg.de/~as3/TimeInQT.pdf ) by Dieter H Zeh has brought my attention to the question of the `speed of quantum changes'. While the classical discussions of nonlocality in Quantum Mechanics (QM) and consequences of Bell's Theorem are widely published, there are some other situations where nonlocality is rather hard to grok.

Consider a hydrogen atom in excited state. The electron wavefunction has some specific form, extending with exponentially vanishing factor, to infinity. Now, when the atom emits a photon (preferably for this analysis in spontaneous emission) the wavefunction changes.

The appropriate passage by Zeh is as follows:

A wave function(al) obeying a relativistic Schrödinger equation never

propagates faster than light with respect to the underlying presumed absolute spacetime. Recent reports of apparently observed superluminal phenomena were either based on inappropriate 'clocks', or on questionable interpretations of the wave function. For example, the exact energy eigenstate of a particle, bound to an attractive potential in a state of negative energy E = -|E|, would extend to spatial infinity according to exp(-√|E|r) outside the range of the potential. It has therefore been claimed to be able in principle to cause effects at an arbitrary distance within any finite time [10]. However, if the wave function of the bound system forms dynamically (according to the Schrödinger equation rather than by quantum jumps), it can only subluminally approach the exact eigenstate with its infinite exponential tail. This time-dependence requires a minimum energy spread that is in accord with the timefrequency

Fourier theorem.

When one looks up treatments of emission a little more detailed than simple Bohr pictures (in which, yes, the wavefunction changes instantaneously throughout the whole space!) one may get some sort of time dependence, especially for forced emission (as there is external element to the Hamiltonian - the external EM field. But the real question is for spontaneous emission in zero field?

Question: does the wavefunction change at the same moment in the whole space? Or, as Zeh suggests, is there a `wave' of changing wavefunction, spreading our from the atom?

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# Locality/nonlocality for bound states - a question

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