# Continuity of photons

DarMM
Gold Member
I think the problem is that QM is silent on the question of path (because of the nature of the model) that does not mean the (single)particle doesn't have a path. But if you have model that does predict the path( electron or photon) you are welcome to publishing it.
QM simply doesn't use paths at all. I think this is "silence" in the same way GR is silent about the universe being embedded in a larger spacetime. Similarly Maxwellian electromagnetism is silent on the notion of the EM field being a limiting case of some more general field.

Really the success of QM shows the notion of paths just doesn't seem to be needed at all for current observations.

I think it should be mentioned that attempting to come up with paths for particles is highly constrained by no-go theorems such as the Kochen-Spekcer theorem and the PBR theorem.

DarMM
Gold Member
Consequently also a "particle-number observable" is available only for asymptotic free states. The interpretation of "transient states" in scattering processes in terms of "particle states" is at least problematic. If I understand @DarMM right, it's even mathematically impossible within mathematically more rigid formulations of the theory!
Sorry forgot to answer this. Yes indeed, impossible.

When a light source (or more generally a matter source) causes an effect in a given detector, if the detector is of an appropriate design and placed far enough away from areas of interaction then the effects on the detector can be understood in particulate terms using asymptotic particle states. If not, then it can't.
Sorry for the delay, but I wanted to follow up on this. Suppose we have a macroscopic device which experimentalists would consider a good single photon source. What would be a concrete (can actually be built) detector of appropriate design which we could use to measure this emission in such a way that the effect could *not* be understood in terms of an asymptotic 1 photon state?

DarMM
Gold Member
Sorry for the delay, but I wanted to follow up on this. Suppose we have a macroscopic device which experimentalists would consider a good single photon source. What would be a concrete (can actually be built) detector of appropriate design which we could use to measure this emission in such a way that the effect could *not* be understood in terms of an asymptotic 1 photon state?
Well if the source is defined in terms of a single photon state, the statistics of experiments are going to be compatible with a single photon state. This is like how if you prepare a momentum (near) eigenstate the statistics of any experiment are going to be compatible with a momentum eigenstate, both position and momentum measurements. Simply because that is the state. However the statistics in the two bases exhibit complimentarity. Thus it is for a single photon state, it can be measured in a non-photon basis. However even ignoring this most states in quantum optics are not single photon states and even calling something a "single photon state" is an idealisation.

Asher Peres has some interesting points (https://arxiv.org/abs/quant-ph/0212023):
Although states with a definite number of particles area useful theoretical concept, a look at quantum optics techniques or at the Table of Particle Properties shows that experimentally accesible quantum states are usually not eigenstates of particle number operators. In general any process that is not explicitly forbidden by some conservation law has a non-zero amplitude (Weinberg, 1995;Peskin and Schroeder, 1995; Haag, 1996). There are multiple decay channels, extra soft photons may always ap-pear, so that the so-called ‘one-photon’ states are often accompanied by soft multiphoton components,
$\alpha|\Omega\rangle + \beta|1_{\omega}\rangle + \gamma|2_{\omega^{′}\omega^{′′}}\rangle +..., |\beta|∼1$ (63)
Thus the physical realization of a single qubit is itself necessarily an idealization.
So a single photon state is a more fraught concept than one would think.

Thus it is for a single photon state, it can be measured in a non-photon basis
Right, I am just asking how exactly this can be done in practice. Typically (afaik) a coherent state is measured by 1) recording the number of clicks across many runs, 2) treating each click as indicative of an individual photon, 3) confirming the distribution of clicks converges to the Born rule distribution of the number states which describe the coherent state in the number basis. I am not aware of a detector which can directly measure radiation on a non-number basis.

Likely I am just missing a counterexample because I haven't been exposed to all the experimental possibilities but I haven't had luck finding one so far.

DarMM