How does a photon travel?

[Green dwarf]

TL;DR Summary

A photon takes 4 years to get from the Sun to Alpha Centauri. 2 years after setting off, is it in one place, multiple places or nowhere?

Is it at a single point half way between the two stars, or is it in a superposition of locations forming a hemispherical shell around the sun, or does it just not exist at all until it interacts with a particle in Alpha Centauri?

 

[PeterDonis]

Is it at a single point half way between the two stars, or is it in a superposition of locations forming a hemispherical shell around the sun, or does it just not exist at all until it interacts with a particle in Alpha Centauri?

None of the above. A photon in QM, or more precisely in QFT since you need to use that to model photons for this scenario, has no well-defined "position" operator at all. That is simply not a concept that applies here.

 

[Nugatory]

TL;DR Summary: A photon takes 4 years to get from the Sun to Alpha Centauri.

No. A beam of light takes 4 years to get from the sun to alpha centauri, but photons are something completely different.
When you hear that "a photon is a particle of light" or something similar it's natural to think that light moving through space is made up of photons the same way that a river is made up of water molecules moving along the riverbed.... but in fact that model is hopelessly misleading. As @PeterDonis says above, there is no position operator, no position operator means no trajectory, no way of saying that a photon followed this path or that path through space.

 

[Green dwarf]

Saying the particle has no position operator - is that different from saying it is not at any location or that it is nowhere?

 

[hutchphd]

Saying the particle has no position operator - is that different from saying it is not at any location or that it is nowhere?

You will need to define "at any location" and "it is nowhere". Also define "the particle". Then perhaps one can answer the question.

 

[johntpl]

It means ‘position’ and ‘nowhere’ don’t apply.

 

[Nugatory]

Saying the particle has no position operator - is that different from saying it is not at any location or that it is nowhere?

It means that it makes no sense to apply the concept of position to it, the same way that it makes no sense to talk about the mass and electric charge of $\pi$.

 

[PeterDonis]

Saying the particle has no position operator - is that different from saying it is not at any location or that it is nowhere?

Yes.

 

[weirdoguy]

the same way that it makes no sense to talk about the mass and electric charge of $\pi$

Unless $\pi$ stands for pi meson

 

[PeroK]

Saying the particle has no position operator - is that different from saying it is not at any location or that it is nowhere?

The fundamental concept (in QFT) is the quantized EM field. This is in contrast to classical physics, where the fundamental concept is a fixed number of distinguishable particles. The EM field created by a distant star has a given probability of interacting with a detector on Earth. In fact, it results in a fairly well-determined number of interactions per second - depending on the location and characteristics of the detector. Each interaction represents a "photon", which is the quantum of the EM field, and is also called a particle. So, the particles represent the quantized interaction between the EM field and a detector.

There is no concept of a fixed number of photons setting out from Alpha Centauri and travelling in a classical trajectory through space. That is simply not part of the mathematical model in QFT.

What you can say is that the EM field in this case (and in many cases) can be approximated by EM waves travelling through space and obeying Maxwell's equations. I.e. that QFT reduces to classical EM in this case. These waves, however, are not waves of photons. That would make no sense. Instead, they can be modelled as oscillating electric and magnetic fields. Then you are in the realm of modelling light as classical EM waves, rather than as a quantum field.