How do single photons travel from here to there

Question

I know there have been similar questions but I'm still unclear what the overall consensus is. (1) I assumed and have read that photons travel in straight lines unless deflected by gravity but there are conflicting theories. (2) I have heard that single photons takes every possible path but that makes no sense. Why would a single photon traveling from here to the moon go to every other place in the universe along the way. (3) I can understand a single photon traveling as a particle or packet of energy but I have a hard time understanding a single photon traveling as a wave. I have never understood any attempts to answer this. (4) Does a single photon have a frequency and what causes the frequency? If not then how does it have energy? I have many questions about single photons and their frequency.

Answer 1

I think CuriousOne's comment provides most of the answers to your question, but for completeness I'll expand it into an answer.

Light is described by quantum field theory and can only be fully understood in this context. We sometimes talk about photons and sometimes talk about light rays, but these are only approximations. As a general principle light behaves like a particle when energy is being exchanged with something else, and like a wave when energy is propagating. So light travels like a wave and interacts like a particle.

Taking your questions in turn:

1. When we look at light propagating in the classical limit then it travels in straight lines (though these straight lines may appear curved in a curved spacetime).

2. When we look at light in the quantum regime then the whole concept of a trajectory is meaningless because the trajectory is a classical limit. At quantum scales no particle, including light, has a perfectly defined trajectory. This is why an electron can go through both slits in the Young's slits experiment - because it doesn't have a single perfectly defined trajectory. The calculation of the classical trajectory can be done in various ways, and the Feynmann sum over paths is one approach. This calculation assumes that light simultaneously travels over all possible paths. To what extent this is just a calculational device and to what extent it reflects an underlying physical reality is a matter of opinion.

3. (and 4) these don't have answers because the questions are based on a misunderstanding of what light is. If you attempted to describe a propagating light ray as photons you would have to use some description like a coherent superposition of many photons.

While it is not the same as a photon, we could think about a light pulse i.e. a short section of a light wave. This is also called a wave packet. Wave packets have an average frequency, but they contain a spread of frequencies so a wave packet does not have a single perfectly defined frequency.

Answer 2

Mainstream physics has described the microcosm of molecules, atoms, elementary particles with the theory of quantum mechanics, and in particular the quantum mechanical standard model of elementary particles, and it has a mathematical form, a Lagrangian. . In this Lagrangian the elementary particles, including the photon, are entered as point particles with the mass and quantum numbers shown in the table.

The word "wave" comes in quantum mechanical solutions from the first quantization level. The potential problems at first quantization level are solutions of quantum mechanical equations (Schrodinger, Dirac, Klein-Gordon) where interactions are represented by potentials. These equations are called wave equations because their solutions are sinusoidal functions, and sines and cosines are what describe waves in the macroscopic world, from water waves to sound waves and even to classical electromangetic waves.

The innovation in Quantum Mechanics is that the solutions of these equations are not to be considered trajectory solutions, but are to be complex conjugate squared and the value interpreted as a probability for a particle to be at (x,y,z) at time t. It is an axiom that has been very successful in describing molecules and atoms cf atomic orbitals . In elementary particle interactions the solutions had to be estimated by expansions in pertubative series because of the complexity . This led to the development of the mathematics of second quantization where the solutions for the free QM equations (no potential), the wave functions , are used to build what is called second quantization and quantum field theory, various mathematical formats.

The photon in this framework has its own quantum mechanical equations and its own wavefunction solution. This is a complex wave function and carries the electromagnetic potential information A in complex phases. It can be shown that a classical electromagnetic wave obeying Maxwell's equation emergenes from a confluence of photons with energy h*nu, and nu is the frequency of the macroscopic wave.

So how does the photon move from A to B? It moves with energy=h*nu and velocity c, and carries information about putative electric and magnetic fields of a macroscopic light beam. In first quantization one says that its probability of being at (x,y,z) is the square of the free photon wavefunction which probability does vary with frequency nu.

Photons are usually treated with second quantization, which mathematically assumes that the vacuum is composed by the fields of the elementary particles at a ground state, and creation operator manifests the elementary particle at that point in time.

I have heard that single photons takes every possible path but that makes no sense

You are confusing mathematics with reality, a common enough mistake, (particularly with the concept of virtual particles, but that is another story). The mathematics of calculating the progress of a photon can be formulated in a least action type integral. It does not mean that the photon takes all those paths, as in classical mechanics formulated with the least action, the object does not take all those paths.