Particles and fields

From high school physics we are taught that photons are both waves and particles, and that they do not need a medium to travel through, being transverse waves. In QFT, we learn that particles are simply excitations of their respective fields. In this sense, is it correct to say that the medium in which photons propagate is its field itself? Further, do these fields permeate all spacetime, and if so, are propagating particles simply moving excitations on these fields, kind of like waves in the ocean?

Particles and fields are different things in classical physics, whereas in quantum theory everything is a field. Speaking of particle-wave duality, i.e., that something is at the same time a field and a particle is really a misnomer - what one really means is that all objects show both particle-like and wave-like properties (I say "objects" in order to avoid adding an extra layer of confusion by calling them "elementary particles".)

A typical example of a wave-like property is interference - which in classical physics is reserved for waves. An example of a particle-like property is countability - classically one can count the number of particles, whereas a wave is continuous (has continuous amplitude.)

In this sense, is it correct to say that the medium in which photons propagate is its field itself?

So no, this is not correct - particles themselves are fields. One can speak of them as an excitation of a field, but then field is a more general concept that can be characterized by excitations, rather than an alternative to a particle. Ultimately, the problem here is likely trying to think of quantum objects in classical terms (moreover, in terms of material waves - like those in water rather than elementary ones.) In other words, while classical analogies are helpful, overusing them makes only complicated understanding - sometimes it is better to accept that the world acts according to the laws that do not seem very "intuitive", but which can be studied and codified in equations - and eventually becomes one's intuition with time.

• Keep in mind the concept of "virtual particles" which are also considered as an excitation of a field. For example the polarized spin of electrons in iron leads to the magnetic field surrounding a bar magnet. These virtual particles are considered as an excitation of the magnetic field. It is not as if electrons are leaking out of the iron to create this field, but it is certainly there. Commented Jul 22 at 15:33
• @foolishmuse you might be confusing virtual particles with quasiparticles. E.g., see this thread: physics.stackexchange.com/q/604029/247642 Commented Jul 22 at 16:36
• Quasiparticles is a new one for me. Looking on Wiki, quasiparticle can only exist inside interacting many-particle systems such as solids. So I don't think this would fit for the magnetic field outside a bar magnet. Commented Jul 22 at 20:47
• Isn't the magnetic field also active inside/within the bar magnet as well? Commented Jul 23 at 3:16
• The statement "the medium in which photons propagate is its field itself" is not opposite to that "particles themselves are fields." Let's compare the statement "water waves in a pond are (classical) excitation of the water surface" with the statement "photons are (quantum) excitations of the photon field." Where is the difference? I agree with the dangers of overusing classical analogies. Still, I do not think assigning different statuses to two sentences is a good idea based on the same mathematical modeling of the phenomena. At least not without good explicit arguments. Commented Jul 23 at 4:37

'Photons obey the laws of quantum mechanics, and so their behavior has both wave-like and particle-like aspects. When a photon is detected by a measuring instrument, it is registered as a single, particulate unit. However, the probability of detecting a photon is calculated by equations that describe waves. This combination of aspects is known as wave–particle duality. For example, the probability distribution for the location at which a photon might be detected displays clearly wave-like phenomena such as diffraction and interference. A single photon passing through a double slit has its energy received at a point on the screen with a probability distribution given by its interference pattern determined by Maxwell's wave equations.[66] However, experiments confirm that the photon is not a short pulse of electromagnetic radiation; a photon's Maxwell waves will diffract, but photon energy does not spread out as it propagates, nor does this energy divide when it encounters a beam splitter.[67] Rather, the received photon acts like a point-like particle since it is absorbed or emitted as a whole by arbitrarily small systems, including systems much smaller than its wavelength, such as an atomic nucleus (≈10−15 m across) or even the point-like electron.' https://en.wikipedia.org/wiki/Photon

• [+1] Ah, is the wave function of a photon then essentially the Klein Gordon equation with $m=0$? Commented Jul 22 at 13:49
• @James see Does a photon have a wave function or not? Existence of a wave function is a big deal for electron, which is classically a particle, but for photons it is a trivial matter, as they are already fields/waves in classical physics - a solution of Maxwell equations is Photon's wave function. In this sense yes - solutions of wave equation (i.e., Klein-Gordon equation with $m=0$) are photon wave functions. Commented Jul 22 at 14:18
• @James We are talking about classical field here - so nothing is probabilistic and nothing collapses, but it is already a field that can interfere. Quantizing EM field can be viewed as imposing commutation relation of $E$ and $B$, just like we impose commutation relations on $[x,p]=i\hbar$ when quantizing particles - the two fields are not simultaneously measurable at the same point of time-space. If we measure one, the other is completely uncertain, hence the collapse. [contd.] Commented Jul 22 at 15:03
• [contd.] The difficulty of drawing parallels between quantization of particles and fields is that quantization of fields is formally identical with the second quantization quantization for particles. Once fields are quantized and particles are second quantized, they are treated identically, but we then do not speak about probability density determined by wave function - we have field operators creating/annihilating particles - for classical "particles" these are traced to the wave function $\psi^\dagger,\psi$, but for EM field they are traced to fields $E,B$ (or to potentials $A,\phi$.) Commented Jul 22 at 15:07
• @James In the Lorenz gauge the wave equation holds. This can indeed be interpreted as a massless ~Klein-Gordon equation, for a four vector potential. This potential tells you the probability of finding energy, momentum etc of a certain frequency. Hence it tells you the probability of finding photons. Commented Jul 23 at 8:27