Particles and fields

Question

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?

Answer 1

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.

Related:
Difference between classical fields and wavefunctions? Relation between QM and Classical field theory
Are particles and waves limits of quantum fields?
Particle- and wave-like properties

Answer 2

'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