Do electromagnetic fields propagate continuously?

Question

Having learned about plancks constant it is easy to mentally assign a grid-like structure to reality, almost starting to think of it as being pixellated in a way. This raises the question in me though - when an electromagnetic wave travels, say as a photon, through space does it do so continuously or kinda existing in one pixel, then appearing in the next and disappearing from the previous, and moving in such discrete jumps on and on. I once remember hearing somewhere that when a photon propagates it keeps borrowing energy from the future and then paying it back but i can't find any explanation of that phenomenon online.

Do electromagnetic wave excitations, and for that matter excitations of any of the fundamental quantum fields, move through space continuously or in discrete pixel-like jumps?

Answer 1

In mainstream particle physics, the quantum field theory of elementary particles, light is a quantum mechanically superposition of a great number of photons, which are elementary particles. The energy of the photons is = hν where ν is the frequency of the classical electromagnetic wave. This is an important experimental evidence of how photons are different from classical electromagnetic light but nevertheless build it up.

Figure 1. Single-photon camera recording of photons from a double slit illuminated by very weak laser light. Left to right: single frame, superposition of 200, 1’000, and 500’000 frames.

These are photons of the same frequency, on the left they look random , on the right the interference pattern of the classical two slits appears.

In mainstream physics, space time is continuous, not "pixilated" as you imagine. All variables are continuous except in bound states where energy levels and orbitals exist. The photons of an electromagnetic wave are not bound, the superposition is quantum mechanical and can be described with quantum field theory.

There exists an off the main stream theory that has space "pixilated"

Loop quantum gravity is an attempt to develop a quantum theory of gravity based directly on Einstein's geometric formulation rather than the treatment of gravity as a force. To do this, in LQG theory space and time are quantized analogously to the way quantities like energy and momentum are quantized in quantum mechanics. The theory gives a physical picture of spacetime where space and time are granular and discrete

It is still under research and I do not know how it treats photons and electromagnetic waves.