I would like to know how to imagine light and especially a light quantum "particle". If I understand right, an EM wave consists of light quanta, a light quantum is massless, and it is moving along a waveline. But if this pointlike EM-field is moving along a waveline, it is doing a wave movement and that means that a particle describes the path of an EM-wave or is an EM-wave (?) Where is my error?
It's difficult to really visualize what it means for things to be both particles and waves at the same time. The best I can usually do is to think of the wave as a sort of probability distribution, and the particle as being somewhere in it. In this perspective, one doesn't think about the path traced out by the point particle (that's always a mistake in quantum mechanics). Instead, one thinks about how the wave function evolves with time, then imagines randomly grabbing a particle from somewhere in the wave function when it becomes relevant (eg. when a measurement is taken, or when an atom absorbs the photon, etc.) This kind of picture does eventually break down, but only at the point when you have to do more precise calculations. There is one thing to be careful of, no matter which perspective you take. A beam of light does not trace out a "waveline" in space. Light travels in a straight line until it hits something. If you plot the phase of a beam of light against its position, the plot will be some sort of sin curve. But it's important to realize that this sin curve has nothing to do with the beam's path through space.
This is the answer that I needed, thank you very much, Fednis48. There is no wave path of light in spacetime. I didn't know that.
Glad I could help! Please Register or Log in to view the hidden image! You're not alone in making that mistake - in the intro physics lab I TA'd, the distinction between oscillating polarization and wavelike motion was one of the "most common mistakes" that we were supposed to emphasize.
I think it is a mistake to try to put a label defined in our everyday work, such as particle or wave, onto something utterly outside of our experience. Our language developed through a need to describe/refer to things in our lives and the quantum world is not something we experience directly. As a vague example imagine you showed plastic to someone from 1000BC. They might ask "What kind of wood is it?" and when you say "It is not wood" they might ask "Is it metal?" but it isn't metal. They had no word for 'plastic' because it was something outside of their experience, there was no need to have a label to refer to a concept no one had ever thought. You don't see people doing material/chemical engineering asking their professors "Is plastic a metal or a wood?", it assumes a false dichotomy. Sure, plastic can have properties from each; by gentle heating it can be reworked, just like metal but not wood. Expose it to fire and it will burn, like wood but not metal. Quantum objects (which are unfortunately often just called 'particles', confusing this issue) exhibit properties which we associate to particles and waves from our everyday lives. A ping-pong ball in a tumble drier bounces around in a particle fashion, ripples in a lake spread out as wave fronts. Both of these we see quantum objects do in some sense. Trying to pigeon hole quantum systems into categories and classifications developed separate from quantum mechanical work is, in my opinion, a mistake. When we have discovered new crazy states of matter we do not ask "Is this a liquid, solid or gas?", demanding the new state fit into a set of categories developed thousands of years ago, we add new categories. When we started discovering matter is made of different elements we didn't stick to the Ancient Greek concept of the 4 elements; earth, fire, wind and water, instead we created an entirely new method of classification (the chemical elements and the periodic table). We didn't have words for what we now call hydrogen, helium, oxygen, etc so we created them. When we discovered there's more than just gravity and electromagnetism at work in the universe we didn't rigidly stick to "How does gravity and electromagnetism explain this?", eventually we realised new forces were at work, which we gave names to and added them to the list of forces known to act in the universe. History is rife with examples of how previous classifications and labelling systems were invalidated by new discoveries and either expanded or utterly replaced. The same should be done for quanta, they are not categorisable if you ask "Is the photon a particle or a wave?", that is a false dichotomy.
