alexandrinushka said:
Summary:: I have understood that any elementary particle (and even bigger entities) are both waves and particles, they "travel as waves and interact at a point as a particle".
What determines its behaviour as the one or the other?
In order to trigger this "interaction at a point as a particle" does an entity need to meet a certain criteria?
Why doesn't any other entity on its way force this transition?
Can the properties of this wave be altered?
Thank you.
The problem is that there's a large inertia with how quantum theory it taught, and I also don't know a solution for the dilemma how to introduce quantum theory (QT) in a way to avoid this confusion. QT is the result of observations of the behavior of matter on a microscopic scale, which has revealed that matter on the most fundamental scale (as far as we know it) by what we call "elementary particles" and hold together by "fields".
This borrows the names "particle" and "field" from classical mechanics and classical electrodynamics, respectively. Historically, starting with these classical concepts, the physicists tried to make sense of observations that could not be explained with these very concepts, and one should keep this always in mind: Modern QT has been developed because of the failure of the classical concepts, and it has come with the prize that we have to modify our classical thinking quite drastically.
Given that history, it is pretty obvious that there were also many misconceptions on the way to develop this new thinking, which is partially radically different from the classical pictures we have last but not least also from our everyday experience: It deals with matter in form of macroscopic objects like solids, which behave pretty much as you learn in the very beginning of your physics studies as "point-particle mechanics" as well as liquids and gases, which you then (hopefully) learn to describe in terms of a field theory called fluid dynamics. It also deals with the electromagnetic field, mostly, because light is just electromagnetic radiation in a certain range of wave lengths our eyes are sensitive to. To lesser extent we also have experience with the electric field causing interactions between charged objects.
Now the historical development was such that the necessity of some changes of the classical world view came through the impossibility to explain an apparently simple phenomenon, i.e., to describe the spectrum of the light emitted from hot bodies. It's well known that a piece of iron starts glowing red when it's made hot, becoming yellow and finally even bluish white when getting hotter and hotter. It was also clear from classical thermodynamics that for an ideal black body (realizable by a cavity with its walls brought to a certain constant temperature for a sufficiently long time, which then becomes filled with ideal thermal radiation) this spectrum is universal and depending only on the temperature of the radiation, but to really explain the spectrum from the fundamental laws of mechanics and electrodynamics Planck figured out that he had to assume that the exchange of energy of electromagnetic waves with a given frequency with matter (like the walls of the cavity) can only be in integer multiples of ##E=h \nu##, where ##h## is a (then) new fundamental constant of nature. This was radically different from the predictions of the classical electrodynamics describing the interactions of charged particles with the electromagnetic field (and thus also the electromagnetic interaction between the charged particles as "mediated" by the em. field).
The next step then was taken by Einstein, who took this "discreteness" of the energy exchange serious and made the bold claim (carefully calling it a "heuristic point of view") that light as some "particle properties", i.e., he interpreted the exchange of radiation energy with charged particles in discrete portions ("quanta") as resulting from collisions between "light particles" (later named "photons") and the charged particles. It's also known from classical electrodynamics that the electromagnetic field has a momentum, and Einstein figured out that the photons of electromagnetic radiation with a wave length ##\lambda## carry a momentum of the magnitude ##p=h/\lambda## or written in vectorial form ##\vec{p}=\hbar{\vec{k}},## where ##\hbar=h/(2 \pi)##.
Now this "naive photon picture" seemed to be confirmed by (a) the photoelectric effect (Millikan 1916) and (b) the Compton effect (1923), and that's why the idea of "wave-particle dualism" came into the description of the phenomena on a microscopic level.
Theoretical physicists now tend to look for unifying concepts, and indeed in analogy with Einstein's "wave-particle duality" of light, Louis de Broglie came up with the idea that also the elementary particles (at this time particularly electrons but also protons) might have "wave properties", and this idea was then worked out by Schrödinger describing the particle by a wave equation. His first conception was that the electron "is" just this field as the photon just "is" the electromagnetic wave. On the other hand this was in conflict with the observation that one never observes one electron as a continuously smeared out object when registered at a photo plate but only as a single dot.
The until today at least by the majority of physicists accepted interpretation is that the wave function's modulus squared ##|\psi(t,\vec{x})|^2## is the probability distribution to register a particle at position ##\vec{x}## when looking at time ##t## (Born 1926).
So nowadays there is no "wave-particle duality" anymore, but a drastically changed concept of how particles have to be described. It is not possible to have a particle prepared in any way such that all its observables take predetermined values. Born's probability interpretation together with the rest of the formalism, which explains how observables and the dynamics of particles are described with operators that act on the wave function, implies famously that position and momentum obey the Heisenberg uncertainty relation. It says that when a particle's position-vector component in some directly is pretty accurately determined, then the momentum component in this same direction must necessarily be pretty unsharp and vice versa.
When it comes to a relativistic description, and photons as "massless particles" are necessarily relativistic, one also has to abandon the idea that a photon has a position observable at all. It's just not possible to localize a photon at a pretty certain place. At relativistic interaction energies it is also always possible that some particles get destroyed and/or new ones are produced. That's why relativistic QT is necessarily described by a formalism, which allows for such annihilation and creation processes, and the most convenient description is to formulate the theory as relativistic quantum field theory. In this sense, on a fundamental level, everything "particles" (fermions with half-integer spin) and "fields" like the electromagnetic fields also have particle-like aspects, also describing "particles" (bosons with integer spin). In this modern sense a single particle is just a specific type of states of the quantum field used to describe it.
So the modern answer is that "particles" and "fields" are neither purely particles or fields nor is there something contradictory as a "wave-particle dualism" but there's a description in terms of probabilities for the outcome of measurements in terms of an abstract mathematical theory, called QT. As disappointing this might be for some (and that's why we have a special section on this forum, where the "interpretation" of this formalism is discussed, sometimes in a heated fashion) it's at the same time the most comprehensive and successful theory ever. The only thing it cannot satisfactorially describe is the gravitational interaction, for which we still use the classical (in the sense of non-quantum) theory of General Relativity (GR). Since GR is at the same time our most comprehensive model of space and time (or rather spacetime), and Q(F)T needs a spacetime model (though usually we can neglect gravity and use special relativity or even Newtonian spacetime to describe particles and matter) to begin with, there's still not everything consistently solved, but on the other hand there are no observable facts hinting at the direction how a even more comprehensive theory including all known matter and interactions in the universe might look like. Indeed, gravity becomes important for macroscopic matter (usually in the astronomical context, when we want to describe stars, planets, moons, galaxies, and even the universe as a whole in cosmology), and there the classical-field description of GR is utmost accurate. More and more ever more accurate tests under ever more extreme conditions confirm the predictions of GR (e.g., by "pulsar timing" observations, gravitational-wave signals, etc.). All the known elementary particles are on the other hand described, neglecting the gravitational interaction, by the Standard Model of particle physics, which is a relativistic quantum field theory describing all particles in terms of quarks and leptons (where "free" quarks are never observed but only bound states into hadrons, including proton and neutron making up the atomic nuclei forming, together with electrons, the matter around us) as well as the fields describing the interactions (with the corresponding "particles" being the photon, the W, and Z bosons, which together describe the electromagnetic and weak interactions as well as gluons, which are the field quanta of the field mediating the strong interaction) as well as the Higgs field, which is repsonsible for all the elementary masses of the quarks, leptons and W- and Z-bosons with the Higgs boson as its "particle".
