Why can’t particles be detected in more than one location?

Question

Sure, there are interpretations of quantum mechanics where the particle really is a little “speck”, so of course it can’t be detected in more than one place. My question is mainly geared toward interpretations where the wave function is seen as a real spread out thing, especially Everettian QM.

For simplicity, let’s say there are just 3 locations where a particle could be detected on a screen. If the particle starts in a superposition of “place A” + “place B” + “place C”, then it makes sense that the wave function will branch (to use Everettian language) into three parts, one for each of these superimposed states. What I don’t get is why the particle can’t be in a superposition of something like “place A AND place B” + “place B AND place C”. Then on one branch the particle will be detected at both A and B, and on another branch it will be detected at both B and C.

Does it just come down to “that’s how the world is, go ask a philosopher.” Or is there something about decoherence or something that will help make sense of this?

Answer 1

One of the most important foundational experiments leading to quantum mechanics was the photoelectric effect. Experimentally, it was found that arbitrarily small intensity light could eject electrons from a material, so long as the frequency of the light was above a threshold value. This is impossible to explain with classical wave theory (since the energy is proportional to the intensity). Einstein explained this phenomenon with the idea that light comes in discrete packets of energy (photons) with energy proportional to their frequency, $E=\hbar \omega$, where $\omega$ is the frequency of the photon. Crucially, it is not possible to divide these particles into smaller amounts; when photons of a given frequency are generated they either have enough energy to eject an electron or they don't, there is no middle ground.

Quantum mechanics is a theoretical framework constructed to reproduce this and other basic experimental facts about reality.

Since Einstein's time, there have been many other phenomenal experimental demonstrations of the correctness of the predictions of quantum mechanics. For example, CCD chips can detect single photons, and never detect half a photon. Photons are always detected with energies in integer multiples of $\hbar \omega$, and never with a some fraction of this amount.

Within the framework of quantum mechanics, (independently of whether you are using the Copenhagen or Many Worlds interpretation or some other interpretation that gives physically equivalent results) your question is tautological. The answer to "Why can't one particle be observed to be at place A and place B simultaneously" is that one particle can only be observed in one place at once. If you want to observe something at two locations simultaneously, you need two (or more) particles. Mathematically, to describe one particle, we can write down a basis of states of the form "particle is at location A" and "particle is at location B", and a general one particle state (the wavefunction) is a superposition of these one particle basis states. To describe a two particle state, we would need a basis for states with two particles; such a basis would include a state with one particle at location A and one particle at location B; another basis state with one particle at A and one particle at C; and so on; and a general two-particle state would be a superposition of these two-particle basis states. Note that, if there were some object, that could be detected at two locations at once, the word "particle" would not be a very good word for whatever it was the theory was trying to describe, since it is behaving like "two things" would in our classical world.

A very important and subtle distinction here is the difference between a state and a wavefunction. A wavefunction is a state for one particle expressed in the position basis. A state is more general and abstract, and can be expressed in any basis and describe any number of particles. In particular, to correctly describe what's happening when you detect one particle at location A, your state can't be described a wavefunction for one particle; you should also include the detector in your state. Immediately after "collapse" [Copenhagen] or "in some branch" [many worlds], the state of the system is described by a combination like "particle at A and detector at A saw something". If you insist on using a wavefunction picture, you have to imagine the wavefunction is a function over a space not just including the position of the particle, but also the possible states of detector. Then, immediately before collapse [Copenhagen] or considering all branches [many worlds], there is a "peak" in the wavefunction near "particle at A and detector A lit up" and a "peak" near "particle at B and detector B lit up" but the wavefunction near "particle at A and detector B lit up" is zero. There's a wonderful paper by Mott that describes this very clearly [1].

(I realize it is a bit of a contradiction for me to say that the answer is both tautological and depends on something very subtle; in my defense I would say that the answer is tautological if you fully understand quantum mechanics, but many students fail to realize the subtle distinction between states and wavefunctions at first, and this can lead to all kinds of confusion)

You might ask, why is quantum mechanics constructed like this? The answer is that it was constructed to reproduce experimental facts like the ones that I gave at the beginning. If we observed that particles (or "things" that we probably wouldn't call particles) could sometimes be observed in two places at once, we would use a theory other than quantum mechanics to explain the experimental facts. But we don't, and quantum mechanics has never failed to correctly predict the results of an experiment in the regimes where it can be applied.

[1] Nevill Mott, "The Wave Mechanics of α-Ray Tracks", Proceedings of the Royal Society (1929) A126, pp. 79-84, doi:10.1098/rspa.1929.0205.

Answer 2

Particle physics, which you are discussing, has a large data base of experimental measurements that are fitted by the quantum field theoretical standard model, and all interpretations have to fit the same data in order to be interpretations and not a new theory.

Here is one of the thousands upon thousands of bubble chamber photographs from the experiments that led to the standard model.It is a prediction of the standard model that Omega minus should exist, and it was found.

It is interpreted as particles:

$$ {\newcommand{Subreaction}[2]{{\rlap{\hspace{0.38em} \lower{25px}{{\rlap{\rule{1px}{20px}}} {\lower{0.5ex}{\hspace{-1px} \longrightarrow {#2}}}}}} {#1} }} {K}^{-} ~~ p ~~ {\longrightarrow} ~~ {\Subreaction{{\Omega}^{-}}{ {\Subreaction{{\Lambda}^{0}}{p ~~ {\pi}^{-}}} ~~ {K}^{-}}} ~~ {K}^{+} ~~ {K}^{+} ~~ {\pi}^{-} $$

and shows the generation and decay of an ${\Omega}^{-},$ the particle that fills up the prediction in the decuplet of hadrons.

We call the kaons, protons, pions "particles" because macroscopically their footprint is that of a charged particle with a given momentum traversing an ionizable medium.

Do you think your hypothesis " “place A AND place B”

could give such a coherent generation of particles?

Answer 3

The answer to your question is that the photon is the detection event, and if there is only one photon (emitted), then there is only one detected (at the same time).

Think of it this way: A photon is the detection event. When there is only one photon, there is only one detection event. The probability distribution of detection events is associated with the photon's wavefunction.

If a photon truly goes through both slits (at the same time), then why can't we detect it at both slits (at the same time)?

In your case, you have a single photon emitter, which emits an excitation in the electromagnetic field, and this excitation propagates to the detector, where it gets detected (fully absorbed) only once (at the same time), emphasis on the same time. The emitter and the EM field (and its excitation the photon) and the detector are creating an entangled system, and only those states are allowed where the photon gets absorbed once (at the same time).

That being said, please note that there are cases where the photon's energy can be absorbed partially in increments at different times (not at the same time), and we call this inelastic scattering.

https://en.wikipedia.org/wiki/Inelastic_scattering

Answer 4

Others have explained it using the standard model. But there is a theory called One-electron universe (it is a false/incomplete theory put forward by John Archibald Wheeler) which postulates that all electrons and positrons are a single particle moving forward and backward in time. But the big fatal failure of this theory is that it predicts that the number of electrons and positrons should either be same or have difference of 1. But we know that there are many more electrons than positrons. Another failure of this theory is that it can't properly explain why we observe causality when we consider the electrons as different particles even though the electron can move freely in backword and forward time. If these failures are somehow resolved maybe then it will make sense for a particle to be at multiple places.

Answer 5

Does it just come down to “that’s how the world is, go ask a philosopher.” Or is there something about decoherence or something that will help make sense of this?

Have you never wondered why, in edge and slit experiments (even with single edges, the intensity distribution on a screen has the equation of a wave), the edges do not matter? Is there no interaction at all between the photon or electron and the edges?

In a discussion on phys.org, the following was noted:

At the time, most quantum physicists adopted the "shut up and calculate" philosophy: get on with the job, and don't worry about philosophical issues – just get the predictions.

Einstein would have the same opinion today, because "shut up and calculate" is still by far the dominant opinion among physicists. The problem with quantum mechanics is that despite being an extremely powerful and successful mathematical theory, it has nevertheless done very little to advance our understanding of the nature of physics. Quantum allows you to calculate results, but gives no insight about the reason for the results.

Some pheomena we could think about:

1. The surface of edges in principle is made of electrons - the outer electrons of atoms and molecules. These electrons have an electric field around and a magentic field.
2. The spins, pointing in the same directions as the electrons magnetic dipoles are interacting by Paulis exclusion principle. In short, (surface) electrons interact.
3. Quasiparticles and collective excitations (which are closely related) are emergent phenomena that occur when a microscopically complicated system such as a solid behaves as if it contained different weakly interacting particles in vacuum. For example, as an electron travels through a semiconductor, its motion is disturbed in a complex way by its interactions with other electrons and with atomic nuclei.

One of the possible conclusions could be that a photon or an electron could be under the influence of a bunch of surface electrons, which in turn form quasiparticles and cause a quantised deflection of the passing particle.

Why can’t particles be detected in more than one location?

It never has been detected in more than one position (empirical fact) and the reason is that a particle - be this an electron or a photon - is an indivisible particle under such interactions.