Where is an electron "physically" in superposition?

Question

According to simple Google search:

When an electron is in superposition, its different states can be thought of as separate outcomes, each with a particular probability of being observed. An electron might be said to be in a superposition of two different velocities or in two places at once.

I know that the electron is described by a probability distribution (a "cloud of possibilities"). But this is mathematically true. Is an electron literally (physically) at different locations at a given time? If no, is randomness truly fundamental to an electron? If yes, what does it physically mean? Does an electron stretches itself or what?

Answer 1

The question "where is an electron ?" only arises because we think of the electron as a point particle. But this is also a mathematical model of an electron, and it is a model that is only accurate when we measure the electron in such a way as to pin down its position. In between such measurements the electron behaves as a "cloud of possibilities" (called a wave function in technical terms) which evolves in accordance with the Schrodinger wave equation. And a wave function has no location. So asking "where is an electron between measurements ?" is like asking "what colour is an electron ?" i.e. it is not a meaningful question.

Answer 2

As @gandalf61 pointed out, some questions about physical properties of quantum systems could be meaningless. However, some of them could have a meaning if we provide a context.

According to Bohr viewpoint about quantum mechanics (see for example, his answer for EPR paradox), we could talk about physical properties if, and only if, we provide the experimental context, i.e., the measuring apparatus settled for measuring it. So, to talk about the electron position, we should provide what is the experiment that is being realized to measure it.

Once you measure the electron's position, you could ask: "what is the electron's position?" And your question have a well defined and objective answer: the result of your measurement. But without its context, it is meaningless to talk about it.

Bohr's point of view influenced many authors in his time and after him, creating what we call the Copenhagen interpretation todays. The idea that a system should have properties by its own, independently of the measurement apparatus or any other thing, is the hypothesis of physical realism. Until now, there is no experiment capable to confirm or reject the realism hypothesis; the strongest result in this direction is the Bell theorem, which proves that quantum mechanics is incompatible with Local Realistic models, i.e., models that satisfy Locality and Realism jointly.

Answer 3

1. You are probably aware that there are the so-called Interpretations of quantum mechanics. One's preference for one or the other is largely considered philosophical. That's because they make identical predictions for experimental outcomes.

a. Several interpretations say that electrons are point particles with definite positions at all times. Bohmian Mechanics is one such, it claims particles have definite positions at all times. Any wave-like appearance is simple an expression of our lack of knowledge.

b. On the other hand: the usual more orthodox interpretation (sometimes labeled "Copenhagen") of QM often refers to the complementary wave and particle natures of particles. Note that these descriptions are not entirely mutually exclusive: you can dial the descriptions to be something like 50% wave and 50% particle at will. Generally, the Heisenberg Uncertainty Principle (HUP) provides a precise expression of that trade-off.

2. There are a number of physical experiments that demonstrate that an electron can be in two places at once. This demonstration (or proof) depends on some simple assumptions that in turn go back to the Interpretation one adopts. So what I say next is really an expression of some basic ideas, but ones everyone might not completely agree with. I assume you have heard of Feynman's path integral ideas. In that, particles do not move from point A to point B in a single path. Instead, all possible paths contribute to the predicted results of experiments. They sum, and can interfere both constructively and destructively due to phase effects.

a. The Double Slit Experiment (DSE) is an example of this. A particle passing through 2 slits exhibits self-interference and creates a characteristic pattern. That pattern is inconsistent with the particle going exclusively through one slit or the other.

b. Another example is reflection of a beam of light on a mirror at (say) 45 degrees. If the light only took a single path, that would imply an exact single point of reflection. But in actual experiments, you can etch small gratings on the mirror at precise spots away from that exact single point. The etchings prevent any potential reflection at those points. Preventing reflection at points should - if anything - decrease the light beam's intensity. And yet, in contradiction to "common sense": the light beam gets brighter.

So the point of all this: There is certainly evidence to convince us that particles such as electrons and photons are in some senses in 2 or more places at once. On the other hand, there are philosophical considerations (assumptions which are part of your chosen Interpretation) that might lead you to reject the conclusion implied by the evidence. That is true even if you don't intend to adopt one Interpretation over another.

Personally, I simply picture the quantum particle according to the setup of the experiment. If it is more of a particle-like experiment, it's a particle. If it is more of a wave-like experiment, it's a wave; has no single location; and takes many paths. Neither view is strictly more correct than the other in all situations. But I would definitely label it as "physical", because you can demonstrate the predicted effects in physical experiments.

Answer 4

An electron can only be measured at one place at the time. Once it is measured somewhere, the wavefunction collapses so the probability density is re-centered about this somewhere.

Before measurement the electron can have non-localized wavefunctions yielding more than one peak in the probability density. One then colloquially states that the electron is at two (or more) places, although it is never measured at but a single place: you have only one position detector that clicks, not 2.

Answer 5

The only way to answer the question of "where" something is, is to measure its position. If the electron is in state corresponding to a superposition over different possible positions, then we have not measured its position. Therefore, quantum mechanics does not answer the question of "where" an electron is during a superposition. All we can say is that we are more likely to find the electron in some places than others, if we look.

Most working physicists have just learned to accept that there is no point asking a question that can't be answered experimentally even in principle, so have accepted that "where the electron is during a superposition" is just not a question we should ask. Some philosophers argue that there must be an answer, but no one has come up with a compelling universally agreed upon solution.

Therefore, I would say that the correct response to your question is that there is no scientific answer. It's just not a meaningful scientific question. You seem shocked by this, which is a quite common response, and means you've understood what quantum mechanics is saying. But, there's not much more comfort anyone here can give you, this is really how Nature seems to work, as far as humans have been able to figure out.

The reason we shouldn't say "an electron is in two positions at once" is because if we start with one electron and measure its position, we only ever find it in one place. We never find two electrons in two different places, we never find a stretched out electron, we never find half an electron.

Answer 6

According to simple Google search:

Google's AI generated answer is worth about as much as you paid for it.

I know that the electron is described by a probability distribution (a "cloud of possibilities").

The probability distribution describes what would happen, if you were able to repeat the same experiment with an identically prepared electron many times.

For example, you have probably heard that (matter wave) interference in the electron double slit experiment can cause a diffraction pattern to emerge. The amplitude of the diffraction pattern is the wave function describing the system. But you will never see this pattern (which is the square of the wave function) unless you fire thousands or millions of electrons at the double slit and record the outcome of each measurement.

But this is mathematically true. Is an electron literally (physically) at different locations at a given time?

A single electron is never measured to be at different locations at the same time. Measurement is a irreversible process and is not described by the evolution of the wave function

If no, is randomness truly fundamental to an electron?

There is at least some aspect of "randomness" that is seemingly fundamental to our best method of understanding how an electron does electron things (i.e., quantum mechanics).

Does an electron stretches itself or what?

No.