How can you know an unmeasured quantum particle is in several states at once?

Question

If a quantum particle/system has not been measured/observed yet, how can you know it is in several places/states at the same time?

Answer 1

Weak measurements allow you to find out stuff without causing the collapse of the wavefunction.

In quantum mechanics (and computation & information), weak measurements are a type of quantum measurement that results in an observer obtaining very little information about the system on average, but also disturbs the state very little.

On a side note, I don't believe it's common to say that the body's in several states at once: it's better to say that it's described by a single linear superposition state.

Answer 2

If a quantum particle/system has not been measured/observed yet,

In quantum mechanics models, the only deterministic solutions are the moduli of the wavefunctions , and what these moduli determine is the probability distribution of measuring a particle at (x,y,z,t) or with specific energy momentum fourvector. If you have modeled your system well, that is the only "know" you have.

how can you know it is in several places/states at the same time?

A particle or a system when measured give one instance in the probability distribution, and it will need many measurements to validate the distribution and be sure the model is correct. One measurement will not do it, because the system will be in one of the allowed locations by the predicted probability distribution.

Here is an experiment with a simple system : " one electron at a time scattering on two slits of specific width and distance apart"

Each individual electron materializes at the $(x,y,z_0)$ of the screen at different times from the others. It leaves a footprint of a point particle. It is not spread all over the available phase space. At the top, the footprints look random and countable. Accumulating many electrons illustrates the build up of the probability distribution, and lo, an interference pattern appears. This validates that the electron is a quantum mechanical entity, described by a wavefunction solution of the Dirac equation, and the specific accumulation of points builds up the probability distribution expected from interactions of quantum mechanical entities.

That is the only thing we can "know" of quantum mechanical entities. The mathematics used to model the behavior of quantum mechanical systems should not be taken as describing mass and energy distribution spreads , because experiments show that they do not.(There is no measurement of spread out single electrons).

Answer 3

If a quantum particle/system has not been measured/observed yet, how can you know it is in several places/states at the same time?

That is not a good description of what's going on in quantum theory. In quantum theory measurable quantities have discrete values and if you measure that quantity with enough sensitivity in the right circumstances you can detect that discreteness. For example, if you pass a monochromatic laser beam through dark filters you can reduce the amount of energy in the beam and if you use enough filtering a sensitive enough detector will go off intermittently and will always detect the same energy when it does go off.

Now, if you take this dimmed laser beam and shine it at a pair of slits in an interference experiment and wait for many photons to go through the experiment you will see a pattern of light and dark bars. If you cover up one of the slits you'll see a different pattern of light and dark bars. This means that some places on the detector that was light with one slits is dark with two slits. So something is coming through the second slit to prevent the arrival of photons at that dark location. If you put a detector in the experiment then you will only ever see a photon at one place so the photon isn't splitting into chunks. And whatever is causing the change in pattern is affected by lenses, mirrors etc just as light would be affected. The only account I have seen of what is happening during the experiment claims that there are multiple versions of the photon interacting between the slits and the detectors but we can only directly interact with one version. But this means that the multiple versions of the photon are interacting with lenses, detectors etc that we don't see so all of those objects exist in multiple versions too. In this view reality looks a bit like a collection of parallel universes: this is called the many worlds interpretation. Despite the fact that there is no other explanation of what's happening in single particle interference experiment and many other experiments the MWI is rejected by many physicists for reasons that are unclear.

For more explanation see "The Fabric of Reality" by David Deutsch and

https://arxiv.org/abs/2205.00568

https://www.youtube.com/watch?v=51hikWhM8vE

https://arxiv.org/abs/quant-ph/0104033

https://arxiv.org/abs/0707.2832

Answer 4

This is a crucial question in quantum foundations, but any time you're asking about what's happening when you're not looking, your answer will necessarily be model-dependent. Different approaches to quantum foundations will therefore give you a different answer to your question.

One perspective in which it's not true that a particle is in two places at once is called Bohmian mechanics. In this approach, each particle really is just one classical particle, on one particular trajectory through space and time. Meanwhile, that particle interacts with an invisible "wavefunction" which steers it around, essentially providing each particle information about what is going on elsewhere. In the double-slit experiment, the wavefunction goes through both slits, while each particle only goes through one. The interactions between the particle and the wavefunction then explain the eventual observed interference pattern.

One perspective in which it is true that a particle is in two places at once is the Everettian or Many-Worlds interpretation. In this case, there's no division between things than happen in spacetime (like Bohmian particles) and things that happen in a massive configuration space (like Bohmian wavefunctions). Instead, absolutely everything is in the latter category, even the experimental apparatus and any experimenters. Since each particle is now part of a massive entangled wavefunction, at any moment it's impossible to identify one point in spacetime at which the particle exists (and arguably difficult to make sense of spacetime in the first place). Indeed, even if you think you've measured a particle to be at point A, an Everettian view would insist that the "you" who thinks that the particle is at point A is just part of the bigger reality, and other aspects of the particle will still necessarily also be somewhere else entirely (perhaps as observed by some other version of "you" in the universal wavefunction). So in this case it's absolutely fair to say that each particle is two places at once... and curiously, this conclusion doesn't change upon measurement.

A more conventional view is to read off the standard quantum mathematics and assume that those mathematical quantities represent the underlying reality. To the extent that this is coherent, such a view would take the collapse of the quantum wavefunction literally, in which case you would say that the particle is more than one place at a time until it's measured, at which point it becomes localized. Of course this also happens to track with our knowledge of the particle -- we don't know where it is until we look -- and it also brings in the famous "measurement problem" of somehow finding a way to formally distinguish a measurement from a mere interaction in a non-anthropocentric manner.

So, I'm afraid that there's no scientific consensus as to the answer to your question because there's not yet any consensus in the field of quantum foundations.