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When it comes to the mystical field of quantum physics, I am often told that a particle system, such as an electron, can exist in many states at once and is thus able to occupy many different volumes of space at once. This, however, has confused me ever since I first heard it; the reason? Well, it's primarily due to my belief that regardless of the nature of the system in question, no system should be able to exist in many different states at once.

So now, I will now engage in the act of using my energy to perform the action of asking this very simple question:

When it is said that an object is in many different locations at once, is it actually meant that it has many position vector properties and that during observations of that object, information about only one of those position vectors is able to be accessed at a time?

I noticed that this is a somewhat lengthy question, but I guess that if the answer to it is essential "yes", then I can safely (maybe... maybe?) assume that the whole “a quantum system exists in many states at once before it is observed” is some kind of analogy or something that scientists use to help explain quantum phenomena.

  • Edited, since I figured that I should make the question a little easier to understand.
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closed as too broad by WillO, rob May 19 '18 at 18:43

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Nobody should be saying anything like "a quantum system is in many states at once". State has a perfectly well defined meaning in Quantum mechanics and you can only be in the state you are in. $\endgroup$ – jacob1729 May 19 '18 at 17:56
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    $\begingroup$ When it comes to the mystical field of arithmetic, I am usually told that a number, such as 8, is able to have many values at once. Please explain to me exactly what this means. $\endgroup$ – WillO May 19 '18 at 18:09
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    $\begingroup$ A lot of your concerns are addressed when you consider quantum field theory rather than the nonrelativistic quantum mechanics, but my feeling is that an answer making that connection is beyond the scope of what we can do here. However, if your reading has left you with the impression that quantum mechanics is "mystical," you should consider reading something different. $\endgroup$ – rob May 19 '18 at 18:47
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    $\begingroup$ A quantum system isn't in many states at once. The state of a quantum system can be decomposed in eigenstates of an observables, kind of like your position in space can be decomposed in a linear combination of $x$,$y$ and $z$, the state of a quantum system can be expressed as a linear combination of some particular states that are associated in a physical quantity, for instance position, hence a particle can be in the state $a|x_1\rangle+b|x_2\rangle$ where $|x_1\rangle$ and $|x_2\rangle$ are position eigenstates, but this does not mean the particle is in two states, the state is still one. $\endgroup$ – user2723984 May 19 '18 at 22:17
  • $\begingroup$ @rob This closure feels rather excessive. OP is basically asking whether quantum superpositions can be understood as probabilistic mixtures / hidden-variable theories (to which the answer is, of course, no, but with an opportunity to talk about the reasons why) and that's fairly well scoped for this site. $\endgroup$ – Emilio Pisanty May 19 '18 at 23:09
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The hydrogen atom's electron can be described to have a probable $\left(x,y,z\right)$ position, called an orbital, not an orbit.
$\hspace{50px}$horbital

Each little dot is an electron "caught" , i.e. detected, in a series of measurements of hydrogen atoms. This is a calculation, but an actual experiment has verified the form.

Each electron is measured, and gives one $\left(x,y,z\right)$ point. It is the accumulation of measurements that generates the probability distribution.

To understand probabilities, look at this:
$\hspace{125px}$birthdays.

It does not mean that a child is spread all over the months. The child has a probability to be born according to the statistical curve, and is one point.

Birth probabilities depend on various social relations and conditions. Quantum mechanical probabilities depend on specific potentials and boundary conditions for quantum mechanical equations. Each electron when measured (in analogy with each child born) has a probability of having a specific $\left(x,y,z\right)$ value in the orbital plot above.

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