# Is the concept of superpositions saying that the electron is actually in many states?

Basically when I read about it, yes. But I don't completely get why. Let me explain:

If I throw a ball into a room and don't look, I would surely say that the ball is at one point in this room. Maybe I don't know which, maybe I can give probabilities of it being in different areas. But I wouldn't claim that it is at multiple positions.

Same goes for Schrödingers cat, I would never claim that the cat is dead AND alive. Why don't we say that it is either dead or alive, and we don't know which it is? I know it's just a thought experiment, but it doesn't make sense to me in the macroscopic world. Also, the cat itself would be sentient now that I think about it, so wouldn't it observe itself in some way?

Now come to electrons: Which one is correct?

• The electron is in a superposition between infinite positions, until we measure it, then it is a particle in one position
• The electron is at one position, but we only have a probabilistic idea which position it is in until we measure it

If it is the second case, I assume that the differnce is that the cat is macroscopic, and the electron not. But still, technically both the quantum and the classic theory can explain me why the cat ended up in it's state - the quantum one just seems a bit weird.

What is different with the electron? Why does the explanation saying "The electron is at one position, but we only have a probabilistic idea which position it is in" not also explain the world correctly? Where does it break down?

• The super short answer is that it's the first option for electrons, and the second one for cats. The relevant concepts are hidden variables, Bell's theorem, and decoherence. – Javier Jul 10 at 22:16
• If I ask my friends to name their favorite movies, they have no trouble answering. But If I ask an electron to name its favorite movie, I get no response. Is that because a) the electron actually has no favorite movie or b) the electron has a favorite movie, but I can have only a probabalistic notion which movie it is? And more importantly: Does a) somehow strike you as so "weird" that you want to replace it with b)? – WillO Jul 10 at 23:09
• Be aware that, due to nature of the state space, any state can be expressed as a superposition of other states. For example, if the electron state is one of definite position, that state can be written as a superposition of, e.g., energy eigenstates or momentum eigenstates. Measurement 'collapses' the state to an eigenstate of the measured observable but that eigenstate is generally a superposition of eigenstates of other observables. – Alfred Centauri Jul 10 at 23:42
• Also, note that the question of "Which one is correct?" is essentially the question of "which interpretation is correct?". According to Bohmian mechanics, the quantum particle (beable) always has a definite location and velocity whereas the 'standard' interpretation is that, generally, the quantum particle does not have a definite value for an observable (position, energy, momentum, etc.) just before measurement. – Alfred Centauri Jul 10 at 23:48

## 3 Answers

Is the concept of superpositions saying that the electron is actually in many states?

Using the Copenhagen interpretation, no. The electron is in a single state $$|\Psi\rangle$$ whose time evolution is determined (usually) by the Schrodinger equation. This state can be expressed as a superposition of basis states depending on which basis you choose to express $$|\Psi\rangle$$ in, but this superposition does not mean that the electron is simultaneously in all the states in the superposition. The superposition tells us which basis states we could find the electron to be in upon measurement as well as the probability of observing the election to be in that state upon measurement. Before measurement, the state is the superposition. After measurement the state is one of the states that was in the original superposition (at which point the new state evolves according to the Schrodinger equation).

Anything saying "the cat is both dead and alive" or "the electron is in all locations at once" is just a pop-sci description to help the general public get a feel for this stuff, but when you dig deeper you should abandon this notion.

Why does the explanation saying "The electron is at one position, but we only have a probabilistic idea which position it is in not also explain the world correctly?

The probabilities involved with measurement of a quantum system are not like the usual usage of probability where it's due to our limited knowledge of the system. We can know everything about our system (state before measurement), yet there is no way to determine what the outcome of a single measurement will be. Contrast this with something like a classical coin flip, where if we knew everything about the system (initial conditions, forces acting on the coin, etc.) we could then know what the outcome of the flip would be every single time.

The questions "Is the cat alive or dead before we open the box?", or "Where is the electron before measuring its position?" are meaningless questions (according to the Copenhagen interpretation). The states of these systems are superpositions, and that's all we can say before performing a measurement.

The difficulty of accepting superposition has to do with the fact that you have a certain idea in your head, based on a lifetime of observing the physical world around you, about how to model reality, and you are applying it to the system of the ball in the room. But quantum theory models reality in a different - and much more complicated - way than classical physics. The space of states that a quantum system can be in is simply much bigger and richer than the space of states for a classical system. That is why we need superposition.

When you talk about putting a ball in a room, you are essentially imagining that there is a computer program running somewhere that simulates the evolution of this physical system over time, and that the current state of the program is encoded in a variable that contains information of the sort “the ball is in position $$(1,0.8,2.3)$$ in the coordinate system of the room, and is at rest”. If one neglects complications like the air in the room and the orientation and composition of the ball, the state of the system can be described with a very small number of real-valued parameters. The computer program requires very little “memory” to perform the calculation of what is going to happen.

In quantum theory, just to describe the state of the simplest quantum system consisting of a single electron in a “room”, we need an infinite “computer memory” that contains infinitely many parameters. Essentially, we have one variable to describe the “amplitude” (an arbitrary word that goes back to the historical idea of particle-wave duality) for the particle to “be” (whatever that means) in any position in the room - simultaneously! (Also, each of the amplitudes is a complex number, so is encoded by two real parameters.) Thus, a description of the state of the system might look like

the particle has an amplitude of $$0.3+0.5 \sqrt{-1}$$ to be in position $$(1,0.8,2.3)$$ in the coordinate system of the room,

and an amplitude of $$-5.6+0.187 \sqrt{-1}$$ to be in position $$(3,4,5)$$,

and an amplitude of $$123-43 \sqrt{-1}$$ to be in position $$(7,6.5,4)$$,

... (etc)

Now, quantum mechanics gives us a tool that says how the computer program “runs” when given the initial value of this “memory”. The basic version of this tool is called Schrodinger’s equation. And it’s important that Schrodinger’s equation really does require all that information about this complicated “superposition of states” (which is merely the technical name used to describe this large set of numbers encoding the state of the system) to compute how the system is going to evolve over time. And we believe that the tool is correct because we have tested it in a huge number of different situations and confirmed that our understanding is correct (up to some deep level involving high energy elementary particles at which point we are no longer sure we understand the rules completely).

If you try to add in the assumption that the system must be in a “pure” state at all times, and model our lack of knowledge of which pure state it is in in terms of probabilities, what breaks down is that we have to discard Schrodinger’s equation and replace it with some other tool that can work with that initial probabilistic data and make predictions that are in agreement with reality. No one has found such a tool (though I understand that Bohmian mechanics is claimed by some people to be such a tool, but it is mathematically equivalent to the standard interpretation and has problematic aspects of its own that cause it to not be very accepted among mainstream physicists). So, we really do believe that there’s no way around accepting that the electron is in a superposition of states.

The most famous (and arguably, simplest) example that illustrates why superposition is an essential feature of reality is the double slit experiment, discussed in Wikipedia, Feynman Lectures, various questions on physics.se, and many other places.

The simple answer comes from the double slit experiment. https://en.m.wikipedia.org/wiki/Double-slit_experiment

The experiment still creates a wave pattern when electrons (or even atoms) are fired through one at a time. The only way this is possible is if a single atom / electron exists in 2 physical places at once, then interferes with itself when it goes through both slits at the same time. When a passive sensor is placed at one slit, the superposition collapses, and a pattern of 2 simple lines forms instead. The math and theory behind this gets messy, but the general idea is that a particle can actually be in multiple places at the same time when not interacting with another particle. This is a true superposition, not a bouncing ball.

• The only way this is possible is if a single atom / electron exists in 2 physical places at once, then interferes with itself when it goes through both slits at the same time. - I absolutely hate this pop-sci description of the double slit experiment. – Aaron Stevens Jul 11 at 3:20
• the general idea is that a particle can actually be in multiple places at the same time - this one as well – Aaron Stevens Jul 11 at 3:21
• What @AaronStevens states as fact is an opinion, not fact. There are very good reasons to believe that a quantum mechanical particle's wavefunction in the double-slit experiment passes through both slits. A key principle behind quantum computers is that each qbit can have branching trajectories in state space. – S. McGrew Jul 11 at 4:33
• @S.McGrew What you talk about is not what I'm talking about. If your are referring to path integrals, I am fine with that idea. – Aaron Stevens Jul 11 at 4:40
• @S.McGrew What did I even state as fact? – Aaron Stevens Jul 11 at 4:45