Is this system a superposition?

[KDPhysics]

TL;DR Summary

If I randomly paint three objects without looking at them, are these objects in a superposition?

Suppose a blind man builds a machine that paints three apples with three colors, either red, blue or green. Once the machine has done this, are the three apples in the following superposition:

or is the wavefunction just one of

It feels like because the man is blind, the apples should be in a superposition as any measurement (say by asking someone else to check the colour of the apple) will lead to the wavefunction collapsing to one of the states in the superposition. However, on the other hand it feels like because the machine definitely assigns a colour to each apple, the wave-function should not be in a superposition. So which is it?

 

[hilbert2]

If the machine decides the colors of the apples from the results of some quantum measurement, e.g. the direction an alpha particle is emitted to from a radioactive sample, then it's similar to the Schrödinger's cat problem, but the person simply not seeing what he's doing doesn't cause any quantum randomness.

 

[KDPhysics]

So the wave function is not a superposition, it's just that the blind man can't perform the necessary measurements?

 

[PeroK]

Summary:: If I randomly paint three objects without looking at them, are these objects in a superposition?

Suppose a blind man builds a machine that paints three apples with three colors, either red, blue or green. Once the machine has done this, are the three apples in the following superposition:

View attachment 284559
or is the wavefunction just one of View attachment 284560

It feels like because the man is blind, the apples should be in a superposition as any measurement (say by asking someone else to check the colour of the apple) will lead to the wavefunction collapsing to one of the states in the superposition. However, on the other hand it feels like because the machine definitely assigns a colour to each apple, the wave-function should not be in a superposition. So which is it?

The apple is either red, blue or green. It's not in a superposition of those colours in any quantum-mechanical sense of the word.

 

[KDPhysics]

But couldn't you apply that logic to an electron's spin as well? It's either spin up or spin down.

 

[PeroK]

But couldn't you apply that logic to an electron's spin as well? It's either spin up or spin down.

An electron is an elementary particle; an apple isn't.

 

[KDPhysics]

just because an apple isn't an elementary particle doesn't mean that it can't be in a superposition right?

 

[KDPhysics]

I guess my question is what makes something capable of being in a superposition, and other things not?

 

[Vanadium 50]

@KDPhysics, it appears you have one answer in mind. So why did you ask the question?

 

[Nugatory]

or is the wavefunction just one of

There is a more general formalism, the density matrix, that can be used to describe both superpositions ("the apple has no definite color unlesss and until we measure it") and incomplete information situations ("the apple is red, green, or blue but we don't which because we haven't looked yet") such as the one you have described.

 

[KDPhysics]

There is a more general formalism, the density matrix, that can be used to describe both superpositions ("the apple has no definite color unlesss and until we measure it") and incomplete information situations ("the apple is red, green, or blue but we don't which because we haven't looked yet") such as the one you have described.

Thank you. So this case would fall under "incomplete information situations" rather than superpositions as you have described?

 

[PeroK]

just because an apple isn't an elementary particle doesn't mean that it can't be in a superposition right?

It's not in a superposition of different colour states just because you don't know which colour it is. Painting apples is a macroscopic process involving so many particles that the QM nature of each elementary particle is lost. The apple behaves as a sum of its parts, not like each of its parts.

 

[KDPhysics]

It's not in a superposition of different colour states just because you don't know which colour it is. Painting apples is a macroscopic process involving so many particles that the QM nature of each elementary particle is lost. The apple behaves as a sum of its parts, not like each of its parts.

Thank you. Suppose then that instead of colouring apples i consider randomly assigning a spin to an electron (here surely quantum effects are coherent).

If I don't observe the spin of the electron, then does this mean that the electron is in a definite spin state, but I just haven't performed a measurement to confirm this? It seems paradoxical, how can the electron be in a definite spin state if I have no way of confirming this?

EDIT: is the main difference due to the fact that if I do eventually measure the spin, it will always yield one value, while if it is in a superposition the results will vary?

 

[PeterDonis]

Suppose then that instead of colouring apples i consider randomly assigning a spin to an electron

How would you do that? You can't just "assign" a spin to an electron the way you paint an apple, or any other macroscopic object.

If I don't observe the spin of the electron, then does this mean that the electron is in a definite spin state, but I just haven't performed a measurement to confirm this? It seems paradoxical, how can the electron be in a definite spin state if I have no way of confirming this?

You need to focus on how the electron is prepared as well as on how it is measured. What process prepares the electrons, and what state does it produce? Then you look at what observable you intend to measure on the electrons (spin? position? energy?), and whether the state produced by the preparation process is an eigenstate of that observable or not. That is how you figure out whether the electrons, between preparation and measurement, are in a superposition or not.

In the case of the apple-painting in your OP, the preparation process puts a definite color on each apple; and since color is the observable you are interested in, the process obviously prepares eigenstates of that observable, so there is no superposition. The fact that the blind man can't actually see the colors is irrelevant; you've stipulated that color is the observable of interest so that's how you evaluate the states produced by the preparation process.

More generally, any preparation process for macroscopic objects that only involves macroscopic processes, like painting things, won't be able to prepare states that aren't eigenstates of macroscopic observables. This is why classical physics works so well for macroscopic objects. Note that Schrodinger, in his "cat" thought experiment, had to invoke a microscopic quantum process, radioactive decay, in order to get his cat into a superposition of "alive" and "dead" states.

In the case of electrons, there are plenty of processes that can prepare electrons in states that aren't eigenstates of spin, or position, or energy, so those processes will prepare superpositions. But there are also processes that prepare electrons in states that are eigenstates of such observables, so those processes won't prepare superpositions. Similar remarks apply to any quantum particles.

 

[KDPhysics]

So the so-called act of measurement in the OP is the painting process, not the blind man somehow "measuring" the colour of the apple? This seems to make a lot more sense now.

 

[PeterDonis]

the so-called act of measurement in the OP is the painting process

Strictly speaking, that's the preparation, not the measurement. But in fact preparation and measurement are very similar in QM; a measurement can also count as a preparation for future measurements.

not the blind man somehow "measuring" the colour of the apple?

It's worth noting that, even though the man is blind, the color of the apple has many other effects; for example, the way the apple reflects photons. Those effects count as "measurement" as far as QM is concerned (the more technical way of putting it is that they cause decoherence). In other words, the apple's environment "measures" its color (and all of its other macroscopic properties, like size, location, weight, etc.) even though the blind man can't. And for macroscopic systems this is going on all the time. That's another reason why classical physics works so well for macroscopic objects.

 

[KDPhysics]

Strictly speaking, that's the preparation, not the measurement. But in fact preparation and measurement are very similar in QM; a measurement can also count as a preparation for future measurements.It's worth noting that, even though the man is blind, the color of the apple has many other effects; for example, the way the apple reflects photons. Those effects count as "measurement" as far as QM is concerned (the more technical way of putting it is that they cause decoherence). In other words, the apple's environment "measures" its color (and all of its other macroscopic properties, like size, location, weight, etc.) even though the blind man can't. And for macroscopic systems this is going on all the time. That's another reason why classical physics works so well for macroscopic objects.

Thanks, very clear explanation!

 

[PeroK]

Thank you. Suppose then that instead of colouring apples i consider randomly assigning a spin to an electron (here surely quantum effects are coherent).

If I don't observe the spin of the electron, then does this mean that the electron is in a definite spin state, but I just haven't performed a measurement to confirm this? It seems paradoxical, how can the electron be in a definite spin state if I have no way of confirming this?

EDIT: is the main difference due to the fact that if I do eventually measure the spin, it will always yield one value, while if it is in a superposition the results will vary?

First, "definite state" and "superposition" are not mutually exclusive. If we stick with an electron, then it may be in the following spin state: $$\frac 1 {\sqrt 2}(\uparrow + \downarrow)$$
How we know that the electron is in that state is a different question. The key point is that it has a definite state, which is a superposition of spin up and spin down.

In general, the laws of QM are statistical in nature and you must do a large number of experiments with an ensemble of identically prepared particles. In the double-slit expriment, for example, the particle makes a single dot on the screen. It's only when a large number of identically prepared particles is fired at the slits do you see an interference pattern or not.

Finally, in general it makes no sense to try to apply QM directly to objects such as apples. If apples behaved quantum-mechanically, we would notice.

 

[Nugatory]

Thank you. Suppose then that instead of colouring apples i consider randomly assigning a spin to an electron (here surely quantum effects are coherent).

Whether that creates a coherent superpostion of spin states depends on how you do that random assignment.

If I don't observe the spin of the electron, then does this mean that the electron is in a definite spin state, but I just haven't performed a measurement to confirm this? It seems paradoxical, how can the electron be in a definite spin state if I have no way of confirming this?

Some of the problem here is in the English language description we are using. The statement "The electron is in the spin-up state along the vertical axis" sounds like we're saying that electron has a definite spin, namely "up", and that is not what it means. It means "It is meaningless to ascribe any spin to the electron because we have not measured it, but we have prepared the electron in such a way that if we were to measure its spin along the vertical axis the result would be spin-up with 100% probability". The latter statement works whether we make the measurement or not, and can be verified by using the same preparation procedure on a large number of electrons and measuring enough of them to come up with a satisfactory statistical certainty.

It is worth noting that the spin-up state on the vertical axis is also a superposition. It is, for example, a superposition of spin-up and spin-down on the horizontal axis; it is also a superposition (with different weights) of spin-up and spin-down along any other axis. That is, measurement doesn't change the state from superposition to non-superposition; it changes it from one state to another state.

 

[PeterDonis]

The statement "The electron is in the spin-up state along the vertical axis" sounds like we're saying that electron has a definite spin, namely "up", and that is not what it means. It means "It is meaningless to ascribe any spin to the electron because we have not measured it, but we have prepared the electron in such a way that if we were to measure its spin along the vertical axis the result would be spin-up with 100% probability".

Actually, one way (and in fact the simplest way) to prepare an electron in the state you describe is to measure its spin along the vertical axis and get an "up" result. In other words, "fire a beam of electrons into a spin measuring device aligned along the vertical axis, and take the electrons that come out in the up beam" is not just a measurement process, it is a preparation process that outputs electrons in the spin-up state along the vertical axis.

The reason we need to be careful about saying that this state has a "definite spin" is that if we measure the spin of an electron in this state about any other axis, besides vertical, we won't always get the same result; we will get "up" with some probability $p$, or "down" with probability $1 - p$, and $p$ will depend on the angle between the axis we are measuring spin about and the vertical axis. (Your note that the spin-up state about the vertical axis is also a superposition is getting at the same point.)

 

[Dali]

But couldn't you apply that logic to an electron's spin as well? It's either spin up or spin down.

This is a common, and understandable, confusion most people have when hearing about quantum superpositions. When people hear about Schrödingers cat for example, it is not at all clear why, or if, there is any difference between just not knowing and being "in a superposition".

The difference comes down to if it is possible to see/measure any interference effects between the two states. In a classical picture a cat is either dead or alive, a particle spins in one direction or another, an apple is either red, green or blue etc. And in a classical world that would be true regardless if we or anyone knows what state it is in or not.

But in the quantum would (ie our reality!) there are strange situations where we can measure interference effects that could not arise if that classical assumption was correct. For example, assuming an electron does go though one slit or the other can never yield the interference pattern one sees in the double-slit experiment. This fact is further developed in Bell's theorem that proves that any objective theory (where things have properties whether or not they are measured) have to be non-local. Otherwise they can never yield the results that are confirmed over and over again in modern experiments with entangled pairs of particles.

So - no, it is not possible to assume that electrons always are spin up or spin down. And there is a big difference between not knowing what color an apple is, and having an apple being in a superposition of different colors!

 

[hilbert2]

I think it's possible to construct a hypothetical quantum state where an apple is in a superposition of being red and green, but you can't prepare that kind of state in practice without it collapsing immediately due to decoherence. You can't control every particle of a macroscopic system accurately enough.

 

[PeterDonis]

I think it's possible to construct a hypothetical quantum state where an apple is in a superposition of being red and green

Sure, just let the choice of which color to paint the apple be controlled by some process that involves quantum uncertainty, such as the decay or lack of decay of a radioactive atom (as in the Schrodinger's cat experiment). But, as you note, any such state will quickly decohere because of the huge number of degrees of freedom involved and our inability to control them all. (The same applies to the Schrodinger's cat thought experiment; the cat will decohere itself almost immediately regardless of how long it takes before the experimenter opens the box to look at it.)

 

[EPR]

Summary:: If I randomly paint three objects without looking at them, are these objects in a superposition?

No. One of the reasons is that macroscopic 'randomness'(inabiility to know perfectly deterministic processes) is different from quantum randomness(unknowable in principle until measurement non-deterministic processes).

Your apples, each of them had a very definite color from the beginning. QM doesn't apply in any obvious way to your scenario.

 

[Heidi]

painting is a physical process. you have to describe all the details if you want to know if at the end of the process you have a superposition or not. Give the interaction hamiltonian and you will have your answer!

 

[EPR]

This question is similar to the question if a pregnant woman's baby is in a superposition of being a girl and a boy.