Quantum Physics: Are entangled electrons in absolute states?

Question

I was having a discussion about quantum physics with a friend, and we came to realise that we perceived the same situation in two very different ways. After searching online, we still weren't able to come to a conclusion on who is correct. Here is the situation:

Lets say we have two electrons that are quantum entangled, such that the spin of electron A is opposite to the spin of electron B.

You then measure the spin of electron A, and find it to be up spin.

My interpretation:

• By observing electron A, you improve upon your knowledge about the second one. To someone who knows the spin of A, they can deduce the spin of B. To someone who doesn't know the spin of A, they have a 50-50 chance of guessing correctly. The entire time, ever since they were entangled, electron A was spin up and B was spin down. Simply no one knew it yet.

Their interpretation:

• By observing electron A, you physically change the state of electron B. When you observed that A was spin up, electron B physically changed from being undetermined to become spin down, whereas before neither was individually a definite state, but in some combined state that exists in the tensor product space of A and B.

So my overall question: Whose interpretation is correct?

Are the electrons in an absolute state of having either up or down spin from the moment of being quantum entangled and we simply do not yet have enough information to know (until we observe A), or does observing electron A's spin physically change the spin of electron B, such that the results may have been different if electron B was measured first?

Answer 1

In my view, both interpretations are incorrect (contradictory with the usual interpretations of QM). Before measurement the system of two electrons is in a superposition of $|\uparrow\downarrow\rangle$ and $|\downarrow\uparrow\rangle$. At that point, it doesn't really make sense to say that "electron $B$ is in a state", even undefinite. Measurement doesn't act on electron $B$, it acts on the entangled system of $2$ particles. After the measurement, the state of the $2$-particle system is un-entangled, so it makes sense to say "electron $A/B$ is in the state up/down".

• The first interpretation is incorrect : the spin of $A$ is not defined before measurement. The act of measurement forces the system into a state in which the spin of $A$ has a definite value.

• The second interpretation is incorrect as well : When you observe $A$ in the state "up", you acted physically on the whole system of $2$ particles. You didn't "change the state of $B$", since the state of $B$ was not defined before measurement

Answer 2

There is no universally "correct" interpretation of what a measurement in quantum mechanics "really does" or what the quantum states "really mean". This is the measurement problem, and the various attempts to resolve it at are the different quantum interpretations. Crucially, these interpretations affect only how we think - or rather, tell stories - about quantum mechanics, they do not affect what we predict for the results of measurements. As such, they are metaphysical beliefs rather than integral parts of the physical formalism.

Your interpretation is that of a hidden variable theory - underlying the probabilistic notions of states of the ordinary formalism of quantum mechanics is a theory where all observables really do have well-defined quantities. Bell's theorem tells us that any such theory is necessarily non-local, i.e. must involve interactions that can affect the whole universe instantaneously. Note that this means that such interpretations, while perhaps at first glance somewhat easier to swallow, will likely involve other scenarios where they run counter to our usual conceptions of causality.

Your friend's interpretation is closer to how one would often phrase interpretations with instantaneous wave-function collapse. Measurement changes the state of the things being measured. Note that this in itself does not lead to issues with locality due to the no-communication theorem - no information can be transmitted only by measuring entangled states.

Answer 3

Your discussion here closely mirrors early discussions by Einstein, Bohr, and others around the nature of quantum mechanics and how to interpret it. I hesitate to declare you or your friend more "correct" here, since there are elements of your interpretation that I think many would agree with.

Your idea sounds like a hidden-variable theory, where a particle's physically observable properties exist prior to our measurement and the act of measurement merely reveals them to us. This is I think an extremely natural and intuitive reaction to a description of quantum entanglement, so much so that it was explored quite thoroughly (most famously the EPR paper). John Bell later showed that many such hidden-variable theories are not merely alternate interpretations but are incompatible with quantum theory, and subsequent experimental confirmations of Bell's theorem seemed to finish brushing hidden-variable theories into the dustbin of physics history, although there are definitely versions of it still around to some degree.

Your friend's interpretation I think has the correct attitude on the indeterminacy prior to measurement being part of the physical nature of the system, but there is some issue with the characterization of the collapse of the wavefunction of one electron actively causing the other to collapse in a complementary way; this violates the principle of locality and is the very "spooky action at a distance" that was the thrust of the EPR experiment. This is where I think elements of your interpretation have value, in that the measurement of the one particle doesn't physically act on the other and merely changes our knowledge about its state. See this excellent answer for a better explanation than I could give.

Answer 4

When we say that a pair of particles are entangled, we mean that their joint state cannot be expressed as a product of single particle states; i.e. there is not a separate state of $A$ and state of $B$. For the case of a pair of spin-$\frac12$ particles with opposite spins, we can say that they are in the spin state $\frac{1}{\sqrt{2}}(\lvert\uparrow\downarrow\rangle-\lvert\downarrow\uparrow\rangle)$. Note that this cannot be expressed as a product of single particle states. $$\frac{1}{\sqrt{2}}(\lvert\uparrow\downarrow\rangle-\lvert\downarrow\uparrow\rangle) \ne (\alpha\lvert\uparrow\rangle+\beta\lvert\downarrow\rangle)_A(\gamma\lvert\uparrow\rangle+\delta\lvert\downarrow\rangle)_B\quad\forall\alpha,\beta,\gamma,\delta$$

In this state, the particles do not have definite spins, so your interpretation is incorrect. If they did have definite spins, such as in the state $\lvert\uparrow\downarrow\rangle$, they would not actually be entangled, since $\lvert\uparrow\downarrow\rangle=\lvert\uparrow\rangle_A\lvert\downarrow\rangle_B$. Your friend is correct that measuring the spin of $A$ does change the state, but it cannot change the "state of $B$," since there is no separate state for $B$. Instead, the measurement changes the state of the system consisting of $A$ and $B$. If you measure the spin of $A$ to be up, then the system transitions to the state $\lvert\uparrow\downarrow\rangle$, meaning that you would measure the spin of $B$ to be down. While this may seem like you changed the spin of $B$, it doesn't really make sense to say that, since that implies that $B$ was in some spin state $\gamma\lvert\uparrow\rangle+\delta\lvert\downarrow\rangle$ prior to the measurement, which we know to not be the case.

Answer 5

RulerOfTheWorld,

Both interpretations are possible, yet the second violates the principle of locality , since the effect of A on B is instantaneous. Therefore, your first interpretation is most likely the correct one since it is in agreement with the rest of physics, like relativity.

Answer 6

I read that you can practically force a state BEFORE a measurement with the use of strong magnets. 50/50 becomes something akin to barrier tunneling almost 100%. The polarity of the magnet is the bias for "Up" or "Down"