Wednesday, August 21, 2013

Is the wavefunction ontological or epistemological?

Part 6: Is the Moon there if we are not looking at it?

What does objective reality mean? Intuitively this is very clear: the world is out there independent of me, it exists “objectively”. But is this in agreement with quantum mechanics and with experimental evidence? Quantum mechanics predicts only the probabilities of experimental outcomes, and Einstein thought this must mean quantum mechanics is incomplete. By now we know quantum mechanics is the entire story so how can we reconcile probabilities with realism? One possible quantum mechanics explanation is the Bohmian interpretation ( Here, particles exists objectively and they are guided by a “quantum potential” allowing them to move in such a way that they recover the predictions of standard quantum mechanics.

But wait a minute; didn’t Bell prove the impossibility of local realism? How can this guiding potential allow the particle to achieve super-classical correlations, especially when one particle can be here and the other one at the other end of the galaxy? Simple: the particles move faster than the speed of light but without being able to carry signals!! No, no, no, unicorns and Santa Claus you may say. What about an electron? If the electron is whisked away it should radiate and we should see this radiation all around us. Also what happens in an atom if the electrons have definite positions? Would this mean the atom is unstable?

Because in part of the radiation problem there are no known generalizations of Bohmian mechanics for relativistic quantum field theory, and very likely there is not possible to obtain one. Also in this interpretation, the atom consists of stationary electrons at a fixed distance. Not only the existence of this particular distance is very strange, but also in general the Bohmian trajectories are known to be “surreal”.

But is there a more formal way to disprove classical realism, even non-local one? We need to start by the definition of realism. The best place to start is from EPR’s reality criterion:

 “If without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of reality corresponding to that quantity”

So for example, if I measure the position of a particle and I find a definite value, measuring again in quick succession would yield the same value because “the particle is there”. The reverse implication is given by EPR realism: if I predict with certainty the position of the particle (and any measurement would confirm my prediction) then the particle must really be there.

We can now prove that EPR’s reality criterion is actually inconsistent with quantum mechanics, and to do this we will reason very similarly with Bell from his famous theorem.

The gist is as follows: we will consider a quantum system for which we can predict with certainty both an outcome and a correlation. But given one measurement, a subsequent measurement (in a different configuration) must respect a quantum mechanics rule and this can be shown to destroy the correlation. In other words, the law of subsequent measurements, the certainty of the outcome and the certainty of the correlations are incompatible.  So which one should be sacrificed? The law of subsequent measurements is iron-clad and validated by experiments. Quantum correlations are indisputable also. What remains is realism. Late Asher Peres use to say: “unperformed experiments have no results”. But this is stronger. We may say: “unperformed experiments for which the outcome can be predicted with certainty have no results”.

The technical description of the argument is presented in

Basically the argument is as follows:

Start with a Bell singlet state: (|+>|-> - |->|+>) and have Alice and Bob measure this on the vertical axis: one will get spin up and the other one spin down. Supposing the spins do exists independent of measurement, then they must be oriented on vertical axis (we don’t know how for each person) to achieve perfect anti-correlation. [Suppose they are oriented in opposite directions, randomly distributed. Then the measurement correlation is no longer minus the cosine of the angle between the measurement axis-as predicted by quantum mechanics and validated by experiments, but minus 1/3 of the cosine of the angle between the measurement axis]. This may look conspiratorial (after all we can select any other axis to the same end), but it is an experimental fact.

Because we can predict with certainty the spin alignment direction, the alignment direction must really exist by EPR reality criterion.

But now we can ask if this direction is compatible with Bell correlation. When measurement directions for Alice and Bob are orthogonal, the total correlation is zero. Is the vertical axis correlation compatible with this correlation? The answer is no by an impossible inequality: ¼=0.25 < sin^2(π/8) ≈ 0.1464 (see

There is still a way out however: remember Bohmian mechanics and non-local realism. Suppose the axis were in a place compatible with the correlation, but the very act of the intermediate measurement made the axis instantaneously realign. Fortunately relativity comes to the rescue and proves this is impossible. Why? Because if Alice and Bob are spacelike separated in a reference frame Alice does her measurement first and realigns the axis on her measurement direction, and in another Bob does his measurement first and realigns the axis on his direction. And the spin direction cannot have two values at the same time. The only way out is to conclude EPR realism is false.

But what about the Moon then? The Moon is there even when we don’t look at it because of decoherence: the moon is “observed” by the solar wind, cosmic radiation, etc, so someone is constantly looking at it!

And what about Bohmian mechanics? Would this argument not disprove this interpretation as well? Nope, because ve…eery conveniently, spin is not (cannot be) treated classically in this interpretation. 

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