Many-Worlds and locality

Commenter Amanurea pointed out that the Many-Worlds Interpretation of quantum mechanics doesn’t require spooky at action at a distance even with locality. I didn’t realize MWI could be a local theory and yet produce violations of Bell’s Inequality as Nature seems to do. I’ve been thinking about this for a bit, and I think I understand it now. A local MWI is such a delightful thing I thought I’d write up a post about my new understanding. Brickbats and corrections welcomed.

The Many Worlds Interpretation views Objective Reality as a many branched tree in which each possible quantum event occurs! Instead of having a wavefunction collapse, quantum decoherence provides the appearance of a wavefunction collapse, but no collapse actually occurs. In MWI, the full wavefunction of the universe exists and continues to evolve in a unitary fashion. Any (quantum) measuring device becomes entangled in many different ways with the (quantum) environment of the system being measured, and therefore can no longer measure any interference or superposition of states in the system under measurement. When the measuring device is entangled with the environment in a very large number of ways, it is extremely probable that any measurement will return only a single value, and even though the other states exist in the many-branched tree, these other states cannot be measured from the point of view of the environment entangled with the measuring device. We say the universe ‘splits’ into N branches when we have N possible values of the measured quantum state, in effect giving rise to N ‘copies’ of the entire universe. Each ‘copy’ will contain one distinct state of the (former) superposition of states. Further, in each ‘copy’, for all other systems entangled with the measured state, only those states that are consistent with the measured value of the state will appear. This may be a little non-intuitive, so a classical example might help!

Suppose we have two coins, a gold coin and a silver coin. We put the coins into two different envelopes, and mix the envelopes up. The coins in the envelopes are thus ‘classically entangled’ in the sense that if we open one envelope, we instantly know what opening the other envelope will reveal, regardless of the distance between the two envelopes. No superluminal communication was necessary so the coin in the second envelope would be the correlated color. Our understanding of this is intuitive.

It is mostly straightforward to use the coin analogy to consider a system of two entangled photons with correlated polarized states of VERTICAL and HORIZONTAL. Unlike the coin in the envelope, each photon is a superposition of the two polarized states, and we can’t be sure which state we’ll get until we actually measure the polarization. In MWI, when we measure photon 1, the universe ‘splits’ into two universes, one with photon 1 VERTICAL and one with photon 1 HORIZONTAL. The properties of quantum entanglement of the two photons insures that in VERTICAL photon 1’s universe, only HORIZONTAL photon 2 is present. Therefore, photon 2 is no longer a superposition of states, and when we measure photon 2, we must get HORIZONTAL as the result. There is no other possible outcome in VERTICAL photon 1’s universe! You see no superluminal communication is takes place (the world is local). The correlated values always come out correctly when we measure both photons, regardless of which photon is measured first or how far apart they are when the measurement takes place. It is interesting that the universe no longer has a ‘split’ when photon 2 is measured, because no quantum decoherence is necessary to produce a single polarization value. This is what prevents Bell’s Inequality from being valid, and hence a violation of that inequality no longer requires a non-local universe.

Whew! It may not be the best analogy, but it is where I am in understanding how MWI does not require non-local interactions, even if Bell’s Inequality does not hold.

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