On Philosophy

May 8, 2007

Nonlocality

Filed under: Metaphysics — Peter @ 12:00 am

Previously I argued that some of the strangeness of quantum physics, namely that which arises when trying to understand how a particle can have indeterminate properties, can be made comprehensible by modifying our understanding of what a property is. Instead of thinking of a disposition to have a specific result when measured as a property we should think of having a particular quantum state as a property. Under such an understanding properties are not actually indeterminate, and that their seeming indeterminacy results from how the quantum state of the particles changes upon being measured. This leaves two fundamentally strange aspects of quantum mechanics in need of a sensible explanation. One is to understand what the quantum state (superposition) of a two particle system that is entangled is, since it cannot be understood as simply some summation of the quantum states of the particles involved. And the other is to understand how measurement of one part of such a multi-particles quantum state can affect the quantum state of all the particles involved instantaneously, even if they are separated by great distances, with seemingly no medium of transmission for this effect. This second mystery is called nonlocality, and the strangeness associated with it is what I will attempt to dispel here.

My approach to nonlocality is that it only seems like action at a distance, and that there is no actual nonlocal causation or transmission of information at all. But before we tackle the quantum case let me provide two examples of apparent action at a distance in classical physics. Understanding why these examples don’t actually involve action at a distance will help us resolve the apparent action at a distance encountered in quantum mechanics. Consider then two boxes, one that contains a right-hand glove and one that contains a left-hand glove. The gloves have been placed in the boxes by a completely random (classically random) process, such that no one knows which glove is in which box. NASA then launches one of the boxes into deep space. Later, when the other box is very far away, you open your box and find the left-hand glove. At the same time you learn that the far away box contains the right-hand glove. Thus it would seem that information about the contents of the other box have made their way to you faster than the speed of light. Of course that isn’t actually the case, information is not making its way from the other box to you. Rather information about the original event (when the gloves were placed into the boxes) has been received, and that information followed a path that never exceeded the speed of light. Now consider being in a room in which everything is painted so that it reflects either a specific shade of blue or a specific shade of red. If you put on glasses that are tinted so that they only let that specific shade of blue through all the objects painted red will instantaneously seem to turn black. Since those close to you and those far away turn black at the same time it will seem like putting on the glasses causes an effect that turns red objects black which propagates instantaneously, certainly much faster than light. Of course in this case no effect is propagating at all, it just seems like one is; all changes are strictly local.

But before I can explain away the apparent nonlocality of quantum mechanics I need to say a little bit more about what the supposed nonlocal effects are. First we need to quickly review what a superposition is. Remember that the state of each particle is represented by a vector in some vector space. Remember also that each measurable “property” corresponds to a set of perpendicular vectors in that vector space. Now given any arbitrary measurable and any arbitrary vector we can write that vector in terms of some sum of the perpendicular vectors that correspond to that measurable. The original vector and this sum are one and the same, it is just a mathematical convenience that allows us to describe one vector in terms of others. Now if that vector is identical to one of the vectors that corresponds to our measurable we say that the particle has a determinate value for that measurable. Otherwise we say that the particle is in a superposition. Now for a single particle one of the vectors of the measurable might correspond to x-spin up and the other might correspond to x-spin down, so we might talk about the particle having a determinate x-spin or being in a superposition of x-spin up and x-spin down. Now when particles interact they can become entangled. Then the state of both particles, let’s call them A and B, becomes represented by a single vector. Instead of being able to express this state vector in terms of vectors that represent x-spin up and x-spin down it must be expressed in terms of vectors that represent the measurables of both particles. In this case it could be expressed in terms of four vectors: A x-spin up & B x-spin up, A x-spin up & B x-spin down, A x-spin down & B x-spin up, and A x-spin down & B x-spin down. Now let us say that we have two such particles and we measure the x-spin of A, what happens to the quantum state of the two particle system? Well as you remember from last time observing a system forces it to transition to a state that is one of the vectors associated with the measurable. Let’s say it actually transitions to x-spin up. In this case we go to our two particle system, whose state was represented as a sum of four vectors, as mentioned above, and we look at the A x-spin up & B x-spin up and A x-spin up & B x-spin down components of that sum. We do a little normalization (I’m intentionally being vague about the details) and come back with a state for B in terms of a sum of x-spin up and x-spin down, a superposition. That shouldn’t strike you as too surprising. But consider what happens if the state of our two particle could be represented as just a sum of A x-spin up & B x-spin down and A x-spin down & B x-spin up. This means that if we measured the x-spin of A there would be only one possibility for the x-spin of B, and thus by measuring the x-spin of A we have remotely given B a determinate x-spin. And this seems to many like nonlocal action at a distance.

The way to get rid of this apparent nonlocality is to adopt a no-collapse interpretation of quantum mechanics. Remember how I said that by measuring the system we force it to adopt one of the vectors associated with the measurable as its state? The no-collapse interpretation says that measurement doesn’t cause any change in the state of the particle, rather it is we who change. Specifically we become entangled with the particle, and enter into a superposition of measuring it having one outcome and measuring it having another. How does this work? Well, remember how vectors can be represented as a sum of other vectors? The mathematical rules behind quantum mechanics say that if you know how certain special vectors evolve over time in a given situation then you can find out how a vector that can be represented as a sum of those vectors evolves by taking that sum and evolving each component as though it were the state of the system. Now consider an observer measuring x-spin. If the particle is determinately x-spin up then the observer will measure x-spin up, and if the particle is determinately x-spin down the observer will measure x-spin down. So if the particle is in a superposition of x-spin up and x-spin down then we can use the mathematical trick just described to argue that the observer in that scenario would be in a superposition of measuring x-spin up and x-spin down. Let’s go back now to the special case of the observer measuring a two particle system which is in a superposition of just a sum of A x-spin up & B x-spin down and A x-spin down & B x-spin up. I say that in this case no there are no non-local effects. Rather it is like putting on a specific shade of glasses. You, the observer, change, entering into a superposition of your own by measuring the superposition. (Of course it doesn’t feel like you have entered into a superposition, but this is because each part of the superposition has its own consciousness.) And from within one part of the superposition the reason you can tell what the spin of B is is the same reason you can tell which glove is in the box in deep space, because really the information you are getting is about an outcome of an event in the past that gave the particles that particular superposition.

So adopting a no-collapse interpretation of quantum mechanics allows us to explain the apparent nonlocality of quantum mechanics without positing any faster than light causation. Of course if you don’t accept the no-collapse interpretation then nonlocal effects remain a mystery; which in my opinion is a compelling reason to accept the no-collapse interpretation, because it provides an explanation for certain otherwise unexplained quantum phenomena.

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3 Comments

  1. Here’s a thought I just had: has anyone ever done a theory of quantum mechanics where it’s not just the position/momentum/etc of a particle that can be in a superposition, but which of the fundamental particles a particle is can be in superposition? To my knowledge, no. But why is being a particular fundamental particle so much more determinate than other, fuzzier properties of a particle?

    I’m not a physicist, so I can’t answer my own question, but someone who can do all the relevant math might be able to make some hay out of the question.

    Comment by Carl — May 8, 2007 @ 1:00 am

  2. To consider that the effects of quantum entanglement do have a cause one can ask what would such a cause be for and what properties it could possess other than acting non-locally.

    So for entanglement to occur there needs to be measured a correlation betwen objects of particular forms of behaviour, Measure spin up from one of a pair of quantum components and spin down down will be measured from the other component at a distance.

    Now, you can’t measure this effect as having any strength that varies or ceases with increasing distance between objects (except that experiments have been able to measure the effects to occur at fater than the speed of light). So you can’t describe any properties of the cause by mathematical formulae. Nor can you even decribe a cause of quantum entanglement as attracting or repelling objects or acting in fields that surround them. And it is for these reasons that physicists can regard the effects of entanglement as having no cause.

    However ther is a non-quantative property that you can describe of a cause of quantum entanglement. so you can say that for this effect to occur something needs to act so as to maintain or conserve the correlation between the forms of behaviour.

    Thus you can consider that, while the physics only descibes forces powerfully attract or repel between subatomic components of matter, should there not be a cause that acts universally and constantly so as to maintain or conserve the subatomic organisation of matter into atoms and molecules. And wouldn’t such a cause act without pushing or pulling objects and so with no strength of effect that can vary or cease with increasing distance betweem objects?

    Comment by Andrew Daw — May 8, 2007 @ 3:49 am

  3. Carl- the property of being a KS meson is a superposition of being a K0 meson and a ~K0 meson. Likewise the being a KL meson is a similiar superposition.

    Comment by Peter — May 8, 2007 @ 8:14 am


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