Monday, 4 August 2014

Yet More Quantum madness the so called Cheshire cat

For those like me, who despair at the increasing tendency to the irrationality of the world, even in science. The recently published claim that it has been possible to separate out the spin component of a quantum object from it's spatial component can only cause one to wonder whether the world has gone mad.

For those who aren't aware this BBC post is typical of the hype

and the original paper is here

So the claim at first appears to be  by a special arrangement of beam splitters it is possible to disembody a particles spin from it's location. So that in one path only the location of the particle can be determined on another part it's magnetic moment which seems to have magically been disentangled from the particle. A literal interpretation of this is just not credible.

First of all spin has no spatial properties so it can't move anywhere. Spin is a vector which is allowed quantum mechanically to take a number of fixed directions usually up or down. it is a property of a quantum object. So if the authors of the paper are claiming what the hype says they are then that would require a rewriting of the whole of quantum mechanics of spin and as far as I can tell the authors are not seeking to challenge the standard quantum mechanical concept of spin.

So what exactly have the authors shown? The key to interpreting the experiment is the concept of quantum superposition there are essentially two interpretations

The first beloved of the popular literature, and it would seem journalists who want to peddle the alleged mysterious aspects of quantum mechanics, is called the ontic (short for ontological)  interpretation.

The ontic view is that quantum superpositions are real namely that a cat really is in limbo between being alive or dead or in the case of interferometer experiments each particle really does travel down both paths simultaneously or in the two slit experiment passes through both slits simultaneously.

The solution to Schrodinger's equation is a real wave and something physical (even though it doesn't actually affect anything (for example exert a force on a particle as an electric fiield does), For an N  body problem, it is some sort of field in 3N + 1 configuration space as opposed to our 3+1 dimensional space time. Also when a measurement is made the solution to Schrodinger's eqaution collapses into one of the states. This is usually  called wave-packet collapse but it really should be called the solution to Schrodinger's equation collapse.

On the ontic view, it is only by measurement that a system jumps from it's state of limbo of possible states into a definite state. Extrapolating (slightly unfairly I admit) this means the moon really isn't there when one looks at it. It would seem from the language used by the authors talking of the wavefunction travelling down both paths simultaneously they subscribe to the ontic view.  On this view in this experiment, it really does seem that the spin part of a qauntum objects solution to Schrodinger's equation can be detached from it's spatial part. But just what disembodied spin means hasn't really been explained and if it really was disembodied then all the text books on quantum mechanics would have to be rewritten.

Conversely from an epistemic (statistical) point of view, the solution to Schrodinger's eqaution is a probability amplitude who's modulus squared gives when suitably normalised gives rise to a probability density function. The Born interpretation, on this view the superposition of states represents the lack of knowledge of an observer about a given situation and nothing physical. As the solution to Schrodinger's equation is primarily a statistical quantity, applying it to work out the behaviour of one particle is just as meaningful, as trying to predict the roll of a single dice or a spin of a roulette wheel. When the solution to Schrodinger's equation 'collapses' all that happens is that one of the possibilities is realised. Albeit in order to get the correct probabilities for a given situation one has to use complex numbers which accounts (mathematically at least) for all the interference effects associated with many quantum phenomenon.

I have discussed how this works for two state systems in previous posts

Where I also point out that the Dirac notation can also be applied to classical systems. But in order to explain many quantum phenomenon, one has to extend our notion of probability to include complex numbers.

On this epistemic\statistical view then when a beam of particles passes through a beam splitter, a single particle, does not travel through both paths simultaneously, but the solution to Schrodinger's equation represents the probability amplitude that it will traverse one path or the other. On this view in the Cheshire Cat experiment, if the neutron passes one path it's location, will be measured on the other it's magnetic moment will be measured. There is no disembodiment  of the spin part of the neutron's solution to Schrodinger's equation  from it's spatial part. That realtively prosaic account of course won't attract attention and so would be ignored by most people.

The epistemic view and the ontic view, as they are interpreting the same mathematical object, namely the Solution to Schrodinger's equation cannot be empirically distinguished from each other. However given the more modest claims of the epistemic view vis a vis our notions of quantum wierdness I know which one I prefer. All the epistemic (statistical view) is asking is that we extend our notions of probability to include complex numbers. In contrast the ontic view would claim that wavepacket collapse is real, that spin's can be dismbodied from their constituent particles and that act's of measurement do create reality. Of course some people would find the epistemic\statistical view  unsatisfactory, accusations of instrumentalism etc but if there are no hidden variables then there can be nothing behind the statistics.   

I really do have to ask why is there such a hunger for irrational explanations of quantum phenomenon. I really do despair some times.


  1. Have you actually read the paper?

  2. I have I guess my attack is directed at those who really do believe that the paper shows how the spin of a particle can be detached from the particle itself.

    However equations 2 and 3 of the paper show that the initial and final states of the ensemble are still products of the spin and spatial parts. So there is no detachment. What the experiment has done is show that the average expectation value of the position state is 1 in one path and 0 in another and vice versa for the z component of the spin.

    Unfortunately such subtleties are lost on journalists who want to sensationalise such results and latch onto rreally quite misleading analogies such as the Cheshire Cat one. Which the aouthors of the paper use right from the start.