Sunday, 7 July 2013

What is an explanation ?

This post is motivated by some debates I've been having on the OU quantum physics fora about the nature of explanation especially in physics. In quantum mechanics we have what I consider to be, a rather bizzare claim that despite the fact that trained physicists are able to use the formalism to predict measurable quantities about atomic systems such as the energy levels or particle decay rates. The claim is made in many circles that no one is able to understand quantum physics. Yet clearly those who can use the formalism of quantum mechanics to successfully model say the properties of solids, lasers, the properties of stars etc obviously do understand a great deal about how qunatum physics works.

I suppose the problem is that quantum physics (at least in it;s Non-relativistic formalism) uses a quantity called the wavefunction, but, as I've argued before in previous posts better seen as a probability state vector who's modulus squared gives rise to a probability density function and whos eigenvalues can be related to the energy levels or decay rates of atoms, molecules or solids.  The problem is that for an N body system the so called wavefunction becomes a function of the 3 N coordinates of the system. So if it is seen as a field analagous to an electromagnetic field or the gravitational field. It is a field in the 3N+1 configuration space of the system rather than our normal 3 dimensional space. Matters are even more complicated when extra variables such as spin are also included. Spin has no spatial or time component so what is spin really ?

The other key issue is the notorious collapse of the wave function if there is a possibility that a particle can be in one of two or more states then it is said to be in limbo until a measurement is made and then it collapses into one of it;s states and in situations like the Aspect experiment this influence is said to occur at speed's faster than the speed of light because given a pair of photons emitted from a common source then so the story goes if I measure the spin of one photon it immediately causes the other photon which could be miles away to have the opposite spin.

So alleged mystery on mystery even if the formalism gives a precise mathematical description of the wave function and there are precise rules which can be learnt by anyone prepared to put the effort in learning the maths how to use it to predict the essential features of quantum systems.

As I've explained before much of the mystery can be dissolved if the wave function is seen for what it is mathematically namely the complex square root of a probability distribution function or a complex probability amplitude. The configuration space of an N body system is simply the probability sample space associated with the system  and one can include spin variables in this with out any worry about the existence  of such an entity as  a field in configuration space. The only difference between qunatum probability and every day probability is that one needs to use complex probability amplitudes and the Born rule in order to obtain the correct probability density function for a given situation.

I explain how all this works here

I can not stress to highly how it really is quite instructive to cast the language of classical probability in terms of quantum probablilty. No one claims that the probability state vector of a coin or dice is a real superposition of head or tail states why should we do the same for quantum systems.

Accepting the intrinsic statisitical nature of quantum physics seems to me to dissolve a lot of the conceptual problems associated with quantum physics. The superposition of quantum states is a superposition of  quantum probablities and the quantum state is a mathematical description of the possibilities open to a given system. Nothing collapses physically when a measurement is made and nothing exists in (3N+1)*S configuration space where S is the sum of all the allowable spin states.

OK we still don't know why we have to use complex probability amplitudes, but once we accept that  then the rest follows.  I would say the successful use of the formalism by physicists to model more and more complicated situations does mean that we do understand how quantum physics works and those who are able to use it can genuinely be said to understand the phenomenon they are trying to model.

As a final point even Classical physics which was claimed to be understood used quantities which were quite mysterious, No one knew what gravity was apart from the fact that it obeyed an inverse square law. No one knew how electromagnetic waves could propagate through free space or what entropy was. Of course that didn't stop people (as today with the wave function) trying to visualise what an electric field was but these speculations got no where. Helmholtz in a move, seen as desperate by a lot of the people at the time. getting so tired of the endless speculation, claimed that Maxwell's theory was Maxwell's equations.
 A statement very similar to the 'Shut up and calculate' approach of Feynman.and other successful physicists who want to develop the applications of quantum mechanics rather than indulge in pretty fruitless speculation about the real nature of the wave-function. If you want to understand quantum physics learn how it is used engage with the maths and learn how to apply it to the phenomenon you are interested in. That way you will begin to get a feel for how quantum mechanics works, and just as no one claimed we didn't understand classical physics even if we couldn't visualise what an electric field was so we should stop claiming that we don't understand how quantum physics works.


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