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Quantum mechanics, the measurement problem, and the nature of reality
1.0 Quantum mechanics is a theory that works.
The wave formulation of energy and particles, the techniques that have been built up to deal with it, and the predictions that can be made all correspond with observable reality to a very high degree.
At it's most basic, the framework of quantum mechanics consists of an experimentally unobservable wave (the effects of which can be calculated) which can be manipulated in various ways. Quantum mechanics shows the evolution of this wavefunction.
2.0 And now the bad news...
QM brings with it a number of problems. The wavefunction around which the entire theory is based is an unobservable entity. What exactly it means has been under much debate since it was first formulated - form the first ideas of Schrodinger (which themselves underwent considerable evolution) to the wide spread of orthodox to more controversial ideas today, over 70 years on.
2.1 Interpretation is important.
Interpretation of a theory sounds at first philosophical - divorced from the physical reality - and irrelevant. The 'Shut up and calculate' position is popular. If the common method of using the formulae works, then why bother questioning it? The fact of the matter is that simple interpretation can actually widen the scope of the theory bring with it not juts greater understanding, but actual predictions of behaviour in reality too.
In short, interpretation can be as important as the Schrodinger equation itself.
Consider, for example, the relativistic equations with the quantity v/c. We could just throw away all solutions where this is greater than unity. However, by simply changing our interpretation and allowing superluminal particles to exist, it is possible to explore the whole idea of tachyons and all that brings with it. Interpretation can widen models.
Or perhaps we could think about interpretation as a metaphor. When wave mechanics was first conceived it was thought that the wavefunction represented the actual position of, say, the electron in the atom. It would give a result which would tell us the probability of actually finding the electron in a particular place within the orbital. This metaphor - a probability metaphor - would constrain minds into thinking that there was indeed absolute position.
Shifting metaphors changes this - we now consider instead an electron cloud, an area of distributed probability. While the equations themselves haven't actually changed, the mental shift grants greater understanding into shapes chemical bonds and why they occur. Indeed, the probability being related to the wavefunction is an interpretation in itself - something we shouldn't forget.
So interpretation is important. It can even help out with problems that appear to stem directly from the equations themselves.
2.2 A Problem
The two greatest theories of our time - general relativity and QM - are not easy bedfellows. Consider a particle moving from A to B, and observers measuring the same quantity at these points.
If the particle is not in an eigenstate of this quantity when at A, then the wavefunction will collapse and a definite answer will be obtained; the same answer will then we obtained at B. However, these points are spacelike - it is possible to have a frame of reference where the measurement at B takes place before that at A. In this frame the wavefunction would collapse at B first, which is obviously not consistent. (Indeed, just where the wavefunction collapses has been and still is a source of major contention.)
In this case then either different observers see different wavefunctions for the same object, or quantum mechanics demands that there is an absolute 'arrow of time' showing in which order the events are taking place. This would seem odd, given that no other theories have to contain this and treat time an evenhandedly as any other dimension.
It is possible to attack this problem with various different interpretations (the Transactional approach, and a kind of relativity of information can be useful, both of which I'll be addressing later), but still there is a problem reconciling the two theories.
Physics is pushing forwards towards a Grand Unified Theory, and this is a major obstacle. Finding a theory of quantum gravity is a serious preoccupation. Definite values of energy and momentum in relativity and the necessarily probabilistic answers of quantum do not fit together.
2.3 Another problem.
In the earlier example I talked about the wavefunction collapsing, and I said that it was a source of major contention. Why should this be? Surely we can see, in the mathematics, that a wavefunction collapses when we measure it - ie when we do the physical equivalent of operating on it.
There is no mechanism for creating events in QM. We have to interpret the wavefunction in order to simulate what happens when an event occurs, that is, when we measure it. It's not dynamic; we just see the before and after. What actually occurs to this unobservable wave when we ask, say, where the particle is? How does a superposition of different possibilities resolve itself into a particular observations? Indeed, what actually is an observation? This, in a nutshell, is the Measurement Problem.
What an observation is goes hand in hand with where the wavefunction collapses. We regard the change of the wave into an eigenstate as a result of the measurement, or observation - but ludicrous results can arise, which is where Schrodinger's Cat emerges.
The experimental set-up I'll regard as familiar. What is not clear in this thought experiment is where the wavefunction collapses. The quantum system has expanded from being merely a radioactive particle with a given chance of decaying into a box with a cat in a superposition of alive/dead states in it. Does the wavefunction only collapse when we open the box and observe, or has it happened earlier? This is what the interpretations attempt to address.