My posts on quantum mechanics have made a number of statements that not everyone would agree with:
- That particles, like electrons, can behave as particles or waves (wave-particle duality, post 19.25)
- That we cannot simultaneously know the position and the energy of a particle, like an electron (Heisenberg’s uncertainty principle, post 19.26)
- That a wavefunction multiplied by its complex conjugate (post 18.16) gives the probability of finding a particle, like an electron, at a point in space (post 19.28).
These statements mean that quantum mechanics is not deterministic but provides statistical information.
Einstein objected to the statistical interpretation of quantum mechanics by saying, “God does not play dice”. This view and the strange nature of wave-particle duality have led people to search for other interpretations.
In this post, I will try to show that there are alternative explanations to the ones I have given. I won’t explain these other ideas because I don’t understand them well enough – my aim is simply to provide balance. However, the approach I have taken in my previous posts is the one that appears in most textbooks on the subject.
But first I want to explain why I believe that we shouldn’t object to statistical interpretations of quantum theory and why physics doesn’t have to be deterministic. I don’t believe that anyone objects to the statistical interpretation of entropy (post 16.38). So why object to a statistical interpretation of the wavefunction? An arch made of blocks of stone can remain in static equilibrium under a range of different loading conditions. There is not a unique set of forces that we can calculate that must be responsible for its stability – the arch is statically indeterminant. As long ago as 1873, the Scottish physicist James Clerk Maxwell pointed out (in an unpublished essay) that, in some dynamical systems, very small changes could give rise to very much larger effects; this idea is the basis on what we now call chaos theory. The butterfly effect described by the American meteorologist Edward Lorenz provides an example. In 1972, he described the influence of events that had previously been ignored as, “a butterfly flapping its wings in Brazil can cause a tornedo in Texas”; the butterfly effect makes exact weather forecasting almost impossible, even with the most powerful computers. Before quantum theory, it might have seemed that physics was completely deterministic – we can predict tides and astronomical events. But I believe that the evidence of this paragraph shows that it really wasn’t.
Although de Broglie predicted the wave properties of the electron, he didn’t believe in wave-particle duality (post 19.25). Instead, he believed that the particle and wave existed simultaneously and that the particles were guided by the waves to areas of constructive interference (post 18.10). This idea, originally called the pilot wave model, was developed by the English physicist David Bohm who called it the hidden variable theory.
It has also been suggested that electrons are simply particles and not waves. How could this explain electron diffraction (post 19.24)? The idea is that electrons are scattered by collisions (post 17.30) with atoms but only in certain directions because, according to quantum theory, their momentum can’t have any value (post 16.2). On the other hand, the American physicist Carver Mead believed that electrons weren’t particles but were waves in matter.
A completely different interpretation was given by the American Hugh Everett who gave up physics for operational research because his ideas were not taken seriously at the time. He believed that every mathematical solution existed in some other world or universe; these parallel universes were descriptions of different realities that formed a multiverse. Then the wavefunction describes the distribution of parallel universes. This idea has been a gift to writers of fiction. The Phillip Pullman trilogy “His Dark Materials” begins with a girl living in contemporary Oxford, England (pictured above) but in an Oxford where people’s beliefs and lifestyles are completely different to those of the people we know who live there.
This is not an exhaustive list of all the interpretations and apparent paradoxes that have been debated in an attempt to fully understand quantum theory. I simply wanted to show the sort of ideas that people have had. I will end with two quotations:
“There is now … no entirely satisfactory interpretation of quantum mechanics,” Steven Weinberg (Nobel prize in physics, 1979)
“I think I can safely say that nobody understands quantum mechanics”, Richard Feynman (Nobel prize in physics, 1965).