One of the conceptual difficulties of quantum theory- for some physicists at least- is to do with the change that a particle's wave undergoes when the particle manifests itself through an interaction with other matter. This is often given the name 'the collapse of the wave packet'. We'll look into it in a bit more detail now.

There is nothing in principle in quantum theory that stops a particle's wave from spreading out very widely. If you remember that the height of the wave at any given point represents the probability of the particle appearing there, then a widely spread-out wave means that the particle could appear anywhere over a wide area.

When the particle does actually make its presence felt by interacting with other matter then we know much more precisely where it is. The particle's wave suddenly contracts to become a single tall ripple where the particle has appeared.

For some physicists, the idea that the wave suddenly shrinks is a problem. In theory, at least, the wave could have spread enormously beforehand, so to assume it shrinks to a point in an instant conflicts with other principles in physics that say that sudden changes, or 'discontinuities' are unnatural, so any physical theory that includes or implies them must be wrong.

You only have to read a physics forum on the Internet to see that there are lots of conflicting views on this subject from within the physics community. Some argue that the particle wave doesn't really have any physical existence- it's just a measure of our uncertainty about where the particle is. There are other mathematical formalisms of quantum theory in which the particle waves don't explicitly appear.

Another complexity that we have ignored so far is that particle waves overlap and 'interfere' with each other. Imagine the surface of a glassy pond upon which you cause a single ripple to spread-out in a beautifully pure circular wave, the evolution of which you can clearly see. Suppose someone else on the pond causes another ripple in a different place. That too spreads out smoothly. But where the waves meet they create a more choppy pattern. Where the peak of one wave coincides with the peak of another they add together to give a doubly tall peak. Likewise the troughs. And when the peak of one wave coincides with the trough of another they cancel each other out. The resulting pattern changes all the time as the waves cross each other. Now imagine more and more waves get started by people all over the pond, some being gentle waves from the flick of a finger, others being big waves where someone had dropped a huge boulder. As more and more waves coincide and overlap the surface gets more and more chaotic and you can no longer recognise the existence of the individual waves, even though mathematically they are all still there, and the random chaos you are seeing is just the sum of thousands of beautifully symmetric waves.

The real universe is more like the choppy chaotic surface of the ocean than the ideal glassy pond with a single ripple. Many of the calculations that physicists perform using quantum theory ignore the individual interactions between a particle and the millions of other individual particles that make up real physical objects. Instead the physicists adopt simplified models in order to make the calculations easier. It is amazing that in spite of the simplifying assumptions the models can still make very precise predictions of the physical properties of matter.

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