A new, fractal-geometry interpretation of quantum mechanics

''Einstein thought this was all a bit much, believing it to be evidence of major problems with the theory, as many critics still suspect today. Quantum enthusiasts point to the theory's extraordinary success in explaining the behaviour of atoms, electrons and other quantum systems. They insist we have to accept the theory as it is, however strange it may seem.''

''But what if there were a way to reconcile these two opposing views ...
A simple way of thinking about it is to imagine a swinging pendulum that slows down due to friction before eventually coming to a complete standstill. Here the invariant set is the one that describes the pendulum at rest.
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Complex systems are affected by chaos, which means that their behaviour can be influenced greatly by tiny changes. According to mathematics, the invariant set of a chaotic system is a fractal.''

''For example, it may point to a natural explanation for one of the biggest puzzles of quantum physics, what physicists refer to as its "contextuality". Quantum theory seems to insist that particles do not have any properties before they are measured. Instead, the very act of measurement brings their properties into being. Or, put another way, quantum systems have meaning only in the context of the particular experiments performed on them.
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Palmer's idea suggests a third possibility ... Suppose you perform the Kochen-Specker thought experiment and measure the position of an electron. Then you ask what you would have found if you repeated the experiment, only this time measuring the electron's velocity instead.

According to Palmer, when you repeat the experiment you are testing a hypothetical universe that is identical to the real one except that the position-measuring equipment is replaced with velocity-measuring equipment.
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Due to the spare and wispy nature of fractals, even subtle changes in the hypothetical universes could cause them to fall outside the invariant set. In this way, Spekkens says, Palmer's hypothesis may help to make some sense of quantum contextuality.''
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