Monday, May 25, 2009

Infinite Regression versus Causality

Because infinite regression is a fallacy, the fact that quantum mechanics isn't entirely deterministic should be completely unsurprising. You can construct any chain of causality like a proof; this cause happened and therefore there was this effect, and that effect caused a further effect...* But since infinite regression is a fallacy, the chain of causation must stop at the most basic levels. Why does an electron exist? Just because. It looks like physics will actually get more fundamental than this, but the logic is the same; why is the ToE or GUT true? Well, it just is.

*(This fact is equivalent to the fact that the universe is mathematically describable. Also applies to constructing objects out of particles; each particle is a premise and the properties of the higher-level thing are the conclusions. If you assume a bunch of H2O at STP, you conclude water. Also, to recap, to apply infinite regression either requires "And electrons are made of yet smaller electrons!"-type circular logic, or else positing every possible particle, and thus every possible property. )

Because electrons just exist, there is particular reason why some of its properties may be uncaused; using the physicalist existence axiom, existence is defined by interactions, which are defined by properties. When electrons decohere, the choice of state just happens. Again, there may be a reason* behind this, but then there will be no reason for the reason.

*(Talking pure physics here. Since you're reading this, you'll probably know I think it goes directly into spiffy stuff at this point.)

Locality is just a property of causality. The general principle is that you can be causally linked only with things you're directly adjacent to. To affect something distant you have to generate an adjacent projectile and send it to bump into what you want to affect.* Because locality is in fact a property of causality, when causality breaks down at the fundamental levels due to the infinite regression fallacy, locality must break down with it. In short; entanglement or something like it is inevitable. It will occur in all universes that follow recognizable logical laws.

*(And ultimately locality just refers to the set of things you can directly interact with, whether they happen to actually be what we think of as 'local' or not.)

(All this raises an interesting question; in the continuous approximation of physics, what does 'adjacent' mean? Naturally quantized spaces such as LQG elegantly solves the problem.)

My favourite story about this is actually semi-mainstream. It says all this in basically a different way; the information available to fundamental particles is limited, and so you can't specify the states of entangled particles independently, and so they have to spontaneously generate information when you interact with them. The article proposes that quantum physics is the realization of the law of excluded middle; that all questions are either yes, no, or meaningless: not questions at all.

Incidentally, the theory helps illustrate why I think information per se isn't really physical; it isn't conserved. It is created when the particle is measured and then, when it goes back to a superposition, it disappears again. Physical systems can represent information, and there can be information about them, but they are not information.

On the other hand;

The Schrodinger equation says exactly that the photon goes down both paths and interferes with itself. In this interfered state it then interacts with the detector. However, if you put a detector on one of the paths, it interacts with that detector instead, changing the situation. It seems pretty straightforward to me. Particles are waves that transfer energy stoichiometrically with other waves, and of course change during this interaction.

This same idea applies to the very beginning of the universe. At some point the chain of causality must simply end. The first event was a cause, but not an effect, which means it wasn't an event at all. Equivalently, it's meaningless to talk about 'before' the Big Bang, because there was no time there to be 'before' relative to.

Indeed, time without space is meaningless, as is space without time. The first is change without structure, the second structure without change.

"The spatialization of time is not something abrupt; it is a continuous process. Viewed in reverse as the temporalization of (one dimension of) space, it implies that time can emerge out of space in a continuous process. (By continuous, I mean that the timelike quality of a dimension, as opposed to its spacelike quality, is not an all-or-nothing affair; there are shades in between. This vague statement can be made quite precise mathematically.)"

Oh, good. I had suspected something like this ever since I realized that for causality to function at all, there needs to be an independent variable. Everything is described by f(t). It also suggests yet again that physics can grow organically, starting from a single axiom and repeatedly going through something like quantum collapse to form new laws, each time the lone axiom runs into a situation with an ambiguous solution. Problem being that if two different collapses happen to make a particular situation permanently ambiguous, and yet not subject to the infinite regression fallacy, the collapse will produce a new law, yes...but it won't be physics.

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