My quantum field theory professor (Predrag Cvitanovic) wrote a book about this most modern theory of how the world works; it starts like this:
what are long-leggedy beasties?
Of course if you read that and it seemed a bit weird, fear not. The
second chapter is more revealing. Devoid of any information about the physics of our Universe, chapter 2 nonetheless contains everything we might need in order to understand how modern physics is organized. When you get to the series at the top of page 11, you're probably wondering what the hell we're all smoking. Nonetheless, this formulation is right, and it's been verified by every experiment humans have been able to perform. Particles appear or disappear whenever they like; they're combined into reality by the Feynman rules (Lagrangian).
So let's go back to the beginning. In the beginning, there was Fermat's principle:
http://en.wikipedia.org/wiki/Fermat's_principle
This describes how light moves. We can imagine little "pieces" of light that fly around, governed by Fermat's principle. This imagination is wrong -- that's not how quantization works -- but it is illustrative. It turns out classical mechanics, which is governed by Newton's laws, can be mathematically turned into Hamilton's principle:
http://en.wikipedia.org/wiki/Hamilton's_principle
This is actually the same as Fermat's principle, but instead of an index of refraction we have a potential energy. That is: the potential energy affecting particle in space is like the index of refraction affecting photon going through a lens. As the particle moves into a region of higher potential, some of its kinetic energy becomes potential energy, and it slows down. As the light moves into thick glass, it is refracted more strongly, and it too slows down.
So physicists realized that both light and matter are really governed by the same rules. Maxwell, Planck, and Einstein together developed the modern postulate that a photon of light is really a quantized (integer) excitation of the electromagnetic field. Since light behaves identically (Fermat-Hamilton principle) to matter, it isn't a huge cognitive leap to say, perhaps, an electron is an excitation of the "electron field", and as we derive a wave equation for light we can also do so for the electron, or any other type of "particle" which is treated as an excitation of a corresponding "particle field".
This wave equation is the Klein-Gordon equation, which governs the world. Unfortunately, the Klein-Gordon equation relates the square of energy to the square of momentum. Since math is commutative, though, a^2 + b^2 ≠ (a + b)^2. When I take (a + b)^2, I have a^2 + ab + ba + b^2, and since math is commutative, this is a^2 + 2ab + b^2, which is not a^2 + b^2. A really smart guy named Paul Dirac said "what if we just decided math was anticommutative?", i.e. ab = -ba? Then we get (a + b)^2 = a^2 + ab + ba + b^2 = a^2 + ab - ab + b^2 = a^2 + b^2, and we can relate energy to momentum directly. This anticommutative math is called a Clifford algebra, it is computed using matrices called Dirac matrices, and it is the reason for all of the trouble in the world. All strange phenomena, like antimatter, and M-theory, are the fault of this Clifford algebra, which leads to more shit than a giant red dog.
But all the strings and so forth are just math's problem.
Our problem is this: if there's an "atara" field, it could have an excitation wherever it wants, but atara is sitting on the bed in only one place. Furthermore, atara's phone is also on the bed in one place. We solve this by
not solving it: physics doesn't describe how anything relates to itself, i.e. my experience of myself as here is just the way consciousness is, not physics. But I know that I'm
entangled with the phone in that "me on the bed" corresponds to "phone on the bed", and that is part of the physics: the things I experience in my reality are just those things which are entangled with me. The only time I go away from the QFT is when I choose where and what I am, which leads to the
relational interpretation of quantum mechanics:
http://en.wikipedia.org/wiki/Relational_quantum_mechanics
So measurement just means that the measuring device is now entangled with the system. We can't view the world outside ourselves: we are always inside ourselves. If I open Schrödinger's box, I am now entangled with the cat. When I start, the cat is (|alive> + |dead>)/√2, and I am (|yay> + |boo>)/√2, so the system is (|alive> + |dead>) (x) (|yay> + |boo>), with the combinatorial factor excluded for convenience (it was wrong anyway). Me experiencing the cat is an operator: |alive><yay| + |dead><boo|, so now the combined atara-cat system looks like (|alive-yay> + |dead-boo>). Of course, something about me demands I only experience one thing at a time, so of course
my experience is instead (|dead-boo>), because another strange unphysical phenomenon is that I always have bad luck.
Most of this essay is incomprehensible gibberish, but I'm in a hurry. Anywho, laters.