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A list of some posts that are pretty awesome
I recommend the major sequences to everybody, but I realize how daunting they look at first. So for purposes of immediate gratification, the following posts are particularly interesting/illuminating/provocative and don't require any previous reading:
- Your Intuitions are Not Magic
- The Apologist and the Revolutionary
- How to Convince Me that 2 + 2 = 3
- Lawful Uncertainty
- The Planning Fallacy
- Scope Insensitivity
- The Allais Paradox (with two followups)
- We Change Our Minds Less Often Than We Think
- The Least Convenient Possible World
- The Third Alternative
- The Domain of Your Utility Function
- Newcomb's Problem and Regret of Rationality
- The True Prisoner's Dilemma
- The Tragedy of Group Selectionism
- Policy Debates Should Not Appear One-Sided
- That Alien Message
More suggestions are welcome! Or just check out the top-rated posts from the history of Less Wrong. Most posts at +50 or more are well worth your time.
Welcome to Less Wrong, and we look forward to hearing from you throughout the site.
I see it exactly like you. I too see the overwhelming number of theories that usually make more or less well hidden mistakes. I too know the usual confusions regarding the meaning of density matrices, the fallacies of circular arguments and all the back doors for the Born rule. And it is exactly what drives me to deliver something that is better and does not have to rely on almost esoteric concepts to explain the results of quantum measurements.
So I guarantee you that this is very well thought out. I have worked on this very publication for 4 years. I flipped the methods and results over and over again, looked for loopholes or logical flaws, tried to improve the argumentation. And now I am finally confident enough to discuss it with other physicists.
Unfortunately, you are not the only physicist that has developed an understandable skepticism regarding claims like I make. This makes it very hard for me to find someone who does exactly what you describe as being hard work, thinking the whole thing through. I'm in desperate need of someone to really look into the details and follow my argument carefully, because that is required to understand what I am saying. All answers that I can give you will be entirely out of context and probably start to look silly at some point, but I will still try.
I do promise that if you take the time to read the blog (leave the paper for later) carefully, you will find that I'm not a smuggler and that I am very careful with deduction and logic.
To answer your questions, first of all it is important that the observer's real state and the state that he assumes to be in are two different things. The objective observer state is the usual state according to unitary quantum theory, described by a density operator, or as I prefer to call them, state operator. There is no statistical interpretation associated with that operator, it's just the best possible description of a subsystem state. The observer does not know this state however, if he is part of the system that this state belongs to. And that is the key result and carefully derived: The observer can only know the eigenstate of the density operator with the greatest eigenvalue. Note that I'm not talking about eigenstates of measurement operators. The other eigensubspaces of the density operator still exist objectively, the observer just doesn't know about them. You could say that the "dominant" eigenstate defines the reality for the observer. The others are just not observable, or reconstructable from the dynamic evolution.
Once you understand this limitation of the observer, it follows easily that an evolution that changes the eigenvalues of the density operator can change their order too. So the dominant eigenstate can suddenly switch from one to another, like a jump in the state description. This jump is determined by external interactions, i.e. interactions of the system the observer describes with inaccessible parts of the universe. An incoming photon could be such an event, and in fact I can show that the information contained in the polarization state of an incoming photon is the source of the random state collapse that generates the Born rule. The process that creates this outcome is fully deterministic though and can be formulated, which I do in my blog and the paper. The randomness just comes from the unknown state of the unobserved but interacting photon.
So as you can see this is fundamentally different from MWI, and it is also much more precise about the mechanism of the state reduction and the source of the randomness. And the born rule follows naturally. No decision theory and artificial assumptions about state robustness, preferred basis or anything like that. Just a natural process that delivers an event with a probability measurable by counting events.
Your last question about the environment being classical is a very good one. I do not model the environment to be classical, in fact there is no assumption about it other than that it belongs to a greater quantum system and that it is not part of the system that the observer wants to describe. There are also no restrictions about anything being in a superposition. That problem resolves itself because the state described by the observer turns out to be a pure state of the local system, always. So even if you assume some kind of superposition of these events, you will always get a single outcome. The scattering process in fact has the property of sending superpositions to different eigensubspaces of the state operator, so that it cleans up everything and makes it more classical, just like the measurement postulate would.
I know I am demanding a lot here, but I really think you will not regret spending time on this. Let me know what else I can explain.
Here's another question. Suppose that the evolving wavefunction psi1(t), according to your scheme, corresponds to a sequence of events a, b, c,... and that the evolving wavefunction psi2(t) corresponds to another sequence of events A, B, C... What about the wavefunction psi1(t)+psi2(t)?