If you've recently joined the Less Wrong community, please leave a comment here and introduce yourself. We'd love to know who you are, what you're doing, what you value, how you came to identify as a rationalist or how you found us. You can skip right to that if you like; the rest of this post consists of a few things you might find helpful. More can be found at the FAQ.
A few notes about the site mechanics
A few notes about the community
If English is not your first language, don't let that make you afraid to post or comment. You can get English help on Discussion- or Main-level posts by sending a PM to one of the following users (use the "send message" link on the upper right of their user page). Either put the text of the post in the PM, or just say that you'd like English help and you'll get a response with an email address.
* Normal_Anomaly
* Randaly
* shokwave
* Barry Cotter
A note for theists: you will find the Less Wrong community to be predominantly atheist, though not completely so, and most of us are genuinely respectful of religious people who keep the usual community norms. It's worth saying that we might think religion is off-topic in some places where you think it's on-topic, so be thoughtful about where and how you start explicitly talking about it; some of us are happy to talk about religion, some of us aren't interested. Bear in mind that many of us really, truly have given full consideration to theistic claims and found them to be false, so starting with the most common arguments is pretty likely just to annoy people. Anyhow, it's absolutely OK to mention that you're religious in your welcome post and to invite a discussion there.
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.
There must be something that you have fundamentally misunderstood. I will try to clear up some aspects that I think may cause this confusion.
First of all, the scattering processes presented in the paper are very generic to demonstrate the range of possible processes. The blog contains a specific realization which you may find closer to known physical processes.
Let me explain in detail again what this section is about, maybe this will help to overcome our misunderstanding. A photon scatters on a single qubit. The photon and the qubit each bring in a two dimensional state space and the scattering process is unitary and agrees with conservation laws. The state of the qubit before the interaction is known, the state of the photon is external to the observer's system and therefore entirely unknown, and it is independent of the state of the qubit.
The result of the scattering process is traced over the external outgoing photon states to get a local objective state operator. You then write I apply the Born rule, but that's really exactly what I don't do. I use the earlier derived fact that a local observer can only reconstruct the eigenstate with the greatest eigenvalue. This will result in getting either the qubit's |0> or |1> state.
In order to get the exact probability distribution of these outcomes you have to assume exactly nothing about the state of the photon, because it is entirely unknown. If you assume nothing then all polarizations are equally likely, and you get an SU(2) invariant distribution of the coefficients. That's all. There are no assumptions whatsoever about the generation of the photons, them being thermal or anything. Just that all polarizations are equally likely. This is a very natural assumption and hard to argue against. The result in then not only the Born rule but also an orthogonal basis which the outcomes belong to.
So if you accept the derivation that the dominant eigensubspace is the relevant state description for a local internal observer and you accept that the state of the incoming photons is not known, then the Born rule follows for certain scattering processes. If you use precisely the process described in my blog is up to you. It merely stands for a class of processes that all result in the Born rule.
You don't need any modification of quantum mechanics for that. Why do you think you would? Also, this is not just a random combination of algebraic conditions and random distributions. Th assumption about the state distribution of the photon is the only valid assumption if you don't want to single out a specific photon polarization basis. And all the results are consequences of local observation and unitary interactions.
Have you worked through my blog posts from the beginning in the meantime? I ask because I was hoping that they describe all this very clearly. Please let me know if you disagree with how the internal observer reconstructs the quantum state, because I think that's the problem here.
I understand that you have an algebraic derivation of Born probabilities, but what I'm saying is that I don't see how to make that derivation physically meaningful. I don't see how it applies to an actual experiment.
Consider a Stern-Gerlach experiment. A state is prepared, sent through the apparatus, and the electron is observed coming out one way or the other. Repeat the procedure with identical state preparation, and you can get a different outcome.
For Copenhagen, this is just a routine application of the Born rule.
Suppose we try to explain this outco... (read more)