"And both spatial infinity and inflation are standard in the current model of physics."

As mentioned by a commenter above, spatial infinity is by no means required or implied by physical observation. Non-compact space-times are allowed by general relativity, but so are compact tori (which is a very real possibility) or a plethora of bizarre geometries which have been ruled out by experimental evidence.

Inflation is an interesting theory which agrees well with the small (relative to other areas of physics) amount of cosmological data which has been collected. However, the data by no means implies inflation. In fact, the term "inflation" refers to a huge zoo of models which have many unexplained parameters which can be tuned to fit the date. Physicists are far from absolutely confident in the inflationary picture.

Furthermore, there are serious, serious problems with Many Worlds Interpretation (and likewise for Mangled Worlds), which you neglect to mention here.

I enjoy your take on Quantum Mechanics, Eliezer, and I recommend this blog to everyone I know. I agree with you that Copenhagen untenable and the MWI is the current best idea. But you talk about some of your ideas like it's obvious and accepted by anyone who isn't an idiot. This does your readers a disservice.

I realize that this is a blog and not a refereed journal, so I can't expect you to follow all the rules. But I can appeal to your commitment to honesty in asking you to express the uncertainty of your ideas and to defer when necessary to the academic establishment.

Eliezer:I wouldn't be surprised to learn that there is some known better way of looking at quantum mechanics than the position basis, some view whose mathematical components are relativistically invariant and locally causal. There is. Quantum Field theory takes place on the full spacetime of special relativity, and it is completely lorentz covariant. Quantum Mechanics is a low-speed approximation of QFT and neccessarily chooses a reference frame, destroying covariance.

Hal Finney: The Schrodinger equation (and the relatavistic generalization) dictate local evolution of the wavefunction. Non-locality comes about during the measurement process, which is not well understood.

CPT symmetry is required by Quantum Field Theory, not General Relativity.

The Feynman path integral (PI) and Schrรถdinger's equation (SE) are completely equivalent formulations of QM in the sense that they give the same time evolution of an initial state. They have exactly the same information content. It's true that you can derive SE from the PI, while the reverse derivation isn't very natural. On the other hand, the PI is mathematically completely non-rigorous (roughly, the space of paths is too large) while SE evolution can be made precise.

Practically, the PI cannot be used to solve almost anything except the harmonic oscillator. This is a serious handicap in QM, since SE can be used to solve many problems exactly. But in quantum field theory, all the calculations are perturbations around harmonic oscillators, so the PI can be very useful.

Many physicists would agree that the PI is more "fundamental" because it's gives insight into QFT and theoretical physics. But the distinction is largely a matter of taste.

Psy-Kosh: Position-space is special because it has a notion of locality. Two particles can interact if they collide with each other traveling at different speeds, but they cannot interact if they are far from each other traveling at the same speed.

The field, defined everywhere on the 4-D spacetime manifold, is "reality" (up until the magical measurement happens, at least). You can construct different initial value problem (e.g. if the universe is such-and-such at a particular time, how will it evolve?) by taking different slices of the spacetime. Just because there are are many ways to pose an initial value problem for the same spacetime history doesn't mean there isn't one field which is reality.

Eliezer is obviously unable to address all these issues here, as they are well outside his intended scope.

Chris, in case you didn't see me ask you last time...

http://www.overcomingbias.com/2008/04/philosophy-meet.html#comment-110472438

do you know of a good survey of decoherence?

Psy-Kosh: In Quantum Field Theory, the fields (the analog of wavefunctions in non-relativistic Quantum Mechanics) evolve locally on the spacetime. This is given a precise, observer-independant (i.e. covariant) meaning. This property reduces to the spatially-local evolution of the wavefunction in QM which Eliezer is describing. Further, this indeed identifies position-space as "special", compared to momentum-space or any other decomposition of the Hilbert space.

Eliezer: The wavefunctions in QM (and the fields in QFT) evolve locally under normal (Hermitian) evolution. However, Bell-type experiments show that wavefunction collapse is a non-local process (be it the preposterous Copenhagen-style collapse, or some flavor of decoherence). As far as I have read, the source of this non-locality is not understood.

Chris, could you recommend an introduction to decoherence for a grad student in physics? I am dumbstruck by how difficult it is to learn about it and the seeming lack of an authoritative consensus. Is there a proper review article? Is full-on decoherence taught in any physics grad classes, anywhere?

Psy-Kosh: I have never heard of anyone ever successfully formulating quantum (or classical) mechanics without the full spectrum of real numbers. You can't even have simple things, like right triangles with non-integer side length, without irrational numbers to "fill in the gaps". Any finite-set formulation of QM would look very different from what we understand now.

Psy-Kosh: I have never heard of anyone ever successfully formulating quantum (or classical) mechanics without the full spectrum of real numbers. You can't even have simple things, like right triangles with non-integer side length, without irrational numbers to "fill in the gaps". Any finite-set formulation of QM would look very different from what we understand now.