On Wednesday, September 4, 2002, at 02:44 PM, Hal Finney wrote:
> Tim May wrote: > >> In weaker forms of the MWI, where it's the early state of the Big Bang >> (for example) which are splitting off into N universes, De Witt and >> others have speculated (as early as around 1970) that we may >> _possibly_ >> see some evidence consistent with the EWG interpretation but NOT >> consistent with other interpretations. > > I'm not familiar with the details of this. But I know that much of > the impetus for increased acceptance of MWI models comes from the > cosmologists. It was in DeWitt's article, "Quantum mechanics and reality," Physics Today, September 1970, reprinted in the collection "The Many-Worlds Interpretation of Quantum Mechanics," edited by Bryc DeWitt and Neill Graham, 1973. "Moreover a decision between the two interpretations may ultimately be made on grounds other than direct laboratory experimentation. For example, in the very early moments of the universe, during the cosmological "Big Bang," the universal wave function may have possessed an overall coherence as yet unimpaired by condensation into non-interfering branches. Such initial coherence may have testable implications for cosmology." (p. 165 of the reprint volume). (Glad to see my memory hasn't failed me. DeWitt's article made a big splash when it first got wide notice with that 1970 article. Around that time, "Physics Today" was where we found many wild things. A beautiful cover painting of a black hole, the first such graphic I'd seen...perhaps it's scanned and on the Web someplace, as it was a seminal image, from January 1970, if I remember correctly. And another cover from around that era was of O'Neill's proposal for L-5 colonies and powersats.) >> >> What's the problem here? I find it utterly plausible that we would be >> in a universe where matter exists, where stars exist, where entropy >> gradients exist, etc., and NOT in a universe where the physical >> constants or structure of the universe makes life more difficult or >> impossible (or where the densities and entropy gradients mean that >> evolution of complex structures might take 100 billion years, or more, >> instead of the billion or so years it apparently took). > > The problem is more formal, that if we abandon measurement as a special > feature of the physics, there is no longer an axiom that says that > probability is proportional to amplitude squared. I'm not an expert on this. Jeffrey Bub, in "Interpreting the Quantum World," 1997, cites several classes of resolutions of the "measurement problem." He calls them the "For all practical purposes" (FAPP) model, after Bell, the "change the linear dynamics" model, and the "modify the orthodox Dirac-von Neumann interpretation principle." From what I can tell, the Copenhagen interpretation is already a mixed state, so to speak, of bits and pieces of Bohr's and Heisenberg's interpretations. By the way, issues of observers and measurements are obviously fraught with "Chinese boxes" types of problems. In the Schrodinger's Cat pedantic example, if the "cat alive or cat dead" measurement is made at the end of one hour by opening the sealed box, what if a video camera had been also sealed inside the box, and had seen the cat breathe in the cyanide gas at 10 minutes into the experiment? Does this imply the "wave function collapsed" at the time of the measurement by the human observers, at the one hour point, or at the time the video camera unambiguously recorded the cat's death? One could arrange a thought experiment involving literally a series of boxes within boxes, each being opened at, say, one minute intervals after the cyanide was released or not released. One set of observers sees the cat either alive or dead at the end of the canonical one hour period. But they are sealed inside a box. After one minute, their box is opened, and the observers in the next-larger box then see the "collapse of the wave function at the 61-minute point." After another minute, their box is opened and a new set of observer sees "the collapse of the wave function at the 62-minute point." And so on. (I don't know if I'm just reinventing a thought experiment someone developed many decades ago...it seems like a natural idea.) Seen this way, the "collapse of the wave function" in the Schrodinger's Cat thought experiment is seen as a problem of knowledge, not something quasi-mystical about an instantaneous collapse of some psi-squared function. (More interesting are the delayed choice experiments.) My hunch is that the answer will lie in some of the work Chris Isham is doing (I've cited this in some past messages). What is characteristic of quantum events is that "honest observers will never disagree on what happened" (to paraphrase what Lee Smolin cites in his book, "Three Roads...") To an outside observer, the humans watching the box, the outcome is unknowable until they open the box. Once they open the box, they and everyone else observing will agree unambiguously as to the outcome. And they will agree with what the video camera recorded. The measurement or observation process is just acting as a subobject classifier, with one of the key properties of such topos-theoretic structures being that once a subobject classification has been made, there's no going back. Heyting --> Boolean, where there is never a situation where some observers report "alive" and others report "dead." (Smolin makes this point about cosmology, but it also applies to quantum cosmology, and perhaps to many other areas. John Baez has been writing recently about "q-logic" being a superset of "logic." He may be on to something, or he may just be giving a new name to some topos theory notions...I need to spend more time thinking and learning.) > The conventional formulation, as described for example at > http://www.wikipedia.com/wiki/ > Mathematical_formulation_of_quantum_mechanics, > has special axioms related to measurement. Systems evolve according to > the Schrodinger equation except when they are being measured, when we > get wave function collapse. MWI rejects the axioms related to > observables > and collapse. In the page above we can eliminate axiom 3 and probably > axiom 2 as well. You are left with nothing but Hilbert space and the > Schrodinger equation. It's a simpler set of axioms. The Tegmark and Wheeler paper (in Sci Am, IIRC) talks about this issue. I'm not very convinced that MWI is simpler in any meaningful way. But I'll be thinking about it more. Deutsch is pretty convincing in his argument that the double slit experiment, a century old now, is compelling evidence that single photons going through one or the other of two slits "must be" interfering with the myriad of photons in all the nearby universes where similar experiments are happening. (Of course, the alternate interpretation is just the familar wave-particle duality, with photons sometimes exhibiting particle-like properties (as in the photoelectric effect) and other times exhibiting wave-like properties (double slits). I have no particular problem believing this is "just as simple" as postulating nearby universes. I have a thought experiment on this which I'll put into a separate post, after I sleep on it tonight.) More convincing to me has always been the quantum computer situation. if someone builds a QC which can factor a 1000-digit number, I'll be convinced other nearby universes exist. (Though even here there is a "wave-like" interpretation favored by some, that "qubits" are handling the parallelism.) > >> ... >> effects, etc.) are only known to, say, 20 decimal places (if that, of >> course). Because the "actual" positions, masses, sphericities, static >> charges, etc. are perhaps defined by 40-digit or even 200-digit >> numbers, the Laplacian dream of a suffiicently powerful mind being >> able >> to know the future is dashed. > > This is true in practice, but I think there is still a significant > difference between deterministic systems like classical physics or the > MWI, and inherently non-deterministic systems like the conventional > Copenhagen interpretation of QM. In the latter you have the difficult > philosophical problem of explaining where all the information comes > from. I'll ponder this. > This is what led Schmidhuber to suggest that quantum randomness is > generated by a pseudo random number generator; otherwise you can't > simulate the universe on a computer because computers can't create > true random bits. The Copenhagen interpretation is fundamentally > non-computable. Maybe too much is made of randomness vs. pseudorandomness. Here's an example where even in a universe with "no local randomness" (no spontaneous decay, nothing not locally deterministic) unpredictable bits can be generated. The example is impractical, slow, etc., but it makes the point. Imagine powerful telescopes aimed at two distant and very, very fuzzy galaxies approximately at opposite ends of the observable universe. If Galaxy A produces a supernova before Galaxy B does, call it a "1." Otherwise, a "0." This Galactic Random Number Generator, or GNRG, cannot be predicted or influenced (outcome altered) by any being subject to the laws of relativity. The two galaxies are "spacelike to the max," being separated by perhaps 15 billion light years, yadda yadda. We on Earth can see the supernovae if and when they occur, but neither galaxy can see the other. I can imagine many variants of this example, all cases where finite beings or computers in the universe are limited in what they can know by physics and cosmology constraints. Now I am not saying that this has anything to do with quantum randomness, just making the point that we know of no omniscient, omnipresent, omnipotent beings which could see all galaxies and know whether a "1" or a "0" would be recorded in this experiment. Are folks here familiar with the "holographic" picture of information flow near event horizons? --Tim May "Aren't cats Libertarian? They just want to be left alone. I think our dog is a Democrat, as he is always looking for a handout" --Unknown Usenet Poster
