tag:blogger.com,1999:blog-5592542.post804565543489245500..comments2019-09-08T23:04:03.923-07:00Comments on Rondam Ramblings: The Trouble with Many WorldsRonhttp://www.blogger.com/profile/11752242624438232184noreply@blogger.comBlogger88125tag:blogger.com,1999:blog-5592542.post-5997022880528017512019-07-28T21:02:17.225-07:002019-07-28T21:02:17.225-07:00@Ron:
A natural question to ask, then, is: can bra...@Ron:<br /><i>A natural question to ask, then, is: can branch weights be measured? In particular, can we measure our own branch weight? The answer turns out to be no, you can't. Branch weights are an IPU -- provably, necessarily -- just like parallel universes themselves.</i><br /><br />Since I have been disagreeing with some things you've said, I should emphasize that I am not disputing Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-89314385591127114692019-07-28T17:31:14.962-07:002019-07-28T17:31:14.962-07:00@Don:
Flatland is not a bad analogy, but it's...@Don:<br /><br />Flatland is not a bad analogy, but it's flawed in one very significant way. Going from two dimensions to three is very similar to the process of going from three to four. That is not true for going to the classical to the quantum. There is a fundamental unbridgeable chasm in the form of the no-cloning theorem. The only way you can take any kind of point of view about Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-5643122006322261192019-07-28T17:12:38.865-07:002019-07-28T17:12:38.865-07:00@Ron:
I am given to understand that the Dirac equ...@Ron:<br /><i> I am given to understand that the Dirac equation is structurally the same as the SE, just with some higher order terms in the Hamiltonian.</i><br /><br />This is basically true of the Dirac equation as it was originally constructed, to be an analogue of the Schrodinger Equation for a spin-1/2 particle. However, the Dirac equation in this interpretation is not QFT. It's an earlyPeter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-30731445823533552252019-07-28T15:02:45.504-07:002019-07-28T15:02:45.504-07:00@Ron: "The wave function is analogous to the ...@Ron: "<i>The wave function is analogous to the DVD</i>"<br /><br />I enjoyed (and appreciated) the analogy. Although of course, the old idea of a "block universe" (as one perspective on the "illusion" of time) doesn't even depend on quantum mechanics. That's a philosophical concept even in a Newtonian universe.<br /><br />"<i>you have no choice but toDon Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-17979828504635468332019-07-28T14:28:11.777-07:002019-07-28T14:28:11.777-07:00> configuration space is not ordinary space for...> configuration space is not ordinary space for any quantum system other than a single spinless particle<br /><br />That doesn't matter. From a mathematical point of view, psi is still a function of a bunch of numbers, and you can partially evaluate that function with respect to any subset of the input variables, at least in principle. The special nature of time is a reflection of the *Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-74099719772823939672019-07-28T11:34:32.644-07:002019-07-28T11:34:32.644-07:00@Ron:
From a God's-eye point of view, which is...@Ron:<br /><i>From a God's-eye point of view, which is the POV you have to take in order to see the multiverse, it's static.</i><br /><br />I disagree. A "God's eye point of view" can be taken simply by viewing the wave function--by which I mean the wave function at a particular value of the time parameter t--as describing the entire universe. Then the evolution of the wave Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-34019907648286008902019-07-28T11:27:53.580-07:002019-07-28T11:27:53.580-07:00@Ron:
You can choose to view t as a parameter, an...@Ron:<br /><i> You can choose to view t as a parameter, and the resulting function of x as telling you the "state" of the particle at a "point" in time. But you could just as well choose to view x as a parameter, and the resulting function telling you the evolution of the amplitude of the particle over time at a point in space.</i><br /><br />But the first view, viewing t as aPeter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-91631391389278549252019-07-28T09:37:30.295-07:002019-07-28T09:37:30.295-07:00@Peter:
> configuration space is not ordinary ...@Peter:<br /><br />> configuration space is not ordinary 3-space<br /><br />Yes, I should not have said 4-D. But I stand by "static" because...<br /><br />> time in this formalism is not a coordinate--it's not a label for points in spacetime. It's a parameter<br /><br />So? What difference does it make what the semantics of the time parameter are? It's still an Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-27967223781602714372019-07-27T17:47:35.648-07:002019-07-27T17:47:35.648-07:00@Ron:
if you're going to take the math serious...@Ron:<br /><i>if you're going to take the math seriously, then you need to take the math seriously, and the math says that the solution to the SchrÃ¶dinger equation is a function of configuration and time.</i><br /><br />More precisely, it says that the *time derivative* of the wave function is given by the Hamiltonian operating on that wave function. But time in this formalism is not a Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-58710008385100040042019-07-27T17:36:33.810-07:002019-07-27T17:36:33.810-07:00@Ron:
see the Wikipedia quote above. It is using t...@Ron:<br /><i>see the Wikipedia quote above. It is using the word "ray" to mean the representation-independent mathematical object, and "state vector" to mean some particular representation of that ray.</i><br /><br />Yes, this is a valid point; strictly speaking, any vector on the same ray in a Hilbert space represents the same physical state, so we have to pick one in order Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-46824676580968652762019-07-27T12:11:36.412-07:002019-07-27T12:11:36.412-07:00> I certainly prefer MWI to "Copenhagen c...> I certainly prefer MWI to "Copenhagen conscious observation collapse", which is just incoherent.<br /><br />That's one of the beautiful things about QIT: it makes this coherent. QIT is the *only* interpretation that really takes the math seriously. In particular, it's the one interpretation that takes the no-cloning theorem seriously, and the consequent fact that in Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-10085962537231822692019-07-27T07:56:17.012-07:002019-07-27T07:56:17.012-07:00@Ron: "The disagreement is over whether the B...@Ron: "<i>The disagreement is over whether the Born rule needs to be accepted as an axiom, or whether it can be derived from something else</i>"<br /><br />Sure, although I might word it as: <i>everyone</i> would love to derive the Born rule from something more fundamental. But only some people think they have such a derivation. The others, realizing that you can't do without it, Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-60797379458141938902019-07-26T23:10:20.495-07:002019-07-26T23:10:20.495-07:00@Don:
I'm going to respond out of order, beca...@Don:<br /><br />I'm going to respond out of order, because I've left you with a very wrong impression:<br /><br />> If that's what you think, no wonder it didn't hold much appeal for you.<br /><br />It's not that the MWI doesn't "hold much appeal." It's not that I dislike it. It's not even that I think it's *wrong*; I don't. It isn't. Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-5556183973705596882019-07-26T19:25:33.995-07:002019-07-26T19:25:33.995-07:00@Ron: I don't think you're being fair to M...@Ron: I don't think you're being fair to MWI. At some point, you need to predict the outcomes of experiments. E.g., If you run a million of these tests, your counter is going to report ("very close to") 3/4 "A" result and 1/4 "B" result. <i>Every</i> QM interpretation needs to yield the same predictions. MWI gets those predictions by a Born rule. MWI Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-49247473904220779002019-07-26T18:15:29.164-07:002019-07-26T18:15:29.164-07:00@Don:
> The original MWI (as I understand it) ...@Don:<br /><br />> The original MWI (as I understand it) does seem to have the Born rule as an additional, not well-understood, "hack".<br /><br />No. In the MWI there is no collapse. Everything is completely deterministic. There are no probabilities, so the Born rule is not only unnecessary, it's *incoherent*. (That's why Deutsch's argument is framed in terms of the Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-41827227720425814702019-07-26T16:59:43.792-07:002019-07-26T16:59:43.792-07:00@Ron: "The *whole point* of the MWI is that y...@Ron: "<i>The *whole point* of the MWI is that you *don't* have to introduce random hacks like the Born rule</i>"<br /><br />I'm not sure that I would have described the situation that way. The original MWI (as I understand it) does seem to have the Born rule as an additional, not well-understood, "hack". This is why the attempt by Deutsch/Wallace is so interesting, Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-34971385924979733022019-07-26T16:23:05.877-07:002019-07-26T16:23:05.877-07:00> If a particular textbook doesn't use it a...> If a particular textbook doesn't use it at all, that is not evidence that its meaning, as it is used in places that do use it, is open to interpretation.<br /><br />That's true, but Griffiths is not just any old textbook. It's widely considered to be the leading textbook. So while the omission of a definition for "state vector" there is not probative, it is indicativeRonhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-13715118389395239472019-07-26T12:17:43.485-07:002019-07-26T12:17:43.485-07:00@Ron:
I think it's fair to say that the meani...@Ron:<br /><i> I think it's fair to say that the meaning of the term "state vector" is open to some interpretation.</i><br /><br />If a particular textbook doesn't use it at all, that is not evidence that its meaning, as it is used in places that do use it, is open to interpretation.<br /><br />The mathematical framework of vectors in a Hilbert space is standard QM, and I'vePeter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-55541405637918243552019-07-25T23:21:44.481-07:002019-07-25T23:21:44.481-07:00(part 2 of 2)
> The wave function ... doesn...(part 2 of 2)<br /><br />> The wave function ... doesn't add time to the configuration space.<br /><br />I didn't say it did. I said it added time as another dimension of the *domain* (of the function).<br /><br />> Strictly speaking, the wave function "changing with time" really means there is a functional...<br /><br />Sure, but why make it more complicated than it Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-56758016684715863612019-07-25T23:21:26.083-07:002019-07-25T23:21:26.083-07:00@Peter:
> The state vector is just an abstract...@Peter:<br /><br />> The state vector is just an abstract vector in a Hilbert space<br /><br />Maybe.<br /><br />Griffiths, for example, does not use the term "state vector" at all. It does not appear in the index of "Introduction to quantum mechanics (second edition)." (Why do I suddenly feel like Hermione Granger?) So at worst I think it's fair to say that the Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-18666510964928497932019-07-25T15:58:39.658-07:002019-07-25T15:58:39.658-07:00@Ron:
The state vector is a function whose range ...@Ron:<br /><i> The state vector is a function whose range is complex numbers and whose domain is the configuration space of a system.</i><br /><br />Strictly speaking, that's the wave function. The state vector is just an abstract vector in a Hilbert space, with no commitment to any interpretation in terms of a particular configuration space or set of square integrable functions on it. For Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-74122835557847566312019-07-25T15:53:11.350-07:002019-07-25T15:53:11.350-07:00Sorry, I referenced @Don in my last comment, but I...Sorry, I referenced @Don in my last comment, but I meant @Dr. Guy Gordon.Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-79398287294471018952019-07-25T15:51:26.729-07:002019-07-25T15:51:26.729-07:00@Don:
the wave *function* is a function that predi...@Don:<br /><i>the wave *function* is a function that predicts the evolution of the State Vector with time.</i><br /><br />No, that's the Hamiltonian. The wave function is the state vector--more precisely, it's what you get when you pick a particular representation for the state vector in the space of square integrable functions from the configuration space to the complex numbers.<br />Peter Donishttps://www.blogger.com/profile/09122769947782402203noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-65147952175824458512019-07-23T17:45:09.701-07:002019-07-23T17:45:09.701-07:00@Ron: "I don't share your optimism that t...@Ron: "<i>I don't share your optimism that their efforts will ultimately succeed.</i>"<br /><br />I may have misled you! I'm agnostic about the specific effort of Deutsch/Wallace. (I'm not informed enough to have a useful opinion on their effort.) I was only expressing confidence that there will eventually be <i>some</i> satisfying explanation of the Born rule -- by Don Geddishttps://www.blogger.com/profile/04214642122689048677noreply@blogger.comtag:blogger.com,1999:blog-5592542.post-87367734004049438812019-07-23T17:16:33.627-07:002019-07-23T17:16:33.627-07:00@Don:
I agree with you that Deutsch and Wallace&#...@Don:<br /><br />I agree with you that Deutsch and Wallace's investigations are worthwhile, but I don't share your optimism that their efforts will ultimately succeed. Finding Born in MWI faces a fundamental problem: it depends entirely on branch weights (there is nothing else) but branch weights are inherently unknowable. Like I said above, it's the exact same problem that Bohmian Ronhttps://www.blogger.com/profile/11752242624438232184noreply@blogger.com