tag:blogger.com,1999:blog-8148573551417578681.post7423909958194248640..comments2022-08-14T18:21:15.167-07:00Comments on Dark Buzz: The Underground Cult of Many-WorldsRogerhttp://www.blogger.com/profile/03474078324293158376noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-8148573551417578681.post-18908955482321744112021-08-16T13:47:46.510-07:002021-08-16T13:47:46.510-07:00Having pissing contests over the precision of how ...Having pissing contests over the precision of how many imagined infinities of angels are really dancing on your theoretical pin head is not a conversation worth having.<br /><br />No matter how many imaginary eggs you postulate out your mathematically pontificating posteriors, you will never be able to make an actual omelette out of them, so please stop trying. CFTnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-21929488160840357452021-08-16T12:16:33.157-07:002021-08-16T12:16:33.157-07:00Peter,
OK. Let's consider the example I gave ...Peter,<br /><br />OK. Let's consider the example I gave above. (It's not realistic, but a toy model of reality like that is useful.)<br /><br />Suppose I have a hypothetical isolated system having just ten position detectors (which can be described classically) and exactly one electron (which is always described QMcally). <br /><br />Initially, at t = t0 = 0, let's say that the state is: the position of the electron is not yet measured, and there is some wavefunction describing its initial condition. So, for times t > t0, the Schrodinger evolution applies---which is by postulates unitary. <br /><br />Then, at time t1 = say 1 second, the electron is detected at, say, D6 (detector 6). <br /><br />According to the mainstream QM (MSQM for short), the time-evolution process ceases to be unitary at t1. (Am I correct?) According to MSQM, the state of the electron is given, in the position representation, by a Dirac's delta situated at the position of D6. <br /><br />According to the MSQM, it's the Dirac's delta at D6 which now forms the IC (initial condition) for any further time passage t > t1, and the further evolution up to the next measurement is once again governed by Schrodinger's equation. <br /><br />Since \Psi is basically defined all over the physical space (even when it's been "reduced" to a Dirac's delta), right in an infinitesimal time dt after t1, the \Psi gets spread over the entire domain, including all the ten detectors. Hence, the electron can be detected, in principle, at any of the ten detectors. There is a very high probability of getting detected at D6---but there also are very small but in principle non-zero probabilities of detection at the other 9 detectors. (Am I correct?) <br /><br />This completes the first stage of measurements.<br /><br />Suppose the next position measurement occurs at D3, for which a similar set of statements can be made. The correlation of M1 (measurement 1) yielding position P3 (at D3) and M2 yielding P3 again is very high, but it's not the perfect 1.0. Not in principle---even if the evolution from just after the time t1 up to the instant t2 follows Schrodinger's equation, and hence is unitary. (Am I correct?)<br /><br />So, my Q1 is this: Why should unitarity imply a perfect correlation between two successive measurements on the same particle?<br /><br />And Q2: OK, now, please tell me what happens in MWI. How would you describe the process(es) before, at, and after M1 at t1? Also, please repeat, for M2 at t2, too. <br /><br />Best,<br />--Ajit<br />Ajit R. Jadhavhttps://ajitjadhav.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-79945087740611112332021-08-16T11:40:04.517-07:002021-08-16T11:40:04.517-07:00You only said many. Technically correct, but then,...You only said many. Technically correct, but then, size matters. <br /><br />"Many" can be just a finite number too (say 200). Or, countably infinite (say the set of integers). Or, uncountably infinite (say the real line). <br /><br />But what we have isn't even infinity raised to a finite number (say points in a 3D volume, which is infinity^3), but a "quantity" like Q(femtosecond), i.e., infinity of exponentions where each exponent itself is infinity...<br /><br />Calling the last kind of a ridiculously big abstraction just by the word "many" is misleading. That's what I meant.<br /><br />Best,<br />--Ajit<br />Ajit R. Jadhavhttps://ajitjadhav.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-747116399454816482021-08-16T10:53:36.155-07:002021-08-16T10:53:36.155-07:00Ajit, compute the correlation between a measuremen...Ajit, compute the correlation between a measurement A now and the same measurement at a later time, given that evolution is unitary: you'll find that there's a perfect correlation between the two results. The same is true for all measurements, in the absence of collapse. That is, Roger's account is justified by the mathematics: "our world is one of many worlds, according to the MWI", as you put it. There can be no branching, because for *all* measurements now, any two branches would have to give the same result, so there's no distinction to justify "this is one world, that is another", unless there was already such a distinction.<br />This "no branching" result arguably makes MWI exactly the same as probabilistic classical physics, with a Liouville state, which I suspect is part of why some people like it, however IMO one has to have a relatively sophisticated approach to understand why incompatible measurements are a classically useful concept.Peter Morganhttps://www.blogger.com/profile/06075268176382429701noreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-45559645067876058572021-08-16T10:45:53.399-07:002021-08-16T10:45:53.399-07:00How is that different from what I said?How is that different from what I said?Rogerhttps://www.blogger.com/profile/03474078324293158376noreply@blogger.comtag:blogger.com,1999:blog-8148573551417578681.post-42126666480654231772021-08-16T09:58:47.793-07:002021-08-16T09:58:47.793-07:00Dear Roger,
In your closing paragraph, you didn&#...Dear Roger,<br /><br />In your closing paragraph, you didn't get the "tree" right.<br /><br />It's not just that our world is one of many worlds, according to the MWI. That's what people often believe, but it's not correct. So, let's get the MWI idea right.<br /><br />First, let's consider a hypothetical scenario, one in which a measurement (say of position) results in one out of only 10 possible alternative measurements (with some probability, not necessarily equal, associated with each possible measurement). This is an abstraction, not reality, because the wavefunction is continuous in space, and also evolves continously in time. But it's a useful toy model to begin with. <br /><br />Since we are in abstractions, let's also say that there is a beginning instant, and that, initially, we are at that moment. Note, there is only one world at this moment.<br /><br />Then, measurement occurs, and according to the MWI, the initial one world now splits into ten---not two. <br /><br />Note, the word "splits" isn't exactly correct. 9 more worlds are "created" (in the sense, they weren't present at the initial instant, but now are).<br /><br />Each of these ten worlds is ruled by the ordinary postulates of the mainstream QM. Hence, further measurements are always possible---in each of them.<br /><br />Now, suppose a further measurement, once again of one outcome out of the 10 possible ones, occurs in the world #6. This measurement splits not just the world #6, but also each of the remaining 9 (including ours). Again, splits = created.<br /><br />But right at this stage (measurements set #2) the same process could in principle occur also in every world other than the world #6. Hence, at the end of the second set of measurements, there are 100 worlds in all---not 2 and not even 4 but 100. 98 of these are created by the two measurements.<br /><br />Point to note. Each measurements must create copies of *all* the previously created worlds. So, after any n-th stage of measurements, the number of worlds is 10^n. It's an exponential function.<br /><br />Unfortunately, the matter isn't as simple as the above abstraction. A little thought shows the following.<br /><br />Every small change in the wavefunction (say via the Schrodinger evolution) also implies a change in every potential measurement of every potentially measurable physical quantity. The latter includes the place where the detectors are (in each of the set of worlds which exists at any instant). Now, detectors can change their own position vectors continuously, but in the MS QM, it's not meaningful to talk of the positions except after measurements. All these and similar considerations together make the measurement possibilities, at every stage, an uncountably infinite set.<br /><br />So, the formula would now go as:<br /><br />one^{Infinity} at the end one first stage, and, after the elapse of an infinitesimally small passage of time, <br />one^{Infinity^{Infinity}}. <br /><br />So, for denoting the number of worlds after any finite amount of time, say even just one femtosecond, you still would need a new mathematical notation which has an infinity of nested operations of "raised to infinity". Call this quantity, say, Q(1 femtosecond).<br /><br />Notice, all these Q(1 femtosecond)-1 number of worlds have been created; only one existed at t=0. Each has mass, energy, entropy content, electric charge, magnetic field, etc., not to mention the Sun, the moon, the galaxies, the neutron stars, and all that. All of these---not infinite, but infinite raised to infinite raised to infinite... an infinity of times---number of worlds keep on coming in existence, with ever *greater* quantity, after each infinitesimal time dt.<br /><br />That's what MWI actually proposes.<br /><br />I am not clear if professors understand this point before they talk about MWI.<br /><br />Best,<br />--Ajit<br />Ajit R. Jadhavhttps://ajitjadhav.wordpress.comnoreply@blogger.com