5 ms·

[4/4] > Base states are arbitrary things, like a trap or a goal in QMM, but you can still ask what the chances are of a particle being in one of them. You're

by evanb 10y ago

[4/4] > Base states are arbitrary things, like a trap or a goal in QMM, but you can still ask what the chances are of a particle being in one of them. You're right that basis states can be arbitrary. However, that's not their most important characteristic. We say we have a basis if we have a set of states that covers all the possibilities and they're not redundant. That is, if any state can be written as a unique sum of basis states. > Stationary states are more like wavefunctions in QMM that have settled into a stable condition. Their phase may go on changing, but the amplitude doesn’t. The set of stationary states is a special basis. It's the set that when evolved in time only change by a phase, as you suggest---these states don't get mixed together when time marches on. So, how can a system "settle" into such a state? In other words, if you rewind the Schrodinger equation, what state was the system in before? Simple: it was in the same stationary state! Because stationary states form a basis, any non-stationary state is a unique sum of stationary states. In fact, if you know this basis and their corresponding energies you know all there is to know about a system's dynamics! If you take an arbitrary state and decompose it as a sum over stationary states (which is always possible, since they form a basis) then you immediately know how that state evolves in time, because you know how the individual components evolve in time. Since the individual stationary-state components don't mix together, the only thing that changes in time is their relative phases. So, if a system doesn't start in a stationary state, it cannot possibly reach one, without there being some kind of perturbation (ie. alteration of the system). Postscriptum Not having played, I can't say that it's not faithful to a deep understanding of quantum mechanics. But, I am skeptical, because your write-up seems to have a lot of confusion about what QM actually is / says. That's OK---it's a tricky subject. But I would avoid trying to push your game as a pedagogical learning tool unless it's been thoroughly vetted by actual physicists, because you could easily confuse neophytes. In some sense, the learning approach you have laid out stresses the parts of quantum mechanics that are the least interesting and least novel---they can be understood from playing with a wave equation. What's new is superposition, commutation of operators (or failure to commute), interference. That's why most modern approaches start with two-state systems (which immediately require bras and kets) and only go to systems with spatial extent later. In other words, it's better pedagogically to understand the operating system (quantum mechanics) before you start studying particular programs (particular systems). When you study particular systems there's a lot of intricate detail that doesn't matter for you to learn the lesson. You don't really need to know about the Laguerre polynomials or whatever. The way you learn quantum mechanics is by showing a bunch of wavefunctions are orthogonal---it's not about performing integrals. You're better off understanding orthogonality, linearity, and unitarity. > I found myself baffled trying to understand the connection between state notation, continuous wavefunctions... Moving from bras and kets to wavefunctions is, honestly, trivial---if you have a firm understanding of what's going on. That's why I'm nervous about trying to translate your game (which again, may be faithful to QM---I haven't played) into actual education. [continuity] https://en.wikipedia.org/wiki/Continuity_equation#Quantum_mechanics https://en.wikipedia.org/wiki/Continuity_equation#Quantum_me... [isospin] https://en.wikipedia.org/wiki/Isospin https://en.wikipedia.org/wiki/Isospin [fourplet] after triplet the words we use vary a bit. I've seen sextet, octet, and decuplet, but almost everything else is a n-plet or, generically, a multiplet. [weak] https://en.wikipedia.org/wiki/Weak_isospin https://en.wikipedia.org/wiki/Weak_isospin Sorry about the multi-comment. When I tried to post it as one thing I just got "That comment was too long."

sideshowb 10y ago
Hi evanb, thank you for your efforts in writing a detailed assessment. That's all very enlightening indeed. I'm sure I'll have more to ask about individual parts once it's all sunk in but thought I'd acknowledge the whole response right now!
sideshowb 10y ago
Right, guardians dispatched, onto the boss :) There’s lots of really interesting stuff here to follow up, some of which will take me a very long time. All of it is appreciated as I haven’t yet had the opportunity to discuss the subject with somebody who truly has a handle on the subject - at least not since the optional first year physics module I took as part of my CS degree 17 years ago, and that didn’t go this far. In no particular order… > I would avoid trying to push your game as a pedagogical learning tool unless it's been thoroughly vetted by actual physicists Noted, though vetting is exactly what I’m trying to make a start on here :) Your comments on the learning process are interesting and don’t square with my own experience, though perhaps they would if I were formally taught. I might scale them back. While we’re talking about vetting, if you’d like to be credited for your efforts towards that, by real name or HN handle, please let me know as I feel it would only be fair to add an acknowledgement. >Gauge symmetry isn't the independence of the global phase---it's the independence of a spacetime-dependent phase. I don’t quite follow what the latter means, but is it correct to say that independence of global absolute phase arises from gauge symmetry? >That's exactly the opposite of what the Schrodinger equation says! Noted and understood. I should replace “can’t exist” with “has low probability” and modify accordingly. >If you can find a way to simulate an arbitrarily-sized quantum computer with a reasonable amount of computing, you will get famous. A few particles should be possible but it won't scale well. Yup. A few particles was what I had in mind. >> Nuclear forces arise when … >Oy. This is wrong. Excellent advice, thanks for the heads up: I’ll cut the entire footnote. Are nuclear forces getting beyond QM then – into QFT? I would love to go on and learn that but haven’t got there yet. >> Until that question is answered, then we can’t rule out the possibility that consciousness does have something to do with it. >Are you sure you only read Feynman? This is an extreme fringe position. I don't know any physicists who actually holds this position, unless they're trying to get on TV. >No. Decoherence is the thing that lets you avoid the need to collapse at all. >This is the claim of the Many Worlds interpretation With interpretations of QM I think we’re getting more into philosophy than physics, until the day comes that we get different predictions from any of them. Somehow this makes me feel qualified to argue with a nuclear physicist... I may be discussing a fringe position, but am I right in thinking your counterargument relies on invoking many worlds, which isn’t mainstream either? To summarize the popular interpretations - Copenhagen is mainstream but doesn’t explain collapse - Many worlds is quite popular but possibly the least parsimonious theory in the entire history of science - Pilot wave theory holds promise as it doesn’t need collapse, it isn’t mainstream though seems to be gaining popularity at the moment So at the moment I’d say there is still room for a consciousness based interpretation. I’m a former AI researcher btw, I used to take the strong AI consciousness-as-emergence position but I no longer think that explanation cuts the mustard. At the present state of science I think all we can say about consciousness is “there is some very big important process going on and we don’t have the first clue what, where and how”... as such I don’t think it’s scientific to completely rule out the possibility that consciousness is involved in collapse as the latter is a process we haven’t adequately explained yet either. Presumably most physicists steer clear of this as consciousness is so far beyond where science is now that they’d rather (quite sensibly) not speculate, lest they be remembered as the Victorian engineer who thought life came from electricity. My aim is to discuss not support that view by the way – I think a newcomer to the subject would naturally be curious about why some people think consciousness is involved. Still, until there’s experimental evidence I’m hedging my bets. Anyway enough pub chat! Finally I’d be interested to know your take on leni536’s point about uncertainty further down this thread? That seems to be an unresolved technical discussion to me.

by evanb 10y ago

sideshowb 10y ago

Hi evanb, thank you for your efforts in writing a detailed assessment. That's all very enlightening indeed. I'm sure I'll have more to ask about individual parts once it's all sunk in but thought I'd acknowledge the whole response right now!

sideshowb 10y ago

Right, guardians dispatched, onto the boss :) There’s lots of really interesting stuff here to follow up, some of which will take me a very long time. All of it is appreciated as I haven’t yet had the opportunity to discuss the subject with somebody who truly has a handle on the subject - at least not since the optional first year physics module I took as part of my CS degree 17 years ago, and that didn’t go this far. In no particular order… > I would avoid trying to push your game as a pedagogical learning tool unless it's been thoroughly vetted by actual physicists Noted, though vetting is exactly what I’m trying to make a start on here :) Your comments on the learning process are interesting and don’t square with my own experience, though perhaps they would if I were formally taught. I might scale them back. While we’re talking about vetting, if you’d like to be credited for your efforts towards that, by real name or HN handle, please let me know as I feel it would only be fair to add an acknowledgement. >Gauge symmetry isn't the independence of the global phase---it's the independence of a spacetime-dependent phase. I don’t quite follow what the latter means, but is it correct to say that independence of global absolute phase arises from gauge symmetry? >That's exactly the opposite of what the Schrodinger equation says! Noted and understood. I should replace “can’t exist” with “has low probability” and modify accordingly. >If you can find a way to simulate an arbitrarily-sized quantum computer with a reasonable amount of computing, you will get famous. A few particles should be possible but it won't scale well. Yup. A few particles was what I had in mind. >> Nuclear forces arise when … >Oy. This is wrong. Excellent advice, thanks for the heads up: I’ll cut the entire footnote. Are nuclear forces getting beyond QM then – into QFT? I would love to go on and learn that but haven’t got there yet. >> Until that question is answered, then we can’t rule out the possibility that consciousness does have something to do with it. >Are you sure you only read Feynman? This is an extreme fringe position. I don't know any physicists who actually holds this position, unless they're trying to get on TV. >No. Decoherence is the thing that lets you avoid the need to collapse at all. >This is the claim of the Many Worlds interpretation With interpretations of QM I think we’re getting more into philosophy than physics, until the day comes that we get different predictions from any of them. Somehow this makes me feel qualified to argue with a nuclear physicist... I may be discussing a fringe position, but am I right in thinking your counterargument relies on invoking many worlds, which isn’t mainstream either? To summarize the popular interpretations - Copenhagen is mainstream but doesn’t explain collapse - Many worlds is quite popular but possibly the least parsimonious theory in the entire history of science - Pilot wave theory holds promise as it doesn’t need collapse, it isn’t mainstream though seems to be gaining popularity at the moment So at the moment I’d say there is still room for a consciousness based interpretation. I’m a former AI researcher btw, I used to take the strong AI consciousness-as-emergence position but I no longer think that explanation cuts the mustard. At the present state of science I think all we can say about consciousness is “there is some very big important process going on and we don’t have the first clue what, where and how”... as such I don’t think it’s scientific to completely rule out the possibility that consciousness is involved in collapse as the latter is a process we haven’t adequately explained yet either. Presumably most physicists steer clear of this as consciousness is so far beyond where science is now that they’d rather (quite sensibly) not speculate, lest they be remembered as the Victorian engineer who thought life came from electricity. My aim is to discuss not support that view by the way – I think a newcomer to the subject would naturally be curious about why some people think consciousness is involved. Still, until there’s experimental evidence I’m hedging my bets. Anyway enough pub chat! Finally I’d be interested to know your take on leni536’s point about uncertainty further down this thread? That seems to be an unresolved technical discussion to me.