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[1/4] Source: I am a nuclear physicist. Full disclosure: I didn't play. I'm not launching a Java applet. So I'm just reading your description for physics con

by evanb 10y ago

[1/4] Source: I am a nuclear physicist. Full disclosure: I didn't play. I'm not launching a Java applet. So I'm just reading your description for physics content. > (The independence of quantum systems from absolute phase is called gauge symmetry) Gauge symmetry isn't the independence of the global phase---it's the independence of a spacetime-dependent phase. This is a much much bigger symmetry than the independence of global absolute phase. > 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. > Interestingly, the Schrodinger equation states that a particle can’t exist at all in a place with more potential than the particle has energy. It will simply “jump” down any available holes to satisfy the equation. The same jumping behaviour is what gives rise to tunelling, when a particle jumps as if by magic from one hole to another. That's exactly the opposite of what the Schrodinger equation says! A particle can exist in a place where the potential energy is more than the total energy. That cannot happen classically, but is allowed quantum-mechanically. However, the wavefunction dies off exponentially fast. But it's never 0 unless the potential is infinite. That's what allows tunneling---the exponentially small tail is real. There is no "jumping" in quantum mechanics. The Schrodinger equation implies the continuity equation [continuity].

evanb 10y ago
[2/4] > Decoherence doesn’t explain, though, why the wavefunction collapses to a singular thing we call “reality”. So quantum mysticism still has room to flourish. No. Decoherence is the thing that lets you avoid the need to collapse at all. The point of decoherence is that many quantum particles interacting together looks like a quantum superposition of many classical systems. So if you "are" one of those particles and look around, you'll see things behaving classically---only if you are "outside" (ie. have full access to the wf) can you see anything quantum going on. If the wavefunction doesn't collapse, why does it look like it does collapse?! Well, you're inside the wavefunction. Before the different classical possibilities decohere, you wait with anticipation. After decoherence, a version of you is in each branch of the wavefunction, each observing different outcomes, wondering how the wavefunction collapsed! But, it didn't---it's just hard to see that from where you're standing. This is the claim of the Many Worlds interpretation --- the wavefunction never collapses. Everything just evolves according to the Schrodinger equation, forever. There is no place or regime where quantum mechanics breaks down. Every branch of the wavefunction is equally real and continues to exist forever. So, why don't we see all sorts of zany, quantum effects in our every day life? Decoherence saves the day: even with a few dozen particles the different branches of the wavefunction have decohere enough that it'd take a massive, huge, gargantuan coincidence for two parts of the wavefunction to interfere. It's still possible! But it's extremely unlikely. Now scale up to Avogadro's number of particles, and forget it: things just look classical.
evanb 10y ago
[3/4] > You could also massively simplify particle interactions to make some reasonable gameplay; perhaps even simulate a quantum computer. Do get in touch with me if you want to do this; I’d be keen to help. 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. You're right to worry about how to draw it. You might consider (fixed-in-space) spin systems instead, where you can draw the density matrix with (relative) simplicity. But then you lose the moving-around-in-space intuition. > Feynman dedicates a lot of his book to two state systems, because these are ultimately responsible for the strong and weak nuclear forces. > Nuclear forces arise when you vary the size of the system, and the two possible stationary states display slightly different energy characteristics. This means the system has a lower energy at a certain size. Oy. This is wrong. Two state systems are interesting in-and-of-themselves because you can exactly solve them, they have many actual instatiations in nature (in fact, anything you might consider making a qubit out of!), and they provide toy models for many kinds of other physical systems. Nuclear forces do not arise from two state systems. There is a pecularity in nuclear physics---the proton and the neutron look (almost) exactly the same. OK, they have different electric charge, but nuclear force doesn't care about electromagnetism. What's interesting is that they have almost exactly the same mass: m_Neutron = 939 MeV, m_Proton = 938 MeV. Well, that's quite surprising! Why should that be? Most particles we know have dramatically differing masses (eg. m_electron = 0.511 MeV, etc). So, what's making these masses come out the same? Moreover, people noticed empirically that the interaction between protons and neutrons seemed to look roughly the same (once you account for electromagnetism). This led people to hypothesize a symmetry called isospin symmetry---the symmetry between protons and neutrons [isospin]. You can make a lot of progress by assuming that protons and neutrons form two-state system and that the nuclear force doesn't care which state you're in. Then, you can incorporate the slight differences on top. In fact, you can get a lot farther once you have this idea in hand. You realize that the pions form an iso-triplet, the delta baryons form an iso-fourplet, etc [fourplet]. Then you find particles with strangeness, and you really get going. You wind up recognizing deeper underlying patterns that reveal beautiful symmetry. Isospin symmetry is not a true symmetry of nature, but it's a very good approximation, and it's related in some ways to weak isospin [weak].
- 10y ago
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."
Steuard 10y ago
Not that a quality post like this needs it, but for what it's worth, as a physics professor I'd happily endorse just about everything you've said in this detailed response to the text accompanying the game (all four parts). (My own comments focused mostly on the game itself, to the extent that I get what's going on under the hood.)
- dxbydt 10y ago
  Aside: Hey you are the guy who wrote those awesome tutorials on lagrange multipliers!!! I actually used your materials multiple times at official presentations, devtimes and other occasions where the management and developers wanted to know how bidding optimization worked under the hood. Thank you so much for writing so well.
  - Steuard 10y ago
    I'm glad to hear that you've appreciated that tutorial! It's especially neat to hear about it being useful to people who aren't just cramming for a class.
- evanb 10y ago
  Well, thanks! Now if you know any tenure-track job openings looking for a lattice gauge theorist / nuclear physicist... I do side projects on string theory and BSM physics, if that helps :P

by evanb 10y ago

evanb 10y ago

[2/4] > Decoherence doesn’t explain, though, why the wavefunction collapses to a singular thing we call “reality”. So quantum mysticism still has room to flourish. No. Decoherence is the thing that lets you avoid the need to collapse at all. The point of decoherence is that many quantum particles interacting together looks like a quantum superposition of many classical systems. So if you "are" one of those particles and look around, you'll see things behaving classically---only if you are "outside" (ie. have full access to the wf) can you see anything quantum going on. If the wavefunction doesn't collapse, why does it look like it does collapse?! Well, you're inside the wavefunction. Before the different classical possibilities decohere, you wait with anticipation. After decoherence, a version of you is in each branch of the wavefunction, each observing different outcomes, wondering how the wavefunction collapsed! But, it didn't---it's just hard to see that from where you're standing. This is the claim of the Many Worlds interpretation --- the wavefunction never collapses. Everything just evolves according to the Schrodinger equation, forever. There is no place or regime where quantum mechanics breaks down. Every branch of the wavefunction is equally real and continues to exist forever. So, why don't we see all sorts of zany, quantum effects in our every day life? Decoherence saves the day: even with a few dozen particles the different branches of the wavefunction have decohere enough that it'd take a massive, huge, gargantuan coincidence for two parts of the wavefunction to interfere. It's still possible! But it's extremely unlikely. Now scale up to Avogadro's number of particles, and forget it: things just look classical.

evanb 10y ago

[3/4] > You could also massively simplify particle interactions to make some reasonable gameplay; perhaps even simulate a quantum computer. Do get in touch with me if you want to do this; I’d be keen to help. 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. You're right to worry about how to draw it. You might consider (fixed-in-space) spin systems instead, where you can draw the density matrix with (relative) simplicity. But then you lose the moving-around-in-space intuition. > Feynman dedicates a lot of his book to two state systems, because these are ultimately responsible for the strong and weak nuclear forces. > Nuclear forces arise when you vary the size of the system, and the two possible stationary states display slightly different energy characteristics. This means the system has a lower energy at a certain size. Oy. This is wrong. Two state systems are interesting in-and-of-themselves because you can exactly solve them, they have many actual instatiations in nature (in fact, anything you might consider making a qubit out of!), and they provide toy models for many kinds of other physical systems. Nuclear forces do not arise from two state systems. There is a pecularity in nuclear physics---the proton and the neutron look (almost) exactly the same. OK, they have different electric charge, but nuclear force doesn't care about electromagnetism. What's interesting is that they have almost exactly the same mass: m_Neutron = 939 MeV, m_Proton = 938 MeV. Well, that's quite surprising! Why should that be? Most particles we know have dramatically differing masses (eg. m_electron = 0.511 MeV, etc). So, what's making these masses come out the same? Moreover, people noticed empirically that the interaction between protons and neutrons seemed to look roughly the same (once you account for electromagnetism). This led people to hypothesize a symmetry called isospin symmetry---the symmetry between protons and neutrons [isospin]. You can make a lot of progress by assuming that protons and neutrons form two-state system and that the nuclear force doesn't care which state you're in. Then, you can incorporate the slight differences on top. In fact, you can get a lot farther once you have this idea in hand. You realize that the pions form an iso-triplet, the delta baryons form an iso-fourplet, etc [fourplet]. Then you find particles with strangeness, and you really get going. You wind up recognizing deeper underlying patterns that reveal beautiful symmetry. Isospin symmetry is not a true symmetry of nature, but it's a very good approximation, and it's related in some ways to weak isospin [weak].

10y ago

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."

Steuard 10y ago

Not that a quality post like this needs it, but for what it's worth, as a physics professor I'd happily endorse just about everything you've said in this detailed response to the text accompanying the game (all four parts). (My own comments focused mostly on the game itself, to the extent that I get what's going on under the hood.)

dxbydt 10y ago
Aside: Hey you are the guy who wrote those awesome tutorials on lagrange multipliers!!! I actually used your materials multiple times at official presentations, devtimes and other occasions where the management and developers wanted to know how bidding optimization worked under the hood. Thank you so much for writing so well.
- Steuard 10y ago
  I'm glad to hear that you've appreciated that tutorial! It's especially neat to hear about it being useful to people who aren't just cramming for a class.
evanb 10y ago
Well, thanks! Now if you know any tenure-track job openings looking for a lattice gauge theorist / nuclear physicist... I do side projects on string theory and BSM physics, if that helps :P