3 ms·

My turn to nitpick: > as the wavefunction evolves in time, its probability amplitude spreads throughout space sed 's/probability//' Probability is a real n

My turn to nitpick: > as the wavefunction evolves in time, its probability amplitude spreads throughout space sed 's/probability//' Probability is a real number embodied in a state of mind[1]. Amplitude are (as far as current physics believes) a complex number out there in the world. I know, squared norm and Born statistics, but still.[2] http://lesswrong.com/lw/oj/probability_is_in_the_mind/ http://lesswrong.com/lw/oj/probability_is_in_the_mind/ http://lesswrong.com/lw/r5/the_quantum_physics_sequence/ http://lesswrong.com/lw/r5/the_quantum_physics_sequence/

darkmighty 13y ago
Oh god who writes those? It's a convention in physics to call it probability amplitude because, you know, it makes sense, as a direct analogous to energy. (http://en.wikipedia.org/wiki/Probability_amplitude http://en.wikipedia.org/wiki/Probability_amplitude) If you want to learn quantum mechanics there are far better places than sketchy, hand waving articles. I'd start here: http://www.youtube.com/watch?v=hUJfjRoxCbk http://www.youtube.com/watch?v=hUJfjRoxCbk
- loup-vaillant 13y ago
  > It's a convention in physics to call it probability amplitude because, you know, it makes sense, as a direct analogous to energy. Wait, what? Could you please flesh out the analogy between probability and energy? --- From the Wikipedia article: > Probability amplitudes provide a physical meaning of the wave function, a link first proposed by Max Born, and this is a pillar of the Copenhagen interpretation of quantum mechanics. Oh, my… I'd say the real pillar of the Copenhagen interpretation is the word "probability". Which is rather weak, compared to the fact that the collapse postulate of the Copenhagen interpretation is non-linear, non-unitary, non-differentiable (even discontinuous!), non-local, violates CPT-symmetry and Liouville's Theorem, non-deterministic, and faster-than-light. Oh, and it's strictly more complex than a many-world interpretation, since it adds an extra postulate on top of existing equations. http://lesswrong.com/lw/q6/collapse_postulates/ http://lesswrong.com/lw/q6/collapse_postulates/ Seriously, how many arrows to the chest does the Copenhagen Interpretation must endure before we declare it dead, and stop saying "probability" before every occurrence of "amplitude"? --- Fire a photon through a half sieved mirror, with 2 sensors to catch the 2 possible paths, such that no matter what, one of the sensors will go off. What do you think happens? The equations (you know them more than I do) say the amplitude will flow and decohere into 2 non-interacting blobs. The blob where sensor 1 goes off, and the blob where sensor 2 goes off. (Note from Captain Obvious: the equations are deterministic. They do not say that God plays dice with the universe.) Now say you fire the photon, and observe sensor 1 going off. What do you think happened to the other blob, the one you don't interact with? Do you think it went away just like that? It would be like believing that a colonization spaceship going beyond the observable universe disappears, not only from your view, but for good. http://lesswrong.com/lw/pb/belief_in_the_implied_invisible/ http://lesswrong.com/lw/pb/belief_in_the_implied_invisible/ --- Of course this sequence is sketchy and hand waving (it doesn't even try to hide it). Its purpose is not to teach us Quantum Physics. Only certain aspects of it, to serve a philosophical agenda (most notably questions around personal identity and Free Will).
- Jach 13y ago
  What makes sense about a probability that can take on negative or complex values and collections of which don't sum to 1? Convention is no excuse for bad terminology or notation, especially for beginners to the subject who may not have the math or physics background to appreciate the connection with the continuity equation. You lose nothing by removing the word "probability" and avert possible confusion. "Amplitude" and either "squared modulus" or "amplitude density" work fine. I think Feynman's QED is mandatory reading for an intro to quantum thinking (and Feynman in general is fantastic). I also think his several comments on wave v. particle indicate another abuse of conventional terminology. Sometimes he'll insist light is not a wave but a particle, but it's actually a screwy kind of particle and you need to think about arrows and paths. ("Collapse" is another word that'd be better off going away...) My favorite beginner-level approach to QM nowadays, at least for beginners who are familiar with linear algebra, is actually Scott Aaronson's (edit: who is an expert in the field, and I believe has even commented on some of Eliezer's quantum posts...) (quantum) computer scientist approach: http://www.scottaaronson.com/democritus/lec9.html http://www.scottaaronson.com/democritus/lec9.html It introduces QM as "What if we tried to make something like probability theory but allowing negative or complex values?" It wouldn't be probability, but it would be like probability. Once you set up the math, the usual "weird" quantum effects of experiments can be shown as a direct consequence of the math.
eli_gottlieb 13y ago
I'm gonna have to agree with darkmighty here: learn your physics from physicists, not from Eliezer. No matter how well or badly he actually understands quantum physics (which I'm not qualified to judge), we should be learning from actual expert practitioners rather than from a fellow amateur who happened to "ace the class", so to speak. If physicists say probability amplitude, it's called probability amplitude.
- loup-vaillant 13y ago
  I'm willing to believe experts when I know nothing about a subject. Given the apparent current reception of MWI[1], I concede that things are not looking good for Everett. On the other hand, arguments trump authority[2]. And Eliezer produced specific, very convincing arguments in favour of Everett. To this day, I don't know of any specific strong objection to his writings on the subject. Therefore I believe him. (For now. Please let me know if you know of any objection he did not address.) Physicists say "probability amplitude"? I don't care. I'll go on saying "amplitude" alone. The term is less confusing, and physicists will understand me regardless. [1]: https://en.wikipedia.org/wiki/Many-worlds_interpretation#Polls https://en.wikipedia.org/wiki/Many-worlds_interpretation#Pol... [2]: http://lesswrong.com/lw/lx/argument_screens_off_authority/ http://lesswrong.com/lw/lx/argument_screens_off_authority/
- Xcelerate 13y ago
  I'm taking a QFT class at my university right now, and it's very different than any discussion of quantum mechanics I see online. It's pages upon pages of math and linear algebra. Very little text or discussion. Physicists don't really care whether you call it "probability", "probability amplitude", or "fish". What you end up with is an equation that you can take to the lab and use to predict experimentally measured results. I'll add that at some point the math just becomes so bizarre that you can't (or at least I'm unable to) come up with some kind of textual analogy for it. (This is what QFT is like for me: Manipulate symbols according to mathematical rules until you end up with an equation. Realize the equation can't be solved analytically. Realize exponential computing power would be required to solve it numerically. Make an approximation and modify the equation. Solve numerically and see how well it agrees with experiment.)

darkmighty 13y ago

Oh god who writes those? It's a convention in physics to call it probability amplitude because, you know, it makes sense, as a direct analogous to energy. (http://en.wikipedia.org/wiki/Probability_amplitude http://en.wikipedia.org/wiki/Probability_amplitude) If you want to learn quantum mechanics there are far better places than sketchy, hand waving articles. I'd start here: http://www.youtube.com/watch?v=hUJfjRoxCbk http://www.youtube.com/watch?v=hUJfjRoxCbk

loup-vaillant 13y ago
> It's a convention in physics to call it probability amplitude because, you know, it makes sense, as a direct analogous to energy. Wait, what? Could you please flesh out the analogy between probability and energy? --- From the Wikipedia article: > Probability amplitudes provide a physical meaning of the wave function, a link first proposed by Max Born, and this is a pillar of the Copenhagen interpretation of quantum mechanics. Oh, my… I'd say the real pillar of the Copenhagen interpretation is the word "probability". Which is rather weak, compared to the fact that the collapse postulate of the Copenhagen interpretation is non-linear, non-unitary, non-differentiable (even discontinuous!), non-local, violates CPT-symmetry and Liouville's Theorem, non-deterministic, and faster-than-light. Oh, and it's strictly more complex than a many-world interpretation, since it adds an extra postulate on top of existing equations. http://lesswrong.com/lw/q6/collapse_postulates/ http://lesswrong.com/lw/q6/collapse_postulates/ Seriously, how many arrows to the chest does the Copenhagen Interpretation must endure before we declare it dead, and stop saying "probability" before every occurrence of "amplitude"? --- Fire a photon through a half sieved mirror, with 2 sensors to catch the 2 possible paths, such that no matter what, one of the sensors will go off. What do you think happens? The equations (you know them more than I do) say the amplitude will flow and decohere into 2 non-interacting blobs. The blob where sensor 1 goes off, and the blob where sensor 2 goes off. (Note from Captain Obvious: the equations are deterministic. They do not say that God plays dice with the universe.) Now say you fire the photon, and observe sensor 1 going off. What do you think happened to the other blob, the one you don't interact with? Do you think it went away just like that? It would be like believing that a colonization spaceship going beyond the observable universe disappears, not only from your view, but for good. http://lesswrong.com/lw/pb/belief_in_the_implied_invisible/ http://lesswrong.com/lw/pb/belief_in_the_implied_invisible/ --- Of course this sequence is sketchy and hand waving (it doesn't even try to hide it). Its purpose is not to teach us Quantum Physics. Only certain aspects of it, to serve a philosophical agenda (most notably questions around personal identity and Free Will).
Jach 13y ago
What makes sense about a probability that can take on negative or complex values and collections of which don't sum to 1? Convention is no excuse for bad terminology or notation, especially for beginners to the subject who may not have the math or physics background to appreciate the connection with the continuity equation. You lose nothing by removing the word "probability" and avert possible confusion. "Amplitude" and either "squared modulus" or "amplitude density" work fine. I think Feynman's QED is mandatory reading for an intro to quantum thinking (and Feynman in general is fantastic). I also think his several comments on wave v. particle indicate another abuse of conventional terminology. Sometimes he'll insist light is not a wave but a particle, but it's actually a screwy kind of particle and you need to think about arrows and paths. ("Collapse" is another word that'd be better off going away...) My favorite beginner-level approach to QM nowadays, at least for beginners who are familiar with linear algebra, is actually Scott Aaronson's (edit: who is an expert in the field, and I believe has even commented on some of Eliezer's quantum posts...) (quantum) computer scientist approach: http://www.scottaaronson.com/democritus/lec9.html http://www.scottaaronson.com/democritus/lec9.html It introduces QM as "What if we tried to make something like probability theory but allowing negative or complex values?" It wouldn't be probability, but it would be like probability. Once you set up the math, the usual "weird" quantum effects of experiments can be shown as a direct consequence of the math.

eli_gottlieb 13y ago

I'm gonna have to agree with darkmighty here: learn your physics from physicists, not from Eliezer. No matter how well or badly he actually understands quantum physics (which I'm not qualified to judge), we should be learning from actual expert practitioners rather than from a fellow amateur who happened to "ace the class", so to speak. If physicists say probability amplitude, it's called probability amplitude.

loup-vaillant 13y ago
I'm willing to believe experts when I know nothing about a subject. Given the apparent current reception of MWI[1], I concede that things are not looking good for Everett. On the other hand, arguments trump authority[2]. And Eliezer produced specific, very convincing arguments in favour of Everett. To this day, I don't know of any specific strong objection to his writings on the subject. Therefore I believe him. (For now. Please let me know if you know of any objection he did not address.) Physicists say "probability amplitude"? I don't care. I'll go on saying "amplitude" alone. The term is less confusing, and physicists will understand me regardless. [1]: https://en.wikipedia.org/wiki/Many-worlds_interpretation#Polls https://en.wikipedia.org/wiki/Many-worlds_interpretation#Pol... [2]: http://lesswrong.com/lw/lx/argument_screens_off_authority/ http://lesswrong.com/lw/lx/argument_screens_off_authority/
Xcelerate 13y ago
I'm taking a QFT class at my university right now, and it's very different than any discussion of quantum mechanics I see online. It's pages upon pages of math and linear algebra. Very little text or discussion. Physicists don't really care whether you call it "probability", "probability amplitude", or "fish". What you end up with is an equation that you can take to the lab and use to predict experimentally measured results. I'll add that at some point the math just becomes so bizarre that you can't (or at least I'm unable to) come up with some kind of textual analogy for it. (This is what QFT is like for me: Manipulate symbols according to mathematical rules until you end up with an equation. Realize the equation can't be solved analytically. Realize exponential computing power would be required to solve it numerically. Make an approximation and modify the equation. Solve numerically and see how well it agrees with experiment.)