4 ms·

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. (ht

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.

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.