If you think you’ve learned quantum mechanics from it, you’re a fool. If you think you’ve learned enough about quantum mechanics to be justified as a physical realist, you’re correct. Oodles of things are left out, and many others simplified, but there are few things that are actually wrong, and they have little impact.
in Configurations and Amplitude, a multiplication factor of i is used for the mirrors where −1 is correct.
The main question is relative phase, and the transmitted portion can have an arbitrary phase shift, by selecting the thickness of the mirror. Therefore, the error is even more minor than it seems.
Edited to add: I have a PhD in physics.
Also edited to add: it is possible to build a device that actually has the exact phases listed, not even just relative. It’s not an off-the-shelf half-silvered mirror, to be sure.
Got one of those, too, and my opinion is basically the same, except for the MWI advocacy, which takes away from the QM sequence’s usefulness (advocacy always does).
In a nutshell:
There are no particles, only fields (described by amplitudes evolving in space, time and other coordinates). Particles/waves show up as pattern matching to classical concepts, depending on the experiments.
The measurement step (the Born rule) is still mysterious (i.e. an open problem in Physics), despite what anyone, including EY, says. Hence the dozens of “interpretations”.
Well, that and demonstrating that Identity Isn’t in Specific Atoms because there is no such thing as specific atoms, and being a good example of weirdness being a reaction of the mind, not a property of the physics.
And, subordinate to those three, the point that Occam’s Razor applies to code not RAM (so to speak). Worth mentioning since I think that’s the part that went over shminux’s head.
And, subordinate to those three, the point that Occam’s Razor applies to code not RAM (so to speak). Worth mentioning since I think that’s the part that went over shminux’s head.
You are right, it did the first time I tried to honestly estimate the complexity of QM (I wish someone else bother to do it numerically, as well). However, even when removing the necessary boundary conditions and grid storage (they take up lots of RAM), one still ends up with the code that evolves the Schroediger equation (complicated) and applies the Born postulate (trivial) for any interpretation.
But collapse interpretations require additional non-local algorithms
Not for computations, they do not. If you try to write a code simulating a QM system, end up writing unitary evolution on top of the elliptic time-independent SE (H psi = E psi) to describe the initial state. If you want to calculate probabilities, such as the pattern on the screen from the double-slit experiment, you apply the Born rule. And computational complexity is the only thing thing that matters for Occam’s razor.
And, subordinate to those three, the point that Occam’s Razor applies to code not RAM (so to speak). Worth mentioning since I think that’s the part that went over shminux’s head.
I think the supposed Occamian benefit is overstated. E.g., the transactional interpretation has an Occamian benefit in that you don’t asymmetrically reject advanced wave solutions to Maxwell’s equations, and yet I don’t see anyone telling me that therefore the T.I. is obviously correct. Mirror matter: predicted by fundamental-ness of supersymmetry, Occamian benefit, still highly speculative. (Don’t have a PhD in physics (dropped out of high school physics), only felt justified in replying to wedrifid because AFAIK he doesn’t have a PhD in physics either. Someone with domain knowledge, please correct/refine/embarrass my point.)
Mirror matter comes from “N=2” supersymmetry, where along with the usual particle and its superpartner, you have a mirror partner for both of those. Ordinary “N=1″ supersymmetry doesn’t have the mirrors. N=2 supersymmetry is of major interest mathematically, but it’s difficult to get the standard model from an N=2 theory. But if you did, the mirror matter might be the dark matter. It’s in my top ten of cool possibilities, but I can’t say it’s favored by Occam.
I think the supposed Occamian benefit is overstated.
To clarify, do you mean that Eliezer overstated the degree to which the RAM vs code simplicity point applies to this specific physics example, or that Eliezer overstated the principle itself? I’m more inclined to accept the former than the latter.
Maybe he didn’t overstate the significance of the principle even when it comes to interpreting QM, but I think using it to pick out a particular interpretation (whether MWI or TI) leads to overconfidence, and isn’t very good evidence in itself, compared to relatively naive considerations like “using straightforward physical intuition, this idea that other worlds are somehow in a metaphysical sense as ‘real’ as our world doesn’t seem likely to hold water”. In retrospect I might be attributing connotations to Eliezer’s original argument that weren’t in that specific argument and only implicit in the overall tone of the sequence. It’s been two years since I read the QM sequence.
Maybe he didn’t overstate the significance of the principle even when it comes to interpreting QM, but I think using it to pick out a particular interpretation (whether MWI or TI) leads to overconfidence, and isn’t very good evidence in itself, compared to relatively naive considerations like “using straightforward physical intuition, this idea that other worlds are somehow in a metaphysical sense as ‘real’ as our world doesn’t seem likely to hold water”.
I place less value on metaphisical intuitions about what ‘real’ means. I do not particularly like the baggage that comes with MWI, I do like the principle of asserting that we can consider reality as we understand it to be more or less just like the core math—with any additional mechanisms required to make our intuitions fit rejected out of hand.
The undesirable baggage of “MWI” extends to the titular concept. The whole idea of “Many Worlds” seems to be a description that would be made by those stuck in the mindset of someone stuck with trying to force reality to be like our metaphisical intuitions of a simple classical world. As far as I am aware experiments have not identified any level at which the worlds are discrete like that (except for the sense in which you could allocate each possible configuration of a universe down to the level of plank distances and suchforth as a ‘World’.) So the question “are the other Worlds ‘real’” doesn’t seem to qualify for a yes or no answer so much as a “huh? There’s just a ‘reality’ of the stuff in this wave equation. Call some specific subset of that a ‘world’ if you really want to.”
It’s been two years since I read the QM sequence.
It’s been at least that for me too (it isn’t a sequence that works in audio format, which is my preferred media). I place very low confidence on what I remember of QM from there and research elsewhere and only placed slightly higher confidence on my understanding even back when I remembered it.
There are certain assertions that I am comfortable rejecting but the specific positive assertions I have little confidence. For example I have no qualms with dismissing “but they are all just ‘interpretations’ and all interpretations are equal” sentiments. If additional mechanisms are introduced that isn’t just interpretation. Interpretation is a question of which words are used to describe the math.
the point that Occam’s Razor applies to code not RAM (so to speak).
This is true only if you are using some variant of a Kolmogorov prior. Many ways of dealing with Pascal’s mugging try to use other priors. Moreover, this will be not true in general for any computable prior.
This might be a good time for me to respond to one of your earlier comments.
I was under the impression that it’s a big mystery what complex numbers are doing (i.e., what is their physical function, what do they mean) in QM. I was under the impression that this is a matter of much speculative debate. Yet when I said that, I was downvoted a lot, and you implicitly alleged that I was obviously ignorant or misinformed in some way, and that we have a perfectly good understanding of what complex numbers are doing in the Dirac equation. Could you or someone please give me some background info, so that I can better understand the current state of understanding of the role of complex numbers in QM?
Note that complex numbers can be replaced with 2x2 real matrices, such as i=(0,-1;1,0), since multiplication by i is basically rotation by 90 degrees in the complex plane. Given that the Dirac equation is already full of matrices, does it make you feel better about it?
A momentary note on why the conversation went the way it did:
what the hell are complex numbers doing in the Dirac equation?
Hopefully you can see why this looked like a rhetorical objection rather than a serious inquiry.
~~~~
So, what IS the i doing in Dirac’s equation? Well, first let’s look into what the i is doing in Schrödinger’s equation, which is
ihbar;partial_{t}|psi>=H|psi>
with H the ‘Hamiltonian’ operator: the operator that scales each component of psi by its energy (so, H has only real eigenvalues. Important!)
The time-propagation operator which gives the solutions to this equation is
To see how you can take e to the power of an operator, think of the Taylor expansion of the exponential. The upshot is that each eigenvector is multiplied by e to the eigenvalue.
In this case, that eigenvalue is the eigenvector’s energy, times time, times a constant that contains i. That i turns an exponential growth or decay into an oscillation. This means that he universe isn’t simply picking out the lowest energy state and promoting it more and more over time—it’s conserving overall state amplitude, conserving energy, and letting things slosh around based on energy differences.
The i in the Dirac equation serves essentially the same purpose—it’s a reformulation of Schrödinger’s equation in a way that’s consistent with relativity. You’ve got a field over spacetime, and the relation between space and time is that in every constant-velocity reference frame, it looks a lot like what was described in the previous paragraph.
IF on the other hand you aren’t bothered by that i, and you mean ‘what are the various i doing in the alpha or gamma matrices’, well, that’s just part of making a set of matrices with the required relationships between the dimensions—i in that case is being used to indicate physical rotations, not complex phase. You can tell because each of those matrices is Hermitian—transposing it and taking the complex conjugate leaves it the same—so all of the eigenvalues are real. If it had anything to do with states’ complex phase as a thing in itself instead of just any other element of the state it’s operating on, it would let some of the imaginary part of the matrix get out. Instead, it keeps it on the inside as an ‘implementation detail’.
Could you or someone please give me some background info, so that I can better understand the current state of understanding of the role of complex numbers
I did (on the physical usefulness and non-mysteriousness of complex numbers, not quantum mechanics specifically).
And thanks for that, but I’m interested in their role in QM specifically. I don’t have an objection to complex numbers, I just want to know what they’re doing, if you see what I mean.
If you think you’ve learned quantum mechanics from it, you’re a fool. If you think you’ve learned enough about quantum mechanics to be justified as a physical realist, you’re correct. Oodles of things are left out, and many others simplified, but there are few things that are actually wrong, and they have little impact.
The main question is relative phase, and the transmitted portion can have an arbitrary phase shift, by selecting the thickness of the mirror. Therefore, the error is even more minor than it seems.
Edited to add: I have a PhD in physics.
Also edited to add: it is possible to build a device that actually has the exact phases listed, not even just relative. It’s not an off-the-shelf half-silvered mirror, to be sure.
Got one of those, too, and my opinion is basically the same, except for the MWI advocacy, which takes away from the QM sequence’s usefulness (advocacy always does).
In a nutshell:
There are no particles, only fields (described by amplitudes evolving in space, time and other coordinates). Particles/waves show up as pattern matching to classical concepts, depending on the experiments.
The measurement step (the Born rule) is still mysterious (i.e. an open problem in Physics), despite what anyone, including EY, says. Hence the dozens of “interpretations”.
I’m pretty sure I recall that EY says (repeatedly) that the Born rule is not yet understood.
Well, except for the fact that the MWI advocacy was pretty much the whole point of the sequence!
Well, that and demonstrating that Identity Isn’t in Specific Atoms because there is no such thing as specific atoms, and being a good example of weirdness being a reaction of the mind, not a property of the physics.
And, subordinate to those three, the point that Occam’s Razor applies to code not RAM (so to speak). Worth mentioning since I think that’s the part that went over shminux’s head.
You are right, it did the first time I tried to honestly estimate the complexity of QM (I wish someone else bother to do it numerically, as well). However, even when removing the necessary boundary conditions and grid storage (they take up lots of RAM), one still ends up with the code that evolves the Schroediger equation (complicated) and applies the Born postulate (trivial) for any interpretation.
But collapse interpretations require additional non-local algorithms, which to me seem to be, by necessity, incredibly complicated
Not for computations, they do not. If you try to write a code simulating a QM system, end up writing unitary evolution on top of the elliptic time-independent SE (H psi = E psi) to describe the initial state. If you want to calculate probabilities, such as the pattern on the screen from the double-slit experiment, you apply the Born rule. And computational complexity is the only thing thing that matters for Occam’s razor.
I think the supposed Occamian benefit is overstated. E.g., the transactional interpretation has an Occamian benefit in that you don’t asymmetrically reject advanced wave solutions to Maxwell’s equations, and yet I don’t see anyone telling me that therefore the T.I. is obviously correct. Mirror matter: predicted by fundamental-ness of supersymmetry, Occamian benefit, still highly speculative. (Don’t have a PhD in physics (dropped out of high school physics), only felt justified in replying to wedrifid because AFAIK he doesn’t have a PhD in physics either. Someone with domain knowledge, please correct/refine/embarrass my point.)
Mirror matter comes from “N=2” supersymmetry, where along with the usual particle and its superpartner, you have a mirror partner for both of those. Ordinary “N=1″ supersymmetry doesn’t have the mirrors. N=2 supersymmetry is of major interest mathematically, but it’s difficult to get the standard model from an N=2 theory. But if you did, the mirror matter might be the dark matter. It’s in my top ten of cool possibilities, but I can’t say it’s favored by Occam.
I’d be interested in reading more about your top ten cool possibilities. They sound cool.
To clarify, do you mean that Eliezer overstated the degree to which the RAM vs code simplicity point applies to this specific physics example, or that Eliezer overstated the principle itself? I’m more inclined to accept the former than the latter.
Maybe he didn’t overstate the significance of the principle even when it comes to interpreting QM, but I think using it to pick out a particular interpretation (whether MWI or TI) leads to overconfidence, and isn’t very good evidence in itself, compared to relatively naive considerations like “using straightforward physical intuition, this idea that other worlds are somehow in a metaphysical sense as ‘real’ as our world doesn’t seem likely to hold water”. In retrospect I might be attributing connotations to Eliezer’s original argument that weren’t in that specific argument and only implicit in the overall tone of the sequence. It’s been two years since I read the QM sequence.
I place less value on metaphisical intuitions about what ‘real’ means. I do not particularly like the baggage that comes with MWI, I do like the principle of asserting that we can consider reality as we understand it to be more or less just like the core math—with any additional mechanisms required to make our intuitions fit rejected out of hand.
The undesirable baggage of “MWI” extends to the titular concept. The whole idea of “Many Worlds” seems to be a description that would be made by those stuck in the mindset of someone stuck with trying to force reality to be like our metaphisical intuitions of a simple classical world. As far as I am aware experiments have not identified any level at which the worlds are discrete like that (except for the sense in which you could allocate each possible configuration of a universe down to the level of plank distances and suchforth as a ‘World’.) So the question “are the other Worlds ‘real’” doesn’t seem to qualify for a yes or no answer so much as a “huh? There’s just a ‘reality’ of the stuff in this wave equation. Call some specific subset of that a ‘world’ if you really want to.”
It’s been at least that for me too (it isn’t a sequence that works in audio format, which is my preferred media). I place very low confidence on what I remember of QM from there and research elsewhere and only placed slightly higher confidence on my understanding even back when I remembered it.
There are certain assertions that I am comfortable rejecting but the specific positive assertions I have little confidence. For example I have no qualms with dismissing “but they are all just ‘interpretations’ and all interpretations are equal” sentiments. If additional mechanisms are introduced that isn’t just interpretation. Interpretation is a question of which words are used to describe the math.
Where can I get the sequences in audio format?
I recommend TextAloud.
This is true only if you are using some variant of a Kolmogorov prior. Many ways of dealing with Pascal’s mugging try to use other priors. Moreover, this will be not true in general for any computable prior.
Eliezer describes the Born probabilities as a “serious mystery” and an “open problem”.
This might be a good time for me to respond to one of your earlier comments.
I was under the impression that it’s a big mystery what complex numbers are doing (i.e., what is their physical function, what do they mean) in QM. I was under the impression that this is a matter of much speculative debate. Yet when I said that, I was downvoted a lot, and you implicitly alleged that I was obviously ignorant or misinformed in some way, and that we have a perfectly good understanding of what complex numbers are doing in the Dirac equation. Could you or someone please give me some background info, so that I can better understand the current state of understanding of the role of complex numbers in QM?
Note that complex numbers can be replaced with 2x2 real matrices, such as i=(0,-1;1,0), since multiplication by i is basically rotation by 90 degrees in the complex plane. Given that the Dirac equation is already full of matrices, does it make you feel better about it?
A momentary note on why the conversation went the way it did:
Hopefully you can see why this looked like a rhetorical objection rather than a serious inquiry.
~~~~
So, what IS the i doing in Dirac’s equation? Well, first let’s look into what the i is doing in Schrödinger’s equation, which is
ihbar;partial_{t}|psi>=H|psi>
with H the ‘Hamiltonian’ operator: the operator that scales each component of psi by its energy (so, H has only real eigenvalues. Important!)
The time-propagation operator which gives the solutions to this equation is
To see how you can take e to the power of an operator, think of the Taylor expansion of the exponential. The upshot is that each eigenvector is multiplied by e to the eigenvalue.
In this case, that eigenvalue is the eigenvector’s energy, times time, times a constant that contains i. That i turns an exponential growth or decay into an oscillation. This means that he universe isn’t simply picking out the lowest energy state and promoting it more and more over time—it’s conserving overall state amplitude, conserving energy, and letting things slosh around based on energy differences.
The i in the Dirac equation serves essentially the same purpose—it’s a reformulation of Schrödinger’s equation in a way that’s consistent with relativity. You’ve got a field over spacetime, and the relation between space and time is that in every constant-velocity reference frame, it looks a lot like what was described in the previous paragraph.
IF on the other hand you aren’t bothered by that i, and you mean ‘what are the various i doing in the alpha or gamma matrices’, well, that’s just part of making a set of matrices with the required relationships between the dimensions—i in that case is being used to indicate physical rotations, not complex phase. You can tell because each of those matrices is Hermitian—transposing it and taking the complex conjugate leaves it the same—so all of the eigenvalues are real. If it had anything to do with states’ complex phase as a thing in itself instead of just any other element of the state it’s operating on, it would let some of the imaginary part of the matrix get out. Instead, it keeps it on the inside as an ‘implementation detail’.
I did (on the physical usefulness and non-mysteriousness of complex numbers, not quantum mechanics specifically).
And thanks for that, but I’m interested in their role in QM specifically. I don’t have an objection to complex numbers, I just want to know what they’re doing, if you see what I mean.