A couple of physics questions, if anyone will indulge me:
Is quantum physics actually an improvement in the theory of how reality works? Or is it just building uncertainty into our model of reality? I was browsing A Brief History of Time at a bookstore, and the chapter on the Heisenberg uncertainty principle seem to suggest the latter—what I read of it, anyway.
If this is just a dumb question for some reason, feel free to let me know—I’ve only taken two classes in physics, and we never escaped the Newtonian world.
On a related note, I’m looking for a good physics book that will take me through quantum mechanics. I don’t want a textbook because I don’t really have the time to spend learning all of the details, but I want something with some equations in it. Any suggestions?
Is quantum physics actually an improvement in the theory of how reality works?
It explains everything microscopic. For example, the stability of atoms. Why doesn’t an electron just spiral into the nucleus and stay there? The uncertainty principle means it can’t be both localized at a point and have a fixed momentum of zero. If the position wavefunction is a big spike concentrated at a point, then the momentum wavefunction, which is the Fourier transform of the position wavefunction, will have a nonzero probability over a considerable range of momenta, so the position wavefunction will start leaking out of the nucleus in the next moment. The lowest energy stable state for the electron is one which is centered on the nucleus, but has a small spread in position space and a small spread in momentum “space”.
However, every quantum theory ever used has a classical conceptual beginning. You posit the existence of fields or particles interacting in some classical way, and then you “quantize” this. For example, the interaction between electron and nucleus is just electromagnetism, as in Faraday, Maxwell, and Einstein. But you describe the electron (and the nucleus too, if necessary) by a probabilistic wavefunction rather than a single point in space, and you also do the same for the electromagnetic field. Curiously, when you do this for the field, you get particles as emergent phenomena. A “photon” is actually something like a bookkeeping device for the probabilistic movement of energy within the quantized electromagnetic field. You can also get electrons and nucleons (and their antiparticles) from fields in this way, so everywhere in elementary particle physics, you have this “field/particle duality”. For every type of elementary particle, there is a fundamental field, and vice versa. The basic equations that get quantized are field equations, but the result of quantization gives you particle behavior.
Everyone wants to know how to think about the uncertainty in quantum physics. Is it secretly deterministic and we just need a better theory, or do things really happen without a cause; does the electron always have a definite position even when we can’t see it, or is it somehow not anywhere in particular; and so on. These conceptual problems exist because we have no derivation of quantum wavefunctions from anything more fundamental. This is unlike, say, the distributions in ordinary probability theory. You can describe the output of a quincunx using the binomial distribution, but you also have a “microscopic model” of where that distribution comes from (balls bouncing left and right as they fall down). We don’t have any such model for quantum probabilities, and it would be difficult to produce (see: “Bell’s theorem”). Sum over histories looks like such a model, but the problem is that histories can cancel (“interfere destructively”). It is as if, in the quincunx device, there were slots at the bottom where balls never fell, and you explained this by saying that the two ways to get there cancelled each other out—which is how sum-over-histories explains the double-slit experiment: no photons arrive in the dark regions because the “probability amplitude” for getting there via one slit cancels the amplitude for getting there from the other slit.
As a practical matter, most particle physicists think of reality in quasi-classical terms—in terms of fields or particles, whichever seems appropriate, but then blurred out by the uncertainty principle. Sum over histories is an extension of the uncertainty principle to movement and interaction, so it’s a whole process in time which is uncertain, rather than just a position.
The actual nature of the uncertainty is a philosophical or even ideological matter. The traditional view effectively treats reality as classical but blurry. There is a deterministic alternative theory (Bohmian mechanics) but it is obscure and rather contrived. The popular view on this site is “the many-worlds interpretation”—all the positions, all the histories are equally real, but they live in parallel universes. I believe this view is, like Bohmian mechanics, a misguided philosophical whimsy rather than the future of physics. Like Bohmian mechanics, it can be given a mathematical and not just a verbal form, but it’s an artificial addition to the real physics. It’s not contributing to progress in physics. Its biggest claim to practical significance is that it helped to inspire quantum computation; but one is not obliged to think that a quantum computer is actually in all states at once, rather than just possibly in one of them.
So, I hold to the traditional view of the meaning of quantum theory—that it’s an introduction of a little uncertainty into a basically classical world. It doesn’t make sense as an ultimate description of things; but I certainly don’t believe the ideas, like Bohm (nonlocal determinism) or Everett (many worlds), which try to make a finished objective theory by just adding an extra mathematical and metaphysical facade. The extra details they posit have a brittle artificiality about them. They do link up with genuine aspects of the quantum mathematical formalism, and so they may indirectly contribute to progress just a little, but I think the future lies more with the traditional view.
However, every quantum theory ever used has a classical conceptual beginning.
I don’t know if I’m the only person who thinks this is funny, but every theory in physics has a basis in naive trust in qualia, even if it’s looking at the readout from an instrument or reading the text of an article.
The conclusion may be that matter is almost entirely empty space, but you still have to let your interactions with the way you get information about physics use the ancient habit of assuming that what seems to be solid is solid.
I think you may misunderstand what the physics actually says. Compared to the material of neutron stars, yes, terrestrial matter is almost entirely empty space … but it’s still resists changes to shape and volume. And you don’t need to invoke ancient habits anywhere—those conclusions fall right out of the physics without modification.
I’ve beginning to think that I’ve been over-influenced by “goshwow” popular physics, which tries to present physics in the most surpising way poosible. It’s different if I think of that “empty space” near subatomic particles as puffed up by energy fields.
thanks, but I was hoping for a quick answer. Working through that sequence is on my “Definitely do sometime when I have nothing too important to do” list.
OK, a quick answer: classical physics cannot be true of the reality we find ourselves in. Specifically, classical physics is contradicted by experimental results such as the photoelectric effect and the double-slit experiment. The parts of reality that require you to know quantum physics affect such important things as chemistry, semiconductors and whether our reality can contain such a thing as a “solid object”. The only reason we teach classical physics is that it is easier than quantum physics. If everyone could learn quantum physics, there would be no need to teach classical physics anymore.
The only reason we teach classical physics is that it is easier than quantum physics. If everyone could learn quantum physics, there would be no need to teach classical physics anymore.
Really? Isn’t classical physics used in some contexts because the difference between the classical model and reality isn’t enough to justify extra complications? I’m thinking specifically of engineers.
Isn’t classical physics used in some contexts because the difference between the classical model and reality isn’t enough to justify extra complications?
True. Revised sentence: the only reasons for using classical physics are that it is easier to learn, easier to calculate with and it helps you understand people who know only classical physics.
On the first point: I try never to categorize questions as intelligent or dumb, but is quantum mechanics an improvement? Unquestionably. To give only the most obvious example, lasers work by quantum excitation.
I, too, would be interested in learning quantum mechanics from a good textbook.
It was my undergraduate textbook. It is certainly thorough, but other than that, I’m not sure I can strongly recommend it. (The typography is painful).
I think starting with Quantum Computation and Quantum Information and hence discrete systems might be a better way to start, and then later expand to systems with continuous degrees of freedom.
The typesetting of the equations in particular. There were several things that hampered the readability for me—like using a period for the dot product, rather than a raised dot. I expect a full stop to mean the equation has ended. Exponents are set too big. Integral signs are set upright, rather than slanted (conversely the “d”s in them are italicized, when they should be viewed as an operator, and hence upright). Large braces for case expansion of definitions are 6 straight lines, rather than smooth curves. The operator version of 1 is an ugly outline. The angle brackets used for bras and kets are ugly (though at least distinct from the less than and greater than signs).
I’m not being entirely fair: these are really nits. On the other hand, these and other things actually made it harder for me to use the book. And it’s not an easy book to start with.
A couple of physics questions, if anyone will indulge me:
Is quantum physics actually an improvement in the theory of how reality works? Or is it just building uncertainty into our model of reality? I was browsing A Brief History of Time at a bookstore, and the chapter on the Heisenberg uncertainty principle seem to suggest the latter—what I read of it, anyway.
If this is just a dumb question for some reason, feel free to let me know—I’ve only taken two classes in physics, and we never escaped the Newtonian world.
On a related note, I’m looking for a good physics book that will take me through quantum mechanics. I don’t want a textbook because I don’t really have the time to spend learning all of the details, but I want something with some equations in it. Any suggestions?
It explains everything microscopic. For example, the stability of atoms. Why doesn’t an electron just spiral into the nucleus and stay there? The uncertainty principle means it can’t be both localized at a point and have a fixed momentum of zero. If the position wavefunction is a big spike concentrated at a point, then the momentum wavefunction, which is the Fourier transform of the position wavefunction, will have a nonzero probability over a considerable range of momenta, so the position wavefunction will start leaking out of the nucleus in the next moment. The lowest energy stable state for the electron is one which is centered on the nucleus, but has a small spread in position space and a small spread in momentum “space”.
However, every quantum theory ever used has a classical conceptual beginning. You posit the existence of fields or particles interacting in some classical way, and then you “quantize” this. For example, the interaction between electron and nucleus is just electromagnetism, as in Faraday, Maxwell, and Einstein. But you describe the electron (and the nucleus too, if necessary) by a probabilistic wavefunction rather than a single point in space, and you also do the same for the electromagnetic field. Curiously, when you do this for the field, you get particles as emergent phenomena. A “photon” is actually something like a bookkeeping device for the probabilistic movement of energy within the quantized electromagnetic field. You can also get electrons and nucleons (and their antiparticles) from fields in this way, so everywhere in elementary particle physics, you have this “field/particle duality”. For every type of elementary particle, there is a fundamental field, and vice versa. The basic equations that get quantized are field equations, but the result of quantization gives you particle behavior.
Everyone wants to know how to think about the uncertainty in quantum physics. Is it secretly deterministic and we just need a better theory, or do things really happen without a cause; does the electron always have a definite position even when we can’t see it, or is it somehow not anywhere in particular; and so on. These conceptual problems exist because we have no derivation of quantum wavefunctions from anything more fundamental. This is unlike, say, the distributions in ordinary probability theory. You can describe the output of a quincunx using the binomial distribution, but you also have a “microscopic model” of where that distribution comes from (balls bouncing left and right as they fall down). We don’t have any such model for quantum probabilities, and it would be difficult to produce (see: “Bell’s theorem”). Sum over histories looks like such a model, but the problem is that histories can cancel (“interfere destructively”). It is as if, in the quincunx device, there were slots at the bottom where balls never fell, and you explained this by saying that the two ways to get there cancelled each other out—which is how sum-over-histories explains the double-slit experiment: no photons arrive in the dark regions because the “probability amplitude” for getting there via one slit cancels the amplitude for getting there from the other slit.
As a practical matter, most particle physicists think of reality in quasi-classical terms—in terms of fields or particles, whichever seems appropriate, but then blurred out by the uncertainty principle. Sum over histories is an extension of the uncertainty principle to movement and interaction, so it’s a whole process in time which is uncertain, rather than just a position.
The actual nature of the uncertainty is a philosophical or even ideological matter. The traditional view effectively treats reality as classical but blurry. There is a deterministic alternative theory (Bohmian mechanics) but it is obscure and rather contrived. The popular view on this site is “the many-worlds interpretation”—all the positions, all the histories are equally real, but they live in parallel universes. I believe this view is, like Bohmian mechanics, a misguided philosophical whimsy rather than the future of physics. Like Bohmian mechanics, it can be given a mathematical and not just a verbal form, but it’s an artificial addition to the real physics. It’s not contributing to progress in physics. Its biggest claim to practical significance is that it helped to inspire quantum computation; but one is not obliged to think that a quantum computer is actually in all states at once, rather than just possibly in one of them.
So, I hold to the traditional view of the meaning of quantum theory—that it’s an introduction of a little uncertainty into a basically classical world. It doesn’t make sense as an ultimate description of things; but I certainly don’t believe the ideas, like Bohm (nonlocal determinism) or Everett (many worlds), which try to make a finished objective theory by just adding an extra mathematical and metaphysical facade. The extra details they posit have a brittle artificiality about them. They do link up with genuine aspects of the quantum mathematical formalism, and so they may indirectly contribute to progress just a little, but I think the future lies more with the traditional view.
I don’t know if I’m the only person who thinks this is funny, but every theory in physics has a basis in naive trust in qualia, even if it’s looking at the readout from an instrument or reading the text of an article.
I just take all scientific theories to ultimately be theories about phenomenal experience. No naive trust required.
What do you mean?
The conclusion may be that matter is almost entirely empty space, but you still have to let your interactions with the way you get information about physics use the ancient habit of assuming that what seems to be solid is solid.
I think you may misunderstand what the physics actually says. Compared to the material of neutron stars, yes, terrestrial matter is almost entirely empty space … but it’s still resists changes to shape and volume. And you don’t need to invoke ancient habits anywhere—those conclusions fall right out of the physics without modification.
I’ve beginning to think that I’ve been over-influenced by “goshwow” popular physics, which tries to present physics in the most surpising way poosible. It’s different if I think of that “empty space” near subatomic particles as puffed up by energy fields.
The Quantum Physics Sequence
thanks, but I was hoping for a quick answer. Working through that sequence is on my “Definitely do sometime when I have nothing too important to do” list.
OK, a quick answer: classical physics cannot be true of the reality we find ourselves in. Specifically, classical physics is contradicted by experimental results such as the photoelectric effect and the double-slit experiment. The parts of reality that require you to know quantum physics affect such important things as chemistry, semiconductors and whether our reality can contain such a thing as a “solid object”. The only reason we teach classical physics is that it is easier than quantum physics. If everyone could learn quantum physics, there would be no need to teach classical physics anymore.
First of all, thanks.
Really? Isn’t classical physics used in some contexts because the difference between the classical model and reality isn’t enough to justify extra complications? I’m thinking specifically of engineers.
True. Revised sentence: the only reasons for using classical physics are that it is easier to learn, easier to calculate with and it helps you understand people who know only classical physics.
On the first point: I try never to categorize questions as intelligent or dumb, but is quantum mechanics an improvement? Unquestionably. To give only the most obvious example, lasers work by quantum excitation.
I, too, would be interested in learning quantum mechanics from a good textbook.
I understand that Claude Cohen-Tannoudji et al.’s two-volume Quantum Mechanics is supposed to be exceptional, albeit expensive, time consuming to work through fully, and targeted at post-graduates rather than beginners. (Another disclaimer: I have not used the textbook myself.) Cohen-Tannoudji got the 1997 Nobel Prize in Physics for his work with...lasers!
It was my undergraduate textbook. It is certainly thorough, but other than that, I’m not sure I can strongly recommend it. (The typography is painful).
I think starting with Quantum Computation and Quantum Information and hence discrete systems might be a better way to start, and then later expand to systems with continuous degrees of freedom.
I’m confused: “typography”? The font on the Amazon “LOOK INSIDE” seems perfectly legible to me.
The typesetting of the equations in particular. There were several things that hampered the readability for me—like using a period for the dot product, rather than a raised dot. I expect a full stop to mean the equation has ended. Exponents are set too big. Integral signs are set upright, rather than slanted (conversely the “d”s in them are italicized, when they should be viewed as an operator, and hence upright). Large braces for case expansion of definitions are 6 straight lines, rather than smooth curves. The operator version of 1 is an ugly outline. The angle brackets used for bras and kets are ugly (though at least distinct from the less than and greater than signs).
I’m not being entirely fair: these are really nits. On the other hand, these and other things actually made it harder for me to use the book. And it’s not an easy book to start with.
Thanks for the elaboration. I’ll bear that in mind if I have a chance to pick up a copy.