Sorry, not in this post, but upcoming. I’m scheduled to do another episode of Bloggingheads.tv with David Albert, and we’ve decided to spend the whole hour talking about quantum mechanics. Start with the basics, try to explain this crazy theory and some of its outlandish consequences in ways that anyone can understand, and then dig into some of the mysteries of measurement, superposition, and reality.
So — what do you want to know? What are the really interesting questions about QM that we should be talking about?
One thing I don’t think we science-explainers get as clear as we could is the idea of the Wave Function of the Universe. It sounds scary and/or pretentious — an older colleague of mine at MIT once said “I’m too young to talk about the wave function of the universe.” But it’s a crucial fact of quantum mechanics (arguably the crucial fact) that, unlike in classical mechanics, when you consider two electrons you don’t just have a separate state for each electron. You have a single wave function that describes the two-electron system. And that’s true for any number of particles — when you consider a bigger system, you don’t “add more wavefunctions,” you beef up your single wave function so that it describes more particles. There is only ever one wave function, and you can call it “of the universe” if you like. Deep, man.
Here is another thing: in quantum mechanics, you can “add two states together,” or “take their average.” (Hilbert space is a vector space with an inner product.) In classical mechanics, you can’t. (Phase space is not a vector space at all.) How big a deal is that? Is there some nice way we can explain what that means in terms your grandmother could understand, even if your grandmother is not a physicist or a mathematician?
(See also Dave Bacon’s discussion of teaching quantum mechanics as a particular version of probability theory. There are many different ways of answering the question “What is quantum mechanics?”)
Ooh, I’m looking forward to this. As a layman, one thing I’d love to see covered is the measurement problem. It seems like a lot of scientists that know better can fall into lazy language that makes it sound to the layman like consciousness itself changes reality. But some lucid, repeatable-by-someone-like-me explanation of why that’s definitely not the case would be very well appreciated.
Also, some discussion of the different “interpretations” of QM would be great. I’ve never gotten my head around the Copenhagen interpretation.
(if this is not a question about QM, then please ignore.)
So-called “wave-particle duality” is sometimes described as a paradox. Is it?
What about decoherence? How many physicists today believe it is correct? Does it solve the so-called “measurement problem”? Can we finally be sure that Schroedinger’s Cat is either alive (yay!) or dead (Oh, dear!), and not in a state of superposition?
I’m looking forward to this, Sean, but honestly what I want to know is if there is a book about quantum mechanics written for laymen that actually explains the theory in detail _without_ using analogies that oversimplify and _without_ constantly resorting to poetic language? I wouldn’t mind having to think and work a bit to understand what’s being said, I wouldn’t mind having to read a few equations, I wouldn’t even mind having to learn some math I don’t know. I’d just like to read a book from an author that really tries to make me understand QM, as opposed to giving us a rough idea of what it might be like if I understood it. I want The Blind Watchmaker of quantum mechanics. 🙂
I would like to hear more about what a Hilbert space is vs vector space?
Also, maybe you can start with the double slit experiment and what it means for a photon to interfere with itself leading to path integral representation of QM.
either way can’t wait!
I’m a complete layperson, but I’ve always been intrigued by the inability to directly see quantum states (maybe what Matt means by ‘the measurement problem’?). Why is it that they can’t be directly measured? Pretend I’m the grandmother. Without the physics degree.
Here are a few ideas. I’m a somewhat educated layperson, so probably the right target audience for Bloggingheads.
1. Do any of the proposed solutions to the measurement problem (or “interpretations” of QM more generally) have consequences that would allow us to distinguish them empirically, or get evidence one way or another?
2. What is the math behind quantum mechanics like? I’m not asking for a math class, of course — maybe just an impressionistic sense of the major pieces & how they fit together. The heart of Newtonian mechanics seems to be calculus and differential equations — are those equally central to QM or is there something more? Is group theory involved? (The point isn’t to understand the math — it’s that knowing what mathematical tools a theory involves can help give a sense of what the theory itself is like.)
3. Is it accurate or inaccurate to say that the “quantum” in QM means that the world is digital rather than analog?
4. Quantum computing. Revolutionary or overhyped, and why?
And finally, an anti-request. There are so many good discussions out there of the basics on the uncertainty principle, wave-particle duality, and the two-slit experiment that you won’t be doing much of a service if you spend a lot of time on yet another layman’s version of those things. Explain them of course, but don’t get too bogged down in the details!
I’d like a cogent discussion of Aspect’s experiment and it’s relationship to Bell’s inequality. Did it firmly prove Bell’s inequality?
Bell’s inequality itself is a pretty intereting topic.
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I also like some discussion of Bell and very recent experiments – Leggett, Zeilinger, realism vs locality, etc.
Perhaps you can work in the “church of the larger Hilbert space” into the discussion about the wavefunction of the universe.
For those outside quantum information theory, the church of the larger Hilbert space is a joking reference to the fact that any quantum states which are ‘mixed’ in the sense of being a probabilistic combination of two or more ‘pure’ states (pure states being those which live in the Hilbert space) can always be thought of as part of an even larger system which is pure. So one speaks of “purifying” a mixed state, or, in cases of extreme need, going to the church of the larger Hilbert space. So it’s relevant to the discussion of the wavefunction of the universe. sorta.
When one talks about a quantum of stuff, you are talking about the smallest possible piece of something. Quantum Mechanics basically states that there IS a smallest piece of energy. Quantum Mechanics also makes the assertion that one can say that there is a smallest distance, measure of time, velocity, force, etc. When one is talking about the smallest pieces of space does it make sense to think about these piece of space as having a shape?
From a layman, perhaps you could discuss the practical applications of QM. For example, I conceptually understand why GPS clocks have to be adjusted for Special and General Relativity. Yet, my understanding of the only detectable effect of QM in the “macro” world occurs with a precision device like a comb 1/10th as thick as a human hair at a temperature of about 78 above absolute 0.
I would enjoy being enlightened.
Thanks,
Sam
Question 1: Does “measurement” of a particle mean the same thing as “the world line of some particle interacts irreversibly with the world line of another particle”?
Question 2: Can any other type of physics be formulated with this weird-ass probabilities-in-Hilbert-space formalism? Could you, for example, rework the Kepler problem with the position and momentum observables as the eigenvalues of some Hamiltonian? Would there be any advantage to it?
Question 3: In a delayed choice two-slit experiment, a particle knows when it’s emitted whether its path is going to be through one of two slits or a superposition of both paths based on how it’s going to be measured, even if the measurement happens 50,000,000 years later. HOW THE HELL … ahem. Excuse me. How does it GOD DAMN KNOW HOW … ahem excuse me again.
If that damn thing can somehow look 50,000,000 years into the future and see the laboratory it’s going to wind up in and see the scientist with his finger on a button and it makes its decision on how to propagate based on that, then the universe is rigidly deterministic to an extent that makes me want to just go and slit my wrists.
Like Clive Bruckman says in the X-Files: “How can I see the future if it doesn’t already exist?”
Is it reasonable to say; Wave=analog, particle=digital?
Is a photon, as a quanta of light, analogous to a drop of water, in that its consistency of size is a function of factors operating on it, much like the surface tension of water vs. gravity makes drips of water similarly sized. Or is it a fundamental…I wouldn’t say structure, but possibly internal constraint?
To further Phil’s question, is it that these past these smallest units of measurement, is it simply too blurred to distinguish one unit from the next, or are there clear units which cannot be further subdivided?
I have to protest (again…) that I don’t see the linearity of the Schrodinger equation (i.e the fact that you can add wavefunctions) as a distinguishing property of QM. In both classical and quantum mechanics the observable quantities (say, expectation value of operators) obey non-linear equations, and there is something describing the “state” of the system (wavefunction, or phase space distribution function), which is interpreted as probability and obeys a linear equation (Liouville or Schrodinger equation).
It so happens that in classical mechanics you typically deal with the former set of objects, and in QM (but not QFT…) you usually deals with the latter. That is a matter of pedagogy, nothing else.
1) What does it really mean that there is a measurement problem? (Looking for good speculation that has some depth to it, not textbook recitation…)
2) Where does ’empirical data’ stop and ‘speculation’ begin when it comes to the problem of state selection?
3) What’s up with the quantum Zeno effect? (Please relate answer to answers to one or both of above questions.)
4) Can the equations of QM be modified to accomodate a)probabilities that change with time, and/or b) bi-directional flows of time with non-equivalent influences?
5) Why default to equivalent starting probabilities when using QM to make predictions? Are there instances when previous data allows for fore-knowledge of a bias?
6) What’s the point of quantum field theory? Why/How was it developed? What does it allow you to do, exactly? Why has it not been reconciled with gravity? What are its limitations – ie, it’s good for predicting behavior of a large set of data, but not an individual observation, etc.?
This is fun! I’ll be thinking of some more questions…
I’m a biochemist so my understanding of quantum mechanics is limited so hopefully this doesn’t stray too far from what you were hoping to see:
1. What are virtual photons? Why can virtual photons cause a force of attraction between + and – charges but regular photons cannot do the same?
2. If we have, say, 8 qubits of entangled electrons trapped in holes on a chip of some sort and we also have a way of measuring the array of quibits then how is any information transmitted and stored? For instance, if the first and third electrons were excited to be spin-up but all the rest were untouched and spin-down then what would the superposition that resulted be and how would you use that to calculate something like the factorization of the number 15? Oh so confusing!
3. Half silvered mirrors are interesting. If a single wavelength of light is emitted and half of the photons will pass through the silvered mirror and continue on until they reach another silvered mirror, in which half again will pass through, then a detector on the other side will read 1/4 the number of photons as were presumably emitted. Now if a full reflective mirror is used to reflect the photons that were reflected off the first half slivered mirror and then reflected again to hit the second half silvered mirror such that the path length is equal to 1/2n times the wavelength of the light (where n is odd) then all of a sudden the detector will read 0 because the photons have canceled each other out. Does the size of n matter? If n were absolutely huge then the time it takes for the photon to get to the detector along the direct path is much much shorter than the time it takes the photon to get around the more circuitous path to detector, but yet they are still able to cancel each other out. (I don’t even know if this is true the way I have written it, so if anyone knows what I am talking about please correct my question to make more sense than I assume it does in this form). Therefore the photon’s path is determined at the time it is emitted. Could this be used for faster than light communication? For instance, if an emitter on a stationary satellite near earth passed light through two silvered mirrors as explained above and there were two mirrors on a satellite millions of miles away that could interrupt the signal by moving one of the mirrors into place then suddenly there would be a signal way back at the earth satellite instantly…again, this is assuming I know at all what I am talking about.
What I find very odd in QM is that we can make a reliable specific superposition, like for a photon, but no one is supposed to be able to find out the details later. IOW, we can make a photon equivalent to elliptical polarization, given the wave function: A |R> + Be^(i theta) |R> and e.g. 0.6 for A and 0.8 for B. The phase then provides an angle, not just an ellipse shape, so we can be sure a filter tuned to that wave would let the photon through (as it would also have ideal 100% transmission for the equivalent classical polarized light beam.) If I am a confidante of the photon’s creator, I can know just how to orient the right filter (say, combo of QWP and LPF) to get all “hits” etc. But if I don’t already know, I can’t find out for sure: all I can do is try a filter and orientation and I might get transmission or not. Either way, the photon is “ruined” by either being absorbed or changed into the new filter’s base. (Projection postulate? I wonder why that doesn’t have its own Wikipedia article.) All I really know is, that photon couldn’t have been the orthogonal to the filter base if it went through. But if the trait is “real” (unlike the literal contradiction in Fourier analysis of exact momentum and exact position), why can’t I find out? (I know, doing so might lead to weird effects in entangled states, like FTL communication, but suppose it didn’t?)
This seems silly, like a kid saying “If you don’t know, I’m not going to tell you!” In some other comments around, I explained how we might circumvent that restriction by using the accumulation of angular momentum: Keep reflecting a photon around with mirrors, sending it through the same half-wave plate over and over (re-flipped by a second HWP if needed.) The HWP reverses the rotational sense (spin) but maintains the specific proportions of A and B (you may be surprised, but it does – known fact, and to be consistent with the affect on the classical wave.) If we did it enough, all those transits would build up detectable angular momentum in the HWP. It would be along a range, not an either/or because the result needs to be consistent with sending many many “separate” photons through (indistinguishability.) IOW, if the photon came out of a linear polarizer, the many transits wouldn’t build up net spin since the average effect is no rotation. Maybe it wouldn’t work, but it’s worth mulling over. It seems to resemble “weak measurements” as propounded by Yakir Aharonov.
What are the implications of QM on the arrow of time? When reality splits under Everett’s Many Worlds interpretation into a “parallel universe” does this constitute a third direction of time and, subsequently with another split, a fourth, and then a fifth … (ad infinitum)?
Correction, I mean the HWP swaps the values of A and B, so the proportion is in a sense “preserved” but saying it that way is confusing. Hence 0.6 for A and 0.8 for B turns into 0.8 for A and 0.6 for B, etc., which is then restored by a second transit through a HWP (and so on, hence the intuitively expected but legally challenging result …)
For Matt and LoCut, asking about the measurement problem, I think you should look up and read about the Stern-Gerlach experiment. I tend to use this experiment whenever a non-physicist friend/family member asks me about QM, simply because I think its an experiment that is fairly transparent and can be well understood from a good explanation about the actual setup and results, without needing to analogize about quantum mice traveling through a cheese field; it also provides an excellent experimental demonstration of many important and fundamental principles of QM.
1) quantization of particle properties (angular momentum in this case.)
2) How, after measurement, we don’t know all the information about the initial state (only magnitudes of constants, no phases), and
3) Multiple Stern-Gerlach apparati in a row demonstrate measurement changing a state. There’s also a lot of information here about how a state can be a combination of two states when described in a particular way (basis), but be conveniently described as a pure state in another basis.
Collapse of the Wave Function. This is related to the measurement problem (in fact it is fundamental to it!). As a physicist, I am mostly comfortable with QM, but I can’t shake the overwhelming feeling of guilt that I get whenever I refer to wavefunction collapse! It is the only example I can think of where a fundamental physical process is described by a non-unitary operation.
By the way – you are clearly going to have to expand this episode to a full semester…
Yeah, there’s clearly no way we’re getting to all of this in an hour. If we’re lucky, we might be able to agree on a definition of “quantum mechanics.”
But it’s good stuff, and we’ll try. Certainly we’ll talk a lot about the measurement problem and related issues. Bell’s inequality, maybe — that’s another thing for which I don’t yet have a good 30-second explanation.
Moshe, I’m not sure I get the heart of your objection. I wouldn’t think that we should draw an analogy between wave functions in QM and classical distribution functions; wave functions are analogous to points in phase space, and density matrices are analogous to distribution functions. But I suspect this isn’t the place to resolve that.
Janus, David himself has written a book which might be just what you are looking for. A couple of equations at the level of algebra, but most of the focus is on concepts, and it’s unfailingly precise.