A thousand years from now, the twentieth century will be remembered as the time when we discovered quantum mechanics. Forget wars, computers, bombs, cars and airplanes: quantum mechanics is a deep truth that will continue to be a part of our understanding of the universe into the foreseeable future.
So it’s kind of embarassing that we still don’t understand it. Unlike relativity, which seems complicated but is actually quite crystal clear when you get to know it, quantum mechanics remains somewhat mysterious despite its many empirical successes, as Dennis Overbye writes in today’s New York Times.
Don’t get me wrong: we can use quantum mechanics quite fearlessly, making predictions that are tested to the twelfth decimal place. And we even understand the deep difference between quantum mechanics and its predecessor, classical (Newtonian) mechanics. In classical mechanics, any system is described by some set of quantities (such as the position and velocity), and we can imagine careful experiments that measure these quantities with arbitrary precision. The fundamentally new idea in quantum mechanics is that what we can observe is only a small fraction of what really exists. We think there is an electron with a position and a velocity, because that’s what we can observe; but what exists is a wavefunction that tells us the probability of various outcomes when we make such a measurement. There is no such thing as “where the electron really is,” there is only a wavefunction that tells us the relative likelihood of observing it to be in different places.
What we don’t understand is what that word “observing” really means. What happens when we observe something? I don’t claim to have the answer; I have my half-baked ideas, but I’m still working through David Albert’s book and my ideas are not yet firm convictions. It’s interesting to note that some very smart people (like Tony Leggett) are sufficiently troubled by the implications of conventional quantum mechanics that they are willing to contemplate dramatic changes in the basic framework of our current picture. The real trouble is that you can’t address the measurement problem without talking about what constitutes an “observer,” and then you get into all these problematic notions of consciousness and other issues that physicists would just as soon try to avoid whenever possible.
I feel strongly that every educated person should understand the basic outline of quantum mechanics. That is, anyone with a college degree should, when asked “what’s the difference between classical mechanics and quantum mechanics?”, be able to say “in classical mechanics we can observe the state of the system to arbitrary accuracy, whereas in quantum mechanics we can only observe certain limited properties of the wave function.” It’s not too much to ask, I think. It would also be great if everyone could explain the distinction between bosons and fermions. Someday I will write a very short book that explains the major laws of modern physics — special relativity, general relativity, quantum mechanics, and the Standard Model of particle physics — in bite-sized pieces that anyone can understand. If it sells as many copies as On Bullshit, I’ll be quite happy.
But if physics is merely the results of measurements, how can it attain algorithmic compression? You need some conceptual framework to understand those measurements, and that is (at least) as much a part of physics as numbers in a column. Physical theories are notoriously underdetermined by measurements.
George
George, I am not claiming that every element of the theory has to be a measurable quantity, just that one has to be minimalist in what is claimed to “exist”, and listen to the theory instead of trying to validate one’s favorite mental pictures (which are after all derived from a very narrow range of experience). Lot of the discussion about “intepretation” seem to me not to offer any measurable differences between the alternatives, though some of it (more recently) seems much more concrete.
Moshe, re the measurement problem you could perhaps worry about things like the standard gedanken-experiment used to illustrate Bell’s inequalities (the one due to Bohm, where two particles in a spin singlet state go off in opposite directions, eventually to hit polarization detectors) modified to have one detector orientation randomly selected at the last moment, when it’s too late for the information to reach the other detector even at the speed of light. QM says it doesn’t matter, the correlation between polarizations measured at the two detectors is unaffected. Experiments with photons confirm it. So the wavefunction is collapsing instantaneously over a spacelike separation, light cone be damned. Granted, you can’t use spin correlations to exchange information at superluminal speed, but many would (and do) argue that the spirit of relativity doesn’t sit well with this state of affairs.
I am completely unsympathetic to the positivist idea, that things only “exist” if they can be measured. I think physics is about understanding, and if some concept provides a more powerful and economical understanding of how the universe works, I’m happy to say that it exists, whether or not I can measure it directly, and whether the notion involves quarks, the Big Bang, or the quantum-mechanical wavefunction. I do appreciate that there are people out there who disagree, and this disagreement is one of the things that makes it hard to explain quantum mechanics to non-experts — we don’t even agree about it ourselves!
George, in my view it’s misleading to say that certain things don’t exist until they are measured — that’s taking a backwards view, that there really is something called “the position of the electron,” but it doesn’t somehow “exist” until we measure it. I’m arguing for a much more straightforward interpretation: the wavefunction exists, and from it you can calculate the probability of different measurements, but there really is no such thing as “the position of the electron” in the classical sense. Observations don’t map isomorphically onto reality.
Andrew and Amara– Perhaps some day I will be convinced that it’s not useful to think that wavefunctions are real, but in the meantime I should just note that Bohr and Heisenberg and Schrodinger and Einstein all were lousy philosophers, and spouted all sorts of nonsense about quantum mechanics and reality. They may occasionally have been right, and these are certainly smarter people than me, but I don’t think they get much benefit of the doubt on this particular set of issues. The modern stuff is interesting, but I don’t know anything about it.
Sean, I am also unsympathetic to the positivist idea, what I said above is that in my mind things “exist”, and can be a useful part of the theory, only if they affect the results of measurments, I don’t need them to be measurable directly themselves. I would be happier if different interpretations would have measurable differences, so the question could be in principle decidable, maybe they do…
Hi, Moshe. You ask:
If you regard quantum mechanics as a recipe for predicting the results of measurements, and essentially one no different from the principle that the probability of a result is given by the fraction of times that result has been obtained before under similar circumstances, then it is not necessary that the classical world should emerge from quantum mechanics. Statements about the classical world, such as “the cup is on the table” are statements about the actual results of experiments (namely, the state of affairs), rather than a statement about the method which needs to be used to predict results.
That is, the classical world is to be found in the results of experiments and not in the formulae used to predict them. What I’m trying to say is that if we want to interpret something which will tell us what really exists, we should apply our interpretive powers to the empirically given data, rather than the method for processing and predicting it.
A lot of attention has been drawn to the fact that the “cut” between the classical and the quantum world is arbitrary to a large extent – we can include the measuring device in the quantum world and regard our own experience of seeing it as a measurement, and so on. When we include more and more of the classical world into the quantum world, the cut moves to the retina, up the optic nerve, and into the brain. The quantum formalism allows us to predict results regardless of whether we consider our predictions to be predictions of events in our brain, images on our retina, pointers of measurement devices, or locations of subatomic particles. However, the transition from “I see a green spot” to “the electron is at this location” is called interpretation, and quantum mechanics has to be able to work at any level of interpretation. That is why, whenever all of the predictions made by quantum mechanics has been taken into account, what remains is pure, uninterpretable randomness. (Incidentally, this relation to interpretability is what necessitates the occurrence of the “classical” world in the understanding of quantum mechanics – causation, in which every effect has a determinate cause must necessarily be present in order for any interpretation of experimental results).
Best,
R.
Fair enough, but “things exist only if they affect the results of measurements” is a more slippery standard than it first appears (and, I would argue, not a very good one). Does the Big Bang exist? What about things that are outside my current light cone?
Of course, the wavefunction certainly effects the results of measurements — I change the wavefunction, the experiments give different results.
Why not just leave it at “There are things that exist and are measured/observed; there are things that probably exist and can plausibly be measured/observed; there’s the rest which science cannot address.”
I thought decoherence pretty much resolved the observer/observed “paradox” in QM experiments. Being an aggregate of sufficiently many particles and their frenzied interactions, the observer and their apparati simply fail to behave in a measurably quantum manner, whilst some ion in a trap, which we measure using a minimum amount of interaction, does. The rest about quantum cats and the quantum nature of consciousness, and so forth, is nothing but metaphysical flapdoodle reflecting our evolved classical bias regarding “reality”.
Wasn’t it Feynman who said trying to “understand” it will make you nuts? Shut up and calculate, and all that? Why does this quantum vs. classicle false dichotomy continue to bug people, as it is, after all, a falsehood?
If we take the wave function to exist then we have to reconcile ourselves to e.g, something that might be a light-year across suddenly collapsing to a point when an observation is made. It is slightly less likely to make one seasick if one takes the wavefunction to be a description, containing in itself what is knowable.
I feel strongly that every educated person should understand the basic outline of quantum mechanics. That is, anyone with a college degree should, when asked “what’s the difference between classical mechanics and quantum mechanics?”, be able to say “in classical mechanics we can observe the state of the system to arbitrary accuracy, whereas in quantum mechanics we can only observe certain limited properties of the wave function.”
And I could feel just as strongly that “every educated person” should know, say, the basic mechanism of transmission of genetic information, or that anyone with a college degree should be able to tell me the difference between natural selection and genetic drift. And a classics scholar would have her own shibboleths, a poet hers, a lawyer yet another set, and so on and on.
We all tend, I think, to over-rate our own specialized branches of study. It might be nice if every education could provide a basic grasp of philosophy, law, biology, physics, chemistry, mathematics, a handful of languages, visual arts, music, literature, etc etc etc — but I don’t think it’s possible, and I think it a bit presumptuous to say, in effect, “everyone should follow that field which interests me most”.
Sean, I now understand the sentence in question and agree with it. I would also, with some discomfort, grant the existence for things that are inferred from a theory that is itself well-tested. What I am uncomfortable with is discussions of what is the “correct” way to think about a theory, as long as these different intepretations don’t have any measurable differences.
As we can never really “know” which is the “real” situation, what does it matter whether we get seasick or not? If one wishes to approach the concept without a dose of dramamine, one can comfort themselves with the idea that large objects are composed of a large number of particles, feverishly interacting, and hence no particle or collection of particles within that system can remain in a superposition for very long.
Either way, you get the same answer, so, again, what is the problem?
Decoherence ultimately doesn’t explain anything; that’s the problem. If you want to claim that it’s QM all the way up, the ultimate question is then turned into, ‘why do we only perceive one branch of the wavefunction’ which is fuzzy enough to make me run away.
Sean-
Actually, I was being much less a positivist (and even less a philosopher!) than you are giving me credit/blame for. A bit of technical stuff follows: The problem with the ‘reality’ of the wavefunction becomes most evident when you start dealing with the full density matrix (i.e., so-called mixed states), which is the most general way of describing a quantum system. The problem is, there’s no unambiguous way to split the density matrix between the ‘quantum probabilities’ described by wavefunctions and the ‘classical probabilities’ that describe our lack of information about which wavefunction is the correct description. (And this is all aside from other problems, such as the interpretation of the wavefunction/density matrix within special relativity, of which the EPR paradox is the most famous symptom.)
But yes, something out there is certainly real. It’s not all in our heads (not mine, anyway; I’m not smart enough). And let me be a bit more careful: you did use the word “useful” — I agree that it’s “useful” to think of the wavefunction as real. It just might not be true. (And see the work of the aforementioned Fuchs on trying to construct a more operational definition of the wavefunction.)
I’ve always felt that if you corner most physicists and scratch away enough, you’ll find an instrumentalist, but I don’t think anyone actually thinks that way in practice; it’s more of a philosophical refuge against hard questions.
“Perception” is registering an observation, which involves an interaction, and so forth. Some collections of interactions have the rather subjective quality of being “conscious” of the interaction, I suppose, whilst others do not. Really, consciousness and perception have not proven themselves to be phenomena that cannot be explained in a purely classical framework, so I see no reason to jump ahead to the need to somehow reconcile perception with quantum reality. If classical mechanics is enough to describe all the parts of a brain being “conscious” (whatever that winds up meaning), then decoherence fully accomodates the “it’s quantum all the way up” description. Approximate classicality is probably good enough, and there’s no need to stay up nights wondering why we don’t “perceive wavefunctions”. It could be you need a classical (or the quantum approximation, which yields virtually the same result) system to “perceive” at all. I certainly don’t know whether that’s truly the whole story, but no one else does either, and it’s ultimately quite likely to be an answerable question. ‘Til then, “shut up and calculate” agnosticism seems the only scientifically valid opinion. The rest is empty philosophising, a product, I think, of the romantic notion that seemingly mysterious things must be really special somehow.
then decoherence fully accomodates the “it’s quantum all the way up” description.
No, it really doesn’t. Decoherence just tells you that the reduced density matrix approximately diagonalizes, but it doesn’t tell you anything about why that should be physically (or perceptually relevant).
If it’s quantum all the way up, there are no classical systems, but he fundamental tension is that we perceive a classical world. Decoherence looks like it ought to be relevant in explaining it, but as best I can see, all it does it make the relevant experiments much, much more difficult.
This isn’t completely philosophy, either. There is a fundamental dichotomy in the ‘interpretation’ of QM: collapse vs. no-collapse. These should be, in princile, experimentally distinguishable. In that sense, ‘interpretation’ is a misleading word. There is an honest physical question to be investigated here.
But until some clever experimentalist does an experiment that gives more than just vanilla QM, I subscribe to the ‘have no clue’ interpretation.
D. Biologist, I think some interpretations may be more easily be seen to be compatible with special relativity than others, i.e., may allow us to avoid phrases such as “super-luminal but carries no information”.
I guess we are left then to ponder the subject with our own devices?
If anything, the renewed debate “amongst the knowledgeable” helps to set up further information for us lay people.
Should read:
Ponder the subject
I rather thought that the “honest physical question” (being, I think: “Can we observe a system transitioning from an entangled collection of quantum entities in superposition to one that exibits approximate classical behavior in a measurable duration?) is being probed experimentally, especially in the field of quantum computing. I’m not sure how far along this area of investigation has proceded to something definitive, so I’ve been hesitant to come out in favor of decoherence any more than proposing it as perhaps a more philosophically satisfying model for those who choose to bother themselves with such matters.
If it possible to indentify measurable differences between one quantum interpretation or another (e.g., the collapse of the cat’s wavefunction is NOT instantaneous, ever, just too fast to feasibly measure), then I suppose it’s a scientifically relevant concern. If it isn’t, even in principle, then, again, how rational concern over quantum interpretations differs from any other form of philosphy other than “science” is not at all clear to me.
There are a whole class of experiments generally called “quantum eraser” experiments which probe this sort of thing, I think. Various people have predicted an irreversible collapse of the wavefunction. This could be measured in such experiments.
Decoherence is an honest physical effect that can be measured. It’s not an issue of philosophy. My personal belief, however, is that its explanatory powers are often overstated.
I think Newton’s laws of motion in their original form and in Hamiltonian form are indistinguishable, experimentally speaking. Nevertheless, the latter is more easily extended to quantum mechanics than the original formulation. That is why, IMO, interpretation is not merely philosophy. (Of course, these different interpretations of QM are not leading to multiple equivalent mathematical formulations, and perhaps that is part of the problem?).
#30 Sean and #40 Andrew:
I think that the Bayesians would say that the quantum mechanical probabilities involved inthe EPR scenario become simply Bayesian probabilities.
In 1998, I heard a talk by Ariel Caticha [1] describing a different way to treat state vectors. He calls the idea “array entropy”, which was originally introduced by Edwin Jaynes [2], but Jaynes thought that it was inadequate for the entropy of a quantum system. Caticha, however, expanded on Jaynes’ idea in a nice way. He assigned amplitudes and wave functions, not just to the system, but to _the whole experimental setup_.
[In the following, I synthesize a bit from Caticha’s article. For the full article, get the conference proceedings [1] or look at the xxx server, where he he has two slightly earlier articles available:
http://xxx.lanl.gov/abs/quant-ph/9803086 “Consistency and Linearity in Quantum Theory”
http://xxx.lanl.gov/abs/quant-ph/9804012 “Consistency, Amplitudes and Probabilities in Quantum Theory”]
We know that one of the objectives of quantum theory is to predict the outcomes of experiments. Amplitudes are used to predict the outcomes of experiments, where, mathematically, the amplitudes are calculated via Hilbert norms (For the nontechnical people here, these norms, or inner products, are the means to measure the distance between wave functions). Interpreting the amplitudes can then be used to prove the Born postulate provided that amplitudes are assigned to the experimental setup. Caticha calls this extra assignment a “constraint” that the amplitudes be assigned consistently.
NOTE: Caticha says in his appendix that Born’s postulate is a theorem that has been independently discovered several times: A.M. Gleason, J. Rat. Mech. Anal. 6, 885 (1957); D. Finkelstein, Trans. NY Acad. Sci. 25, 621 (1963); J.B. Hartle, Am. J. Phys. 36, 704 (1968); N. Graham, in “The Many-Worlds Interpretation of Quantum Mechanics” ed. by B.S. DeWitt and N. Graham (Princeton, 1973). The limit N->infinity where N is the number of replicas of the system is further discussed in E. Farhi, J. Goldstone, and S. Gutman, Ann. Phys. 192, 368 (1989).
His approach, to consistently assign amplitudes to the experimental setup, is to assign a single complex number to each setup in a way that relations among the experimental parts translate into relations among the corresponding complex numbers. The consistency comes in by the requirement that if there are two different ways to compute this complex number, then the two answers must agree.
Caticha uses a path integral approach [3] to cover all possible combinations of starting points and interactions prior to the observing time. These lead to the same numerical value for the amplitude, that is, the outcome of the experiment. These amplitudes can then be inserted in the quantum mechanical equation of motion- the Schroedinger equation.
How to get from the Schroedinger equation to the Born postulate? The Born postulate states that the probability of N independent particles is the product of the wavefunction (amplitude-squared) for each of the particles, and the sum of each those is unity. [Note: here might be a connection to the Many Worlds Interpretation.] The Schroedinger equation is the equation of motion. Caticha shows that the connection can be made by using a Hilbert norm.
After Caticha shows the connection, he wants to evolve the system in time, and he does that with an entropy array. Once he applies the entropy array, then he can measure any observable in the system, and he says that the time evolution of states is “linear” and “unitary”.
So his is a Bayesian approach. If one adopts a Bayesian approach to probability, then the Schroedinger wave equation becomes a posterior probability describing our incomplete information about the quantum system, rather than wave functions that collapse in reality upon our observation.
Bohr’s Copenhagen Theory says that even when the QM state vector gives only probabilities, it is a complete description of reality in the sense that nothing more can ever be known; not because of technological limitations, but because of fundamental principles. But Jaynes seems pretty convinced (‘Clearing Up Mysteries,the Original Goal’) about Bohr’s way of perceiving physics problems. He says that persistent in Bohr’s writings is a common logical structure which indicates that Bohr was never on the ontological level traditional in physics. Always he discussing not Nature, but our information about Nature, but that physics at that time did not have the vocabulary for expressing ideas on that level, so then his words appeared muddy.
On Dirac (the late Dirac was not a positivist, and the young Dirac was probably not either): I learned from Jaynes’ writings that Dirac was working with Harald Jeffreys (a Bayesian) side by side for a little while at St. John’s College, and he seems to have not realized what Jeffrey’s probability theory could offer, that is, a vehicle for expressing epistemological notions quantitatively. Jaynes said that if either Bohr or Dirac understood the work of Jeffreys, the recent history of theoretical physics might have been very different: they would have the language and the technical apparatus with which Bohr’s ideas could be stated and worked out precisely without mysticism. Had they done this, and explained clearly the distinction between the ontological and epistemological levels, Einstein would have understood it and accepted it.
References
[1] Caticha, Ariel, _Probability and Entropy in Quantum Theory_ in Maximum Entropy and Bayesian Methods_ (conf proceedings from MaxEnt’98 conference, Garching, Germany, July 1998), Kluwer Academic Publ., 1999. (BTW: This 9page mathematical paper is surprisingly readable..!)
[2] Jaynes, E.T. “Jaynes: Papers on Probability, Statistics and Stastical Physics,” edited by R.D. Rosenkrantz, Reidel, Dordrecht, 1983.
[3] R.P. Feynman, Rev. Mod. Phys. 20, 267 (1948); R.P. Feynman and A.R. Hibbs, “Quantum Mechanics and Path Integrals,” (McGraw-Hill, 1965).