that some properties by their very nature must take determinate values or not exist at all
This is not a scientific principle. Science lives or dies only on the accuracy of its predictions - probabilistic or deterministic. Don't be confused by the fact that pre-quantum, pre-thermodynamics laws were deterministic - that was just a lucky fact, that persuaded people that all laws had to be the same.
As for the "some properties", quantum mechanics asserts (and experiments back it up) that there is no such thing as position, or momentum - that the combination of the two is the actual property that exists.
As for the different interpretations of quantum mechanics - they're all equivalent, or they differ in ways we can't measure yet. So none of them on their own say anything about how we should view reality. Only the predictions of quantum mechanics tell us about reality, not the models.
Actually, I don't think I agree with the thrust of this post. As long as you don't argue "this is weird, hence it is wrong", I think the if you find quantum mechanics strange you're more likely to prosper in the field that if you force your sense of normality to match quantum reality.
In the first case, you can easily discover a new physical law, find it weird, and cheerfully accept it. In the second case, a new law may be an assault on your feeling of reality, so you may be less willing to accept it - and if you did, you'd have to go through the whole process of updating your instincts again.
People can develop very good intuition about things they find strange, without having to find them any less strange.
Eliezer,
What is ironic about this posting is your indignation. Offhand it sounds like you are as guilty as those you criticize.
There is nothing weird about people finding a theory to be weird that does not correspond with their everyday surface perceptions, even when they are able to comprehend it intellectually. Also, and others have noted this more or less, there are a lot of different interpretations out there of what quantum physics "really means," and some are a lot weirder than others. Is it ontological that Schrodinger's Cat does not either exist or not exist until actually observed being one (or not) being the other?
And again, I remind all that we do not have the definite answer on how to put quantum mechanics and general relativity together, leaving some doubt about some fundamental aspects of both. Some of the proposed resolutions are perceived by many as even weirder than either, e.g. string theory, but given that it has neither been proven nor disproven, should we all get on a big high horse about people who find string theory to be "weird"? There have just been some pretty intelligent books out criticizing it, with some of their arguments in some sense coming down to how weird it is, although that is not the terminology used.
Maybe when we finally figure all this out, if we do, quantum physics might be redone in a way that makes it seem "less weird" than it does now (and again, some of its most extreme apparent "weirdness" comes from some interpretations of it that are not universally accepted).
In actuality, the biggest barrier to understanding modern physics is the math. The math models are what generate the "weirdness". Trying to use english to describe what the math models are telling us is what generates the "weirdness".
But if you suspend disbelief and go where the math takes you, useful things can be done, like nuclear power, solid state physics, etc.
This is one of the worst posts I've read here.
If you truly think "This person will never understand physics no matter how many books they read." then you are making great assumptions based on your personal prejudices.
If you don't find quantum physics weird (or at least understand why someone may), you don't have a grasp on current human intuition. Just because you recognize that quantum physics differs from everyday experience doesn't mean you can't understand quantum physics. It actually means you have a BETTER grasp on understanding human intuition, and has no bearing on whether you know (or have the capability of knowing) less or more about quantum physics.
Another way of looking at this is to realize that we are all pretty much hard wired to operate in a surface reality that more or less fits a Newtonian-Euclidean model of the world. We now know that this does not hold at high accelerations or at very large or very small scales in a lot of ways. So, these deviations, many of which have been clearly established beyong any doubt, seem weird to most people when they first hear of them, and may even still "feel weird" even after they have long come to intellectually comprehend and accept them.
Heck, even now, after quite a few decades, there is a part of me that finds the simple outcomes implied by special relativity with respect to time dilation still a bit weird at an emotional level, although delightfully and fascinatingly so, even though they are clearly the direct logical implications of the (apparently) "universal" constancy of the speed of light.
"Anyone who is not shocked by quantum theory has not understood it." Neils Bohr. It is not just that one has to greatly revised one's view of what there is in the world; physicists still don't understand very well what quantum theory implies about what in fact there is in a quantum world.
Exactly the quote and reference I was going to make. Should we believe Bohr didn't understand Physics?
Are there data on how many physicists believe in astrology? I can understand how a few would, but I'd be astonished if the percentage weren't a lot lower than for Americans as a whole. Hey, there are PhD biologists who reject evolution--but not many.
If Richard Feynman can say:
What I am going to tell you about is what we teach our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You see my physics students don't understand it. ... That is because I don't understand it. Nobody does.
then it may be strange to the point of being beyond understanding.
(Nobel Lecture, 1966, The Strange Theory of Light and Matter)
This is a great post. I just want to add: we might fail to understand physics and mass murderers for different reasons. When a terrorist slams a jet into a skyscraper, someone can say "I don't understand why that person did that? It's bizarre." But they seem to fail in understand because victims have a biased recall of transgressions (according to the work by Baumeister on the myth of pure evil). Perpetrators seem to actually have more accurate and complete understandings of transgressions. This is one of my favorite findings from social science.
In contrast, we seem to think physics is bizarre for different reasons.
Well, the main lesson I learned today is:
Never use quantum mechanics as an example of anything.
I could have talked about relativity, the counterintuitive mixing of space and time, and non-flat spacetime metrics, but noooo, I had to say "quantum".
I haven't learned any general relativity yet, but from what I know of special relativity, it actually makes perfect sense. You start with the assumption that no observation can allow you to deduce where you are or how fast you are moving, and then follow that premise to its logical extremes.
There are things, if you look at them hard enough, you can understand it intuitively, and they cease to be weird.
Quantum mechanics, on the other hand, is one of those things that even if you look at it really, really hard, you still can't understand it. So no, I think quantum mechanics is the only example you could have used here.
Relativity of simultaneity makes perfect sense to you?
I'm prepared to accept that my intuitions are defective and the world really does operate this way... but I can't seem to actually adjust my intuitions accordingly. There's still this little voice in the back of my mind saying, "But which one is the real now?"
I haven't learned any general relativity yet, but from what I know of special relativity, it actually makes perfect sense. You start with the assumption that no observation can allow you to deduce where you are or how fast you are moving, and then follow that premise to its logical extremes.
You also need to know that there's something that travels at a finite speed in vacuum, otherwise Galilean relativity is consistent with that assumption too.
But if you hadn't used that example I would have never read this Wikipedia edit summary, and never heard about you or LessWrong!
One thing that happens with new theories is that at first they seem strange, but then gradually the concepts filter into the popular consciousness and then they are easier to accept. It's commonplace to say, "everything is relative", or "the observer affects what he observes". Also, better ways are found to instruct students in the principles, which also helps with acceptance. QM and relativity do not seem all that odd to me, because I have known about them for so long.
One theory that still baffles me is the holographic principle, which suggests that space is actually two-dimensional. The third dimension is an illusion. Informed by Eliezer's commentary, I will no longer say, "How bizarre that is!" but rather, "How bizarre I am!"
Don't jump the gun; we have no experimental confirmation of the holographic principle.
Unlike say the Schrodinger equation, which is one of the most precisely verified equations in the history of physics.
Shakespeare, Feynman wrote that in 1966, which was before Everett's absolutely essentialy (and stunningly obvious in retrospect) insight spread through the physics community. Feynman's claim in 1966 that "Nobody understands QM" thus inadvertantly illustrates one of the other great truths, which is that nobody knows what nobody knows. The accumulated pool of scientific knowledge is far too vast for any one human mind to hold more than a tiny fraction. There are six billion people in the world, and you don't know what they know. Feynman should have stuck to saying "I don't understand QM", to which he could have attested of his own knowledge.
Quantum mechanics really was a very poor choice as my first example, because the application of "Think like reality" to QM is nontrivial. Before you conform your intuitions to reality, you should be very sure of what reality is.
Quantum mechanics tells us unambiguously that reality is over points in configuration space and that quarks and photons have no individual identities - if you pretend that a point in configuration space with photon 1 at A and photon 2 at B is different from a point in configuration space with photon 1 at B and photon 2 at A, you will get the wrong answer. So you have got to toss your intuitive understanding of little billiard balls, because it is definitely wrong, and start trying to wrap your understanding around configuration spaces until they seem normal, because they are definitely normal.
Once you have achieved a state where configuration spaces seem normal, many-worlds will also seem much more normal. If you insist on thinking of particles as individuals you will start to ask nonsensical questions like "Which branch am I in?" or "When does the 'observation' occur?" It seems to me that many-worlds is also cut-and-dried correct, but I understand that the reasons for this verdict may not be easily apparent to everyone. Questions like "How are amplitudes converted to subjective probabilities?" are not automatically dictated by the theory in the way that configuration spaces and lack of individual particle identities is dictated by the theory. So in this case, there is a legitimate question of what it is that you need to reshape your intuitions to regard as normal. If a QM interpretation seems weird, it may be that the interpretation in question is wrong and that you should not wrap your intuitions around it.
But what doesn't change, and this is the main point I was trying to make, is that you have to pick one or the other. If a theory seems bizarre to your intuitions, then either the theory is wrong or your intuitions need reshaping. Feynman felt he didn't understand QM, and lo and behold there was an additional insight required to make it seem normal. If Feynman thought that QM seemed bizarre and that this was okay, a state of affairs that didn't indicate a problem with either the theory or his intuitions, then that was historically incorrect - though I don't believe Feynman said as much in that many words.
"Which branch am I in?" is clearly not a nonsensical question, because I actually have these memories which follow a sequence of single events---things being here and not over there. You can say it's a pointless question, because there is another me somewhere in the other branches; but it's clearly not meaningless, because we only experience and remember one result from each experiment.
Feynman's claim in 1966 that "Nobody understands QM" thus inadvertently illustrates one of the other great truths, which is that nobody knows what nobody knows.
I don't think he was actually trying to say nobody understands quantum, I'm pretty sure he was actually saying (albeit in less words): "just because you don't understand quantum, does not mean that you are unintelligent, or that the theory is incorrect". I believe that as you pointed "nobody knows what nobody knows", implies that he wouldn't make such a statement with the intentions that it should be take literally, and consequently it seems significantly more probable that the intentions of the statement were something else entirely.
I would also like to note that the statement "nobody knows what nobody knows" has only one piece of evidence attached to it, and I am curious were else you noticed it taking effect.
Questions like "How are amplitudes converted to subjective probabilities?" are not automatically dictated by the theory
You might find this paper by David Deutsch interesting. Although, equation 14 bugs me, it seems to me |Psi_2> as defined doesn't necessarily exist.
Stuart, I said determinate, not determinist. I was objecting to the notion of an objectively indeterminate property - as if it made sense to say of a particle that it has a position, but no particular position... You yourself say "there is no such thing as position, or momentum... the combination of the two is the actual property that exists." I would be very surprised if that is anything more than a slogan. Can you explain to me the exact nature of this 'combination' that is the actual property? (Please don't just say that the formalism provides the details, without doing so yourself. I want to see the propositions of quantum theory, such as assertions about observables taking particular values, cashed out in terms of your ontology.) Can you explain to me how, though neither A nor B exists, a combination of A and B exists? Is this done using logical conjunction, counterfactuals, perhaps algebraic means?
Eliezer, how does abandoning the notion of particles as individuals save you from the questions you mention? For that matter, what is your alternative to the notion of particles as individuals? I can see more or less how I would think about the matter. For particles of the same species, instead of any product state ab being possible, you can only have states like ab+ba or ab-ba; so I might conclude that particle species are the individuals, the things-with-states. But then particles of different species can also get entangled, and so you end up with just one thing, the universe itself, its state described by the universal wave function. On the other hand, if you allow yourself the notion of a relative state, I would think that the notion of particle individuality could be retained, and the symmetry conditions interpreted as being 'trans-world' properties, properties of the ensemble of all branches of the wavefunction.
Presumably the actual property is the state of the wavefunction.
So for instance we could have a Gaussian wavefunction... and that would be the determinate physical variable. It has no particular position or momentum, because there are nonzero amplitudes for various different positions and momenta. We could choose a different wavefunction to get a more determinate position, but then because it's a Fourier transform the momentum would grow ever more indeterminate.
Interestingly, there are apparently ways of working around this, by carefully choosing your observables to be operators that commute. http://arstechnica.com/science/2010/08/quantum-memory-may-topple-heisenbergs-uncertainty-principle/
as if it made sense to say of a particle that it has a position, but no particular position
That might or might not make sense (mathematicians have been tearing their hair out about non-computable numbers, see Chaitin's constant). But most quantum mechanists do not say that a particle has a position. In fact if you interpret Quantum mechanics in terms of "hidden variables" (there are underlying values for the objects, like spin and momentum, but we can't get at them) then you will generally come unstuck.
Can you explain to me the exact nature of this 'combination' that is the actual property?
The property is exactly the one in the quantum formalism. I don't really see why you object to the formalism. It gives specific predictions that have been confirmed, with high probability, in experiments.
If you want an ontological view, then my position is that science is only about making predictions about the results of experiments and then testing them. Properties such as position, energy, etc... are only valid in that they predict a lot of different experiments. In classical mechanics, it emerged that a mathematical concept called "position" led to great predictive power, giving universal laws. So classically, "position" existed.
In quantum mechanics, laws based on "position" don't work, so the concept of position doesn't make sense in a quantum framework (just as "colour" makes no sense in acoustics). Other concepts did make sense - they had to be expressed in certain formal mathematical ways, but they made sense.
So, to sum up, position doesn't exist, momentum doesn't exist, but certain other objects (such as the product of the uncertainties of momentum and position) do make sense.
Aha! But have I not defined "uncertainty of position"? How can I claim this exists if position doesn't? The problem is just the name (and this is going back to Elizer's original point, and causing me to think I may have been a bit hasty in rejecting it). This is just the standard deviation of an observable. It's only called "uncertainty of position" because of an analogy with the classical "position" - a wrong analogy (and an observable, like a classical "position", is just a mathematical object that seems to make sense in experiments).
And so, like kudzu, the thread is taken over by the Great Quantum Debate... but Mitch, do you agree with the central point of the original post, that true facts cannot be "weird" or "bizarre" except insofar as we think like primates and not like reality? That we are always faced with a dilemma to eventually discard either the mistaken intuition or the mistaken fact?
As to your quantum-question: as I understand it, the presences of particle species at particular locations are the dimensions of the configuration space, points within which are that-which-exists. There is not only one thing; there are many points within the configuration space, and amplitude relations within neighborhoods of these points, and the dynamics are within these amplitude relations.
There is no reason to try to retain the idea of particle individuality - it has been explained away as a lossy approximation arising from the macroscopic case of configuration spaces. We understand evolutionarily why humans think in terms of individual particles, just as we understand why humans think in terms of flat space, and we know it isn't true. So, out the window it goes.
For the same reason, there is no legitimate justification for clinging to the idea that a particle must have a single definite "position" - again, this is a lossy macroscopic approximation that has been entirely explained away, regardless of how intuitive humans find it. The points in configuration space do involve the exact locations of species, because these are the dimensions of the configuration space; but it is a very severe mistake to try to identify the observed universe with a single point in this configuration space - as severe as trying to identify the whole universe with a single one of its particles. Computations take place in the amplitude relations among neighborhoods of points - you can't do anything with just one of them. A cloud of amplitude relations can compute, a single point cannot.
What fools our intuitions is that, relative to the macroscopic level, there are very narrow concentrations of amplitude that look to humans like single points. But this has been explained away by the microscopic theory; to think that there is necessarily a single "real" position is like thinking that there must be a single "real" space of simultaneity.
The issue has been vastly confused by early physicists interpreting the process of multiplying an amplitude cloud into a degree of thermodynamic freedom so that the subclouds are too distant to substantially interact, as "observing" a particle and finding out that it was "really" at a particular spot. But to suppose that physics contains a basic account of "observation" is like supposing that physics contains a basic account of being Republican; it is the projection of a complex, intricate, high-order biological cognition onto fundamental physics. What was previously attributed to "observation" has been explained away as the multiplication of amplitude subclouds into degrees of thermodynamic freedom, which at the macroscopic level we experience as our local subcloud of mutually interacting points having only a very narrow concentration at a particular particle-species-location, giving rise to the ridiculous and illusory experience of things being in only one place.
I am proud to report that it actually does seem absurd to me now that things could be in only one place. They'd fall apart, or be frozen in time, or just blink out of existence - it's not possible to imagine it coherently, really. And it's equal nonsense to suppose that things could be nonentangled - how could you possibly see them?
Eliezer, If a theory seems bizarre to your intuitions, then either the theory is wrong or your intuitions need reshaping.
I'm leaning towards embracing your point more, but still two issues: 1) "need". If my intuition tell me something, but I know it's wrong, and I can deal with it without letting my intuition interfere, why do I need to reshape my intuition - shouldn't I just go with "don't trust my intuition"? 2) As a mathematician, I have good mathematical intuition. It helped me when I took a course on quantum mechanics and relativity. However, the QM results offended my everyday intuition, and still do. However, I could still develop QM results, based on my mathematical intuition and knowledge (and I'd get them right). If I considered the world of QM as a non-existent mathematical fiction, I could still can work in it. So why do I need to make my everyday intuition match QM reality? What do I gain?
So does MWI actually bring anything to the table in terms of testable predictions that differ from Copenhagen et. al.?
Yes, in that it doesn't postulate this weird non-unitary indeterministic "collapse" business which is never actually observed.
Matthew C: My criticisms of Kent's criticisms of MWI (as formulated by Everett), in the paper you link to:
A Hilbert space has an inner product by definition, so mu is already an entity of the theory without needing any extra postulates.
In the example given, decoherence will result in the two terms of the RHS of (2) not being able to interfere with one another, which justifies considering them to be independent worlds, no intuition required.
Kent's talk about bases seems confused, the dimensionality of a basis is fixed by the dimensionality of the state space. What he refers to as a 1-dimensional basis is in fact a 2-d basis (the two terms being added together are basis vectors).
In practice, one can chose a basis as follows: when a measurement is made, decoherence results in the system seperating into a noninterfering subsystem for each outcome. If there is a unique state for each measurement outcome, put together they are a basis; otherwise choose a basis for each outcome and put all the bases together to make the basis for the whole system, the ambiguity has no effect on the measurement outcome because different bases only mix together states with the same outcome. This doesn't need to be made an axiom; any basis can be used in principle but some are a lot more useful in practice than others.
Of course, Everett didn't know about decoherence, but we do now.
As for determining probabilities, I suggest you read the paper I linked earlier. It might be flawed, as I mentioned, but if so I think it can probably be amended to work.
I think it's unfortunate that this thread has veered off into debates about the inner workings of quantum theory and indignant defenses of what is and is not known in physics. Eliezer used quantum mechanics as an example to illustrate a larger point which has scarcely been mentioned here, a point which connects very clearly to the name of this blog -- Overcoming Bias, and yet everyone seems more interested in the metaphor than what it represents; they are mistaking the map for the terrain, as Eliezer might say =)
As I understand it, Eliezer is making a point about how short-sighted and self-centered it is to label a phenomena "weird". To call something weird is, in essence, identifying it as an outlier in our (woefully limited) data set of experiences. As Eliezer points out, this is a shortcoming of our model and not an inherent “eccentricity” in reality. Now I believe that being surprised is completely natural and in fact unavoidable, but what I believe Eliezer is really railing against is how fixated people can become with the “weirdness” of a universe which refuses to conform to our simple models and heuristics.
In cognitive psychology, there is a theory of cognitive growth espoused by Jean Piaget which describes learning as a dialectic of assimilation and accommodation. When faced with the unfamiliar, we have two options: assimilate the new data to fit our current models, or modify our models to accommodate the new data. Both of these processes are vital to cognitive development: assimilation allows us to use our limited experiences to generalize to the unfamiliar and make relatively quick decisions without a thorough investigation, and accommodation leads to more mature and nuanced thinking which takes more facts into account and is thus more "accurate". In fact, this is exactly how scientific progress is made--outliers disrupt the tidiness of old models, and the scientist must either explain the outlier as erroneous data points or expand the model to accommodate the new data; what the scientist cannot do, however, is ignore the errant data point altogether. What I think Eliezer is railing against is the mental stance we take towards this process. By fixating on our own incredulity, we are forgetting that nature has absolutely no obligation to fit into any models. As developing individuals who are constantly learning the dizzying depths of our own ignorance, we should be aware of the tenuous nature of human knowledge and thus not be paralyzed by cognitive dissonance in the face of “spooky” phenomena like quantum entanglement and other such boogeymen of science. In fact, we should be thankful that we have been able to generalize from experience at all. I like how Eliezer referenced billiard balls, which I’m pretty sure is a nod to David Hume and his artful deconstruction of causal inference as an innately irrational process with no essential basis in nature. I agree with Eliezer that we demonstrate a profound ignorance for the overwhelming complexity and mystery of the universe by expressing sustained surprise that reality has betrayed our expectations. Man is a hairless ape with a thicker neocortex than his primate cousins, occupying a single speck of matter in a single solar system in one galaxy in….you see where I’m going with this. Let us not forget our laughably insignificant place in the grand scheme of things, and let us not feign comprehension of that which is beyond us.
What I am advocating is that we accommodate more and assimilate less; as Eliezer says “spending emotional energy on incredulity wastes time you could be using to update”. Let us not cling to our ignorant beliefs as if they were prized possessions; to do so would be to prefer vanity and ego preservation over truth.
"We have to live today by what truth we can get today and be ready tomorrow to call it falsehood." -William James
Preach on brother.
Does anyone have a book they can recommend that explains the actual math of quantum mechanics? Once I actually see the equations, things always start making sense to me. For example, my introductory modern physics course talked about the Schroedinger equation and had an optional section on operators and wave functions. Having suffered through Fourier analysis in my electrical engineering courses, the way the Heisenberg uncertainty principle comes from the application of transformations to wave functions made a kind of intuitive sense. I know an awful lot of math - and am very good at it - so I want to find some way of understanding modern physics on the level of mathematical formalization other than taking lots of physics courses in a university. I could try reading university physics textbooks, I guess, but I'm worried about what they might assume I already know; you can't Google the symbol for a partial derivative in order to find out what it means.
Does anyone have a book they can recommend that explains the actual math of quantum mechanics?
You could try "The structure and interpretation of quantum mechanics" by R I G Hughes or "The Interpretation of quantum mechanics" by Roland Omnes. Either has enough math to articulate the problem.
I also really liked "Quantum mechanics and experience" by David Z Albert - it was this book that led me to realize that many-worlds is obviously true (as it now seems to me). Albert himself does not believe in many-worlds but he explains it really well.
I'm now working through the university physics texts because none of the above cover relativistic QM. They physics texts though are - to a man - in the "shut up and calculate" school of thought. It is claimed that many a promising physicist has disappeared down the rat-hole of the philosophical interpretation of QM.
You may also enjoy "A Different Universe: Reinventing Physics from the Bottom Down" by Robert Laughlin. He argues that so-called fundamental physics is just the lowest layer of emergent froth that we are able to see. Quantum Field Theory shows that "empty space" is full of stuff for example.
You write: "There are no surprising facts, only models that are surprised by facts."
That's deterministic thinking. Surprising facts happen every once in awhile. Rarely, but occasionally.
But I agree with your general point. Surprise is an indication that you have a problem with your model, or that you have prior information that you have not included in your model.
but Mitch, do you agree with the central point of the original post, that true facts cannot be "weird" or "bizarre" except insofar as we think like primates and not like reality? That we are always faced with a dilemma to eventually discard either the mistaken intuition or the mistaken fact?
The reality is that possibilities are very large in number and actual knowledge is shockingly small. To genuinely "think like reality" might mean to maintain as constant and thorough an awareness as possible of every uncertainty in your existential situation that you can discern - since that would reflect the epistemic reality.
Another observation: a follow-up post on how to act "like reality" could be warranted.
A few more words on quantum theory. In effect, there is a prevailing myth and a rising heresy. The prevailing myth is the Copenhagen interpretation, the rising heresy is the many-worlds interpretation. They have this much in common, that both are full of fuzzy thinking but their acolytes believe them to be exact. Therefore, when you press the acolytes for details, you never get quite the same answers, because the belief that the interpretation does provide answers comes first, and then the details are invented in response to scrutiny, in faith that they are there already and the acolyte needs merely to think things through and rediscover them. One consequence of this situation is that it becomes very difficult to critique or rebut these interpretations, because the details are always different depending on one's disputant, and if they can't make it make sense, they will eventually appeal to authority and say that Bohr or Everett would have explained it better.
It is easier to see that Stuart is tying himself in knots. There is no such thing as position, but there is an observable called position, but it has no exact value, but it has an uncertainty in its value... (I had better observe in passing that whether physical continua are more like the reals or the rationals should make no difference to the illegitimacy of the idea that an entity can have a location without having a particular location. If anyone wants jargon with which to make this idea precise, see Armstrong on determinates and determinables. The illegitimate - because self-contradictory - idea is that of an objectively indeterminate determinable property.) The philosophical charisma of Bohr et al, while still strong, has declined a little, and so increasingly people are opting for the Everett approach. It sounds cleaner: there are many worlds, they all exist, that's that! It sounds like a pleasing resolution to the problem of superposition.
But again, if you go into the details, you find discord among the acolytes, because the emperor, if not naked, is rather threadbare. For example: given that the state of the multiverse is described by some universal wavefunction, which part of the formalism corresponds to a "world", an individual universe? One might try breaking down that wavefunction into linearly independent components, and saying that those are the worlds. But if they are linearly independent, then they evolve independently, which means that any one of them, alone, could have been the whole thing - so why would we need to postulate the other worlds? And anyway, aren't the worlds supposed to be interacting? Double-slit diffraction is due to photons in the universes next door, for example... The problems in defining a world are so severe that one will find many-worlds advocates saying that the worlds aren't really real, they only have an approximate existence. The seamless multiverse is the real reality, and a world is just an approximation and reification of a chunk of it. At this point the interpretation has declined from mathematics into rhetoric, i.e. handwaving. If one asks what part of the universal wavefunction correponds to the particular empirical realities which physical theory is ultimately supposed to account for, one is liable to get remarks about brain observables correlated with external-world observables - except it turns out that the existence of brains is no more objective than the existence of worlds... As I said, it is hard to rebut because it is so amorphous.
My feeling is that Bohm escapes these problems, at the cost of requiring nonlocal information transfer (a high price, but one I'm willing to pay).
But if they are linearly independent, then they evolve independently, which means that any one of them, alone, could have been the whole thing—so why would we need to postulate the other worlds? And anyway, aren’t the worlds supposed to be interacting?
Can't this be answered by an appeal to the fact that the initial state of the universe is supposed to be low-entropy? The wavefunction corresponding to one of the worlds, run back in time to the start of the universe, would have higher entropy than the wavefunction corresponding to all of them together, so it's not as good a candidate for the starting wavefunction of the universe.
I had, but I had the wrong idea about it. At a glance, Mohrhoff's ontology appears to be as follows. There is a fundamental reality which is standard-issue Formless Infinite Oneness, and then there is a multiplicity of elementary physical facts ('observables' taking definite values) out of which everything physical is made. Every single one of those facts is utterly uncaused, both with respect to location in space and time, and the specific value taken. But quantum mechanics gives us the probabilities.
I do not, so far, see anything illuminating in what he says about the relationship between the Oneness and the physical facts. In fact, I don't think I've ever heard anyone say anything illuminating about the relationship between the world of particulars and a world of allegedly primordial undifferentiated being. I think people are prone to misidentify a straightforward cessation of cognition as an experience of 'cognition of pure being'.
But I will say something about the idea of uncaused fundamental events, which is actually orthodoxy and not just in Mohrhoff. (I might wonder what role the Oneness has in Mohrhoff's theory if he thinks quantum events are absolutely uncaused, but evidently he's promoting an idealist ontology in which those events are actually free choices of the cosmic mind. So it's a combination of absolute idealism, belief in free will, and the ensemble interpretation of quantum mechanics!) Celia Green has already said it well:
"... no one has noticed the reification of statistical concepts that goes on, and physicists talk of a thing being 'caused by chance' as if 'chance' sat there pushing the right proportion of electrons to the left. If an electron chooses to turn left, this is either caused by something, which may or may not be known to the human race at present, or it is caused by nothing, which is shockingly inconceivable. In neither case is it caused by a cosy little homebody figure called 'Chance'." (The Human Evasion, Chapter 10)
My point about probabilities may not be clear. If individual events are genuinely uncaused, then there is equally no explanation for the distribution they exhibit collectively. Statistical reasoning in domains outside of fundamental physics can be justified by distributional hypotheses, e.g. that events are normally distributed, and that hypothesis may have a causal explanation arising in another domain. But when you get to fundamental physics there's no more scope for passing the buck. Justifications for fundamental probabilistic laws can be imagined: for example, one might assert that all possible worlds exist, that there is a natural measure on the set of those worlds, and that this is where the fundamental probabilities come from. (At that point, the next thing which needed explaining would be why all possible worlds exist, and not just some, or none.) Or, you could trace it back to cosmological initial conditions (such an approach might be feasible in Bohmian mechanics). But normally people don't even notice this problem.
Indeed, a well-defined probability distribution cries out "deterministic complex system!"; it doesn't really support indeterminism at all. We know how a die roll manages to obey a probability distribution, because it's designed specifically to have several stable states reachable through highly unstable bifurcation points, and the whole thing is made to be as symmetric as possible. But how could the universe manage to obey a probability distribution?
But how could the universe manage to obey a probability distribution?
How could it not? The Kolmogorov axioms are not very restrictive.
Obviously, the probability distribution over the state of the universe is not going to be as easy to characterize as the die's Multinomial(1/6,1/6,1/6,1/6,1/6,1/6).
Mitchell,
What I find particularly interesting reading his papers is his emphasis that space and time are features of the macroscopic world, and don't go "all the way down".
They seem absolute and real to us because of our evolutionary psychology and especially the "space and time" orientation of the visual maps in our brains. He contrasts his view with interpretations which postulate an infinitely sliced spatial manifold which is fundamentally real, but cannot be measured at the finest scales. I'm assuming by that he is referring to MWI.
I also find his arguments about particle identity intriguing. That all our notions of separate identity are predicated on spatial and other measurable properties. And again, that at the quantum level it is seen that those properties can no longer be distinguished absolutely.
Another thing he says that seems "right" to me is the emphasis on going back to our measurements. If something is measured, it is physically real, and if it is not measurable then it is simply not part of physical reality.
Some of this may be very orthodox quantum mechanics, or at least orthodox under certain interpretations. But I'm not that familiar with all of the literature. I just know that this is what stood out to me when reading PIQM.
In any event, this is not my domain of expertise. However I think it is extremely important for anyone who aspires to an understanding of reality to try and come to grips with quantum mechanics, so I give it my best shot.
interpretations which postulate an infinitely sliced spatial manifold which is fundamentally real
Strictly speaking, I suppose that is part of the interpretation, but it's a pretty mild part of the interpretation of QM, or at least QFT. Many people expect that this to stop being true in a unification with GR, but that's about physical law, not interpretation.
Wow...intellectual elitism turned sour and venomous. Your indignation is palpable and, frankly, quite off-putting. I'm not sure what the point of this post is....we should watch our syntax when we express awe?
Christopher,
Who else has the guts to talk to the audience like this? And hasn't your ratio of surprises gone down as you've learned more about the world?
The flagrant breaking of rule #12 in this post is one of the things that really makes it priceless. The other is just that it makes a valid point.
I agree with James Somers. Best post on this blog I've read so far. Best short writing that I've read in a while anywhere, Eliezer.
I see the point of the post, but it's too harsh. Naive physics (like folk etymology) is important, a facet of the human mind worth studying and paying attention to. It should be overcome, but it can't be replaced by some higher form of intuition. No one can force themselves (him/herself?) to intuit quantum physics. Naive physics can and should be superseded by real physics, but our original intuitions remain intact. The two forms of understanding can live side by side, each with its proper function. Reminded me of a recent piece by Chomsky. Excerpt:
Descartes had been able to formulate a relatively clear mind-body problem: it arose because he observed phenomena that, he plausibly argued, could not be accounted for in terms of automata. He was proven wrong, for reasons he could never have guessed: nothing can be accounted for within the mechanical philosophy, even the simplest terrestrial and planetary motion. Newton established, to his great dismay, thata purely materialistic or mechanistic physics . . . is impossible'' (Koyre 1957:210). Newton was bitterly criticized by leading scientists of his day for reverting to the mysticism from which we were at last to be liberated by the scientific revolution. He was condemned for reintroducingoccult qualities'' that are no different from the mysterioussympathies'' andantipathies'' of the neoscholastic Aristotelian physicists, which were much ridiculed. Newton agreed. He regarded his discoveries as an utterabsurdity,'' and for the rest of his life sought some way around them: he kept searching for acertain most subtle spirit which pervades and lies hid in all gross bodies,'' and would account for motion, interaction, electrical attraction and repulsion, properties of light, sensation, and the ways in whichmembers of animal bodies move at the command of the will'' - comparable mysteries, he felt. Similar efforts continued for centuries, but always in vain. The absurdity was real, and simply had to be accepted. In a sense it was overcome in this century, but only by introducing what Newton and his contemporaries would have regarded as even greater absurdities. We are left with theadmission into the body of science of incomprehensible and inexplicable `facts' imposed upon us by empiricism'' (Koyre 1957:272). Well before Priestley, David Hume wrote thatNewton seemed to draw to the veil from some of the mysteries of nature,'' buthe shewed at the same time the imperfections of the mechanical philosophy; and thereby restored [Nature's] ultimate secrets to that obscurity, in which they ever did and ever will remain'' (Hume [1778] 1983:542). The world is simply not comprehensible to human intelligence, at least in the ways that early modern science had hoped and expected. In his classic study of the history of materialism, Friedrich Lange observes that their expectations and goals were abandoned, and we graduallyaccustomed ourselves to the abstract notion of forces, or rather to a notion hovering in a mystic obscurity between abstraction and concrete comprehension.'' Lange describes this as aturning-point'' in the history of materialism that removes the surviving remnants of the doctrine far from those of the ``genuine Materialists'' of the seventeenth century, and deprives them of much significance (Lange 1925:308). The turning point also led gradually to a much weaker concept of intelligibility than the one that inspired the modern scientific revolution: intelligibility of theories, not of the world - a considerable difference, which may well bring into operation different faculties of mind, a topic some day for cognitive science, perhaps. - Linguistics and Brain Science, in A. Marantz, Y. Miyashita and W. O'Neil (eds.) Image, Language and Brain (MIT Press, 2000).
I see the point of the post, but it's too harsh. Naive physics (like folk etymology) is important, a feature of the human mind deserving of study. It is indeed the case that some beliefs arising from intuition should be overcome, but they can't be replaced by some higher form of intuition (no one can force himself to intuit quantum physics). Naive physics can and should be superseded by real physics, but our original intuitions remain intact. The two forms of understanding can live side by side, each with its proper function. See this recent piece by Chomsky, about (among other things) how we've been forced to believe in apparent "absurdities" since Newton.
This post makes a valuable point, but the point is weakened by too much hyperbole -- or rather by hyberbole that seems like a plausible non-hyperbolic statement that the writer might actually believe.
Whenever I hear someone describe quantum physics as "weird" - whenever I hear someone bewailing the mysterious effects of observation on the observed, or the bizarre existence of nonlocal correlations, or the incredible impossibility of knowing position and momentum at the same time - then I think to myself: This person will never understand physics no matter how many books they read.
I take the last clause ("This person will never understand physics no matter how many books they read") to mean "will never understand physics no matter what they do", since nobody seriously thinks you can really understand physics by just reading books, and there is no special relation between books and the other point being made, so I take that as evidence that 'books' is incidental and not intrinsic to the point.
If that is the case, then Eliezer would be committed to the idea that Einstein and Feynman, no matter how long they lived, would not be capable of understanding physics. Which is absurd! Yes, Einstein had intuitions that he found very hard to give up; yes, Feynman was limited to the theory of his day; but you still cannot mean that they would not have ever been able to understand physics, no matter how long they lived and what they did.
Surprise and weirdness are not qualities of the world but of model-making monkeys in the world. This is a valuable point. And thank you for it.
Don't confuse scientific models with truth or reality.
Quantum mechanics, relativity, Newtonian and Aristotilian dynamics are all models that, in certain situations, do a good job of predicting reality. Light is not a probabilistic model any more than it is a particle or a wave. It is light and every way we currently have of understanding is an inperfect model -- even if we don't understand just how it's imperfect yet. If the history of science has taught us anything, it's that.
I think the real issue here is not that it is unacceptable to perceive real phenomena as weird or bizarre, but that it is unacceptable to think that something real ought not be so (based on some model of reality) and continue without updating the model or understanding why the weirdness or bizarreness leaks in.
To pick on C.S. Lewis and the religious in particular, Lewis conflates many times the Laws of Nature with the 'Laws' of Morality. Laws of nature cannot be broken; those of morality most definitely can be and are. And perhaps as another facet of the naturalistic fallacy, those who would conflate laws of morality (loosely speaking--anything which 'ought' to be) with laws of nature, may come across an exception to the laws of nature (their model thereof), and not flinch because they are used to the laws of morality, or that-which-ought-to-be, being breached. Laws cannot be broken, and when they appear to be, one ought to enter into a state of cognitive panic, not passive acquiescence.
Sometimes people use words like "bizarre", "incredible", "unbelievable", "unexpected", "strange", "anomalous", or "weird" to mean "counterintuitive". Is that really all that different from noticing that you're confused but not yet deciding whether your model is at fault or your perception of the new information is? When you hear about something that seems like it's at odds with everything you've ever observed, saying that it's "unexpected" at the very least is truthful, isn't it? Whether or not you intend to investigate further and integrate it (or not) into your map is another matter.
Surprising facts seems like too useful a term to have it be defined out of existence.
In practice, the term seems to refer to facts that many people find to be surprising.
When the world turns out to be counter-intuitive you can be surprised by how sucky your intuition is ("An absolute time frame? Seriously?") rather than by the state of the world.
No, it makes sense to be surprised by the world - when that surprise is the sound of you updating to a theory that will be less surprised next time.
Pedantry codicil: information-theoretic surprise doesn't always indicate that your model needs to be updated. I wasn't expecting the lottery numbers to be what they were on Saturday.
“That’s weird” is a colloquialism for “I notice that I am confused.” Saying so is an important intermediate step towards understanding... or so I’ve heard. Once you understand, then weirdness is a non-issue -- you are no longer confused.
Yes, quantum mechanics is weird. It violates my intuitions, and the intuitions of (nearly?) every human. No, we can't rewrite our intuitions, and knowing quantum mechanics is weird is important because if it wasn't weird we might think we didn't have to shut up and integrate. I won't simply accept that reality is weird just because a scientific theory like quantum mechanics implies it is. Especially since there is such a good chance of quantum mechanics being wrong -- since it clashes with General Relativity. I can't say that the successor to quantum-GR will be any less weird, but I sure hope so.
While many things have become less weird for me as a familiarize myself with them, I don't see that happening with quantum mechanics*. It doesn't help any that not only is the math difficult, but can't actually be used directly for things larger than hydrogen without resorting to algorithmic computation of simplified approximations (and even hydrogen we couldn't do without pretending all the quarks were one particle). Contrast all that nasty math with things we have built in systems for -- addition is like linear distance, multiplication is like area or repeated addition -- quantum is always going to stay at "shut up and integrate" intuitiveness level for me.
*barring a future where implantable brain enhancements give me access to intuitive/subconscious integration, trigonometric functions, and exponentiation with complex numbers; maybe also Taylor series approximations and other algorithms as well.
It's interesting how we use the word "model" to mean two different, perhaps even opposite things. In this post we have "models" describing "reality", and in logic we have "theories" describing "models".
For some reason it felt like a big insight to me to realize that computers aren't identical to any particular piece of math, but rather are a model of that math, which can also be studied with other math. Any given piece of computer-related math might ignore some properties of computers that another formalism would bring to the forefront.
A weak theory could have both reality and mathematically simple structures as its models, from the point of view of an informal metatheory that allows talking about reality (and motivates the theory). A familiar structure (as a "model") can be used both to study a complicated formal system (natural numbers for PA with its other nonstandard models), and a vaguely defined reality (classical mechanics for the real world with its black holes and quantum mechanics).
Well, speaking your own language, the reality is supposedly not "weird", but nothing prevents a good map of reality to be still weird. There were a lot of moments in development of science when the current, working picture looked weird, until a deeper understanding came. Take, say the expression of quantum basics given by people who failed to "shut up" http://lesswrong.com/lw/q5/quantum_nonrealism/ or just how it was at sufficiently young state. It was the physics of that time (not a reality) and as we agree now it is weird.
So what does prevent our current picture to look poor and odd partially and hence unnatural and nonsense to the subsequent, more advanced generations of physicists, in the same way as I described above, the way the preceding picture seems to us? On the other hand, a genuine attempt to "think like reality" may stick you to, say, idea of wave function collapse, because it is (kind of) what you do observe.
PS, I agree that the reality itself carries a nice history of mysteries being made a reasonable and elegant piece of the physics and I share you feelings towards, say, calling relativity "irregular" when one simply didn't learn it properly. But when Feynmann said that "no one understood quantum mechanics", well, at least no one did understand decoherence at some point, thus, I guess, they had their right to call the apparent physics strange, which was a sign that certain qualitative improvement is to be done here...
"What many people refer to as common sense is nothing more than a collection of prejudices accumulated before the age of eighteen." -- Einstein (first quote I ever memorized, at age nine)
Actual physical reality is "out there" somewhere, and quantum mechanics is a map we use to find our way around parts of it. Often in physics two maps can be identical in their predictions, but differ substantially in the presentation. Hilbert-space quantum mechanics gives us a presentation of complex amplitudes in configuration space. Phase space quantum mechanics is mathematically equivalent, but the presentation is in terms of (possibly negative) probability fields in "real" x,y,z,px,py,pz,t phase space.
Quantum mechanics does indeed model some real measurable phenomena that are contrary to most humans intuitions (eg. Bell inequalities), but in addition to that presentations of quantum mechanics also prescribe other "weird" features that may not be strictly needed. That is, the territory is certainly confusing, but the map should cause as little confusion as possible. (The "least weird" possible map of the weird territory). Maps should strive for readability as well as accuracy (although clearly the latter should never be sacrificed for the former).
So, the issue I take with this post, is that if we take it seriously we have effectively decided that projects that aim to improve physical theories (or any theories) by making them more readable are pointless. I do no think they are.
Whenever I hear someone describe quantum physics as "weird" - whenever I hear someone bewailing the mysterious effects of observation on the observed, or the bizarre existence of nonlocal correlations, or the incredible impossibility of knowing position and momentum at the same time - then I think to myself: This person will never understand physics no matter how many books they read.
Reality has been around since long before you showed up. Don't go calling it nasty names like "bizarre" or "incredible". The universe was propagating complex amplitudes through configuration space for ten billion years before life ever emerged on Earth. Quantum physics is not "weird". You are weird. You have the absolutely bizarre idea that reality ought to consist of little billiard balls bopping around, when in fact reality is a perfectly normal cloud of complex amplitude in configuration space. This is your problem, not reality's, and you are the one who needs to change.
Human intuitions were produced by evolution and evolution is a hack. The same optimization process that built your retina backward and then routed the optic cable through your field of vision, also designed your visual system to process persistent objects bouncing around in 3 spatial dimensions because that's what it took to chase down tigers. But "tigers" are leaky surface generalizations - tigers came into existence gradually over evolutionary time, and they are not all absolutely similar to each other. When you go down to the fundamental level, the level on which the laws are stable, global, and exception-free, there aren't any tigers. In fact there aren't any persistent objects bouncing around in 3 spatial dimensions. Deal with it.
Calling reality "weird" keeps you inside a viewpoint already proven erroneous. Probability theory tells us that surprise is the measure of a poor hypothesis; if a model is consistently stupid - consistently hits on events the model assigns tiny probabilities - then it's time to discard that model. A good model makes reality look normal, not weird; a good model assigns high probability to that which is actually the case. Intuition is only a model by another name: poor intuitions are shocked by reality, good intuitions make reality feel natural. You want to reshape your intuitions so that the universe looks normal. You want to think like reality.
This end state cannot be forced. It is pointless to pretend that quantum physics feels natural to you when in fact it feels strange. This is merely denying your confusion, not becoming less confused. But it will also hinder you to keep thinking How bizarre! Spending emotional energy on incredulity wastes time you could be using to update. It repeatedly throws you back into the frame of the old, wrong viewpoint. It feeds your sense of righteous indignation at reality daring to contradict you.
The principle extends beyond physics. Have you ever caught yourself saying something like, "I just don't understand how a PhD physicist can believe in astrology?" Well, if you literally don't understand, this indicates a problem with your model of human psychology. Perhaps you are indignant - you wish to express strong moral disapproval. But if you literally don't understand, then your indignation is stopping you from coming to terms with reality. It shouldn't be hard to imagine how a PhD physicist ends up believing in astrology. People compartmentalize, enough said.
I now try to avoid using the English idiom "I just don't understand how..." to express indignation. If I genuinely don't understand how, then my model is being surprised by the facts, and I should discard it and find a better model.
Surprise exists in the map, not in the territory. There are no surprising facts, only models that are surprised by facts. Likewise for facts called such nasty names as "bizarre", "incredible", "unbelievable", "unexpected", "strange", "anomalous", or "weird". When you find yourself tempted by such labels, it may be wise to check if the alleged fact is really factual. But if the fact checks out, then the problem isn't the fact, it's you.