CFP: Least Favorite Misconceptions

I should probably stick to doing only one audience-participation thing at a time (there are more Top Eleven posts on the way), but it’s a busy week for me at work, and I’m not really going to have time to post a lot of long articles, so there will be a few “talk among yourselves” entries over the next few days, in hopes of generating some interesting content without a whole lot of typing on my part.

Back when I posted my request for “Great Experiments” in other sciences, Kate remarked that another good topic would be something along the lines of “Most annoying misconception about your field.” Given the number of biologists in blogdom, “Most annoying misconception that isn’t ‘Evolution is only a theory’” might be better, but however you choose to phrase it, I’d like to hear what people think.

I was reminded of this today in class, as I was lecturing about the Heisenberg Uncertainty Principle, which is probably the source of my personal least favorite misconception. The Heisenberg Uncertainty Principle, as any fule kno, is prominently displayed in the banner graphic for this blog, and also discussed in one of my very first blog posts, back on Steelypips. In its best-known form, it states that the product of the uncertainty in the position of a particle and the uncertainty in the momentum of the same particle is greater than or equal to h-bar divided by two. Or, put more simply, that it is impossble to know both the position and the momentum of an object to arbitrary precision.

It’s a deceptively simple equation, but a really difficult idea to grasp, and it’s probably been mangled and misused more than any other concept in physics. The most flagrant abuse I think I’ve seen was a SF novel that use uncertainty as the basis for a star drive– by defining the position really well, they magically attained really high velocity.

Of course, that’s too stupid a misconception to really get worked up over. The more annoying misuse is a subtler one, that re-casts the Uncertainty Principle as a statement that measurement necessarily changes the state of a system. That’s not a bad thing to keep in mind in and of itself, but it’s not what the Uncertainty Principle is about.

The problem with that take on the Uncertainty Principle is that it implictly assumes a sort of local realism. That is, it allows you to imagine that the object in question actually has a perfectly well defined position, and a perfectly well defined momentum, and your inability to measure both is simply a matter of screwing up one when you try to measure the other. An attempt to measure the position necessarily introduces some uncertainty in the momentum that wasn’t there before, and so on.

(There’s a standard textbook illustration that develops the Uncertainty Principle along these lines. I’ve talked about it in past versions of this class, but I dropped it from my notes this year, because I think it creates more confusion than anything else.)

The actual quantum situation is much stranger than that. In reality, neither the position nor the momentum are perfectly defined at all. There are no “real” values that you’re simply unable to measure– what Heinsenberg was getting at is that given the quantum nature of the world, the very idea of a perfectly defined position or velocity is physically unreasonable. Asking what the “real” position and velocity are is not a sensible question. At the most fundamental level, it’s simply impossible to perfectly define those quantities.

It’s a subtle point, but it’s one that gets on my nerves, largely because it’s usually deployed as justification for some sort of fuzzy relativism. It’s one of the strangest and coolest points of quantum theory, and I hate seeing it used in an attempt to claim some sort of hard-science basis for an abstract point of literary theory.

Anyway, that’s my pet peeve about popular conceptions of modern physics. I’d love to hear what gets under the skin of people in other fields.

Comments

  1. #1 Corkscrew
    January 30, 2006

    I don’t know about the one that annoys me most, but most horrific I’ve encountered is probably “Einstein’s theory of Relativity == ‘everything is relative’”. Or, speaking as a maths type, “oh yeah, degree-level maths would have been easy for me, I have a great head for sums”. Groan.

  2. #2 razib
    January 30, 2006

    chad, i assumed you’d pick the uncertainy principle one. but, speaking as a bio person, the most annoying physics misconception is that the second law of thermodynamics means evolution can’t happen!

  3. #3 Aaron Bergman
    January 30, 2006

    Since you’ve already grabbed mine, I’ll go with one that I think is overbelieved by physicists: that the second law of thermodynamics is somehow more fundamental than everything else.

    Or, from the old Usenet days: that special relativity and FTL (necessarily) imply time travel.

  4. #4 Anonymous
    January 30, 2006

    How about Godel’s Incompleteness Theorem? Nothing can ever be proved! You can never really know anything!

  5. #5 T. Bruce McNeely
    January 30, 2006

    In my field (medicine) the worst among many is: (altmed treatment de jour) strengthens the immune system. Well, how the fzzk do you know???? I have yet to see any mention of studies of how AMTDJ does this or how it’s measured. I suspect the evidence consists of “Well, it just does!” I wouldn’t accept that from my 7 year old daughter.

  6. #6 Adam Ierymenko
    January 30, 2006

    My most annoying misconception is “evolution is random” or “evolution is just a chance process.” Evolution is a highly non-random process.

    That I have two legs of equal length, or that my cat can wake up from deep sleep more quickly than me, or that trees have leaves that face up… these things are not merely a result of chance. The universe has a nature; some things work and some things don’t. Evolution discovers things that work. It is not arbitrary.

    Several of the replies to this seem to intersect with a blog entry that I wrote recently on a site that I write for:

    http://www.greythumb.org/blog/index.php?/archives/71-Popular-limitations.html

    The way Godel’s theorem is misinterpreted annoys me too.

  7. #7 Tim M.
    January 30, 2006

    In Meteorology: toilets swirl the opposite direction in the southern hemisphere because of the Coriolis force.

  8. #8 Matt McIrvin
    January 30, 2006

    Wow, Aaron’s taste in misconceptions is far more refined than everyone else’s.

  9. #9 coturnix
    January 30, 2006

    In my narrow field: “Adolescents stay up late and cannot wake up in the morning because they are lazy and/or rebellious and giving them some discipline can fix the problem.”

  10. #10 Aaron Bergman
    January 31, 2006

    Well, Chad sto^H^H^H used my usual one…. (And I keep having horrible flashbacks to sci.physics.relativity).

  11. #11 Arcane Gazebo
    January 31, 2006

    I’ve met a number of people who know some CS theory but not very much quantum information, and seem to believe that Shor’s factorization algorithm for quantum computers implies P=NP, or that a working quantum computer would settle the question of whether P=NP, or similar things along these lines.

  12. #12 Matt McIrvin
    January 31, 2006

    Actually, Aaron, the reason I said that may have been a misreading of what you were saying.

    Are you complaining about the people who say that SR + FTL necessarily implies the possibility of backwards time travel, or the people who say that SR + FTL always results in backwards time travel? Because I can think of reasons to deny the former but to my mind they are pretty arcane, whereas the latter is just blazingly wrong and I’ve seen it propounded.

    I agree about the second law of thermodynamics, because aside from the statistics it’s basically a statement about cosmological boundary conditions.

  13. #13 Ben V-L
    January 31, 2006

    As a fan of the 2nd law and someone pretty familiar with its “inner workings,” I am surprised by Aaron and Matt’s comments. I haven’t encountered physicists who think it is more “fundamental” than anything else – that would be a pretty hard view to defend.

    By the way, the 2nd law isn’t really a law, because we can derive it from ergodicity. The “law” should really be updated to something like “ergodicity provides accurate averages in thermal equilibrium”. This is something my colleagues don’t agree with but admit that it’s right.

  14. #14 Alejandro Rivero
    January 31, 2006

    Obviously the greatest scientific misconception is the popular and even erudite views of Evolution Theory. Nobody stops to thing about the processes of species diferentiation and the processes of extintion, which are the main drivers of the theory. And almost nobody stops to buy the penguin edition of Darwin even if it available in most airport bookshops.

  15. #15 v.botkin
    January 31, 2006

    How about “quantum mechanics is fundamentally nondeterministic, because of wave function collapse”?

  16. #16 Derek Lowe
    January 31, 2006

    An annoying misconception about my field of science is that organic chemistry is just a pile of reactions to be memorized, sort of like classical zoology but with test tubes.

    There are plenty to choose from that relate to my pharma-industry job, though. How about “Every disease has a natural herbal treatment with no side effects, unlike those toxic drugs” or “The drug companies already have cures for (nasty disease), but they’re not selling them to us.” Lots of folks manage to hold both these opinions at the same time.

  17. #17 Mark Paris
    January 31, 2006

    “Ballistic missile defense will work.” Oh, wait, that’s not science. Never mind.

  18. #18 Moshe
    January 31, 2006

    I like Chad’s choice, but it is more subtle and far less annoying than the mantra “quantum mechanics is non-local”, which even has a whole genre of literature around it.

  19. #19 Dave S.
    January 31, 2006

    How about, “Big Bang theory says the universe came from nothing”.

    That’s a classic.

  20. #20 JK
    January 31, 2006

    Oh dear. Either my head is full of misconceptions or I have a peculiar view of what matters.

    On uncertainty:

    I’m not convinced by Chad.

    I argree that the idea of the uncertainty principle as a limit on measurement is widespread, and that this misunderstands the deeper message of QM, namely, that position and momentum are not simultaneously defined. But, despite it all, I do think there is still something to be said, in a certain sense, for worrying about “real values”.

    Physicists find it easy not to worry because almost always work is done with the wavefuntion. After a while it becomes very easy to believe that the wavefunction is all there is. But it’s important to remember that measurement is a real process, too.

    In my opionion talking about decoherence or waffle about “many worlds” just brushes the real problem of wavefunction collapse under the carpet. The best we know, light and electrons are point particles. It is point particles that carry momentum, according to QM.

    I don’t think these are easy questions. If you are teaching undergraduates then, sure, getting them to focus on what the wavefunction is telling you is what matters. It seems hard to find examples where the intepretation of QM isn’t a philosophical debate without practical interest. But then again, the existence of the classical world is a pretty significant phenomenological fact.

    v.botkin:

    Are you saying that QM is fundamentally deterministic, or that it is fundamentally non-deterministic but not because of wave function collapse?

    The second law:

    I think the second law is deeper than is being acknowledged here. It has survived the coming of the quantum and of relativity. From what I can see as a non-expert it has given us our most reliable results about quantum gravity (black hole thermodynamics) whatever the complete theory turns out to be.

    The second law is also fundamental in the sense that it touches every area of science from physics through to chemistry through to biology.

    The complaints that it is “merely” statistical or based on a boundary condition are interesting. But it seems to me that this again points to its profound character. To compare it to something of comparable importance we could take the idea of symmetry which could also be dismissed as a mathematical inevitability or a consequence of boundary conditions.

  21. #21 a cornellian
    January 31, 2006

    “The best we know, light and electrons are point particles.”
    I would take issue on that for a couple reasons. The point particle stuff initially (i belive) came from assumptions to make the math easier and because it is the logical limit of “really small”.

    And they both form diffraction patterns (well, so does just about anything else with the proper set up). This only makes sense from a wave interpertation.

  22. #22 Jamie Bowden
    January 31, 2006

    Contrary to popular belief, computers do not run on magic, even a twit like YOU (the generic thrid person you, not you personally of course, Dr. ‘Can) is capable of learning the basics. Really. You do not need 20 years experience to know how to move a file from directory to another.

  23. #23 John Novak
    January 31, 2006

    I can’t really think of anything engineering-related that gets misinterpretted at that deep a scale. (Although engineers misinterpretting physics and biology annoys the crap out of me.) Maybe the idea that Moore’s Law is a law of nature, but I’m too busy enjoying the benefits of it.

    From computer science, though, Goedel’s Incompleteness Theorem does it every time. It’s subtle. It’s powerful. And it’s just rarified enough that, like relativity or quantum mechanics, it gets latched onto by dime store deontologists to “prove” whatever they want to prove.

    We hates them, hates them all.

    Someone else mentioned the combination of quantum computing and NP-completeness. That would qualify, but that level of confusion requires enough knowledge that it’s not really common, ’round here.

  24. #24 Aaron Bergman
    January 31, 2006

    Matt — I was talking about the people who believe that any system that allows FTL must also allow time travel.

    JK — Regardless of how one deals with the measurement problem (and, modulo that, QM is deterministic), the idea that there are hidden variables that we a prevented from seeing due to measurement has pretty good experimental evidence against it.

    Without getting into too much detail, I’ve always been deeply suspicious of the application of the second law to strongly gravitating systems, in particular, cosmological ones. I’ve always found it weird that physicists who regularly suggest the violation of pretty much every other physical ‘law’ they can think of quail at the suggestion of violating the second law.

  25. #25 Moshe
    January 31, 2006

    To elaborate a bit: even for classical system you can set correlations between them, then separate them for the special effects value… Then, lo and behold, their subsequent behavior is correlated no matter how far apart they are. Yes, quantum entanglement is more than just classical correlation, but that has nothing to do with locality, which just confuses the issue. You don’t even need to separate the systems to enjoy the weirdness of entanglement.

    But, there is far more interesting ways in which QM is necessarily local. It seems that, with very few exceptions, consistency with QM requires one to have locality, that is to have a local Hamiltonian (this is one of the cornerstones of quantum field theory). This fact gets obscured by all the talk about quantum non-locality.

    In fact the only conceivable way to set up the aforementioned correlations is to bring your qubits to the lab and act on them with some local Hamiltonian.

  26. #26 Jeff
    January 31, 2006

    Maybe not as important as the rest of the misconceptions already listed, but from aerospace engineering, that a wing derives lift because the top surface is longer than the bottom surface. Most of the diagrams showing this don’t show any downwash, either, ignoring Newton’s 2nd and 3rd laws.

  27. #27 JK
    January 31, 2006

    Aaron,

    I’m not suggesting that there are hidden variables. I’m claiming that there are hard problems with the interpretation of QM. I think relegating the randomness introduced by measurement to a paranthesis and then claiming determinism is an example of what I meant by brushing the problem under the carpet. It works fine for day to day physics but it’s not so helpful if you want to step back and ask what the equations mean (of course some people have respectable philosophical reasons to say they don’t want to).

    On the second law, you’re right to say there are subtleties with gravitation and cosmology. I would need to know more to offer a properly informed opinion, but I certainly wouldn’t rule out the need for modification a priori. However, I do think the idea that the second law is amongst the most significant laws of physics is highly defensible.

  28. #28 Ben V-L
    January 31, 2006

    JK, Aaron said “fundamental”, not “significant”. For me, there is a HUGE difference.

  29. #29 wheatdogg
    January 31, 2006

    I teach astronomy from time to time. Among my high school students, the biggest common misconception is that we have seasons because the earth is closer to the sun during the summer and farther during the winter. They are also a little hazy on how the moon has phases, and the whole nearside/farside of the moon thing. Drives me nuts! It seems simple enough that they should have learned all this by 6th grade.

  30. #30 Kate Nepveu
    January 31, 2006

    wheatdogg: in mild defense of your students, it took large amounts of time of my high school science teacher waving around little Earths, moons, and suns for me to understand the phases of the moon–I’m just not a 3-D thinker. (And I appear to have misremembered a good deal about the seasons, based on a conversation I had with Chad recently, the details of which elude me now and I’ll thank him not to bring them up if he remembers better, because it was embarassing.)

    As for the topic, I dunno–that admission to the bar requires the surgical removal of your ethics? That lawyers make tons of money? Somehow I think I’m not the target audience.

  31. #31 Chad Orzel
    January 31, 2006

    JK: I argree that the idea of the uncertainty principle as a limit on measurement is widespread, and that this misunderstands the deeper message of QM, namely, that position and momentum are not simultaneously defined. But, despite it all, I do think there is still something to be said, in a certain sense, for worrying about “real values”.

    I wasn’t trying to dismiss the problem of measurement in quantum mechanics when I talked about “real values”– I was thinking more of the hidden-variable sort of idea, where the system has a definite but unknown state. Attempts to reconstruct QM with local hidden variables have been shown not to work.

    The problem of quantum measurement is a fascinating one, and something I wish I understood better than I do.

    Moshe: To elaborate a bit: even for classical system you can set correlations between them, then separate them for the special effects value… Then, lo and behold, their subsequent behavior is correlated no matter how far apart they are. Yes, quantum entanglement is more than just classical correlation, but that has nothing to do with locality, which just confuses the issue. You don’t even need to separate the systems to enjoy the weirdness of entanglement.

    Of course, the important difference is that the classical correlated system will always have a definite state, while the state of the quantum system is fundamentally indeterminate. But you knew that.

    I think part of the problem is that “local” is used to mean a couple of similar but slightly different things in different contexts. “Local” in the sense of “local realism” and “local” in the sense of “local Hamiltonian” aren’t quite the same thing, and people get them confused.

    Kate: (And I appear to have misremembered a good deal about the seasons, based on a conversation I had with Chad recently, the details of which elude me now and I’ll thank him not to bring them up if he remembers better, because it was embarassing.)

    Actually, I was wrong about some of what I said, too, so we’ll call it even.

  32. #32 Moshe
    January 31, 2006

    Thanks Chad, but let me insist: locality has nothing to do with it, you can set up two entangled qubits (say spin systems) and discuss all the paradoxes you get from assuming naive classical realism without ever talking about their spatial relations. When you do worry about the spatial relations between objects you are forced to introduce field theory, which only makes sense if it is local.

    Ultimately this is about semantics, but sometimes choosing the most confusing way to discuss something results, well, in a lot of confusion…

  33. #33 Chad Orzel
    January 31, 2006

    Thanks Chad, but let me insist: locality has nothing to do with it, you can set up two entangled qubits (say spin systems) and discuss all the paradoxes you get from assuming naive classical realism without ever talking about their spatial relations.

    Absolutely.
    I think we’re in violent agreement on this point. The key difference between quantum and classical has to do with the indeterminacy of the states, not the fact that they’re still correlated when spatially separated.

    As for the difference between local and non-local, I suspect that if I understood Bohm’s theory of QM, it might be relevant. Sadly, I don’t.

  34. #34 Anonymous
    January 31, 2006

    Thanks, did not mean to bring the word “violent” to mind, it is hard to control the tone in such comments… Context was common misconceptions, and let me note I was particualrly civilized in not bring up any in my actual field of research…(now if I could only learn how to insert those smilies…).

    Anyhow, fun game, thanks.

  35. #35 Moshe
    January 31, 2006

    Last comment was me, as is clear from the context, sorry.

  36. #36 Mark Paris
    January 31, 2006

    I didn’t see “evolution can’t explain how life began on Earth,” but maybe I missed it.
    Biology isn’t my field, but even I can read the title of the seminal work, which pretty clearly mentions “origin of species” rather than “origin of life.”

  37. #37 Roman Werpachowski
    January 31, 2006

    Mathematically, quantum mechanics IS non-local. If you take a look at the free propagator for the Schroedinger equation, you will notice that for t>0, K(x,x’,t) > 0 for any |x-x’| — even as far away as on Alpha Centauri. This totally different than in electrodynamics, where in 3 dimensions you have the lightcone carrying all the information about the initial conditions.

  38. #38 Matt McIrvin
    January 31, 2006

    Oh! Oh! I know one!

    “Global warming is the same thing as destruction of the ozone layer.”

    (Which brings up another one: “Mount Pinatubo destroyed more ozone than all of human civilization”, promulgated by Rush Limbaugh on the basis of claims that first appeared in a Lyndon LaRouche magazine. But I don’t know if this discussion encompasses Least Favorite Politically Motivated Nonsense.)

    Jeff’s one about airplane wings really irritates me too.

  39. #39 Moshe
    January 31, 2006

    Roman, I think what you have in mind is the distinction between relativistic and non-relativistic theories, not quantum vs. classical. So for example both in classical and quantum electrodynamics disturbances will move inside the future lightcone. On the other hand if you use non-relativistic classical or quantum mechanics you will not know the speed of light is finite.

    Concretely about your example, I assume you mean the Schrodinger equation for free massive particle. In that case what you have is some version of the diffusion equation. So it is true that according to this equation if you turn on the heater at your place the temperature at Alpha Cantauri increases instantly a little bit. Do you belive that to be the case? I don’t, rather I would say that the heat equation does not apply all the way there. Similarly with the non-relativitic Schrodinger equation, for large enuogh velocities it does not describe the physics and has to be replaced with a relativitic Schrodinger equation (aka QFT).

  40. #40 Matt McIrvin
    January 31, 2006

    Though the extent to which “quantum mechanics is nonlocal” is something that people who actually understand it argue about endlessly, there’s a popular variant that irks me and is just plain wrong: namely, the misunderstanding of Bell’s inequality as an instantaneous communication device.

    It’s now almost universally believed by non-physicists who are au courant with hip scientific ideas that you can get two particles into some sort of correlated state in which you can separate them by a million miles and do something to one of them (“reversing the spin” is often cited), whereupon the other will register a measurable change instantaneously, so that you can use this to send faster-than-light messages.

    On one level I don’t entirely blame people for believing this because the true statement that it’s a distortion of (the nature of nonlocal spin correlations and particularly Bell’s Inequality) is hard to explain, but it still bothers me that the distorted version is so popular. It seems to have been spread by some TV science documentaries in the 1990s. It’s become a standard trope in science fiction just in the past few years.

  41. #41 Matt McIrvin
    January 31, 2006

    Oh, here’s another one: “Special relativity cannot properly describe accelerated motion.” Usually brought up when discussions of the twin paradox go off the rails.

  42. #42 Roman Werpachowski
    January 31, 2006

    Concretely about your example, I assume you mean the Schrodinger equation for free massive particle. In that case what you have is some version of the diffusion equation. So it is true that according to this equation if you turn on the heater at your place the temperature at Alpha Cantauri increases instantly a little bit. Do you belive that to be the case? I don’t, rather I would say that the heat equation does not apply all the way there. Similarly with the non-relativitic Schrodinger equation, for large enuogh velocities it does not describe the physics and has to be replaced with a relativitic Schrodinger equation (aka QFT).

    Sure. But this non-relativistic quantum mechanics is non-local in the way I described in the previous post, nevertheless. I know it’s unphysical since such tiny changes of the wavefunction are undetectable. But it’s there.

    How about another misconception (don’t know if anyone mentioned it): the myth of the “thermal death of the Universe”?

  43. #43 Matt McIrvin
    January 31, 2006

    They’re all coming back to me now (thanks in part to Google Groups). Here’s one I’ve heard full professors say:

    “Spin is not really angular momentum; it’s just a mathematical property of particles that is metaphorically called that because it bears a purely algebraic similarity to angular momentum.”

  44. #44 Chad Orzel
    January 31, 2006

    They’re all coming back to me now (thanks in part to Google Groups). Here’s one I’ve heard full professors say:

    “Spin is not really angular momentum; it’s just a mathematical property of particles that is metaphorically called that because it bears a purely algebraic similarity to angular momentum.”

    To be fair, that’s mostly a matter of going overboard in an attempt to head off a different misconception, namely that fermions are literally spinning.

    I remember doing a calculation for my intro quantum class showing that the rotation rate needed for a spinning ball the size and mass of a proton to have the right angular momentum was physically unreasonable. I’ll have to reproduce that to assign this term…

  45. #45 Matt McIrvin
    January 31, 2006

    True, though as I’ve probably posted here before, there is a field-theoretic analysis of spin angular momentum as a circulating momentum density field; it’s just that it circulates around the wave function rather than around the particle.

    (Belinfante figured this out for the Dirac electron long ago and H. C. Ohanian publicized it in a famous American Journal of Physics paper. A few years ago I had a paper all written up about how you could even do it in nonrelativistic QM using a trick of Feynman’s, but I think somebody scooped me.)

  46. #46 perpetualstudent
    January 31, 2006

    From Engineering. Infinite zoom on grainy security videos. Usually done to find the reflection of the bad guy on a door knob. Worst offenders include Law and Order, Alias, and CSI (Although their sins tend to be less than most)

  47. #47 Loganayagam R
    February 1, 2006

    Roman Werpachowski wrote :

    Sure. But this non-relativistic quantum mechanics is non-local in the way I described in the previous post, nevertheless. I know it’s unphysical since such tiny changes of the wavefunction are undetectable. But it’s there.

    What Moshe was trying to say is that reality is actually relativistic. So, the “changes”you are talking about are really not “there”. They are an artifact of non-relativistic approximation.

    In relativistic QFT, all field commutators vanish outside the lightcone- the statement of locality.

  48. #48 Loganayagam R
    February 1, 2006

    Matt McIrvin wrote

    Here’s one I’ve heard full professors say:”Spin is not really angular momentum;..”

    and

    there is a field-theoretic analysis of spin angular momentum as a circulating momentum density field; it’s just that it circulates around the wave function rather than around the particle.

    Yeah, this among my favourite misconceptions too. True, spin does not correspond to anything “spinning”. But, hey in classical electromagnetism if you look at angular momentum carried by electromagnetic fields- E,B fields are not “spinning” there either . So already in classical mechanics, you have the concept of an angular momentum which is there even though objects may not be literally “spinning”. In fact, classical EM makes it clear that you can have non-zero momentum with static E,B fields !

  49. #49 Roman Werpachowski
    February 1, 2006

    So, the “changes”you are talking about are really not “there”. They are an artifact of non-relativistic approximation.

    Well, yes. I ‘meant “there” as “in non-relativistic QM”. I know it is an approximation, but works pretty well ;-)

    BTW, here’s something which has always puzzled me: what’s the difference in how measurement is described between relativistic and non-relativistic QM?

  50. #50 Thomas Larsson
    February 1, 2006

    “Gauge symmetries represent a redundancy in our description of the theory”, stated as late as today by Seiberg in hep-th/0601234.

    The catch is that after quantization, a classical gauge symmetry can become a conventional, non-gauge symmetry which acts non-trivially on the physical Hilbert space, due to gauge anomalies. This does not necessarily render the theory inconsistent. Main example: conformal symmetry of the free subcritical string.

  51. #51 Evil Monkey
    February 1, 2006
  52. #52 Roman Werpachowski
    February 1, 2006

    The catch is that after quantization, a classical gauge symmetry can become a conventional, non-gauge symmetry which acts non-trivially on the physical Hilbert space, due to gauge anomalies.

    Can’t it be removed by quantizing gauge-independent classical quantities?

  53. #53 Mark Paris
    February 1, 2006

    Chad, my field isn’t physics (although the degree says something like “atmospheric physics”), so I look at some of these misconceptions somewhat as an educated layman. It seems to me that some of the misconceptions that aren’t really abstruse, that is, misconceptions that an educated layman might have, are at least partly a product of language. I think it’s mainly because we use everyday terms to describe things that aren’t everyday things and don’t really behave in intuitive ways. Photons come to mind. Much is made of the fact that at times they behave as particles and at times as waves, so we say, “Gee, what are they, particles or waves? Or both?” In fact, I say they are neither; they are unlike anything we experience in our normal lives, but in order to describe them we have to use language that was developed to describe things we can experience in our normal lives. This is a sort of analogy, and it can lead people to speak of the thing as if it were the analogue.

  54. #54 Thomas Larsson
    February 1, 2006

    Roman:
    A gauge anomaly means that a classical gauge variable becomes physical after quantization. The classical gauge invariant variables are thus too few in this situation.

    Based on experience with the standard model, people usually dismiss all gauge anomalies as inconsistent. However, there are counterexamples. Classically, the free string has a conformal gauge symmetry in any dimension, but after quantization the symmetry is gauge only if D = 26. The unreduced theory is nevertheless consistent if D &lt 26, but not if D &gt 26. This is explicitly stated in GSW, section 2.4:

    “Classical free string theory can be consistently formulated for any spacetime dimension, but quantization with a ghost-free spectrum requires D &lt= 26.”

    Thus, the no-ghost theorem only rules out D &gt 26, but not D &lt 26.

    Seiberg knows about this, of course. The problem is that his slogan gives the impression that all classical gauge symmetries remain redundant or become inconsistent after quantization, which is simply not true.

  55. #55 Roman Werpachowski
    February 1, 2006

    Aha. What is GSW?

  56. #56 Roman Werpachowski
    February 1, 2006

    Roman, it is all about semantics so it is hard to make a tight argument, my point was that your argument implies non-relativitic QM is non-local in a very wide sense, so wide that any non-relativitic classical mechanics is non-local as well (for example any diffusion process as I pointed out). The usual arguments for quantum non-locality are different, I think they are misguided but at least they are specific to quantum mechanics.
    Classical mechanics of point particles is local — they interact upon touch.

  57. #57 Aaron Bergman
    February 1, 2006

    Without getting too much into it, let’s just say that Thomas’s views are somewhat heterodox on this subject.

    But I do have a good misconception: If we can’t predict the weather two weeks from now, how can we possibly predict the climate?

  58. #58 v.botkin
    February 1, 2006

    JK, Aaron pretty much answered already, but what I was saying was that QM is deterministic. It really irritates me that this is nearly always taught incorrectly. I didn’t really understand quantum mechanics until I started learning quantum field theory. In fact, as Moshe points out, a lot of the things that bother people about QM are just obviously not issues in QFT, because QFT is obviously local and causal and all that good stuff.

    But it annoys me to no end that, despite the complete lack of experimental evidence for it, otherwise sane and intelligent people talk about this spooky mysterious nonunitary process of “wave function collapse.” Might it happen? Well, sure, but shouldn’t we look for some evidence of it before we jump to such a totally crazy conclusion?

    It seems to me that people make this leap because the real problem, properly understood, is just incredibly difficult. The real problem is the phenomenological fact you point out, that the world appears classical. Some people wish this away by talking about decoherence, but that’s not really a complete answer to the question. I don’t have an answer, but I wish everyone would formulate it in a proper way and be honest about what we know instead of insisting on some magic which is both experimentally unchecked and theoretically nonsensical.

  59. #59 Mark Paris
    February 1, 2006

    Aaron, predicting weather vs climate is like dumping a large box of balls down a set of stairs and then trying to predict what one ball will do vs what most of the balls will do. But, you assume both that we cannot predict the weather two weeks in advance and that we can predict climate.

  60. #60 Thomas Larsson
    February 2, 2006

    Without getting too much into it, let’s just say that Thomas’s views are somewhat heterodox on this subject.

    I guess this means that you cannot find a good counterargument :-)

  61. #61 gengar
    February 2, 2006

    Once this got me thinking, I got a bit carried away thinking of popular geological misconceptions, so I posted them here.

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