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Science

An Improvement Upon Heisenberg's Uncertainty Theorem 58

Mick Mick writes "This New Scientist article claims that Heisenberg's uncertainty theorem has been improved upon by replacing an inequality with an equation. It also says that the Schrödinger equation has been derived from this new equation. Google found the paper here."
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An Improvement Upon Heisenberg's Uncertainty Theorem

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  • by Jeremiah Cornelius ( 137 ) on Saturday May 04, 2002 @09:08PM (#3464108) Homepage Journal
    We are more sure than ever of our lack of certainty!
  • You cannot measure both the position and the momentum of any particle with perfect accuracy.

    This describes the management at my last job, quite well. They had know idea of where they where going, but it went really fast.

    Most employees jumped ship, before it was too late.
  • 5-7-5 (Score:4, Funny)

    by aozilla ( 133143 ) on Saturday May 04, 2002 @09:47PM (#3464169) Homepage
    Heisenberg was right
    That God really does play dice
    With the universe
  • I always keep seeing that we measure position and calculate momentum. Anoyone with any links to the contrary?
  • Improving on uncertainty is akin to saying The original formula is back and it's better than ever.

    Did Breck Shampoo provide the funding for this?

  • I thought the heisenberg equation gave uncertainty as err(momentum * position) > CONSTANT, where the constant was some defined number (which I don't know offhand). So does this define the CONSTANT more accurately, or did Heisenberg just say the constant exists, and now we have a figure? The article was a little light on details...
    • I thought the heisenberg equation gave uncertainty as err(momentum * position) > CONSTANT, where the constant was some defined number (which I don't know offhand). So does this define the CONSTANT more accurately, or did Heisenberg just say the constant exists, and now we have a figure?

      Heisenberg said err(momentum * position) >= CONSTANT. This says err(momentum * position)=(some equation).

      • I always wondered about something. Bose-Einstein condensates are a direct consequence of the Heisenberg principal, because the momentum of an atom becomes so close to zero at those rediculously low temperatures, that the error of the position must increase, and so a bunch of atoms "share" the same space. What is the limit of this? At absolute zero, wouldn't the position error be infinite, and thus the atom could be anywhere in the universe? That would be another singularity, like a black hole, right.
        • I doubt that the equation has some value over temperature (or momentum, KE, whatever). This really isn't saying that there is error in its own position or momentum in real life, but just in how we calculate it.

          Our mathematical abilities are far... far from those necessary to fully understand the universe.
        • Re:Help me... (Score:3, Informative)

          by bcrowell ( 177657 )
          At absolute zero, both the error in position and the error in momentum have finite values. Sounds like you're thinking of temperature as a measure of energy per particle (or degree of freedom). That's classically correct, but at very low temperatures it's not. The energy per particle isn't zero at T=0.
      • Re:Help me... (Score:3, Informative)

        by bcrowell ( 177657 )
        Heisenberg said err(momentum * position) >= CONSTANT
        No, he said err(momentum)*err(position)>=constant.
        • No, he said err(momentum)*err(position)>=constant.

          Yes, yes, you're right. (Does "momentum * position" even make sense?)

        • No, if it were >= a constant, it would mean uncertainty could be infinite.

          The principal states:
          err(momentum) * err(position) <= Plank's Constant / 4 * PI.

          Plank's Constant, called h is often found divided by 2 * PI and the result is called h bar written as an h with a line through the top so the principal is usually written as:

          err(momentum) * err(position) <= h-bar / 2
  • sounds like vaporware to me. I mean, the article didn't even include the equation itself! :)
  • I'm wondering where I could acquire the knowledge necessary to *fully* comprehend stuff like particle physics, quantum phenomena, etc.
    I'd rather not school for it, since I don't trust the quality of even the best Uni education.
    I'd rather read. Anyone got a good 'get up to speed' reading list?
    • Anyone got a good 'get up to speed' reading list?

      As far as speed reading goes, I would recommend you take a look at http://www.the-reading-edge.com/ [the-reading-edge.com]. I went through their program and can know scan /. at amazing speed. For example, I read this whole page in 2 seconds, with perfect comprehension.

    • by Jerf ( 17166 ) on Sunday May 05, 2002 @01:50AM (#3464671) Journal
      You want to fully comprehend this? Unless you are a highly motivated mathematical mega-genius (and you can't drop either criterion... merely being a mega-genius won't help if you're not motivated), a good University education is the only way to go. Even if you are a highly motivated mathematical mega-genius, you'll still want to use the actual textbooks you'd use in a Uni course series. . . be prepared to read more then just a couple of books, and be prepared to learn a hell of a lot of math.

      And if math isn't easy for you (and I mean math, not namby-pamby arithematic, I mean real math, like topology and geometry and all forms of calculus), and you aren't truly seriously motivated to spend years on this, even the Uni won't be enough; most people drop out of the serious Physics courses!

      I can't give you a reading list; all I can say is if anyone else gives you one, and you can understand the books past the third chapter (assuming you know little/nothing about the subject, which I'm inferring from not trusting Uni educations right where they are the absolute strongest (hard sciences)), you're getting a "Slashdot" understanding, i.e., absolute crap. This isn't really a reading list problem; more of a reading bookshelf thing.

      Quantum mechanics drives PhDs nuts; you probably aren't going to just "pick it up". And I say this as a guy who "picks things up" pretty routinely (not just computer stuff). You have to know your limits, and if you're asking, this is extremely highly likely this is beyond yours. (And if you have trouble understanding that sentence literally, don't even bother starting... statistically, there's a chance I'm wrong but I wouldn't bet, well, anything on that remote chance.)

      Now, if you don't mind being a poser, as I am, then there are lots of great choices; the best thing to do is hike on down to a good physical bookstore, peruse the science shelves, and look for something that looks to be at your level, or better, slightly above. But don't think for a second you're getting anything more then the cliff notes of the cliff notes of a summary of quantum physics. (And highly opinionated ones, too; when physicist run out of math to talk about in popular-interest books, they tend to start shooting their mouths off and irresponsibly speculating wildly about cosmology. It makes good copy, but frankly, they're only slightly better equipped to speculate about the nature of the universe then you are; if anything, they get to be even more wildly wrong. You gotta seperate the physicist's wanking from the real facts.)

      • And highly opinionated ones, too; when physicist run out of math to talk about in popular-interest books, they tend to start shooting their mouths off and irresponsibly speculating wildly about cosmology. It makes good copy, but frankly, they're only slightly better equipped to speculate about the nature of the universe then you are; if anything, they get to be even more wildly wrong. You gotta seperate the physicist's wanking from the real facts.


        In which category are the "A brief history of time", and Stephen Hawking's latest book (i dont remember the name - universe in a nutshell or something)?
    • The highest math you need to be able to understand this is partial differential equations. If you want a good Quantum physics textbook I suggest "Introduction to Quantum Mechanics" by Bransden and Joachain. Also the Schaum's notes for Quantum Mechanics are quite good. (they got me through QM this semester!)
      • That depends on what you want to call a good understanding of quantum mechanics. I agree, that most of quantum is accessible through PDEs, but to really understand where a lot of it came from, you also need linear algebra, group theory, and a really good grasp of hamiltonian mechanics and field theory.
    • I found this John Gribbon book very informative: Schrodinger's Kittens and the Search for Reality. Its a few years old (1995) so if someone has a pointer to something newer, speak up!
    • by skwang ( 174902 ) on Sunday May 05, 2002 @03:01PM (#3466362)

      Okay, you want a reading list. I have one for you.

      First brush up on your classical mechanics, you will need to study Lagragians and the Hamitonian formulation as they are both very important for the formation of Quantum Mechanics. Lets see, you could try:

      • Marion and Thorton, Classical Dynamics, Saunders College Publ., Philadelphia, 1995.
      • Goldstein, Classical Mechanics 2nd ed. , Addison-Wesley, Reading, MA, 1980.

      For a good mathematical methods reference read:

      • Arfkin and Weber, Mathematical Methods for Physicists,Harcourt / Academic Press, 2000.

      You want to rigorously learn all of Electricity and Magentism; there is only one source:

      • Jackson, J.D., Classical Electrodynamics 3rd ed., John Wiley & Sons, 1998.

      Now you have to start on Quantum Mechanics. There are many different books you could try; here are some of them:

      • Sakurai, Modern Quantum Mechanics
      • Dirac, Principles of Quantum Mechanics
      • Cohen-Tannoudji, Diu and Laloe, Quantum Mechanics
      • Merzbacher, Quantum Mechanics

      Now that you have learned Quantum Machanics you can move onto some field theory:

      • Riazzudin & Fayazzudin, A Modern Introduction to Particle Theory, World Scientific.
      • Mohapatra, Unification and Supersymmetry, Springer Veriag.
      • Marshak, Conceptual Foundations of Particle Physics, World Scientific.

      At this point you may want to deviate slightly and read some books on relativity and cosmology

      • Misner, Wheeler and Thorne, Gravitation,W H Freeman & Co, 1973.
      • Peebles, Principles of Physical Cosmology,Princeton Univ Press, 1993.



      When I started college, I chose physics because I liked it. I soon realized that the physics you learn at a univeristy is not the physics a physicists does. Instead, everything you learn as an undergraduate classes are tools. These tools are to be used in graduate school as a foundation for more complex concepts.

      It's been four years and I am about to go off to grad school to study elementry particle physics (experimental). I don't claim to have read any of the books above, but I hope it might show you that if you want to "*fully* comprehend stuff like particle physics, quantum phenomena, etc." it is not easy. Most popular science books you will find on a bookshelf do not contain much substance. Many are good reads. Brian Green's Elegant Universe and Stephen Hawking's A Brief History are good examples that are constantly recommended here on slashdot. But if you really (and I mean really) want to learn physics, you can do one of two things:

      1. Read all the books above while doing most if not all the problems.
      2. Spend a good amount of time (most people spend four undergraduate years) learning the "tools of the trade" and then spend five to six years in graduate studies, researching a single topic.

      My purpose of this post is not to be harsh, but realistic. I am glad you are fasinated with physics. My fasination led me to the point where I want to spend years in school studying it. But I think many people don't realize that the subject is really difficult, and that it takes years of university education to even begin to understand it.

      • There are short cuts into many of these subjects and it's a pity that they aren't exploited. For example you really don't need much to get started in quantum mechanics. If you limit yourself to finite dimensional systems like electron spins or two level atoms you can go a long way with basic linear algebra. Enough, at least, to start pondering things like Shrodinger's cat, EPR, the Aspect experiment, the quantum no-clnoe theorem and some quantum computing. You don't need to understand the Schrodinger equation - just know that time evolution is a certain linear operator. QM courses generally seem to start with the hard examples first: the one dimensional Schrodinger equation which (1) requires differential equations and (2) is set in an infinite dimensional Hilbert space. Unfortunately none of the textbooks I know of do this (except maybe some newer quantum computing books).
      • I'm currently in the PhD part of the process, and I agree with the books on your list, for the most part.

        However, I would add Griffiths Introduction to Electrodynamics before Jackson as a much more approachable and physical textbook. Jackson is kind almost more of a course in solving PDEs under insane boundary conditions.

        And, for physical insight, I would add the Feynman Lectures. The examples are well thought out, and they're kind of fun to read in their own right. But, these are for reading after you understand the math; before hand, they're practically useless.

        I would also tend to add a few books in the Landau and Lifshitz series, most noteably their Mechanics and their Quantum Mechanics books.

        And I agree, that a realistic foray into physics is not to be undertaken lightly. It takes years to get to the point where you can even begin to read journal articles and begin to understand them.

    • This website [wolfram.com] is great for getting a taste of what a good science education could teach you.
    • For some good physics fun, there is "Feynman's Lectures". And loosen up a bit. There's nobody who can *fully* comprehend *stuff* !
  • There's a growing school of thought within physics that the Heisenburg uncertainty prinicple could be a misconception arising from inexact experimental tools, and from an unwillingness to abandon the idea of the point perticle. Carver Mead, a past student of Richard Feynman and one of the most important practical scientists of the past 50 years discusses this in an interview [gilder.com] in the American Spectator.
    • intellectual fraud (Score:3, Insightful)

      by iskander ( 9699 )

      [To the author of the post to which I am replying: please, don't take this as an attack on you.]

      The "Heisenburg [sic] uncertainty prinicple [sic]" is not a misconception arising from inexact experimental tools; it has nothing to do with the quality of experimental means. The inequality that some (most?) physicists like to call the Heisenberg Uncertainty Principle is not a principle at all but a sort of litmus test for the applicability of classical models to systems exhibiting so-called quantum behavior; that is, the Heisenberg inequality can be used as a way to determine whether a given so-called classical model {still | no-longer} constitutes an accurate description of the behavior of the system in question. I suppose I could agree with someone saying that the Heisenberg inequality was a "feature" of quantum-mechanical models much more readily than I could agree with someone claiming that it was a principle. (You might look up "principle" in the dictionary to see what I mean.)

      There's no "growing school of thought" to speak of because Physics is not a belief system, and I don't even think that a significant change in the thinking of the average physicist is currently taking place. There are many practicing physicists who haven't the integrity to admit (to others or to themselves) that they are a fraud and who propagate their misunderstanding to their students and to the public through their lectures and their publications -- and it may well be that attrition and budget cuts are weeding these posers out. Evidently, however, we've still a long way to go: the closing paragraph of the scholarly paper referenced in the story demonstrates how Ye Olde Rhetorick can survive even the strongest refutation. I can think of two reasons why people will continue to "believe in" the Heisenberg Uncertainty Principle and other such historically justified nonsense:

      1. In order to get ahead, a scientist (like everyone else, I suppose) may choose to say what his peers (especially those who hold power) already believe, even when he knows better.
      2. Very often, those who discover evidence refuting a given proposition are too firmly in its grip to realize the significance (or even the meaning) of their finding, and sometimes even misinterpret it so as to corroborate their erroneous belief.

      Fear not for the fate of science, though: it is quite possible to use the knowledge framework developed by Real Scientists (amongst whom I would include Real Mathematicians) to make Real Discoveries and devise Real Technology -- even in the absence of Real Understanding. (I am confident that the reader can provide his own examples. :-> ) And, in a very real way, we depend on these contributions to build the venerable edifice of science.

      • The "Heisenburg [sic] uncertainty prinicple [sic]" is not a misconception arising from inexact experimental tools; it has nothing to do with the quality of experimental means.
        Indeed. That American Spectator article linked above is junk science at its worst. I considered writing a detailed criticism of the article, but why bother? It is crystal clear that the guy has only a superficial and often-incorrect knowledge of the theories he is trying to debunk. E.g., he ridicules the correspondence principle as if it were a law of physics, when it is actually a combination of 1) an acid test used to rule out incorrect quantum theories, and 2) a demonstration that quantum mechanics can produce the world that is observed at the scale of everyday life.
      • I Really enjoyed also generally agreed with your remarks about intellectual fraud (unfortunately, it's not restricted to the sciences, but exists throughout academia, from the sophists up to the present, although I am sure that doesn't mark its limits either).

        However, I am still wondering (1) whether you read the interview [gilder.com] with Mead about his book [amazon.com], or are just taking the first part of Elby's [slashdot.org] quote (about imprecise equipment) at face value; and (2) whether you are accusing Mead of being an intellectual fraud.

        I did read the article, and looked at the sample pages from the book, and read another interesting speech [gilder.com] of Mead's, and think that it might be possible that there is a lot of merit in wanting to consider some particles - particularly electrons - as manifolds with boundary in stead of as singular points.

        To deal with the first question, I think that Mead's main intent was to say that the Copenhagen Interpretation went wrong in insisting upon dogmatic adherence to the point particle model. He says that they understandably did not have access to the kind of data we do now, such as being able to see a single electron, but even more importantly, they had no experimental experience with coherent systems. Since their only experience was of incoherent systems, then of necessity, statistical models were all they could talk about. Mead is saying that with mounting evidence of coherent systems such as Lasers, Masers, Bose-Einstein condensates, etc. (he lists 10 in his book), that it appears to him that this is an even more important litmus test for understanding properties of "pure particles" (my paltry words here) than something like the Heisenberg Uncertainty Criterion.

        The other thing I think Mead is addressing are logical paradoxes, which like you also mention, we all know must be created by lesser minds misapplying theoretical concepts. But like you, I feel unqualified to talk about these in physics at present. My gut feeling, however, is that dogmatism has been poisoning academic physics for decades.

        Finally, our thread root poster, Elby, mentioned a "growing school" of thought. The article quotes Mead as follows:

        John Cramer at the University of Washington was one of the first to describe it as a transaction between two atoms. At the end of his book, Schrodinger's Kittens and the Search for Reality, John Gribbin gives a nice overview of Cramer's interpretation and says that "with any luck at all it will supercede the Copenhagen interpretation as the standard way of thinking about quantum physics for the next generation of scientists."
        Does anybody here know what the numbers of scientists, Real or not, are, who are publishing articles similar to Cramer's [washington.edu] in peer-reviewed journals?

        Well, that's my quick summary. I'd be curious to know what a "Real" scientist thought about Mead's perspective; I found it very interesting. [Disclaimer: I am not a scientist although I have a fair background in graduate mathematics and a bit as well in undergrad physics. But,] In fact, I have enough experience [wolfram.com] with math to have a certain skepticism about the wisdom of unthinkingly applying things as basic as the real number field, with its Archimedean property, or the idea of a mathematical point, with unqualified enthusiasm to great unknowns such as the elementary particles of nature. And for criticizing such an unthinking approach to matter, I would like to know if I am truly justified in applauding Mead (i.e. in the name of Real science).

        In any case, I would be grateful to be educated out of any of my own misconceptions. Best of luck to you in producing Real science - I hope I get to read about the results some day!

  • Wanted... (Score:3, Funny)

    by danamania ( 540950 ) on Sunday May 05, 2002 @02:29PM (#3466237)
    Schroedinger's Cat

    Wanted:

    DEAD and ALIVE
  • To clarify (Score:3, Informative)

    by JPMH ( 100614 ) on Sunday May 05, 2002 @04:46PM (#3466769)
    The /. headline is rather misleading.

    Hall and Reginatto's paper does not supersede Heisenberg's uncertainty principle, nor does their paper change or challenge any of the fundamental results of quantum mechanics.

    To explain:

    Heisenberg's relation can be seen as an example of a (classical) result in Fourier theory about pairs of variables which are Fourier transforms of each other (for example time <> frequency), sometimes known as the bandwidth theorem. This is relevant because quantum wave mechanics asserts that wavefunction for a particle's momentum is essentially [a Constant times] the Fourier transform of the wavefunction of the particle's position.

    Why should there be this Fourier relationship between x and p ? (After all, in classical physics both position and momentum are point quantites, assumed to exist independently to infinite precision.) Well typically, the position taken is either that you've drawn a picture of some waves wiggling along according to the Schrodinger equation, and you say you believe in your picture; or it's because you're stating the relation as an axiomatic principle, [\hat{x},\hat{p}] = ih/2pi, which with some other axioms you then use to derive Schrodinger's equation.

    What Hall and Reginatto are really interested in is this: what other questions could you have set up, that would have led to the Schrodinger equation as a solution. (In statistics this approach is sometimes known as 'characterisation' of a distribution or evolution equation -- what "principles" might have caused it to come about).

    Here they show that the Schrodinger equation and the x <> p Fourier transform relationship are in some senses the most 'natural' outcome, if you start with the classical Lagrangian of the Hamilton-Jacobi equation for the evolution of a probability distribution of a particle, and add a new term which adds an extra uncertainty to the momentum at each possible point, proportional to the local Fisher information of the probability distribution for position (ie its local sharpness, more or less).

    This equation for an evolving probability distribution does not (necessarily) involve wavefunctions as physical entities; which may or may not make it a more useful and focussed way to think about what makes quantum mechanics "different".

    The authors caution that their approach does not attempt to provide a 'realistic' [ie mechanistic] model for where the extra momentum uncertainty comes from; any such attempt, they write, 'would require a whole new (and nonlocal) theory that goes beyond quantum mechanics'.

  • by radsoft ( 103659 )
    Improvement on the Uncertainty Theorem? I'm not sure about this...

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