An Improvement Upon Heisenberg's Uncertainty Theorem
Posted by
Hemos
on from the making-things-more-efficent dept.
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."
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).
Re:Help me...
by
bcrowell
·
· Score: 3, Informative
Heisenberg said err(momentum * position) >= CONSTANT
No, he said err(momentum)*err(position)>=constant.
Re:Help me...
by
bcrowell
·
· Score: 3, Informative
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.
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?
-- Brak: What's THAT?
Thundercleese: A light switch.. of TOTAL DEVASTATION!
Re:Physics fascinates me
by
Jerf
·
· Score: 4, Insightful
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.)
Re:Physics fascinates me
by
Quizme2000
·
· Score: 3, Interesting
This website is great for getting a taste of what a good science education could teach you.
Heisenberg pondering Somebody comes up with an equation Werner looks like fool.
EBADHAIKU
intellectual fraud
by
iskander
·
· Score: 3, Insightful
[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:
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.
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.
--
-- Kuro5hin.org: where the good times never end.;-)
A reading list [Re:Physics fascinates me]
by
skwang
·
· Score: 5, Informative
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.
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:
Read all the books above while doing most if not all the problems.
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.
Re:A reading list [Re:Physics fascinates me]
by
SIGFPE
·
· Score: 2
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).
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'.
conclusion/ posers in the scientific establishment
by
iskander
·
· Score: 3, Informative
All that interesting typing and then you left out your conclusion.
That depends on whether you can infer that which I may have been too chicken to say more intelligibly. I realize you might be trolling me, but that's OK. The previous post dealt with two issues: (1) the trouble with referring to the Heisenberg inequality as the Heisenberg Uncertainty Principle and (2) the larger problem of which the foregoing is only a symptom. Since I believe the first point was adequately explained in my previous post, I will only elaborate on the second point.
A great many people who would call themselves scientists are posers, and some of them are outright frauds. A great many professors do not really understand much of what they teach; they cover up their incompetence by assigning buttloads of homework, giving clever problems on tests that are designed to prey on students' lack of experience, and avoiding truly open discussion with their students lest their own ignorance be revealed in the process. A great many researchers do not understand much of the theoretical framework they employ; they cover up their incompetence by doing lots of (often unnecessary) laboratory work (they say "experiments") or writing computer programs (they say "simulations"), writing karmawhorific articles for so-called scholarly journals, and avoiding truly open discussion with their peers lest their own ignorance be revealed and their peers aggravated in the process.
Yep, the scientific establishment is currently overrun by conniving intellectual midgets who pose as Real Scientists and uncritically certify each other. That may be disappointing, but it doesn't have to be a Bad Thing. If the goal is simply to catalog natural phenomena, discover new materials, and characterize known materials in order to exploit all this knowledge in "new technologies", then it may be acceptable for science professionals to be intellectual frauds because their incompetence will not prevent them from making a useful contribution. In fact, as long as there are a few Real Scientists around to straighten things out, the work of so-so scientists can be quite useful even when it does not consist of observation and classification. Consider, for example, the journal article to which the story refers: the article's closing paragraph gives me ample reason to believe that the authors have either (1) not properly understood their own result or (2) chosen to lean on the traditional aesthetic (and perhaps the dogma -- I'd have to talk to them to find out) in order to gain the favor of their peers -- but this does not in itself detract from the value of the result they present, which must be judged independently. [FYI, my previous post addresses conventional discourse on the Uncertainty Principle and gives context to the previous statement.]
So, that was my conclusion: many scientists (including, apparently, the authors of the article in question) are posers of one kind or another -- and that's probably OK. Mediocrity, when effective, is often also efficient, especially when combined with connivance. That may be hard for individuals of unassailable integrity (Real Physicists and Real Programmers included) to accept, but we have every indication that it is true.
[Disclaimer: I am a scientist (what you might call a mathematical physicist) and I hope, someday, before I am too old, to discover whether I, too, am a fraud. The last thing I want is to waste my life publishing bullshit articles in order to legitimize my last bullshit grant and support my next bullshit grant application.]
Slashdot Mirror
We are more sure than ever of our lack of certainty!
"Flyin' in just a sweet place,
Never been known to fail..."
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.
Carbon based humanoid in training.
Heisenberg was right
That God really does play dice
With the universe
ok then your [sic] infringing on my copyright! Could you as [sic] me next time before STEALING my comments for your own?
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...
-- Is "Sig" copyrighted by www.sig.com?
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?
Brak: What's THAT?
Thundercleese: A light switch.. of TOTAL DEVASTATION!
Heisenberg pondering
Somebody comes up with an equation
Werner looks like fool.
EBADHAIKU
[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:
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.
Schroedinger's Cat
Wanted:
DEAD and ALIVE
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:
For a good mathematical methods reference read:
You want to rigorously learn all of Electricity and Magentism; there is only one source:
Now you have to start on Quantum Mechanics. There are many different books you could try; here are some of them:
Now that you have learned Quantum Machanics you can move onto some field theory:
At this point you may want to deviate slightly and read some books on relativity and cosmology
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:
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.
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'.
That depends on whether you can infer that which I may have been too chicken to say more intelligibly. I realize you might be trolling me, but that's OK. The previous post dealt with two issues: (1) the trouble with referring to the Heisenberg inequality as the Heisenberg Uncertainty Principle and (2) the larger problem of which the foregoing is only a symptom. Since I believe the first point was adequately explained in my previous post, I will only elaborate on the second point.
A great many people who would call themselves scientists are posers, and some of them are outright frauds. A great many professors do not really understand much of what they teach; they cover up their incompetence by assigning buttloads of homework, giving clever problems on tests that are designed to prey on students' lack of experience, and avoiding truly open discussion with their students lest their own ignorance be revealed in the process. A great many researchers do not understand much of the theoretical framework they employ; they cover up their incompetence by doing lots of (often unnecessary) laboratory work (they say "experiments") or writing computer programs (they say "simulations"), writing karmawhorific articles for so-called scholarly journals, and avoiding truly open discussion with their peers lest their own ignorance be revealed and their peers aggravated in the process.
Yep, the scientific establishment is currently overrun by conniving intellectual midgets who pose as Real Scientists and uncritically certify each other. That may be disappointing, but it doesn't have to be a Bad Thing. If the goal is simply to catalog natural phenomena, discover new materials, and characterize known materials in order to exploit all this knowledge in "new technologies", then it may be acceptable for science professionals to be intellectual frauds because their incompetence will not prevent them from making a useful contribution. In fact, as long as there are a few Real Scientists around to straighten things out, the work of so-so scientists can be quite useful even when it does not consist of observation and classification. Consider, for example, the journal article to which the story refers: the article's closing paragraph gives me ample reason to believe that the authors have either (1) not properly understood their own result or (2) chosen to lean on the traditional aesthetic (and perhaps the dogma -- I'd have to talk to them to find out) in order to gain the favor of their peers -- but this does not in itself detract from the value of the result they present, which must be judged independently. [FYI, my previous post addresses conventional discourse on the Uncertainty Principle and gives context to the previous statement.]
So, that was my conclusion: many scientists (including, apparently, the authors of the article in question) are posers of one kind or another -- and that's probably OK. Mediocrity, when effective, is often also efficient, especially when combined with connivance. That may be hard for individuals of unassailable integrity (Real Physicists and Real Programmers included) to accept, but we have every indication that it is true.
[Disclaimer: I am a scientist (what you might call a mathematical physicist) and I hope, someday, before I am too old, to discover whether I, too, am a fraud. The last thing I want is to waste my life publishing bullshit articles in order to legitimize my last bullshit grant and support my next bullshit grant application.]
Improvement on the Uncertainty Theorem? I'm not sure about this...
radsoft.net