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."
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.
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.
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
Heisenberg said err(momentum * position) >= CONSTANT
No, he said err(momentum)*err(position)>=constant.
Find free books.
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.
Find free books.
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.]