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"Exact uncertainty" brought to quantum world
NewScientist.com ^ | April 02 | Eugenie Samuel

Posted on 05/07/2002 11:50:28 AM PDT by sourcery

 
 

"Exact uncertainty" brought to quantum world

 
00:01 27 April 02
 
Exclusive from New Scientist Print Edition
 

Exact uncertainty sounds like a contradiction in terms, but that is what governs the quantum world, according to a theoretical physicist who has created an improved version of the famous Heisenberg uncertainty principle.

Heisenberg worked out that there is a degree of inherent fuzziness to the world. You cannot measure both the position and the momentum of any particle with perfect accuracy. The better the accuracy of your momentum measurement, the more uncertain your position measurement must be, and vice versa.

Heisenberg quantified this in the uncertainty relation, which says that the product of the two uncertainties must always be greater than a certain fixed amount. This does not say how big the uncertainty might actually be, however.

Michael Hall, who is a visiting fellow at the Australian National University's Institute of Advanced Studies in Canberra, wondered whether this could be quantified more exactly. He supposes that quantum systems can be broken down into two parts: there is a classical part that can in principle be measured exactly, and a quantum part that has only probabilities of having different values. In other words, it is fuzzy and cannot be measured precisely.


Strong relation

To quantify this quantum uncertainty, Hall borrowed a mathematical tool developed in 1925 by British statistician Ronald Fisher. Fisher worked out how to quantify differences between human populations by sampling a few members of each. This kind of method gives you an uncertainty in your results, and Hall saw that making measurements on quantum particles was a mathematically similar process.

The result is an expression that looks like Heisenberg's original relation, but gives the exact uncertainty in the measurements of position and momentum. Hall says it is an equation rather than an inequality, which is "a far stronger relation".

So strong, in fact, that in a paper published this month in Journal of Physics A, Hall and Marcel Reginatto of the Physical-Technical Institute in Braunschweig, Germany, have managed to derive the basics of quantum mechanics from it, including the Schrödinger equation that describes the behaviour of quantum-mechanical wave functions.


God-given

"I find it remarkable that the Schrödinger equation no longer has to be god-given," says Wolfgang Schleich, who studies the foundations of quantum mechanics at the University of Ulm. You still have to make the assumption that there is some quantum uncertainty, but this is much simpler than assuming Schrödinger's equation.

Unusually for work in such fundamental physics, the new formulation might even have practical applications. Hall says it implies a tight relationship between uncertainty and energy that makes it easier to understand why, in quantum mechanics, systems have a minimum kinetic energy even if there aren't any forces acting. "There's a kind of quantum kinetic energy that comes from the uncertainty," he says.

What's more, the new uncertainty equation makes it possible to estimate the minimum energy that a given quantum system should have. This is useful in cases when it's not possible to calculate the lowest energy levels precisely, particularly in complicated systems such as atoms with many orbiting electrons.

 

Eugenie Samuel



TOPICS: Miscellaneous; News/Current Events
KEYWORDS: heisenberg; quantummechanics; uncertaintyprinciple

1 posted on 05/07/2002 11:50:29 AM PDT by sourcery
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To: Physicist; longshadow; RightWhale
FYI
2 posted on 05/07/2002 12:02:23 PM PDT by sourcery
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To: sourcery
Wolfgang Schleich

An important name in optics, theoretical physics. Dropping the name here increases the modality of this exact uncertainty theory.

3 posted on 05/07/2002 12:09:30 PM PDT by RightWhale
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To: sourcery
This article doesn't make much sense. Population sampling statistics do not involve immediately mutual effects, and I think that mutual measurement effect interaction has a role in further specifying the uncertainty. Here's hoping that the new equation is not simply the inequality after removing the "or greater than". It seems to me that the image analysis field has provided more food for thought on the same topic. One relevant concept in that field is the Fisher matrix.
4 posted on 05/07/2002 12:09:42 PM PDT by apochromat
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To: sourcery
The result is an expression that looks like Heisenberg's original relation, but gives the exact uncertainty in the measurements of position and momentum. Hall says it is an equation rather than an inequality, which is "a far stronger relation".

But it will still be an inequality. Nothing prevents you from having a more uncertain measurement than that allowed by the uncertainty relation, whatever that relation might be.

5 posted on 05/07/2002 12:23:53 PM PDT by Physicist
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To: sourcery
bttt
6 posted on 05/07/2002 1:01:50 PM PDT by ImaGraftedBranch
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To: sourcery
Thumbtack.
7 posted on 05/07/2002 1:10:51 PM PDT by AndrewC
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To: sourcery
dp dx = h / (2 x pi) + y

See, I can do it too. ; )

8 posted on 05/07/2002 1:18:08 PM PDT by Believe_In_The_Singularity
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To: apochromat
But the question then surfaces of whether or not the quantity of uncertainty required differs with differing external environmental or statistical situations, if so, that implies that you could extract energy from the quantum uncertainty..
9 posted on 05/07/2002 1:22:06 PM PDT by Technocrat
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To: Technocrat
Is it just me, or does reading that without thinking about it make you laugh?
10 posted on 05/07/2002 1:23:11 PM PDT by Technocrat
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To: RadioAstronomer; ThinkPlease; PatrickHenry; VadeRetro; Scully; edwin hubble; Doctor Stochastic
Does this mean Schrödinger's Cat is more dead (and more NOT dead) than we used to think it was?
11 posted on 05/07/2002 1:34:00 PM PDT by longshadow
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To: Technocrat
I think spontaneous energy beneath the uncertainty floor is "imaginary" energy, "imaginary" in the same way the impedances in a network of perfect capacitors and inductors are imaginary.
12 posted on 05/07/2002 1:38:11 PM PDT by apochromat
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To: sourcery
BUMP for later read
13 posted on 05/07/2002 2:03:40 PM PDT by AFreeBird
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To: Physicist
I just skimmed the paper but it looks like the measured uncertainty is greater than the "intrinsic" [my name, not theirs] uncertainty because of the Cramer-Rao inequalities. The paper's equality is between the dispersions of the conjugate variables.
14 posted on 05/07/2002 2:08:14 PM PDT by Doctor Stochastic
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To: Physicist
Nothing prevents you from having a more uncertain measurement than that allowed by the uncertainty relation, whatever that relation might be.

Soitinly! (or a reasonable facsimile of that pronunciation).

15 posted on 05/07/2002 2:09:44 PM PDT by AndrewC
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To: longshadow
The result is an expression that looks like Heisenberg's original relation, but gives the exact uncertainty in the measurements of position and momentum.

Lemme see now ... I'm no QM man, but I guess this means that we used to be uncertain about how much uncertainty there was in such matters. Now we are less so. The article makes it sound as if we are far less so. This sounds like a significant improvement. But QM is definitely outside the range of my conversational topics.

16 posted on 05/07/2002 2:19:21 PM PDT by PatrickHenry
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To: PatrickHenry
We used to know that we didn't know and we knew how much we didn't know. Now we know by how much we don't know that we don't know. Y'know.
17 posted on 05/07/2002 2:49:28 PM PDT by Doctor Stochastic
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To: Doctor Stochastic
Now we know by how much we don't know that we don't know.

People always feel that they have a handle on something if they can stick numbers to it. It's a control thing.

18 posted on 05/07/2002 2:59:45 PM PDT by VadeRetro
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To: PatrickHenry
This sounds like a significant improvement. But QM is definitely outside the range of my conversational topics.

This is clearly a topic within the domain of "Plato the Platypus"....... [creating yet another posting opportunity for the jpg image of "Plato," the fuzzy, furry, and maniacal monotreme.]

19 posted on 05/07/2002 3:37:03 PM PDT by longshadow
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To: longshadow
[creating yet another posting opportunity for the jpg image of "Plato," the fuzzy, furry, and maniacal monotreme.]

How about the opportunity for the personal primate assistant?

Who rates the article on which this thread is based, 0 BS. There is no BS in it.

20 posted on 05/07/2002 4:10:57 PM PDT by AndrewC
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To: VadeRetro
First you say you do, and then you don't,
And then you say you will, and then you won't;
You're undecided now, so what are you gon - na do?

Now you want to play, and then it's no,
And when you say you'll stay, that's when you go --
You're undecided now, so what are you gon - na do?

21 posted on 05/07/2002 4:40:30 PM PDT by PatrickHenry
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To: PatrickHenry
Well did you ever have to make up your mind?
Pick up on one, and leave the other behind?
Collapse your wave function,
Stuff of that kind . . .
22 posted on 05/07/2002 5:42:40 PM PDT by VadeRetro
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To: sourcery
"I find it remarkable that the Schrödinger equation no longer has to be god-given," says Wolfgang Schleich, who studies the foundations of quantum mechanics at the University of Ulm.

Don't let some of these people see that!

23 posted on 05/07/2002 5:44:14 PM PDT by VadeRetro
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To: VadeRetro
One way to answer Einstein's objection to QM ("God does not play dice") is to remove God from the equation. When the God's away, the dice will play...
24 posted on 05/07/2002 5:53:14 PM PDT by sourcery
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To: Technocrat
"you could extract energy from the quantum uncertainty"

Some search algorithms use randomness. In a way, I think it's possible to extract computational leverage from quantum uncertainty. Perhaps the brain is able to use quantum uncertainty in this way.

25 posted on 05/07/2002 6:17:32 PM PDT by apochromat
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To: apochromat
Hall's description of the function and Heisenberg's description of the function......
EXACTLY THE SAME, BUT DIFFERENT !
26 posted on 05/08/2002 2:06:37 AM PDT by UCANSEE2
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To: VadeRetro
Or from P.D.Q.Bach's "Iphigenia in Brooklyn": Who knows what it means to be running; only he who is running, running, knows. Run, running knows....
27 posted on 05/08/2002 6:15:17 AM PDT by Doctor Stochastic
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To: sourcery
God's dice are more like Big Jule's. The faces are indistinguishable.
28 posted on 05/08/2002 6:19:30 AM PDT by Doctor Stochastic
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To: VadeRetro
QM love song
(modified from "You Don't Know Me," Ray Charles)

I give velocity
And then I say goodbye
You watch me fly away
Beside that lucky guy
You'll never, never know
The thing you want to know
No, You don't know me.

29 posted on 05/08/2002 7:29:56 AM PDT by PatrickHenry
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To: PatrickHenry
What it all means, I'm not exactly uncertain, but what it was was Quantum Mechanics.
30 posted on 05/08/2002 7:34:26 AM PDT by VadeRetro
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Comment #31 Removed by Moderator

To: apochromat
You may have hit on the missing link for creativity. What a fascinating idea - worth a few experiments...
32 posted on 05/08/2002 7:36:05 AM PDT by Technocrat
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To: Doctor Stochastic
God's dice are more like Big Jule's. The faces are indistinguishable.

"Big Jule" from Chicago had the dots removed "for good luck," but he "remembers where they were."

Thanks for the Damon Runyon moment....[fade to black as "The Oldest Established, Permanent Floating Crap Game in NY" is heard in the background...]

33 posted on 05/08/2002 9:08:53 AM PDT by longshadow
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