Free Republic
Browse · Search
General/Chat
Topics · Post Article

Skip to comments.

Proving uncertainty: First rigorous formulation supporting Heisenberg's famous 1927 principle
Phys.Org ^ | 04-29-2014 | Provided by American Institute of Physics

Posted on 04/29/2014 10:27:28 AM PDT by Red Badger

Nearly 90 years after Werner Heisenberg pioneered his uncertainty principle, a group of researchers from three countries has provided substantial new insight into this fundamental tenet of quantum physics with the first rigorous formulation supporting the uncertainty principle as Heisenberg envisioned it.

In the Journal of Mathematical Physics, the researchers reports a new way of defining measurement errors that is applicable in the quantum domain and enables a precise characterization of the fundamental limits of the information accessible in quantum experiments. Quantum mechanics requires that we devise approximate joint measurements because the theory itself prohibits simultaneous ideal measurements of position and momentum—and this is the content of the uncertainty relation proven by the researchers.

"Curiously, since Werner Heisenberg, one of the founders of quantum mechanics, gave an intuitive formulation of this principle, it was only recently that serious attempts were made to make the statement precise enough so that one could check its validity," said Paul Busch, Professor of Mathematical Physics at the University of York, who collaborated with Pekka Lahti of the University of Turku in Finland and Reinhard F. Werner of Leibniz Universität in Hannover, Germany on the work.

"Our method of defining the error and disturbance in quantum measurements enabled us to prove an error-disturbance trade-off relation just the way Heisenberg envisaged it," Busch said.

The first step was to prove an uncertainty relation for a special class of approximate joint measurements of the position and momentum; a class with nice symmetry properties. The main difficulty was then to find a way of reducing the most general case to this symmetric case. This involved a fairly complex chain of arguments using some deep ideas of advanced mathematics. Formulating and proving a family of measurement uncertainty relations for canonical pairs of observables resulted in one possible rigorous interpretation of Heisenberg's 1927 statements.

"We were able to define measures of error and disturbance as figures of merit characterizing the performance of any measuring device; thus, our measures describe how well a given device allows one to determine, for instance, the position of an electron, and how much it disturbs the momentum," explained Busch. "We believe that our approach is the first to provide error measures that are not merely mathematically plausible but more importantly, can be estimated from the statistical data provided by the measurement at hand, so that the numbers one identifies as "errors" are in fact indicators of the quality of the experiment."

This work is particularly timely and significant since some recent research calls the Heisenberg principle into question. The quantum mechanical inequality proposed by M. Ozawa in Japan, if its interpretation were correct, would suggest that quantum uncertainty might be less stringent than had been thought for the last 80 or so years. If these claims were tenable, it would seriously impact our understanding of the workings of the physical world. Busch, Lahti and Werner argue that this approach is flawed as Ozawa's inequality is meaningful as an error-disturbance relation only in a limited set of circumstances.

The results of this research—a proof of a variety of formulations of measurement error (and disturbance) relations—highlights the fundamental limits of measurements in quantum physics. Since modern technology has been progressing steadily to controlling smaller and smaller objects (e.g., nanotechnology, quantum computation, quantum cryptography), the time is approaching where device performance may confront the ultimate quantum limits. These results may, for example, corroborate the security of quantum cryptographic protocols insofar as these are based on the validity of the uncertainty principle and the Heisenberg effect.

What is next for this research? "Surprisingly, we are only just witnessing the beginnings of a systematic conceptualization of measurement error and disturbance," Busch said. "No doubt researchers will find interesting new error relations, for instance, based on entropic measures. It appears that the recent quantum uncertainty controversy has already inspired numerous researchers to start their own investigations in this area."

Explore further: Physicists prove Heisenberg's intuition correct

More information: The article, "Measurement uncertainty relations" is authored by Paul Busch, Pekka Lahti and Reinhard F. Werner. It will be published in the Journal of Mathematical Physics on Tuesday April 29, 2014. DOI: 10.1063/1.4871444


TOPICS: Astronomy; Education; History; Science
KEYWORDS: mathematics; physics; quantum; science; stringtheory; uncertaintyprinciple; wernerheisenberg

Nearly 90 years after Werner Heisenberg pioneered his uncertainty principle, a group of researchers from three countries has provided substantial new insight into this fundamental tenet of quantum physics with the first rigorous formulation supporting the uncertainty principle as Heisenberg envisioned it. Credit: AIP Emilio Segre Visual Archives, Segre Collection

Nearly 90 years after Werner Heisenberg pioneered his uncertainty principle, a group of researchers from three countries has provided substantial new insight into this fundamental tenet of quantum physics with the first rigorous formulation supporting the uncertainty principle as Heisenberg envisioned it. Credit: P.Busch/York

Read more at: http://phys.org/news/2014-04-uncertainty-rigorous-heisenberg-famous-principle.html#jCp

1 posted on 04/29/2014 10:27:28 AM PDT by Red Badger
[ Post Reply | Private Reply | View Replies]

To: Red Badger

One day, while driving, Heisenberg was stopped by a police car.

“Do you know how fast you were going?” asked the cop.

“No, but I know where I am.” he replied...................


2 posted on 04/29/2014 10:29:10 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Red Badger

No worries, I’ll just use one of these:

http://en.memory-alpha.org/wiki/Heisenberg_compensator


3 posted on 04/29/2014 10:29:49 AM PDT by GraceG
[ Post Reply | Private Reply | To 1 | View Replies]

To: GraceG

beat me to it! hahaha


4 posted on 04/29/2014 10:35:02 AM PDT by left that other site (You shall know the Truth, and The Truth Shall Set You Free.)
[ Post Reply | Private Reply | To 3 | View Replies]

To: Red Badger

Sounds like this is a bit late to the party. I thought this was well-established by mathematical physics long ago.


5 posted on 04/29/2014 10:50:19 AM PDT by expat2
[ Post Reply | Private Reply | To 1 | View Replies]

To: Red Badger

I can’t find my car keys...

Probably know too much about their momentum.


6 posted on 04/29/2014 10:52:19 AM PDT by glorgau
[ Post Reply | Private Reply | To 2 | View Replies]

To: expat2
I thought this was well-established by mathematical physics long ago.

I guess they were uncertain.................

7 posted on 04/29/2014 10:52:26 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 5 | View Replies]

To: glorgau

When they stop, you’ll find them....................


8 posted on 04/29/2014 10:53:08 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 6 | View Replies]

To: Red Badger

Interesting. I’ve wondered about the Uncertainty Principle but every time I got close to understanding it, it got away from me


9 posted on 04/29/2014 10:54:29 AM PDT by bigbob (The best way to get a bad law repealed is to enforce it strictly. Abraham Lincoln)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Red Badger

“Say my name!”


10 posted on 04/29/2014 10:56:41 AM PDT by TurboZamboni (Those who make peaceful revolution impossible will make violent revolution inevitable.-JFK)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Red Badger
But are they really sure they've found a substantial proof ??
11 posted on 04/29/2014 10:56:41 AM PDT by mikrofon (F(z,x) BUMP)
[ Post Reply | Private Reply | To 1 | View Replies]

To: mikrofon

They’re apparently certain........................


12 posted on 04/29/2014 10:58:11 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 11 | View Replies]

To: Red Badger
Heisenberg? Is that you?

Sorry, I could not help myself...

13 posted on 04/29/2014 10:58:12 AM PDT by tpmintx (Gun free zones are hunting preserves for unarmed people.)
[ Post Reply | Private Reply | To 1 | View Replies]

To: bigbob

Then you need this:

http://en.memory-alpha.org/wiki/Heisenberg_compensator


14 posted on 04/29/2014 10:58:44 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 9 | View Replies]

To: Red Badger

what is Heisenberg cooking these days . . ?
WWWWD


15 posted on 04/29/2014 10:58:54 AM PDT by ▀udda▀udd (>> F U B O << "What the hell kind of country is this if I can only hate a man if he's white?")
[ Post Reply | Private Reply | To 1 | View Replies]

To: mikrofon
But are they really sure they've found a substantial proof?

Of course not. They do know how fast it's moving, though.

16 posted on 04/29/2014 10:59:21 AM PDT by Billthedrill
[ Post Reply | Private Reply | To 11 | View Replies]

To: ├čudda├čudd

HE was cancelled...............


17 posted on 04/29/2014 11:00:20 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 15 | View Replies]

To: Red Badger
Quantum mechanics requires that we devise approximate joint measurements
Theoreticians have it easy.

Just plug in a decimal here or an integer there and keep on keepin' on.



18 posted on 04/29/2014 11:03:18 AM PDT by Bratch
[ Post Reply | Private Reply | To 1 | View Replies]

To: Red Badger
It's Elementary, My Dear Data
19 posted on 04/29/2014 11:03:51 AM PDT by mikrofon ( F[z,x] BUMP)
[ Post Reply | Private Reply | To 14 | View Replies]

To: expat2
I thought this was well-established by mathematical physics long ago.

FTFA

This work is particularly timely and significant since some recent research calls the Heisenberg principle into question.

20 posted on 04/29/2014 11:04:32 AM PDT by E. Pluribus Unum ("The more numerous the laws, the more corrupt the government." --Tacitus)
[ Post Reply | Private Reply | To 5 | View Replies]

To: E. Pluribus Unum

If Heisenberg is right then lasers shouldn’t work.


21 posted on 04/29/2014 11:15:06 AM PDT by Politically Correct (A member of the rabble in good standing)
[ Post Reply | Private Reply | To 20 | View Replies]

To: mikrofon

My favorite episode.....................


22 posted on 04/29/2014 11:20:28 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 19 | View Replies]

To: Red Badger

I’m reserving judgement until I get Sheldon Cooper’s take on it.


23 posted on 04/29/2014 11:33:59 AM PDT by Stormdog (A rifle transforms one from subject to Citizen)
[ Post Reply | Private Reply | To 1 | View Replies]

To: Politically Correct

Heisenberg, Goedel, and Chomsky were having a discussion.
Heisenberg says “we can’t know if it’s a joke”.
Goedel says “of course it’s a joke, but we can’t tell if it’s funny because we’re IN the joke”.
Chomsky says “of course it’s funny, it just hasn’t been told right yet”.


24 posted on 04/29/2014 11:37:12 AM PDT by MrB (The difference between a Humanist and a Satanist - the latter admits whom he's working for)
[ Post Reply | Private Reply | To 21 | View Replies]

To: Stormdog

25 posted on 04/29/2014 11:42:54 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 23 | View Replies]

To: MrB

Two hydrogen atoms walked into a bar.
One says, “I’ve lost and electron.”
The other says, “Are you sure?”
The first one says, “I’m positive.”...................


26 posted on 04/29/2014 11:51:25 AM PDT by Red Badger (Soon there will be another American Civil War. Will make the first one seem like a Tea Party........)
[ Post Reply | Private Reply | To 24 | View Replies]

To: tpmintx

That’s the first thing I thought of.

I am not a deep thinker.

:-)

.


27 posted on 04/29/2014 11:55:40 AM PDT by Mears
[ Post Reply | Private Reply | To 13 | View Replies]

To: Red Badger; 6SJ7; AdmSmith; AFPhys; Arkinsaw; allmost; aristotleman; autumnraine; ...
Thanks Red Badger. I tried to ping this for about five minutes, but the "Post" button kept not having absolute position.


· List topics · post a topic · subscribe · Google ·

28 posted on 04/29/2014 12:45:24 PM PDT by SunkenCiv (https://secure.freerepublic.com/donate/)
[ Post Reply | Private Reply | View Replies]

Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.

Free Republic
Browse · Search
General/Chat
Topics · Post Article

FreeRepublic, LLC, PO BOX 9771, FRESNO, CA 93794
FreeRepublic.com is powered by software copyright 2000-2008 John Robinson