## Proof Mooted For Heisenberg's Uncertainty Principle 158

Posted
by
Soulskill

from the he's-the-one-who-knocks dept.

from the he's-the-one-who-knocks dept.

ananyo writes

*"Encapsulating the strangeness of quantum mechanics is a single mathematical expression. According to every undergraduate physics textbook, the uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle — the more precisely one knows the particle's position at a given moment, the less precisely one can know the value of its momentum. But the original version of the principle, put forward by physicist Werner Heisenberg in 1927, couches quantum indeterminism in a different way — as a fundamental limit to how well a detector can measure quantum properties. Heisenberg offered no direct proof for this version of his principle. Now researchers say they have such a proof. (Pre-print available at the arXiv.) If they're right, it would put the measurement aspect of the uncertainty principle on solid ground — something that researchers had started to question — but it would also suggest that quantum-encrypted messages can be transmitted securely."*
## You keep using that word... (Score:1)

Not to be all pedantic, or anything, but "to moot" something is to debate. If they're mooting a proof, then the proof is very much under debate. /sunglasses

## Re: You keep using that word... (Score:2, Informative)

I too found the title odd

[moot]

- adjective

1. open to discussion or debate

2. of little practical value

## Re: You keep using that word... (Score:5, Informative)

http://dictionary.reference.com/browse/moot [reference.com] says:

verb (used with object)

4. to present or introduce (any point, subject, project, etc.) for discussion.

5. to reduce or remove the practical significance of; make purely theoretical or academic.

So meaning 4 seems appropriate. Strange that a word simultaneously means to introduce it and to remove it from consideration, but it is a pretty old word I think so it has probably evolved quite a bit.

Origin:

before 900; Middle English mot ( e ) meeting, assembly, Old English gemt; cognate with Old Norse mt, Dutch gemoet meeting. See meet1

## Re: (Score:1)

http://dictionary.reference.com/browse/moot [reference.com] says:

verb (used with object) 4. to present or introduce (any point, subject, project, etc.) for discussion. 5. to reduce or remove the practical significance of; make purely theoretical or academic.

So meaning 4 seems appropriate. Strange that a word simultaneously means to introduce it and to remove it from consideration, but it is a pretty old word I think so it has probably evolved quite a bit.

Origin: before 900; Middle English mot ( e ) meeting, assembly, Old English gemt; cognate with Old Norse mt, Dutch gemoet meeting. See meet1

Sounds like "theory" to me. What's with science and ambiguous words? :)

## Re: (Score:3)

http://dictionary.reference.com/browse/moot [reference.com] says:

verb (used with object) 4. to present or introduce (any point, subject, project, etc.) for discussion. 5. to reduce or remove the practical significance of; make purely theoretical or academic.

So meaning 4 seems appropriate. Strange that a word simultaneously means to introduce it and to remove it from consideration, but it is a pretty old word I think so it has probably evolved quite a bit.

Origin: before 900; Middle English mot ( e ) meeting, assembly, Old English gemt; cognate with Old Norse mt, Dutch gemoet meeting. See meet1

Sounds like "theory" to me. What's with :)

the media's reporting ofscience and ambiguous words?FTFY

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Or gravity

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http://www.talkorigins.org/indexcc/CC/CC200.html [talkorigins.org]

http://www.talkorigins.org/indexcc/CC/CC250.html [talkorigins.org]

http://en.wikipedia.org/wiki/Origin_of_the_domestic_dog [wikipedia.org]

http://www.talkorigins.org/indexcc/CB/CB901.html [talkorigins.org]

## Re: (Score:2)

moot; whether it meant "to discuss" or "to dismiss need of discussion." A perfect word for the topic, if you think about it.## Re: (Score:1)

I would say the two meanings come from the same source, but with different spins.

Meaning 4: Needs to go to the moot to be debated: truth still uncertain

Meaning 5: Taken out of current consideration by postponing until the moot (which was an annual event)

I.e. meaning 4 regards the moot as a place where complex things are debated, while meaning 5 regards it as an annual event where a lot of hot air is expended about nothing. Both are probably correct.

## Re: (Score:2)

before 900; Middle English mot ( e ) meeting, assembly, Old English gemt; cognate with Old Norse mt, Dutch gemoet meeting. See meet1

Wow! I finally understand the term Entmoot [wikia.com]. Thanks!

## Re: (Score:2)

Given that Tolkein's day job was as a philologist and etymologist for the OED, I'm moderately surprised that you didn't know by the time you'd finished reading the chapter where the Entmoot starts. Or am I the only person here who first read the book curled up in a chair beside the bookshelves with dictionaries, encyclopedia, etc?

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"So meaning 4 seems appropriate"

4 may be appropriate, but I think it's a thin argument. But even so... so what? Even if 4 is the way it was intended to be used, how is that even remotely headline-worthy?

## Re: (Score:2)

I am not a native English speaker butt..

To me, mooted in the past sense meant some (since irrelevant) argument being leveled.

This puts a lot of things i read/heard in the past into a new (almost the opposite) perspective..

Butt pun intended of course.

## Re: (Score:2)

The joy of English is that it often makes little sense, even to its native speakers (like me). Your understanding of 'moot' is the most common usage, but it can also mean to debate, and a bunch of other vaguely related things.

http://www.merriam-webster.com/dictionary/moot [merriam-webster.com]

## Re: (Score:2)

"Not to be all pedantic, or anything, but "to moot" something is to debate. If they're mooting a proof, then the proof is very much under debate. /sunglasses"

My thought exactly. To moot is to label something debatable, or (perhaps more accurately in context) to make something inconsequential or to render it of no importance.

But I saw nothing in TFA that suggests to me the word "moot". Not a thing.

## Uncertaintiy principle and Foruier Transforms (Score:5, Interesting)

## Re: (Score:2)

If the wave is on for a long time, you get a nice sine wave and the uncertainty in the frequency is low, but the uncertainty in

the timeis now high.What do you mean by "the time"? Duration?

## Re: (Score:2, Informative)

He means the location of the sonic event. If you think of sound as particulate (a series of events a la granular synthesis) then the frequency of each event and the location in time of each event satisfy a sort of uncertainty principle. It's because the FFT of sine * normal curve is sine * normal curve, but the width of the normal curve is conjugate in each case (the limiting case is sine * delta -> sine * 1). This width represents the "certainty" that the actual frequency or location in time is at th

## Re: (Score:2)

Another interesting way to think about it is in terms of seeing if you can figure out where you are in the graph by looking only at the curve. For example, if the frequency curve is a simple blip, you can tell exactly where you are on the frequency axis by looking only at the blip, it's like driving past the Lonely Mountain on the highway. But then you couldn't tell where you are on the time axis by looking only at the curve because the FT of the blip is a sine wave. It would be like driving down a long

## Re: (Score:3)

What do you mean by "the time"?

Frequency (or period, or wavelength) is an inherently non-local idea. It's easy to forget when you're looking at a graph, but mathematically, sine waves are eternal -- they go from t= -inf to +inf. The period is defined such that for all time:

sin(t) = sin(t + period)

If you cut off the sine wave (making a pulse), that's no longer true, and you can't say it has one period (or frequency, or wavelength) anymore. The shorter your sine pulse gets, the less meaningful that single number becomes. Now let's say you

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You mean to say that the frequency spectrum of a finite time duration signal is inifinte, while the frequency spectrum of a signal with infinite time duration is finite.

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There is no uncertainty in the output of a Fourier transform. What you are refering to are the frequency components of the transients. If you flip a switch, there

isa huge amount of non-linearity.Also, a non-noisy Fourier transform is reversible. This is the exact opposite of uncertainty. :)

## Re: (Score:2)

The uncertainty principle is the same as taking a Fourier transform of a sound pulse.

Which explains why one can't be sure if MP3's are music or not.

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The AC just stated this, but I'll expound -- the "Fourier transform" uncertainty you describe comes from the simple mathematics of the basics of Quantum theory and I don't really see a way to refute it if you accept those basics (observables of position and momentum are described by linear operators which don't commute). Heisenberg's uncertainty principle (observation of position disturbs momentum and vice versa) is usually described as limitation in the way we can make observations and as such seemed to b

## Re: (Score:2)

observation of position disturbs momentum and vice versa

That's the observer effect, which TFA seems to be talking about. The observer effect implies that there is an exact position and momentum; particles can be little billiard-balls if we like, but any attempt to measure them will disturb them.

The uncertainty principle, as it is currently understood, says that there is no such thing as an exact position or momentum. Particles are wave-packets in force-fields. When we introduce quantum constraints, eg. the integral of (area under) the wave packet is some discret

## only "discrete" Fourier/Integral transforms (Score:2)

## Re: (Score:2)

This has nothing to do with discrete transforms. "Simple" example: \int_{-\inf}^{+\inf} \delta(x) f(x) dx = f(0)

where \delta(x) is the Dirac delta distribution and f(x) a smooth function (e.g.: exp(-itx)/sqrt(2\pi) ).

This uncertainty is also the cause why every laser has a finite spectral width: even a perfect sinoidal electromagnetic wave must have a length in the time regime which is finite - else the wave would hold an infinite amount of energy.

## Re: (Score:2)

You don't even need a Fourier transform to get an intuition for the principle. Both the Fourier transform and the uncertainty principle are consequences of the Cauchy-Schwarz integral inequality:

http://en.wikipedia.org/wiki/Cauchy%E2%80%93Schwarz_inequality#Physics [wikipedia.org]

So like everything else in physics, it's a consequence of math, not incomprehensible magic.

## Certain uncertainty (Score:1)

The uncertainty principle applies to everything, not just subatomic particles. Just that most of the time the precision required to test it is impossible to achieve (see the wavelength of the Sun for instance). As examples of macroscopic systems where it does apply, see uncertainty relations for the superconducting state.

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The uncertainty principle applies to everything,

How uncertain are you that this is true?

## Yo Yo Mr. White,....... (Score:5, Funny)

Don't fuck with Heisenberg folks.

## Fixed the summary (Score:2, Informative)

measurethe exact position and momentum of a subatomic particle the more precisely one knows the particle's position at a given moment, the less precisely one can know the value of its momentum.Fix.

## Re:Fixed the summary (Score:4, Informative)

## Re: (Score:2)

My fix is valid. The article summary is simply wrong.

The post you link is only a simplified explanation for a lay man (and has nothing to do with heisenberg, it has btw its own name: "Shannons sampling theorem").

## Re: (Score:2, Informative)

Indeed. I don't know what crap "undergraduate textbooks" people use near the north pole, but here down under, the principle of Heisenberg is taught using _math_.

It has always been about measuring (not "knowing", the universe doesn't give a damn about what you know or don't know or it would forbid god from existing. Instead, it just hampers aquiring new knowledge of the full state vector ;p). And it has always been a nice mathematical, strictly quantified trade off between the precision you'll get out of

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Schrodinger and his cat disagree with you.

Just like the cat is in a superposition of states before you measure, so is the particle in a superposition of states before you measure. The particle is

notin a single classical-like state until disturbed by the measurement.## Re: (Score:1)

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and you can teach you grandmother to suck eggs. You are wrong.

"it doesn't say that in theory the particle won't have a specific momentum at a specific position."

Wow, that's not even wrong.

That's not what anyone is saying. You can not measure it's momentum and position with the same measurement, not to be confused with the observer effect.

The theory says its in the fundamental nature of all quantum systems. IN fact, it's in all systems, just the the quantum system i'ts more obvious.

How to you explain your s

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Historically, the uncertainty principle has been confused[4][5] with a somewhat similar effect in physics, called the observer effect, which notes that measurements of certain systems cannot be made without affecting the systems. Heisenberg offered such an observer effect at the quantum level (see below) as a physical "explanation" of quantum uncertainty.[6] It has since become clear, however, that the uncertainty principle is inherent in## Re: (Score:2)

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everything is deterministic, all the properties are exactly determined, it's just that since we are part of the system ( = universe ) it's computably impossible to measure their exact and determined values. It's like godel's incompleteness theorem applied to the universe. We would have to be "out of the universe", know all the data, all the laws and simulate it, in order to have an exact measurement, ot

## Re: (Score:2)

Check chapter 9, (pages 237 and following), of the second edition of

Principles of Quantum Mechanicsby Ramamurti Shankar. Or, section 1.6 (page 18-20) and section 3.5 (page 110-118), of the second edition ofIntroduction to Quantum Mechanicsby David J. Griffiths.I'm sorry that I can't hyperlink to a physical book. But maybe you could go to your local public library and find a copy of one of them.

## Re: (Score:3)

Correct fix: The uncertainty principle states that it is impossible for a particle to be in a state in which both the position and momentum (or any pair of observables represented by non-commuting operators) are exactly defined, or even well-defined beyond a certain limit determinable from the commutator of the pair of operators.

It has nothing to do with measurement, and everything to do with the mathematical existence of quantum states with certain properties. TFA is actually dealing with the observer eff

## Re: (Score:2)

Your definitionis wrong, sorry. Perhaps read it up on wikipedia, or perhaps tze american wikipedia page is wrong, too? ... a moving free electron already falls under the uncertainty principle.

Bottom line it is notmeven about quantum states

## Define "secure" in this day and age. (Score:1)

"...but it would also suggest that quantum-encrypted messages can be transmitted securely."Well, I suppose that would depend on the level of ignorance one carries around when defining "secure".

Somehow, I strongly doubt this will be above and beyond NSA's illegal and highly classified activity to ensure we're all safe from terrorists.

## Just accept QM already (Score:1)

the uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a subatomic particle

I find phrases like this misleading. I think it's more intellectually honest to say something along the lines of:

the uncertainty principle states that position and momentum are not independent quantities, but (incompatible) expressions of a more fundamental property.

Popsci keeps claiming that 'everything we thought knew is wrong' based on the slightest whiff of a strange experimental result, yet when quantum mechanics *does* prove wrong everything we thought we knew (like the concepts of position and momentum), with repeated experiments of incredible precision, popsci clings to those old notions and acts like QM is wacky.

## Re: (Score:2)

I find phrases like this misleading.

John Q Public finds that sort of phrase quickly and easily understandable, which, I would say, are not attributes of your proposed replacement.

## I laughed... (Score:5, Funny)

## Re:I laughed... full version ;) (Score:5, Funny)

Heisenberg and Schrodinger are driving, and get pulled over.

Heisenberg is in the driver's seat, the officer asks "do you know how fast you were going?"

Heisenberg replies, "No, but I know exactly where I am!"

The officer looks at him confused and says "you were going 108 miles per hour!"

Heisenberg throws his arms up and cries, "Great! Now I'm lost!"

The officer, now more confused and frustrated orders the men outside of the car, and proceeds to inspect the vehicle. He opens the trunk and yells at the two men, "Hey! Did you guys know you have a dead cat back here?"

Schrodinger angrily yells back, "We do now, asshole!"

## I just read the article ( arXiv PDF ) (Score:4, Interesting)

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in principleto eavesdrop on (measure) a quantum system without disturbing it.## Re: (Score:1)

Quantum cryptography leans very heavily if it is possible to measure two different attributes of a quanta. For most quantum cryptography the quantum is a single photon and the different attributes:

- horizontal or vertical polarization

- the two diagonal polarization.

It is important that you can only measure either the top two (horizonal/vertical) or the bottom two (two diagonals) but never both.

## Proof is already from 1929 (Score:5, Interesting)

Robertson proved in 1929 already the general form of the uncertainty relation. It has nothing to do with Fourier transforms, wavefunctions and disturbance by measurements, but only with the operator character of (some) quantum mechanical observables. I got the proof from this textbook by Stephen Gasiorowicz, unfortunately they skipped this important result from the latest edition (that circulates on internet in the usual places). More information can be found in https://en.wikipedia.org/wiki/Uncertainty_principle#Robertson.E2.80.93Schr.C3.B6dinger_uncertainty_relations [wikipedia.org]

From Quantum Physics by Stephen Gasiorowicz, ISBN 0 471 29281-8

It is important to note that the uncertainty relation

(Delta A)^2 (Delta B)^2 >= \langle i[A,B] \rangle^2 / 2

was derived without any use of the wave concepts or the reciprocity between

a wave form and its fourier transform. The results depends entirely on the

operator properties of the observables A and B.

## Re: (Score:3)

I find it interesting that there is generally such discomfort with Heisenberg's Uncertainty. I'll grant that its application to quantum cryptography is practical, but for the most part I think this discomfort is rooted in people not liking that something isn't just unknown, but unknowable.

Doesn't bother me a bit - once you accept that idea that quantum mechanics actually does describe reality.

Or another way of looking at it - if you consider all of reality to be a giant simulation, "Aitch-Bar" (Credit for

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unknowable but nor unpredictable. If I know it's movement I can predict* it's location at a latter time of measurement. Of course at the later time I will not know the momentum at that particular time.

*Probably :)

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unknowable but nor unpredictable.

It is as unpredictable as it is unknowable - that is, to a certain degree as defined by the HUP - because prediction requires knowledge. If your knowledge is imperfect, your prediction will be imperfect.

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It smells of learned men believing that while they might not know everything, anything that they don't even know where to start with must be magic. How many times does hum

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Yeah. this all sounds like what we went through one week in my Functional Analysis class back in Grad School circa 1988. Anyone know what is new?

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Ok, here is some mathematical object called a state. What can I do with a state? Well, I can apply linear operators to a state. Given the properties of linear operators, there are some states that are unaffected (up to an overall scalar multiplication) by each operator. Call those "eigenstates". Call one of the operators the "position" operator. Find the eigenstates of the position operator. Now, I can compute, for any given state, how much overlap with each position eigenstate there is as a function of the corresponding eigenvalue. That overlap is a complex scalar function of position, which we can call a wave function, if we like.

It's actually much cleaner to start from this sort of abstraction and define the more concrete "wave function" from it than the other way around, partly because it allows you to more easily consider state spaces that, for example, don't have any operators with continuous eigenvalue spaces, like the spins of the ions in a ferromagnetic lattice, or the excitations of atoms/molecules in laser cavity.

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I believe it was Heisenberg that formulated QM as infinite matrices, rather than waves. And Schroedinger came up with Schroedinger's equation, which is a partial differential wave function.

Then Dirac came on the scene and formulated it all with abstract infinite-dimensional linear spaces, and pointed out that, depending on the coordinate systems you used on those spaces, you could get either Heisenberg's formulation or Schroedinger's.

## Re: (Score:2)

OK, I should have been more clear. Of course it is applied to wavefunctions and measurements, but the derivation of the uncertainty principle can be done completely without those concepts.

## Phrasing (Score:2)

What always struck me about the above statement is it seems to imply that there is an exact simultaneous position and momentum to subatomic particles that cannot be known. Maybe the truth is stronger than that - subatomic particles simply don't have precise position/momentums.

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subatomic particles simply don't have precise position/momentums.

This is exactly correct. Exact position and exact momentum are not properties that a particle may possess simultaneously, no matter how well or poorly you might try to measure them.

## Re: (Score:1)

Yes, the truth is as you explain. Particles don't have precise positions and momentums.

The only way to coherently persuade yourself that they DO have a precise position when you know their momentum is to believe in a global hidden state model of the universe. Basically you say "Oh, the universe knows where exactly that particle is, but sadly that information is stashed outside of our light cone so we can't access it". Which is pretty ridiculous and most physicists agree it's a more ridiculous thing to belie

## Duh... (Score:2)

Everyone knows you need to have good, fully functional Heisenberg compensators, right?

## A Clarification (Score:3)

In the early days, people debated whether uncertainty was just a practical issue of imperfect measuring devices/methods or a fundamental feature of the system.

We now know that it is a fundamental feature. Even if you had a perfect measuring device that did not disturb the system being measured, the act of measuring in any capacity is subject to uncertainty and collapsing of the wave function.

Despite the fact that it seems to violate our common sense (developed at room temperatures with macroscopic physical forces, thus unsuited for quantum reasoning), the world at that tiny level really is probabilistic. It is not a side-effect of our measurement methods or anything else... It simply works that way. Reality as we know it is just a side-effect of all those quantum states interacting and causing wave function collapse... Same reason a quantum computer is harder and harder to make the more bits it has.

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Nope. There is no limit to the resolution of reality, only of the instruments we use to measure it. So stop trying to make others accept your obscurantist idea that there's a limit to what there is to know.

## FINALLY! (Score:1)

They ended up recognizing the fucking difference between the limitation of the INSTRUMENT and the precision of REALITY.

Took long enough. We're living in interesting times.

## Re:That's nice (Score:5, Funny)

Yet another proof of the principle.

Now let's see what the cat has to say about it.

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My guess would be 'miaow'

Only if it's still alive when you open the box.

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But before you open the box the answer is "Miaow" as stated by the GP.

The cat being both dead and alive both makes the sound and does not.

Therefore the sound is definitely heard.

Of course if you listen for the miaow then you are in fact making a measurement. :)

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Just because something emits a sound doesn't mean you can measure it.

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If you hear it then you've measured it.

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## Re: That's nice (Score:2)

Oh wait, the cats dead. Or is it?

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Is the box in the shape of a hat?

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Oh, open the goddamned box already, ferchrssakes.!

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## Re: That's nice (Score:5, Funny)

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## Re:That's nice (Score:4, Funny)

I'm more confused than before

Just look in this box. In it, you'll find either a better summary or a dead cat.

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https://en.wikipedia.org/wiki/Marie_Curie [wikipedia.org]

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Haha dude, you seriously need to hang around with more laid, back chicks!

fixed.

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If they try to do the measurements at the same time, they will disturb each other's measurement.

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Because the only thing that relativity changes in respect to the uncertainty relation is is that the velocity is no longer proportional to the momentum, so you cannot say "velocity" instead of "momentum" here (in particular, the uncertainty relation also holds for the photon, but that doesn't change the fact that the photon goes exactly with c, because for photons a momentum uncertainty does not translate to a velocity uncertainty). But other than that, relativity doesn't add anything relevant to the uncert

## Re: (Score:1)

Ah,. now I get how you got relativity in. Well, if we measure the same particle, we necessarily do it at the same location, and the relativity of "same time" only happens for measurement on different places; more exactly, for spacelike intervals. Operators belonging to spacelike separated points commute, and therefore there's no uncertainty relation between them (well, formally there's the uncertainty relation with >=0, but since on the left there are only nonnegative quantities anyway, that inequality d