Heisenberg Uncertainty Principle

Heisenberg was a physicist who realized that one can not discover both the momentum and position of a sub-atomic particle. Measuring one affects the other and both may not be measured simultaneously. This means that one will always be uncertain about the exact properties of a sub-atomic particle.

I'm not an expert, but isn't the reality (if that word applies at the quantum level) that these particles actually do not have a measurable instantaneous momentum and position pair. It isn't that measuring one changes the other, but rather that there is no measurement to be made.

[Correct. The first theory described on this page is the HeisenbergCouchCushionPrinciple.]

That rings a bell. Didn't RichardFeynman suggest that Heisenberg's principle as usually stated is required only if one is trying to understand quantum phenomena using a classical vocabulary? And that if one abandons classical thinking and proceeds by his path-integral method then the uncertainties in measurement arise automatically. So, Heisenberg's principle correctly identifies incompatible quantities, but leads people to muddy their mental waters by reverting to some classical notion of measuring hidden "absolute" quantities.

Way before Feynman, Heisenberg deduced this inequality from his alternative formalism for quantum theory in 1925, "matrix mechanics", which later turned out to be mathematically equivalent to Schroedinger's "wave mechanics" which arrived a year later. The formula provides absolute limits on how clearly position and momentum can be defined simultaneously, whether they're "measured" or not. And "reality" surely does apply to the phenomena described by Schroedinger's equation, just as Maxwell (or any other nineteenth century physicist) would have considered his electromagnetic equations to refer to "reality". In both cases, the reality concerned has been increasingly uncovered and confirmed by vast numbers of experiments. -- RichardDrake

Do you know the third theory that was found mathematically equivalent to wave mechanics? IIRC, Feynman's sum-over-histories theory is not equivalent to wave mechanics. Personally, I think the HUP is complete nonsense; does anyone have any recommendations for books that explain modern concepts like quantum entanglement and mutual unobservables without resorting to magical thinking and "duality of light" BS? -- RichardKulisz

I think that you are thinking of JulianSchwinger?'s model, but I'm not sure. If memory serves, that proved to be a sub-set of QuantumChromoDynamics?. - JayOsako

The mathematics of quantum mechanics doesn't have any duality built in; particles are just field quanta, i.e. waves, all of the time. So all you have to do is explain why they show up like particles in certain experiments, right? I think multi-universe does this fairly well; observers interacting with superpositions go into superpositions (just like other fields would) with different slices of the observer corresponding to different particlish states. Does that count as magical thinking, even though it goes more or less from the premises?

Or as JohnPolkinghorne's T-shirt has it, EpistemologyEntailsOntology - a WikiName to dream of?

It seems to me that what we really need to do is discard the usual terminology of 'waves' and 'particles' entirely. Funny thing, I thought that was exactly what was being done in the 1920s... but the old terms reappeared because most people couldn't get a suitable mental model for matrix mechanics. -- JayOsako

A Doctor Writes: Particles are just field quanta - just waves. Yep. The waves come in short pulses because they are generated by short-term events (decay of energy level.) And I mean short pulses. That's partly why they look like particles. The other reason is that many of them have very high frequencies (high energies.) So it's all waves. If you insist on interpreting it as particles, then you can try to measure the "position" but there isn't one. That's HeisenbergUncertaintyPrinciple in a nutshell. You get a random answer because you're misinterpreting the real answer. Try measuring the position lots of times, and you'll slowly, statistically build up a picture of the real thing: a wave. Wave functions don't collapse.

This theory is often used in connection with super-atomic events or objects. This is not accurate however because it is possible to measure both momentum and position of large objects. Sometimes it is difficult to imagine how, but enough money and thought will eventually solve the problem. Heisenberg *proved* that this was not the case with the sub-atomic world. -- BryanDollery

It isn't possible to measure the exact momentum and position of large objects. The matter wave, however, is absorbed in the error in measurement, so we don't notice. On another note, IBM once published an article on "Hungarian Ghoulash and Matter Transportation" which described how to measure the exact momentum and position of a proton. Link anybody? IBM seems to have lost it in their great rewebbing.

A large (bigger than a handful of molecules anyway) object travelling in sunlight over a piece of paper will have its speed constantly affected by the bombardment of photons and air resistance. It is possible to measure the position and speed of its shadow without actually adding any additional energy to the object. Therefore the matter wave isn't absorbed in the error in measurement because it never interacts with the object. Given an error free measurement device (which may be impractical but probably not impossible) one would have the position of the object. Two such measurements over a short distance would at the second measurement give the speed and position at the time the speed was recorded. Therefore it is *possible* to accurately measure the speed and location of a large object without affecting either.

Just not exactly accurate. There exists a positive lower limit to the error in such a measurement. The fact that photons are striking the object in this example is the flaw in the example. Regardless, no matter what measurement method is used (photons, neutrinos, whatever), there is a lower limit to the error in that measurement. See the paragraph*.

Careful, the fact that we have to bounce particles off something to measure it is not what is responsible for the HUP. If they had some sort of position and momentum to find interference wouldn't work. In fact, I think a while ago some people came up with a way of measuring something without disturbing it - anyone remember that SciAm? Of course, HUP still applies even then.

If you're talking about Non-Destructive Measurement then it does allow a way around the HUP. NDMs are premised on an object being in only one of a finite set of positions and testing all of the wrong positions to find out the object isn't there. Done successfully, you know where the object must be without having disturbed it.

I think that's what I'm talking about... I don't remember it very well. But being able to take a measurement without disturbing something isn't good enough to get you around the HUP, since that's not was causes it in the first place. What causes it is the fundamental wave-ish nature of the particles, which don't have precise parameters to measure.

Wait a second. This NDM you're talking about is another example of a QuantumMisunderstanding?. How exactly do you know that the object is in one of two positions? Why because its wave function specifies two positions. But as soon as you detect that the object isn't in one of those positions, you've collapsed the wave function, so you have disturbed the object. The Feb 2001 issue of ScientificAmerican has an article called 100 Years of Quantum Mysteries by Max Tegmark and John Archibald Wheeler that deals with this very subject. It ought to clear up a lot of the misconceptions floating around. -- RobHarwood

Two things to keep in mind, though. First, collapsing the wave function is something that only takes place within the CopenhagenInterpretation, and so the procedure need not be interpreted as disturbing the object. Second, no matter how you look at it, this is very little like the bounce-photons-off-it-type disruption that most people refer to, and I think it wouldn't be too good to pretend the two effects were at all related. I'm simply reiterating that because the point that disruption is not what causes the limitations imposed by the HUP, but rather the underlying reality we are looking at, is important. -- JoshuaGrosse

But we're talking about quantum mechanics, so what 'most people refer to' doesn't really count. After all, most people don't think of an object as a wave-function that can be in two places at the same time. If you want to debate the underlying reality, I'm afraid nobody really knows for sure so it won't be much of a debate. I concede that 'striking the object' is wishy-washy, but then so was the point I was refuting.

"After all, most people don't think of an object as a wave-function that can be in two places at the same time." -- seems like most people get it right ;)

An object is not a wave-function. The system as a whole (including an object, a piece of paper, photons, air molecules and, of course, an observer) is. --NikitaBelenki

BellsInequality possible consequence 2 implies that the HeisenbergUncertaintyPrinciple is fundamental to the universe and not just some artificial limitation.

Although the more general principle that "Observing a thing changes it", is not strictly speaking Heisenberg's, it is nevertheless useful and deserves a name.

Yep, like all QuantumAnalogies?, this one can be used and abused. Which no doubt is rich coming from the "wooly thinker" who wrote the first line of WikiUncertaintyPrinciple. The reason I enjoyed TheQuantumSelf so much was precisely because of its daring use of such analogies in respect of human identity, personal responsibility, "realistic" psychotherapy (ie anti-Freudian and other self-obsessed approaches), intimate relationship and community. Even if the book is lousy science (which I'm not at all sure that I concede), it's a great kick in the teeth for the fatalistic individualism that does appear to have been spawned in the social arena by the now discredited mechanistic and atomistic Cartesian/Newtonian world view. -- RichardDrake

The effect can be observed at a macro level - a new plastic garbage bag has no open end until it is inspected, at which point the other end becomes open.

Similarly, DB-9 and DB-25 plugs are not polarized until you try to connect them to a socket, at which point they become polarized opposite to the way you are trying to plug them in.

Toast is similar in that the moment it leaves your plate then each side of toast becomes neither buttered or unbuttered, but the moment it hits the floor the wave function collapses and the butter is on the bottom. Either that, or God does not like me, personally.

Toast falls buttered side down because the height it typically falls from (just above 1 meter) allows it to make half a revolution but never a full revolution.

If your toast does happen to fall butter side up that is because you buttered the wrong side. Next time do it right.

The Heisenberg Inequality of quantum mechanics (position times momentum is greater than a fixed, non-zero lower bound) has analogs in several other fields. Radar engineers speak of the time-bandwidth product (time duration of a radar pulse times its half-height bandwidth in the frequency spectrum), which is bounded away from zero for all radar systems. The Nyquist bound of a communication system governs how much information can be transmitted in a given time interval.

This looks like the best place to add this.

I never really understood the Heisenberg Inequality until I ran across it in information theory. It turns out that what Heisenberg actually proved is a simple mathematical result, that if you take any signal, its localization in time times the localization of its Fourier transform has an absolute minimum that you cannot go below. (That minimum is achieved by a bell-curve.) This purely mathematical result about Fourier transforms says something about physics when two physical properties (eg position and momentum, or energy and time) are related to each other by a Fourier transform.

I cannot honestly claim that I really understand the HeisenbergUncertaintyPrinciple now that I have learned how the it limits what wavelet transforms of sampled data can do. But at least I know that I am misunderstanding something different than I thought I was misunderstanding before. :-)

-- BenTilly

Heisenberg Paradox: I have a subatomic particle. I put it in a chamber with a device which measures its exact position and one which measures its exact momentum. I have one of these activate, randomly selected based on measuring the spin of an electron with indeterminate spin. They both display their output on a screen on the side of this setup. I leave the room, and the whole thing occurs. Until I walk into the room, both the position and the momentum of the particle have been measured.

This is simplistic and inaccurate.

Shouldn't the statement be: "Until I walk into the room, both the position and the momentum of the particle have been both measured and not been measured."?

That is even more inaccurate. If anyone can grow up to President, why can't me and my best friend grow up and be President together?

But there is a more subtle misconception too, because the uncertainty principle is not strictly about how precisely you can measure, but about how repeatable any precise measurements are. If both your detectors run together, they both produce precise numbers on the screen - Heisenberg does not come out with a big hammer and wreck the display panel!

Let's set up both pieces of kit to work every time, then both screens will display an answer, a precise measurement of the subatomic particle. It is quite possible to get an exact measurement of both quantities at once, in the sense of a very long decimal displayed on a screen. The uncertainty is that those values will not be repeated if you make the same measurement of the same particle again.

So lets change the experiment again, so that each device makes three very precise measurements, and so the position device always works, but the momentum is only sometimes measured. Possible outcomes are either three identical measurements of position, or three different measurements of position and three different measurements of momentum.

Until you walk in the room, the three numbers on the position display are all the same and are all different. -- RiVer

What is an "exact" position and what is an "exact" momentum? Try to answer that question and you will begin to understand the impossibility of measuring these things.

Take as a 'very precise' measurement of both position and momentum a pair of measurements that appears to be more precise than the HUP allows. Those measurements can indeed be made to that precision, but the catch is that if you repeat the measurements you are very likely to get different results. You can measure as precisely as you like, whether that means anything is philosophy not physics because beyond the HUP limit your measurements are not repeatable.

And the classical mechanics view I think it behind the "exact" statement about doesn't lead to impossibility, either (it does lead to a considerations of limits etc, but classically exact momentum and position are perfectly well defined

[This section mixes up quantum entanglement and the uncertainty principle. First for the entanglement: the wave function of the whole apparatus collapses by interaction with many particles outside the apparatus. You cannot prevent this, for whatever you do, you cannot shield gravity. The bigger the system the faster its wave function collapses. So walking into the room doesn't change anything, the observer is completely irrelevant and anyone who starts sentences with "Until I walk into the room" is megalomanical.

Back to the uncertainty: it's not about measurement, it's about what is there that could be measured. The particle in question cannot even have precise momentum and position. You can set up your experiment so that the position is essentially precise, but then the momentum will be completely undetermined. You are implicitly doing this whenever you try to measure position. Likewise you can fix momentum and information about position will be lost. These two are also a completely insufficient description of a particle.]

it turns out that a universally complete understanding of both metaphysics and quantum mechanics is not possible by a single individual-- it's either one or the other, but never both at the same time. ;-) [copied from personal page of CarstenKlapp]

A disk, rotating at a speed alpha rad/s. Mark a point on the disk. Plot the vertical position of the point. A sine wave, no?

Let's say we don't know exactly what alpha is. Alpha +/- Delta. As we proceed from a known initial state, our "point on the disk" becomes spread out. Plot the average of its vertical location. After enough rotations, the initial position is smeared evenly around the disk. We get the classic "wave packet" trace. The greater that delta is, the more bunched-up the wave packet.

If we know exactly what alpha is, we get a wave-packet spread over infinity. If we know exactly the "location" (a single spike), we get a fourier transform spread evenly over infinity. Between these two extremes, the uncertainty in location and the uncertainty in frequency vary inversely.

This is somewhat different from the physical Heisenburg uncertainty principle, since it still relies on a point having a location to know exactly, but is closely related. In general, the smaller support a function has, the larger its Fourier transform must have. All the rest are just special cases of this.

The play Copenhagen (which was very interesting and entertaining, btw) shed some light on the two versions of the HUP. Apparently, the explanation Heisenberg originally came up with, and published, was the one about measurements affecting the underlying reality of the object in question. The other explanation, about complimentary aspects of particles, was suggested by Bohr and made it into the paper as an addendum. Apparently, not many people paid much attention to it initially, which explains how common the former explanation is.

CategoryPhysics