Violation of Heisenberg's Uncertainty Principle

mbone writes "A very interesting paper (PDF) has just hit the streets (or, at least, Physics Review Letters) about the Heisenberg uncertainty relationship as it was originally formulated about measurements. The researchers find that they can exceed the uncertainty limit in measurements (although the uncertainty limit in quantum states is still followed, so the foundations of quantum mechanics still appear to be sound.) This is really an attack on quantum entanglement (the correlations imposed between two related particles), and so may have immediate applications in cracking quantum cryptography systems. It may also be easier to read quantum communications without being detected than people originally thought."

Comments

Insert Breaking Bad Joke Here

[Anonymous Coward]

Let's just get all the Walter White jokes out of the way...

I have the fix

[Anonymous Coward]

I learned about it on the factual science TV show (currently honored on Google.com), Star Trek. They need a Heisenberg compensator.

Re:I have the fix

[feepness]

It's *decouple*. And now I'm disgusted by both of us.

Re:Magic

[Seumas]

This is exactly how I feel when it comes to quantum-anything. Especially quantum-computing, which leaves me looking at papers on it the way my cat looks at me when I ask him to do my taxes. It's one of the best examples I've encountered of anything sufficiently advanced enough being indistinguishable from magic.

Re:Magic

[rossdee]

Back in the day we didn't have Quantum Computers, but we did have Quantum hard drives. You were never certain when they were going to fail

Argh science journalism.

[Phanatic1a]

This article is horrible.

"The Heisenberg uncertainty principle is in part an embodiment of the idea that in the quantum world, the mere act of observing an event changes it."

That's not the Heisenberg uncertainty principle. That's just the observer effect, and it's not something peculiar to quantum mechanics. You want to measure the temperature of a system, so you stick a thermometer in there. Okay, the mercury in the thermometer absorbs a bit of heat from the system, providing you with a temperature measurement at the same time it changes the temperature of the system. If you want to measure the parameters of a particle, you stick a bubble chamber in the way, and as the particle flies through the chamber it smacks into hydrogen molecules, showing you what it's doing but also taking a different path than it would have if none of those hydrogen molecules were in the way. Big fat hairy deal.

The HUP doesn't just say that you can't simultaneously measure the position and momentum of a particle, it says that a particle *does not simultaneously possess* a well-defined position and momentum. If the particle's doing something in a system and is interacting in such a way that you can define its position to arbitrary precision, then it *does not have* a well-defined momentum for you to measure, and vice versa. Position and momentum are what are called quantum conjugate variables, and the HUP says that when you have a pair of those variables, then the product of their uncertainties is greater than or equal to a constant. There is *no state* in which that particle is even *allowed* to exist in which it possesses both a well-defined position and well-defined momentum.

A signal processing analogy, for any analog people. A particle's wavefunction carries information about its position and its momentum. Where the wave exists is where the particle actually is, and the wavelength is the particle's momentum. Take a particle whose momentum you know to the utmost precision, and graph that. Range of momentums on the x axis, probability of the particle having that momentum on the y axis. You'll get a graph that looks like a Dirac function, a value of 0 everywhere except for a single spike corresponding to the particle momentum, area under the curve of 1.

Now switch domains, change from the momentum to the position domain, this is mathmatically the same thing as changing from a time domain to a frequency domain, which means you can use your old friend the Fourier Transform.

What do you get when you do an FT of a Dirac function? You get a constant value everywhere, from -infinity to +infinity. If you know exactly where that particle is, you have no idea *where* it is, and it's not because you disturbed it in measuring it, it's because *it* has no idea where it is, a well-defined position does not exist; since the uncertainty in the momentum measurement approaches zero than the uncertainty in the position measurement has to approach infinity so that the product of those uncertainties remains greater than a constant.

The "you change the system by measuring it" is an analogy, and it's one that Heisenberg himself used to explain the HUP, but *that is not what it says*. The HUP is not a statement about the process of measuring things, it is a statement about the nature of the universe, and finding a way to improve a measuring system to reduce the disturbance it creates in the system it's measuring has nothing to do with the HUP.

Re:Argh science journalism.

[SoftwareArtist]

While the article is terrible, the actual paper is very clear about this. There are two different things that are commonly referred to as "the Heisenberg uncertainty principle". One refers to the intrinsic properties of a wavefunction and the impossibility of being in an eigenstate of two noncommuting observables. The other - which is what Heisenberg originally proposed - refers to the fact that performing a measurement alters the state of the thing being measured. Many people, including the authors of quantum mechanics textbooks, frequently talk about these as if they were equivalent, but they aren't.

Here's the first paragraph of the paper, which lays all this out very clearly:

The Heisenberg Uncertainty Principle is one of the cornerstones of quantum mechanics. In his original paper on the subject, Heisenberg wrote “At the instant of time when the position is determined, that is, at the instant when the photon is scattered by the electron, the electron undergoes a discontinuous change in momentum. This change is the greater the smaller the wavelength of the light employed, i.e., the more exact the determination of the position” [1]. Here Heisenberg was following Einstein’s example and attempting to base a new physical theory only on observable quantities, that is, on the results of measurements. The modern version of the uncertainty principle proved in our textbooks today, however, deals not with the precision of a measurement and the disturbance it introduces, but with the intrinsic uncertainty any quantum state must possess, regardless of what measurement (if any) is performed [2–4]. These two readings of the uncertainty principle are typically taught side-by-side, although only the modern one is given rigorous proof. It has been shown that the original formulation is not only less general than the modern one – it is in fact mathematically incorrect [5]. Recently, Ozawa proved a revised, universally valid, relationship between precision and disturbance [6], which was indirectly validated in [7]. Here, using tools developed for linear-optical quantum computing to implement a proposal due to Lund and Wiseman [8], we provide the first direct experimental characterization of the precision and disturbance arising from a measurement, violating Heisenberg’s original relationship.

Uncertainty

[Nkwe]

So the paper says we are not sure about the uncertainty principle?

Re:Magic

[N7DR]

Bearing in mind that it's generally an error to try to summarise anything about quantum mechanics in a paragraph or two:

Actually, it's the equivalent of finding socks in the dark. If two photons are produced by an interaction of spin zero then the two photons will have spin up and spin down, although you can't know which is which without measuring one. .

I'm sorry,. but the way you write that makes it seem that they have spin up and spin down, and then you measure them to find out which is which. If that's indeed what you meant, I'm afraid that's fundamentally incorrect.

The whole point about the weirdness of quantum entanglement is that the quanta are NOT in a state where one is up and one is down prior to the measurement. Only when you make the measurement does this happen. Prior to the measurement, quantum mechanics says that they are both in a state that is BOTH up and down at the same time.

In other words, quanta are not like socks. We can be reasonably sure that socks' measurable properties are fixed before we actually look at them. Not so with quanta.

You can think of this in this way: when you make a measurement on one of the quanta, it flips a coin that tells it whether to be up or down. Its twin quantum is then bound to give the opposite result. But prior to the coin toss, neither quantum knows how it will respond to a measurement. The most that can be said is that whatever the result of measuring one, the other will give the opposite result.

Re:Magic

[aBaldrich]

This has been tested experimentally. http://en.wikipedia.org/wiki/Bell_test_experiments