# Uncertainty in quantum mechanics

If I understand the principle correctly, the more accurately one measures a particle’s position, the more one disturbs its velocity, thus lowering the accuracy of the measurement of velocity. IOW, the more accurate one measurement is, the less accurate the other will be.

Doesn’t that just mean, then, that there will always be an amount of uncertainty in our knowledge about the particle’s position and velocity at any moment, not that the particle is in some sort ghost-like state where its position and velocity don’t have definite values?

They don’t call it the Uncertainty Principle for nothing.

Lobot:

Yes, you hit on it exactly. You can think about it this way. In order to measure it’s position you have to hit it with something, say a photon. But that photon will then affect it’s velocity.

QM is NOT intuitive. We simple have no physical experience to draw upon when dealing with things on the QM scale.

True on the notion of experience - but QM has a sense of logic that is quite understandable. QM didn’t appear so at first simply because the scale was so alien. The Uncertainty Principle is quite sensical. Do note that intuition is about insight, rather than simply extrapolating practical experience.

[quote]
not that the particle is in some sort ghost-like state where its position and velocity don’t have definite values?*You are putting the cart before the horse somewhat. It is wave-particle duality which is behind the “observation” (ie. “collapse of the wavefunction”) of a body. The momentum and position have indefinite values before this observation. Heisenberg’s Uncertainty Principle governs the observation itself.

We think that until a particle interacts, its position and momentum are not only unknown but undefined. Not completely undefined, of couse, but it’s a probability distribution rather than a definite value. The classic demonstration is the double slit experiment where two slits are set up between a light source and a screen. Since light acts like a wave, the light that passes through the two slits interact and create an interference pattern on the screen. Now, you reduce the light source intensity until you get, say, one photon per second, and use a high sensitivity film in place of the screen. You’d find out that you still get a diffraction pattern. Since only one photon at a time comes out of the light source, it must be going through both slits and interacting with itself. So we think that until the photon is detected by the screen, it travels as a probability distribution, in effect going through every possible path.

Most QM textbook address that very question, since it is very common. The textbooks disagree with you. They explicitly state that the uncertainty principle does not reflect a shortcoming of our knowledge, it is the way nature works. Then they go on to give some supporting evidence.

Whether or not you agree with the textbook orthodoxy is another matter.

Skeptico has it right. One way of thinking about it is:

Not only does the uncertainity principle limit our knowledge of the properties of a particle, it limits the ‘knowledge’ that other particles can have about that particle too.

One of the things that QM and Relativity made me realize (warning - this is bordering on IMHO) is that Events and Observers are interlinked and not independent. Both effect each other. In simple words you always see what your eyes want to see - but that may be stretching it too far.

Let me be the dissenting opinion here. It is conceivable that particles do, in fact, have both definite position and definite momentum, but that those values simply aren’t measureable. But one must then ask what it means to say that the momentum has a definite value, when it can’t be measured by any means whatsoever. Either interpretation yields the same predictions for measurements, though, so it doesn’t much matter, as far as science is concerned, which interpretation is correct.

Chronos, what about zero-point energy? Also, how can something be both definite and unmeasurable?

http://www.hawking.org.uk/lectures/lindex.html

Chronos already acknowledged that “one must then ask what it means to say that the momentum has a definite value, when it can’t be measured by any means whatsoever”. I suppose you have obeyed his command.

My objection to Chronos’ statement that “It is conceivable that particles do, in fact, have both definite position and definite momentum, but that those values simply aren’t measureable”.

If this is conceivable, how can a single particle interfere with itself in the double slit experiment? Unless, by “definite” you mean it falls into a well defined probability wave function, which I would in turn call “uncertain”. Am I misunderstanding?

Right – I was in essence taking issue with his first statement, that one can in fact conceive of a particle having definite position and momentum, i.e. that the word definite is contradicted by the word unmeasurable.

However, my real question is with regard to zero-point energy, which is a physical manifestation of uncertainty in a particle’s momentum due to localization of its position. No direct measurement is being made – the uncertainty in the momentum is not just a lack of knowledge about the momentum the particle happens to have, but is a physical increase in the average kinetic energy of the system.

Chronos,

Every reference to Bell’s theorem I’ve seen (well, except the ones that use it to validate telepathy and suchlike) says that if you assume 1) Quantum Mechanics, 2) Objective Reality (hidden variables), and 3) Local Causality, then you arrive at a contradiction. The usual conclusion is that Objective Reality must be abandonded. How do you reconcile Bell’s result with your post which, to me, seems to imply that you believe that there are hidden variables?

Thank you for the replies, everyone! Very helpful.

Actually, yes, the double-slit experiment is partly what had me confused, because the uncertainty principle, as I understood it, really only applied to how our knowledge is limited. However, the experiment seems to show otherwise.

Doesn’t this then suggest that particles are actually better described as waves, or are there times when it is still more appropriate to view them simply as particles?

(I realise this touches on wave-particle duality, but I don’t fully grasp this aspect.)

Chronos post doesn’t imply a belief in hidden variables–just that there could be hidden variables.

It is true that your #2 is the one usually thrown out, but then it was thrown out long before Bell’s theorem and its tests. That is what is known as the Copenhagen interpretation, and von Neumann thought he’d proven that hidden variables couldnt’ exist. Bohm disproved von Neumann.

Why not throw out #3? The experimental tests have shown that quantum entanglement is not local, so #3 doesn’t really work anyway, in that sense.

Lobot – regarding describing photons as waves or particles, remember that ‘waves’ and ‘particles’ are just two different mathematical models that we like to use because they’re simple. But there’s absolutely no reason that an object in the world has to correspond to one of those models.

In other words, asking whether a photon is a wave or particle makes as much sense as asking whether a honeycomb cell is a square or circle, or maybe better yet asking whether the outline of North America is a square or circle. Or asking whether Magic Johnson was a guard or forward, if you’d like a different analogy. They are what they are, and we just try and describe them, using simple terms.

Actually, I think you might understand it :

Exactly, and there are times when it’s more appropriate (i.e. useful) to view them as waves.

And there are times when both must be considered.

DrMatrix, I was about to post in essence the same explanation as to “hidden variables,” but, while I understand that it has been shown to be a contradiction, I dont understand it. The cites I have seen for this dont provide an explanation of it, either.

Do you have a cite for a scientific explanation of the contradiction?

(an interesting side note: if you posit absolutely no hidden variables, this disproves the Pantheistic interpretation of the Ontological Existence of God, since the universe is then not omniscient! But thats more GD territory)