Uncertanity Principle

Every time I’ve seen it explained, the only impossibility mentioned is that of measuring both speed/direction and position accurately. Still, people use it as if quarks can’t even have a precise position and speed/direction.
Now, I won’t claim to have anything more than a basic understanding (or maybe not even that) of quantum mechanics, but I’ve never seen anything resembling a convincing argument as to why quarks can’t have both these.

Who’s wrong, and why?

The uncertainty principle states that certain observables cannot both be measured with infinite precision. If you know the exact position of a particle, you cannot know anything about it’s momentum. This is usually expressed, mathematically, as the product of the uncertainties of the two pairs being proportional to a constant (Planck’s constant). But there are other uncertainty “pairs” as well-- Energy and time, for example.

BTW, “speed” isn’t quite right, but you could use “veolcity” instead of momentum. Veolicity is a vector quantity-- it contains information about direction as well as speed.

You’re still speaking solely of measurement, as far as I can see. Insufficient measurement alone doesn’t allow for actual chance.

If I understand the question right, you’re asking which of these two interpretations is correct:

  1. Quantum objects have a definite velocity and a definite position, but in attempting to measure either, we disturb the either.

  2. Quantum objects don’t have a definite position and a definite velocity, and the lack of definiteness in both is described in a certain relation.

I’m not an expert, but my understanding is that 2) really is the right answer, and it’s just a property of quantum objects. I’m not sure there’s any a priori reason why it should be so, but that’s the way iti .s

It’s not that the quark has a specific position and velocity that you can’t measure. It’s that it doesn’t have a specific position and velocity – which is why you can’t measure one.

That is, the uncertainty principle applies to the quark’s reality (leaving aside QM interpretation questions) rather than to the process of measurement.

Or maybe you’re asking why that’s true…

Ugh, I’m guessing this would require rather a complex explanation.
By the way, I should perhaps add that in reading about this, I’ve seen good explanations as to why measurement disturbs position/ velocity and thus you cannot get them both right. If velocity/ position is indefinite, why make a point that measuring one makes the other even more indefinite? It also does sound like you actually can measure one quite definately.

I’d love to hear as complex an explanation as anyone would care to give, by the way. I’m just a bit worried I might not make much sense out of it. But hell, I’m sure I’ve had worse, so if anyone has any time to waste, enlighten us!

This topic gets hashed out about every six months. You might try searching for other threads on point.

What it basically comes down to is this: quantum objects just aren’t like classical objects. There’s a mathematical theory that describes very well what they do and how they interact with each other, but it doesn’t translate into intuitive plain English the way that, say, Newton’s equations do.

Spin is a good example of a quantum property that has no intuitive meaning. It works in the theory, but there’s nothing else you can say about it to make it make more sense.

Almost. #1 is the wrong answer, although it is often used to illustrate the uncertainty princple. #2 isn’t quite correct, although it’s close. If we could measure position with infinite precision, we’d have no idea where and how fast the thing was going. In practice, though, we can’t measure anything with infinite precision, so it’s kind of a meaningless statement. In principle, though, there is nothing inherent in QM that says we cannot know the position of a particle with any arbitrary level of precision. It’s just that as that precision increases, so does the knowledge of its velocity decrease.

Frankly, I’m not sure what the OP is asking, since I’ve never heard anyone state it that way. Is there some reason the OP is using “quark” instead of “particle”? And just to be clear, phsycists speak of “particles” even though we don’t think they’re tiny little balls, like miniature golf balls or something. We don’t really know what they are, but “particle” is the word that is used.

There is also a principle in QM that states that no two particles can occupy the same quantum state. Maybe that’s what the OP is thinking…?

People tend to confuse the uncertainty principle and the observer effect. It’s true that you can’t make a measurement without disturbing the measured system – but that’s not the reason why you can’t simultaneously measure the exact position and exact momentum of a quantum particle. You can’t measure them because a quantum particle doesn’t have an exactly defined position and an exactly defined momentum at the same time, and that’s what (that version of) the uncertainty principle says.

As for why scientists are convinced that a quantum particle doesn’t have a precisely defined position and momentum, it’s because this is what quantum mechanics tells us, and quantum mechanics is a theory that makes many predictions which are confirmed by experiment. Essentially, quantum mechanics claims that a quark (for example) isn’t really a classical particle, but instead is something more like a wave packet.

Think of a wave extending forever in both directions. It has a precisely defined wavelength, and thus a precisely defined momentum. (In quantum mechanics, momentum is just Planck’s constant divided by the wavelength). However, it doesn’t have a defined position (since it extends forever in both directions.)

You can add several waves with different wavelengths together in such a way that their sum becomes more and more bunched up with each wave you add. (See the link above, and this one). Thus, its position is more and more precisely defined. However, its wavelength gets less defined, since you keep adding waves with different wavelengths.

If you could add infinitely many waves together, this “wave packet” could be made so tightly “bunched up” that it would look like a single spike. (Such a spike is called a Dirac delta function.) Now the position is precisely defined, but the wavelength is completely undefined (since the spike is the sum of infinitely many waves, each with a different wavelength).

So you can either have an exactly defined wavelength/momentum, but a completely undefined position (the case of a single wave with fixed wavelength), or you can have an exactly defined position but a completely undefined wavelength/momentum (the Dirac delta function), or you can have something in between, where there is some uncertainty in both position and momentum (the wave packet). But you can’t have an exactly defined position and momentum at the same time.

Quantum mechanics (which, as I said, is well-confirmed by experiment) tells us that quantum particles behave like wave packets, and thus have this property of uncertainty. (In fact, even macroscopic objects have it, but the effect isn’t noticable because Planck’s constant is so small.) And it is uncertainty of this sort, not any claim that “the observer affects the observed” which is the essence of the uncertainty principle.

I thought quarks was the fuzzy bit. But particles it is, then. And ultrafilter got the question right.
Well, now that I’ve gotten the question answered directly, I’m one step closer to surrendering. It makes sense that it doesn’t make sense, though. Monkeys probably couldn’t grasp evolution, why would we, a step up, grasp (intuitively, that is) quantum mechanics?

I should add that of course there are lots of practical reasons why you can’t measure the “exact” position or momentum of a particle, but the point is that even in principle position and momentum can’t be simultaneously measured to arbitrary precision. And in fact the more precisely you measure one, the less precisely you can measure the other.

One other point I left out of my above explanation for the sake of simplicity (but include here for the sake of completeness) is that by performing a measurement you can change the wavefunction of the particle, so if you want to measure the particle’s position really precisely you can force the wavefunction to become “more bunched up”, causing the particle’s position to become more precisely defined and its momentum to become less precisely defined. (Likewise by precisely measuring momemtum you can cause the wavefunction to become “more spread out”.) So it is in this way that the uncertainty principle is related to measurement.

tim314: That made perfect sense! I’ve heard that particles are explained as waves, but somehow I’ve still thought of them as points. But it seems to me now that QM is the result of giving up the point explanation and just plain hypothesizing, that the bricks of the universe are waves, not points, without any proof for this, except that the results deducted from this postulate add up with reality. Am I getting this right?

I don’t think the problem is that we’re too stupid to get it. It’s just that our intuition is shaped by our day-to-day experience, and quantum mechanical effects happen on such a small scale as to not generally be noticeable in our daily experience. If Planck’s constant were much larger, we’d probably have a much better intuition for quantum mechanics (assuming we were still around to experience it – which I strongly suspect we wouldn’t be.)

Yes, that’s right. Once you assign a wave function to these observable characteristics, the uncertainty principle just comes out in the math.

But that doesn’t mean that an electron (or any other particle) is a wave. It is neither a wave nor a particle, but ometimes it behaves like a wave, and sometimes it behaves like a particle.

The bricks of the universe can be expressed in many ways. They can be vibrating strings, for example, which is the basis for string theory. And these strings can have two ends or have their ends connected. Expressing the bricks as waves is another approach.

The virtue of these approaches is that they work. They predict the types of “particles” that we encounter. String theory even predicts their masses, which QM can’t do.

But there isn’t any theory which works when you think of all the particles as being points. And there is no experimental evidence that particles are points.

What makes you think that particles are - or rather should be - points? It’s not physics that says this should be true as much as human prejudices about everyday macroworld experiences. But everything we know says that the macroworld is nothing at all like the microworld. (And, going the other way, the makeup of the universe as a whole is nothing like the makeup of the earth.) It may be non-intuitive for humans, but in the scope of the universe, we’re the odd exception to normality and we just need to acknowledge that.

There is probably an organism that couldn’t grasp the simplest of concepts no matter how hard you tried to teach it, right?
There is probably an organism that evolved from the last one, that could grasp some concepts.
Who’s to say there are limits to this evolution? Bang, we’ve evolved to humans, and we now have the potential to truly and intuitively grasp EVERYTHING, if we, or someone else teaches us?
Until the day someone explains infinity to me in detail, I’ll believe we have a limited potential.

There are infinities in math, but there are no infinities in nature. We live in a finite universe. BIG, but finite.

Very well then, explain the end of the universe to me. Oh, it’s somehow circular. Explain how something can excist without being created. We can accept a lot of these things, and even to some extent explain them, but I doubt we’ll understand them intuitively, as I would say we do with a lot of other things that we have learned rather than know instinctively.
Better yet: I don’t think anyone here will ever be able to truly grasp more than four dimentions.
I could be wrong, of course, but my main objection is that it wouldn’t make sense for an evolution of awareness to have an end.