Is the Heisenburg Uncertainty Principle a theory or a fact? Is it possible to prove? If it’s just a theory that’s impossible to prove why is it so important?
I can’t answer the core of your question, but in this context ‘theory’ and ‘fact’ are virtually synonymous. It is not a ‘hypothesis’, no one is guessing, it’s a very strongly proven theory, to the point that’s it’s considered a ‘principle’, something consistently proven through observation and it’s relation to other observations of the universe. So even though I can’t explain the principle at all I do know it should be considered a fact.
But by the very nature of it is it possible to be certain about the uncertainty principle?
Why not? To be uncertain about it is to assert certainty over what it’s uncertain about. Which is harder to prove than the opposite.
Or you could try asking Schrödinger’s cat…
The uncertainty relations follow rigorously from the principles of quantum mechanics, from which they can be derived in the form of a mathematical theorem. Thus, if you believe in quantum mechanics, then you’ll have to accept uncertainty, as well.
However, might there be a theory that can yield improved predictions in comparison to quantum mechanics?
To answer this question, one needs to understand how deeply intertwined quantum mechanics is with the uncertainty relations. In some sense, every experiment in agreement with the quantum predictions contains a test of the uncertainty principle: the reason for this is that one can derive quantum mechanics from classical mechanics upon imposing the uncertainty principle (mathematically speaking, one deforms the classical theory, adding a parameter—Planck’s constant—which, if it is taken to zero, reproduces the original theory; this has the effect that a quantum state can only be ‘localized’ in phase space up to within a certain area of the size of that parameter—but this is the uncertainty principle).
Thus, in some sense, quantum mechanics = classical mechanics + uncertainty. Hence, without the uncertainty principle, many quantum phenomena simply wouldn’t occur, and thus, their observation also functions as a confirmation of uncertainty.
Nevertheless, one still might imagine that some future theory could explain the same phenomena, while giving more information about the state of a system than the uncertainty relations allow. Interestingly, that’s not the case: according to a theorem of Colbeck and Renner, there exists no theory that recaptures all of the experimental successes of quantum theory, and extends the latter in the sense that it yields additional information about physical systems.
Thus, to all appearances, uncertainty is here to stay.
It’s actually a little simpler than that-- it derives from the use of a wave equation to describe the system. Anything with a wave equation is going to have some type of “uncertainty principle”, QM or not.
Do not confuse the uncertainty principle with The Observer Effect.
Yes, because the uncertainty principal is about specific kinds of quantum level observations. It’s not a philosophy about life in general.
The more precisely the position of some particle is determined, the less precisely its momentum can be known, and vice versa.
This isn’t to say that the position and momentum aren’t knowable, or don’t exist with precise values, they’re just not observable at the same time.
It’s easy to see how this works. Think of light as waves. To see with light more precisely, you need to shorten the wavelength. The problem is that as you shorten the wavelength, the energy goes up until the photons become so energetic that they don’t just harmlessly bounce off the particle you’re observing, they impart a significant amount of energy to it. They give it more momentum. Conversely, if you want to know the momentum, then you need to hit it with light that’s not going to change that momentum and so the wavelengths must be longer and the precision of position goes down.
Well you gotta stop to know where it’s at 
This thought experiment is call Heisenburg’s microscope and there are a few peoblems with it as an explanation of the uncertainty principle. In particular it makes it seem like the uncertainty is an engineering problem, but in QM it is deeper than that. A particle with a definite position doesn’t have a (well defined) momentum, which is a stronger statement than it having a momentum and us just not being able to observe it because our equipment is too clumsy.
I’m fairly certain that it’s Heisenberg.
Tomato, tomuto.
So on that Wikipedia page that you linked to, it mentions that the observer effect has been confused with the uncertainty principle, but then goes on to describe the observer effect for particle physics by relating the uncertainty of a particle’s momentum and position, with Planck’s constant. But that IS the uncertainty principle! It seems to me that the “observer effect” phrase can apply to other areas, but when it’s talking about particle physics, they’re pretty much the same thing.
What’s the difference? If we can’t, even in principle, even indirectly, find out the exact momentum and position of a particle, then how is that different from the view that nature itself doesn’t know them, or that the exact values of those parameters just don’t exist?
Suppose you were analyzing a claimed perpetual motion machine, and it turned out that the reason it failed was because the builder didn’t account for the laws of mechanical advantage, and that for some given amount of torque, the force at the tip of the lever is half as much if the lever is twice as long.
It’s not right to say that the laws of mechanical advantage are the same as conservation of energy, even though MA is how CoE is enforced in this particular case. In another situation, some other effect would manifest to enforce CoE.
The observer effect is the same kind of idea; in some particular situations, it happens to be the method by which the uncertainty principle is enforced. But it’s by no means the only way, and if one somehow avoids it (by not using particles to detect other particles, for instance), then some other effect will manifest and the HUP will remain true. The HUP is a direct mathematical result of QM and can’t be engineered around.
HUP is the best case and the observer effect can be far worse . The observer effect certainly can’t be reduced to the same or better than the amount specified by HUP.
HUP is about knowing. Suppose you generate a particle and you can generate them to know the momentum very very precisely , and you can generate them to know the position very very precisely . Now try generate them knowing the momentum and position precisely… In concept, you are doing this without observing… but it must be similar to observing, whether it is or isn’t observing, what you know must obey HUP.
Well if we were sure we could never in principle find those values at the same time then there’d be no practical difference of course.
But if we really thought it was just an engineering issue, I’m not sure how we could ever declare it to be impossible in principle.
If we were to say that it is impossible using photons, for example, the obvious counter is that photons are not the only game in town; and we already know our town doesn’t have the complete set of, err, games.
Yes, but one should be careful not to overinterprete this similarity—while it’s indeed the case that wave mechanics of any kind bears several analogies to quantum mechanics—besides the uncertainty principle, also superposition and interference—their interpretation is different, and if one isn’t careful about it, this picture is ultimately as misleading as the ‘Heisenberg’s microscope’ account of uncertainty.
The reason for this is that the Fourier uncertainty principle of, say, acoustics concerns physical quantities, while the wave function in quantum mechanics (ultimately, via the squared modulus rule) gives probabilities of observations. Thus, for an acoustic wave packet, it’s simply the case that it’s associated with a real spread in duration, and a real range of frequencies that can be attributed to the wave packet; while a quantum system, upon observation, yields only one of the possible values consistent with uncertainty, with the variation in this value only becoming noticeable in the statistical limit of many repeated measurements on identically prepared systems.
Compare the case of superposition: there, too, it’s the case that the sum of, say, two sound waves is again a sound wave, just as the sum of two state vectors in quantum mechanics is again a valid state vector. But for the sound waves, you can interpret this as both original waves simply being present simultaneously, while such an interpretation is impossible for quantum mechanics—all you can say is that an observation will yield either of the possibilities.
So while they are mathematically analogous, both are in fact very distinct in their implications.
The Heisenburg Principle states that, at any given moment, you only can determine either the position or the velocity of a zeppelin, but not both at the same time.
Corollary: If it’s too dark to see the label for the enclosed gas, you can always light a match.
It’s worth noting that the Uncertainty Principle applies to any two measurements, not just position and momentum. For any given pair of measurements, you can calculate a lower bound of the uncertainty on their product. For measurements which commute (that is, which give the same result when measured in either order), this lower bound of uncertainty is 0. For measurements which do not commute, the lower bound is proportional to the commutator.
Other famous non-commuting pairs include energy and time, and any two components of angular momentum.
Idle question, so do these get sheeted home to Noether’s theorem in any fundamental way?