Uncertainty principle.?

Question

so according to the uncertainty principle, we cant know the position or velocity of a particle to any degree of certainty. so a particle could be thought of as a tiny cloud of probability.

but that just addresses the position part of it. if we dont know velocity of a particle, we dont know where it moved to in a given amount of time.

for example, if you have a single particle you cant know exactly how fast its going, so it would have a range of speeds that it could be going. so lets say it could be moving 1 m/s - 1.1 m/s. in one second, it moved somewhere between 1 and 1.1 meters. so the position of the particle should "blur" more because you dont know how far it moved.

shouldnt that continually happen over and over again each second. how can the uncertainty principle be correct, considering particles dont have a nearly infinitely large "probability cloud"

Answer 1

You are making the mistake of using classical mechanical reasoning with quantum mechanics, for which there is (alas!) no story, no conceptual model of what is "really' going on.

The Copenhagen convention - the view most physicists have - is that there is NO underlying reality. That means, not that we cannot see or measure it, but that it does not exist. That is a VERY unsatisfying  idea for people who hope to make some sense of it all. Einstein himself was not happy with this idea, but whenever he proposed conflicting situations, his objections were resolved.

When one uses the maths to find the momentum-location pair, you find that as time increases, the location and momentum gradually resolves to a more or less 'real' location. But the truth is that initially, the probability cloud IS infinitely large in all 4 dimensions; that is, including time.

If you find this answer satisfying, you have not understood it!

Answer 2

The uncertainty principle is all about pairs of properties of  a particle called conjugate variables.  If you multiply the uncertainty of two conjugate variables together you get Planck's constant h; 6.67E-34 joule seconds.  For instance, position and momentum are conjugate variables.  The more accurately you determine one, the less you know about the other.  Another way of stating this is that to find the position of, say, an electron you need to bounce another particle, like a photon, off it, and by doing so you've given it a kick which increases the uncertainty of its momentum.  The more accurately you want to know its position, the shorter the wavelength of the photon and the more energetic the collision.  Alternatively, to measure its momentum accurately you need to measure its velocity, say by detecting its electric field as it passes two gates, and by detecting its field you have to subject it to another electric field, which deflects it.  

Answer 3

The uncertainty principle is not the basis of quantum mechanics; it is only one of many results. The basis of QM is the Schrödinger Equation. The particle has no definite position or momentum, but its properties, the wave function, do obey physical laws that we understand.

But yes, if a particle is localized momentarily by, say, interaction with another particle, then thereafter it definitely has a tendency to spread out, yea, verily, even unto infinitely large. The rate of dispersion with time is a basic calculation we give to introductory students. It will continue to disperse until it interacts with something else, collapses the wave function, and thus once again becomes more localized.

Answer 4

The uncertainty principle expresses the maximum accuracy you can get from a pair of conjugate measurements. We can know the velocity of a particle accurately, but not at the same time as knowing its (accurate) position.  Of course this limit is meaningless for macroscopic (every day physical) objects.

In the standard theory of QM, the Copenhagen interpretation, the wave equation collapses and the probability goes to either zero or one.

There are real problems with this interpretation, but they're philosophical rather than practical.

And remember, sub atomic particles are no more "particles" than they are "waves".  They are what they are.