Physics question: is the macro world a convergence of probabilities?

[tim314]

@II Gyan II

So should you. I implied nothing of the sort. I asked about how we could discard the notion of an epistemological barrier and infer its ontology. Even if there’s no way, even potentially, for us to assign the exact values, how do we know that’s because that’s how things are, rather than because of the nature of our means to discover knowledge?

Because the uncertainty principle isn’t based on an empirical failure to measure both position and momentum exactly, it’s based on the fact that quantum mechanical particles behave like objects that have no definite position or momentum. Such objects exist even in the classical, macroscopic world.

Consider, for instance, a wave propagating through space. It has a momentum which can be computed from its frequency and propagation speed, but no defined position (because it’s spread out in space).

Alternatively, a Dirac delta function (a normalized distribution which has a non-zero value at only a single point) has an exact position, but no defined momentum. (To express it as a superposition of waves, we’d need to use waves over an infinite range of frequencies.)

Now consider something in between the two – a wave packet. (Basically, a wave bounded by a bell curve.) This has a somewhat localized position, and can be decomposed into waves of a somewhat localized range of frequencies. That is, the amplitude falls off if you get too far outside the range in either case.

The reason we say a quantum particle has neither an exact position nor an exact momentum (except at the moment one is measured) is basically because they behave like wave packets.

[John_Mace]

@Chronos

Particles have many properties, some of which are vectors and some of which are scalars. There’s no property of a particle you can point to and say “that’s its vector”. I think what you meant to say is that the more you know about a particle’s momentum, the less you know about its position, but both of these are vectors. There are, incidentally, a great number of pairs of conjugate quantities like this, which cannot both be known at once; position and momentum are just the best-known.

And it’s important to note that we’re talking about quantities known in QM as “conjugate pairs”. Position vs Momentum -or- Energy vs Time are two sets of conjugate pairs. The more accurately you know one quantity of the pair, the less accurate your measurement of the other pair will be. There are lots of “conjugate pairs”, some that are difficult to describe physically, but we’re not talking about just any old pair of observable quantities.

[Mathochist]

@II Gyan II

So should you. I implied nothing of the sort. I asked about how we could discard the notion of an epistemological barrier and infer its ontology. Even if there’s no way, even potentially, for us to assign the exact values, how do we know that’s because that’s how things are, rather than because of the nature of our means to discover knowledge?

The question in the OP asked specifically about quantum theory, which means immediately reading in the quantum model. I don’t know how much clearer I can be about the model without giving a basic course in functional analysis.