# When qm effects begin

1. Aug 18, 2013

### susskind99

I'm pretty sure a proton's location does not have much quantum uncertainty but an up quark does. So qm uncertainty begins around 10^-15m and is full blown at 10^-18m

If my numbers are wrong please let me know.

2. Aug 18, 2013

### ZapperZ

Staff Emeritus
Your assumptions are wrong. We have seen interference effects on not only protons, but also molecules as big as buckyballs.

Thus, quantum effects (and consequently, the HUP) apply to protons and much bigger sizes.

Zz.

3. Aug 18, 2013

### tom.stoer

The uncertainty of the position x of a quantum object in a certain state psi can be calculated as

$\Delta x^2 = \langle\psi|(x-\bar{x})^2|\psi\rangle$

Usually what you find is an uncertainty comparable to the typical size S of the quantum system. So the uncertainty of an electron in an atom / of a proton inside a nucleus / of a quark inside a proton is comparable to the size S of the atom / nucleus / proton.

4. Aug 18, 2013

### Bill_K

By definition. The "size of a quantum system" is defined by the uncertainty of the position of its constituents. We say an atom is an Angstrom in diameter because that describes the region in which the electrons can be found.

5. Aug 18, 2013

### tom.stoer

No, by experiment ;-)

We see structures in scattering experiments which can be (approximately) explained by (e.g.) charge distributions. The typical size of these distributions can be derived from the experiments. The calculations result in comparable sizes, thefore the idea of what "size" could mean, the experimental results and the definitions used in QM agree.