The Planck scale

[Enola Straight]

From this thread over at the SDMB:
http://boards.straightdope.com/sdmb/sho ... st11450980

Lets look at space at the Planck scale, where space is supposedlydivided into discrete chunks.

Move up one Planck length, from the origin and to the side one planck length.
You are now 1.414...PLs from the origin.

Can you move diagonally back to the origin? Will the distance be 1 OR 1.414... PLs?


Furthermore, if at the Planck Scale, can such motion in quantized linear measurement be governed by an equally quantized angular measurement?

[Sriad]

Based on my intuitive (that is to say, bullshit) understanding of QM, a particle "1.414" PL from the origin point would have a 58.5% chance of being detected 1 PL away, and 42.4% of being 2 away.

But like I said, "intuitive".

[Wyrm]

Planck length doesn't mean that space is divided into discrete chunks. Physics is arranged such that any attempt to measure distances smaller than the Planck length will fail, but that doesn't mean that space is divided into Planck-length chunks any more than the 1 mm graduations of your ruler mean that space is divided into 1 mm chunks. There is nothing theoretically preventing you from measuring back to the origin with precision fine enough to tell it's (probably) equal to √2 Planck lengths, although since particles are characterized by their wavefunctions, you can only get a distribution on the distances at best.

[Modax]

Remember that the Planck length is ridiculously small. Consider this: if we scaled up the universe so that the Planck length was 1 cm, the diameter of an electron would be equal to 1 light year! So even without the Uncertainty Principle it's pretty much meaningless to talk about measuring anything to that level of precision.

Planck Length ≈ 10^-35 m, Electron ≈ 10^-18 m, Light Year ≈ 10^15 m

[Wyrm]

In the standard model, electrons are treated as point particles. The measurement you cite is the upper bound on the diameter of the electron. That is, the electron can be localized into spaces not more than 1e-18 m wide. That doesn't mean that the electron is 1e-18 m wide.

Protons have a definite diameter because they are known to have structure. We do not know that electrons have a structure more detailed than a point.