phil 105 fall lecture xx

Phil 105: Science and Philosophy - Fall 2004 Lectures

!You will be sorely disappointed if you think that these are a substitute for attending class!

Topic Six: Quantum Philosophy

Lecture 28 – Quantum Philosophy II (12/1/04)

Weyl Tile Problem: the two sides adjoining the right angle have length 10e m, so according to the Pythagorean Theorem the length of the diagonal is about 14.12e m, which is not a whole number multiple of e m. The distance up the steps is 20m, which is not right either.

One 'typical' consequence of QM is that quantities are 'quantized' = discrete – so one might expect quantum space to be discrete.

We can solve Weyl's problem by supposing that the length of the diagonal is exactly 14e m
That the Pythagorean theorem fails does not show that quantum space is geometrically impossible, if we assume that lengths along different lines are not necessarily compatible:

That is, in some quantum states the sides adjoining the right angle have definite lengths, while in other states the diagonal does.

Then send the objects as far apart as you like – suppose they continue in the same state, so neither has a particular colour.

Then measure the colour of the one on the left. Suppose it's red – because they are anti-synchronized, the one on the right will be blue, instantaneously!
But how can the measurement of the one 'do' anything to the other?

Einstein thought that this was an argument to show that the quantum clock didn't capture all the properties of an object – i.e., that the one on the right was 'really' blue all along.

But it turns out – again for technical reasons we won't go into – that even if the objects have other properties, interactions on the left affect what happens on the right.