Lecture 27 – Quantum Philosophy I (11/29/04)

• Imagine a world in which:
• quantum mechanics (QM) describes even large things
• objects can be either of two shapes (round and square) and two colours (blue and red).

• QM:
• says that every object is described by an analog 'clock'
• gives a deterministic law describing how 'fast' an object's clock runs under different circumstances
• says that when the clock reads …
• … 12 o'clock, then the object is red
• … 6 o'clock, then the object is blue
• … 3 o'clock, then the object is round
• … 9 o'clock, then the object is square
• but at any time other than …
• … 12 or 6 attributes no particular colour
• … 3 or 9 attributes no particular shape

The 'quantum clock' of this object shows 12 o'clock, so it is red, but QM doesn't specify any particular shape. When its clock reads 3 o'clock, the object is round, but QM doesn't specify any particular colour. And so on.

2. The problem with quantum mechanics

• Suppose that we perform an experiment to determine the shape of an object whose quantum clock reads 12 – suppose that we do it using an echo sounder (i.e., by measuring soundwaves reflected off it).
• Barring experimental error, we will find the object to be either round or square.
• If we measure the shape of a whole bunch of objects whose quantum clock reads 12, 50% will be round and 50% square.
• Thus QM says that if an object's quantum clock reads 12, then the chance of it being square (or round) when its shape is measured is 1/2.
  

• There's nothing strange in the story so far, since there are a variety of ways we could understand what is going on – however, none of them is easily reconciled with QM.

1. It could just be that the quantum clock doesn't tell us everything about the object:
• For instance, if all we know about a die is that it has just been rolled then we don't know which number 1-6 it will come up, but its precise state does determine which number it will come up. There are 'hidden variables'.
• Einstein thought that something similar was the case in QM.
  
• For technical reasons we won't go into, it turns out to be (nearly) impossible that all the properties that QM describes are well-defined – you just can't have a particular colour and a particular shape at once.
• Still, David Bohm's QM takes just one property to be well-defined – position.

2. Or if the clock does tell us everything, it could be that the way we perform the experiment determines what outcome we get:
• This happens when we toss a coin at a fixed rate of rotation: the moment we catch it – the 'experiment' – determines whether it comes up heads or tails – a little earlier or later and we would have got the other result.
• The problem is that experiments are designed so that small differences in how the experiment is performed do not produce large differences in the outcome – we'd have to be very mistaken about how our experiments work.
  

3. Or, again supposing that the clock tells us everything, it could be that an indeterministic 'jump' occurs:
• This is what most physicists assume – as a practical matter it works very well. The idea is that the very fact that shape is measured causes the clock to to jump to 3 or 9.
• However, the deterministic evolution of the clock according to QM will not produce such a jump – the usual law is momentarily suspended. But under what circumstances exactly? I.e., what, in physical terms is a 'measurement'? Is it that we are conscious of the outcome? Our minds make the clock jump?

• Other understandings make the world out to be very differenent from the way it appears:
• Many Worlds – the clock doesn't jump when there's a measurement, but the world splits into two copies, identical except for the outcome of the measurement!
• Many Minds – the clock doesn't jump when there's a measurement, but our minds split into two copies, identical except for the outcome of the measurement!