Probability is how likely something is to happen. The probability of getting ‘tails’ when you toss a coin is a 1 in 2 chance, so the probability is 1/2, 50%. In the reality illustrated by Lockwood’s diagram, described in Schrödinger’s Cat, the origin of probability becomes perfectly clear.
Before he makes the observation, Schrödinger exists in all worlds in which there is a cat in the box. This is the green section. He is in an equal number of worlds where the cat lived and the cat died, the green is the blue and the yellow at the same time. So, when he makes the observation, thus ruling out a class of worlds, the chance of his making an observation of the cat being alive is 50%. What happens is that he exists in only half of the worlds, say the yellow. And his counterpart, who observed the cat dead, lives in the other half.
In the superworld of the mind, the origin and the meaning of probability is self-evident. It is simply the percentage of worlds in which a particular event will happen.
If the experiment was modified so that the cat had a only a 30% chance of survival, then the yellow section would be much smaller, being 30% of the total, and the blue section much larger, 70% of the total, as in the diagram below. In this case, the probability of Schrödinger finding himself in a world where the cat survived is just 30% because only 30% of the worlds he is in have a live cat.
As Lockwood states, the observed probabilities are explained in the same way as:
… the empirical finding that one is twice as likely to draw a black as a white ball when drawing blind from a jar [with] twice as many black as white balls in the jar. In short, each quantum-mechanical observation, as experienced in a given world, is to be regarded as a sampling of the multiverse, the multi-faceted reality corresponding to the universal state vector. (1996, 173)
The multiverse is the many-worlds universe of Everett. The universal state vector is the wave function of the whole universe, the ‘unitary wave function’ as Everett denotes it.
Deutsch describes the basis of probability along the same lines in his book The Fabric of Reality. If you toss a coin:
… all copies of you would have seen the coin spinning at first. Later, half the copies of you would see ‘heads’ come up, and the other half would see ‘tails’. (1996, 280)
Although this is contested, it seems reasonable on this basis to account for probability as an objective feature of the space of all possible worlds.
Everett’s theory has often been challenged because it seems there is no meaning to the concept of probability in his theory. All possible outcomes are going to happen, for sure. So what does it mean to say I have a fifty percent chance of seeing heads? I will also be seeing tails, though that will be a different version of me.
It seems to me that the superworld resolves this conundrum. The meaning of the probability is that I am already in all the worlds where these outcomes will play out. The probability is the likelihood that I will become one or other of the versions of me as I make the crucial observation.
The next section is Logical Type.