Skip to main content

Probability and Many Worlds

not really a problem

Many Worlds and probability

What does it mean if we say that the Worlds resulting from a quantum measurement each have a particular probability? If we repeat the measurement we have an expectation of the chances of each outcome, or in the Everettian view, the chances that we will be in a particular World. If the measurement is repeated many times a distribution emerges that agrees with that expectation.


So, for example, consider a quantum superposition set up so that there are 2 expected outcomes with probabilities 0.75 and 0.25. Under the Many Worlds interpretation (MWI) both outcomes occur every time the measurement is made. So how can one be more likely than the other? Does it make sense to say that both worlds are created but one is more likely to be the one in which the “observer” finds themself? Each time an “observer” finds themself in the more likely World, there’s another version that finds themself in the less likely World.

Arriving at different Worlds via weighted paths

Infinite outcomes

Let’s imagine/pretend that each quantum measurement gives rise to an infinite number of Worlds. In this case the chances of you being in a World with a particular outcome can easily be other than 50/50. One outcome may appear in 25% of the Worlds and the other in 75% of the Worlds, so the “observer” would have a greater chance of seeing one outcome over the other. Having been created, these infinite Worlds would consist of 2 groups, each of which has an infinite number of identical Worlds. If each of these groups of identical Worlds then “merged” to be just one World or even remained as an infinite number of identical Worlds, the expected statistical result (frequency distribution) would be observed. Whether this actually happens is less important than the fact that it demonstrates that there are scenarios where two outcomes can be other than equally likely.


Is an infinite number of outcomes possible? When a “photon”, say, having traversed a pair of slits and being in a superposition of paths travelled, is detected at any one of an effectively infinite number of locations on the detecting screen, would the MWI claim that an effectively infinite number of Worlds are created? And then to accommodate the probabilities of the various locations, would these infinite outcomes each contain an infinite number of Worlds but a greater or lesser infinite number to match the probabilities expected? So that’s a lot of Worlds!


Partial Worlds

If the splitting of Worlds only occurs locally and spreads outward at either the speed of light or at the speed that any evidence of the “measurement” outcome spreads, could we have space riddled with pockets where two alternative “Worlds” exist but the “inhabitants” view the rest of space to be in a “superposition” where either outcome is still possible? If the spread is mediated by the evidence of the outcome, how far can this evidence spread before one outcome is no longer distinguishable from the other? In this case would this “superposed” evidence cause a split to the same two Worlds when “measured” and would these new Worlds send evidence back to the original Worlds and so join up? So in effect be entangled with the original “measurement”? I don’t know but …


In the instant that a measurement with a ¼ : ¾ probability of two alternative outcomes is made, there could be, locally, for an infinitesimally short duration, an infinite number of “local” Worlds created that are weighted ¼ : ¾ for the two outcomes. This would then be two distinct groups of identical “local” Worlds that could each resolve into single Worlds, but the chances of finding yourself in each World would be the same as the expected chances.

Both Worlds would exist but an observer in either would have arrived there via an infinite but weighted number of perhaps infinitesimally brief and infinitesimally local “pocket” Worlds and so observe expected frequencies on repeated observations of similar measurements.