I have been doing a lot of research on weak measurements and the Many Worlds Interpretation (MWI) of quantum physics. I am a quantum interpretation skeptic and I don’t really subscribe to a particular interpretation, even my own which is, admittedly, just a variation of the MWI (a more sensible one IMHO).
I spoke to Lev Vaidman the other day who is one of the main proponents of the MWI and very active in the field. (He wrote the Stanford Encyclopedia of Philosophy entry on it not to mention numerous papers, including recent ones.) I was picking his brain about weak measurements and the MWI trying to understand how it all works.
If you don’t know what weak measurements are, they are basically measurements that you can make of quantum particles that don’t affect them enough to cause them to become collapsed or localized or split the worlds (depending on your interpretation). An example would be placing a thin glass plate in front of a laser. The individual photons will pass through the plate but it isn’t interacting with them strongly enough (being transparent) to be considered a strong measurement. You can, therefore, see the effect of the glass plate when you finally do a strong measurement.
Since weak measurements let you make measurements of particles that are in quantum superposition, you could say that they let you peek into alternate realities.
This is sort of true.
In reality, you can’t really interpret weak measurements that easily. First, you need a large number of particles to even interpret the measurements because there is a large error on the reading. So any weak measurement is a statistical measurement. Second, you have to both pre- and post-select your particles.
Pre-selection just means preparation. For example, putting a laser through some beam splitters, adjusting relative phases of the waves with mirrors, and so on before you make your weak measurement.
Post-selection is where you make a strong measurement. This can be done with more beam splitters to combine things back together, for example, and using cameras and photo diodes to make sure that the final result is what you are looking for.
In quantum mechanics, all measurement, indeed all reality and experience (what Vaidman called elements of reality), exists within the context of pre- and post-selection.
In a typical experiment, post-selecting in weak measurement means making sure a large number of particles in a row meet a particular criteria. This ends up being like flipping a coin over and over and only using the results if you get heads 20 times in a row. The events are very rare. Thankfully, we can produce many particles pretty easily.
Now, let us, for the sake of understanding, assume that the MWI is true. In the Two Vector formulation of quantum mechanics, this means we exist as a wavefunction evolving both forwards and backwards in time. In other words, we evolve forwards from pre-selection and backwards from post-selection. This ensures that quantum mechanics is time symmetric.
Now, when we make a weak measurement at some time, that weak measurement samples that wavefunction, across all the worlds that exist between pre- and post-selection. These worlds are, of course, not really separate. It is only our experience that is separate. There is no actual splitting of worlds going on. That is just a conceptual notion for the dividing of our experience into more and more worlds.
When we make a weak measurement on a particle, we can sometimes get counter-intuitive results. For example, we have the three box paradox. In this paradox, a particle is in a box A and a box B with certainty such that if we look in box A will be sure to find it and if we look in box B we will also be sure to find it. If, however, we look in both A and B simultaneously, we won’t find it.
If you see the particle as a wave, this is not really difficult to interpret. What you have is a wavefunction that has a positive spike in box A, a positive spike at B, and a negative spike at C. Waves can do that even though we feel like particles shouldn’t be able to.
I think we run into trouble, however, if we start to say: this is happening in the world where the particle is in A and this is happening in the world where the particle is in B. Or, there is just one world where the particle is in A and the vacuum somehow created two opposite particles so that one could be in B and the other in C. That doesn’t make a lot of sense. Splitting the worlds only makes sense if we talk about human experience, meaning strong measurements. Otherwise, there is no split, no multiple worlds, but one world containing one wavefunction.
What the weak measurements actually tell us is the shape of the wavefunction for a particular pre- and post-selected reality. So, it lets us peek at the wavefunction which, you can think of as multiple parallel realities, but in truth they are all one reality.
In the MWI, parallel realities are only defined by a diverging history of strong measurements. Weak measurements can agree with those measurements but they may not. In the cases where they don’t, we cannot define a set of strong measurements, and therefore a set of parallel worlds, that would allow us to describe what the weak measurements are measuring as parallel realities. Instead, the weak measurements are letting us peak at what reality looks like when it is not split, which can be a very different kind of existence from our everyday experience.