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A Simple Mathematical argument against Everett

Any question that we can formulate using quantum mechanics, like the expectation value of an electron's spin in two different states simultaneously, can be given an answer. Simply we can state it as being

P is the projection operator, so that it is a product of two other projection operators on the state of an electrons spin. Such that

These are both projection operators but on a subspace. So that the expectation value of the electron in state "up" corresponding to the first projection operator and expectation value of the electron in the state "down" corresponding to the second projection operator, are both one if the projection operator P is one. So that we have

Given that

We should see that 

We then have an answer for the probability of finding the electron in both states simultaneously

The probability of finding the electron in both the spin up and the spin down state is zero. By contrast the Everett or Many Worlds Interpretation imagines that both states of the electron are equally real in parallel branches of the wave function which would surely correspond to a value of one not zero. We then see that the error in the Everett interpretation is that they misidentify the logical conjunction as something other than binary multiplication. The principles of quantum mechanics as it is standard to formulate them and the Everett Interpretation are two proposals that should then be taken as incompatible. 


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