So I know you said you were simplifying, but what if the worlds interfere? You don’t necessarily get the same amount of mass before “collapse” (that is, decoherence) and after, because you may have destructive interference beforehand which by construction you can’t get afterwards.
As an aside, in amplitude analysis of three-body decays, it used to be the custom to give the “fit fractions” of the two-body isobar components, defined as the integral across the Dalitz plot of each resonance squared, divided by the integral of the total amplitude squared. Naturally this doesn’t always add to 100%, in fact it usually doesn’t, due to interference. So now we usually give the complex amplitude instead.
A) If they’re able to interfere, you shouldn’t have called them separate worlds in the first place.
B) That’s not how interference works. The worlds are constructed to be orthogonal. Therefore, any negative interference in one place will be balanced by positive interference elsewhere, and so you don’t end up with less or more than you started with. You don’t even need to look at worlds to figure this out—time progression is unitary by the general form of the Schrodinger Equation and the real-valuedness of energy.
So I know you said you were simplifying, but what if the worlds interfere? You don’t necessarily get the same amount of mass before “collapse” (that is, decoherence) and after, because you may have destructive interference beforehand which by construction you can’t get afterwards.
As an aside, in amplitude analysis of three-body decays, it used to be the custom to give the “fit fractions” of the two-body isobar components, defined as the integral across the Dalitz plot of each resonance squared, divided by the integral of the total amplitude squared. Naturally this doesn’t always add to 100%, in fact it usually doesn’t, due to interference. So now we usually give the complex amplitude instead.
A) If they’re able to interfere, you shouldn’t have called them separate worlds in the first place.
B) That’s not how interference works. The worlds are constructed to be orthogonal. Therefore, any negative interference in one place will be balanced by positive interference elsewhere, and so you don’t end up with less or more than you started with. You don’t even need to look at worlds to figure this out—time progression is unitary by the general form of the Schrodinger Equation and the real-valuedness of energy.