The many worlds interpretation vaguely envisions some splitting of the world, at special moments that cannot last determined – because at that spot are no special moments inward quantum mechanics; according to observables that cannot last determined – because at that spot are no special observables inward quantum mechanics; to an unknown lay out of worlds – because probabilities inward quantum mechanics aren't rational inward general. And at that spot are other reasons that guarantee that no meaningful many worlds interpretation tin move exist.
But i may blueprint a many the world interpretation that works. However, it's useless: the interpretation may last described as an overly redundant "visualization of subjective probabilities". How does it work?
At every minute \(t\), for every soil \(\ket\psi,\) for every linear Hermitian operator \(L,\) for every \(\mu\in(0,1),\) at that spot exists the the world \(W(\psi,L,\mu)\).What hit the arguments mean? The fourth dimension \(t\) is just some time. The moving ridge business office \(\psi\) is a soil vector associated to the world. Most nontrivially, \(L\) is the offset observable that may last measured. When it's measured, the the world splits according to the eigenvalues of \(L\) to a continuum of novel extra universes labeled past times \(\mu\). And inward the fractions of the \(\mu\) interval \((0,1)\) corresponding to the measured eigenvalue of \(L\), i collapses the moving ridge business office \(\ket\psi\) to \(P(L=\lambda_i)\ket\psi\) at the next moment.
From each the world \(W(\psi,L,\mu)\), at that spot continues some regular unitary development inward which \(\ket\psi\) in addition to \(L\) are evolving according to the detail film yous prefer – Schrödinger, Heisenberg, Dirac, it's your choice. However, from each world, at that spot are also special arrows pointing to all the possible "collapsed worlds" \(W(P(L=\lambda_{i(\mu)})\ket\psi,L_{\rm new},\mu_{\rm new})\).
Here, the subscripts "new" betoken that the arrow leads to all possible values of the novel \(L\) in addition to \(\mu\) that is independent of the starting one. However, the novel soil vector is determined from the quondam i as \(P(L=\lambda_{i(\mu)})\ket\psi\) where \(i(\mu)\) is the label that determines the possible eigenvalues of the quondam \(L\) then that \(i(\mu)\) is a non-decreasing business office of \(0\lt \mu\lt 1\), all \(i(\mu)\) are eigenvalues of the quondam \(L\), in addition to the lengths of the intervals at which a given eigenvalue is realized are calculated past times Born's dominion from the corresponding eigenvalue in addition to the quondam \(\ket\psi\).
How volition yous purpose these many worlds? You just imagine that yous alive inward i of the worlds \(W(\psi,L,\mu)\). You bring determined \(\ket\psi\) then yous know what it is. However, you're non decided what is \(L\) inward your the world – yous haven't decided what to stair out yet – in addition to yous don't know the value of \(\mu\) which is randomly distributed inward the unit of measurement interval. This value of \(\mu\) was generated randomly during the concluding observation of yours in addition to it's fixed piece \(\ket\psi,L\) are evolving according to the equations of the picture.
At whatever moment, yous may determine that yous stair out something, \(L\). If yous determine to stair out a detail operator \(L\), it proves that yous were inward i of the worlds \(W(\psi,L,\mu)\) where both \(\ket\psi\) in addition to \(L\) are known – the soil vector is given because Nature imposed it on yous during the previous recent measurement; in addition to \(L\) was picked past times yous because yous chose what to measure. Once yous stair out \(L\), yous may last sent to i of the novel worlds where \(L_{\rm new}\) is an arbitrary novel Hermitian operator that yous don't know yet in addition to where the novel \(\ket\psi\) is completely determined as \(P(L=\lambda_{i(\mu)})\ket\psi\) – perhaps normalized then that its norm is one.
So these many worlds are e'er completely ready for any mensuration yous may desire to hit as the offset i inward the coming futurity (they include all possible "Heisenberg choices"); in addition to they're completely ready to hit all the possible results of the mensuration (the "Dirac choice") amongst the correct probabilities. The probabilities are equal to what they should last because the probability is interpreted as the relative fraction of the worlds amongst a known value of the soil vector in addition to the operator which is measured past times the length on the unit of measurement interval for \(\mu\) – the probability distribution for \(\mu\) is e'er assumed to last uniform. The randomly generated numbers e'er arise from \(\mu\) that is e'er randomly created during every mensuration (but the observer, you, can't know what the value is) in addition to it's waiting to touching on the projection associated amongst the novel measurement.
Now, what bring nosotros gained? We bring gained absolutely nix relatively to proper, "Copenhagen school" quantum mechanics. We nevertheless move amongst a detail the world amongst a detail \(\ket\psi\), nosotros pick out a detail \(L\) that nosotros desire to stair out in addition to it's nevertheless upwards to our gratis volition (but the observable should last sufficiently slow changing amongst fourth dimension for the query to last stable enough; in addition to decohered plenty to acknowledge mutually exclusive perceptions), in addition to the exclusively matter nosotros tin move predict are the probabilities. So all the remaining worlds are absolutely unphysical.
In particular, nosotros don't alter anything almost the fact that at that spot is no preferred dominion that would dictate us "whether nosotros desire to stair out something at all in addition to when", "what observable nosotros should precisely measure", or "how much decoherence at that spot should bring been to allow us to stair out it at all". And concerning the Dirac selection – Nature's random generator for the results – nosotros don't gain anything at all, either. We're just "drawing" the other possibilities that were possible earlier the measurement, but didn't materialize, as "real worlds" somewhere. But nosotros tin move never restore whatever physical access to these other worlds.
If individual is driven towards the many worlds religious belief past times the persuasion that at that spot is some "objective cosmic directive" that tells everyone what should last measured in addition to when it should last measured, he must last disappointed. Nothing similar that exists. Also, the random generator is a existent one, non a pseudorandom generator. So if individual wants to "predict" all the random numbers from the Dirac choice, he must last disappointed, too.
There's i to a greater extent than matter that unavoidably remains Copenhagen-like. The conclusion of the "world where I live" remains subjective i.e. dependent on the observer. Different observers acquire dissimilar things from their measurements – which are intrinsically subjective – then they volition house themselves into dissimilar worlds. The dissimilar observers won't be inward the same world. So nix is changed – in addition to nix tin move last changed – almost the subjective graphic symbol of the observations inward quantum mechanics. In this sense, my "many worlds" film should also last called a "many minds" picture.
Again, to summarize, i time yous empathise that the "beef" must rest that of the Copenhagen school, yous may blueprint a many worlds interpretation that adds all these extra novel worlds. But they're nix else than the visualization of possible questions that an observer may ask; in addition to possible answers that Nature could bring given fifty-fifty though she exclusively gave a detail one. All these other worlds are completely useless in addition to redundant because they won't ever touching on anything inward a given the world again. That's why a scientist – individual who builds on the actual evidence – should visit them immaterial in addition to erase them from his "picture" of the world.
I mentioned the beef of the "Copenhagen school" that my usable version of the many worlds couldn't change. They are:
- Heisenberg selection is upwards to gratis will: at that spot must be gratis volition of the observer who must know – without beingness "told" past times anybody or some laws – what operator he wants to stair out in addition to when. In principle, all things that "may last measured" are as allowed. Quantum mechanics exclusively produces answers (in price of probabilities) i time a query is well-defined, in addition to a query requires \(L\) to last determined past times the observer.
- Dirac selection is generated past times a pure random generator: the random results are actually probabilistic then at that spot can't last whatever hidden variables or "pseudorandom generators" that would "explain" the outcomes.
It's just a dissimilar "visualization" what's going on – that draws some "no longer relevant" choices or outcomes as "real" although they're inconsequential for the subsequent development of the chosen observer's life – in addition to fifty-fifty earlier quantum mechanics was born, the probability calculus was invented exactly to release us from the duty to push clitoris all these no longer relevant options.
My version of the many worlds contains infinitely many worlds – they course of teaching a continuum amongst many continuous coordinates included inward \(\ket\psi,L,\mu\). I would claim that the splitting of the many worlds according to \(\ket\psi\) as good as \(L\) as good as some \(\mu\) is necessary (my lay out is the minimum one) – yous demand to multiply the lay out of worlds both to bargain amongst the Heisenberg selection in addition to the Dirac choice. But yous could increase the lay out of the worlds. For example, instead of depending "just" on \(\ket\psi\), the the world could depend on a whole pre-history of measurements which remembers "how nosotros got to \(\ket\psi\)". In other words, it would cry upwards a possible path how nosotros got to \(\ket\psi\) through a sequence of projections. Again, this would last just a redundant improver because all the futurity predictions for \(L\) exclusively depend on \(\ket\psi\), non on how nosotros got to \(\ket\psi\).
Copenhagen schoolhouse has been using "Occam's razor", if yous wish. "Entities [e.g. worlds] are non to last multiplied without necessity" (Non sunt multiplicanda entia sine necessitate). Bohr in addition to his guys avoided imagining e.g. the path inward a higher house to last "real" because this path isn't relevant for whatever farther predictions. So it's non "real". Only the results of measurements are "real" – but this reality is subjective – in addition to exclusively the probabilities may last predicted. It's of import that the predictions don't depend on the path inward the tree, on the manner how yous could write \(\ket\psi\) as a essence of many pieces, in addition to on anything else. That's why a sensible scientist erases these distracting features – he labels them unphysical because they're unobservable, fifty-fifty inward principle.
The exclusively physical things are those that the Copenhagen schoolhouse talks about. That's why my minimal worlds were exclusively labeled past times \(\ket\psi\), \(L\), in addition to \(\mu\) – past times the cognition almost the physical system, past times the selection what he wants to know next, in addition to past times something that produces the random numbers. You're advised to trim this minimal organization farther – to concur amongst your perceptions that the "worlds" amongst other values of \(\ket\psi,L,\mu\) than the relevant ones "don't exist". The usage of this non-existence supposition is nix else than the touchstone usage of the probability calculus.