At the risk of starting yet another quantum interpretation debate, the argument that ‘Copenhagen is simpler than MWI’ is not a well-presented one. For instance, a quantum computer with 500 qubits will, at some point in processing, be in the superposition of 2^500 states at once. According to Copenhagen, one of these is randomly chosen at measurement. But to know the probability, you still have to keep track of 2^500 states. It’s not simple at all. If you could get by with many fewer states (like, say, a polynomial function of the number of qubits), it would be possible to efficiently simulate a quantum computer on a classical one. While the impossibility of this hasn’t been proven, the consensus opinion seems to be that it is unlikely.
MWI simply acknowledges this inherent complexity in quantum mechanics, and tries to deal with it directly instead of avoiding it. If it makes you more comfortable, you can consider the whole universe as a big quantum computer, and you’re living in it. That’s MWI.
And another attractive aspect of MWI is that it is entirely deterministic. While each individual universe may appear random, the mulitverse as a whole evolves deterministically.
you can consider the whole universe as a big quantum computer, and you’re living in it
I recall hearing it argued somewhere that it’s not so much “a computer” as “the universal computer” in the sense that it is impossible to principle for there to be another computer performing the calculations from the same initial conditions (and for example getting to a particular state sooner). I like that if it’s true. The calculations can be performed, but only by existing.
the multiverse as a whole evolves deterministically
So to get back to my question of what predictability means in a QM universe under MW, the significant point seems to be that prediction is possible starting from the initial conditions of the Big Bang, but not from a later point in a particular universe (without complete information about the all other universes that have evolved from the Big Bang)?
Rather, the significant point is that you can predict the future with arbitrary precision, but the prediction will say things like “you are superpositioned into these three states”. That result is deterministic, but it doesn’t help you predict your future subjective experience when you’re facing down the branch point.
(You know that there will be three yous, each thinking “Huh, I was number 1/2/3”—but until you check, you won’t know which you you are.)
So, to get this clear (being well outside my comfort zone here), once a split into two branches has occurred, they no longer influence each other? The integration over all possibilities is something that happens in only one of the many worlds? (My recent understanding is based on “Everything that can happen does happen” by Cox & Forshaw).
There are no discrete “worlds” and “branches” in quantum physics as such. Once two regions in state space are sufficiently separated to no longer significantly influence each other they might be considered split, which makes the answer to your question “yes” by definition.
There are no discrete “worlds” and “branches” in quantum physics as such.
This seems to conflict with references to “many worlds” and “branch points” in other comments, or is the key word “discrete”? In other words, the states are a continuum with markedly varying density so that if you zoom out there is the appearance of branches? I could understand that expect for cases like Schroedinger’s cat where there seems to be a pretty clear branch (at the point where the box is opened, i.e. from the point of view of a particular state if that is the right terminology).
Once two regions in state space are sufficiently separated to no longer significantly influence each other...
From the big bang there are an unimaginably large number of regions in state space each having an unimaginably small influence. It’s not obvious, but I can perfectly well believe that the net effect is dominated by the smallness of influence, so I’ll take your word for it.
In other words, the states are a continuum with markedly varying density so that if you zoom out there is the appearance of branches?
Yes, but it’s still continuous. There’s always some influence, it can just get arbitrarily small. I’m unsure if this hypothetically allows MWI to be experimentally confirmed.
(The thesis of mangled-worlds seems to be that, in fact, in some cases that doesn’t happen—that is, world A’s influence on world B stays large.)
Schroedinger’s cat
If it helps, think of half-silvered mirrors. Those are actually symmetric, letting through half the light either way; the trick is that the ambient lighting on the “reflective” side is orders of magnitude brighter, so the light shining through from the dark side is simply washed out.
To apply that to quantum mechanics, consider that the two branches—cat dead and not-dead—can still affect each other, but as if through a 99.9-whatever number of nines-silvered mirror. By the time a divergence gets to human scale, it’ll be very, very close to an absolute separation.
Thanks, so to get back to the original question of how to describe the different effects of divergence and convergence in the context of MW, here’s how it’s seeming to me. (The terminology is probably in need of refinement).
Considering this in terms of the LW-preferred Many Worlds interpretation of quantum mechanics, exact “prediction” is possible in principle but the prediction is of the indexical uncertainty of an array of outcomes. (The indexical uncertainty governs the probability of a particular outcome if one is considered at random.) Whether a process is convergent or divergent on a macro scale makes no difference to the number of states that formally need to be included in the distribution of possible outcomes. However, in the convergent process the cases become so similar that there appears to be only one outcome at the macro scale; whereas in a divergent process the “density of probability” (in the above sense) becomes so vanishingly small for some states that at a macro scale the outcomes appear to split into separate branches. (They have become decoherent.) Any one such branch appears to an observer within that branch to be the only outcome, and so such an observer could not have known what to “expect”—only the probability distribution of what to expect. This can be described as a condition of subjective unpredictability, in the sense that there is no subjective expectation that can be formed before the divergent process which can be reliably expected to coincident with observation after the process.
At the risk of starting yet another quantum interpretation debate, the argument that ‘Copenhagen is simpler than MWI’ is not a well-presented one. For instance, a quantum computer with 500 qubits will, at some point in processing, be in the superposition of 2^500 states at once. According to Copenhagen, one of these is randomly chosen at measurement. But to know the probability, you still have to keep track of 2^500 states. It’s not simple at all. If you could get by with many fewer states (like, say, a polynomial function of the number of qubits), it would be possible to efficiently simulate a quantum computer on a classical one. While the impossibility of this hasn’t been proven, the consensus opinion seems to be that it is unlikely.
MWI simply acknowledges this inherent complexity in quantum mechanics, and tries to deal with it directly instead of avoiding it. If it makes you more comfortable, you can consider the whole universe as a big quantum computer, and you’re living in it. That’s MWI.
And another attractive aspect of MWI is that it is entirely deterministic. While each individual universe may appear random, the mulitverse as a whole evolves deterministically.
I recall hearing it argued somewhere that it’s not so much “a computer” as “the universal computer” in the sense that it is impossible to principle for there to be another computer performing the calculations from the same initial conditions (and for example getting to a particular state sooner). I like that if it’s true. The calculations can be performed, but only by existing.
So to get back to my question of what predictability means in a QM universe under MW, the significant point seems to be that prediction is possible starting from the initial conditions of the Big Bang, but not from a later point in a particular universe (without complete information about the all other universes that have evolved from the Big Bang)?
Rather, the significant point is that you can predict the future with arbitrary precision, but the prediction will say things like “you are superpositioned into these three states”. That result is deterministic, but it doesn’t help you predict your future subjective experience when you’re facing down the branch point.
(You know that there will be three yous, each thinking “Huh, I was number 1/2/3”—but until you check, you won’t know which you you are.)
So, to get this clear (being well outside my comfort zone here), once a split into two branches has occurred, they no longer influence each other? The integration over all possibilities is something that happens in only one of the many worlds? (My recent understanding is based on “Everything that can happen does happen” by Cox & Forshaw).
There are no discrete “worlds” and “branches” in quantum physics as such. Once two regions in state space are sufficiently separated to no longer significantly influence each other they might be considered split, which makes the answer to your question “yes” by definition.
This seems to conflict with references to “many worlds” and “branch points” in other comments, or is the key word “discrete”? In other words, the states are a continuum with markedly varying density so that if you zoom out there is the appearance of branches? I could understand that expect for cases like Schroedinger’s cat where there seems to be a pretty clear branch (at the point where the box is opened, i.e. from the point of view of a particular state if that is the right terminology).
From the big bang there are an unimaginably large number of regions in state space each having an unimaginably small influence. It’s not obvious, but I can perfectly well believe that the net effect is dominated by the smallness of influence, so I’ll take your word for it.
Yes, but it’s still continuous. There’s always some influence, it can just get arbitrarily small. I’m unsure if this hypothetically allows MWI to be experimentally confirmed.
(The thesis of mangled-worlds seems to be that, in fact, in some cases that doesn’t happen—that is, world A’s influence on world B stays large.)
If it helps, think of half-silvered mirrors. Those are actually symmetric, letting through half the light either way; the trick is that the ambient lighting on the “reflective” side is orders of magnitude brighter, so the light shining through from the dark side is simply washed out.
To apply that to quantum mechanics, consider that the two branches—cat dead and not-dead—can still affect each other, but as if through a 99.9-whatever number of nines-silvered mirror. By the time a divergence gets to human scale, it’ll be very, very close to an absolute separation.
Thanks, so to get back to the original question of how to describe the different effects of divergence and convergence in the context of MW, here’s how it’s seeming to me. (The terminology is probably in need of refinement).
Considering this in terms of the LW-preferred Many Worlds interpretation of quantum mechanics, exact “prediction” is possible in principle but the prediction is of the indexical uncertainty of an array of outcomes. (The indexical uncertainty governs the probability of a particular outcome if one is considered at random.) Whether a process is convergent or divergent on a macro scale makes no difference to the number of states that formally need to be included in the distribution of possible outcomes. However, in the convergent process the cases become so similar that there appears to be only one outcome at the macro scale; whereas in a divergent process the “density of probability” (in the above sense) becomes so vanishingly small for some states that at a macro scale the outcomes appear to split into separate branches. (They have become decoherent.) Any one such branch appears to an observer within that branch to be the only outcome, and so such an observer could not have known what to “expect”—only the probability distribution of what to expect. This can be described as a condition of subjective unpredictability, in the sense that there is no subjective expectation that can be formed before the divergent process which can be reliably expected to coincident with observation after the process.
With the caveat that I’m not a physicist, and don’t understand much of the math involved—yes, this seems to be correct.
Though note that quantum physics operates on phase space; if two outcomes are the same in every respect, then they really are the same outcome.