3 ms·

Right, but my point is that this doesn't mean that the initial state contains very much information. Maybe a different example makes this clearer. Suppose you

Right, but my point is that this doesn't mean that the initial state contains very much information. Maybe a different example makes this clearer. Suppose you use a quantum random number generator to choose letters from A to Z, and write out a full book this way. If you consider the entire (multiple) world, it's basically Borges' Library of Babel: it has non-zero amplitudes for every possible book. So one possible "thing that can happen" is that Shakespeare's Hamlet gets written. But that doesn't mean that the initial state of the universe somehow encodes the text of Hamlet. The initial state of the universe doesn't have any information at all, in quantum fluctuations or otherwise. You only see Hamlet emerge if you restrict your attention to some particular branches of the world. It was "bound to happen" that Hamlet would get written, but only because every book would get written.

kgwgk 7y ago
The initial state contains as much information as the current state if the evolution is unitary (only Schroedinger’s equation matters according to the MWI, right?). And surely the wavefunction of a system of 10^80 particles (or whatever) does contain some information about what happens... or do you think that “every book would get written” independently of the form of the universal wavefunction?
- vilhelm_s 7y ago
  But the "current state" of the entire wavefunction doesn't necessarily contain very much information. You only get most of the complexity (solar flares, novels) if you look at subsystems of it. I think the situation is exactly analogous to the Library of Babel in Borges' story. If someone sends you the entire library in the mail, they have given you zero bits of information. If they only send you a particular room of it you get more information, and narrowing it down to sending a particular book gives you more bits still. It's the same with the multiverse. If we start out with the photon about to go through the half-silvered mirror, the state looks like |photon>⊗|me>, and then over time it evolves into (1/√2)|photon went left>⊗|me observing left> + (1/√2)|photon went right>⊗|me observing right> and the latter state contains no more information than the former one (you can run the time evolution backwards to recover the original state). However, if you restrict your attention and only consider one of the branches, e.g. |photon went right>⊗|me observing right>, then you have added (one more bit) of information. And most macroscopic processes can be explained "one branch at a time", since in practice decoherence means that there are no noticable interactions between branches. I think in the MWI this is the source of most complexity in the universe: not detailed information encoded in the initial state, and not objective collapse, but the bits of information you implicitly create if you only consider one branch of an experimental outcome. I imagine the same thing happens in general: we start with some uniform soup (with ~zero information), in a bunch different MWI branches it self-gravitates slightly differently so we get a different set of galaxies and stars in each branch, then for each branch that has a planet, different quantum randomness may cause different intelligent life to develop, and eventually they may write different books. Of course, it's also possible that some small initial state gets magnified, as a separate mechanism, but that's the same in objective-collapse and MWI. The random bits created by objective collapse are the same same the ones you get by looking at particular branches in MWI.
  - kgwgk 7y ago
    > If we start out with the photon about to go through the half-silvered mirror, the state looks like |photon>⊗|me>, But in the MWI what we start with is the universal wavefunction |Psi>. Say there are 10^80 particles in the universe and they may have a spin and could be in infinite locations. That makes for an ininite-dimensional Hilbert space. If we consider that the precision in the location variables is limited by Planck's length there are still around 10^180 possible locations in the universe for each particle. The Hilbert space where the quantum state of the universe is defined is huge. Now, you say "the state looks like |photon>⊗|me>". To keep things simple and in the realm of Schroedinger's equation I will consider an electron instead of a photon, prepared in the state spin z=+1/2. Is "|up>⊗|me>" shorthand for "(1 |up> + 0 |down>)⊗|me, the electron at that position, the rest of the universe>" which would be the "in-branch" quantum state of the universe? If indeed |Psi> can be written as a superposition of that state and an inconceivable huge number of orthogonal states, are all those states (when their coefficient is non-zero) the multiple worlds? But given |Psi> there are infinitely many (or at least a lot of) possible basis to express the pure state as a decomposition (including of course the one where the only non-zero "world" in the superposition is the one described by the wave function |Psi>). Do we count as "worlds" as well the states appearing in other basis? Is this slicing of |Psi> into other states just a mathematical trick or does it have a physical meaning? Even if we can redo the operation at different times on the evolving |Psi(t)>, how are the "emergent substates" at different times related? The answer to all these questions is far from trivial.
    - vilhelm_s 7y ago
      Indeed not, but is any of this relevant to the original quote, that deterministic dynamics means that the initial state of the universe must have lots of information hidden in the far-off decimals? I would hope that one could consider a simplified setting for that and then extrapolate back to the continuous case.
      - kgwgk 7y ago
        I agree the original quote doesn’t present a very strong argument against the MWI. In the same way that arguments against determinism in classical physics are not very convincing. But seemed worth pointing out. In the MWI case it’s not clear how sensitive the “worlds” are to the in initial state. It’s not even clear how sensitive they are to the current state! Better understanding of how (and how many) worlds “emerge” would be needed to say if the “problem” is or not as bad as in the classical case. Is the number of worlds stable? Is it increasing? In any case, those worlds are the inevitable consequence of the initial conditions even though we can’t even estimate how much fine-tuning is needed. I don’t think “randomness generated along the way” is a satisfactory counter-argument.

kgwgk 7y ago

The initial state contains as much information as the current state if the evolution is unitary (only Schroedinger’s equation matters according to the MWI, right?). And surely the wavefunction of a system of 10^80 particles (or whatever) does contain some information about what happens... or do you think that “every book would get written” independently of the form of the universal wavefunction?

vilhelm_s 7y ago
But the "current state" of the entire wavefunction doesn't necessarily contain very much information. You only get most of the complexity (solar flares, novels) if you look at subsystems of it. I think the situation is exactly analogous to the Library of Babel in Borges' story. If someone sends you the entire library in the mail, they have given you zero bits of information. If they only send you a particular room of it you get more information, and narrowing it down to sending a particular book gives you more bits still. It's the same with the multiverse. If we start out with the photon about to go through the half-silvered mirror, the state looks like |photon>⊗|me>, and then over time it evolves into (1/√2)|photon went left>⊗|me observing left> + (1/√2)|photon went right>⊗|me observing right> and the latter state contains no more information than the former one (you can run the time evolution backwards to recover the original state). However, if you restrict your attention and only consider one of the branches, e.g. |photon went right>⊗|me observing right>, then you have added (one more bit) of information. And most macroscopic processes can be explained "one branch at a time", since in practice decoherence means that there are no noticable interactions between branches. I think in the MWI this is the source of most complexity in the universe: not detailed information encoded in the initial state, and not objective collapse, but the bits of information you implicitly create if you only consider one branch of an experimental outcome. I imagine the same thing happens in general: we start with some uniform soup (with ~zero information), in a bunch different MWI branches it self-gravitates slightly differently so we get a different set of galaxies and stars in each branch, then for each branch that has a planet, different quantum randomness may cause different intelligent life to develop, and eventually they may write different books. Of course, it's also possible that some small initial state gets magnified, as a separate mechanism, but that's the same in objective-collapse and MWI. The random bits created by objective collapse are the same same the ones you get by looking at particular branches in MWI.
- kgwgk 7y ago
  > If we start out with the photon about to go through the half-silvered mirror, the state looks like |photon>⊗|me>, But in the MWI what we start with is the universal wavefunction |Psi>. Say there are 10^80 particles in the universe and they may have a spin and could be in infinite locations. That makes for an ininite-dimensional Hilbert space. If we consider that the precision in the location variables is limited by Planck's length there are still around 10^180 possible locations in the universe for each particle. The Hilbert space where the quantum state of the universe is defined is huge. Now, you say "the state looks like |photon>⊗|me>". To keep things simple and in the realm of Schroedinger's equation I will consider an electron instead of a photon, prepared in the state spin z=+1/2. Is "|up>⊗|me>" shorthand for "(1 |up> + 0 |down>)⊗|me, the electron at that position, the rest of the universe>" which would be the "in-branch" quantum state of the universe? If indeed |Psi> can be written as a superposition of that state and an inconceivable huge number of orthogonal states, are all those states (when their coefficient is non-zero) the multiple worlds? But given |Psi> there are infinitely many (or at least a lot of) possible basis to express the pure state as a decomposition (including of course the one where the only non-zero "world" in the superposition is the one described by the wave function |Psi>). Do we count as "worlds" as well the states appearing in other basis? Is this slicing of |Psi> into other states just a mathematical trick or does it have a physical meaning? Even if we can redo the operation at different times on the evolving |Psi(t)>, how are the "emergent substates" at different times related? The answer to all these questions is far from trivial.
  - vilhelm_s 7y ago
    Indeed not, but is any of this relevant to the original quote, that deterministic dynamics means that the initial state of the universe must have lots of information hidden in the far-off decimals? I would hope that one could consider a simplified setting for that and then extrapolate back to the continuous case.
    - kgwgk 7y ago
      I agree the original quote doesn’t present a very strong argument against the MWI. In the same way that arguments against determinism in classical physics are not very convincing. But seemed worth pointing out. In the MWI case it’s not clear how sensitive the “worlds” are to the in initial state. It’s not even clear how sensitive they are to the current state! Better understanding of how (and how many) worlds “emerge” would be needed to say if the “problem” is or not as bad as in the classical case. Is the number of worlds stable? Is it increasing? In any case, those worlds are the inevitable consequence of the initial conditions even though we can’t even estimate how much fine-tuning is needed. I don’t think “randomness generated along the way” is a satisfactory counter-argument.