3 ms·

De Broglie-Bohm is probably not the correct theory, since (if I am not mistaken) it's not reconcilable with relativity, and has a host of other problems which l

by tbabb 8y ago

De Broglie-Bohm is probably not the correct theory, since (if I am not mistaken) it's not reconcilable with relativity, and has a host of other problems which led its original proponents to abandon it. Copenhagen is also probably not correct, though it is still frustratingly mainstream. Copenhagen has the well known problem of lacking a physical definition of "observer", but it also has conflicts with delayed choice quantum eraser experiments (which suggest that the wavefunction never collapses), and contradictions that arise when you try to locate the proposed wave collapse in spacetime. The Everett many-worlds interpretation is gaining favor, and has none of the problems of the other two pictures. In the Everett view, scientists and experiments and instruments and universes are ensembles of particles like any other, and enter superpositions upon interacting with other systems in superposition. In a sense, every possible outcome of a quantum measurement actually happens in due proportion to the probabilities described by quantum mechanics, but upon becoming entangled with the experiment result, the different outcomes can no longer influence or measure each other. It is the most ontologically minimal theory, since it proposes no other events or laws beyond the already-known laws of quantum mechanics.

effie 8y ago
In the Everettian interpretation, experiments do not have results (!) and it is not clear what probability even means, much less how the Born rule and observed statistics arise. That's because it is not a theory about our world, but about an imagined world where the only things existing is the psi function. > every possible outcome of a quantum measurement actually happens in due proportion to the probabilities described by quantum mechanics This cannot work, because those probabilities are defined by a basis in Hilbert space and that basis is defined by details of the experiment, which does not actually happen in the Everettian view.
- tbabb 8y ago
  I am not sure what you mean by "experiments do not have results." A measurement in Everett is the environment becoming entangled with the measured system, and a "result" is a particular basis of the combined wavefunction.
  - im3w1l 8y ago
    If you square the probability amplitude and take the absolute value, that you get something that works very much like a probability. But there is nothing in many-worlds theory that says this quantity has any special significance.
    - tbabb 8y ago
      I still either don't see why you say that, or don't follow what you are trying to say. The Born rule is a fundamental feature of all quantum theories, and I don't see why Everett is an exception. If you want an intuitive picture of what the squared amplitude means, it seems that it would suffice to think of it as the fraction of phase space which evolves into the configuration associated with that amplitude.
      - TheOtherHobbes 8y ago
        In fact you can't get to the Born rule from WMI without doing some (IMO) strange things. See e.g. https://arxiv.org/abs/1405.7907 https://arxiv.org/abs/1405.7907
  - effie 8y ago
    > what you mean by "experiments do not have results." Let the experiment measure spin projection s_y of an atom previously prepared in spin state |s_x+>. It is known empirically that this experiment has two possible mutually exclusive results, +1/2 and -1/2, with probability of each being 1/2. Standard quantum theory accepts this and uses mathematics to predict those probabilities from data on the mutual arrangement of preparator and analyser of the spin. Such predictions are difficult to be made in Everettian theory, because that theory describes both the particle with spin and those forming the measuring apparatus in the same way. When that is done, the physical process of measurement can be mathematically described by the Schroedinger equation, which may seem like a win, but it has a big downside: all it gives is a ray in the big Hilbert space of particle plus apparatus at later times; it is not clear what this calculation result is good for. It is not the prediction of real experiment's result; it is not even clear how to use it to calculate probabilities of those results. Certainly not by Born's rule - because what is the eigenfunction to be used in the Born formula? Such eigenfunction is, in standard theory, determined by the classical settings of the apparatus, such as orientation of the SG magnet. But there is no such thing in Everettian theory, there is just psi function.
CuriouslyC 8y ago
The stock many worlds hypothesis has a couple of really big problems. For one, the information content of the multiverse expands exponentially towards infinity. Second, it basically makes the amplitude of the wavefunction meaningless, since everything that can happen, does. If you make the assumption that the measure of the multiverse is fixed and quantized, things become a bit less conceptually problematic, but that breaks the math. Regardless, it still has the fewest problems among current paradigms.
- tbabb 8y ago
  > For one, the information content of the multiverse expands exponentially towards infinity. I don't agree. I would say that the biggest difference-- really, the fundamental difference-- between Everett and Copenhagen is that Everett says that the state evolution of the wave function is always unitary, while Copenhagen says that it's only unitary sometimes but not others (and don't ask about how to calculate which way it will act). Under unitary state evolution the volume of phase space is preserved and no information is globally created or destroyed. So the "branching" picture of Everett is not precisely correct, though it is handy language for building intuition. This should not be surprising because of complementary observables-- confining the state of one property will cause some other property to become proportionally unconfined, per Heisenberg.

by tbabb 8y ago

effie 8y ago

In the Everettian interpretation, experiments do not have results (!) and it is not clear what probability even means, much less how the Born rule and observed statistics arise. That's because it is not a theory about our world, but about an imagined world where the only things existing is the psi function. > every possible outcome of a quantum measurement actually happens in due proportion to the probabilities described by quantum mechanics This cannot work, because those probabilities are defined by a basis in Hilbert space and that basis is defined by details of the experiment, which does not actually happen in the Everettian view.

tbabb 8y ago
I am not sure what you mean by "experiments do not have results." A measurement in Everett is the environment becoming entangled with the measured system, and a "result" is a particular basis of the combined wavefunction.
- im3w1l 8y ago
  If you square the probability amplitude and take the absolute value, that you get something that works very much like a probability. But there is nothing in many-worlds theory that says this quantity has any special significance.
  - tbabb 8y ago
    I still either don't see why you say that, or don't follow what you are trying to say. The Born rule is a fundamental feature of all quantum theories, and I don't see why Everett is an exception. If you want an intuitive picture of what the squared amplitude means, it seems that it would suffice to think of it as the fraction of phase space which evolves into the configuration associated with that amplitude.
    - TheOtherHobbes 8y ago
      In fact you can't get to the Born rule from WMI without doing some (IMO) strange things. See e.g. https://arxiv.org/abs/1405.7907 https://arxiv.org/abs/1405.7907
- effie 8y ago
  > what you mean by "experiments do not have results." Let the experiment measure spin projection s_y of an atom previously prepared in spin state |s_x+>. It is known empirically that this experiment has two possible mutually exclusive results, +1/2 and -1/2, with probability of each being 1/2. Standard quantum theory accepts this and uses mathematics to predict those probabilities from data on the mutual arrangement of preparator and analyser of the spin. Such predictions are difficult to be made in Everettian theory, because that theory describes both the particle with spin and those forming the measuring apparatus in the same way. When that is done, the physical process of measurement can be mathematically described by the Schroedinger equation, which may seem like a win, but it has a big downside: all it gives is a ray in the big Hilbert space of particle plus apparatus at later times; it is not clear what this calculation result is good for. It is not the prediction of real experiment's result; it is not even clear how to use it to calculate probabilities of those results. Certainly not by Born's rule - because what is the eigenfunction to be used in the Born formula? Such eigenfunction is, in standard theory, determined by the classical settings of the apparatus, such as orientation of the SG magnet. But there is no such thing in Everettian theory, there is just psi function.

CuriouslyC 8y ago

The stock many worlds hypothesis has a couple of really big problems. For one, the information content of the multiverse expands exponentially towards infinity. Second, it basically makes the amplitude of the wavefunction meaningless, since everything that can happen, does. If you make the assumption that the measure of the multiverse is fixed and quantized, things become a bit less conceptually problematic, but that breaks the math. Regardless, it still has the fewest problems among current paradigms.

tbabb 8y ago
> For one, the information content of the multiverse expands exponentially towards infinity. I don't agree. I would say that the biggest difference-- really, the fundamental difference-- between Everett and Copenhagen is that Everett says that the state evolution of the wave function is always unitary, while Copenhagen says that it's only unitary sometimes but not others (and don't ask about how to calculate which way it will act). Under unitary state evolution the volume of phase space is preserved and no information is globally created or destroyed. So the "branching" picture of Everett is not precisely correct, though it is handy language for building intuition. This should not be surprising because of complementary observables-- confining the state of one property will cause some other property to become proportionally unconfined, per Heisenberg.