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> ... although it relies on reifying particles embedded in waves to essentially select a single world, ... Is the mathematical formalism actually more unwieldy

> ... although it relies on reifying particles embedded in waves to essentially select a single world, ... Is the mathematical formalism actually more unwieldy, or is it just this interpretation of what it's doing? The 'select a single world' sounds like taking some of the conceptual framework from Everett and trying to paste it on here, rather than giving the Bohm interpretation its own conceptual framework which could possibly be more elegant?

jostylr 8y ago
The Bohm interpretation is quite simple. It does start with the idea that the world is made of particles and that we are satisfied if we can make correct predictions of where stuff is. In other words, I have a computer in front of me and a particle theory would say that is because there are particles making up the computer and they are located in front of me. So that is the correspondence with reality. For some, this is a reasonable starting point. For most others, it is blasphemy for some reason. Once we settle on stuff with position, then we have to ask how that stuff changes. One option is that we specify accelerations; that's Newton's way. Another option is to specify velocities. That is the Bohm way. Specifically, the velocity is derived from the wave function of quantum mechanics. It is basically the derivative of the wave function, normalized and made real. Done. You can see a simple derivation of the equations here: https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivations https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivat... The first one derives Bohm's equation very quickly and simply from the starting wave relation equations of Einstein and de Broglie. The complication is that the wave function is a function of the configurations of all the particles. Thus, to get the velocity, one technically needs the positions of all of the particles of the universe. Practically, one only needs the positions of entangled particles, but still. It is a non-trivial setup though the most basic, natural setup one could possibly have given particles and a wave function. Also, the particle positions do not influence the wave function evolution. This is rather unusual. For the Dirac wave function, it is even simpler. That object directly gives the velocity of the particles; no derivative needed. Contrast this with MW which says, I guess, that the fundamental thing that we are concerned with is the wave function. It does not seem that particles exist in any meaningful sense in that theory. It is as if we are machines able to track a singular aspect of the change of an abstract vector in Hilbert space. It is not clear why this vector is often represented as a function on configuration space when there is no configuration of stuff. The theory essentially says that actual reality is nothing at all like what we perceive. I would think an honest account of a theory which only has a wave function would be to formulate the theory on an abstract Hilbert space and derive configuration space and, thus, configurations from that. Not very likely, by the way. Reality may be deceptive, but I certainly prefer to start with theories in which our experience is explained in a pretty simple and straightforward way: it looks like stuff is over there because there is stuff over there. We have singular experiences because a single experience is what actually happens. Also note that in Bohmian mechanics, we specify the initial wave function and the initial particles and then evolve the system using differential equations. All of the operator stuff, collapse, etc., comes out of that evolution; we don't need to have any special considerations about them. The quantum formalism becomes analogous to thermodynamics, not a fundamental theory, but a useful practical one replacing the individual evolutions with some useful shorthand. In MW, there is this question of how to model an experimental situation. Where are the measurement operators coming from? What is a subsystem? In BM, these things arise essentially by conditioning on the configuration of the environment. In certain situations, this will give rise to roughly an isolated system evolving according to its own Bohmian dynamics. The measurement interaction is then represented by an operator, or its generalization, depending. But all of that emerges from the basic differential equations evolving the universe. It is not clear to me how easy it is to do that kind of analysis in MW. After all, there is no singular experience to break it down to, there is no subsystem, there is no definitive experiment being done. It is not really clear how one would falsify a theory which, more or less, assumes everything happens.
- nessus42 8y ago
  > Reality may be deceptive, but I certainly prefer to start with theories in which our experience is explained in a pretty simple and straightforward way: it looks like stuff is over there because there is stuff over there. We have singular experiences because a single experience is what actually happens. This assertion does not make sense to me. The Everett Interpretation and the Bohm Interpretation are experimentally indistinguishable from each other, as I understand things. Consequently, there is no mystery at all with the Everett Interpretation as to why things appear to us the way that they do. Since the Everett Interpretation is a significantly simpler theory than Bohm's, we should prefer it due to Occam's Razor. On the other hand, since they are experimentally indistinguishable from each other, we can never scientifically assert which of the two is correct, no matter how much evidence we have.
  - jostylr 8y ago
    Everett's theory categorically tells us that the results of experiments differ from the results in Bohmian mechanics. In Bohmian mechanics, a typical experiment will have one result. In Everett, experiments have all possible outcomes happening. These are not the same. The "indistinguishable" part happens because, according to Everett, there is some version of the experimenter that will have the same experience as the single experimenter in the Bohmian world. This is not simpler. I have no reason to believe that there are infinitely many copies of me out there. Everett's theory says that there are. Fine. I can't disprove it. I also can't disprove that every instant of my experience is being carefully orchestrated by a thousand angels. It is experimentally indistinguishable from any theory you care to posit. But I prefer theories where my actual experience is supposed to be a reasonable reflection of reality. I experience a single me and therefore I would prefer a theory in which there is a single me. Bohmian mechanics provides that and in a completely natural and reasonable way. Everett categorically disputes my experience as being reflective of reality. There are infinitely many copies of me and my experience of being singular is an illusion. I can't dissuade people from embracing that, but it certainly strikes me as peculiar. Also, in terms of experiments, Everett has infinitely many copies of the universe where all of the statistics of the experiments come out wrong. There are infinitely many that come out right. Is that experimentally indistinguishable? I don't know. Kind of a strange question in the context of "most everything happens".

jostylr 8y ago

The Bohm interpretation is quite simple. It does start with the idea that the world is made of particles and that we are satisfied if we can make correct predictions of where stuff is. In other words, I have a computer in front of me and a particle theory would say that is because there are particles making up the computer and they are located in front of me. So that is the correspondence with reality. For some, this is a reasonable starting point. For most others, it is blasphemy for some reason. Once we settle on stuff with position, then we have to ask how that stuff changes. One option is that we specify accelerations; that's Newton's way. Another option is to specify velocities. That is the Bohm way. Specifically, the velocity is derived from the wave function of quantum mechanics. It is basically the derivative of the wave function, normalized and made real. Done. You can see a simple derivation of the equations here: https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivations https://en.wikipedia.org/wiki/De_Broglie–Bohm_theory#Derivat... The first one derives Bohm's equation very quickly and simply from the starting wave relation equations of Einstein and de Broglie. The complication is that the wave function is a function of the configurations of all the particles. Thus, to get the velocity, one technically needs the positions of all of the particles of the universe. Practically, one only needs the positions of entangled particles, but still. It is a non-trivial setup though the most basic, natural setup one could possibly have given particles and a wave function. Also, the particle positions do not influence the wave function evolution. This is rather unusual. For the Dirac wave function, it is even simpler. That object directly gives the velocity of the particles; no derivative needed. Contrast this with MW which says, I guess, that the fundamental thing that we are concerned with is the wave function. It does not seem that particles exist in any meaningful sense in that theory. It is as if we are machines able to track a singular aspect of the change of an abstract vector in Hilbert space. It is not clear why this vector is often represented as a function on configuration space when there is no configuration of stuff. The theory essentially says that actual reality is nothing at all like what we perceive. I would think an honest account of a theory which only has a wave function would be to formulate the theory on an abstract Hilbert space and derive configuration space and, thus, configurations from that. Not very likely, by the way. Reality may be deceptive, but I certainly prefer to start with theories in which our experience is explained in a pretty simple and straightforward way: it looks like stuff is over there because there is stuff over there. We have singular experiences because a single experience is what actually happens. Also note that in Bohmian mechanics, we specify the initial wave function and the initial particles and then evolve the system using differential equations. All of the operator stuff, collapse, etc., comes out of that evolution; we don't need to have any special considerations about them. The quantum formalism becomes analogous to thermodynamics, not a fundamental theory, but a useful practical one replacing the individual evolutions with some useful shorthand. In MW, there is this question of how to model an experimental situation. Where are the measurement operators coming from? What is a subsystem? In BM, these things arise essentially by conditioning on the configuration of the environment. In certain situations, this will give rise to roughly an isolated system evolving according to its own Bohmian dynamics. The measurement interaction is then represented by an operator, or its generalization, depending. But all of that emerges from the basic differential equations evolving the universe. It is not clear to me how easy it is to do that kind of analysis in MW. After all, there is no singular experience to break it down to, there is no subsystem, there is no definitive experiment being done. It is not really clear how one would falsify a theory which, more or less, assumes everything happens.

nessus42 8y ago
> Reality may be deceptive, but I certainly prefer to start with theories in which our experience is explained in a pretty simple and straightforward way: it looks like stuff is over there because there is stuff over there. We have singular experiences because a single experience is what actually happens. This assertion does not make sense to me. The Everett Interpretation and the Bohm Interpretation are experimentally indistinguishable from each other, as I understand things. Consequently, there is no mystery at all with the Everett Interpretation as to why things appear to us the way that they do. Since the Everett Interpretation is a significantly simpler theory than Bohm's, we should prefer it due to Occam's Razor. On the other hand, since they are experimentally indistinguishable from each other, we can never scientifically assert which of the two is correct, no matter how much evidence we have.
- jostylr 8y ago
  Everett's theory categorically tells us that the results of experiments differ from the results in Bohmian mechanics. In Bohmian mechanics, a typical experiment will have one result. In Everett, experiments have all possible outcomes happening. These are not the same. The "indistinguishable" part happens because, according to Everett, there is some version of the experimenter that will have the same experience as the single experimenter in the Bohmian world. This is not simpler. I have no reason to believe that there are infinitely many copies of me out there. Everett's theory says that there are. Fine. I can't disprove it. I also can't disprove that every instant of my experience is being carefully orchestrated by a thousand angels. It is experimentally indistinguishable from any theory you care to posit. But I prefer theories where my actual experience is supposed to be a reasonable reflection of reality. I experience a single me and therefore I would prefer a theory in which there is a single me. Bohmian mechanics provides that and in a completely natural and reasonable way. Everett categorically disputes my experience as being reflective of reality. There are infinitely many copies of me and my experience of being singular is an illusion. I can't dissuade people from embracing that, but it certainly strikes me as peculiar. Also, in terms of experiments, Everett has infinitely many copies of the universe where all of the statistics of the experiments come out wrong. There are infinitely many that come out right. Is that experimentally indistinguishable? I don't know. Kind of a strange question in the context of "most everything happens".