Loading ...
Sorry, an error occurred while loading the content.
 

Bohm & Relativity

Expand Messages
  • Jeff L Jones
    Hi, I m not sure if anyone is even on this list yet (Bell/Bohm), but I ve got something to say in regards of something Eric Dennis and I discussed earlier in a
    Message 1 of 8 , Oct 12, 2000
      Hi,

      I'm not sure if anyone is even on this list yet (Bell/Bohm),
      but I've got something to say in regards of something Eric Dennis
      and I discussed earlier in a private email...

      Bell's theory involves parameters which are presumed to be either
      not determinable, or not determined yet.

      Eric mentioned that he preferred to believe that they were not
      determined yet.

      But I have thought about this since and I believe that this
      alternative (the parameters being determinable by humans) is
      disprovable using relativity. In fact, I think the theory as
      a whole is probably disprovable or at least metaphysically
      inconsistant when combined with relativity--but this part at
      least, I think can easily be shown as contradictory with
      relativity.

      The reason is, that if these parameters were ever determined,
      you could send signals faster than the speed of light, and
      therefore backwards in time (to tell yourself what the lottery
      numbers are the next week if you wanted). This is different
      than the orthodox interpretation of quantum, where the state
      of a system can be affected faster than the speed of light but
      cannot be used to transmit signals in the form of information.

      Just consider the classic EPR experiment where two particles
      are entangled so that whatever happens to the state of one
      of them (the potential, according to Bohm), happens to the other
      and vice versa. The particles are sent in opposite directions
      and isolated in non-local regions. Then each is measured with
      a polarizer at a different angle by two different people (Alice
      and Bob).
      If Alice agrees ahead of time to set her polarizer to 0 degrees
      fixed, then Bob can transmit information to Alice by setting
      his to different degrees depending on what he wants to transmit.

      This normally can't happen because there is no way for either of
      them to predict what the outcomes of the experiment on either end
      will be based on different angle measurements.
      But if the hidden parameters were known, then they would know
      based on any particular combination of angles what the results at
      both ends would be (photon transmitted or reflected). All they
      would have to do is find two different angles for Bob, one
      which will result in Alice's photon passing through her polarizer
      and another which will result in Alice's photon being reflected.
      (Since half of the angles in the 360 degree circle will be pass
      and the other half will be reflect, this shouldn't be difficult).

      Therefore, Bob can transmit a stream of bits instantaneously to
      Alice regardless of how many light-years Alice and Bob are separated
      by. Now, if you add relativity to that here's what happens:

      If Alice and Bob are both on separate spaceships travelling at the
      same speed in the same direction away from Earth, but separated by
      a great distance from each other, then from the Earth based frame
      of reference Bob will be transmitting information backwards in time
      to Alice. After this happens they could both stop their spaceships
      and then Alice could transmit the same information back to Bob
      instantaneously. But now this will be Bob's *past* self, before he
      originally transmitted the information.
      The grandfather paradox rules this out as possible, so therefore
      either relativity has to be wrong, or the hidden parameters of Bell's
      theory can never be discovered. This doesn't mean that the theory
      is non-deterministic, just that we will never be able to predict
      it in a deterministic fashion because the parameters will remain
      eternally hidden from us.

      I'm not sure what the background of everyone on this list is, but
      I know Eric is a physics grad student so will probably have a
      decent chance of understanding what I've written. If any clarification
      is needed I'd be happy to expand on any part of it.

      Jeff L Jones
    • Eric Dennis
      Jeff is correct in pointing out that in Bohm, there is nothing at the fundamental level prohibiting faster-than-light communication. This is in contrast to
      Message 2 of 8 , Oct 13, 2000
        Jeff is correct in pointing out that in Bohm, there is nothing at the
        fundamental level prohibiting faster-than-light communication. This is in
        contrast to standard QM, in which faster-than-light influences _do_ occur,
        but can never be controlled by a classical observer. That standard QM--or
        any theory duplicating its predictions for EPR experiments--is non-local
        in this way follows directly from Bell's theorem, as Bell himself made
        clear (see section 4 of "Bertlmann's socks and the nature of reality" in
        _Speakable and unspeakable in quantum mechanics_).

        Now the question is, is there some major difference between a theory which
        says non-local influences occur and one that says they occur and a human
        being is not in principle prevented from utilizing them? I don't believe
        there is. I don't believe such a question could play a fundamental role
        in evaluating a theory of physics. Either kind of theory is inconsistent
        with fundamental relativity. The conclusion I draw is that relativity is
        true statistically, but not metaphysically--that there's some underlying
        theory which has a preferred frame.

        Technical point: I'm not sure the grandfather (killing) paradox actually
        rules out a theory which allows you to control EPR signals, even assuming
        fundamental SR. The two EPR events are space-like separated (in all
        frames) so even though in some frames the singal may go back in time, it
        can never get into the backward light-cone of the singal source, hence the
        signal can never do anything to influence the source (assuming no further
        faster-than-light activity). In Bohm, the influences are always
        instantaneous in some frame, so they're always between two space
        space-like separated events in all frames.

        > Bell's theory involves parameters which are presumed to be either
        > not determinable, or not determined yet.

        Just to clarify: these parameters are just the (initial) positions of
        Bohmian particles in the system (including any measuring devices
        involved).
      • Jeff L Jones
        ... This is not true. I gave the example of the spaceship for a reason, to point out one of the features of relativity which is widely known: namely, that
        Message 3 of 8 , Oct 13, 2000
          On Fri, Oct 13, 2000 at 10:58:46AM -0400, Eric Dennis wrote:
          > Technical point: I'm not sure the grandfather (killing) paradox actually
          > rules out a theory which allows you to control EPR signals, even assuming
          > fundamental SR. The two EPR events are space-like separated (in all
          > frames) so even though in some frames the singal may go back in time, it
          > can never get into the backward light-cone of the singal source, hence the
          > signal can never do anything to influence the source (assuming no further
          > faster-than-light activity). In Bohm, the influences are always
          > instantaneous in some frame, so they're always between two space
          > space-like separated events in all frames.

          This is not true. I gave the example of the spaceship for a
          reason, to point out one of the features of relativity which is
          widely known: namely, that any ability to send signals faster
          than light can be used to send signals to the *same* point in space
          backwards in time.

          Take a look back at the example I gave: Alice and Bob are in the
          same reference frame which is different from Earth. Bob transmits
          the info to Alice, they both stop moving immediately (with respect
          to Earth), and Alice transmits it instantaneously back to Bob.

          During the first transmission it is going backwards in Earth-time.
          When they stop, they are now both in Earth's frame, so it moves
          directly across space without changing times. It ends up in the
          past, at Bob's location (where it originated, but further back
          in time). [This may be slightly simplifying the situation since
          you'd have to account for Bob moving in the past and not after
          the time they stop, but I would be happy to work out the Lorenz
          transformations if you're interested in seeing exactly how it
          could work.]

          This is why relativity implies the speed of light as such a hard limit;
          because if it is correct (which it seems to be in all things observed
          so far) then it means that faster than light signals are logically
          contradictory (not just metaphysically confusing).

          >
          > > Bell's theory involves parameters which are presumed to be either
          > > not determinable, or not determined yet.
          >
          > Just to clarify: these parameters are just the (initial) positions of
          > Bohmian particles in the system (including any measuring devices
          > involved).

          Maybe I'm misinterpretting what you're saying here, but it seems to me
          that this is oversimplifying the issue.

          Let's say you've got one photon passing through one polarizer. Even
          if you knew exactly what its position and velocity is, along with
          its exact polarization angle as it heads into the polarizer: this still
          is only enough to give you a probability as to whether it will pass
          through the polarizer. Standard quantum theory stops there, saying
          "ok, you've got a probability. That's all there is, nothing more."
          But Bohm goes on to say "ok, there must be some law governing whether
          it passes through, but we don't know it yet." This extra information
          about whether or not it will pass through is the hidden parameters
          I'm talking about; how would the initial position of the photon give
          you any information about that?

          I was assuming that along with the position, momentum, polarization,
          and wave equation, you would also have some additional state that's
          carried around and transforms according to some dynamic law, which
          determines what happens when it comes to a probability.
          Is this not what you were thinking of?

          Jeff L Jones
        • Eric Dennis
          ... You re right. There s no reason to assume no further faster-than-light activity . I didn t read your message carefully. Two signals does the job. Of
          Message 4 of 8 , Oct 13, 2000
            On Fri, 13 Oct 2000, Jeff L Jones wrote:

            > On Fri, Oct 13, 2000 at 10:58:46AM -0400, Eric Dennis wrote:
            > > Technical point: I'm not sure the grandfather (killing) paradox actually
            > > rules out a theory which allows you to control EPR signals, even assuming
            > > fundamental SR. The two EPR events are space-like separated (in all
            > > frames) so even though in some frames the singal may go back in time, it
            > > can never get into the backward light-cone of the singal source, hence the
            > > signal can never do anything to influence the source (assuming no further
            > > faster-than-light activity). In Bohm, the influences are always
            > > instantaneous in some frame, so they're always between two space
            > > space-like separated events in all frames.
            >
            > This is not true. I gave the example of the spaceship for a
            > reason, to point out one of the features of relativity which is
            > widely known: namely, that any ability to send signals faster
            > than light can be used to send signals to the *same* point in space
            > backwards in time.

            You're right. There's no reason to "assume no further faster-than-light
            activity". I didn't read your message carefully. Two signals does the job.
            Of course, this doesn't affect my position, which is that _any_
            faster-than-light influence, controllable or not, is in conflict with
            fundamental relativity.

            > Let's say you've got one photon passing through one polarizer. Even
            > if you knew exactly what its position and velocity is, along with
            > its exact polarization angle as it heads into the polarizer: this still
            > is only enough to give you a probability as to whether it will pass
            > through the polarizer. Standard quantum theory stops there, saying
            > "ok, you've got a probability. That's all there is, nothing more."
            > But Bohm goes on to say "ok, there must be some law governing whether
            > it passes through, but we don't know it yet." This extra information
            > about whether or not it will pass through is the hidden parameters
            > I'm talking about; how would the initial position of the photon give
            > you any information about that?

            Not just the initial conditions for the photon, but also for the
            polarizer/detector (which can be adequately modelled as one quantum degree
            of freedom that gets entangled with the photon and subsequently couples to
            many further degrees of freedom in a FAPP irreversible way). There are no
            additional "hidden varibales". In this sense Bohm is a totally complete
            theory.
          • Jeff L Jones
            ... In conflict, yes, but there is more than one meaning for conflict . Most quantum theories (including Bohm s, if you assume the initial parameters are not
            Message 5 of 8 , Oct 13, 2000
              On Fri, Oct 13, 2000 at 05:08:53PM -0400, Eric Dennis wrote:
              >
              > Of course, this doesn't affect my position, which is that _any_
              > faster-than-light influence, controllable or not, is in conflict with
              > fundamental relativity.

              In conflict, yes, but there is more than one meaning for "conflict".
              Most quantum theories (including Bohm's, if you assume the initial
              parameters are not discoverable) involve no predictions which contradict
              relativity. They may involve a metaphysics which is different for
              different frames, or must transform with the Lorenzian (such as cause
              and effect might be reversed in one frame as opposed to another), but
              they don't have anything observable that conflicts with relativity. This
              isn't to say that I'm ok with that; I think the idea of cause and effect
              reversing depending on what perspective you take is extremely ugly and a
              simpler model should be used. But when it comes down to it, you cannot
              violate the Heisenberg Uncertainty principle or discover the hidden
              variables (or "initial conditions") of Bohm's theory without directly
              contradicting the experimental results of relativity.

              Also, there are theories which claim be local but "incomplete" in that
              they do not ascribe any real properties to quanta until they are measured.
              It's these theories that I think have the best chance in the long run,
              (because of their compatibility with relativity) although I admit I am
              still learning and do not fully undestand how all aspects fit together.
              This type of theory is the most difficult to understand because it is
              so different than anything we're used to in terms of how the macroscopic
              world operates.

              > Not just the initial conditions for the photon, but also for the
              > polarizer/detector (which can be adequately modelled as one quantum degree
              > of freedom that gets entangled with the photon and subsequently couples to
              > many further degrees of freedom in a FAPP irreversible way). There are no
              > additional "hidden varibales". In this sense Bohm is a totally complete
              > theory.

              Yes, it is totally complete. But that's precisely why it has issues with
              relativity. Incomplete theories are much more compatible.

              Jeff L Jones
            • Hakan2
              Hi Jeff and Dennis, Although I am not a physicist, nor a scientist I am interested in these topics rather philosophically and would like to say a few humble
              Message 6 of 8 , Oct 21, 2000
                Hi Jeff and Dennis,
                Although I am not a physicist, nor a scientist I am interested in
                these topics rather philosophically and would like to say a few
                humble words :

                If Bohm's (or whoever's in general)theory is complete it can not be
                regarded as a theory because any theory must be incomplete by
                definition in order for it to be consistent.But if it is incomplete,
                then it can be consistent but cannot explain the world.

                I draw these coclusions from Goedel's incompleteness theorem.Thus any
                theory which is powerful enough to explain everything is doomed to
                suffer from either being complete and inconsistent, or consistent but
                incomplete!!

                What we mortals are left with is simply choosing from which to suffer.


                Regards.

                Hakan.








                --- In bell_bohm@egroups.com, Jeff L Jones <jeff@t...> wrote:
                > On Fri, Oct 13, 2000 at 05:08:53PM -0400, Eric Dennis wrote:
                > >
                > > Of course, this doesn't affect my position, which is that _any_
                > > faster-than-light influence, controllable or not, is in conflict
                with
                > > fundamental relativity.
                >
                > In conflict, yes, but there is more than one meaning for "conflict".
                > Most quantum theories (including Bohm's, if you assume the initial
                > parameters are not discoverable) involve no predictions which
                contradict
                > relativity. They may involve a metaphysics which is different for
                > different frames, or must transform with the Lorenzian (such as
                cause
                > and effect might be reversed in one frame as opposed to another),
                but
                > they don't have anything observable that conflicts with
                relativity. This
                > isn't to say that I'm ok with that; I think the idea of cause and
                effect
                > reversing depending on what perspective you take is extremely ugly
                and a
                > simpler model should be used. But when it comes down to it, you
                cannot
                > violate the Heisenberg Uncertainty principle or discover the hidden
                > variables (or "initial conditions") of Bohm's theory without
                directly
                > contradicting the experimental results of relativity.
                >
                > Also, there are theories which claim be local but "incomplete" in
                that
                > they do not ascribe any real properties to quanta until they are
                measured.
                > It's these theories that I think have the best chance in the long
                run,
                > (because of their compatibility with relativity) although I admit I
                am
                > still learning and do not fully undestand how all aspects fit
                together.
                > This type of theory is the most difficult to understand because it
                is
                > so different than anything we're used to in terms of how the
                macroscopic
                > world operates.
                >
                > > Not just the initial conditions for the photon, but also for the
                > > polarizer/detector (which can be adequately modelled as one
                quantum degree
                > > of freedom that gets entangled with the photon and subsequently
                couples to
                > > many further degrees of freedom in a FAPP irreversible way).
                There are no
                > > additional "hidden varibales". In this sense Bohm is a totally
                complete
                > > theory.
                >
                > Yes, it is totally complete. But that's precisely why it has
                issues with
                > relativity. Incomplete theories are much more compatible.
                >
                > Jeff L Jones
              • Jeff L Jones
                ... Hakan, welcome to the list... I have thought of the connection between completeness in physical theories and completeness in formal logic systems before
                Message 7 of 8 , Oct 21, 2000
                  On Sat, Oct 21, 2000 at 03:51:48PM -0000, Hakan2 wrote:
                  > Hi Jeff and Dennis,
                  > Although I am not a physicist, nor a scientist I am interested in
                  > these topics rather philosophically and would like to say a few
                  > humble words :
                  >
                  > If Bohm's (or whoever's in general)theory is complete it can not be
                  > regarded as a theory because any theory must be incomplete by
                  > definition in order for it to be consistent.But if it is incomplete,
                  > then it can be consistent but cannot explain the world.
                  >
                  > I draw these coclusions from Goedel's incompleteness theorem.Thus any
                  > theory which is powerful enough to explain everything is doomed to
                  > suffer from either being complete and inconsistent, or consistent but
                  > incomplete!!
                  >
                  > What we mortals are left with is simply choosing from which to suffer.
                  >
                  >
                  > Regards.
                  >
                  > Hakan.

                  Hakan, welcome to the list...

                  I have thought of the connection between completeness in physical theories
                  and completeness in formal logic systems before and there are definitely
                  some analogies there. But as far as anyone knows there is no real
                  connection between the two.

                  Goedel's Theorem applies to formal logic systems, and it says that any
                  system which is isomorphic to the integers (can be represented by the
                  integers) can never be characterized by a set of axioms such that every
                  statement you could make about that system is formally provable to be
                  true or false.
                  He did this by showing that you could make statements that say essentially
                  "this statement can not be formally proven". The statement is true, but
                  it can never be formally proven to be true because if it were than it
                  wouldn't be.
                  So in order to have a complete set of axioms you would have to add an
                  axiom that said that the statement was true. This would be consistant
                  with whatever previous set of axioms you had but adjoining the opposite
                  axiom would not be consistant.

                  So what Goedel proved was that no matter how many axioms you add, you still
                  can't prove all statements true or false without adding more (because the
                  more axioms you add the more new weird statements you can make).

                  The closest equivalent I can think of to Goedel's proof in physics would be
                  this: suppose you built a computer which you could enter in initial positions
                  and velocities of all the particles in a system. It would then use some
                  formula to spit out what is going to happen in the future for that system.
                  So if you asked it "will this computer be on or off in 5 minutes", and then
                  based on its answer either unplugged it or kept it plugged in (did the
                  opposite of whatever it spits out) then you'd have a serious contradiction.
                  This contradiction would be the only type that Goedel's Incompleteness
                  Theorem would warn about. And it's precisely because you tried to make the
                  computer give a statement about itself. It *wouldn't* warn anything about
                  having a theory which (given enough time) could predict what will happen
                  in a system isolated from where the calculations are being performed. If
                  you had such a theory you could call it complete in Physics terms, even
                  though you would still have the problem with the computer not being able to
                  predict itself.

                  So the main issue is just that you've got two different definitions of
                  complete, one used by physicists and one used by logicians. And the
                  logician's definition has little bearing on reality (since it would be
                  incredibly inpractical anyway to build such a computer anyway).

                  Speaking of things having little bearing; I suppose this thread has little
                  bearing on Bohm's thoery which is supposed to be the topic on this list.

                  Jeff L Jones

                  P.S. No offense, but it is *really* silly to use the word "suffer" in
                  respect to formal logic, or with things that are impractical
                  anyway.
                • Hakan2
                  Ok.But physical theories also use math and math is based on formalism.Does this not put the physical theories at stake, or render them dubious? Regards. Hakan.
                  Message 8 of 8 , Oct 28, 2000
                    Ok.But physical theories also use math and math is based on
                    formalism.Does this not put the physical theories at stake, or render
                    them dubious?

                    Regards.
                    Hakan.
                    --- In bell_bohm@egroups.com, Jeff L Jones <jeff@t...> wrote:
                    > On Sat, Oct 21, 2000 at 03:51:48PM -0000, Hakan2 wrote:
                    > > Hi Jeff and Dennis,
                    > > Although I am not a physicist, nor a scientist I am interested in
                    > > these topics rather philosophically and would like to say a few
                    > > humble words :
                    > >
                    > > If Bohm's (or whoever's in general)theory is complete it can not
                    be
                    > > regarded as a theory because any theory must be incomplete by
                    > > definition in order for it to be consistent.But if it is
                    incomplete,
                    > > then it can be consistent but cannot explain the world.
                    > >
                    > > I draw these coclusions from Goedel's incompleteness theorem.Thus
                    any
                    > > theory which is powerful enough to explain everything is doomed
                    to
                    > > suffer from either being complete and inconsistent, or consistent
                    but
                    > > incomplete!!
                    > >
                    > > What we mortals are left with is simply choosing from which to
                    suffer.
                    > >
                    > >
                    > > Regards.
                    > >
                    > > Hakan.
                    >
                    > Hakan, welcome to the list...
                    >
                    > I have thought of the connection between completeness in physical
                    theories
                    > and completeness in formal logic systems before and there are
                    definitely
                    > some analogies there. But as far as anyone knows there is no real
                    > connection between the two.
                    >
                    > Goedel's Theorem applies to formal logic systems, and it says that
                    any
                    > system which is isomorphic to the integers (can be represented by
                    the
                    > integers) can never be characterized by a set of axioms such that
                    every
                    > statement you could make about that system is formally provable to
                    be
                    > true or false.
                    > He did this by showing that you could make statements that say
                    essentially
                    > "this statement can not be formally proven". The statement is
                    true, but
                    > it can never be formally proven to be true because if it were than
                    it
                    > wouldn't be.
                    > So in order to have a complete set of axioms you would have to add
                    an
                    > axiom that said that the statement was true. This would be
                    consistant
                    > with whatever previous set of axioms you had but adjoining the
                    opposite
                    > axiom would not be consistant.
                    >
                    > So what Goedel proved was that no matter how many axioms you add,
                    you still
                    > can't prove all statements true or false without adding more
                    (because the
                    > more axioms you add the more new weird statements you can make).
                    >
                    > The closest equivalent I can think of to Goedel's proof in physics
                    would be
                    > this: suppose you built a computer which you could enter in
                    initial positions
                    > and velocities of all the particles in a system. It would then use
                    some
                    > formula to spit out what is going to happen in the future for that
                    system.
                    > So if you asked it "will this computer be on or off in 5 minutes",
                    and then
                    > based on its answer either unplugged it or kept it plugged in (did
                    the
                    > opposite of whatever it spits out) then you'd have a serious
                    contradiction.
                    > This contradiction would be the only type that Goedel's
                    Incompleteness
                    > Theorem would warn about. And it's precisely because you tried to
                    make the
                    > computer give a statement about itself. It *wouldn't* warn
                    anything about
                    > having a theory which (given enough time) could predict what will
                    happen
                    > in a system isolated from where the calculations are being
                    performed. If
                    > you had such a theory you could call it complete in Physics terms,
                    even
                    > though you would still have the problem with the computer not being
                    able to
                    > predict itself.
                    >
                    > So the main issue is just that you've got two different definitions
                    of
                    > complete, one used by physicists and one used by logicians. And the
                    > logician's definition has little bearing on reality (since it would
                    be
                    > incredibly inpractical anyway to build such a computer anyway).
                    >
                    > Speaking of things having little bearing; I suppose this thread has
                    little
                    > bearing on Bohm's thoery which is supposed to be the topic on this
                    list.
                    >
                    > Jeff L Jones
                    >
                    > P.S. No offense, but it is *really* silly to use the word "suffer"
                    in
                    > respect to formal logic, or with things that are impractical
                    > anyway.
                  Your message has been successfully submitted and would be delivered to recipients shortly.