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Re: Quantum Mechanical Probability

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  • june.shippey@ntlworld.com
    Probability itself is also a big Philosophical question of what it is or really means in Physics anyway.And that before you get to QM. There need to be
    Message 1 of 30 , Oct 3, 2002
      Probability itself is also a big Philosophical question of what it is or
      really means in Physics anyway.And that before you get to QM.


      There need to be explaination behind Probability it self beofore ywe
      leave it Oh it just the likely hood of this or that?

      Gordon.
    • Gary Oberbrunner
      Well yes, this is part of the point of FoR. The MWI gives physical meaning to probability, and to counterfactuals as well (at least physically possible
      Message 2 of 30 , Oct 4, 2002
        Well yes, this is part of the point of FoR. The MWI gives physical
        meaning to probability, and to counterfactuals as well (at least
        physically possible counterfactuals).

        -- Gary

        june.shippey@... wrote:
        > Probability itself is also a big Philosophical question of what it is or
        > really means in Physics anyway.And that before you get to QM.
        >
        >
        > There need to be explaination behind Probability it self beofore ywe
        > leave it Oh it just the likely hood of this or that?
      • june.shippey@ntlworld.com
        Gary Oberbrunner wrote: well probability in QM is not primary as Deutsch point out in his paper. as for Macro stuff and the Philosophy of Math of probability
        Message 3 of 30 , Oct 4, 2002
          Gary Oberbrunner wrote:

          well probability in QM is not primary as Deutsch point out in his paper.

          as for Macro stuff and the Philosophy of Math of probability well that
          still got alot of loose ends?

          Gordon.
          >
          > Well yes, this is part of the point of FoR. The MWI gives physical
          > meaning to probability, and to counterfactuals as well (at least
          > physically possible counterfactuals).
          >
          > -- Gary
          >
          > june.shippey@... wrote:
          > > Probability itself is also a big Philosophical question of what it is or
          > > really means in Physics anyway.And that before you get to QM.
          > >
          > >
          > > There need to be explaination behind Probability it self beofore ywe
          > > leave it Oh it just the likely hood of this or that?
          >
          >
          >
          >
          > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
        • Wade Allsopp
          Is this really right? I m not convinced that MWI has anything very useful to say if we try and figure out what we mean when we claim for example: there is an
          Message 4 of 30 , Oct 4, 2002
            Is this really right? I'm not convinced that MWI has anything very
            useful to say if we try and figure out what we mean when we claim for
            example: there is an 80% chance that Michael Schumacher will win the
            next Grand Prix. If I have missed something, I would be delighted to be
            enlightened.

            Wade


            > From: Gary Oberbrunner [mailto:garyo@...]

            >
            > Well yes, this is part of the point of FoR. The MWI gives physical
            > meaning to probability, and to counterfactuals as well (at least
            > physically possible counterfactuals).
            >
            > -- Gary
            >
            > june.shippey@... wrote:
            > > Probability itself is also a big Philosophical question of
            > what it is
            > > or really means in Physics anyway.And that before you get to QM.
            > >
            > >
            > > There need to be explaination behind Probability it self
            > beofore ywe
            > > leave it Oh it just the likely hood of this or that?
          • Gary Oberbrunner
            I think you can restate that claim like this: In 80% of the universes starting from our current universe*, M.S. wins the next Grand Prix. Does that help? --
            Message 5 of 30 , Oct 4, 2002
              I think you can restate that claim like this:
              In 80% of the universes starting from our current universe*, M.S.
              wins the next Grand Prix.

              Does that help?

              -- Gary

              *: by universe I really mean "fungible sheaf of universes" of course.


              Wade Allsopp wrote:
              > Is this really right? I'm not convinced that MWI has anything very
              > useful to say if we try and figure out what we mean when we claim for
              > example: there is an 80% chance that Michael Schumacher will win the
              > next Grand Prix. If I have missed something, I would be delighted to be
              > enlightened.
            • Henry Sturman
              I suppose some MWI ers might claim that the statment there is an 80% chance that Michael Schumacher will win the next Grand Prix means: if we follow the
              Message 6 of 30 , Oct 4, 2002
                I suppose some MWI'ers might claim that the statment "there is an 80%
                chance that Michael Schumacher will win the next Grand Prix" means: if we
                follow the evolution of our current slice of the multiverse, the collection
                of subslices in which Michael Schumacher wins the next Grand Prix, has a
                relative thickness of 80%.

                However, such a view is based on an incorrect understanding of what we mean
                when we talk about probability. Let me give an example. Suppose I throw a
                die in the air and then I ask: what is the probability it will land as a 6.
                The above interpretation of probability may well give an answer above 99%,
                very close to 100%. The reason is that the die is very large, so it can in
                theory be calculated how it will land. Quantum effects are unlikely to be
                large enough to change the result of the calculation, hence the probability
                according to the above view will be very near either 1 or 0.

                The correct answer is, of course, 1/6.

                At 03:53 PM 4-10-2002 +0100, you wrote:
                >Is this really right? I'm not convinced that MWI has anything very
                >useful to say if we try and figure out what we mean when we claim for
                >example: there is an 80% chance that Michael Schumacher will win the
                >next Grand Prix. If I have missed something, I would be delighted to be
                >enlightened.
                >
                >Wade
                >
                >
                > > From: Gary Oberbrunner [mailto:garyo@...]
                >
                > >
                > > Well yes, this is part of the point of FoR. The MWI gives physical
                > > meaning to probability, and to counterfactuals as well (at least
                > > physically possible counterfactuals).
                > >
                > > -- Gary
                > >
                > > june.shippey@... wrote:
                > > > Probability itself is also a big Philosophical question of
                > > what it is
                > > > or really means in Physics anyway.And that before you get to QM.
                > > >
                > > >
                > > > There need to be explaination behind Probability it self
                > > beofore ywe
                > > > leave it Oh it just the likely hood of this or that?
                >
                >
                >
                >
                >
                >
                >Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/


                [Non-text portions of this message have been removed]
              • Wade Allsopp
                I m afriad this still leaves me perplexed. Firstly, how can we ever know or guess how many universes there out there in which MS will or won t win? Secondly I
                Message 7 of 30 , Oct 4, 2002
                  I'm afriad this still leaves me perplexed.

                  Firstly, how can we ever know or guess how many universes there out
                  there in which MS will or won't win?

                  Secondly I was under the impression that under the MWI view of the world
                  there were an invinite number of possible universes. If there are an
                  infinite number of universes where MS does win and an infinite number
                  where he does not, how can we get to the proportion of "MS Win"
                  universes? And what about the presumeably infinite number of universes
                  where say you or I win the Grand Prix ? I suspect it would be possible
                  to get pretty good odds that I won't win at any rate. Yet if one
                  imagines the world as a mass of electrons, quarks etc dansing around in
                  swerls of greater of lesser density, it seems kind of implausible that
                  there is a Schumacher "swerl of atoms" sitting around in Germany or
                  wherever which is on collision cause for winning the Grand Prix, when
                  there are so many billions of similarly complex "swerls of atoms"
                  scattered around the planet, which haven't got a snowball's chance no
                  hell of picking up the champers.

                  This is not to say that I have a better alternative vision of what
                  probability is all about, just that I cannot quite see how claiming that
                  in a certain percentages of universes MS wins, we are really throwing
                  much light on the mystery.

                  Wade

                  > From: Gary Oberbrunner [mailto:garyo@...]
                  >
                  > I think you can restate that claim like this:
                  > In 80% of the universes starting from our current universe*, M.S.
                  > wins the next Grand Prix.
                  >
                  > Does that help?
                  >
                  > -- Gary
                  >
                  > *: by universe I really mean "fungible sheaf of universes" of course.
                  >
                  >
                  > Wade Allsopp wrote:
                  > > Is this really right? I'm not convinced that MWI has anything very
                  > > useful to say if we try and figure out what we mean when we
                  > claim for
                  > > example: there is an 80% chance that Michael Schumacher
                  > will win the
                  > > next Grand Prix. If I have missed something, I would be
                  > delighted to
                  > > be enlightened.
                  >
                • june.shippey@ntlworld.com
                  ... [Gordon] The probability I was refer too was closer to semi Classical or Classical realm and not QM realm.
                  Message 8 of 30 , Oct 5, 2002
                    Henry Sturman wrote:
                    >
                    > I suppose some MWI'ers might claim that the statment "there is an 80%
                    > chance that Michael Schumacher will win the next Grand Prix" means: if we
                    > follow the evolution of our current slice of the multiverse, the collection
                    > of subslices in which Michael Schumacher wins the next Grand Prix, has a
                    > relative thickness of 80%.
                    >
                    > However, such a view is based on an incorrect understanding of what we mean
                    > when we talk about probability. Let me give an example. Suppose I throw a
                    > die in the air and then I ask: what is the probability it will land as a 6.
                    > The above interpretation of probability may well give an answer above 99%,
                    > very close to 100%. The reason is that the die is very large, so it can in
                    > theory be calculated how it will land. Quantum effects are unlikely to be
                    > large enough to change the result of the calculation, hence the probability
                    > according to the above view will be very near either 1 or 0.
                    >
                    > The correct answer is, of course, 1/6.
                    >
                    > At 03:53 PM 4-10-2002 +0100, you wrote:
                    > >Is this really right? I'm not convinced that MWI has anything very
                    > >useful to say if we try and figure out what we mean when we claim for
                    > >example: there is an 80% chance that Michael Schumacher will win the
                    > >next Grand Prix. If I have missed something, I would be delighted to be
                    > >enlightened.
                    > >
                    > >Wade
                    >

                    [Gordon]
                    The probability I was refer too was closer to semi Classical or
                    Classical realm and not QM realm.
                  • Gary Oberbrunner
                    Henry, I think you re just not considering enough universes (IMHO). There are two things we commonly call probability: those which are uncertain due to true
                    Message 9 of 30 , Oct 7, 2002
                      Henry, I think you're just not considering enough universes (IMHO).

                      There are two things we commonly call probability: those which are
                      uncertain due to true quantum uncertainty, and those which are uncertain
                      due to our incomplete or imperfect knowledge ("sensitive dependence on
                      initial conditions" is an example).

                      Both can easily be modeled using the same method, in the MWI: to take
                      your dice example, you just include all the initial universes which vary
                      from "ours" in the ways in which our knowledge is uncertain. So, for
                      instance, if you know the throwing-force is between 6 and 10 newtons,
                      you allow all such universes into the initial sheaf, and similarly for
                      universes in which the wind in the room is blowing the other way, and so on.

                      Then proceed as usual: examine all the outcomes in all universes (can
                      only be done "from outside" of course -- we can't predict the future
                      from our single-universe vantage point) and bin the results. You'll of
                      course find each face of the die occurring with measure 1/6.

                      -- Gary

                      Henry Sturman wrote:
                      > I suppose some MWI'ers might claim that the statment "there is an 80%
                      > chance that Michael Schumacher will win the next Grand Prix" means: if we
                      > follow the evolution of our current slice of the multiverse, the collection
                      > of subslices in which Michael Schumacher wins the next Grand Prix, has a
                      > relative thickness of 80%.
                      >
                      > However, such a view is based on an incorrect understanding of what we mean
                      > when we talk about probability.
                    • Gary Oberbrunner
                      ... This has to be done from outside the multiverse; all we can do from any one universe is to guess the way we usually do; by experiment and theory
                      Message 10 of 30 , Oct 7, 2002
                        Wade Allsopp wrote:
                        > I'm afriad this still leaves me perplexed.
                        >
                        > Firstly, how can we ever know or guess how many universes there out
                        > there in which MS will or won't win?

                        This has to be done from "outside" the multiverse; all we can do from
                        any one universe is to guess the way we usually do; by experiment and
                        theory formation.

                        > Secondly I was under the impression that under the MWI view of the world
                        > there were an invinite number of possible universes. If there are an
                        > infinite number of universes where MS does win and an infinite number
                        > where he does not, how can we get to the proportion of "MS Win"
                        > universes? And what about the presumeably infinite number of universes
                        > where say you or I win the Grand Prix ?

                        Yes there is an infinite number of universes, but using the concept of
                        "measure" you can say that within that infinite set, there are many more
                        elements in which MS or some other competitor wins the GP than there are
                        in which you or I win. It's much like measuring the area of a curve by
                        integration. Even though there are infinitely many dArea elements, it's
                        still easy to compute the total, or in this case the fraction of the total.

                        Does that help at all?

                        -- Gary
                      • Henry Sturman
                        Well, yes. But I was describing how many MWI ers would define probability, and pointing out a problem with that. Indeed, your method is much better, but it
                        Message 11 of 30 , Oct 7, 2002
                          Well, yes. But I was describing how many MWI'ers would define probability,
                          and pointing out a problem with that. Indeed, your method is much better,
                          but it demonstrates that MWI is no longer of much help with these kinds of
                          complex event probabilities (e.g. the chance that Michael Schumacher will
                          win the next Grand Prix), since calculating such a probability now becomes
                          a mainly problem of what kind of knowledge we are assuming in relation to
                          the event.

                          In any case, for the time being, I think the odds out there on the the
                          sports betting market are the best indication of the values we should
                          assume for these kinds of probabilities :-)

                          At 09:37 AM 7-10-2002 -0400, you wrote:
                          >Henry, I think you're just not considering enough universes (IMHO).
                          >
                          >There are two things we commonly call probability: those which are
                          >uncertain due to true quantum uncertainty, and those which are uncertain
                          >due to our incomplete or imperfect knowledge ("sensitive dependence on
                          >initial conditions" is an example).
                          >
                          >Both can easily be modeled using the same method, in the MWI: to take
                          >your dice example, you just include all the initial universes which vary
                          >from "ours" in the ways in which our knowledge is uncertain. So, for
                          >instance, if you know the throwing-force is between 6 and 10 newtons,
                          >you allow all such universes into the initial sheaf, and similarly for
                          >universes in which the wind in the room is blowing the other way, and so on.
                          >
                          >Then proceed as usual: examine all the outcomes in all universes (can
                          >only be done "from outside" of course -- we can't predict the future
                          >from our single-universe vantage point) and bin the results. You'll of
                          >course find each face of the die occurring with measure 1/6.
                          >
                          >-- Gary
                          >
                          >Henry Sturman wrote:
                          > > I suppose some MWI'ers might claim that the statment "there is an 80%
                          > > chance that Michael Schumacher will win the next Grand Prix" means: if we
                          > > follow the evolution of our current slice of the multiverse, the
                          > collection
                          > > of subslices in which Michael Schumacher wins the next Grand Prix, has a
                          > > relative thickness of 80%.
                          > >
                          > > However, such a view is based on an incorrect understanding of what we
                          > mean
                          > > when we talk about probability.
                          >
                          >
                          >
                          >
                          >
                          >
                          >Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/


                          [Non-text portions of this message have been removed]
                        • PaintedDevil@aol.com
                          In a message dated 10/8/2002 2:19:51 AM GMT Daylight Time, henry@sturman.net ... Has anyone *claimed* that the MWI will help decide the outcome of complex
                          Message 12 of 30 , Oct 8, 2002
                            In a message dated 10/8/2002 2:19:51 AM GMT Daylight Time, henry@...
                            writes:


                            > Well, yes. But I was describing how many MWI'ers would define probability,
                            > and pointing out a problem with that. Indeed, your method is much better,
                            > but it demonstrates that MWI is no longer of much help with these kinds of
                            > complex event probabilities (e.g. the chance that Michael Schumacher will
                            > win the next Grand Prix), since calculating such a probability now becomes
                            > a mainly problem of what kind of knowledge we are assuming in relation to
                            > the event.

                            Has anyone *claimed* that the MWI will help decide the outcome of complex
                            events - at least any better than normal methods of prediction? As far as I
                            know the MWI (in DD's formulation at least) simply gives an explanation for
                            what we mean by quantum probability and uncertainty.

                            The only way in which the MWI appears to allow one to predict chance outcomes
                            is in the (rather contentious imho) "quantum suicide" / "quantum lottery" -
                            in which you can allegedly predict that you will win the lottery because all
                            versions of you which don't cease to exist. But that doesn't help us predict
                            who will win the Grand Prix in a branch of the multiverse in which we refrain
                            from such drastic measures.....

                            Charles


                            [Non-text portions of this message have been removed]
                          • Wade Allsopp
                            ... I would have thought that this lefts the theory in a somewhat awkward predicament. As by definition nothing can be outside a universe, the concept is
                            Message 13 of 30 , Oct 8, 2002
                              Gary Oberbrunner wrote:
                              >
                              > This has to be done from "outside" the multiverse; all we can do from
                              > any one universe is to guess the way we usually do; by experiment and
                              > theory formation.

                              I would have thought that this lefts the "theory" in a somewhat awkward
                              predicament. As by definition nothing can be "outside" a universe, the
                              concept is not even in principle applicable or testable.


                              >
                              > Yes there is an infinite number of universes, but using the
                              > concept of
                              > "measure" you can say that within that infinite set, there
                              > are many more
                              > elements in which MS or some other competitor wins the GP
                              > than there are
                              > in which you or I win.

                              Let me introduce another example, which I believe it would be difficult
                              to explain under your interpretation.

                              Suppose I am given a die but am told it is a loaded die, only I am left
                              to guess which number it is loaded in favour of. It seems to me that
                              from my perspective the probability of me rolling a "3" is still 1/6.
                              However as far as I can understand from your account, the probability
                              would either be signicantly greater than this or significantly less than
                              this depending on whether the die was loaded in favour of a "3" or some
                              other number.

                              I think what this type of example illustrates is that it is not possible
                              to give a satisfactory "realist" account of probability in the way you
                              have attempted, any more than it is possible to give say a realist
                              account of ethical values.

                              Wade Allsopp
                            • Gary Oberbrunner
                              ... I agree with you here, mostly; no observer in a single universe can have access to the entire multiverse, so this theory does not help such an observer
                              Message 14 of 30 , Oct 8, 2002
                                Wade Allsopp wrote:
                                > Gary Oberbrunner wrote:
                                >
                                >>This has to be done from "outside" the multiverse; all we can do from
                                >>any one universe is to guess the way we usually do; by experiment and
                                >>theory formation.
                                >
                                > I would have thought that this lefts the "theory" in a somewhat awkward
                                > predicament. As by definition nothing can be "outside" a universe, the
                                > concept is not even in principle applicable or testable.

                                I agree with you here, mostly; no observer in a single universe can have
                                access to the entire multiverse, so this theory does not help such an
                                observer predict the outcomes of any experiment more accurately than any
                                other theory. What it does do is give a physical underpinning, an
                                *explanation*, of why probability should take the form it does, and why
                                it is possible for the multiverse to be deterministic while not allowing
                                any single-universe observer to predict the future. In this I think it
                                has no predicament.

                                > Let me introduce another example, which I believe it would be difficult
                                > to explain under your interpretation.
                                >
                                > Suppose I am given a die but am told it is a loaded die, only I am left
                                > to guess which number it is loaded in favour of. It seems to me that
                                > from my perspective the probability of me rolling a "3" is still 1/6.
                                > However as far as I can understand from your account, the probability
                                > would either be signicantly greater than this or significantly less than
                                > this depending on whether the die was loaded in favour of a "3" or some
                                > other number.

                                Again, this is a choice of point-of-view. See my previous post. From
                                your perspective, when computing the probability, you must consider all
                                those universes in which the die was loaded toward any number of pips
                                (and there *are* such universes). From the die-loader's point of view,
                                he should only consider those universes in which the die is loaded as he
                                knows it was loaded.

                                This is really nothing other than a physicalization of the common
                                concept of conditional probability, P(a|b) = P(a&b)/P(b). As I said
                                above, it does not improve our ability to predict the future, it simply
                                gives it a physical, non-counterfactual, basis.

                                -- Gary
                              • risus_abundat
                                ... of ... more ... there are ... curve by ... it s ... the total. ... Gary, this gives me the pretext to get into this discussion and throw in a few doubts
                                Message 15 of 30 , Oct 15, 2002
                                  > Yes there is an infinite number of universes, but using the concept
                                  of
                                  > "measure" you can say that within that infinite set, there are many
                                  more
                                  > elements in which MS or some other competitor wins the GP than
                                  there are
                                  > in which you or I win. It's much like measuring the area of a
                                  curve by
                                  > integration. Even though there are infinitely many dArea elements,
                                  it's
                                  > still easy to compute the total, or in this case the fraction of
                                  the total.
                                  >
                                  > Does that help at all?
                                  >
                                  > -- Gary

                                  Gary,
                                  this gives me the pretext to get into this discussion and throw in
                                  a few doubts and questions ... thanks in advance for your time.

                                  The reason why integration 'works' is that the actual area of each
                                  dArea you mention 'tends to 0', and although there are an infinite
                                  number of such areas, the "Sum over the dAreas for their number going
                                  to infinity" converges to a finite number. This solves paradoxes
                                  like Zeno's "The Turtle and Achilles" and many similar. Does this mean
                                  that the actual Universes (in the MWI) have any feature that tends to
                                  zero? In the MWI, what is the cardinality of the set of all
                                  multiverses? I would dear suggesting 'numerable' (the cardinality
                                  of N, the set of integral numbers 0, 1, 2, ....), as there can only
                                  be a (incredibly large, but) finite number of particles in each
                                  Universe, which can only 'trigger' an (even larger, but) finite
                                  number of interactions...

                                  Thanks.
                                  Marco
                                • Gary Oberbrunner
                                  ... Yes, the feature that tends to zero is the relative thickness of a given slice of the multiverse, compared to another given slice. A universe should as
                                  Message 16 of 30 , Oct 15, 2002
                                    risus_abundat wrote:

                                    > The reason why integration 'works' is that the actual area of each
                                    > dArea you mention 'tends to 0', and although there are an infinite
                                    > number of such areas, the "Sum over the dAreas for their number going
                                    > to infinity" converges to a finite number. ... Does this
                                    > mean that the actual Universes (in the MWI) have any feature that
                                    > tends to zero?

                                    Yes, the feature that tends to zero is the relative "thickness" of a
                                    given slice of the multiverse, compared to another given slice.

                                    A universe should as far as I understand it, be considered as a sheaf of
                                    a large number, perhaps infinite, of identical (fungible) universes.
                                    Any quantum event causes that sheaf to split into many now non-fungible
                                    sheaves, each of which is "thinner" than the original; if the quantum
                                    event is a proton decay at time t, e.g., then at time t+dt some fraction
                                    of the original sheaf contains the decay products and some fraction
                                    contains the original non-decayed proton. The relative thicknesses
                                    still sum to 1. Then those can split into sub-slices and so on.

                                    Now, can this splitting continue indefinitely? That bears on your next
                                    question:

                                    > In the MWI, what is the cardinality of the set of all
                                    > multiverses?

                                    I assume you mean universes. This is, AFAIK, an open question. Some on
                                    this list have suggested that it is finite but very large, while others
                                    say it has the same cardinality as the integers, while yet others I
                                    think say even that is too small, and it must be at least aleph-1.

                                    I think what some folks argue is that if you keep on making thinner
                                    universe-sheaf slices by quantum events happening, that eventually all
                                    possible combinations of matter and momentum in the entire universe are
                                    "populated" (if you think of each combination as a single cell in a huge
                                    matrix) and any further splitting would just repeat cells. But I'm not
                                    at all sure I agree with that. My current guess is that universes can
                                    be put into 1:1 correspondence with the reals, but I can't prove it.

                                    -- Gary
                                  • PaintedDevil@aol.com
                                    In a message dated 10/15/2002 3:34:52 PM GMT Daylight Time, ... I believe it s the same as the power of a continuum? (I.e. not numerable) Charles [Non-text
                                    Message 17 of 30 , Oct 15, 2002
                                      In a message dated 10/15/2002 3:34:52 PM GMT Daylight Time,
                                      risus_abundat@... writes:


                                      > In the MWI, what is the cardinality of the set of all
                                      > multiverses? I would dear suggesting 'numerable' (the cardinality
                                      > of N, the set of integral numbers 0, 1, 2, ....), as there can only
                                      > be a (incredibly large, but) finite number of particles in each
                                      > Universe, which can only 'trigger' an (even larger, but) finite
                                      > number of interactions...

                                      I believe it's the same as the power of a continuum? (I.e. not numerable)

                                      Charles


                                      [Non-text portions of this message have been removed]
                                    • risus_abundat
                                      ... numerable) ... Ok. But why? Normally, the trick used to handle cardinality with infinity in mathematics is to prove that there is a 1-1 correspondance
                                      Message 18 of 30 , Oct 16, 2002
                                        --- In Fabric-of-Reality@y..., PaintedDevil@a... wrote:
                                        > I believe it's the same as the power of a continuum? (I.e. not
                                        numerable)
                                        >
                                        > Charles

                                        Ok. But why? Normally, the trick used to 'handle' cardinality with
                                        infinity in mathematics is to prove that there is a 1-1
                                        correspondance between set A and set B, where you know the
                                        cardinality of set A. Otherwise, we could prove that such a 1-1
                                        correspondence can not exist (leads to contradiction), which, despite
                                        not acceptable for constructivist, could still be considered an
                                        acceptable enough proof (reductio ad absurdum) just for the sake of
                                        this discussion.... My argument for 'believing' the set of all
                                        universes is at the very maximum numerable (N) is: 'this' universe
                                        (the one of which we have or think to have direct knowledge of)
                                        contains a finite number of particles (the unbelievably large 10^80
                                        or similar sometimes we hear of). The number of particle interactions
                                        between these particles is finite and if a universe 'splits' as a
                                        result of an interaction (at any level), then we can only have a
                                        finite number of 'splits', hence of universes. One observation here is
                                        that we do not know how many 'other universes' exit 'already' (is the
                                        Big Bang the origin of all these splits? Or is the Big Bang just a
                                        'collision' between 'sheets'?). But then isn't it the case that,
                                        because there is no way we can even theoretically have information
                                        exchange between different universes, this is an issue which we will
                                        never be able to solve?

                                        Marco
                                      • PaintedDevil@aol.com
                                        In a message dated 10/15/2002 8:07:35 PM GMT Daylight Time, garyo@genarts.com ... If the SWE is accurate, the outcome of any quantum event is a continuum of
                                        Message 19 of 30 , Oct 16, 2002
                                          In a message dated 10/15/2002 8:07:35 PM GMT Daylight Time, garyo@...
                                          writes:


                                          > I think what some folks argue is that if you keep on making thinner
                                          > universe-sheaf slices by quantum events happening, that eventually all
                                          > possible combinations of matter and momentum in the entire universe are
                                          > "populated" (if you think of each combination as a single cell in a huge
                                          > matrix) and any further splitting would just repeat cells. But I'm not
                                          > at all sure I agree with that. My current guess is that universes can
                                          > be put into 1:1 correspondence with the reals, but I can't prove it.
                                          >
                                          >

                                          If the SWE is accurate, the outcome of any quantum event is a continuum of
                                          possible states. Hence to cope with one quantum event the multiverse must
                                          have the cardinality of a continuum. I believe this can scale up indefinitely
                                          (to any number of quantum events, including a non-denumerable number of
                                          them). If so the MV has the cardinality of a continuum, surely? Is that a 1:1
                                          with the reals? (no if real numbers are expressible as one integer divided by
                                          another, yes if Pi is a real number....I can't remember the definition)

                                          Charles


                                          [Non-text portions of this message have been removed]
                                        • risus_abundat
                                          ... a ... This reminds me of one of the most discussed issues in philosophy about infinity: the distinction between infinity in action (ex. the continuum of
                                          Message 20 of 30 , Oct 16, 2002
                                            --- In Fabric-of-Reality@y..., Gary Oberbrunner <garyo@g...> wrote:
                                            > Yes, the feature that tends to zero is the relative "thickness" of
                                            a
                                            > given slice of the multiverse, compared to another given slice.
                                            >
                                            This reminds me of one of the most discussed issues in philosophy
                                            about infinity: the distinction between "infinity in action" (ex. the
                                            continuum of the points on a segment between 0 and 1) and "potential
                                            infinity" (The numerable, N). In the first case the infinity is a
                                            'fact': there *is* a (in this case non-numerable) infinite number of
                                            points between 0 and 1. But with N the matter differs a lot: you will
                                            *never* see that infinity as a 'fact', for otherwise you should have
                                            'seen' all numerals. You can draw a segment with an infinity of
                                            points, but you will never be able to draw a segment with all
                                            numerables.
                                            It seems to me that our two examples (the integration of a curve and
                                            the 'number' of universes) belong to two different cathegories: the
                                            integration 'works' because it delas with 'infinity in action': you
                                            actually can have an infinity of infinitesimal (approaching zero size)
                                            dAreas whose 'sum' converges to a finite number (mind you: that is not
                                            always the case: the area between x=0 and x=1 delimited by the curve
                                            f(x)=1/x is not finite). But, as I understood from your argument,
                                            the "relative thickness" of a slide 'becomes' thinner as universes
                                            split: so those thickesses would tend to zero in a potentially
                                            infinite amount of time: now those thickess are not zero size,
                                            otherwise they could not get 'thinner'.

                                            I can't help thinking that this 'MWI' and the 'slices' and 'sheets'
                                            are beautiful but forced extrapolations of our mathematical models
                                            about reality: we observe phenomena, we build models, we test them,
                                            we find them successful in explaining a certain amount of other data
                                            and then we jump to assuming that reality *is* that model. Sometimes
                                            that has actually worked (and this is a reason for ecouraging these
                                            speculations and welcoming the sceptics) like the extrapolation from
                                            (if I remember correctly) De Broglie equation to the hypothesis of the
                                            existence of anti-matter. But most of the times it has not (ex. the
                                            ether for electromagnetic propagation).

                                            Marco
                                          • PaintedDevil@aol.com
                                            In a message dated 10/16/2002 2:01:54 PM GMT Daylight Time, ... The short answer is: because the Schrodinger equation describes a continuous range of outcomes
                                            Message 21 of 30 , Oct 16, 2002
                                              In a message dated 10/16/2002 2:01:54 PM GMT Daylight Time,
                                              risus_abundat@... writes:


                                              > Ok. But why? Normally, the trick used to 'handle' cardinality with
                                              > infinity in mathematics is to prove that there is a 1-1
                                              > correspondance between set A and set B, where you know the
                                              > cardinality of set A. Otherwise, we could prove that such a 1-1
                                              > correspondence can not exist (leads to contradiction), which, despite
                                              > not acceptable for constructivist, could still be considered an
                                              > acceptable enough proof (reductio ad absurdum) just for the sake of
                                              > this discussion.... My argument for 'believing' the set of all
                                              > universes is at the very maximum numerable (N) is: 'this' universe
                                              > (the one of which we have or think to have direct knowledge of)
                                              > contains a finite number of particles (the unbelievably large 10^80
                                              > or similar sometimes we hear of). The number of particle interactions
                                              > between these particles is finite and if a universe 'splits' as a
                                              > result of an interaction (at any level), then we can only have a
                                              > finite number of 'splits', hence of universes. One observation here is
                                              > that we do not know how many 'other universes' exit 'already' (is the
                                              > Big Bang the origin of all these splits? Or is the Big Bang just a
                                              > 'collision' between 'sheets'?). But then isn't it the case that,
                                              > because there is no way we can even theoretically have information
                                              > exchange between different universes, this is an issue which we will
                                              > never be able to solve?

                                              The short answer is: because the Schrodinger equation describes a continuous
                                              range of outcomes for any given situation. So *any* split will be into a
                                              continuum of outcomes.

                                              Charles


                                              [Non-text portions of this message have been removed]
                                            • Gary Oberbrunner
                                              ... I guess that depends on quantization, right? If momentum is quantized, then an emitted photon can only take on 1 of N values, and if time is quantized,
                                              Message 22 of 30 , Oct 17, 2002
                                                PaintedDevil@... wrote:
                                                > The short answer is: because the Schrodinger equation describes a continuous
                                                > range of outcomes for any given situation. So *any* split will be into a
                                                > continuum of outcomes.
                                                >
                                                > Charles

                                                I guess that depends on quantization, right? If momentum is quantized,
                                                then an emitted photon can only take on 1 of N values, and if time is
                                                quantized, then it can only be emitted at certain times. Another
                                                question is whether position and/or angle are quantized, however. Those
                                                may not be, in which case Charles' answer is correct.

                                                -- Gary
                                              • PaintedDevil@aol.com
                                                In a message dated 10/17/2002 7:13:15 PM GMT Daylight Time, garyo@genarts.com ... I ve got the impression that quantisation is a local feature which occurs
                                                Message 23 of 30 , Oct 18, 2002
                                                  In a message dated 10/17/2002 7:13:15 PM GMT Daylight Time, garyo@...
                                                  writes:


                                                  > I guess that depends on quantization, right? If momentum is quantized,
                                                  > then an emitted photon can only take on 1 of N values, and if time is
                                                  > quantized, then it can only be emitted at certain times. Another
                                                  > question is whether position and/or angle are quantized, however. Those
                                                  > may not be, in which case Charles' answer is correct.
                                                  >
                                                  >

                                                  I've got the impression that quantisation is a "local" feature which occurs
                                                  within any branch of the multiverse but not the multiverse itself. But I may
                                                  be wrong...

                                                  Charles


                                                  [Non-text portions of this message have been removed]
                                                • risus_abundat
                                                  ... Thanks to both of you. Of course. My mistake was to think of possible outcomes of quantum interactions as in the famous examples cat dead/alive , or
                                                  Message 24 of 30 , Oct 18, 2002
                                                    --- In Fabric-of-Reality@y..., Gary Oberbrunner <garyo@g...> wrote:
                                                    > PaintedDevil@a... wrote:

                                                    Thanks to both of you. Of course. My mistake was to think of possible
                                                    outcomes of quantum interactions as in the famous examples "cat
                                                    dead/alive", or "radioactive atom decayed/not decayed", or "the
                                                    photon went through slit A or B", when I should have thought of
                                                    the "sum over all possible histories" that Feynman proposed. In this
                                                    case, I guess the question is "Is space quantized?", or "Can a photon
                                                    occupy any possible position?". So my next question for you: do you
                                                    think that any thing a part from energy is quantized? What about
                                                    position, time, ...? I would think mass is, as mass is energy.

                                                    Regards
                                                    Marco
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