On Apr 19, 2:17 am, Brent Meeker <meeke....domain.name.hidden> wrote:
> nichomachus wrote:
>
> > On Apr 17, 1:21 pm, Brent Meeker <meeke....domain.name.hidden> wrote:
> >> Telmo Menezes wrote:
> >>> On Thu, Apr 17, 2008 at 2:37 PM, Bruno Marchal <marc....domain.name.hidden> wrote:
> >>>> Are you saying that the second law is verified in each of all
> >>>> "branches" of the (quantum) multiverse?
> >>> I'm not saying that.
> >>>> I would say the second law is
> >>>> statistical, and is verified in most branches. In the MWI applied to
> >>>> quantum field it seems to me that there can be branches with an
> >>>> arbitrarily high number of photon creation without annihilation, and
> >>>> this for each period of time.
> >> I'm not sure what source of photon creation you have in mind, but QFT
> >> doesn't allow violation of energy conservation.
>
> > Maybe it was vacuum energy Bruno was referring to, or else perhaps the
> > creation of virtual particle pairs? Stephen Hawking (who by the way
> > apparently regards Everett's theory as trivally true, in other words,
> > instrumentalistic and without physical significance) used virtual
> > particles to explain how black holes may evaporate. But I don't want
> > to put words in anyone's mouth, and plus, I am not knowledgeable
> > enough on these matters to discuss them.
>
> > But if I may raise one possibility, it seems to me that despite the
> > existence of fluke branches in which the second law is not inviolate,
> > there are no possible branches that experience the outcome of a double
> > slit experiment that does not result in an interference pattern.
>
> > This is according to my understanding that the interference actually
> > takes place across branches, as each path of the photon interferers
> > constructively and destructively with itself.
>
> But that interference is of the wave-function with itself. It's squared
> modulus only determines a probability. So, thru a fluke of probability,
> the photons could strike the screen in a pattern that is arbitrarily close
> to the naive no-interference pattern. I say "arbitrarily close" since in
> principle no photon could land where the probability was zero. But the zero
> probability region is a line of measure zero.
>
> It's not very clear to me how MWI accounts for the pattern. Is it supposed
> that there is a separate world for every point each photon could land; the
> separate worlds having a certain probability weight. Or are there multiple
> worlds for each spot in order that the probability be proportional to the
> number of worlds? And what if the probability is an irrational number?
Mutiple worlds for each spot on the screen, according to my
understanding of Feynman's explanation of the experiment. However, I
think it is important to distinguish between the probability function
that describes the interference pattern registering on the screen/
photodetector array, and the probability function that results from
the square of the psi modulus. IIRC, Feynman said that the
interference pattern from the double slit experiment (or equivalently,
the emergent probability function that is the same across branches)
results from the fact that for any point on the screen where a photon
may fall from the slits there are multiple paths that one photon may
take to get to that point. The next step is to say that there are
other branches (due to MWI), each of which describes another possible
path taken by that same photon, and that, depending on the relative
difference in path lengths to the point in question, summing over all
possible paths taken by a photon to that point results in a value
somewhere between completely desctructive interference and completely
constructive. I take this scenario to mean that the total interference
pattern is a probability function describing how likely it is to
measure a single photon at any point on the screen, and that this
probability function is an emergent property of light particles
interfering with parallel versions of themselves across branches.
Since they are summed across the branches, so to speak, the
interference pattern resulting from the double slit experiement is one
example of getting a deterministic result from probabilistic
interactions, and is in fact the same pattern across all branches
representing outcomes of the experiment. So the psi function may be
thought of as being proportional to the number of universes, but the
probability function representing the distribution of photons on the
screen is not.
This is what I was thinking when I first mentioned the experiment,
although I didn't express what I meant very well. I was also thinking
of a game show scenario thought experiment that arrives at the same
conclusion, i.e., that multiple probabilities may degenerate into
fewer unique branches, and that not every event actually happens
somewhere in the multiverse. For example, Lets say that a contestant
on Deal or No Deal gets down to the last briefcase, so that there is
only the case that she originally selected, or there is the other. All
other cases have been eliminated, so one of the remaining two has one
cent in it, and the other has one million dollars. The contestant has
to choose whether she wants to keep the one she originally selected,
or else switch with the last remaining case. The contestant, who
happens to read the Everything list, has brought along a qubit, a
particle in a superposition of spin states to help her with her
decision. If she measures the particle's spin as positive, she will
elect to switch cases, and if she measures it with a negative spin she
will keep the one she has. This is because she wants to be sure that,
having gotten to this point in the game, there will be at least some
branches of her existence where she experiences winning the grand
prize. She is not convinced that, were she to decide what to do using
only the processes available to her mind, she would guarantee that
same result since it is just possible that all of the mutiple versions
of herself confronted with the dilemma may make the same bad guess.
Is she correct to feel this way?
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Received on Sat Apr 19 2008 - 09:34:00 PDT