nichomachus wrote:
>
>
> 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.
But <psi*|psi> is the probability function. And the some pattern does not
occur across all branches. The patterns are only "the same" in the
statistical sense of having the same limit as the number of particles goes
to infinity; which is to say "in theory", since in practice the number is
always finite. Feynman's multiple-path formulation is mathematically
identical to the Schroedinger equation for and Heisenberg matrix form -
there is nothing new in it except the mental image evoked.
>
> 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.
I'm not familiar with "Deal or No Deal", but if it's like the old "Let's
Make a Deal" with the three doors, the contestant should consult quantum
mechanics, he should always switch.
Brent Meeker
>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 - 16:56:35 PDT