> On 7 Feb 2020, at 05:59, Bruce Kellett <[email protected]> wrote:
>
> From: Bruno Marchal <[email protected] <mailto:[email protected]>>
>> Date: Fri, Feb 7, 2020 at 12:45 AM
>> Subject: Re: Postulate: Everything that CAN happen, MUST happen.
>> To: <[email protected]
>> <mailto:[email protected]>>
>>
>>
>>
>>> On 4 Feb 2020, at 23:13, Bruce Kellett <[email protected]
>>> <mailto:[email protected]>> wrote:
>>>
>>> On Wed, Feb 5, 2020 at 12:13 AM Bruno Marchal <[email protected]
>>> <mailto:[email protected]>> wrote:
>>> On 3 Feb 2020, at 22:46, Bruce Kellett <[email protected]
>>> <mailto:[email protected]>> wrote:
>>>> On Tue, Feb 4, 2020 at 2:48 AM Bruno Marchal <[email protected]
>>>> <mailto:[email protected]>> wrote:
>>>> On 2 Feb 2020, at 12:32, Alan Grayson <[email protected]
>>>> <mailto:[email protected]>> wrote:
>>>>> On Saturday, February 1, 2020 at 11:42:12 PM UTC-7, Brent wrote:
>>>>> First, it's false. You can make it true by interpreting "can happen" to
>>>>> mean "can happen according the prediction of quantum mechanics for this
>>>>> situation", but then it becomes trivial. Second, it's not "at the heart
>>>>> of MWI"; the trivial version is all that MWI implies. Read the first few
>>>>> paragraphs of this paper:
>>>>>
>>>>> arXiv:quant-ph/0702121v1 13 Feb 2007
>>>>>
>>>>> Brent
>>>>>
>>>>> In posing the question, I want to give its advocates such as Clark the
>>>>> opportunity to justify the postulate. It goes way beyond the MWI and QM.
>>>>> E.g., it means that if someone puts on his/her right shoe first this
>>>>> morning, there must be a universe in which a copy of the person puts on
>>>>> his/her left shoe first. It seems way, way over the top, but oddly many
>>>>> embrace it with gusto. AG
>>>>
>>>>
>>>> That is already completely different, as it seems to say that everything
>>>> happen with the same probability, but that is non sense,
>>>>
>>>> No, it is exactly what Everett predicts.
>>>
>>> If that was the case, I don’t think we would still be here discussing
>>> Everett.
>>>
>>>> Everything that happens happens with probability one.
>>>
>>> Everett insists, perhaps wrongly (but then that is what should be debated)
>>> that he recovers the usual quantum statistics, where the probability is
>>> given by the square of the amplitude of the wave.
>>>
>>> It turns out, in fact, that Everett did not prove this result. As in
>>> conventional QM, he just asserted it.
>>
>>
>> He provides argument, which actually were already found by Paulette
>> Février-destouche in France 20 years before Everett, and correspond more or
>> less to the argument made by Graham in the selected paper by DeWitt and
>> Graham on the MWI, and by Preskill in his textbook in Quantum Mechanics.
>> Is that argument totally convincing? Perhaps not, but let us say that I
>> think it is improvable, and it is going in the direction that we can expect
>> when postulating Mechanism (as do Everett, and many others, consciously or
>> unconsciously).
>
> Everett's argument is far from convincing. It is criticized by Simon Saunders
> in the book "Many Worlds?: Everett, Quantum Theory, & Reality", and by David
> Wallace in his book on "The Emergent Multiverse". Perhaps the most telling
> critique of Everett's idea has been given by Adrian Kent in his contribution
> to the book, cited above, that he edited with Simon Saunders and David
> Wallace. I give extensive quotations below, and attach a pdf with these
> comments in a more friendly format. Note that Kent's critique also undermines
> any idea that you can attach probabilities to outcomes in your W/M
> duplication scenarios in Step 3.
>
That explains probably why the papers by Kent (a guy who criticise Everett
since long) never convince me.
Toi be sure, I have stopped to read its last publication. Wallace is more
convincing, but in the last reading he defended Everett, but still in a way
which somehow presuppose an ontological physical universe (an hypothesis which
I cannot use in my “mind-body” context.
>
> Born Rule in Everettian Many Worlds Theory
>
> Everett gives an argument for the Born rule in his 1957 paper. Simon Saunders
> (in his introduction to the volume of essays: "Many Worlds?: Everett, Quantum
> Theory, & Reality", OUP 2010) gives the following summary of Everett's
> argument:
>
> "But Everett was able to derive at least a fragment of the Born rule. Given
> that the measure over the space of branches is a function of the branch
> amplitudes, the question arises: What function? If the measure is to be
> additive, so that the measure of a sum of branches is the sum of their
> measures, it follows that it is the modulus square---that was something. The
> set of branches, complete with additive measure, then constitute a
> probability space. As such, version of the Bernouilli and other large number
> theorems can be derived. They imply that the measure of all the branches
> exhibiting anomalous statistics (with respect to this measure) is small when
> the number of trials is sufficiently large, and goes to zero in the
> limit---that was something more.”
>
So I agree with Saunders here, and its indexical view of time is also coherent
with Mechanism (my working frame).
>
> This account can be criticized on several grounds. Firstly, it relies on the
> limit of infinitely many trials, whereas in practice, we only ever have a
> finite number of such trials.
>
And this is of course wrong when you assume mechanism. By the invariance of the
first person for the number of step to get the reconstitution, in the Universal
Dovetailing, the physical reality comes from a sort of limit on an infinity of
projection from all computations to one first person indexical states. So the
whole of physics is given by a limiting process.
> Another criticism is that there is not any solid basis for the assumption
> that the measure should depend only on the branch weights---why should it not
> depend on the actual structure of the branches themselves?
>
The quantum measure must depend on the relative weight, and then subsequent
relative measure can depend on many things, including the intention of the
observer. The idea is that the quantum probabilities are part of physics and
true “everywhere”. This consists just in assuming QM being true/correct.
> The other main line of objection relates to the simple application of
> Everett's rule in the case where all possible outcomes occur on each trial.
> In that case, all possible sequences of results occur, so that predictions
> using this rule would have been wildly contradicted by the emperical
> evidence---which only goes to show that the Born Rule, far from being an
> obvious consequence of the interpretation of the quantum state in terms of
> many worlds, appears quite unreasonable.
>
That is what motivated Graham (and Preskill) to use the limite that you
describe above. Then the Born rules follows almost by the theorem of
Pythagoras, as Paulette Destouches-Février saw in Paris right at the beginning
of the Quantum theory (her husband was a gifted student of de Broglie).
>
>
> This latter point is made very strongly by Adrian Kent in his contribution to
> the above cited volume of collected essays (pp. 307--354).
>
> Kent considers a toy multiverse, which is classical, but in which branches
> are multiplied to record all possible results. The first such world he
> considers includes conscious inhabitants, but which also includes a machine
> with a red button on it, and a tape emerging from it, with a sequence of
> numbers on it, all in the range 0 to (N-1). When the red button is pressed in
> some universe within the multiverse, that universe is deleted, and N
> successor universes are then created. All the successors are in the same
> classical state as the original (and so, by hypothesis, all include conscious
> inhabitants with the same memories as those who have just been deleted),
> except that a new number has been written onto the end of the tape, with the
> number 'i' being written in the 'i'-th successor universe.
>
> Suppose, further, that some of the inhabitants of this multiverse have
> acquired the theoretical idea that the laws of their multiverse might attach
> 'weights' to branches, i.e., a number p_i is attached to branch 'i', where
> p_i >= 0 and Sum_i p_i = 1. They might have various different theories about
> how these weights are defined.... To be clear: this is not to say that the
> branches have equal weight. Nor are they necessarily physically identical,
> aside from the tape numbers. However, any such differences do not yield any
> natural quantitative definition of branch weights. There is just no fact of
> the matter about branch weights in this multiverse.
>
OK. Note that I cannot assume a multiverse or anything like that. I have only
0, s0, ss0, sss0, …., and the measure will be on the computations (either the
halting one which have a name, thus are numbers, or are nameable sequence of
numbers, + some complications for the machine with oracles), but the whole is
structured by the mathematics of machine self-reference. Formally this provides
a quantisation, and a mesure “one” theory which obeys quantum tautologies. The
toy multiverse seems to assume some brain-mind thesis, which I have explained
is incoherent with Mechanism.
>
> Kent goes on the say:
>
> "Everettian quantum theory is essentially useless, as a scientific theory,
> unless it can explain the data that confirm the validity of the Copenhagen
> quantum theory within its domain---unless, for example, it can explain why we
> should expect to observe the Born rule to have been very well confirmed
> statistically. Evidently, Everettians cannot give an explanation that says
> that all observers in the multiverse will observe confirmation of the Born
> rule, or that very probably all observers will observe confirmation of the
> Born rule. On the contrary, many observers in an Everettian multiverse will
> definitely observe convincing 'discomfirmation' of the Born rule.
>
Here, let me say that the theorem of Gleason reassure me a little bit. Once we
get three dimensions, the formalisme indicates that the measure is unique. To
be sure, the quantum logic “in the head of the universal machine” is not enough
developed to be able to use Gleason theorem, but the evidences add that
something like this is quite plausible.
Mentioning the Copenhagen theory is not convincing to me, as it makes not much
sense, and no sense at all with Mechanism.Everett axiom is not much more than
the idea that observers obeys to QM too.
>
> "It suffices to consider very simple many-worlds theories, containing
> classical branching worlds
>
To be sure, that never really exists. There are no worlds at all, only coherent
collection of histories/computations.
> in which the branches correspond to binary outcomes of definite experiments.
>
Of a finite number if definite experiment, but made in an infinity of histories
at once.
> Consider thus the 'weightless multiverse', a many-worlds of the type outlined
> above, in which the machine produces only two possible outcomes, writing 0 or
> 1 onto the tape. Suppose now that the inhabitants begin a series of
> experiments in which they push the red button on the machine a large number,
> N, times, at regular intervals. Suppose too that the inhabitants believe
> (correctly) that this is a series of independent identical experiments, and
> moreover believe this 'dogmatically': no pattern in the data will shake their
> faith. Suppose also that they believe (incorrectly) that their multiverse is
> governed by a many-worlds theory with unknown weights attached to the 0 and 1
> outcomes; identical in each trial, and seek to discover the (actually
> non-existent) values of these weights.
>
> "After N trials, the multiverse contains 2^N branches, corresponding to all
> 2^N possible binary string outcomes. The inhabitants on a string with pN zero
> and (1 - p)N one outcomes will, with a degree of confidence that tends
> towards one as N gets large, tend to conclude that the weight 'p' is attached
> to zero outcome branches and weight (1 - p) is attached to one outcome
> branches. In other words, everyone, no matter what string they see, tends
> towards complete confidence in the belief that the relative frequencies they
> observe represent the weights.
>
> "Let's consider further the perspective of inhabitants on a branch with 'pN'
> zero outcomes and '(1 - p)N' one outcomes. They do not have the delusion that
> all observed strings have the same relative frequency as theirs: they
> understand that, given the hypothesis that they live in a multiverse, 'every'
> binary string, and hence every relative frequency, will have been observed by
> someone. So how do they conclude that the theory that the weights are '(p,1 -
> p)' has nonetheless been confirmed?. Because they have concluded that the
> weights measure the 'importance' of the branches for theory confimation.
> Since they believe they have learned that the weights are '(p,1 - p)', they
> conclude that a branch with 'r' zeros and '(N - r)' ones has importance p^r(1
> - p)^{N-r}. Summing over all branches with 'pN' zeros and '(1 - p)N' ones, or
> very close to those frequencies, thus gives a set of total importance very
> close to 1; the remaining branches have total importance very close to zero.
> So, on the set of branches that dominate the importance measure, the theory
> that the weights are (very close to) (p,1 - p) is indeed correct. All is
> well! By definition, the important branches are the ones that matter for
> theory confimation. The theory is inded confirmed!
>
> "The problem, of course, is that this reasoning applies equally well for all
> the inhabitants, whatever relative frequency 'p' they see on their branch.
> All of them conclude that their relative frequencies represent (to very good
> approximation) the branching weights. All of them conclude that their own
> branches, together with those with identical or similar relative frequencies,
> are the important ones for theory confirmation. All of them thus happily
> conclude that their theories have been confirmed. And, recall, all of them
> are wrong: there are actually no branching weights.”
>
I do not understand. If the multiverse is that sort of many classical world,
with the machine giving all outputs somewhere, the correct weighting will be
the one given by Pascal Binomial. That comes already with the fact that we get
all 2^N strings. I might have miss something.
Do you agree that in the iterated self- (WM)-duplication, the measure is just
the normal distribution?
>
>
> This argument from Kent completely destroys Everett's attempt to derive the
> Born rule from his many-worlds approach to quantum mechanics. In fact, it
> totally undermines most attempts to derive the Born rule from any branching
> theory, and undermines attempts to justify ignoring branches on which the
> Born rule weights are disconfirmed.
>
They normally just get relatively rare.
> In the many-worlds case, recall, all observers are aware that other observers
> with other data must exist, but each is led to construct a spurious measure
> of importance that favours their own observations against the others', and
> this leads to an obvious absurdity. In the one-world case, observers treat
> what actually happened as important, and ignore what didn't happen: this
> doesn't lead to the same difficulty.
>
With Mechanism (used in Darwin) I don’t see how we can evacuate that the
prediction are given by relative (even conditional) measure, on all
computations.
But in QM, once we simply reject dualism (in philosophy of mind/cognitive
science) the observer has to obey to QM, and we get a measure problem anyway.
A collapse theory invoke an unknown theory of mind, which is not a problem to
use QM in the FAPP mode, but to solve deep problem like the mind-body problem,
such nuance counts, and the Everett Many-Worlds are welcome as they looks like
the many-histories interpretation which is unavoidable for the universal number
existing in the arithmetical reality.
Bruno
>
> Bruce
>
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