On 27-04-2022 04:01, Bruce Kellett wrote:

On Wed, Apr 27, 2022 at 11:35 AM smitra <smi...@zonnet.nl> wrote:On 27-04-2022 03:11, Bruce Kellett wrote:On Wed, Apr 27, 2022 at 10:32 AM smitra <smi...@zonnet.nl> wrote:On 27-04-2022 01:37, Bruce Kellett wrote:I think you should pay more attention to the mathematics of the binomial distribution. Let me explain it once more: If every outcome is realized on every trial of a binary process, then after thefirsttrial, we have a branch with result 0 and a branch with result1.After two trials we have four branches, with results 00,01,10,and11; after 3 trials, we have branches registering 000, 001, 011,010,100, 101, 110, and 111. Notice that these branches represent all possible binary strings of length 3. After N trials, there are 2^N distinct branches, representingallpossible binary sequences of length N. (This is just likePascal'striangle) As N becomes very large, we can approximate thebinomialdistribution with the normal distribution, with mean 0.5 andstandarddeviation that decreases as 1/sqrt(N). In other words, themajority oftrials will have equal, or approximately equal, numbers of 0sand 1s.Observers in these branches will naturally take the probabilityto beapproximated by the relative frequencies of 0s and 1s. In otherwords,they will take the probability of each outcome to be 0.5.The problem with this is that you just assume that all branchesareequally probable. You don't make that explicit, it's implicitlyassumed,but it's just an assumption. You are simply doing branchcounting.The distinctive feature of Everettian Many worlds theory is thateverypossible outcome is realized on every trial. I don't think thatyouhave absorbed the full significance of this revolutionary idea.Thereis no classical analogue of this behaviour, which is why yourlotteryexample is irrelevant. I spelled out the sequences that Everett implies in my earlier response. These clearly must have equal probability -- that is what the theory requires.QM without collapse does not require equal probabilities. Branches are not a fundamental concept of the theory. You just put this in by hand.It is not an assumption on my part -- it is a consequence ofEverett's basic idea. Everett's (or for that matter any other person's) ideas cannot be the basis for doing physics in a rigorous way. Your argument is not based on QM without collapse, you are making ad hoc assumptions about branching when branching isn't a fundamental process in QM.So there is no branch counting involved. That is just another red herring that you have thrown up to distract yourself from the cold hard logic of the situation.You just presented an elaborate presentation involving N branching steps and counted all 2^N branches as equal. That's branch counting and it's known to not be compatible with QM. The MWI can be taken to be QM without collapse and this is known to be a consistent theoryIt would seem that you are claiming that QM without collapse is not based on Everett's ideas. If you claim that such a theory exists and is consistent, then you really should present that theory, and point out that it has nothing to do with Everett, or with obtaining every outcome of a trial on different branches.

`QM without collapse is just that: QM without collapse, nothing more,`

`nothing less. Everett worked out this idea added the concept of branches`

`and developed an effective theory and also attempted to derive the Born`

`rule. But that latter attempt is now recognized to not work and other`

`physicists have later used similar and also other approaches to get to a`

`derivation of the Born rule. But so far no one has succeeded.`

My impression is that you do not have any worked-out theory -- you just throw arbitrary objections to my working through the consequences of Everett's approach to quantum mechanics. I have shown that many problems exist with Everettian QM.

`There only exists a problem with getting to the Born rule, not with QM`

`without collapse.`

If you agree, and are prepared, with me, to throw out Everett, then we agree, and there is nothing more to be argued about (at least, until you present some different complete theory).

`I'm open to the idea that QM itself may only be an approximation to a`

`more fundamental theory. The arguments in favor of no collapse are`

`strong arguments but you then do get this issue with probability that`

`you have discussed here. The disagreement with you about this is that I`

`don't see it as a fatal inconsistency that would prove the MWI to be`

`wrong. Probabilities for the different branches do not have to be equal.`

`But that doesn't mean that this looks to be a rather unnatural feature`

`of the theory. This suggests that a more fundamental theory exists from`

`which one could derive quantum mechanics with its formalism involving`

`amplitudes and the Born rule as an approximation.`

Saibal

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