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 the first trial, we have a branch with result 0 and a branch with result 1. 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, representing all possible binary sequences of length N. (This is just like Pascal's triangle) As N becomes very large, we can approximate the binomial distribution 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 0s and1s.Observers in these branches will naturally take the probability tobeapproximated 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 branches are equally probable. You don't make that explicit, it's implicitly assumed, but it's just an assumption. You are simply doing branch counting.The distinctive feature of Everettian Many worlds theory is that every possible outcome is realized on every trial. I don't think that you have absorbed the full significance of this revolutionary idea. There is no classical analogue of this behaviour, which is why your lottery example 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 of Everett'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 theory. So, if you`

`arrive at a contradiction, you are making assumptions that are not`

`implied by the theory.`

Saibal

BruceThe important point to notice is that this result of all possible binary sequences for N trials is independent of the coefficientsinthe binary expansion of the state: |psi> = a|0> + b|1>. Changing the weights of the components in the superposition doesnotchange the conclusion of most observers that the actualprobabilitiesare 0.5 for each result. This is simple mathematics, and I amamazedthat even after all these years, and all the times I have spelledthisout, you still seek to deny the obvious result. Your logical and mathematical skill are on a par with those of John Clark.-- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/CAFxXSLQo8hZ2XYNfAJ%3DU9%3D9K3VxpZYFF4rWP_6tZ2bCzdDCmbQ%40mail.gmail.com [1]. Links: ------ [1] https://groups.google.com/d/msgid/everything-list/CAFxXSLQo8hZ2XYNfAJ%3DU9%3D9K3VxpZYFF4rWP_6tZ2bCzdDCmbQ%40mail.gmail.com?utm_medium=email&utm_source=footer

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