Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

What a nice little war. Technically Bruce is right, but this just shows 
that we have misunderstood the issue. Of course mass/energy in each branch 
is unaffected by the split; we just need to find another, sane way to 
express the idea.

Here is what I understand; correct me if I am wrong. In the multiverse 
created by a single split, we define the space-time distribution of 
mass/energy in this multiverse as the weighed (Born) sum of the 
distributions of the branches. So, each mass in each branch doesn't change; 
only its contribution to the corresponding "multiverse-total" mass is 
weighed.

What is the point of a multiverse-total mass? I suppose it is intended as 
the source of gravitational field for any observer outside the 
Schroedinger-box in which the split is contained (assuming a separate, 
isolated, contained environment inside the box).

To make it more concrete, consider a double-slit interference experiment, 
using one electron at a time. Instead of a screen there are many tiny 
pockets to capture the electron. Outside the box, there are many 
ultra-sensitive gravitational detectors, aiming to locate the electron in a 
pocket. But if the gravitational field of the electron, outside the box, is 
the weighed sum of all branches (one for each pocket), then the detectors 
will be unable to locate the electron. The gravitational measurements will 
indicate, instead of a single pocket, the interference pattern (which we 
would expect from a large number of electrons).

So the gravitational measurements will produce something like an X-ray 
picture of a wavefunction, without destroying it. I find this queer, but 
here I quit for the night, waiting for any other opinions on this issue.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

> On 4/28/2022 10:45 AM, John Clark wrote:
>
> Exactly what axiom would that be? It can't be the Born rule because that 
> is not an axiom, that is an experimentaly derived fact.
>
> If I take some experimental result as granted, then it is an axiom, in my 
system. If you think we need to be more subtle, I propose that we adopt 
some qualitative principle (e.g., see below) as a practical assessment 
rather than as a formal assumption, and so we introduce "FAPP" (corrected 
as "for a practical purpose"). In my proposal I adopt "workability of QM".

 On Friday, April 29, 2022 at 12:07:08 AM UTC+3 meeke...@gmail.com wrote:

> It was a guess by Born.  If you want a measure on Hilbert space that 
> satisfies Kolmogrov's axioms of probability it must be Born's rule.  The 
> axiom could be, "QM measurement results are probabilistic."
>
 
We also need some additional assumption, For Gleason, it was 
"non-contextuality of measurements". I have seen others.

I think that it is enough to assume "equal measures imply equal 
probabilities", but I do not remember seeing this claim before. (I am 
unsure about that.)

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

On Thursday, April 28, 2022 at 11:49:03 PM UTC+3 meeke...@gmail.com (Bent) 
wrote:

> In unitary evolution per the Schroedinger equation there are no "paticular 
> universes", there's only a ray in Hilbert space.  Multiple universes is a 
> FAPP viewpoint.  But so is wave-function collapse.
>

I am glad to agree with this. Now, the challenge for the MWI is to derive 
apparent collapse and the Born Rule (in the long run) from the approximate 
description "multiple universes". Also to explain, in  what sense this 
approximation is good enough.

The trouble with assuming an actual collapse-with-randomisation is the need 
for some mechanism for it, as I gather you too remark, in other words. I 
admit though that, starting with collapse-with-randomisation, it is easy to 
explain "FAPP".

Probabilities are whatever measures satisfy Kologorov's axioms or their 
> logical equivalent.   The information interpretation is QBism.
>

Formal properties are not enough to explain probabilities as a guide to 
life.

George K.

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Re: Everett and probability

[George Kahrimanis]

On Wednesday, April 27, 2022 at 2:55:37 PM UTC+3 johnk...@gmail.com wrote:

> It's not perfect, no analogy is, but classical thermodynamics can provide 
> a pretty good analogy.[...] but that world is *VASTLY* outnumbered by 
> worlds in which other things happen.
>

You mean, statistical mechanics.

Counting worlds, then? I remember as a young student, the "equal 
probabilities" argument based on sheer ignorance of the microstate made me 
depressed. A much better explanation is based on the sort of agument known 
by the name "arbitrary functions", started by Jules Henri Poincaré. Here is 
an example of mine.

Whatever the microstate is (among those compatible with what we know), let 
us focus on the box in which the gas is contained. It has been constructed 
with some procedure, of which we can obtain (with good approximation) 
probability density functions of errors. For example, if we aim to make the 
height to be 4 meters exactly, then we know that the method of construction 
will give us 4 meters plus some error of known distribution. Therefore the 
dimensions of the box are random variables -- even if we assume for the 
time that the surfaces are perfectly flat and it is perfectly orthogonal. 
Every time a gas molecule hits a wall, its future trajectory becomes 
randomised, as well as that of every other molecule it bounces with. Soon a 
probabilistic description of the gas-in-the-box is all we can do, but these 
probabilities are well grounded on the errors in the construction of the 
box.

(If, instead of errors of construction, you prefer to deal with errors of 
measurement, we shall be mired by the controversy in the foundation of 
statistics. Therefore I suggest that we just consider construction.)

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

On Wednesday, April 27, 2022 at 4:12:12 AM UTC+3 Bruce wrote:

> 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 make no comments on the lottery example, because I would need to 
understand it better, and I have too little time now. But I may suprprise 
you with a parallel from pre-QM philosophical work on the interpretation of 
probability. Cournot's Principle claims that probabilities have no 
interpretation, no relevance to our lives, unless they are close enough to 
0 or 1, "enough" depending on the practical purpose. Before one screams 
"this is crazy", he had better look at the appeal of this idea among the 
most prominent students of these matters in the 20th century. However, what 
little work has been done on a decision theory conforming to this principle 
is patently inadequate, IMO, and this, I think, is the reason for its 
current obscurity. The decision theory I have started for MWI will work for 
Cournot's Principle, too.

If one cares for references, search for "Glenn Shafer" and "Cournot's 
Principle", especially the papers titled
- Why did Cournot’s principle disappear?
- That's what all the old guys said
- A Betting Interpretation for Probabilities and Dempster-Shafer Degrees of 
Belief

[...]  I spelled out the sequences that Everett implies in my earlier 
> response. These clearly must have equal probability -- that is what the 
> theory requires. It is not an assumption on my part -- it is a 
> consequence of Everett's basic idea.


I have already expressed disagreement, as a technical matter. I am not 
certain where the misunderstanding lies, but I suspect it is in presuming 
equal probabilities derived from sheer ignorance, as at least one other 
contributor claims. If you really insist on this opinion, it should be 
discussed in a separate conversation -- appealing to your "logical and 
mathematical skills", as you say.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

On Wednesday, April 27, 2022 at 5:57:03 AM UTC+3 Bruce wrote:
> If one wants to persist with unitary evolution, one cannot avoid the 
Schrodinger equation. This has a number of consequences for the theory. One 
is that the theory is deterministic -- there are no probabilities, and all 
outcomes of an experiment are, in some real sense, equivalent. [...]

Equivalent in terms of possibility, not equally probable. YOU say "there 
are no probabilities".

On Wed, Apr 27, 2022 at 11:35 AM smitra https://groups.google.com/>> (Saibal) wrote:
> 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.

I agree; it is a technical matter. There are two assumptions in deriving 
probability 1/2^N in the binomial construction, if the argument is not 
branch-counting:
-1- that probability-in-some-sense is derived by the theory and it depends 
on the measure only;
and
-2- that the coefficients a and b are of equal measure.
But with these assumptions we can derive probability-in-some-sense with 
just one experiment (N=1).

In previous messages, I have expressed objection to the first assumption, 
but this is only because some work is needed in order to combine "there are 
no probabilities" with "there are probabilities in some sense", else one is 
vague to the point of being ridiculous. One needs to specify "in what 
sense?" and "why?".

George K.

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Re: aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

On Monday, April 25, 2022 at 4:09:23 AM UTC+3 Bruce wrote:

> Despite Carroll's protestations (and the similar protestations of others), 
> energy cannot be conserved in the multiverse -- each split must duplicate 
> the energy of the whole as many times as there are branches.


Thanks for the citation. From the discussion so far, there seems to be no 
meaning in adding energy from different universes, so this is neither right 
not wrong (therefore, nuts). I think that this idea becomes meaningful only 
if we consider something like the gravitational field of an electron in a 
double-slit interference experiment: Caroll's idea implies that field 
(outside the box) would be as if generated by the electron-as wave, without 
decoherence. I suggest that we look at the consequences of this conclusion, 
to assess the plausibility of the idea.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

On Friday, April 22, 2022 at 1:54:36 AM UTC+3 Bruce wrote:

we now know that MWI is inconsistent with any sensible interpretation of 
> probability; strict MWI is inconsistent with the Born rule.


Dittos!!! At least, mostly.

What do you mean "we now know"? Any citations, pretty please?

I gather that by "strict MWI" you mean without FAPP. I argue that since we 
regard QM-without-collapse as a workable theory, we have to introduce FAPP 
(more precisely, moral certainty regarding a given purpose) and 
consequently the Born Rule.

In another thread I insist that we must swallow the pill of no-probability 
for single outcomes, and build a decision theory on that. (Yes, we can!) 
>From QM we obtain only the Born Rule for large enough samples.

George K.

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Re: aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

On Friday, April 22, 2022 at 2:13:43 PM UTC+3 johnk...@gmail.com wrote:

> On Thu, Apr 21, 2022 at 6:04 PM George Kahrimanis  
> wrote:
>  
>
>> > Strictly speaking, zero information implies "undefined probability",
>
>
> Sure, but[...]
>

Sorry, but if it is undefined then there is no "but". You remind me of 
myself a few decades ago, when I was in love with Bayesian inference and I 
defended the use of artificial priors. Later I understood that BI is just a 
heuristic method, not sound inference (unless the prior is true). A flat 
prior, or probabilities 1/2 in this case, are only tools in a heuristisc 
method, not proper descriptions of ignorance.

Anyway, my point in this example was only that probability is a very tricky 
subject.

> For the instrumentalists among us (glad to have you, BTW): the question 
>> of interest to me is not about which way is best to derive probability from 
>> QM -- that would be a pointless discussion,
>
>
> It would be pointless because we have known from experiment for nearly a 
> century that the best way to obtain probability from quantum mechanics is 
> to take the square of the absolute value of a particle's wave-function, 
> a.k.a. the Born rule.
>

Not only I do not argue with this, but I emphasise it: this is one of the 
ways in which QM appears "workable". But my point was to prepare the reader 
for a version of the Born rule concerning large samples only, instead of 
single outcomes. Surely the experimental evidence is from large samples; 
the probability for a single case is an extrapolation which is "a matter of 
course" for a certain way of thinking, but not technically obligatory.

>   
>
>> >The question is whether all of them beg the question, so that we have 
>> to think of a rational decision theory without probability.
>>
>
> Even in the days before quantum mechanics, as soon as physicists started 
> thinking about thermodynamics they knew that a rational decision theory 
> without probability was not viable.
>

In my anwer to Brent (my previous message) I gave an example.

> Although Everett's argument (whose improvement I have proposed) grants 
>> that in the long run (that is, large samples) the Born Rule is practically 
>> certain to apply, this is not technically the same as probability for each 
>> single outcome -- though I admit that it works the same,
>
>
> I would argue that if X works the same as Y then technically X is Y.
>

Careful! You trimmed off the end of my sentence: "... it works the same, to 
trigger an instinctive impulse".  Sorry for my sloppy syntax: I meant "it 
works the same, with regard to triggering an instinctive impulse". Noy 
always, not necessarily.

Instead of "technically" you should have "practically", in the sense "a 
technical distinction without a practical difference".

>
> >  for a RATIONAL decision theory this probability is not granted,
>
>
> *IF* that's true *THEN* a RATIONAL man will consistently make predictions 
> about the outcome of an experiment that are inferior to the predictions 
> that an IRRATIONAL man would make. So there would be no point to 
> rationality or being "rational". *THEREFORE* I conclude that your above 
> statement is not true.
>

(I emphasised "rational" as opposed to an experimentally derived decision 
theory.)

A good point, but I am an inadequate amateur in the subject you bring up. 
Surely it is more fun to be irrational, for a while at least, and we all do 
it. Besides, there is no point in being rational about taking an umbrella 
in the morrning, unless there are grave consequences to reckon with. 
Moreover, rationality is about organising certain basic irrational 
pursuits, typically thinkgs like security, food, sex, and entertainment; 
priorities are for to the agent to define. Not a black-or-white dichotomy, 
therefore.
 
And I did not say that there are rational versus irrational predictions. My 
concern is about the interpretation of probability for a single outcome. If 
it is a matter of pleasure without any worrying consequences, then the 
irrational interpretation is fine, even from the rational point of view,

At least we agree on the MWI! The other issues will be resolved, I hope.

George K.

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Re: aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

On Friday, April 22, 2022 at 1:33:46 AM UTC+3 meeke...@gmail.com wrote:

> On 4/21/2022 3:03 PM, George Kahrimanis wrote:
>
> [...] Strictly speaking, zero information implies "undefined probability", 
> or "imprecise probability between 0 and 1". The reason it is commonly 
> mistaken as 50-50 is an implied strategy, flipping a coin in case of 
> ignorance, but then the odds are of the coin instead of the object of the 
> bet. (This strategy works only if the agent is free to choose which side of 
> the bet she underwrites.)
>
>
> If the odds 50/50 can apply to the coin...because you don't know which way 
> it will come down...then the same concept applies to the horse race.
>

No, I do have information about this coin: I have tossed it many times. I 
am clueless about this horserace. Big difference. Concentrate!

[...]  we have to think of a rational decision theory without probability.
>
> Rational decision theory only exists because of uncertainty.  If there 
> were no uncertainty one wouldn't need theory to inform your choice, you 
> would directly by value.
>

Now you are justified to be buffled, because I have avoided giving any 
example. Here is one, containing a combination of uncertainties and 
certainties -- the latter are "moral certainties", something like "FAPP" 
but well defined.

Example. When I have a choice between acting recklessly and acting 
carefully, and my spirit of adventure overcomes my instict of survival, a 
rational argument IMO is to think of my insurance: they will increase the 
premium or drop me if they classify me as a reckless man. I need insurance 
because of uncertainty, to protect my future selves as well as my loved 
ones in future branches in which I will not exist. To keep the example 
short, I postpone arguing why insurance provides moral certainty (in 
principle).

George K.

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Re: aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

In my current way of thinking, the disagreement between Alan Grayson and 
John K. Clark is about two subtly different concepts under the same name, 
"probability". For example, when I read "80% chance of rain today", I may 
think that in some possible futures it will not rain (so probability is 
meaningless), yet I feel an instinctive urge for protection from bad 
weather, so I take my umbrella. We are programmed to act in this way, due 
to Darwinian selection -- but it is a different matter to claim that QM 
(without collapse) issues a probability for each possible outcome so that 
then we are rationally obliged to apply Maximisation of Expected Utility. I 
grant the former but not the latter.

Part of the trouble is that serious philosophical issues about probability 
are still debated, so that there are traps for anyone who deals with these 
things. Here is an example.

> [...] until Alan Grayson sees the end of the race, or somebody tells Alan 
Grayson about it, Alan Grayson can't be certain what world Alan Grayson is 
in. Alan Grayson could be in a world where horse X won or Alan Grayson 
could be in a world where horse Y won, until Alan Grayson receives more 
information Alan Grayson would have to say the odds are 50-50.

If you mean that on sheer ignorance the odds are 50-50, we need some 
clarifications. Strictly speaking, zero information implies "undefined 
probability", or "imprecise probability between 0 and 1". The reason it is 
commonly mistaken as 50-50 is an implied strategy, flipping a coin in case 
of ignorance, but then the odds are of the coin instead of the object of 
the bet. (This strategy works only if the agent is free to choose which 
side of the bet she underwrites.)

For the instrumentalists among us (glad to have you, BTW): the question of 
interest to me is not about which way is best to derive probability from QM 
-- that would be a pointless discussion, I agree! The question is whether 
all of them beg the question, so that we have to think of a rational 
decision theory without probability.

Although Everett's argument (whose improvement I have proposed) grants that 
in the long run (that is, large samples) the Born Rule is practically 
certain to apply, this is not technically the same as probability for each 
single outcome -- though I admit that it works the same, to trigger an 
instinctive impulse. But for a RATIONAL decision theory this probability is 
not granted, IMO.

I can give examples of a decision theory w/o probability, but they would 
dilute the focus of this message.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

On Thursday, April 21, 2022 at 3:54:04 AM UTC+3 Bruce wrote:

> On Thu, Apr 21, 2022 at 10:05 AM George Kahrimanis  
> wrote:
>
>> -2- The "box" (in which Scroedinger's cat is enclosed, with the lethal 
>> apparatus) contains also its "environment", so a quantum descrition of this 
>> box describes the environment also. Therefore I do not agree that 
>> decoherence INSIDE THE BOX will ruin the superposition ASSESSED FROM 
>> OUTSIDE THE BOX. So, Wigner was right. I suppose that Saibal also is right, 
>> though I have not checked that message (sorry).
>>
>
> Unfortunately for this idea, decoherence does not stop at the box. In the 
> time that Wigner thinks about this before he opens the box, decoherence has 
> enveloped essentially the whole world, so Wigner himself has decohered into 
> either a world with a dead cat or a world with a live cat. He can't 
> dissociate himself from the split that occurs, so from his point of view 
> outside the box, the superposition is long gone, and he has to deal with a 
> simple classical state of either a dead cat or a live cat -- no 
> superposition remains.
>

I see we have converged on other technical issues, so maybe this works out, 
too. Perhaps I did not make it clear enough that the environment inside 
this "box" is isolated from the environment outside the box. Only then the 
cat is in a superposition as commonly understood. Otherwise we need the 
environment to define the superposition, which Saibal does in the recent 
messages, but I think it is pointless. So, I meant that Wigner is right but 
under this assumption only: of the two environments.

I had always made a distinction between faster-than-light influences, which 
> are intrinsically local since they involve the local transfer of 
> information via some medium (albeit FTL), and non-local influences, which 
> do not involve any FTL transfers. They are instantaneous and non-local.  So 
> that does not violate relativity. [...]
>

I cannot tell, from this brief comment, whether HV theories become more 
plausible in this way, but I will congratulate you if this is so. I am not 
ready though to enter this discussion now.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

On Tue, Apr 19, 2022 at 11:09 AM Brent Meeker  wrote:

> The only purpose of the box in Schroedinger's thought experiment was to 
>> put off the observers perception.  Really the thought experiment is over 
>> when the radioactive decay occurs.  That atom has transitioned to a 
>> different nuclear state which is entangled with and recorded in the 
>> environment.
>>
>
On Tuesday, April 19, 2022 at 4:20:49 AM UTC+3 Bruce wrote:

> Yes. Schrodinger had the cat in a box to emphasize the idea that the cat 
> was in a macro-superposition of alive/dead. This misled Wigner to the 
> extent that he thought the state collapsed only when the box was opened. 
> All of this was made redundant when it was realized that decoherence 
>  rendered the state definite almost instantaneously. Saibal makes the same 
> mistake when he claims that Alice, after her measurement, is still in a 
> superposition until Bob sees her result. The idea that the superposition 
> still exists since decoherence is only FAPP is something of a red herring 
> -- in MWI, Alice has branched according to her result into up and down 
> branches that no longer interfere. There is no macro-superposition.
>

-1- Decoherence (by a chaotic environment) turns an entangled superposition 
into a non-coherent density matrix, only if we subsequently omit the 
environment from the description of the system. (Not if we keep the 
environment in the description.)

-2- The "box" (in which Scroedinger's cat is enclosed, with the lethal 
apparatus) contains also its "environment", so a quantum descrition of this 
box describes the environment also. Therefore I do not agree that 
decoherence INSIDE THE BOX will ruin the superposition ASSESSED FROM 
OUTSIDE THE BOX. So, Wigner was right. I suppose that Saibal also is right, 
though I have not checked that message (sorry).

I rephrase my conclusion. I agree with you, on the splits being technically 
non-local, but this is only an artifact of describing the dynamical 
evolution of the wavefunction in space-like slices forming a time-like 
stack. Thus a split affects the whole slice in which it occurs. But seen 
from a moving train, it would be a different slice! Only on and inside the 
light cone, the split is physically meaningful.

Thanks to your insistence, now I see the difference between non-local HV 
theories, which violate relativity, and MWI, which does not.

I am writing in a hurry, because these days are hectic. I may have missed 
some important postings, sorry. I would welcome any hints (with the name 
and time of posting) sent to my G-mailbox: GeKahrim.

George K.

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Re: aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

On Monday, April 18, 2022 at 3:35:22 PM UTC+3 agrays...@gmail.com wrote:

So what, in your view, bugged AE about probability in QM? AG
>

I think I have come to a crisp understanding of this issue, which I want to 
submit to you. However, we must take into consideration that the notion of 
probability many scientists have these days is very different from the one 
implied in Einstein's comment "God doesn't play dice".

Einstein seems to have a good old-fashioned understanding of probability 
based on rolling the dice, shuffling the deck, and so on, which has also 
been formalised as "Kolmogorov complexity". That is, a shuffling 
complicated enough to make it technically impossible to run the needed 
calculations in the next 15 seconds, say, in which I am obliged to play my 
hand. Of course I trust that no other players in this game can run such 
calculations in the prescribed time (I trust with "moral certainty", not 
with absolute certainty).

This outlook of probability is incompatible with certain currently popular 
views of probability. For one, entropy considerations are irrelevant in 
general, unless when they just describe shuffling in other words. So-called 
Bayesian priors are also baseless strictly speaking, though they do serve 
in a "let us try this" approach.

One more notion to shed is that of propability issuing from ANY theoretical 
probabilistic model, for example conventional QM. (Surely, if you are 
comfortable with the latter, then Einstein's comment is meaningless!) I 
cite an important (I think) philosophical work by Wolfgang Schwarz: "No 
Interpretation of Probability" Erkenntnis 83, 1195–1212 (2018), 
. He argued that such models do 
NOT issue probability; they issue just numbers which the users ACCEPT AS 
probabilities -- in whatever interpretation of probability one assumes as 
fundamental. This is the key to understanding Einstein's comment.

So, in plain words, Einstein's comment means the following. If the 
interpretation of QM treats normalised measures as probabilities, we need 
to understand this in terms of our basic notion of probability, that is 
shuffling the deck or rolling the dice. So in each measurement someone must 
roll dice or something, in order that probability will arise. Since QM does 
not allow for such a mechanism, we are left to trusting that probabilities 
issued by QM are as good AS IF generated by a randomising mechanism (of a 
familiar kind). This "as if" creates a doubt whether the notion of 
probability from QM is equivalent to that from shuffling. This is not a 
silly question, because it has relevance to decision theory (in particular, 
on whether Maximisation of Expected Utility is a rationally justified 
method).

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

Just clarifications.

On Sunday, April 17, 2022 at 2:15:48 AM UTC+3 meeke...@gmail.com wrote:

> But the purpose of randomizing the polarizer settings using photon from 
> sources on opposite sides of the universe is to prevent anyone from knowing 
> both settings before a measurement.
>

The point of THIS example is to investigate the issue of non-locality of 
splits in a MWI; not to test the Bell inequalities. Surely, if we aim for 
the latter, we will randomise the polariser settings.

I'm not sure I see any function for your superobserver anyway.  Are you 
> sure you need him?
>

Just as in Schroedinger's famous example with the cat, you need a "box" and 
an observer outside, in order to make sense of the cat being in an 
entangled superposition. Instead of a superobserver, we can do with an 
impersonal quantum description (in any chosen frame of reference), if you 
prefer.

I hope that these inadequacies in my exposition will not prevent you from 
focusing on the "Conclusion" about the locality of splits!

George K. 

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

*CHANGE OF MIND.* Not that I made any technical mistake in my previous 
posting, but I failed to think out the conclusion properly. I was just 
stupid -- am I allowed to flame myself? In brief: splits propagating on 
light cones seems to be the correct conclusion, properly understood. Sorry 
for saying the opposite in my previous posting.

First, a clarification.

On Saturday, April 16, 2022 at 5:48:25 AM UTC+3 meeke...@gmail.com wrote:

> "In George's description" means George knows...what?  Does he know the 
> setting of Alice's polarizer?  Does he know that she got 1 or know that she 
> got 0, on only that she got a result?  Some of these he can know without 
> being the forward light cone of Alice's measurement.


Something like the superobserver of Schroedinger's cat. He knows in advance 
the axes of the two polarisers and the times when Alice and Bob read their 
records. Not the outcomes, of course.

*My stupidity was* to say that when Alice reads the record then Bob splits 
too, without taking into account that simultaneity is relative to the 
system of reference. DUH! The time of Bob's first split is not covariant. 
However, this is not a disaster of the theory, because at first the two 
Bobs are identical for a while, until he is informed of Alice's record -- 
or otherwise affected by it, I add now. So, until the two Bobs begin to 
differ from each other, the split is a distinction without a difference. It 
functions as a technical placeholder  prepared by the theory, to 
accommodate the difference that will occur later.

*Conclusion.* As Bruce says, the split is non-local; but, since the time of 
Bob's first split depends on the frame of reference, it is a technicality 
without physical meaning. Only when the lightcone starting with Alice's 
measurement reaches Bob, then the split becomes "real", so to speak.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

Bruce wrote
> [...] Since I have not been able to formulate an argument that has 
convinced Saibal, there seems little point in continuing the discussion.

Not yet, because I just got an idea of what went wrong in the 
communication. Part of it was the understanding (maybe it was just me!) of 
"local splits" as propagating on light cones, which now makes me laugh.

> The argument that MWI is strictly local is just a mistake, and not an 
argument against MWI itself.

Let me try to back this claim. In the example with Alice and Bob, the 
splits arise in the description ("wavefunction") of a superobserver, 
George, who only knows that, first Alice then Bob, measure entangled spins 
on two pre-set axes, without him knowing the outcomes. Instead of the 
superobserver, you may think of an impersonal quantum description of the 
whole system, but I wonder what does it mean, to assume a quantum 
description without a subject, so I will keep speaking of a superobserver.

When Alice becomes entangled with the spin, and the record becomes 
practically permanent (by decoherence in her head), then in George's 
description the whole system splits. Not separately Alice or Bob; the whole 
system. We should not be confused by the fact that at first the two Bobs 
are exactly identical, until Bob eventually learns Alice's record -- but 
the split had occured earlier, in George's description (of the whole 
system).

When, in turn, Bob (that is, both Bobs) measures the spin with his 
equipment, George's description splits again; so George counts four Bobs 
now. (If the two axes are parallel, then one of the two components of the 
second split has measure zero.) This split also affects each Alice, who 
becomes two IDENTICAL copies (total: four!), until she (that is: each 
Alice) learns Bob's record, and then there are no more identical Alices -- 
but the split had ocurred earlier.

So, "local split" makes no sense: each split arises in the description of a 
superobserver. Without a superobserver, it is unclear whether Alice will 
regard herself as split by her measurement. Bob will tell her "Alice, now 
you are split", but so what? Alice (both of them) may reply "I know that I 
am counted as double by anyone who knows of my measurement without knowing 
the record, but I assure you that I am only one of the two Alices you have 
in mind". (No wonder that many people hate MWI!) And she may add "If I am 
split then you are too!".

I could say more about needing a superobserver -- maybe in another posting.

George K.

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Re: aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

On Wednesday, April 13, 2022 at 8:55:48 PM UTC+3 meeke...@gmail.com (Brent) 
wrote:

Decoherence has gone part way in solving the when/where/what basis 
> questions, but only part way.
>

As I wrote at the end of my first reply to your message, I share your 
concern about decoherence but I see the glass as half-full; that is, with a 
little more subtlety I hope that the matter can be formulated in clear 
terms.

Surely collapse is easier to handle as a general concept (except, on the 
other hand, that it requires new dynamics). I forgot to mention that *my 
argument for deriving the Born Rule works with collapse, too* -- so it is 
an alternative to Gleason's theorem.

Here I define colapse as an irreversible process, violating unitarity of 
course, and I keep it separate from randomisation. The latter means that 
each outcome is somehow randomised -- an assumption we can do without.

*Collapse can also be described in a many-world formulation!* It differs 
from the no-collapse MWI only in being irreversible. My argument in outline 
is
1. assessment that MWI-with-collapse is workable;
2. therefore, outcomes of small enough measure can be neglected in practice;
3. now Everett's argument can proceed, concluding that the Born Rule is a 
practically safe assumption (to put it briefly).

So I have replaced two assumptions of Gleason's theorem, randomisation and 
non-contextuality, by the assessment of workability only.

If you don't feel comfortable yet with formulating collapse in a many-world 
setting, let us also assume randomisation (God plays dice), for the sake of 
the argument, in a single-world formulation. That is, we ASSUME the 
existence of probability; then the previous argument just guarantees that 
this probability follows the Born Rule.

Of course I favour the first version of the argument, using the many-world 
formulation of collapse, to avoid the "God plays dice" nightmare.

Thanks for the comments so far, because they stirred my thinking and 
motivated fresh ideas, some of which I hope will prove helpful and worth 
discussing, if and when they mature.

George K.

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Re: aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

Thanks for the comments!

On Wednesday, April 13, 2022 at 8:55:48 PM UTC+3 meeke...@gmail.com (Brent) 
wrote:

Physics doesn't care about "rationally justified", only about empirically 
> justified.


I admit that I have carried the subject to philosophy of physics, but only 
because this kind of subject cannot be addressed with just experiments. On 
the other hand, do you admit that your comment needs qualifications? You 
cannot possibly mean that we just obtain the Born Rule from experiments, 
and that this is all we care about. Did Einstein make any sense, 
complaining about who plays dice during a measurement? What was the point 
of attempts to introduce hidden variables, even at the cost of 
non-locality? What is the point of MWI, then? I suppose that you are a 
careful thinker, and if you object to MWI it would be on some rational 
grounds.

  Both your examples suffer from choosing the simplest case where symmetry 
> can be invoked.


So that you would not be distracted from the basic issue: do you agree with 
always averaging over future selves (Deutsch) or do you take it for granted 
that the theory provides probability (Zurek and others)? Or none of the 
above? Correct me if I am wrong, but I gather that your responce is "who 
cares", or "po-tah-toes, pot-eight-os".

Once you've assumed the Hilbert space structure of QM, then Gleason's 
> theorem essentially forces the Born rule (correct me if I'm wrong, but I 
> think the theorem has been extended to the two-dimensional case).


I shall respectfully correct you, but not on the question you ask, because 
I cannot remember now, and I admit that I do not care to look it up (but I 
explain why). Gleason's theorem also requires the assumption of 
randomisation (God plays dice) and the assumption of non-contextuality of 
measurements. The reason I do not care about it any more is that I do not 
favour these two assumptions (especially the first one).

I think the problem is that MWI (but not Everett) assume all outcomes are 
> equally realized.  So how does a probability become assigned to them, what 
> does it mean.


I agree, and I am glad you are critical on this point.  I am intrigued, 
though, by the caveat "but not Everett": can you explain, please?

We're told it's the probability of finding ourself in a particular 
> world...but that seems very much like "collapse of the wave-function".  It 
> introduces the same problems of exactly when and where does it happen; with 
> only the advantage that consciousness is not understood in detail so the 
> mystery can be push off.


I emphasise that I have no comment on the above, because I do not endorse 
probability strictly speaking but only on an "as-if" basis. (I agree with 
Deutsch on this narrow point -- Physics doesn't care, really?)

Decoherence has gone part way in solving the when/where/what basis 
> questions, but only part way.
>

I guess you refer to the theoretical possibility of the environment 
occasionally failing to "decohere" the state. Here is one of the 
approximations that are required in the translation from objective, 
deterministic QM (without collapse) to the application of QM in the world 
of experience (with apparent collapse). Surely this approximation must be 
scrutinised, I agree.

George K.

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Re: aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

On Friday, April 8, 2022 at 3:19:08 AM UTC+3 Lawrence Crowell wrote:

> This is an appeal to some sort of imperative that demands the Born Rule 
> because the counterfactual lack this certainty. This is a sort of "It must 
> be true" type of argument.


Thanks for the comments! I wonder though, do you agree with my criticisms 
of previous proposals for deriving the Born Rule, or are you undecided? I 
will challenge you (and you all) on this matter, later in this message.

First, a correction: I have not referred to *counterfactuals* (I think that 
you meant "alternatives") but now that you mention them, I may have implied 
one:
"If QM were not a workable theory, *we would have no direct, experimental 
clue that it is a fundamental theory in physics*".
(Not the typical use of a counterfactual, which is in an "if..." clause, as 
in "*If I was a rich man*...".)

What I say is not exactly
> "It must be true"
but rather
"Although I cannot be certain, it seems to be in my interests to form this 
assessment now, when I decide how to act in the present situation".

If you find this argument too loose: I have pointed out that it is the same 
kind of argument that a judge uses to form a decision based on the 
evidence, or an engineer uses, to trust the theory of real numbers, for her 
project.

My aim has been to complete *Everett's argument,* which I outline next. 
Imagine that we repeat the same trial N times, and we record the ratio 
{statistical "frequency") r of one among the possible outcomes 
(eigenstates). Conventional QM assigns a probability R for this outcome, so 
we need an explanation why r SEEMS to approach R in the long run (though we 
know that in very many worlds it will not be so!). Everett noted that, for 
any positive real ε (however small), the measure of all "outlier" 
sequences, that is: for which r is outside
[R-ε, R+ε],
is small, with limit zero as N increases to infinity. However, *a problem 
remains:* why "small measure" or "vanishing measure" have any significance 
in the interpretation of QM? *My proposal answers this question,* finding 
an argument about "small measure" within the reasoned assessment that QM is 
a workable theory.

*Here is my challenge to you.* I ask you if you agree with either of the 
following two proposals (for deriving the Born Rule in a MWI).

First, Deutsch's (1999) proposal, here in a simplified version. Imagine a 
simulated tossing of a fair coin, using a qubit instead of a coin, with 
which you either win or lose one dollar. If this bet has a definite, single 
value to you (presumably, by some kind of intuitive averaging over possible 
futures) it will necessarily be zero, for symmetry reasons. Caveat: Deutsch 
points out that we do not derive probability strictly speaking. I accept 
the reasoning, but not the premise: I am uncomfortable with averaging my 
future selves, and there is no direct rationale why I SHOULD do so. So, *what 
do you think?*

Second (and last), proposals such as Zurek's are of the following pattern 
(here I reuse the previous example): I am uncertain about the outcome, and 
I expect the theory to give me some clue, which will be probability -- what 
else? For symmetry reasons, the probability here must be 1/2. My objection 
is that there is no randomisation in MWI (no shuffling, stirring, or God 
playing dice) so that the use of probability is not rationally justified. 
Again* I ask for your opinion.*

Clarification. Instead of probability proper, I derive the following. With 
regard to any given application, an Everettian agent may expect "with moral 
certainty" (remember the judge and the engineer!) that statistical 
frequency in the long run will be as close to the Born probability as one 
needs it to be (in the particular application). Some people may think 
"po-tah-toes, pot-eight-os", but at some level of thinking *this* is the 
crucial issue. In particular, a serious consequence for decision theory 
results from failing to find any rationale for probability proper!

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

On Monday, April 11, 2022 at 1:43:12 AM UTC+3 Bruce wrote:

> The point seems to be that the fact that some Alice/Bob pairings violate 
> QM can be known only after they pair up. For the branches that form these 
> problematic pairings not to form requires a non-local effect. That is the 
> point I am trying to get across.
>  
> On Mon, Apr 11, 2022 at 3:07 AM George Kahrimanis wrote:
>
>> A realistic version of the scenario with Bob and Alice [...]
>>
>> There have always been worries about detection inefficiencies and errors 
> in the tests of Bell inequalities. [...]
>

Thanks for the hints! I too think of splits as global; I would be curious 
though to see a CONSISTENT formalism that treats them as propagating in 
light cones, and if "new physics" would be possible.

My comment, as brief as possible: I do not think that "bad pairings" is a 
strong enough argument against a local-split theory, because they arise in 
examples with perfect precision only, which must be treated just as limits 
(we agree, I know), so "pairings of measure zero" is the right way to put 
it. Then I cannot blame a theory just because it predicts violation of 
physical laws in branches of measure zero, or practically zero.

To be more descriptive: think of just one experimenter and a local 
experiment. The pair
|1> |1>
will be "of measure zero" to her when the polarisers are parallel, in the 
limit with decreasing imprecision; not "physically impossible", strictly 
speaking. (It is "impossible" only in the ideal example directly, not in 
the limit of vanishing imprecision.)

For finding a physical difference introduced by assuming locality of 
splits, I would look elsewhere. First, in the EM radiation and the 
gravitational effect of an electron curving (up or down) in a polariser -- 
just a hunch.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

On Tuesday, April 12, 2022 at 10:29:07 AM UTC+3 Bruce wrote:

> If the memory is reversed (whatever that might mean) then there is no 
> evidence that the memory ever existed. You are back into fantasy-land.


No, there is a formal proof that an entanglement can be reversed and 
nonetheless we still have a record indicating that, temporarily, an 
entanglement had been in effect! I remember David Deutsch showing this in a 
lecture, in 1985.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

Bruce wrote
> [...] But by the rules of MWI, there is also a copy of Alice with result 
|1> who meets a Bob who recorded |1> for the 10th trial. This contradicts 
QM, in fact it violates angular momentum conservation, so no such Alice/Bob 
coupling is possible. But, by following the rules of local MWI, such a 
pairing is inevitable. [...] The challenge for the local account of the 
Bell correlations in MWI is: What happens to all these incorrect couplings? 
[...] MWI offers no mechanism for removing these bad pairings.

I find this question very interesting but I am clueless about "the local 
account of the Bell correlations in MWI". So, if my comments are nonsense 
to you, please cite a reference on that subject. And if these comments seem 
to favour that approach, I do not know if I will like it when I study it.

I wonder, is it off-limits of this approach to give special status to any 
branch of a multiverse that, at some later point, violates a law of 
physics? (Or of measure zero?) That is, we anticipate that some of the 
branches will turn out to be just ghosts.

A realistic version of the scenario with Bob and Alice must take into 
consideration unavoidable imprecision, in the polarisers not being 
perfectly parallel, and in the possibility of a transcription error in the 
recording and of the records themselves. So, such branches will not be 
exactly unphysical, but rather of very small measure. So there are no "Bad 
Pairings", strictly speaking.

George K.

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Re: The Nature of Contingency: Quantum Physics as Modal Realism

[George Kahrimanis]

Saibal wrote
> [...] it's not appropriate to fix up the theory by introducing notions 
from the macroscopic domain that should in principle follow from the 
fundamental dynamics at the micro-level. [...]

Brent wrote
> The notion of "result" and "measurement" are not introduced, they are 
fundamental to knowledge.  They are exactly where MWI gets into trouble. 
[...]

If there is a disagreement, we should take care to clarify what is it 
about. A putative reductionist view accepts a theory as fundamental, 
perhaps along with some constraints on initial conditions, and claims that 
"observer", "result", and "measurement" will emerge. Right?

I think that this cannot work, because there is some unavoidable 
approximation in the translation from "a quantum state of a part of the 
world" to "this quasi-solid apparatus, observer, and environment (which may 
be part of the observer)". With conventional QM, we express this 
approximation as the very-very small probability of the apparatus 
quantum-tunneling through the floor, and so on. With a MWI, I do not see 
how we can formulate this approximation from the reductionist point of view.

So there is a dualism: The supposedly fundamental theory applies to an 
imagined, objective world, and it also applies to the world of our 
experience. There is a connection of course, because if the latter were 
untrue then we could have no clue about the validity of the theory in the 
objective world. A key notion here is workability of the theory: that it 
tolerates the impossibility of infinite precision, so it works in both 
worlds.

Brent continued
> [...] By saying there is no result of an experiment it muddles the 
concept of probability.

Although I have seen proposals for introducing probability in a MWI (Zurek, 
Vaidman, John K. Clark), they cannot refer to the notion of aleatory 
probability, involving randomisation, as when one shuffles a deck of cards 
or shakes and rolls dice. On the other hand, conventional QM does assume 
that dice are rolled, and so the requisite randomisation is supposedly 
introduced, and we can speak of probability proper. Where is the 
randomisation in a MWI? (A rhetorical question.) So, there is no 
probability (strictly speaking) in a MWI. We can only identify 
something-like-probability; I have posted about this subject in a recent 
thread.

George K.

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aiming to complete Everett's derivation of the Born Rule

[George Kahrimanis]

Hello Everything. I have a proposal for a common-sense justification of the
Born Rule for QM. The idea was motivated with the Many-World
Interpretations in mind, but it also works for QM-with-collapse, if that is
ever found to be true.

It would be great if you respond with any comment, objection, contribution,
or question. Or you can direct me to another discussion forum.

My current draft of the Introduction is at the following link (to save
"bandwidth"):
https://drive.google.com/file/d/1CE_qkit5PnS-rzKKmlOoDReBJVN1T0kA/view?usp=sharing

To give you an idea, I paste here just the Abstract and the first
subsection of the Introduction.



An argument for workability of QM leads to the Born Rule, for QM without
collapse and for QM with collapse

George Kahrimanis [, ...]
6 April 2022, incomplete work

ABSTRACT
Any interpretation of QM without collapse (a.k.a. a MWI) crucially needs to
produce (not assume) an Everettian analogue of the Born Rule, indispensable
not only in practical decisions but also for testing a theory. Related
proposals have been controversial. The proposal introduced here is based on
an argument for workability of QM and on the old notion of Moral Certainty
(formulated by Jean Gerson, cited by Descartes and many others). There are
consequences for the foundations of decision theory because chance is
undefined for any single outcome, so that Maximisation of Expected Utility
is meaningless as a fundamental rational rule, therefore a different
decision theory is needed.

1- INTRODUCTION

1.1- Comparison with other derivations of the Born Rule, either in MWI or
with collapse

The present study is based on an assessment (not an assumption, strictly
speaking) regarding workability of QM (its usability and testability); that
is, an argument for workability is presented and the assessment is up to
the reader. It avoids a tacit assumption of certain derivations in MWI,
developments of the one by [Deutsch 1999], declaring the utility of a bet
as a single value, rather than a pair (corresponding to a buying value and
a selling value) or an interval -- however, an Everettian agent may well be
unwilling to admit a single value, in view of the diversity of outcomes in
branching futures. Despite this disagreement, we share an essential common
trait: we address the problem outside of pure epistemology, by studying how
QM can be a guide to practical applications. Another difference is that the
present study is based solely on the status of QM as a workable theory, but
Deutsch's derivation also introduces claims about rational behaviour (with
which I agree, except for the one mentioned above).

Other derivations not assuming collapse (for example, Zurek's), nonetheless
invoke the concept of probability in the interpretation, on the basis of
various arguments [Vaidman 2020]. In contrast, the present study adopts a
restriction: probability proper will be considered only for outcomes of a
randomising process. (It is not enough to know that a black box contains
just ten black and ten white balls, or that there are only four aces in a
deck of fifty two cards: the cards must be shuffled and the balls stirred,
with specifications tailored to the game.) In a single-world interpretation
assuming collapse, randomisation is a required assumption (albeit derided
as "God plays dice") so that we may legitimately speak of probability; in a
MWI though, randomisation makes no sense. Therefore the present study does
not invoke a ready concept of probability; it rather discovers what
quantum-mechanical quasi-probability is (and what it is not). The results
are relevant also to the interpretation of non-QM probability, regardless
if it may be ultimately based on QM.

There are derivations of the Born Rule assuming collapse with
randomisation, along with some special assumption. (The first such
derivation was Gleason's theorem, assuming "non-contextuality" of
measurements; for references, see [Vaidman 2020] and [Masanes, Galley,
Müller].) These special assumptions are deemed more plausible than assuming
the Born Rule directly, because they are qualitative properties rather than
quantitative ones; nonetheless any special assumption needs justification,
whether on experimental grounds or by some theoretic argument. The present
study shows that we can replace both randomisation and the additional
special assumption by workability. So the Born Rule is derived from
workability alone, whether we assume collapse or not.

1.2- About Moral Certainty

[...]

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