Re: Deriving the Born Rule

['Brent Meeker' via Everything List]

On 5/17/2020 6:20 PM, Lawrence Crowell wrote:

On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:

On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell
> wrote:

There is nothing wrong formally with what you argue. I would
though say this is not entirely the Born rule. The Born rule
connects eigenvalues with the probabilities of a wave
function. For quantum state amplitudes a_i in a superposition
ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of an
observable O obeys

⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.

Your argument has a tight fit with this for O_i = ρ_{ii}.

The difficulty in part stems from the fact we keep using
standard ideas of probability to understand quantum physics,
which is more fundamentally about amplitudes which give
probabilities, but are not probabilities. Your argument is
very frequentist.



I can see why you might think this, but it is actually not the
case. My main point is to reject subjectivist notions of
probability:  probabilities in QM are clearly objective -- there
is an objective decay rate (or half-life) for any radioactive
nucleus; there is a clearly objective probability for that spin to
be measured up rather than down in a Stern-Gerlach magnet; and so on.


Objective probabilities are frequentism.


No necessarily.  Objective probabilities may be based on symmetries and 
the principle of insufficient reason.  I agree with Bruce; just because 
you measure a probability with frequency, that doesn't imply it must be 
based on frequentism.


The idea from a probability perspective is that one has a sample space 
with a known distribution. Your argument, which I agree was my first 
impression when I encountered the Bayesian approach to QM by Fuchs and 
Schack, who I have had occasions to talk to. My impression right way 
was entirely the same; we have operators with outcomes and they have a 
distribution etc according to Born rule. However, we have a bit of a 
sticking point; is Born's rule really provable? We most often think in 
a sample space frequentist manner with regards to the Born rule. 
However, it is at least plausible to think of the problem from a 
Bayesian perspective, and where the probabilities have become known is 
when the Bayesian updates have become very precise.


However, all this talk of probability theory may itself be wrong. 
Quantum mechanics derives probabilities or distributions or spectra, 
but it really is a theory of amplitudes or the density matrix. The 
probabilities come with modulus square or the trace over the density 
matrix. Framing QM around an interpretation of probability may be 
wrong headed to begin with.


But if it's not just mathematics, there has to be some way to make 
contact with experiment...which for probabilistic predictions usually 
means frequencies.


Brent



The argument by Carroll and Sebens, using a concept of the
wave function as an update mechanism, is somewhat Bayesian.



It is this subjectivity, and appeal to Bayesianism, that I reject
for QM. I consider probabilities to be intrinsic properties -- not
further analysable. In other words, I favour a propensity
interpretation. Relative frequencies are the way we generally
measure probabilities, but they do not define them.


I could I suppose talk to Fuchs about this. He regards QM as having 
this uncertainty principle, which we can only infer probabilities with 
a large number of experiments where upon we update Bayesian priors. Of 
course a frequentists, or a system based on relative frequencies, 
would say we just make lots of measurements and use that as a sample 
space. In the end either way works because QM appears to be a pure 
system that derives probabilities. In other words, since outcome occur 
acausally or spontaneously there are not meddlesome issues of 
incomplete knowledge. Because of this, and I have pointed it out, the 
two perspective end up being largely equivalent.



This is curious since Fuchs developed QuBism as a sort of
ultra-ψ-epistemic interpretation, and Carroll and Sebens are
appealing to the wave function as a similar device for a
ψ-ontological interpretation.

I do though agree if there is a proof for the Born rule that
is may not depend on some particular quantum interpretation.
If the Born rule is some unprovable postulate then it would
seem plausible that any sufficiently strong quantum
interpretation may prove the Born rule or provide the
ancillary axiomatic structure necessary for such a proof. In
other words maybe quantum interpretations are essentially
unprovable physical axioms that if sufficiently string provide
a proof of the Born rule.



I would agree that the Born rule is unlikely to be provable within
some model of quantum mechanics 

Re: Deriving the Born Rule

[Bruce Kellett]

On Mon, May 18, 2020 at 11:20 AM Lawrence Crowell <
goldenfieldquaterni...@gmail.com> wrote:

> On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:
>>
>> On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <
>> goldenfield...@gmail.com> wrote:
>>
>>> There is nothing wrong formally with what you argue. I would though say
>>> this is not entirely the Born rule. The Born rule connects eigenvalues with
>>> the probabilities of a wave function. For quantum state amplitudes a_i in a
>>> superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of an
>>> observable O obeys
>>>
>>> ⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.
>>>
>>> Your argument has a tight fit with this for O_i = ρ_{ii}.
>>>
>>> The difficulty in part stems from the fact we keep using standard ideas
>>> of probability to understand quantum physics, which is more fundamentally
>>> about amplitudes which give probabilities, but are not probabilities. Your
>>> argument is very frequentist.
>>>
>>
>>
>> I can see why you might think this, but it is actually not the case. My
>> main point is to reject subjectivist notions of probability:  probabilities
>> in QM are clearly objective -- there is an objective decay rate (or
>> half-life) for any radioactive nucleus; there is a clearly objective
>> probability for that spin to be measured up rather than down in a
>> Stern-Gerlach magnet; and so on.
>>
>>
> Objective probabilities are frequentism.
>


Rubbish. Popper's original propensity ideas may have had frequentist
overtones, but we can certainly move beyond Popper's outdated thinking. An
objective probability is one that is an intrinsic property of an object,
such as a radio-active nucleus. One can use relative frequencies or
Bayesian updating to estimate these intrinsic probabilities experimentally.
But neither relative frequencies nor Bayesian updating of subjective
beliefs actually define what the probabilities are in quantum mechanics.


The idea from a probability perspective is that one has a sample space with
> a known distribution.
>

These are consequences of the existence of probabilities -- not a
definition of them.

Your argument, which I agree was my first impression when I encountered the
> Bayesian approach to QM by Fuchs and Schack, who I have had occasions to
> talk to. My impression right way was entirely the same; we have operators
> with outcomes and they have a distribution etc according to Born rule.
> However, we have a bit of a sticking point; is Born's rule really provable?
> We most often think in a sample space frequentist manner with regards to
> the Born rule. However, it is at least plausible to think of the problem
> from a Bayesian perspective, and where the probabilities have become known
> is when the Bayesian updates have become very precise.
>

Again, you are confusing measuring or estimating the probabilities with
their definition. Propensities are intrinsic properties, not further
analysable. Whether or not the Born rule can be derived from simpler
principles is far from clear. I don't think the attempts based on decision
theory (Deutsch, Wallace, etc) succeed, and attempts based on self-location
(Carroll, Zurek) are far from convincing, since they are probably
intrinsically dualist.

However, all this talk of probability theory may itself be wrong. Quantum
> mechanics derives probabilities or distributions or spectra, but it really
> is a theory of amplitudes or the density matrix. The probabilities come
> with modulus square or the trace over the density matrix. Framing QM around
> an interpretation of probability may be wrong headed to begin with.
>



The basic feature of quantum mechanics is that it predicts probabilities.
You confuse the way this is expressed in the theory with the actuality of
how probability is defined.

The argument by Carroll and Sebens, using a concept of the wave function as
>>> an update mechanism, is somewhat Bayesian.
>>>
>>
>>
>> It is this subjectivity, and appeal to Bayesianism, that I reject for QM.
>> I consider probabilities to be intrinsic properties -- not further
>> analysable. In other words, I favour a propensity interpretation. Relative
>> frequencies are the way we generally measure probabilities, but they do not
>> define them.
>>
>>
> I could I suppose talk to Fuchs about this. He regards QM as having this
> uncertainty principle, which we can only infer probabilities with a large
> number of experiments where upon we update Bayesian priors. Of course a
> frequentists, or a system based on relative frequencies, would say we just
> make lots of measurements and use that as a sample space. In the end either
> way works because QM appears to be a pure system that derives
> probabilities. In other words, since outcome occur acausally or
> spontaneously there are not meddlesome issues of incomplete knowledge.
> Because of this, and I have pointed it out, the two perspective end up
> being largely equivalent.
>


But these are ways of estimating probabilities -- pro

Re: Deriving the Born Rule

[Lawrence Crowell]

On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:
>
> On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <
> goldenfield...@gmail.com > wrote:
>
>> There is nothing wrong formally with what you argue. I would though say 
>> this is not entirely the Born rule. The Born rule connects eigenvalues with 
>> the probabilities of a wave function. For quantum state amplitudes a_i in a 
>> superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of an 
>> observable O obeys
>>
>> ⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.
>>
>> Your argument has a tight fit with this for O_i = ρ_{ii}.
>>
>> The difficulty in part stems from the fact we keep using standard ideas 
>> of probability to understand quantum physics, which is more fundamentally 
>> about amplitudes which give probabilities, but are not probabilities. Your 
>> argument is very frequentist.
>>
>
>
> I can see why you might think this, but it is actually not the case. My 
> main point is to reject subjectivist notions of probability:  probabilities 
> in QM are clearly objective -- there is an objective decay rate (or 
> half-life) for any radioactive nucleus; there is a clearly objective 
> probability for that spin to be measured up rather than down in a 
> Stern-Gerlach magnet; and so on.
>
>
Objective probabilities are frequentism. The idea from a probability 
perspective is that one has a sample space with a known distribution. Your 
argument, which I agree was my first impression when I encountered the 
Bayesian approach to QM by Fuchs and Schack, who I have had occasions to 
talk to. My impression right way was entirely the same; we have operators 
with outcomes and they have a distribution etc according to Born rule. 
However, we have a bit of a sticking point; is Born's rule really provable? 
We most often think in a sample space frequentist manner with regards to 
the Born rule. However, it is at least plausible to think of the problem 
from a Bayesian perspective, and where the probabilities have become known 
is when the Bayesian updates have become very precise. 

However, all this talk of probability theory may itself be wrong. Quantum 
mechanics derives probabilities or distributions or spectra, but it really 
is a theory of amplitudes or the density matrix. The probabilities come 
with modulus square or the trace over the density matrix. Framing QM around 
an interpretation of probability may be wrong headed to begin with.
 

>
> The argument by Carroll and Sebens, using a concept of the wave function 
>> as an update mechanism, is somewhat Bayesian.
>>
>
>
> It is this subjectivity, and appeal to Bayesianism, that I reject for QM. 
> I consider probabilities to be intrinsic properties -- not further 
> analysable. In other words, I favour a propensity interpretation. Relative 
> frequencies are the way we generally measure probabilities, but they do not 
> define them.
>
>
I could I suppose talk to Fuchs about this. He regards QM as having this 
uncertainty principle, which we can only infer probabilities with a large 
number of experiments where upon we update Bayesian priors. Of course a 
frequentists, or a system based on relative frequencies, would say we just 
make lots of measurements and use that as a sample space. In the end either 
way works because QM appears to be a pure system that derives 
probabilities. In other words, since outcome occur acausally or 
spontaneously there are not meddlesome issues of incomplete knowledge. 
Because of this, and I have pointed it out, the two perspective end up 
being largely equivalent.
 

>
> This is curious since Fuchs developed QuBism as a sort of 
>> ultra-ψ-epistemic interpretation, and Carroll and Sebens are appealing to 
>> the wave function as a similar device for a ψ-ontological interpretation.
>>
>> I do though agree if there is a proof for the Born rule that is may not 
>> depend on some particular quantum interpretation. If the Born rule is some 
>> unprovable postulate then it would seem plausible that any sufficiently 
>> strong quantum interpretation may prove the Born rule or provide the 
>> ancillary axiomatic structure necessary for such a proof. In other words 
>> maybe quantum interpretations are essentially unprovable physical axioms 
>> that if sufficiently string provide a proof of the Born rule.
>>
>
>
> I would agree that the Born rule is unlikely to be provable within some 
> model of quantum mechanics -- particularly if that model is deterministic, 
> as is many-worlds. The mistake that advocates of many-worlds are making is 
> to try and graft probabilities, and the Born rule, on to a 
> non-probabilistic model. That endeavour is bound to fail. (In fact, many 
> have given up on trying to incorporate any idea of 'uncertainty' into their 
> model -- this is what is known as the "fission program".) One of the major 
> problems people like Deutsch, Carroll, and Wallace encounter is trying to 
> reconcile Everett with David Lewis's "Principal Principle", which i

Re: Universe as a simulated strange loop

['Brent Meeker' via Everything List]

On 5/17/2020 6:29 AM, Bruno Marchal wrote:

the appearance of matter as they are explained by the mechanist consciousness 
flux in arithmetic (itself explained by G and G* and their difference).


You frequently say this, but I have not seen this explanation except in 
vague hand waving.


Brent

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Re: Deriving the Born Rule

[Bruce Kellett]

On Mon, May 18, 2020 at 5:18 AM smitra  wrote:

>
> Deriving the Born rule within the context of QM seems to me a rather
> futile effort as you still have the formalism of QM itself that is then
> unexplained. So, I think one has to tackle QM itself. It seems t me
> quite plausible that QM gives an approximate description of a multiverse
> of algorithms. So, we are then members of such a multiverse, this then
> includes alternative versions of us who found different results in
> experiments, but the global structure of this multiverse is something
> that QM does not describe adequately.
>
> QM then gives a local approximation of this multiverse that's valid in
> the neighborhood of a given algorithm, That algorithm can be an observer
> who has found some experimental result, and the local approximation
> gives a description of the "nearby algorithms" that are processing
> alternative measurement results. The formalism of QM can then arise due
> to having to sum over all algorithms that fall within the criterion of
> being close to the particular algorithm that is processing some
> particular data. This is then a constrained summation over all possible
> algorithms. One can then replace such a constrained summation by an
> unrestricted summation and implement the constraint by including phase
> factors of the form exp(i u constraint function) where constraint
> function = 0 for the terms of the original constrained summation. One
> can then write the original summation as an integral over u.
>

And that is all hopelessly ad hoc, without a shred of evidence.

Bruce

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Making a GOOGOL:1 Reduction with Lego Gears

[John Clark]

Making a GOOGOL:1 Reduction with Lego Gears


John K Clark

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Re: Deriving the Born Rule

[smitra]

On 17-05-2020 08:57, Bruce Kellett wrote:

On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell
 wrote:


There is nothing wrong formally with what you argue. I would though
say this is not entirely the Born rule. The Born rule connects
eigenvalues with the probabilities of a wave function. For quantum
state amplitudes a_i in a superposition ψ = sum_ia_iφ_i with
φ*_jφ_i = δ_{ij} the spectrum of an observable O obeys

⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.

Your argument has a tight fit with this for O_i = ρ_{ii}.

The difficulty in part stems from the fact we keep using standard
ideas of probability to understand quantum physics, which is more
fundamentally about amplitudes which give probabilities, but are not
probabilities. Your argument is very frequentist.


I can see why you might think this, but it is actually not the case.
My main point is to reject subjectivist notions of probability:
probabilities in QM are clearly objective -- there is an objective
decay rate (or half-life) for any radioactive nucleus; there is a
clearly objective probability for that spin to be measured up rather
than down in a Stern-Gerlach magnet; and so on.


The argument by Carroll and Sebens, using a concept of the wave
function as an update mechanism, is somewhat Bayesian.


It is this subjectivity, and appeal to Bayesianism, that I reject for
QM. I consider probabilities to be intrinsic properties -- not further
analysable. In other words, I favour a propensity interpretation.
Relative frequencies are the way we generally measure probabilities,
but they do not define them.


This is curious since Fuchs developed QuBism as a sort of
ultra-ψ-epistemic interpretation, and Carroll and Sebens are
appealing to the wave function as a similar device for a
ψ-ontological interpretation.

I do though agree if there is a proof for the Born rule that is may
not depend on some particular quantum interpretation. If the Born
rule is some unprovable postulate then it would seem plausible that
any sufficiently strong quantum interpretation may prove the Born
rule or provide the ancillary axiomatic structure necessary for such
a proof. In other words maybe quantum interpretations are
essentially unprovable physical axioms that if sufficiently string
provide a proof of the Born rule.


I would agree that the Born rule is unlikely to be provable within
some model of quantum mechanics -- particularly if that model is
deterministic, as is many-worlds. The mistake that advocates of
many-worlds are making is to try and graft probabilities, and the Born
rule, on to a non-probabilistic model. That endeavour is bound to
fail. (In fact, many have given up on trying to incorporate any idea
of 'uncertainty' into their model -- this is what is known as the
"fission program".) One of the major problems people like Deutsch,
Carroll, and Wallace encounter is trying to reconcile Everett with
David Lewis's "Principal Principle", which is the rule that one should
align one's personal subjective degrees of belief with the objective
probabilities. When these people essentially deny the existence of
objective probabilities, they have trouble reconciling subjective
beliefs with anything at all.

Bruce


Deriving the Born rule within the context of QM seems to me a rather 
futile effort as you still have the formalism of QM itself that is then 
unexplained. So, I think one has to tackle QM itself. It seems t me 
quite plausible that QM gives an approximate description of a multiverse 
of algorithms. So, we are then members of such a multiverse, this then 
includes alternative versions of us who found different results in 
experiments, but the global structure of this multiverse is something 
that QM does not describe adequately.


QM then gives a local approximation of this multiverse that's valid in 
the neighborhood of a given algorithm, That algorithm can be an observer 
who has found some experimental result, and the local approximation 
gives a description of the "nearby algorithms" that are processing 
alternative measurement results. The formalism of QM can then arise due 
to having to sum over all algorithms that fall within the criterion of 
being close to the particular algorithm that is processing some 
particular data. This is then a constrained summation over all possible 
algorithms. One can then replace such a constrained summation by an 
unrestricted summation and implement the constraint by including phase 
factors of the form exp(i u constraint function) where constraint 
function = 0 for the terms of the original constrained summation. One 
can then write the original summation as an integral over u.


Saibal

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Re: Deriving the Born Rule

['Brent Meeker' via Everything List]

On 5/17/2020 3:31 AM, Bruno Marchal wrote:


On 17 May 2020, at 11:39, 'scerir' via Everything List 
> wrote:


I vaguely remember that von Weizsaecker wrote (in 'Zeit und Wissen') 
that probability is 'the expectation value of the relative frequency'.





That is the frequency approach to probability. Strictly speaking it is 
false, as it gives the wrong results for the “non normal history” 
(normal in the sense of Gauss). But it works retire well in the normal 
world (sorry for being tautological).


At its antipode, there is the bayesian “subjective probabilities”, 
which makes sense when complete information is available . So it does 
not make sense in many practical situation.


Remark: the expression “subjective probabilities” is used technically 
for this Bayesian approach, and is quite different from the first 
person indeterminacy that Everett call “subjective probabilities”. The 
“subjective probabilities” of Everett are “objective probabilities”, 
and can be defined trough a frequency operator in the limit.


That's questionable.  For the frequencies to be correct the splitting 
must the uneven.  But there's nothing in the Schoedinger evolution to 
produce this.  If there are two eigenvalues and the Born probabilities 
are 0.5 and 0.5 then it works fine.  But it the Born probabilities are 
0.501 and 0.499 then there must be a thousand new worlds,  yet the 
Schroedinger equation still only predicts two outcomes.


Brent

The same occur in arithmetic, where the subjective (first person) 
probabilities are objective (they obey objective, sharable, laws).


Naïve many-worlds view are not sustainable, but there is no problem 
with consistent histories, and 0 worlds.


Bruno






Bruce wrote:

It is this subjectivity, and appeal to Bayesianism, that I reject 
for QM. I consider probabilities to be intrinsic properties -- not 
further analysable. In other words, I favour a propensity 
interpretation. Relative frequencies are the way we generally 
measure probabilities, but they do not define them.







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Re: Universe as a simulated strange loop

[Bruno Marchal]

> On 7 May 2020, at 23:00, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 5/7/2020 9:30 AM, Bruno Marchal wrote:
>> I can imagine a materialist psychologist claiming that the natural numbers 
>> are not primitive but explainable by a cultural anthropo-evolutionary 
>> genetic, say. But 1) he is confusing the human natural number theories with 
>> arithmetic, and 2) he is cheating, as his explanation will make only sense 
>> by an implicit acceptance of some universal machinery equivalent to the 
>> belief in RA, so, he is just confusing level of explanation.
> 
> It's not confusion when you explain something in terms of what you 
> understand.  Confusion is to say things must be explained in terms of 
> something infinite and incomprhensible…

Not with mechanism. The assumption are just that Kxy = x, and Sxyz = xz(yz). In 
fact, with mechanism, we can explain why the axiom of infinity has to be false. 
Even, the induction axioms are possibly false ontologically. Mechanism, 
contrary of what I said a long time ago, is consistent with utltrafinithsm.





> and then claim it's incomprehensibility proves it's primitive because is 
> can't have an explanation.


That is provably the case for “simple" things like natural numbers and 
combinators, but is false for the appearance of matter as they are explained by 
the mechanist consciousness flux in arithmetic (itself explained by G and G* 
and their difference).

Evidences for a physical reality are not the same as evidence for a primitive 
physical reality. That is the Aristotelian prejudice, which I think comes from 
a misunderstanding of Plato, or a lack of reasoning. 

There are tuns of evidences for a physical reality, and I understand the 
elegance and appeal the idea that such reality is primitive. 
Yet, I am rationalist and an empiricist. The close observation of the physical 
universe confirms that it cannot be primitive, like digital mechanism predicts.

Bruno



> 
> Brent
> 
>> Yes, the human number theory is a fascinating subject, and it sustains the 
>> idea that 2+2=4 is “really absolutely” true, as all humans agree on this, 
>> and even many other mammals, actually. But that is a different subject 
>> matter than the one number theory is build for.  This one avoid the 
>> philosophy of numbers by using the axiomatic method. It should be obvious 
>> that with mechanism, the discovery of the numbers by the numbers is part of 
>> the meta-arithmetic that Gödel’s showed embeddable in arithmetic. The real 
>> bomb is still Gödel’s 1931, even if it is the two theorems of Solovay which 
>> sums it all in G, and G*.
> 
> 
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Re: Universe as a simulated strange loop

[Bruno Marchal]

> On 7 May 2020, at 23:14, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 5/7/2020 10:00 AM, Bruno Marchal wrote:
>> Existing is when the proposition “ExP(x)” is true in some reality. For 
>> example Ex(prime(x)) is true in the structure/model (N, 0, s, +, x).
> 
> "In some reality" completely drains "reality" of all meaning.  It simply 
> means some set of assertions that is not self-contradictory.

You are right. That follows from the completeness theorem. A (reasonable) 
theory is consistent iff it has a model (a reality which satisfies all the 
theorems). 

Now no machine can prove the existence of a reality satisfying all its belief, 
that is why we use terms like God, or “No-Name” or “Reality” with a big “R”. 
That sort of reality is no more model theory, but is theology, and the first 
theorem in Mechanist theologies is that we cannot define it, nor invoke it in 
arguments.

Here I was just using “reality” for “model”, as “model” when used by physicists 
means what logicians call “theories”.

So now I can deduce that by “it exist”, you refer to some metaphysical reality. 
You need to say which one to be precise. I suspect you mean the physical 
reality, but that early what is questioned when we assume mechanism, where the 
metaphysical reality is only (a part) of the arithmetical truth.

Bruno




> 
> Brent
> 
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Re: Universe as a simulated strange loop

[Bruno Marchal]

> On 16 May 2020, at 17:19, Telmo Menezes  wrote:
> 
> 
> 
> Am Do, 7. Mai 2020, um 16:30, schrieb Bruno Marchal:
>> 
>>> On 6 May 2020, at 12:58, Telmo Menezes  wrote:
>>> 
>>> 
>>> 
>>> Am Mi, 6. Mai 2020, um 10:41, schrieb Bruno Marchal:
 
> On 5 May 2020, at 21:25, 'Brent Meeker' via Everything List 
>  wrote:
> 
> 
> 
> On 5/5/2020 4:54 AM, Bruno Marchal wrote:
>> Physics works very well, to make prediction but as metaphysics, as the 
>> Platonist greeks understood, it simply does not work at all. It uses an 
>> identity thesis between mind and brain which is easy in one direction, 
>> but non-sensical in the other direction. It is not a matter of choice: 
>> if mechanism is true, the many physical histories must emerges from the 
>> many computations in all models of arithmetic, or in the standard model 
>> (as you prefer).
> And you use the identity theory of all possible computation and 
> reality...which has no evidence in support of it and I see no reason to 
> believe.
 
 The existence of all computations is a theorem of arithmetic. If you 
 understand 2+2=4 and similar, you can understand that all computations 
 are emulated in (all) model(s) of arithmetic. That arithmetic is 
 assumed in all theories made by physicists. But when you add an 
 ontological physical universe, we have no mean to restrict the 
 statistics on all computations on the “physical” computations without 
 adding some magic in the theory.
 
 So, it seems you are the one adding an ontological commitment, to make 
 magically disappear the consciousness of the relative number in 
 arithmetic.
 
 The reason to believe this is just Mechanism. I have not find a reason 
 to believe in a physical universe having an ontological primitive 
 status, which would be a reason to believe in non-mechanism (and to 
 reject Darwinism, molecular biology, even most physical equations, 
 whose solutions when exploitable in nature are up to now always 
 computable.
 
 We just can’t invoke an ontological commitment when we do science, 
 especially in theology or metaphysics, unless some evidences are given 
 for it. But there are no evidence at all. People confuse the real 
 strong evidences for physical laws with evidence for laws who would be 
 primary. 
 
 You seem to have understood this better sometimes ago. I Hope you are 
 not having any doubt that the arithmetical reality (not the theories!) 
 emulate all computations, and that a universal machine (with oracles) 
 cannot feel the difference between being emulated by this or that 
 universal machinery.
>>> 
>>> Yes, I have no problem with any of what you say above.
>> 
>> OK.
>> 
>> 
>>> 
>>> What I have been wondering about is something else: what exactly is meant 
>>> by "primitive"? 
>> 
>> 
>> It depends on what you are interested in. To solve the mind-body 
>> problem, the first difficulty is to formulate it, and for this the 
>> notion of “primitiveness” is required, for what we will take for 
>> granted to proceed.
>> 
>> Basically X is considered as primitive if we have some reason to 
>> consider X as non explainable from something else, and judged as being 
>> more simple (technically/conceptually, … there is some matter of debate 
>> here of course).
> 
> Ok, but let me make the analogy with Copernicus' heliocentric model. It 
> provides a simpler model for planetary dynamics in the solar system than 
> assuming the earth at the center, but a more modern view on this debate is 
> that there is really no center anywhere in the universe. You just choose 
> whatever referential makes calculations easier.

It this not more “perspectival” or even “first person” centred. At the 
beginning, some thought that Earth was at the center of the universe. This 
meant that everything else was truly moving around us. Then we understood, that 
a simpler explanation (and also less anthropocentric) was that the Sun is a the 
center, and Earth go around it, and then we understood that even the Sun is 
revolving in a galaxy. We could have decided that our blackhole at the center 
of the Milky Way, is the “center” of the universe, but, as Kant suggested, 
there are other galaxies, etc… 
Today, we know that the “Big Bang” occurred everywhere, somehow, and that the 
notion of center of the (physical) universe might not make sense at all, but it 
is hard to say, as we can see only a tiny fraction of the physical universe, 
and have not yet a coherent theory of the whole, even restricted to the 
physical.

We have not much choice than to use Occam. The theory with the less hypotheses 
and the bigger range of prediction is the best one, until we find a simpler and 
more powerful one.



> 
> I wonder if primitiveness is not like that. I believe that consciousness 
> becomes irreducible if one takes matter as primiti

Re: Deriving the Born Rule

[Bruno Marchal]

> On 17 May 2020, at 11:39, 'scerir' via Everything List 
>  wrote:
> 
> I vaguely remember that von Weizsaecker wrote (in 'Zeit und Wissen') that 
> probability is 'the expectation value of the relative frequency'.
> 
> 

That is the frequency approach to probability. Strictly speaking it is false, 
as it gives the wrong results for the “non normal history” (normal in the sense 
of Gauss). But it works retire well in the normal world (sorry for being 
tautological).

At its antipode, there is the bayesian “subjective probabilities”, which makes 
sense when complete information is available . So it does not make sense in 
many practical situation.

Remark: the expression “subjective probabilities” is used technically for this 
Bayesian approach, and is quite different from the first person indeterminacy 
that Everett call “subjective probabilities”. The “subjective probabilities” of 
Everett are “objective probabilities”, and can be defined trough a frequency 
operator in the limit. The same occur in arithmetic, where the subjective 
(first person) probabilities are objective (they obey objective, sharable, 
laws).

Naïve many-worlds view are not sustainable, but there is no problem with 
consistent histories, and 0 worlds.

Bruno





>> Bruce wrote: 
>> 
>> It is this subjectivity, and appeal to Bayesianism, that I reject for QM. I 
>> consider probabilities to be intrinsic properties -- not further analysable. 
>> In other words, I favour a propensity interpretation. Relative frequencies 
>> are the way we generally measure probabilities, but they do not define them.
>> 
>> 
>> 
> 
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Re: Deriving the Born Rule

['scerir' via Everything List]

I vaguely remember that von Weizsaecker wrote (in 'Zeit und Wissen') that 
probability is 'the expectation value of the relative frequency'.

> Bruce wrote:
> 
> It is this subjectivity, and appeal to Bayesianism, that I reject for QM. 
> I consider probabilities to be intrinsic properties -- not further 
> analysable. In other words, I favour a propensity interpretation. Relative 
> frequencies are the way we generally measure probabilities, but they do not 
> define them.
> 
> 
> 
> 

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Re: Deriving the Born Rule

[Philip Thrift]

On Sunday, May 17, 2020 at 1:57:19 AM UTC-5, Bruce wrote:
>
> On Sat, May 16, 2020 at 11:04 PM Lawrence Crowell <
> goldenfield...@gmail.com > wrote:
>
>> There is nothing wrong formally with what you argue. I would though say 
>> this is not entirely the Born rule. The Born rule connects eigenvalues with 
>> the probabilities of a wave function. For quantum state amplitudes a_i in a 
>> superposition ψ = sum_ia_iφ_i with φ*_jφ_i = δ_{ij} the spectrum of an 
>> observable O obeys
>>
>> ⟨O⟩ = sum_iO_ip_i = sum_iO_i a*_ia_i.
>>
>> Your argument has a tight fit with this for O_i = ρ_{ii}.
>>
>> The difficulty in part stems from the fact we keep using standard ideas 
>> of probability to understand quantum physics, which is more fundamentally 
>> about amplitudes which give probabilities, but are not probabilities. Your 
>> argument is very frequentist.
>>
>
>
> I can see why you might think this, but it is actually not the case. My 
> main point is to reject subjectivist notions of probability:  probabilities 
> in QM are clearly objective -- there is an objective decay rate (or 
> half-life) for any radioactive nucleus; there is a clearly objective 
> probability for that spin to be measured up rather than down in a 
> Stern-Gerlach magnet; and so on.
>
>
> The argument by Carroll and Sebens, using a concept of the wave function 
>> as an update mechanism, is somewhat Bayesian.
>>
>
>
> It is this subjectivity, and appeal to Bayesianism, that I reject for QM. 
> I consider probabilities to be intrinsic properties -- not further 
> analysable. In other words, I favour a propensity interpretation. Relative 
> frequencies are the way we generally measure probabilities, but they do not 
> define them.
>
>
> This is curious since Fuchs developed QuBism as a sort of 
>> ultra-ψ-epistemic interpretation, and Carroll and Sebens are appealing to 
>> the wave function as a similar device for a ψ-ontological interpretation.
>>
>> I do though agree if there is a proof for the Born rule that is may not 
>> depend on some particular quantum interpretation. If the Born rule is some 
>> unprovable postulate then it would seem plausible that any sufficiently 
>> strong quantum interpretation may prove the Born rule or provide the 
>> ancillary axiomatic structure necessary for such a proof. In other words 
>> maybe quantum interpretations are essentially unprovable physical axioms 
>> that if sufficiently string provide a proof of the Born rule.
>>
>
>
> I would agree that the Born rule is unlikely to be provable within some 
> model of quantum mechanics -- particularly if that model is deterministic, 
> as is many-worlds. The mistake that advocates of many-worlds are making is 
> to try and graft probabilities, and the Born rule, on to a 
> non-probabilistic model. That endeavour is bound to fail. (In fact, many 
> have given up on trying to incorporate any idea of 'uncertainty' into their 
> model -- this is what is known as the "fission program".) One of the major 
> problems people like Deutsch, Carroll, and Wallace encounter is trying to 
> reconcile Everett with David Lewis's "Principal Principle", which is the 
> rule that one should align one's personal subjective degrees of belief with 
> the objective probabilities. When these people essentially deny the 
> existence of objective probabilities, they have trouble reconciling 
> subjective beliefs with anything at all.
>
> Bruce
>



*It is this subjectivity, and appeal to Bayesianism, that I reject for QM. 
I consider probabilities to be intrinsic properties -- not further 
analysable. In other words, I favour a propensity interpretation. Relative 
frequencies are the way we generally measure probabilities, but they do not 
define them.*



This is 100% what I said two decades ago on Atoms and the Void 
, and continuing on Free 
Thinkers Physics Discussion Group 
.


I will make this subjective guess: Two decades from now when some of us 
will be in our 90s this same debate will be still going on, the same words 
will be repeated (as they are now from 20 years ago), and no one will 
really change their idea of what QM "means".

@philipthrift 

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