Re: What is comparable and incomparable between casually disconnected universes?

[Bruce Kellett]

On Fri, Jan 11, 2019 at 12:18 PM Brent Meeker  wrote:

> On 1/10/2019 4:21 PM, John Clark wrote:
>
> *So even Feynman knew that there was no theoretical value for the FSC,
>> alpha.*
>>
>
> No,  he knew very well there was a theory that could come up with a value
> because his own Feynman Diagrams could do it. But what he didn't know and
> what nobody knows is why his theory came up with that particular pure
> number when he never specifically stuck that number into the rules on how
> the diagrams should operate.
>
>
> The fine structure constant is e^2/hbar*c.  Those three values are
> measured independent of any Feynman diagrams of quantum field theory.  The
> calculation using Feynman diagrams is of the anamolous magnetic moment.   A
> correction to the value of g that depend on relativistic effects (hence the
> occurence of c in the denominator).  The anamolous magnetic moment can be
> measure experimentally and using Feynman's diagrams and the measured values
> of e, hbar, and c a value can be calculated that includes the relativistic
> effects of quantum field theory. That's why the agreement with measurement
> is significant.
>

Right. The relation between fundamental physical constants, alpha =
e^2/hbar*c, is the closest one gets to a "theoretical" value for the FSC.
But that defines it in terms of other measured quantities. (Except that
these days, c is a defined number, not a measured physical parameter.) The
CODATA group use these theoretical relationships between constants,
together with the best available measurements, to make simultaneous fits to
all the constants and the data.That is where independent, "best values" for
these parameters come from. It is using these in the Feynman diagram
calculation of corrections to g-2 that gives the remarkable agreement
between theory and experiment. The point, though, is that the value of the
FSC used in calculating g-2 must be obtained independently of the g-2
measurement or else it is not a test of QED.. Conversely, of course, the
g-2 measurement can be use to estimate the FSC independently of other
measurements.

Bruce


> Brent
>

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Re: What is comparable and incomparable between casually disconnected universes?

[Brent Meeker]

On 1/10/2019 4:21 PM, John Clark wrote:


/So even Feynman knew that there was no theoretical value for the
FSC, alpha./


No,  he knew very well there was a theory that could come up with a 
value because his own Feynman Diagrams could do it. But what he didn't 
know and what nobody knows is why his theory came up with that 
particular pure number when he never specifically stuck that number 
into the rules on how the diagrams should operate.


The fine structure constant is e^2/hbar*c.  Those three values are 
measured independent of any Feynman diagrams of quantum field theory.  
The calculation using Feynman diagrams is of the anamolous magnetic 
moment.   A correction to the value of g that depend on relativistic 
effects (hence the occurence of c in the denominator). The anamolous 
magnetic moment can be measure experimentally and using Feynman's 
diagrams and the measured values of e, hbar, and c a value can be 
calculated that includes the relativistic effects of quantum field 
theory. That's why the agreement with measurement is significant.


Brent

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Re: What is comparable and incomparable between casually disconnected universes?

[John Clark]

On Wed, Jan 9, 2019 at 10:53 PM Bruce Kellett  wrote:


> > *There is no theoretical value".*
>

>From a book on spectrography by Norman Ramsey discussing the lamb Shift,
the very thing that led to the discovery of the Fine Structure Constant in
the first place:

"*The atomic hydrogen hyperfine separation can be accurately calculated
from theory so comparison to the experimental value provides a crucial test
for a fundamental theory. Historically it was the disagreement between the
theoretical and experimental value of this quantity that stimulated
Schwinger's development of relativistic quantum electrodynamics (QED)*."

Lamb Shift


>> Nobody uses 12,672 Feynman Diagrams to find a measured result.
>>
>
> >The authors of the PRL paper did!
>

I don't know what the "PRL paper" is, I'm talking about the same paper I
referred to before:

Improved Value of the Fine Structure Constant


And that paper specifically discusses what they need "*To compare the
theoretical prediction with the measurement*". It also makes clear the
importance of testing the theoretical predictions made by QED against
actual measurements:

"*The anomalous magnetic moment a e ≡ ( g −2) /2 of the electron has played
the central role in testing the validity of quantum electrodynamics (QED)*"

They also make it clear then are not the ones who made the experimental
measurement:

 "*On the experimental side the measurement of the Harvard group has
reached the astonishing precision*"

But they've calculated a even more accurate value than the experimenters:

 "*we have managed to evaluate it with a precision which leads to theory
more accurate than that of the measurement*"

So now it's up to the experimenters to do better and see if the theoretical
prediction is still correct.


>  > *in the final analysis, the fine structure constant is an arbitrary
>>> physical constant that must be measured*
>>>
>>
>> So is the speed of light, but Maxwell's theory can calculate that speed
>>
>
> > *Maxwell's theory gives the speed in terms of the permittivity and
> permeability of the vacuum, both of which were measured quantities in
> Maxwell's day. *
>

And they still are. if those 2 values were different the speed of light
would be different and the General Theory of Relativity would be different.
And if the Fine Structure Constant were different then Feynman's theory
would have to be different because the existing rules on how the diagrams
work would have produce a result that disagreed with experimental results.

Feynman didn't devise his rules specifically to produce a number close to
137 and there is no obvious reason to think that it would, and yet it does
and it agrees with the measured value to a astonishing degree; 40 years ago
he bragged that his theory was like predicting the distance between New
York and LA to the distance of a human hair, but measurement has gotten
about 60 times better since then so today it more like the distance between
New York and the moon. It's the most accurate prediction in all of science.
He found all this very mysterious and so do I.


> *> But, because of the success of special relativity, they are nowadays
> defined constants, as is the speed of light. *
>

Maxwell's theory requires modification because of Quantum Mechanics but as
far as special relativity is concerned absolutely nothing about Maxwell
needs to change.


> > *One could, therefore say that the speed of light is a theoretical
> value, not a measured value.*
>

Yes, people can say anything regardless of how silly. If the speed of light
or any other law of physics were different our theories would be different,
they'd have to be because theories must dance to experiment's drum not the
other way around.

*> You really ought to read the Wikipedia article more carefully, rather
> than just using it to obtain the CODATA best-fit value, and the value
> measured by the latest g-2 experiment. (Yes, the one calculating all 12,672
> Feynman diagrams to the tenth order.)*
>
> *"The most precise value of α obtained experimentally (as of 2012) is
> based on a measurement of g using a one-electron so-called "quantum
> cyclotron" apparatus,*
>

Right, that's how you get the measured value and it turns out to be
137.035999139


> > together with a calculation via the theory of QED that involved 12672
>  tenth-order Feynman diagrams:[
> *α*−1 = 137.035999173(35)."
>

Right, that's how you get the value Feynman's diagrams predict and it's
137.035999173 in excellent agreement with measurement and therefore we
conclude that Feynman's theory was a good theory.

I asked this before but got no answer, if checking a theoretical prediction
against a 

Fwd: The Case Against Quantum Computing

[Brent Meeker]

Interesting articles.

Brent


 Forwarded Message 

Another rebuttal:
https://www.hpcwire.com/2019/01/09/the-case-against-the-case-against-quantum-computing/

On Wed, Nov 21, 2018 at 1:57 PM :

In the IEEE Spectrum last week, Mikhail Dyakonov presented his overview of the 
field:

https://spectrum.ieee.org/computing/hardware/the-case-against-quantum-computing


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Re: What is comparable and incomparable between casually disconnected universes?

[Lawrence Crowell]

On Wednesday, January 9, 2019 at 8:49:41 PM UTC-6, Bruce wrote:
>
> On Thu, Jan 10, 2019 at 1:36 PM John Clark  > wrote:
>
>> On Wed, Jan 9, 2019 at 7:49 PM Bruce Kellett > > wrote:
>>
>> >>The following 2012 article in Physical Review letters describes a QED 
 calculation involving 12,672 tenth order Feynman diagrams used to 
 calculate both the magnetic moment of the electron and the inverse of the 
 Fine Structure Constant and obtaining a value of 137.035999173 which 
 is almost exactly the same as the experimentally derived value:

>>>
>>> >That is an experimentally derived value!
>>>
>>
>> No,  the experimentally derived value is 137.035999139
>>
>> *>Your original claim was that the fine structure constant was 
>>> computable. *
>>
>>
>> I said that was my intuition, I don't have a proof.   
>>
>> > *it is a physical constant that must be measured.*
>>
>>
>> I know, that's why I said the Fine Structure Constant was defined 
>> physically not mathematically,  and that's why any physical theory that is 
>> in conflict with that measured value for the FSC can not be a good theory. 
>> Feynman's QED is not in conflict with it, in fact it produced the closest 
>> agreement between experiment and theory in the entire history of science.
>>
>> > *But it is not computable from first principles,*  
>>
>>
>> That depends on what the first principle is, if its charged particles 
>> behave the way Feynman said they do then you can compute a value for the 
>> FSC that is very very close to the best measured one. Maybe when 
>> measurement becomes more precise a statistically significant discrepancy 
>> will show up between the experimental value and the theoretical value,
>>
>
> There is no theoretical value". All the values that we have are measured 
> -- often in different ways, or from the results of different experiments to 
> measure the same things, such as g-2, so there can be a range of measured 
> results. The CODATA value is their best-fit value to the whole range of 
> different experimental measurements. But in the final analysis, the fine 
> structure constant is an arbitrary physical constant that must be measured 
> -- there is no "theoretical value".
>
> Bruce
>

Yes and no. The speed of light and Planck's constant for instance are 
measured input. The charge is both measured and estimated with charge 
renormalization. 

LC
 

>
> if so we'll have to fine something better than Feynman Diagrams because in 
>> science when experiment and theory fight experiment always wins.  
>>  
>>
>>> *>You have to define what you mean by "computable". *
>>
>>
>> The Fine Structure Constant is computable if and only if there exists a 
>> finite algorithm that can work on a finite amount of data and produce a 
>> number in a finite amount of time that is arbitrarily close to it.  I don't 
>> claim to have such a algorithm I'm just saying my hunch is it exists and 
>> Feynman gives us reason for optimism. But I could be wrong.
>>
>

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Re: What is comparable and incomparable between casually disconnected universes?

[Lawrence Crowell]

On Wednesday, January 9, 2019 at 4:01:46 PM UTC-6, Bruce wrote:
>
> On Thu, Jan 10, 2019 at 7:53 AM John Clark  > wrote:
>
>> On Wed, Jan 9, 2019 at 1:58 PM Philip Thrift > > wrote:
>>
>> >> Is the Fine Structure Constant a rational number? Is it a algebraic 
 number? Is it a transcendental number? Nobody knows.
>>>
>>>
>>>
>>> *> Is it computable at least?*
>>
>>
>> Because the Fine Structure Constant has a physical and not a 
>> mathematical definition my intuition tells me it must be computable; and 
>> indeed we've already computed a very good approximation of it and there is 
>> no reason to think we couldn't do even better if we had faster computers 
>> that could sum up more of those Feynman diagrams.  
>>
>
> Rubbish. The fine structure constant is not computable by Feynman 
> diagrams. What might be confusing you is that QED calculations of 
> physically measurable  things like the Lamb Shift and g-2 for the electron 
> depend on the value of the FSC. Comparing the calculations with experiment 
> gives an accurate value for the FSC. the fine structure constant itself is 
> an arbitrary constant of nature, and not directly callable.
>
> Bruce
>

Huh? The QED industry of computing Feynman diagrams is to find more 
accurate charge renormalization. That in turn is what computes a more 
accurate fine structure constant.

LC 

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Re: Coherent states of a superposition

[agrayson2000]

On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>
>
> On 9 Jan 2019, at 07:58, agrays...@gmail.com  wrote:
>
>
>
> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:

 On Mon, Jan 7, 2019 at 9:42 AM  wrote:

> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
>>> agrays...@gmail.com wrote:

 On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>> agrays...@gmail.com wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of 
> interference and coherence, without introducing your theory of 
> consciousness. Mainstream thinking today is that decoherence does 
> occur, 
> but this seems to imply preexisting coherence, and therefore 
> interference 
> among the component states of a superposition. If the 
> superposition is 
> expressed using eigenfunctions, which are mutually orthogonal -- 
> implying 
> no mutual interference -- how is decoherence possible, insofar as 
> coherence, IIUC, doesn't exist using this basis? AG*
>

 I think you misunderstand the meaning of "coherence" when it is 
 used off an expansion in terms of a set of mutually orthogonal 
 eigenvectors. The expansion in some eigenvector basis is written as

|psi> = Sum_i (a_i |v_i>)

 where |v_i> are the eigenvectors, and i ranges over the 
 dimension of the Hilbert space. The expansion coefficients are the 
 complex 
 numbers a_i. Since these are complex coefficients, they contain 
 inherent 
 phases. It is the preservation of these phases of the expansion 
 coefficients that is meant by "maintaining coherence". So it is 
 the 
 coherence of the particular expansion that is implied, and this 
 has noting 
 to do with the mutual orthogonality or otherwise of the basis 
 vectors 
 themselves. In decoherence, the phase relationships between the 
 terms in 
 the original expansion are lost.

 Bruce 

>>>
>>> I appreciate your reply. I was sure you could ascertain my error 
>>> -- confusing orthogonality with interference and coherence. Let me 
>>> have 
>>> your indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its 
>> superposition expansion is also expressed in eigenfunctions with 
>> variable 
>> p. Does the phase of the original wf carry over into the 
>> eigenfunctions as 
>> identical for each, or can each component in the superposition have 
>> different phases? I ask this because the probability determined by 
>> any 
>> complex amplitude is independent of its phase. TIA, AG 
>>
>
> The phases of the coefficients are independent of each other.
>

 When I formally studied QM, no mention was made of calculating the 
 phases since, presumably, they don't effect probability calculations. 
 Do 
 you have a link which explains how they're calculated? TIA, AG 

>>>
>>> I found some links on physics.stackexchange.com which show that 
>>> relative phases can effect probabilities, but none so far about how to 
>>> calculate any phase angle. AG 
>>>
>>
>> Here's the answer if anyone's interested. But what's the question? 
>> How are wf phase angles calculated? Clearly, if you solve for the 
>> eigenfunctions of some QM operator such as the p operator, any phase 
>> angle 
>> is possible; its value is completely arbitrary and doesn't effect a 
>> probability calculation. In fact, IIUC, there is not sufficient 
>> information 
>> to solve for a unique phase. So, I conclude,that the additional 
>> information 
>> required to uniquely determine a phase angle for a wf, lies in boundary 
>> conditions. If the 

Re: Coherent states of a superposition

[agrayson2000]

On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>
>
> On 9 Jan 2019, at 07:58, agrays...@gmail.com  wrote:
>
>
>
> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:

 On Mon, Jan 7, 2019 at 9:42 AM  wrote:

> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
>>> agrays...@gmail.com wrote:

 On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>> agrays...@gmail.com wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of 
> interference and coherence, without introducing your theory of 
> consciousness. Mainstream thinking today is that decoherence does 
> occur, 
> but this seems to imply preexisting coherence, and therefore 
> interference 
> among the component states of a superposition. If the 
> superposition is 
> expressed using eigenfunctions, which are mutually orthogonal -- 
> implying 
> no mutual interference -- how is decoherence possible, insofar as 
> coherence, IIUC, doesn't exist using this basis? AG*
>

 I think you misunderstand the meaning of "coherence" when it is 
 used off an expansion in terms of a set of mutually orthogonal 
 eigenvectors. The expansion in some eigenvector basis is written as

|psi> = Sum_i (a_i |v_i>)

 where |v_i> are the eigenvectors, and i ranges over the 
 dimension of the Hilbert space. The expansion coefficients are the 
 complex 
 numbers a_i. Since these are complex coefficients, they contain 
 inherent 
 phases. It is the preservation of these phases of the expansion 
 coefficients that is meant by "maintaining coherence". So it is 
 the 
 coherence of the particular expansion that is implied, and this 
 has noting 
 to do with the mutual orthogonality or otherwise of the basis 
 vectors 
 themselves. In decoherence, the phase relationships between the 
 terms in 
 the original expansion are lost.

 Bruce 

>>>
>>> I appreciate your reply. I was sure you could ascertain my error 
>>> -- confusing orthogonality with interference and coherence. Let me 
>>> have 
>>> your indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its 
>> superposition expansion is also expressed in eigenfunctions with 
>> variable 
>> p. Does the phase of the original wf carry over into the 
>> eigenfunctions as 
>> identical for each, or can each component in the superposition have 
>> different phases? I ask this because the probability determined by 
>> any 
>> complex amplitude is independent of its phase. TIA, AG 
>>
>
> The phases of the coefficients are independent of each other.
>

 When I formally studied QM, no mention was made of calculating the 
 phases since, presumably, they don't effect probability calculations. 
 Do 
 you have a link which explains how they're calculated? TIA, AG 

>>>
>>> I found some links on physics.stackexchange.com which show that 
>>> relative phases can effect probabilities, but none so far about how to 
>>> calculate any phase angle. AG 
>>>
>>
>> Here's the answer if anyone's interested. But what's the question? 
>> How are wf phase angles calculated? Clearly, if you solve for the 
>> eigenfunctions of some QM operator such as the p operator, any phase 
>> angle 
>> is possible; its value is completely arbitrary and doesn't effect a 
>> probability calculation. In fact, IIUC, there is not sufficient 
>> information 
>> to solve for a unique phase. So, I conclude,that the additional 
>> information 
>> required to uniquely determine a phase angle for a wf, lies in boundary 
>> conditions. If the 

Re: Materialism and Mechanism

[Philip Thrift]

On Thursday, January 10, 2019 at 11:20:20 AM UTC-6, Bruno Marchal wrote:
>
>
> On 9 Jan 2019, at 11:20, Philip Thrift > 
> wrote:
>
>
>
> On Monday, January 7, 2019 at 9:44:40 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 6 Jan 2019, at 15:20, Philip Thrift  wrote:
>>
>>
>> In terms of processing, I distinguish *experience processing* from 
>> *information 
>> processing.*
>>
>>
>>
>> OK. That is important, but the machines do that too. Information 
>> processing is like computing and proving, and can be described in 3p terms. 
>> It is the “[]p” in the list of self-referential modes. But the (Löbian) 
>> machine is aware that she cannot know, nor even define precisely, her own 
>> correctness, and that she cannot prove, if true, the equivalence between 
>> []p and “[]p & p”, so she is bounded to find Theatetetus definition of the 
>> soul or of the knower, which is pure 1p, and does not admits any pure 3p 
>> description. I would say that this might corresponds to your “experience” 
>> processing.
>>
>> Then, eventually the notion of “matter” can be explained in term of the 
>> number experience processing (sharable for the quanta, and non sharable for 
>> the qualia). There is no need to invoke some inert substance that nobody 
>> can define nor test.
>>
>> All computers (physical universal machine) and the non material universal 
>> machine are equivalent with respect to computability and emulability. 
>> Please note that they are NOT equivalent with respect to provability, even 
>> if, when self-referentially correct, their provability predicate will all 
>> obey to the same theology (G*), but will differ in their interpretation, 
>> contents, etc. 
>>
>> Bruno
>>
>> https://codicalist.wordpress.com/2018/10/14/experience-processing/
>>
>> https://codicalist.wordpress.com/2018/12/14/material-semantics-for-unconventional-programming/
>>
>> - pt
>>
>> This is interesting for a programming semantics (e.g. denotational) 
> perspective, for experiential processing.
>
> This reminds me of Galen Strawson's argument (which has nothing to do with 
> stochasticism or determinism) about "ree will. He has a definition of 
> "self" such that your self is a real thing
>
>
> OK.
>
>
>
> (that includes your consciousness, which is also a real thing), 
>
>
> OK.
>
>
> and to say your self has free will can't really be right, since you can't 
> say (seriously) "I am free to not be my self" (since it is your self that 
> is doing that): Whatever you chose, it is your self that is choosing.
>
>
>
> Once a universal machine introspect itself relatively to some universal 
> number, it becomes aware that it can predict itself completely and 
> free-will is a vague term alluding to the management of decision in absence 
> of complete information. 
>
>
>
>
>
>
> "Experience Processing": Maybe not this year [ International Conference 
> on Unconventional Computation and Natural Computation 2019  
> http://www.ucnc2019.uec.ac.jp/ ] …
>
>
> I recently (it is nt used in my papers) consider that it implies a lot to 
> admit that all universal machine are maximally conscious, and that the 
> provability predicate (seen as an ideal self-referentially correct 
> brain/body) only filters the consciousness of the universal machine. When 
> unrpogrammed, and without input, its consciousness is quite different from 
> the mundane consciousness, it is more like a highly dissociated state of 
> consciousness, out of time and space, which needs a lot of spatio-temproral 
> experiences to develop the aproprioperception of a body. In the humain 
> brain, that sense is basically innate.
>
> The experience is not “processed” by a code, it is a truth filtered by a 
> body/code. 
>
> Bruno
>
>
>
>
It the brain is biocomputing, as the human is a biocomputer 
[ https://en.wikipedia.org/wiki/Human_biocomputer ], then it is indeed 
processing experience. (Processing is what computers do.)

- pt

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Re: UDA and the origin of physics

[Philip Thrift]

On Thursday, January 10, 2019 at 12:16:33 PM UTC-6, Philip Thrift wrote:
>
>
>
> On Thursday, January 10, 2019 at 7:36:33 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 9 Jan 2019, at 15:13, Philip Thrift  wrote:
>>
>>
>>
>> On Wednesday, January 9, 2019 at 4:06:08 AM UTC-6, Bruno Marchal wrote:
>>>
>>>
>>> On 6 Jan 2019, at 22:27, Philip Thrift  wrote:
>>>
>>>
>>> Why - in  numerical reality (UD)  - can't there be vampires, werewolves, 
>>> that sort of things? They can certainly be "created" in computer 
>>> simulations of stories of them …
>>>
>>>
>>> Exactly, that is why we need to recover physics by a notion of 
>>> “bettable”. If you see a vampire, not explained by the notion of 
>>> observable, you can infer that either:
>>>
>>> Mechanism is false, or
>>> You are dreaming, or
>>> You belong to a “malevolent” simulation (à-la Bostrom, made by angry 
>>> descendent who want to fail us on reality).
>>>
>>> Fortunately, we don’t see vampires, and up to know, thanks to QM, we see 
>>> exactly what mechanism predicts.
>>>
>>> Bruno
>>>
>>>
>>>
>>>
>>
>> Seth Lloyd of course says the universe is a quantum computer. 
>>
>>
>> That would entail Mechanism, but Mechanism entails that the physical 
>> universe is not a quantum computer, unless our substitution level is so low 
>> that we need to emulate the whole physical reality (not just the observable 
>> one) to get “my” consciousness. The term “universe” is also problematical 
>> to me.
>>
>>
>>
>>
>> But what if there are qualia in addition to (or combined with) quanta as 
>> the fundamental elements of nature. 
>>
>>
>> You can always speculate a non existing theory to “contradict” an 
>> existing theory. Why assumes something when we can explain it without 
>> assuming it. What if the thermodynamic of the car motion works only if 
>> invisible horses pull the car?
>>
>> Nature is also a imprecise term. All my scepticism on the existence of 
>> nature comes from the observation of nature. The physical science are not 
>> the metaphysical science, unless we postulate (weak) materialism, which is 
>> inconsistent with mechanism.
>>
>>
>>
>>
>> Then the quantum computer - a purely quantum information processing 
>> (QuIP) machine - needs to be upgraded to a qualium(+quantum) 
>> experience(+information) processing (QuEP) machine.
>>
>>
>> With mechanism, the qualia are “easily” explained by the necessary 
>> variant of provability logic in G*. To add “material” to this would entail 
>> the existence of infinitely many p.zombie in arithmetic, and makes both 
>> consciousness and matter into irreductible mystery. What is the goal?
>>
>>
>>
>>
>> The universe (now a QuEP machine) could have conscious beings who make up 
>> stories about vampires and werewolves.
>>
>>
>> The arithmetical universe? Yes. Necessarily so with the computationalist 
>> hypothesis.
>>
>> Some of your remark shows that you have not studied my contribution. To 
>> avoid repetition, it might be useful to study it. Just criticising a 
>> conclusion because we have another theory is not that much interesting, 
>> especially when the “other theory” is not presented in a specific way (as 
>> your use of many links illustrates).
>>
>> All what I can say is that you are logically coherent: you believe in 
>> matter and you believe that mechanism is false. But the empirical facts go 
>> in the opposite direction. The empirical test of the existence of primary 
>> matter that I have given fails up to now.The world would be Newtonian, 
>> Mechanism would be judged reasonably refuted. Gödel + EPR-Everett saves 
>> Mechanism.
>>
>> Bruno
>>
>>
>>
>  
>
> I don't think your theory refutes the existence of matter. (That would be 
> a surprise to materials scientists, fro example.)
>
> At best, your theory (universal numbers, machines, dovetailers) is a 
> possible *denotational semantics* for experiential processing, which *takes 
> place in matter*.
>
> (But that still can be a contribution, but it is by no means the complete 
> picture.)
>
>
> - pt
>
>
>
A better way: *Matter does explain consciousness, once the true nature of 
matter is appreciated.*

- pt 

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Re: UDA and the origin of physics

[Philip Thrift]

On Thursday, January 10, 2019 at 7:36:33 AM UTC-6, Bruno Marchal wrote:
>
>
> On 9 Jan 2019, at 15:13, Philip Thrift > 
> wrote:
>
>
>
> On Wednesday, January 9, 2019 at 4:06:08 AM UTC-6, Bruno Marchal wrote:
>>
>>
>> On 6 Jan 2019, at 22:27, Philip Thrift  wrote:
>>
>>
>> Why - in  numerical reality (UD)  - can't there be vampires, werewolves, 
>> that sort of things? They can certainly be "created" in computer 
>> simulations of stories of them …
>>
>>
>> Exactly, that is why we need to recover physics by a notion of 
>> “bettable”. If you see a vampire, not explained by the notion of 
>> observable, you can infer that either:
>>
>> Mechanism is false, or
>> You are dreaming, or
>> You belong to a “malevolent” simulation (à-la Bostrom, made by angry 
>> descendent who want to fail us on reality).
>>
>> Fortunately, we don’t see vampires, and up to know, thanks to QM, we see 
>> exactly what mechanism predicts.
>>
>> Bruno
>>
>>
>>
>>
>
> Seth Lloyd of course says the universe is a quantum computer. 
>
>
> That would entail Mechanism, but Mechanism entails that the physical 
> universe is not a quantum computer, unless our substitution level is so low 
> that we need to emulate the whole physical reality (not just the observable 
> one) to get “my” consciousness. The term “universe” is also problematical 
> to me.
>
>
>
>
> But what if there are qualia in addition to (or combined with) quanta as 
> the fundamental elements of nature. 
>
>
> You can always speculate a non existing theory to “contradict” an existing 
> theory. Why assumes something when we can explain it without assuming it. 
> What if the thermodynamic of the car motion works only if invisible horses 
> pull the car?
>
> Nature is also a imprecise term. All my scepticism on the existence of 
> nature comes from the observation of nature. The physical science are not 
> the metaphysical science, unless we postulate (weak) materialism, which is 
> inconsistent with mechanism.
>
>
>
>
> Then the quantum computer - a purely quantum information processing (QuIP) 
> machine - needs to be upgraded to a qualium(+quantum) 
> experience(+information) processing (QuEP) machine.
>
>
> With mechanism, the qualia are “easily” explained by the necessary variant 
> of provability logic in G*. To add “material” to this would entail the 
> existence of infinitely many p.zombie in arithmetic, and makes both 
> consciousness and matter into irreductible mystery. What is the goal?
>
>
>
>
> The universe (now a QuEP machine) could have conscious beings who make up 
> stories about vampires and werewolves.
>
>
> The arithmetical universe? Yes. Necessarily so with the computationalist 
> hypothesis.
>
> Some of your remark shows that you have not studied my contribution. To 
> avoid repetition, it might be useful to study it. Just criticising a 
> conclusion because we have another theory is not that much interesting, 
> especially when the “other theory” is not presented in a specific way (as 
> your use of many links illustrates).
>
> All what I can say is that you are logically coherent: you believe in 
> matter and you believe that mechanism is false. But the empirical facts go 
> in the opposite direction. The empirical test of the existence of primary 
> matter that I have given fails up to now.The world would be Newtonian, 
> Mechanism would be judged reasonably refuted. Gödel + EPR-Everett saves 
> Mechanism.
>
> Bruno
>
>
>
 

I don't think your theory refutes the existence of matter. (That would be a 
surprise to materials scientists, fro example.)

At best, your theory (universal numbers, machines, dovetailers) is a 
possible *denotational semantics* for experiential processing, which *takes 
place in matter*.

(But that still can be a contribution, but it is by no means the complete 
picture.)


- pt


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Re: Materialism and Mechanism

[Bruno Marchal]

> On 9 Jan 2019, at 11:20, Philip Thrift  wrote:
> 
> 
> 
> On Monday, January 7, 2019 at 9:44:40 AM UTC-6, Bruno Marchal wrote:
> 
>> On 6 Jan 2019, at 15:20, Philip Thrift > wrote:
>> 
>> 
>> In terms of processing, I distinguish experience processing from information 
>> processing.
> 
> 
> OK. That is important, but the machines do that too. Information processing 
> is like computing and proving, and can be described in 3p terms. It is the 
> “[]p” in the list of self-referential modes. But the (Löbian) machine is 
> aware that she cannot know, nor even define precisely, her own correctness, 
> and that she cannot prove, if true, the equivalence between []p and “[]p & 
> p”, so she is bounded to find Theatetetus definition of the soul or of the 
> knower, which is pure 1p, and does not admits any pure 3p description. I 
> would say that this might corresponds to your “experience” processing.
> 
> Then, eventually the notion of “matter” can be explained in term of the 
> number experience processing (sharable for the quanta, and non sharable for 
> the qualia). There is no need to invoke some inert substance that nobody can 
> define nor test.
> 
> All computers (physical universal machine) and the non material universal 
> machine are equivalent with respect to computability and emulability. Please 
> note that they are NOT equivalent with respect to provability, even if, when 
> self-referentially correct, their provability predicate will all obey to the 
> same theology (G*), but will differ in their interpretation, contents, etc. 
> 
> Bruno
> 
>> https://codicalist.wordpress.com/2018/10/14/experience-processing/ 
>> 
>> https://codicalist.wordpress.com/2018/12/14/material-semantics-for-unconventional-programming/
>>  
>> 
>> 
>> - pt
>> 
> 
> This is interesting for a programming semantics (e.g. denotational) 
> perspective, for experiential processing.
> 
> This reminds me of Galen Strawson's argument (which has nothing to do with 
> stochasticism or determinism) about "ree will. He has a definition of "self" 
> such that your self is a real thing

OK.



> (that includes your consciousness, which is also a real thing),

OK.


> and to say your self has free will can't really be right, since you can't say 
> (seriously) "I am free to not be my self" (since it is your self that is 
> doing that): Whatever you chose, it is your self that is choosing.


Once a universal machine introspect itself relatively to some universal number, 
it becomes aware that it can predict itself completely and free-will is a vague 
term alluding to the management of decision in absence of complete information. 



> 
> 
> 
> "Experience Processing": Maybe not this year [ International Conference on 
> Unconventional Computation and Natural Computation 2019  
> http://www.ucnc2019.uec.ac.jp/  ] …

I recently (it is nt used in my papers) consider that it implies a lot to admit 
that all universal machine are maximally conscious, and that the provability 
predicate (seen as an ideal self-referentially correct brain/body) only filters 
the consciousness of the universal machine. When unrpogrammed, and without 
input, its consciousness is quite different from the mundane consciousness, it 
is more like a highly dissociated state of consciousness, out of time and 
space, which needs a lot of spatio-temproral experiences to develop the 
aproprioperception of a body. In the humain brain, that sense is basically 
innate.

The experience is not “processed” by a code, it is a truth filtered by a 
body/code. 

Bruno



> 
> - pt
> 
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Re: What is comparable and incomparable between casually disconnected universes?

[Bruno Marchal]

> On 10 Jan 2019, at 07:39, Philip Thrift  wrote:
> 
> 
> 
> On Wednesday, January 9, 2019 at 6:49:05 PM UTC-6, Bruce wrote:
> On Thu, Jan 10, 2019 at 11:38 AM John Clark  > wrote:
> On Wed, Jan 9, 2019 at 5:01 PM Bruce Kellett  > wrote:
> 
> > Rubbish. The fine structure constant is not computable by Feynman diagrams. 
> > What might be confusing you is that QED calculations of physically 
> > measurable  things like the Lamb Shift and g-2 for the electron depend on 
> > the value of the FSC.
> 
> How is using Feynman diagrams to compute the Lamb Shift Shift (which depends 
> on the Fine Structure Constant) different from using Feynman diagrams to 
> compute the Fine Structure Constant?  After all physics didn't determine the 
> Lamb Shift from the Fine Structure Constant, they determined the Fine 
> Structure Constant by looking at the Lamb Shift, in fact the very very fine 
> lines in the spectrum of Hydrogen is how the Fine Structure Constant got its 
> name. 
> 
> The following 2012 article in Physical Review letters describes a QED 
> calculation involving 12,672 tenth order Feynman diagrams used to calculate 
> both the magnetic moment of the electron and the inverse of the Fine 
> Structure Constant and obtaining a value of 137.035999173 which is almost 
> exactly the same as the experimentally derived value:
> 
> That is an experimentally derived value!
>  
> Improved Value of the Fine Structure Constant 
>    
> 
> John K Clark
> 
> Your original claim was that the fine structure constant was computable. But 
> it is not computable from first principles, it is a physical constant that 
> must be measured. The fact that computations might be involved in getting the 
> value from measurements does not mean that the FSC is itself computable.
> 
> You have to define what you mean by "computable". The FSC is a measured 
> quantity, not computable in the way pi or e are computable from mathematical 
> formulae.
> 
> Bruce 
> 
> 
> 
> Constants enter the vocabulary of physics by means of theories. A constant is 
> an entity of a theory, but a constant is not an entity of nature. Nature may 
> have constancy, but it's theories that have constants. 
> 
>Theory != Nature. 

A theory of nature is certainly different of nature, like the brain+telescope 
is different from a far away galaxy.

Note that a theory of the arithmetical reality (like PA or even ZF) is also 
different than the arithmetical reality.

Then, a theory of arithmetic can be seen as a number, like the Gödel number of 
the provability predicate, and a large part of the metamathematics is emulated 
in arithmetic. The arithmetical reality reflects the “talks” of the numbers 
about arithmetic and about themselves, and the arithmetical reality explores 
itself. Physics is retrieved by what the machine can predict in some first 
person plural partially sharable way.

Geometry, analysis, and physics are the unavoidable tools that the “number” 
invents to understand themselves. But consciousness of the human type can 
require a relative rarity combined with a huge continuous explosion in the 
multiple representation. The bottom is highly and completely symmetrical, but 
from inside we break the symmetries (“we” the universal machines).

Bruno



> 
> - pt
> 
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Re: UDA and the origin of physics

[Bruno Marchal]

> On 9 Jan 2019, at 15:13, Philip Thrift  wrote:
> 
> 
> 
> On Wednesday, January 9, 2019 at 4:06:08 AM UTC-6, Bruno Marchal wrote:
> 
>> On 6 Jan 2019, at 22:27, Philip Thrift > 
>> wrote:
>> 
>> 
>> Why - in  numerical reality (UD)  - can't there be vampires, werewolves, 
>> that sort of things? They can certainly be "created" in computer simulations 
>> of stories of them …
> 
> Exactly, that is why we need to recover physics by a notion of “bettable”. If 
> you see a vampire, not explained by the notion of observable, you can infer 
> that either:
> 
> Mechanism is false, or
> You are dreaming, or
> You belong to a “malevolent” simulation (à-la Bostrom, made by angry 
> descendent who want to fail us on reality).
> 
> Fortunately, we don’t see vampires, and up to know, thanks to QM, we see 
> exactly what mechanism predicts.
> 
> Bruno
> 
> 
> 
> 
> 
> Seth Lloyd of course says the universe is a quantum computer.

That would entail Mechanism, but Mechanism entails that the physical universe 
is not a quantum computer, unless our substitution level is so low that we need 
to emulate the whole physical reality (not just the observable one) to get “my” 
consciousness. The term “universe” is also problematical to me.




> But what if there are qualia in addition to (or combined with) quanta as the 
> fundamental elements of nature. 

You can always speculate a non existing theory to “contradict” an existing 
theory. Why assumes something when we can explain it without assuming it. What 
if the thermodynamic of the car motion works only if invisible horses pull the 
car?

Nature is also a imprecise term. All my scepticism on the existence of nature 
comes from the observation of nature. The physical science are not the 
metaphysical science, unless we postulate (weak) materialism, which is 
inconsistent with mechanism.




> Then the quantum computer - a purely quantum information processing (QuIP) 
> machine - needs to be upgraded to a qualium(+quantum) 
> experience(+information) processing (QuEP) machine.

With mechanism, the qualia are “easily” explained by the necessary variant of 
provability logic in G*. To add “material” to this would entail the existence 
of infinitely many p.zombie in arithmetic, and makes both consciousness and 
matter into irreductible mystery. What is the goal?



> 
> The universe (now a QuEP machine) could have conscious beings who make up 
> stories about vampires and werewolves.

The arithmetical universe? Yes. Necessarily so with the computationalist 
hypothesis.

Some of your remark shows that you have not studied my contribution. To avoid 
repetition, it might be useful to study it. Just criticising a conclusion 
because we have another theory is not that much interesting, especially when 
the “other theory” is not presented in a specific way (as your use of many 
links illustrates).

All what I can say is that you are logically coherent: you believe in matter 
and you believe that mechanism is false. But the empirical facts go in the 
opposite direction. The empirical test of the existence of primary matter that 
I have given fails up to now.The world would be Newtonian, Mechanism would be 
judged reasonably refuted. Gödel + EPR-Everett saves Mechanism.

Bruno



> 
> 
> 
> - pt 
> 
> -- 
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Re: Coherent states of a superposition

[agrayson2000]

On Thursday, January 10, 2019 at 11:07:51 AM UTC, Bruno Marchal wrote:
>
>
> On 9 Jan 2019, at 07:58, agrays...@gmail.com  wrote:
>
>
>
> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
>>
>>
>>
>> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com wrote:
>>>
>>>
>>>
>>> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:

 On Mon, Jan 7, 2019 at 9:42 AM  wrote:

> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com 
> wrote:
>>
>> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com 
>> wrote:
>>>
>>> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, 
>>> agrays...@gmail.com wrote:

 On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
>
> On Wed, Dec 5, 2018 at 10:52 PM  wrote:
>
>> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, 
>> agrays...@gmail.com wrote:
>>>
>>> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:

 On Wed, Dec 5, 2018 at 2:36 AM  wrote:

>
> *Thanks, but I'm looking for a solution within the context of 
> interference and coherence, without introducing your theory of 
> consciousness. Mainstream thinking today is that decoherence does 
> occur, 
> but this seems to imply preexisting coherence, and therefore 
> interference 
> among the component states of a superposition. If the 
> superposition is 
> expressed using eigenfunctions, which are mutually orthogonal -- 
> implying 
> no mutual interference -- how is decoherence possible, insofar as 
> coherence, IIUC, doesn't exist using this basis? AG*
>

 I think you misunderstand the meaning of "coherence" when it is 
 used off an expansion in terms of a set of mutually orthogonal 
 eigenvectors. The expansion in some eigenvector basis is written as

|psi> = Sum_i (a_i |v_i>)

 where |v_i> are the eigenvectors, and i ranges over the 
 dimension of the Hilbert space. The expansion coefficients are the 
 complex 
 numbers a_i. Since these are complex coefficients, they contain 
 inherent 
 phases. It is the preservation of these phases of the expansion 
 coefficients that is meant by "maintaining coherence". So it is 
 the 
 coherence of the particular expansion that is implied, and this 
 has noting 
 to do with the mutual orthogonality or otherwise of the basis 
 vectors 
 themselves. In decoherence, the phase relationships between the 
 terms in 
 the original expansion are lost.

 Bruce 

>>>
>>> I appreciate your reply. I was sure you could ascertain my error 
>>> -- confusing orthogonality with interference and coherence. Let me 
>>> have 
>>> your indulgence on a related issue. AG
>>>
>>
>> Suppose the original wf is expressed in terms of p, and its 
>> superposition expansion is also expressed in eigenfunctions with 
>> variable 
>> p. Does the phase of the original wf carry over into the 
>> eigenfunctions as 
>> identical for each, or can each component in the superposition have 
>> different phases? I ask this because the probability determined by 
>> any 
>> complex amplitude is independent of its phase. TIA, AG 
>>
>
> The phases of the coefficients are independent of each other.
>

 When I formally studied QM, no mention was made of calculating the 
 phases since, presumably, they don't effect probability calculations. 
 Do 
 you have a link which explains how they're calculated? TIA, AG 

>>>
>>> I found some links on physics.stackexchange.com which show that 
>>> relative phases can effect probabilities, but none so far about how to 
>>> calculate any phase angle. AG 
>>>
>>
>> Here's the answer if anyone's interested. But what's the question? 
>> How are wf phase angles calculated? Clearly, if you solve for the 
>> eigenfunctions of some QM operator such as the p operator, any phase 
>> angle 
>> is possible; its value is completely arbitrary and doesn't effect a 
>> probability calculation. In fact, IIUC, there is not sufficient 
>> information 
>> to solve for a unique phase. So, I conclude,that the additional 
>> information 
>> required to uniquely determine a phase angle for a wf, lies in boundary 
>> conditions. If the 

Re: Coherent states of a superposition

[Bruno Marchal]

> On 9 Jan 2019, at 07:58, agrayson2...@gmail.com wrote:
> 
> 
> 
> On Monday, January 7, 2019 at 11:37:13 PM UTC, agrays...@gmail.com wrote:
> 
> 
> On Monday, January 7, 2019 at 2:52:27 PM UTC, agrays...@gmail.com <> wrote:
> 
> 
> On Sunday, January 6, 2019 at 10:45:01 PM UTC, Bruce wrote:
> On Mon, Jan 7, 2019 at 9:42 AM > wrote:
> On Saturday, December 8, 2018 at 2:46:41 PM UTC, agrays...@gmail.com <> wrote:
> On Thursday, December 6, 2018 at 5:46:13 PM UTC, agrays...@gmail.com <> wrote:
> On Wednesday, December 5, 2018 at 10:13:57 PM UTC, agrays...@gmail.com <> 
> wrote:
> On Wednesday, December 5, 2018 at 9:42:51 PM UTC, Bruce wrote:
> On Wed, Dec 5, 2018 at 10:52 PM > wrote:
> On Wednesday, December 5, 2018 at 11:42:06 AM UTC, agrays...@gmail.com <> 
> wrote:
> On Tuesday, December 4, 2018 at 9:57:41 PM UTC, Bruce wrote:
> On Wed, Dec 5, 2018 at 2:36 AM > wrote:
> 
> Thanks, but I'm looking for a solution within the context of interference and 
> coherence, without introducing your theory of consciousness. Mainstream 
> thinking today is that decoherence does occur, but this seems to imply 
> preexisting coherence, and therefore interference among the component states 
> of a superposition. If the superposition is expressed using eigenfunctions, 
> which are mutually orthogonal -- implying no mutual interference -- how is 
> decoherence possible, insofar as coherence, IIUC, doesn't exist using this 
> basis? AG
> 
> I think you misunderstand the meaning of "coherence" when it is used off an 
> expansion in terms of a set of mutually orthogonal eigenvectors. The 
> expansion in some eigenvector basis is written as
> 
>|psi> = Sum_i (a_i |v_i>)
> 
> where |v_i> are the eigenvectors, and i ranges over the dimension of the 
> Hilbert space. The expansion coefficients are the complex numbers a_i. Since 
> these are complex coefficients, they contain inherent phases. It is the 
> preservation of these phases of the expansion coefficients that is meant by 
> "maintaining coherence". So it is the coherence of the particular expansion 
> that is implied, and this has noting to do with the mutual orthogonality or 
> otherwise of the basis vectors themselves. In decoherence, the phase 
> relationships between the terms in the original expansion are lost.
> 
> Bruce 
> 
> I appreciate your reply. I was sure you could ascertain my error -- confusing 
> orthogonality with interference and coherence. Let me have your indulgence on 
> a related issue. AG
> 
> Suppose the original wf is expressed in terms of p, and its superposition 
> expansion is also expressed in eigenfunctions with variable p. Does the phase 
> of the original wf carry over into the eigenfunctions as identical for each, 
> or can each component in the superposition have different phases? I ask this 
> because the probability determined by any complex amplitude is independent of 
> its phase. TIA, AG 
> 
> The phases of the coefficients are independent of each other.
> 
> When I formally studied QM, no mention was made of calculating the phases 
> since, presumably, they don't effect probability calculations. Do you have a 
> link which explains how they're calculated? TIA, AG 
> 
> I found some links on physics.stackexchange.com 
>  which show that relative phases can 
> effect probabilities, but none so far about how to calculate any phase angle. 
> AG 
> 
> Here's the answer if anyone's interested. But what's the question? How are wf 
> phase angles calculated? Clearly, if you solve for the eigenfunctions of some 
> QM operator such as the p operator, any phase angle is possible; its value is 
> completely arbitrary and doesn't effect a probability calculation. In fact, 
> IIUC, there is not sufficient information to solve for a unique phase. So, I 
> conclude,that the additional information required to uniquely determine a 
> phase angle for a wf, lies in boundary conditions. If the problem of 
> specifying a wf is defined as a boundary value problem, then, I believe, a 
> unique phase angle can be calculated. CMIIAW. AG 
> 
> Bruce
> 
> I could use a handshake on this one. Roughly speaking, if one wants to 
> express the state of a system as a superposition of eigenstates, how does one 
> calculate the phase angles of the amplitudes for each eigenstate? AG
> 
> One doesn't. The phases are arbitrary unless one interferes the system with 
> some other system.
> 
> Bruce 
> 
> If the phases are arbitrary and the system interacts with some other system, 
> the new phases presumably are also arbitrary. So there doesn't seem to be any 
> physical significance, yet this is the heart of decoherence theory as I 
> understand it. What am I missing? TIA, AG
> 
>  Also, as we discussed, the phase angles determine interference. If they can 
> be chosen arbitrarily, it seems as if interference has no physical 
> significance. AG
> 
> Puzzling, isn't it? We have waves in Wave Mechanics. Waves interfere with 
> each