Re: [Fis] Probability Amplitudes and philosophical basis of QM

[Alexey V. Nikulov]

Dear Lars-Göran and colleagues,
I think that probability amplitudes should have a single meaning as well 
as any concept that our mind can invent. Heisenberg said in his Lectures 
1955-1956 ”Physics and Philosophy”: “Descartes realizes that what we 
know about our mind is more certain than what we know about the outer 
world”. According to this correct notion no theory about the outer world 
can have interpretations and any concept should have a single meaning. 
Theories of physics as theories about the outer world should not have 
interpretations. But it is well known that interpretations of quantum 
mechanics are charaterized by huge diversity. Therefore quantum 
mechanics (QM) can not be considered as a  physical theory. Schrodinger 
was right that QM is failed theory (see the Section “THE MAKESHIFT OF 
WAVE MECHANICS’ in the book Schrodinger E. Science and Humanism. Physics 
in Our Time. Cambridge: University Press, 1952).

Schrodinger craved to interpret his wave function as a real wave. He 
tried to replace particles with wavepackets. But wavepackets diffuse. 
This diffuseness contradicts numerous observations. Most physicists have 
accepted the interpretation of Schrodinger’s wave function as 
probability amplitudes proposed by Born because the probability of 
observation should change at observation. Most physicists believe for 
the present that it was good solution of the problem to say that 
wavepacket can be localized at observation. But they ignore that it is 
localized first of all in the mind of the observer. The probability of 
observation describes the state of the mind of the observer. It is quite 
obvious that our knowledge changes when we observe anything. This change 
of our knowledge is discontinuous. In the Section ”The Copenhagen 
Interpretation of Quantum Theory” of his Lectures 1955-1956 Heisenberg 
stated ”that certainly our knowledge can change suddenly and that this 
fact justifies the use of the term ’quantum jump’”. Just therefore QM 
presupposes the instantaneous and non-local change at observation called 
Dirac jump, wave function collapse, or ’quantum jump’ from the 
’possible’ to the ’actual’. This discontinuous change of the mind of the 
observer takes place at any observation at which an object (for example 
a physical system) has an influence on subject (the mind of the observer).

Schrodinger noted in the Section “THE ALLEGED BREAK-DOWN OF THE BARRIER 
BETWEEN SUBJECT AND OBJECT” of his book “Science and Humanism” that 
”…the mere contention that every observation depends on both the subject 
and the object, which are inextricably interwoven this contention is 
hardly new, it is almost as old as science itself” . But ”… in the 
present order of ideas the direct physical, causal influence between the 
two is regarded as mutual. It is said that there is also an unavoidable 
and uncontrollable impression from the side of the subject onto the 
object. This aspect is new…”. Heisenberg had in mind just this new 
aspect when he said in his Lectures 1955-1956 that “we have to criticise 
from the development of physics in our time” the Cartesian division. 
Quantum mechanics is vague and has numerous interpretation just because 
of the denial of the Cartesian division. Heisenberg said fairly: "The 
mechanics of Newton and all the other parts of classical physics 
constructed after its model started from the assumption that one can 
describe the world without speaking about God or ourselves… If one 
follows the great difficulty which even eminent scientists like Einstein 
had in understanding and accepting the Copenhagen interpretation of 
quantum theory, one can trace the roots of this difficulty to the 
Cartesian partition. This partition has penetrated deeply into the human 
mind during the three centuries following Descartes and it will take a 
long time for it to be replaced by a really different attitude toward 
the problem of reality". But he was not right when he stated that a 
scientific theory could be possible without the acceptance of the 
Cartesian polarity between the 'res cogitans' and the 'res extensa'. No 
science can describe a mutual causal influence between the 'res 
cogitans' and the 'res extensa' (or between the subject and the object). 
Quantum mechanics presumes such mutual influence. Therefore it can not 
be considered as a scientific theory.

Einstein wrote to Schrodinger as far back as 1928: "The soothing 
philosophy-or religion?-of Heisenberg-Bohr is so cleverly concocted that 
it offers the believers a soft resting pillow from which they are not 
easily chased away".  The diversity of opinions about quantum mechanics 
witnesses that Einstein's words turned out prophetic: the dissent can be 
about a religion but our true comprehension must be unified. At least we 
must believe that it is possible. Otherwise no science could be 
possible. The belief in quantum mechanics is a consequence of the 
illusion inherent to most contemporary scientists that what

Re: [Fis] Probability Amplitudes in Macroscopic Processes

[Lars-Göran Johansson]

Let me clarify one point: by saying that probability amplitudes represent real 
physical features I reject the instrumentalist idea that they are mere 
calculational devices. But of course, the probability amplitude is no 
observable. But there is no need to claim that only observables have any 
physical significance.
Robert Chen has, in a couple of papers argued that the square of real part of 
the wave function could be interpreted as the system's kinetic energy, whereas 
the square of the imaginary part represents the potential energy of the system. 
It is as far as I can see a possible and reasonable interpretation.
Lars-Göran


22 jan 2014 kl. 15:14 skrev Joseph Brenner 
mailto:joe.bren...@bluewin.ch>>:

Dear Lars-Göran, Andrei and Hans,

As you (I hope) have seen, I am trying to see how the evolution of macroscopic 
processes can be described in terms of changing probabilities, and I am 
encouraged to believe this is possible. If you allow the extension from QM, all 
of the following would seem to allow this
(I am not concerned about whether QM itself becomes more or less complex):

1. Andrei confirms that the probability (in LIR, degree of potentiality or 
actuality) of a phenomenon can have a direction.
2. Lars-Göran says that probability amplitudes can represent real physical 
features.
3. Even though /a contrario/, Hans wrote:

In order to make contact with real, measurable quantities, it (the probability 
amplitude) must be multiplied by its complex conjugate. This recipe is called 
the Born rule, and it is an ad hoc addition to the quantum theory. It lacks any 
motivation except that it works.
In my Logic in Reality, since there is a reciprocal relation between actuality 
and potentiality, each should be the complex conjugate of the other. I have no 
problem in the two summing to 1 if the values of 0 or 1 are excluded for either 
of them. This non-quantum aspect of reality could provide the missing 
motivation for the recipe in quantum theory ;-)

I am certainly looking for a measurable (or estimatable) quantity of the 
actuality and potentiality of interactive processes that is not a standard 
probability of outcomes, but of changing macroscopic states. This is of course 
an 'underdeveloped' concept, but I am encouraged to believe that this idea of 
another set of "very special probabilities" is neither totally wrong nor 
totally trivial.

Many thanks,

Joseph

- Original Message -
From: Lars-Göran Johansson<mailto:lars-goran.johans...@filosofi.uu.se>
To: fis@listas.unizar.es<mailto:fis@listas.unizar.es>
Sent: Wednesday, January 22, 2014 12:45 PM
Subject: Re: [Fis] Probability Amplitudes

 Dear Andrei, Hans and all
I agree with Andrei. And why make quantum theory more complex than it is? One 
may use all  kinds of mathematical tools in a scientific theory, and the more 
these tools simplify calculations the better. I see no reason to avoid using 
amplitudes or  matrices in quantum theory. Using a mathematical concept for 
making calculations doesn't entail that I accept that that concept represent a 
physical property.

To Hans: Where exactly did Einstein wrote that one should avoid unmeasurable 
concepts in the description of Nature? I can't remember having read that.

The issue is how we should interpret quantum theory, in particular the wave 
function, i.e., probability amplitudes; are they just mathematical tools, or do 
 they describe real physical features of quantum systems? I believe the latter 
alternative is true and so did Schrödinger. But there are formidable 
difficulties to give a realistic interpretation of wave functions, and 
Schrödinger didn't succeed. But I think the difficulties can be overcome and I 
have published my views about these things (Lars-Göran Johansson: Interpreting 
Quantum Mechanics. A realist view in Schrödinger's vein, Ashgate, Aldershot 
2007).
Lars-Göran

22 jan 2014 kl. 10:59 skrev Andrei Khrennikov 
mailto:andrei.khrenni...@lnu.se>>:

  Dear Hans,

I would like just to point that 99,99% of people working
in quantum theory would say that the complex amplitude of
quantum probability is the main its intrinsic property, so
if you try to exclude amplitudes from the model
you can in principle do this and this is well known
long ago in so called quantum tomographic approach of Vladimir
Manko, but in this way quantum theory loses its simplicity and
clarity, yours, andrei

Andrei Khrennikov, Professor of Applied Mathematics,
International Center for Mathematical Modeling
in Physics, Engineering, Economics, and Cognitive Science
Linnaeus University, Växjö-Kalmar, Sweden

From: fis-boun...@listas.unizar.es<mailto:fis-boun...@listas.unizar.es> 
[fis-boun...@listas.unizar.es<mailto:fis-boun...@listas.unizar.es>] on behalf 
of Hans von Baeyer [henrikrit...@gmail.com<mailto:henrikrit...@gmail.com>]
Sent: Wednesday, Januar

Re: [Fis] Probability Amplitudes

[Lars-Göran Johansson]

 Dear Andrei, Hans and all
I agree with Andrei. And why make quantum theory more complex than it is? One 
may use all  kinds of mathematical tools in a scientific theory, and the more 
these tools simplify calculations the better. I see no reason to avoid using 
amplitudes or  matrices in quantum theory. Using a mathematical concept for 
making calculations doesn't entail that I accept that that concept represent a 
physical property.

To Hans: Where exactly did Einstein wrote that one should avoid unmeasurable 
concepts in the description of Nature? I can't remember having read that.

The issue is how we should interpret quantum theory, in particular the wave 
function, i.e., probability amplitudes; are they just mathematical tools, or do 
they describe real physical features of quantum systems? I believe the latter 
alternative is true and so did Schrödinger. But there are formidable 
difficulties to give a realistic interpretation of wave functions, and 
Schrödinger didn't succeed. But I think the difficulties can be overcome and I 
have published my views about these things (Lars-Göran Johansson: Interpreting 
Quantum Mechanics. A realist view in Schrödinger's vein, Ashgate, Aldershot 
2007).
Lars-Göran

22 jan 2014 kl. 10:59 skrev Andrei Khrennikov 
mailto:andrei.khrenni...@lnu.se>>:

  Dear Hans,

I would like just to point that 99,99% of people working
in quantum theory would say that the complex amplitude of
quantum probability is the main its intrinsic property, so
if you try to exclude amplitudes from the model
you can in principle do this and this is well known
long ago in so called quantum tomographic approach of Vladimir
Manko, but in this way quantum theory loses its simplicity and
clarity, yours, andrei

Andrei Khrennikov, Professor of Applied Mathematics,
International Center for Mathematical Modeling
in Physics, Engineering, Economics, and Cognitive Science
Linnaeus University, Växjö-Kalmar, Sweden

From: fis-boun...@listas.unizar.es 
[fis-boun...@listas.unizar.es] on behalf 
of Hans von Baeyer [henrikrit...@gmail.com]
Sent: Wednesday, January 22, 2014 12:21 AM
To: fis@listas.unizar.es
Subject: [Fis] Probability Amplitudes

Dear Dino and friends, thanks for bringing up the issue of probability 
amplitudes.  Since they are technical tools of physics, and since I didn't want 
to go too far afield, I did not mention them in my lecture.  The closest I came 
was the wavefunction, which, indeed, is a probability amplitude.  In order to 
make contact with real, measurable quantities, it must be multiplied by its 
complex conjugate. This recipe is called the Born rule, and it is an ad hoc 
addition to the quantum theory. It lacks any motivation except that it works.

In keeping with Einstein's advice (which he himself often flouted) to try to 
keep unmeasurable concepts out of our description of nature, physicists have 
realized long ago that it must be possible to recast quantum mechanics entirely 
in terms of probabilities, not even mentioning probability amplitudes or 
wavefunctions. The question is only: How complicated would the resulting 
formalism be?  (To make a weak analogy, it must be possible to recast 
arithmetic in the language of Roman numerals, but the result would surely look 
much messier than what we learn in grade school.)  Hitherto, nobody had come up 
with an elegant solution to this problem.

To their happy surprise, QBists have made  progress toward a "quantum theory 
without probability amplitudes."  Of course they have to pay a price.  Instead 
of "unmeasurable concepts" they introduce, for any experiment, a very special 
set of standard probabilities (NOT AMPLITUDES) which are measurable, but not 
actually measured.  When they re-write the Born rule in terms of these, they 
find that it looks almost, but not quite, like a fundamental axiom of 
probability theory called Unitarity.  Unitarity decrees that for any experiment 
the sum of the probabilities for all possible outcomes must be one. (For a 
coin, the probabilities of heads and tails are both 1/2.  Unitarity states 1/2 
+ 1/2 = 1.)

This unexpected outcome of QBism suggests a deep connection between the Born 
rule and Unitarity. Since Unitarity is a logical concept unrelated to quantum 
phenomena, this gives QBists the hope that they will eventually succeed in 
explaining the significacne of the Born rule, and banishing probability 
amplitudes from quantum mechanics, leaving only (Bayesian) probabilities.

So, I'm afraid dear Dino, that the current attitude of QBists is that 
probability amplitudes are LESS fundamental than probabilities, not MORE.  But 
the story is far from finished!

Hans



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Re: [Fis] Probability Amplitudes

[Andrei Khrennikov]

  Dear Joseph,
you are going toward quantum probability theory where 
probabilities are determined by vectors; moreover, the vectors
belong to complex Hilbert space, i.e., roughly speaking each probability
has not only the direction but even the phase, andrei

Andrei Khrennikov, Professor of Applied Mathematics,
International Center for Mathematical Modeling
in Physics, Engineering, Economics, and Cognitive Science
Linnaeus University, Växjö-Kalmar, Sweden

From: fis-boun...@listas.unizar.es [fis-boun...@listas.unizar.es] on behalf of 
Joseph Brenner [joe.bren...@bluewin.ch]
Sent: Wednesday, January 22, 2014 8:54 AM
To: Dino Buzzetti; Hans von Baeyer; fis
Subject: Re: [Fis] Probability Amplitudes

Dear Hans and Dino,

This is a direct question to both of you, to which I have not found a clear 
answer: are value and amplitude the only parameters that have been assigned to 
probability?

In my theory, the changing value of actuality and potentiality of specific 
antagonistic process elements are probability-like in not including 0 and 1, as 
I have said. Can, in addition, probabilities have some vector-like properties, 
that is, include a /direction/?

This concept would be moving toward (and past) Dino and away from Hans . . .

Your comments and those of others would be welcome.

Best wishes,

Joseph
- Original Message -
From: Dino Buzzetti<mailto:dino.buzze...@gmail.com>
To: Hans von Baeyer<mailto:henrikrit...@gmail.com> ; 
fis<mailto:fis@listas.unizar.es>
Sent: Wednesday, January 22, 2014 3:53 AM
Subject: Re: [Fis] Probability Amplitudes

Dear Hans,

Thank you for your explanation about probability amplitudes,
that clarifies a lot.  My only worry was about the *epistemological*
implications of quantum mechanics in its standard formulation,
that in my opinion point to a paradigm shift, which is felt not only
in this domain, but in all fields where *emergent* phenomena are
accounted for—a process that I thought was hinted to by Wheeler's
famous words "It from Bit," that I remember reading for the first
time precisely in your book on information.  That's the ground for
expressing my worry that reverting to classical probability theory
might entail a drawback to this decisive epistemological turn.

But I might misunderstand the whole story, that is certainly not
over yet  :-)  -dino



On 22 January 2014 00:21, Hans von Baeyer 
mailto:henrikrit...@gmail.com>> wrote:
Dear Dino and friends, thanks for bringing up the issue of probability 
amplitudes.  Since they are technical tools of physics, and since I didn't want 
to go too far afield, I did not mention them in my lecture.  The closest I came 
was the wavefunction, which, indeed, is a probability amplitude.  In order to 
make contact with real, measurable quantities, it must be multiplied by its 
complex conjugate. This recipe is called the Born rule, and it is an ad hoc 
addition to the quantum theory. It lacks any motivation except that it works.

In keeping with Einstein's advice (which he himself often flouted) to try to 
keep unmeasurable concepts out of our description of nature, physicists have 
realized long ago that it must be possible to recast quantum mechanics entirely 
in terms of probabilities, not even mentioning probability amplitudes or 
wavefunctions. The question is only: How complicated would the resulting 
formalism be?  (To make a weak analogy, it must be possible to recast 
arithmetic in the language of Roman numerals, but the result would surely look 
much messier than what we learn in grade school.)  Hitherto, nobody had come up 
with an elegant solution to this problem.

To their happy surprise, QBists have made  progress toward a "quantum theory 
without probability amplitudes."  Of course they have to pay a price.  Instead 
of "unmeasurable concepts" they introduce, for any experiment, a very special 
set of standard probabilities (NOT AMPLITUDES) which are measurable, but not 
actually measured.  When they re-write the Born rule in terms of these, they 
find that it looks almost, but not quite, like a fundamental axiom of 
probability theory called Unitarity.  Unitarity decrees that for any experiment 
the sum of the probabilities for all possible outcomes must be one. (For a 
coin, the probabilities of heads and tails are both 1/2.  Unitarity states 1/2 
+ 1/2 = 1.)

This unexpected outcome of QBism suggests a deep connection between the Born 
rule and Unitarity. Since Unitarity is a logical concept unrelated to quantum 
phenomena, this gives QBists the hope that they will eventually succeed in 
explaining the significacne of the Born rule, and banishing probability 
amplitudes from quantum mechanics, leaving only (Bayesian) probabilities.

So, I'm afraid dear Dino, that the current attitude of QBists is that 
probability amplitudes are LESS fundam

Re: [Fis] Probability Amplitudes

[Andrei Khrennikov]

   Dear Hans,

I would like just to point that 99,99% of people working 
in quantum theory would say that the complex amplitude of 
quantum probability is the main its intrinsic property, so 
if you try to exclude amplitudes from the model
you can in principle do this and this is well known 
long ago in so called quantum tomographic approach of Vladimir 
Manko, but in this way quantum theory loses its simplicity and 
clarity, yours, andrei

Andrei Khrennikov, Professor of Applied Mathematics,
International Center for Mathematical Modeling
in Physics, Engineering, Economics, and Cognitive Science
Linnaeus University, Växjö-Kalmar, Sweden

From: fis-boun...@listas.unizar.es [fis-boun...@listas.unizar.es] on behalf of 
Hans von Baeyer [henrikrit...@gmail.com]
Sent: Wednesday, January 22, 2014 12:21 AM
To: fis@listas.unizar.es
Subject: [Fis] Probability Amplitudes

Dear Dino and friends, thanks for bringing up the issue of probability 
amplitudes.  Since they are technical tools of physics, and since I didn't want 
to go too far afield, I did not mention them in my lecture.  The closest I came 
was the wavefunction, which, indeed, is a probability amplitude.  In order to 
make contact with real, measurable quantities, it must be multiplied by its 
complex conjugate. This recipe is called the Born rule, and it is an ad hoc 
addition to the quantum theory. It lacks any motivation except that it works.

In keeping with Einstein's advice (which he himself often flouted) to try to 
keep unmeasurable concepts out of our description of nature, physicists have 
realized long ago that it must be possible to recast quantum mechanics entirely 
in terms of probabilities, not even mentioning probability amplitudes or 
wavefunctions. The question is only: How complicated would the resulting 
formalism be?  (To make a weak analogy, it must be possible to recast 
arithmetic in the language of Roman numerals, but the result would surely look 
much messier than what we learn in grade school.)  Hitherto, nobody had come up 
with an elegant solution to this problem.

To their happy surprise, QBists have made  progress toward a "quantum theory 
without probability amplitudes."  Of course they have to pay a price.  Instead 
of "unmeasurable concepts" they introduce, for any experiment, a very special 
set of standard probabilities (NOT AMPLITUDES) which are measurable, but not 
actually measured.  When they re-write the Born rule in terms of these, they 
find that it looks almost, but not quite, like a fundamental axiom of 
probability theory called Unitarity.  Unitarity decrees that for any experiment 
the sum of the probabilities for all possible outcomes must be one. (For a 
coin, the probabilities of heads and tails are both 1/2.  Unitarity states 1/2 
+ 1/2 = 1.)

This unexpected outcome of QBism suggests a deep connection between the Born 
rule and Unitarity. Since Unitarity is a logical concept unrelated to quantum 
phenomena, this gives QBists the hope that they will eventually succeed in 
explaining the significacne of the Born rule, and banishing probability 
amplitudes from quantum mechanics, leaving only (Bayesian) probabilities.

So, I'm afraid dear Dino, that the current attitude of QBists is that 
probability amplitudes are LESS fundamental than probabilities, not MORE.  But 
the story is far from finished!

Hans



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Re: [Fis] Probability Amplitudes

[Joseph Brenner]

Dear Hans and Dino,

This is a direct question to both of you, to which I have not found a clear 
answer: are value and amplitude the only parameters that have been assigned to 
probability?

In my theory, the changing value of actuality and potentiality of specific 
antagonistic process elements are probability-like in not including 0 and 1, as 
I have said. Can, in addition, probabilities have some vector-like properties, 
that is, include a /direction/? 

This concept would be moving toward (and past) Dino and away from Hans . . .

Your comments and those of others would be welcome.

Best wishes,

Joseph
  - Original Message - 
  From: Dino Buzzetti 
  To: Hans von Baeyer ; fis 
  Sent: Wednesday, January 22, 2014 3:53 AM
  Subject: Re: [Fis] Probability Amplitudes


  Dear Hans, 


  Thank you for your explanation about probability amplitudes, 

  that clarifies a lot.  My only worry was about the *epistemological* 

  implications of quantum mechanics in its standard formulation, 

  that in my opinion point to a paradigm shift, which is felt not only 
  in this domain, but in all fields where *emergent* phenomena are 
  accounted for—a process that I thought was hinted to by Wheeler's 
  famous words "It from Bit," that I remember reading for the first 
  time precisely in your book on information.  That's the ground for  
  expressing my worry that reverting to classical probability theory 
  might entail a drawback to this decisive epistemological turn.   


  But I might misunderstand the whole story, that is certainly not 
  over yet  :-)  -dino





  On 22 January 2014 00:21, Hans von Baeyer  wrote:

Dear Dino and friends, thanks for bringing up the issue of probability 
amplitudes.  Since they are technical tools of physics, and since I didn't want 
to go too far afield, I did not mention them in my lecture.  The closest I came 
was the wavefunction, which, indeed, is a probability amplitude.  In order to 
make contact with real, measurable quantities, it must be multiplied by its 
complex conjugate. This recipe is called the Born rule, and it is an ad hoc 
addition to the quantum theory. It lacks any motivation except that it works.


In keeping with Einstein's advice (which he himself often flouted) to try 
to keep unmeasurable concepts out of our description of nature, physicists have 
realized long ago that it must be possible to recast quantum mechanics entirely 
in terms of probabilities, not even mentioning probability amplitudes or 
wavefunctions. The question is only: How complicated would the resulting 
formalism be?  (To make a weak analogy, it must be possible to recast 
arithmetic in the language of Roman numerals, but the result would surely look 
much messier than what we learn in grade school.)  Hitherto, nobody had come up 
with an elegant solution to this problem.


  To their happy surprise, QBists have made  progress toward a "quantum 
theory without probability amplitudes."  Of course they have to pay a price.  
Instead of "unmeasurable concepts" they introduce, for any experiment, a very 
special set of standard probabilities (NOT AMPLITUDES) which are measurable, 
but not actually measured.  When they re-write the Born rule in terms of these, 
they find that it looks almost, but not quite, like a fundamental axiom of 
probability theory called Unitarity.  Unitarity decrees that for any experiment 
the sum of the probabilities for all possible outcomes must be one. (For a 
coin, the probabilities of heads and tails are both 1/2.  Unitarity states 1/2 
+ 1/2 = 1.)


This unexpected outcome of QBism suggests a deep connection between the 
Born rule and Unitarity. Since Unitarity is a logical concept unrelated to 
quantum phenomena, this gives QBists the hope that they will eventually succeed 
in explaining the significacne of the Born rule, and banishing probability 
amplitudes from quantum mechanics, leaving only (Bayesian) probabilities. 


So, I'm afraid dear Dino, that the current attitude of QBists is that 
probability amplitudes are LESS fundamental than probabilities, not MORE.  But 
the story is far from finished!


Hans



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Re: [Fis] Probability Amplitudes

[Dino Buzzetti]

Dear Hans,

Thank you for your explanation about probability amplitudes,
that clarifies a lot.  My only worry was about the *epistemological*
implications of quantum mechanics in its standard formulation,
that in my opinion point to a paradigm shift, which is felt not only
in this domain, but in all fields where *emergent* phenomena are
accounted for—a process that I thought was hinted to by Wheeler's
famous words "It from Bit," that I remember reading for the first
time precisely in your book on information.  That's the ground for
expressing my worry that reverting to classical probability theory
might entail a drawback to this decisive epistemological turn.

But I might misunderstand the whole story, that is certainly not
over yet  :-)  -dino



On 22 January 2014 00:21, Hans von Baeyer  wrote:

> Dear Dino and friends, thanks for bringing up the issue of probability
> amplitudes.  Since they are technical tools of physics, and since I didn't
> want to go too far afield, I did not mention them in my lecture.  The
> closest I came was the wavefunction, which, indeed, is a probability
> amplitude.  In order to make contact with real, measurable quantities, it
> must be multiplied by its complex conjugate. This recipe is called the Born
> rule, and it is an ad hoc addition to the quantum theory. It lacks any
> motivation except that it works.
>
> In keeping with Einstein's advice (which he himself often flouted) to try
> to keep unmeasurable concepts out of our description of nature, physicists
> have realized long ago that it must be possible to recast quantum mechanics
> entirely in terms of probabilities, not even mentioning probability
> amplitudes or wavefunctions. The question is only: How complicated would
> the resulting formalism be?  (To make a weak analogy, it must be possible
> to recast arithmetic in the language of Roman numerals, but the result
> would surely look much messier than what we learn in grade school.)
>  Hitherto, nobody had come up with an elegant solution to this problem.
>
> To their happy surprise, QBists have made  progress toward a "quantum
>> theory without probability amplitudes."  Of course they have to pay a
>> price.  Instead of "unmeasurable concepts" they introduce, for any
>> experiment, a very special set of standard probabilities (NOT AMPLITUDES)
>> which are measurable, but not actually measured.  When they re-write the
>> Born rule in terms of these, they find that it looks almost, but not quite,
>> like a fundamental axiom of probability theory called Unitarity.  Unitarity
>> decrees that for any experiment the sum of the probabilities for all
>> possible outcomes must be one. (For a coin, the probabilities of heads and
>> tails are both 1/2.  Unitarity states 1/2 + 1/2 = 1.)
>
>
> This unexpected outcome of QBism suggests a deep connection between the
> Born rule and Unitarity. Since Unitarity is a logical concept unrelated to
> quantum phenomena, this gives QBists the hope that they will eventually
> succeed in explaining the significacne of the Born rule, and banishing
> probability amplitudes from quantum mechanics, leaving only (Bayesian)
> probabilities.
>
> So, I'm afraid dear Dino, that the current attitude of QBists is that
> probability amplitudes are LESS fundamental than probabilities, not MORE.
>  But the story is far from finished!
>
> Hans
>
>>
>
>
>
>
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>
>
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