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FQXi FORUM

February 22, 2018

CATEGORY:
Questioning the Foundations Essay Contest (2012)
[back]

TOPIC: Quantum-Informational Principles for Physics by Giacomo Mauro D'Ariano [refresh]

TOPIC: Quantum-Informational Principles for Physics by Giacomo Mauro D'Ariano [refresh]

It is time to to take a pause of reflection on the general foundations of physics, re-examining the solidity of the most basic principles, as the relativity and the equivalence principles that are currently under dispute for violations at the Planck scale. A constructive criticism engages us in seeking new general principles, which reduce to the old ones as approximations holding in the physical domain already explored. At the very basis of physics are epistemological and operational rules for the same formulability of the physical law and for the computability of its theoretical predictions, rules that give rise to new solid principles. These rules lead us to a quantum-information theoretic formulation, hinging on a logical identification of the experimental protocol with the quantum algorithm.

I am professor at the University of Pavia, where I teach "Physical Theory of Information" and "Foundations of Quantum Mechanics", and enjoy research with a marvelous group of much younger collaborators.

Giacomo

Are you agree with my abstract?

http://fqxi.org/community/forum/topic/1413

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Are you agree with my abstract?

http://fqxi.org/community/forum/topic/1413

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Dear Yuri

I do agree on some of your points, but not ll f thm. In particular, I think that timeis discrete. You can always interpolate with a continuum time, but at the price of losing the locality of interactions, a too big price to pay. As for the fondants constants, these are just the three universal constants of Dirac automata, namely: the Planck time, length, and mass. The Panck constant is derived from them, as you can read in my essay.

Thank you

Mauro

I do agree on some of your points, but not ll f thm. In particular, I think that timeis discrete. You can always interpolate with a continuum time, but at the price of losing the locality of interactions, a too big price to pay. As for the fondants constants, these are just the three universal constants of Dirac automata, namely: the Planck time, length, and mass. The Panck constant is derived from them, as you can read in my essay.

Thank you

Mauro

Dear Yuri,

Some typos unexpectedly came out. Sorry. Here's the answer amended.

I do agree on some of your points, but not with all of them. In particular, I think that time is discrete. You can always interpolate with a continuum time, but at the price of losing the locality of interactions, a too big price to pay. As for the fondamental constants, these are just the three universal constants of Dirac automata, namely: the Planck time, length, and mass. The Planck constant is derived from them, as you can read in my essay.

Some typos unexpectedly came out. Sorry. Here's the answer amended.

I do agree on some of your points, but not with all of them. In particular, I think that time is discrete. You can always interpolate with a continuum time, but at the price of losing the locality of interactions, a too big price to pay. As for the fondamental constants, these are just the three universal constants of Dirac automata, namely: the Planck time, length, and mass. The Planck constant is derived from them, as you can read in my essay.

Dear Giacomo

Thank you for attention.

I hope we will discuss after you read all essay.

report post as inappropriate

Thank you for attention.

I hope we will discuss after you read all essay.

report post as inappropriate

Dear Giacomo,

I really appreciate your essay; it has given me some new perspectives on topics I have thought about a great deal. I have a couple of questions and comments:

1. The topic of covariance comes up repeatedly in your essay, and I want to make sure I understand your precise view on how this principle should be regarded. You mention “violation of relativistic...

view entire post

I really appreciate your essay; it has given me some new perspectives on topics I have thought about a great deal. I have a couple of questions and comments:

1. The topic of covariance comes up repeatedly in your essay, and I want to make sure I understand your precise view on how this principle should be regarded. You mention “violation of relativistic...

view entire post

report post as inappropriate

Dear Ben

thank you very much for your careful reading of my paper and your appreciation. By the way, your post also attracted my attention to your essay, which I thus read carefully, and I'm going to report on your FQXi thread. As you have seen (and will better see after my reply), there are some strong common points between our two views, but also some relevant differences, about which...

view entire post

thank you very much for your careful reading of my paper and your appreciation. By the way, your post also attracted my attention to your essay, which I thus read carefully, and I'm going to report on your FQXi thread. As you have seen (and will better see after my reply), there are some strong common points between our two views, but also some relevant differences, about which...

view entire post

Dear Mauro,

Thanks for the response, and I sincerely appreciate your detailed analysis and critique of my ideas on my thread. This is what I was hoping for when I entered the contest. In our discussion, I ask you to bear in mind two points. First, my formal education is mostly mathematical and there may be some initial terminological confusion. Second, besides my own reading, I have...

view entire post

Thanks for the response, and I sincerely appreciate your detailed analysis and critique of my ideas on my thread. This is what I was hoping for when I entered the contest. In our discussion, I ask you to bear in mind two points. First, my formal education is mostly mathematical and there may be some initial terminological confusion. Second, besides my own reading, I have...

view entire post

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Dear Ben

your essay and your ideas go far beyond what one could expect from a purely mathematical training. My best compliments! Getting some things wrong is part of the process at the beginning: better making some starting mistakes, than working unmistakably on a useless program. It is part of the adventure!

Thank you also very much for your appreciation, which I know as sincere,...

view entire post

your essay and your ideas go far beyond what one could expect from a purely mathematical training. My best compliments! Getting some things wrong is part of the process at the beginning: better making some starting mistakes, than working unmistakably on a useless program. It is part of the adventure!

Thank you also very much for your appreciation, which I know as sincere,...

view entire post

Dear

Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regard !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

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Very interesting to see your essay.

Perhaps all of us are convinced that: the choice of yourself is right!That of course is reasonable.

So may be we should work together to let's the consider clearly defined for the basis foundations theoretical as the most challenging with intellectual of all of us.

Why we do not try to start with a real challenge is very close and are the focus of interest of the human science: it is a matter of mass and grain Higg boson of the standard model.

Knowledge and belief reasoning of you will to express an opinion on this matter:

You have think that: the Mass is the expression of the impact force to material - so no impact force, we do not feel the Higg boson - similar to the case of no weight outside the Earth's atmosphere.

Does there need to be a particle with mass for everything have volume? If so, then why the mass of everything change when moving from the Earth to the Moon? Higg boson is lighter by the Moon's gravity is weaker than of Earth?

The LHC particle accelerator used to "Smashed" until "Ejected" Higg boson, but why only when the "Smashed" can see it,and when off then not see it ?

Can be "locked" Higg particles? so when "released" if we do not force to it by any the Force, how to know that it is "out" or not?

You are should be boldly to give a definition of weight that you think is right for us to enjoy, or oppose my opinion.

Because in the process of research, the value of "failure" or "success" is the similar with science. The purpose of a correct theory be must is without any a wrong point ?

Glad to see from you comments soon,because still have too many of the same problems.

Regard !

Hải.Caohoàng of THE INCORRECT ASSUMPTIONS AND A CORRECT THEORY

August 23, 2012 - 11:51 GMT on this essay contest.

report post as inappropriate

Dear Hai

in my approach inertial mass gets naturally a cinematical definition, solving the loophole definition of mechanics (if you are not considering Machian theories): it is just the slowing-down of information. It is a parameter of the automaton, and coincides with the rest-mass of the particle. Gravitation is still a work in embryo, and the idea is that it is a thermodynamical effect of purely quantum nature. The Higg mechanism is not quantum, and is far from the current status of the theory (just Dirac). In few years, if I get sufficient funding, I will be able to tell you if the Higg's mechanism will emerge as a semiclassical one from the quantum automaton in interaction, not the free one.

Thank you for you interest.

I'll take a look at your essay

Cheers

Mauro

in my approach inertial mass gets naturally a cinematical definition, solving the loophole definition of mechanics (if you are not considering Machian theories): it is just the slowing-down of information. It is a parameter of the automaton, and coincides with the rest-mass of the particle. Gravitation is still a work in embryo, and the idea is that it is a thermodynamical effect of purely quantum nature. The Higg mechanism is not quantum, and is far from the current status of the theory (just Dirac). In few years, if I get sufficient funding, I will be able to tell you if the Higg's mechanism will emerge as a semiclassical one from the quantum automaton in interaction, not the free one.

Thank you for you interest.

I'll take a look at your essay

Cheers

Mauro

Dear Giacomo,

Good essay. If I am not mistaken I think you Simplifying principle is actually Ockam's razor. There are some serious researchers that work in the direction of providing alternatives to Bayesian approaches, such as Kevin Kelly from Carnegie Mellon that you may find interesting. I completely agree that there are untouchable dogmas not only in physics.

Your informational principles are appealing, I am tempted to try to understand them in further detail. Your informational view quite challenges my own ideas on an algorithmic world in ways I didn't expect, because you seem to suggest that some of this informational principles are not mechanical, which it is not completely clear from your essay, certainly in part because of the lack of space to further explain it. I am also delighted by your tidy illustrations, apparently using Mathematica =)

It looks to me that your proposal is related to, if not, a theory of quantum gravity, I would have liked this to be made explicit in either direction.

report post as inappropriate

Good essay. If I am not mistaken I think you Simplifying principle is actually Ockam's razor. There are some serious researchers that work in the direction of providing alternatives to Bayesian approaches, such as Kevin Kelly from Carnegie Mellon that you may find interesting. I completely agree that there are untouchable dogmas not only in physics.

Your informational principles are appealing, I am tempted to try to understand them in further detail. Your informational view quite challenges my own ideas on an algorithmic world in ways I didn't expect, because you seem to suggest that some of this informational principles are not mechanical, which it is not completely clear from your essay, certainly in part because of the lack of space to further explain it. I am also delighted by your tidy illustrations, apparently using Mathematica =)

It looks to me that your proposal is related to, if not, a theory of quantum gravity, I would have liked this to be made explicit in either direction.

report post as inappropriate

Dear Hector,

Thank you very much for your appreciation. Personally I have a strong personal belief in the future of the quantum automata extension of quantum field theory proposed in the essay.

Yes, my simplifying principle is the Ockam's razor, since I reduce the whole theory to just quantum theory of interacting systems, plus the Deutsch-Church-Turing principle (information density is bounded from above) and homogeneity. The Dirac equation is then just the free flow of quantum information, with inertial mass defined cinematically as the slowing down of the flow via the coupling between the two chiralities of propagation of information at the maximal speed-i.e. the causal speed (see my essay of last year for d=1). If you want to understand more, I will be happy to explain: what about a Skype meeting?

I would be also very happy if you can provide me a good reference to the work of Kevin Kelly, alternative to my approach, which indeed has a natural Bayesian interpretation, but not necessarily. In a way, also my universe is algorithmic, but of a quantum kind: the algorithm is very small, it is just the automaton, namely a small number of quantum cells (made of few low-dimensional quantum systems) causally connected by a small set of unitary interactions, representing the physical law, or equivalently, the field theory. Can you provide me with a reference to your work on the algorithmic universe?

Yes, the plots are made with Mathematica, with a quite sophisticate parallel graphics! I now will have soon the d=3 automaton: the graphics is astonishingly beautiful, with 3d pixels in space, whose size and transparency represent the quantum amplitude of the superposition, whereas the colors encode some phase and relative weights of the Dirac double spinor!

The proposal is indeed related to the idea of deriving an alternative theory of quantum gravity, essentially via the Jacobson thermodynamic approach. I this point I have some idea in mind, which I will write on a forthcoming manuscript, when it will be clear that it goes to the right direction. For the moment I cannot say more, and you have to wait up to December, when I will have finished teaching my semester course of Quantum Mechanics. At that time I will also post on the arxiv two long technical manuscripts, one with my postdocs Alessandro Tosini and Alessandro Bisio on a powerful asymptotic analytical evaluation of the automaton dynamics in the thermodynamic limit for smooth states (what I call the field limit), and one with Paolo Perinotti on the d=2 and d=3 Dirac automaton from first principles. After that we'll move to QED, but I think we will not need this for gravity. We are four people currently working on this project, with no funding! I hope that we will get some funding soon!

Thank you again,

Mauro

Thank you very much for your appreciation. Personally I have a strong personal belief in the future of the quantum automata extension of quantum field theory proposed in the essay.

Yes, my simplifying principle is the Ockam's razor, since I reduce the whole theory to just quantum theory of interacting systems, plus the Deutsch-Church-Turing principle (information density is bounded from above) and homogeneity. The Dirac equation is then just the free flow of quantum information, with inertial mass defined cinematically as the slowing down of the flow via the coupling between the two chiralities of propagation of information at the maximal speed-i.e. the causal speed (see my essay of last year for d=1). If you want to understand more, I will be happy to explain: what about a Skype meeting?

I would be also very happy if you can provide me a good reference to the work of Kevin Kelly, alternative to my approach, which indeed has a natural Bayesian interpretation, but not necessarily. In a way, also my universe is algorithmic, but of a quantum kind: the algorithm is very small, it is just the automaton, namely a small number of quantum cells (made of few low-dimensional quantum systems) causally connected by a small set of unitary interactions, representing the physical law, or equivalently, the field theory. Can you provide me with a reference to your work on the algorithmic universe?

Yes, the plots are made with Mathematica, with a quite sophisticate parallel graphics! I now will have soon the d=3 automaton: the graphics is astonishingly beautiful, with 3d pixels in space, whose size and transparency represent the quantum amplitude of the superposition, whereas the colors encode some phase and relative weights of the Dirac double spinor!

The proposal is indeed related to the idea of deriving an alternative theory of quantum gravity, essentially via the Jacobson thermodynamic approach. I this point I have some idea in mind, which I will write on a forthcoming manuscript, when it will be clear that it goes to the right direction. For the moment I cannot say more, and you have to wait up to December, when I will have finished teaching my semester course of Quantum Mechanics. At that time I will also post on the arxiv two long technical manuscripts, one with my postdocs Alessandro Tosini and Alessandro Bisio on a powerful asymptotic analytical evaluation of the automaton dynamics in the thermodynamic limit for smooth states (what I call the field limit), and one with Paolo Perinotti on the d=2 and d=3 Dirac automaton from first principles. After that we'll move to QED, but I think we will not need this for gravity. We are four people currently working on this project, with no funding! I hope that we will get some funding soon!

Thank you again,

Mauro

Dear Mauro,

I couldn't see the 3D version of the two particles.

Best,

Hector

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I couldn't see the 3D version of the two particles.

Best,

Hector

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Dear Mauro,

Re Kevin Kelly: http://www.hss.cmu.edu/philosophy/faculty-kelly.php

Re my own algorithmic nature research: http://www.algorithmicnature.org

Best wishes,

-- Hector

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Re Kevin Kelly: http://www.hss.cmu.edu/philosophy/faculty-kelly.php

Re my own algorithmic nature research: http://www.algorithmicnature.org

Best wishes,

-- Hector

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Giacomo wrote:

"Universal automata constants. The three quantities lP ; tP ;mP are the

irreducible universal constants of the automata theory, and the adimensional

mass is the only parameter characterizing the Dirac automaton. The Planck

constant can be now rewritten in terms of the automata universal constants ..."

Dear Giacomo

Be careful with Planck length and read Wilczek doubts about it

Wilczek:"we must extract roots",

"can be taken outside the square roots",

"In the strong system of units no square roots

at all appear in [M], [L], [T ]."

Read Wilczek http://arxiv.org/abs/0708.4361

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"Universal automata constants. The three quantities lP ; tP ;mP are the

irreducible universal constants of the automata theory, and the adimensional

mass is the only parameter characterizing the Dirac automaton. The Planck

constant can be now rewritten in terms of the automata universal constants ..."

Dear Giacomo

Be careful with Planck length and read Wilczek doubts about it

Wilczek:"we must extract roots",

"can be taken outside the square roots",

"In the strong system of units no square roots

at all appear in [M], [L], [T ]."

Read Wilczek http://arxiv.org/abs/0708.4361

report post as inappropriate

Giacomo

Thank you for an initial excellent resume, but can't claim to have kept harmonic resonance to the end. None the less I think I saw some astonishing analogies ("evolutions for finite number of steps2) etc. with some more astonishing findings of mine. I still need to comprehend you 'quantum automaton', but I hope you'll read my essay, considering your; "localized states and measurements, for whose description quantum field theory is largely inadequate," in a slight different way.

I agree it is not "blasphemy to regard the non existence of an absolute reference frame as a dogma," and find a consistent alternative to the illogical 'fixed stars' frame, so problematic to astronomy.

I expose some wrong assumptions, using epistemological elements in an ontological model, proving to reproduce a logical (TPL) construction of hierarchical compound propositions (read 'frames'). The SR postulates (Local CSL) seem to emerge direct from a Quantum Mechanism, looking like unification via Raman scattering and dynamic logic. Which I think may be very important. It certainly looks wrong and too simple at first, so meeting all requirements of the answer we seek, but is quickly intuitive.

I do hope you can read it, visualise the kinetic evolution, and comment and advise.

Very may thanks, and best wishes.

Peter

report post as inappropriate

Thank you for an initial excellent resume, but can't claim to have kept harmonic resonance to the end. None the less I think I saw some astonishing analogies ("evolutions for finite number of steps2) etc. with some more astonishing findings of mine. I still need to comprehend you 'quantum automaton', but I hope you'll read my essay, considering your; "localized states and measurements, for whose description quantum field theory is largely inadequate," in a slight different way.

I agree it is not "blasphemy to regard the non existence of an absolute reference frame as a dogma," and find a consistent alternative to the illogical 'fixed stars' frame, so problematic to astronomy.

I expose some wrong assumptions, using epistemological elements in an ontological model, proving to reproduce a logical (TPL) construction of hierarchical compound propositions (read 'frames'). The SR postulates (Local CSL) seem to emerge direct from a Quantum Mechanism, looking like unification via Raman scattering and dynamic logic. Which I think may be very important. It certainly looks wrong and too simple at first, so meeting all requirements of the answer we seek, but is quickly intuitive.

I do hope you can read it, visualise the kinetic evolution, and comment and advise.

Very may thanks, and best wishes.

Peter

report post as inappropriate

Good job, Mauro! It's great to see you making progress with this.

You talk about gravity in your essay, but I wonder: what about gauge fields? For simplicity, let's take electrodynamics. Implementing electrodynamics in the quantum digital universe should be easier than implementing gravity, no? It seems like a natural intermediate step between the Dirac equation which describes free fermions -- still a relatively simple thing -- and the case of gravity, where all sorts of problems arise (diffeomorphism invariance, possibly indefinite causal structure, etc).

Let me ask more concretely: do you have any idea yet about what will happen to gauge symmetries in the quantum digital universe?

best wishes,

Tobias

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You talk about gravity in your essay, but I wonder: what about gauge fields? For simplicity, let's take electrodynamics. Implementing electrodynamics in the quantum digital universe should be easier than implementing gravity, no? It seems like a natural intermediate step between the Dirac equation which describes free fermions -- still a relatively simple thing -- and the case of gravity, where all sorts of problems arise (diffeomorphism invariance, possibly indefinite causal structure, etc).

Let me ask more concretely: do you have any idea yet about what will happen to gauge symmetries in the quantum digital universe?

best wishes,

Tobias

report post as inappropriate

Dear Tobias

your question got the target as a sharp arrow! Sorry for not having answered soon.

Indeed, what I think is that I will not need to implement qed before getting quantum gravity! I believe that gravity should come out from Dirac alone, and the equivalence principle must be a consequence of the fact that gravity is a quantum effect that emerges at the large scale. How and from where? This is still a secret (I have an idea, but don't have a definite answer yet). But I can just tell that it will come out from the automaton diffusion in 3D.

Believe it or not, this is what it must be if we rely on solid principles, and not in the mere chance that a "theory" may luckily work a posteriori.

Thank you again for the most interesting question

Mauro

your question got the target as a sharp arrow! Sorry for not having answered soon.

Indeed, what I think is that I will not need to implement qed before getting quantum gravity! I believe that gravity should come out from Dirac alone, and the equivalence principle must be a consequence of the fact that gravity is a quantum effect that emerges at the large scale. How and from where? This is still a secret (I have an idea, but don't have a definite answer yet). But I can just tell that it will come out from the automaton diffusion in 3D.

Believe it or not, this is what it must be if we rely on solid principles, and not in the mere chance that a "theory" may luckily work a posteriori.

Thank you again for the most interesting question

Mauro

Dear Mauro:

I have two general philosophical comments on your paper, which, I hasten to add, do not affect your overall argument, which I found quite promising and exciting.

First, as concerns the epistemological principle, you say: "This is the principle that I consider the most solid one: a principle that cannot be violated, even in-principle, because its violation will involve contradicting a logical argument. Somebody would argue that claiming principles only of this [epistemological] kind is equivalent to claiming an 'ultimate theory of everything'. True." (p. 3) I would contend that this is not necessarily true. Even assuming that there is only one such epistemological principle (moreover, as an ineluctable principle of this type), it may only imply an ultimate constraint upon any theory we may have, but it does not imply an ultimate theory of everything. Indeed, it is quite possible that such a theory is in fact impossible, even though there is a definitive principle of that kind. In other words, nature may allow us to have such a principle, and yet disallow us to conceive how it ultimately works, including why we must have such a principle. We may, however, have partial theories conforming to such a principle or, since there may be more than one, such principle. In short, you don’t need to concede even this point to the opponent of epistemological principles.

Secondly, while it may be true that "the non existence of an absolute reference frame" (p. 2) is a dogma (even though some see it as an epistemological principle [p. 3]), I am not sure that "denying the existence of an absolute [reference frame?] is a relic of the repudiation of the anthropocentrism that followed the Keplerian revolution," that is, that it is only a relic of this repudiation. There are physical reasons for this "dogma" (if it is one), especially in Einstein’s special relativity, reasons that are not at all anthropocentric. Also, do you mean by "an absolute" here "an absolute reference frame" or any "absolute"?

Thank you!

Arkady Plotnitsky

Purdue University

email: plotnits@purdue.edu

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I have two general philosophical comments on your paper, which, I hasten to add, do not affect your overall argument, which I found quite promising and exciting.

First, as concerns the epistemological principle, you say: "This is the principle that I consider the most solid one: a principle that cannot be violated, even in-principle, because its violation will involve contradicting a logical argument. Somebody would argue that claiming principles only of this [epistemological] kind is equivalent to claiming an 'ultimate theory of everything'. True." (p. 3) I would contend that this is not necessarily true. Even assuming that there is only one such epistemological principle (moreover, as an ineluctable principle of this type), it may only imply an ultimate constraint upon any theory we may have, but it does not imply an ultimate theory of everything. Indeed, it is quite possible that such a theory is in fact impossible, even though there is a definitive principle of that kind. In other words, nature may allow us to have such a principle, and yet disallow us to conceive how it ultimately works, including why we must have such a principle. We may, however, have partial theories conforming to such a principle or, since there may be more than one, such principle. In short, you don’t need to concede even this point to the opponent of epistemological principles.

Secondly, while it may be true that "the non existence of an absolute reference frame" (p. 2) is a dogma (even though some see it as an epistemological principle [p. 3]), I am not sure that "denying the existence of an absolute [reference frame?] is a relic of the repudiation of the anthropocentrism that followed the Keplerian revolution," that is, that it is only a relic of this repudiation. There are physical reasons for this "dogma" (if it is one), especially in Einstein’s special relativity, reasons that are not at all anthropocentric. Also, do you mean by "an absolute" here "an absolute reference frame" or any "absolute"?

Thank you!

Arkady Plotnitsky

Purdue University

email: plotnits@purdue.edu

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Dear Arkady

thank you for your interesting post, which further clarify my point expressed in a too succint way. I agree with you completely that having epistemological principles is not sufficient to axiomatize a full theory, but we cannot exclude that there is a sufficiently complete set of them, and this seems to me more logically well defined than the not well specified dream of the "final theory" of Weinberg et al. But, in any case, there is no doubt that we cannot dismiss principles of epistemological nature, which are truly meta-theoretical laws. And this was supposedly the case of the principle of relativity-I'm saying the one of Galileo-of which Enstein's principle is just a thorough specification, with the inclusion of Maxwell laws.

Regarding the relativity principle, I anyway agree with you that it is more than a reaction to anthropocentrism, since we witness the principle at work everyday. However, everyday we also see that Earth is flat, but we know taht this is only an approximation, and actually Earth is round. Similarly, the relativity principle may just be an approximate one (and violations of Lorentz covariance are becoming more and more popular in the community). What I am disputing here is that the relativity principle be a truly epistemological one (a thing that I believed for many years), in the sense that it is not logically necessary in order to formulate the physical law. As I noticed in my essay, one can easily formulate the law in a preferred system (playing the role of the Newtonian "absolute") and then transform it to any reference system. And this is what in practice we do normally when invoking the reference system of fixed stars to define an inertial frame (since, as you know, the definition of inertial frame is circular!). And if you ask a cosmologist, he will agree that e.g. the background radiation is a preferred frame that one can experimentally establish even inside a blind black-box.

Thank you so much for your erudite and relevant comments, which gave me the opportunity of clarifying more. I'm looking forward to having the pleasure of discussing more with you also in person.

With my best regards

Mauro

thank you for your interesting post, which further clarify my point expressed in a too succint way. I agree with you completely that having epistemological principles is not sufficient to axiomatize a full theory, but we cannot exclude that there is a sufficiently complete set of them, and this seems to me more logically well defined than the not well specified dream of the "final theory" of Weinberg et al. But, in any case, there is no doubt that we cannot dismiss principles of epistemological nature, which are truly meta-theoretical laws. And this was supposedly the case of the principle of relativity-I'm saying the one of Galileo-of which Enstein's principle is just a thorough specification, with the inclusion of Maxwell laws.

Regarding the relativity principle, I anyway agree with you that it is more than a reaction to anthropocentrism, since we witness the principle at work everyday. However, everyday we also see that Earth is flat, but we know taht this is only an approximation, and actually Earth is round. Similarly, the relativity principle may just be an approximate one (and violations of Lorentz covariance are becoming more and more popular in the community). What I am disputing here is that the relativity principle be a truly epistemological one (a thing that I believed for many years), in the sense that it is not logically necessary in order to formulate the physical law. As I noticed in my essay, one can easily formulate the law in a preferred system (playing the role of the Newtonian "absolute") and then transform it to any reference system. And this is what in practice we do normally when invoking the reference system of fixed stars to define an inertial frame (since, as you know, the definition of inertial frame is circular!). And if you ask a cosmologist, he will agree that e.g. the background radiation is a preferred frame that one can experimentally establish even inside a blind black-box.

Thank you so much for your erudite and relevant comments, which gave me the opportunity of clarifying more. I'm looking forward to having the pleasure of discussing more with you also in person.

With my best regards

Mauro

Hi Mauro, nice one. Like the idea that quantumness is required for the emergence of space-time at the automaton level. I've always been a believer of classicization of a default quantum theory rather than the other way around. I'd like to see how the automaton formulation relates to the Frobenius algebras which correspond with the dots in our graphical language. They represent classical context of which space is one. We can discuss this in Barbados next year!

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Thank you Bob. The quantum nature of the causal network is crucial for getting the isotropy of space for relativistic momenta, and this is because informations flows in a superposition of paths. Otherwise, if you want the causal network to be classical, you need it to be random, as in the Rafael Sorking approach. But then you loose the nice automaton framework for Dirac. In my knowledge, by no way...

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Thank you Bob. The quantum nature of the causal network is crucial for getting the isotropy of space for relativistic momenta, and this is because informations flows in a superposition of paths. Otherwise, if you want the causal network to be classical, you need it to be random, as in the Rafael Sorking approach. But then you loose the nice automaton framework for Dirac. In my knowledge, by no way you can get the same physics of Dirac by a classical random walk. The analogy with your Frobenius algebra is exactly the same as with the operational boxes of Giluio me and Paolo in our informational derivation of quantum theory. We should discuss about this at length in person, and Barbados could be a very inspiring place!

See you soon

My best

Mauro

See you soon

My best

Mauro

Dear Giacomo Mauro D\'Ariano,

I have taken a quick look at your essay. I love that it is written very clearly in comprehensible language and that it is set out into easily digestable sections. You examine the way in which ideas are considered in physics, making it very relevant to the essay question. It strikes me as an essay that I must return to, to read thoroughly, as there is a lot I could learn from it. Well done, Good luck in the contest, Georgina : )

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I have taken a quick look at your essay. I love that it is written very clearly in comprehensible language and that it is set out into easily digestable sections. You examine the way in which ideas are considered in physics, making it very relevant to the essay question. It strikes me as an essay that I must return to, to read thoroughly, as there is a lot I could learn from it. Well done, Good luck in the contest, Georgina : )

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Dear Georgina,

thank you very much for your compliments, which are exactly what desired most to hear, namely that the essay is easily understandable and every point is made clear. I thought for now many years about the issue of reformulating physics on more solid principles. What I consider amazing about the principles proposed in my essay is the fact that by just pursuing them, and without anything else, one can derive so much physics! I strongly believe in this quantum automata program: we are now four people working on it, temporary with no funds, and I hope that this essay will help the program to take off.

thank you very much for your compliments, which are exactly what desired most to hear, namely that the essay is easily understandable and every point is made clear. I thought for now many years about the issue of reformulating physics on more solid principles. What I consider amazing about the principles proposed in my essay is the fact that by just pursuing them, and without anything else, one can derive so much physics! I strongly believe in this quantum automata program: we are now four people working on it, temporary with no funds, and I hope that this essay will help the program to take off.

If you do not understand why your rating dropped down. As I found ratings in the contest are calculated in the next way. Suppose your rating is and was the quantity of people which gave you ratings. Then you have of points. After it anyone give you of points so you have of points and is the common quantity of the people which gave you ratings. At the same time you will have of points. From here, if you want to be R2 > R1 there must be: or or In other words if you want to increase rating of anyone you must give him more points then the participant`s rating was at the moment you rated him. From here it is seen that in the contest are special rules for ratings. And from here there are misunderstanding of some participants what is happened with their ratings. Moreover since community ratings are hided some participants do not sure how increase ratings of others and gives them maximum 10 points. But in the case the scale from 1 to 10 of points do not work, and some essays are overestimated and some essays are drop down. In my opinion it is a bad problem with this Contest rating process. I hope the FQXI community will change the rating process.

Sergey Fedosin

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Sergey Fedosin

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Dear Sergey

I understand your point, the rating is just the average, but nobody knows the average, so many essay are overestimated, because in order to get them up then people vote 10. I'm not sure, but maybe you are right in proposing the rating being visible. I saw indeed big fluctuations in mine. Last nigth was at the 5th place, now is at the 15th ... I hope that it will remain before 35th, and will not miss the opportunity of a judgement from Referees!

I understand your point, the rating is just the average, but nobody knows the average, so many essay are overestimated, because in order to get them up then people vote 10. I'm not sure, but maybe you are right in proposing the rating being visible. I saw indeed big fluctuations in mine. Last nigth was at the 5th place, now is at the 15th ... I hope that it will remain before 35th, and will not miss the opportunity of a judgement from Referees!

Dear Giacomo

A very interesting essay. I find particularly interesting your purification principle: "that irreversibility and mixing can be always regarded as the result of discarding an environment, otherwise everything being describable in terms of pure states and reversible transformations." The question is who or what decides what is included or discarded, and by what mechanism is this implemented? This is some process or choice that takes place at a different level from that of the dynamics itself. So how does this happen?

I fully agree with your view on infinity: "Richard Feynman himself is reported to like the idea of nite information density, because he felt that there might be something wrong with the old concept of continuous functions. How could there possibly be an infinite amount of information in any finite volume?" Yes indeed.

George Ellis

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A very interesting essay. I find particularly interesting your purification principle: "that irreversibility and mixing can be always regarded as the result of discarding an environment, otherwise everything being describable in terms of pure states and reversible transformations." The question is who or what decides what is included or discarded, and by what mechanism is this implemented? This is some process or choice that takes place at a different level from that of the dynamics itself. So how does this happen?

I fully agree with your view on infinity: "Richard Feynman himself is reported to like the idea of nite information density, because he felt that there might be something wrong with the old concept of continuous functions. How could there possibly be an infinite amount of information in any finite volume?" Yes indeed.

George Ellis

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Dear George,

thank you for your interesting post, which gives to me more opportunity of talking about the principles of Quantum Theory (my joint work with Chiribella and Perinotti). Indeed, what we learn at school is that unitariety of Quantum theory is a rule, but this indeed is not true: the theory can survive without the requirement of unitariety keeping perfect thorough logical coherence, and using quantum channels (completely positive trace-preserving maps) instead. Also the motivation for unitariety that "transformations must be reversible for a closed system" is false, since, strictly speaking, for this purpose one needs the evolution to be just isometric. Requiring that the reverse of the reversible transformation is also reversible is a matter of simplicity. I think that unitariety is just for historical reasons, due to the Schroedinger equation, which, however, is needed for the "mechanics" of the theory, quantization rules and so on. If one wants a theory that is autonomous from the classical one (but from which classical mechanics emerges from pure quantum theory of systems, as for the quantum cellular automaton), then unitariety is not strictly needed for the logical coherence and closure of the theory. In the automaton, however, unitariety is dictated by the requirement of having the Dirac field emerging at the Fermi scale.

Therefore, is up to you to believe that the purification actually exists. We know that Quantum Theory allows for purification of any transformation using an environment (and by the way the purification of the postulate is an isometry, which then we know can be further extended with a unitary). But you are not obliged to have the actual purification: everything works as if the purification exists. If now you ask me for "a mechanism" for such a purification (in case you believe that there is an actual environment), that's an interesting question. Maybe one should try to describe the "informaton" as an incompressible fluid, or something similar. By the way, if one believes that the purification always exists, than also the GRW spontaneous collapse is due to an environment! Which means that GRW is always the same quantum theory, but we just add another hidden quantum field (Bassi would say that it can be done with a classical field, but I'm not sure of this). The true point is to decide what is spontaneous, and what is not-the chicken and the egg again.

Finally, let me say that I liked your essay very much (it was one of the first I read). I can agree with your idea of your top-down causation, within my definition of causality (axiom 1 of QT), and as a Bayesian, in the sense that since causal relations are established by parametric dependences of probabilities, in a Bayesian interpretation they are themselves "beliefs", and such they are established by us, as any theory is formulated (this also agrees with the Humean point of view of causation). And, as such, you are right when you say, "Understanding the emergence of genuine complexity out of the underlying physics depends on recognising this kind of causation".

thank you for your interesting post, which gives to me more opportunity of talking about the principles of Quantum Theory (my joint work with Chiribella and Perinotti). Indeed, what we learn at school is that unitariety of Quantum theory is a rule, but this indeed is not true: the theory can survive without the requirement of unitariety keeping perfect thorough logical coherence, and using quantum channels (completely positive trace-preserving maps) instead. Also the motivation for unitariety that "transformations must be reversible for a closed system" is false, since, strictly speaking, for this purpose one needs the evolution to be just isometric. Requiring that the reverse of the reversible transformation is also reversible is a matter of simplicity. I think that unitariety is just for historical reasons, due to the Schroedinger equation, which, however, is needed for the "mechanics" of the theory, quantization rules and so on. If one wants a theory that is autonomous from the classical one (but from which classical mechanics emerges from pure quantum theory of systems, as for the quantum cellular automaton), then unitariety is not strictly needed for the logical coherence and closure of the theory. In the automaton, however, unitariety is dictated by the requirement of having the Dirac field emerging at the Fermi scale.

Therefore, is up to you to believe that the purification actually exists. We know that Quantum Theory allows for purification of any transformation using an environment (and by the way the purification of the postulate is an isometry, which then we know can be further extended with a unitary). But you are not obliged to have the actual purification: everything works as if the purification exists. If now you ask me for "a mechanism" for such a purification (in case you believe that there is an actual environment), that's an interesting question. Maybe one should try to describe the "informaton" as an incompressible fluid, or something similar. By the way, if one believes that the purification always exists, than also the GRW spontaneous collapse is due to an environment! Which means that GRW is always the same quantum theory, but we just add another hidden quantum field (Bassi would say that it can be done with a classical field, but I'm not sure of this). The true point is to decide what is spontaneous, and what is not-the chicken and the egg again.

Finally, let me say that I liked your essay very much (it was one of the first I read). I can agree with your idea of your top-down causation, within my definition of causality (axiom 1 of QT), and as a Bayesian, in the sense that since causal relations are established by parametric dependences of probabilities, in a Bayesian interpretation they are themselves "beliefs", and such they are established by us, as any theory is formulated (this also agrees with the Humean point of view of causation). And, as such, you are right when you say, "Understanding the emergence of genuine complexity out of the underlying physics depends on recognising this kind of causation".

Thanks for that response, appreciated.

"By the way, if one believes that the purification always exists, than also the GRW spontaneous collapse is due to an environment!" - yes indeed.

"Which means that GRW is always the same quantum theory, but we just add another hidden quantum field (Bassi would say that it can be done with a classical field, but I'm not sure of this)." - well I think there is a god case that the "hidden variable: is the local context. It is hidden because its variables are located at the level above the one that one has in mind - and this environment is just taken for granted.

George

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"By the way, if one believes that the purification always exists, than also the GRW spontaneous collapse is due to an environment!" - yes indeed.

"Which means that GRW is always the same quantum theory, but we just add another hidden quantum field (Bassi would say that it can be done with a classical field, but I'm not sure of this)." - well I think there is a god case that the "hidden variable: is the local context. It is hidden because its variables are located at the level above the one that one has in mind - and this environment is just taken for granted.

George

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Dear Mauro,

Good to see you rising up to the top where you belong! Take care,

Ben

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Good to see you rising up to the top where you belong! Take care,

Ben

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Dear Ben

thank you very much for your support. I just discover today your really interesting reply to my post on your thread: I'm going to think about, and try to answer this same evening.

As regards my position in the list, it is fluctuating, so let me cross fingers.

My best to you,

I'm happy that you are at the top.

Mauro

thank you very much for your support. I just discover today your really interesting reply to my post on your thread: I'm going to think about, and try to answer this same evening.

As regards my position in the list, it is fluctuating, so let me cross fingers.

My best to you,

I'm happy that you are at the top.

Mauro

You mainstreamsians controle science for over 50 years. You mainstream and Hawking failed. The bad science is because of the Top-Down controle of the people like you. Why do you need money and fame from FQXI where the authors are mostly jobless, are mostly independent researchers, are mostly viXra.org authers? Do you need money and fame by controling jobless???

I want to rate you 0!

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I want to rate you 0!

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MAX PLANK:

An important scientific innovation rarely makes its way by gradually winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.

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An important scientific innovation rarely makes its way by gradually winning over and converting its opponents; it rarely happens that Saul becomes Paul. What does happen is that its opponents gradually die out and that the growing generation is familiarized with the idea from the beginning.

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Sergey G Fedosin is bombing entrants' boards with the same "why your rating has dropped" message. They are all dated Oct. 4... same message.

WTH? I've seen one fine essay drop 89 (eighty-nine) positions, in "Community Rating" in the past 24 hours, and “Sergey’s note” came BEFORE it plummeted. Hmm.

The vote/scaling of this contest is quite nebulous.

"Hackers Rule!", I suppose!

Well??? What else is one to think? The General Public is... Watching…

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WTH? I've seen one fine essay drop 89 (eighty-nine) positions, in "Community Rating" in the past 24 hours, and “Sergey’s note” came BEFORE it plummeted. Hmm.

The vote/scaling of this contest is quite nebulous.

"Hackers Rule!", I suppose!

Well??? What else is one to think? The General Public is... Watching…

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This corrupted FQXI contest is worse than the Voice Of China showoff.

This corrupted FQXI contest is worse than the USA presidency campaign.

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This corrupted FQXI contest is worse than the USA presidency campaign.

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Hello

You know , my pc is totally checked, people implies confusions. They even superimpose the algorythms for the strategy. They delete, they lie, they invent false name,.....In fact my theory is revolutionary, I can understand but there I need help because it is not integre and well this comportment.

China, India, or USA. That is the question.

Who imply this confusion? me...

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You know , my pc is totally checked, people implies confusions. They even superimpose the algorythms for the strategy. They delete, they lie, they invent false name,.....In fact my theory is revolutionary, I can understand but there I need help because it is not integre and well this comportment.

China, India, or USA. That is the question.

Who imply this confusion? me...

view entire post

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Dear Mauro,

I thought you might be interested in the following idea I posted on George Ellis's thread. Since you also are working with "nonmanifold models that emphasize the role of causality," I thought I'd copy the idea here, although I know you don't favor the causal sets approach.

**********

After initially struggling with the idea, I’ve been thinking a bit about how your [George’s] top-down causation idea might look from the perspective of nonmanifold models of fundamental spacetime structure that emphasize the role of causality. It seems that top-down causation might provide an interesting new perspective on such models. For definiteness and simplicity, I use Rafael Sorkin’s causal sets approach as an example.

Causal sets, as currently conceived, are by definition purely bottom-up at the classical level. Causality is modeled as an irreflexive, acyclic, interval-finite binary relation on a set, whose elements are explicitly identified as “events.” Since causal structure alone is not sufficient to recover a metric, each element is assigned one fundamental volume unit. Sorkin abbreviates this with the phrase, “order plus number equals geometry.” This is a special case of what I call the causal metric hypothesis.

In the context of classical spacetime, top-down causation might be summarized by the statement, “causal relationships among subsets of spacetime are not completely reducible to causal relations among their constituent events.” In this context, the abstract causal structure exists at the level of the power set of classical spacetime, i.e., the set whose elements are subsets of spacetime. Discrete models very similar to causal sets could be employed, with the exception that the elements would correspond not to events, but to families of events. Two-way relationships would also come into play.

Initially this idea bothered me because of locality issues, but such a model need not violate conventional classical locality, provided that appropriate constraints involving high-level and low-level relations are satisfied.

This idea is interesting to me for the following reasons.

1. The arguments for top-down causation presented by you [George] and others are rather convincing, and one would like to incorporate such considerations into approaches to “fundamental theories,” particularly those emphasizing causality.

2. One of the principal difficulties for “pure causal theories” is their parsimony; it is not clear that they contain enough structure to recover established physics. Top-down causation employed as I described (i.e. power-set relations) provides “extra structure” without “extra hypotheses” in the sense that one is still working with the same (or similar) abstract mathematical objects. It is the interpretation of the “elements” and “relations” that becomes more general. In particular, the causal metric hypothesis still applies, although not in the form “order plus number equals geometry.”

3. There is considerable precedent, at least in mathematics, for this type of generalization. For example, Grothendieck’s approach to algebraic geometry involves “higher-dimensional points” corresponding to subvarieties of algebraic varieties, and the explicit consideration of these points gives the scheme structure, which has considerable advantages. In particular, the scheme structure is consistent with the variety structure but brings to light “hidden information.” This may be viewed as an analogy to the manner in which higher-level causal structure is consistent with lower-level structure (e.g. does not violate locality), but includes important information that might be essential in recovering established physics.

4. As far as I know, this approach has not yet been explicitly developed.

I’d appreciate any thoughts you might have on this.

**************

I’d appreciate your thoughts on this too! Take care,

Ben

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I thought you might be interested in the following idea I posted on George Ellis's thread. Since you also are working with "nonmanifold models that emphasize the role of causality," I thought I'd copy the idea here, although I know you don't favor the causal sets approach.

**********

After initially struggling with the idea, I’ve been thinking a bit about how your [George’s] top-down causation idea might look from the perspective of nonmanifold models of fundamental spacetime structure that emphasize the role of causality. It seems that top-down causation might provide an interesting new perspective on such models. For definiteness and simplicity, I use Rafael Sorkin’s causal sets approach as an example.

Causal sets, as currently conceived, are by definition purely bottom-up at the classical level. Causality is modeled as an irreflexive, acyclic, interval-finite binary relation on a set, whose elements are explicitly identified as “events.” Since causal structure alone is not sufficient to recover a metric, each element is assigned one fundamental volume unit. Sorkin abbreviates this with the phrase, “order plus number equals geometry.” This is a special case of what I call the causal metric hypothesis.

In the context of classical spacetime, top-down causation might be summarized by the statement, “causal relationships among subsets of spacetime are not completely reducible to causal relations among their constituent events.” In this context, the abstract causal structure exists at the level of the power set of classical spacetime, i.e., the set whose elements are subsets of spacetime. Discrete models very similar to causal sets could be employed, with the exception that the elements would correspond not to events, but to families of events. Two-way relationships would also come into play.

Initially this idea bothered me because of locality issues, but such a model need not violate conventional classical locality, provided that appropriate constraints involving high-level and low-level relations are satisfied.

This idea is interesting to me for the following reasons.

1. The arguments for top-down causation presented by you [George] and others are rather convincing, and one would like to incorporate such considerations into approaches to “fundamental theories,” particularly those emphasizing causality.

2. One of the principal difficulties for “pure causal theories” is their parsimony; it is not clear that they contain enough structure to recover established physics. Top-down causation employed as I described (i.e. power-set relations) provides “extra structure” without “extra hypotheses” in the sense that one is still working with the same (or similar) abstract mathematical objects. It is the interpretation of the “elements” and “relations” that becomes more general. In particular, the causal metric hypothesis still applies, although not in the form “order plus number equals geometry.”

3. There is considerable precedent, at least in mathematics, for this type of generalization. For example, Grothendieck’s approach to algebraic geometry involves “higher-dimensional points” corresponding to subvarieties of algebraic varieties, and the explicit consideration of these points gives the scheme structure, which has considerable advantages. In particular, the scheme structure is consistent with the variety structure but brings to light “hidden information.” This may be viewed as an analogy to the manner in which higher-level causal structure is consistent with lower-level structure (e.g. does not violate locality), but includes important information that might be essential in recovering established physics.

4. As far as I know, this approach has not yet been explicitly developed.

I’d appreciate any thoughts you might have on this.

**************

I’d appreciate your thoughts on this too! Take care,

Ben

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Dear Ben,

I will answer to you soon thorougly next week, since these last two have been the busiest of the year. I can anticipate that I'm not against the top-down causation of Ellis, and indeed I already commented on this to Ellis: his top-down causation approach fully agrees with my idea of causality. However, even though it is the right approach in general, it is not suitable for formulating theories that, by themselves and by definition must be bottom-up, as is the case of quantum field theory. Regarding Sorking approach, I can anticipate to you that I think that it will never work for quantum field theory, hence for a quantum theory of gravity, but on this I will write more next week.

I find this way of discussing physics very stimulating, and I'm looking forward to continuing our discussion. I want also continue with Ellis about the top-down approach, about which I had thinking seriously only quite recently.

Until next

Cheers

Mauro

I will answer to you soon thorougly next week, since these last two have been the busiest of the year. I can anticipate that I'm not against the top-down causation of Ellis, and indeed I already commented on this to Ellis: his top-down causation approach fully agrees with my idea of causality. However, even though it is the right approach in general, it is not suitable for formulating theories that, by themselves and by definition must be bottom-up, as is the case of quantum field theory. Regarding Sorking approach, I can anticipate to you that I think that it will never work for quantum field theory, hence for a quantum theory of gravity, but on this I will write more next week.

I find this way of discussing physics very stimulating, and I'm looking forward to continuing our discussion. I want also continue with Ellis about the top-down approach, about which I had thinking seriously only quite recently.

Until next

Cheers

Mauro

Dear Giacomo Mauro D'Ariano,

In Coherently-cyclic cluster-matter paradigm of universe, information transfer is the transfer of string-segment from source-string to observer-string that is in continuum, in that the period of time of eigen-rotational cycle of the source-string and that of the observer-string are in reference with the period of time of eigen-rotational cycle of the cluster-matter holon they belong on information transfer. In this paradigm a periodization hierarchy is expressional for quantum information transfer in group waves, in that the difference in emergence of gravity on eigen-rotations of source-string and observer-string is causal for the transfer of information as gravitational mass of string-segment and thus two different time-intervals in temporal sequence is comparable in this paradigm.

With best wishes

Jayakar

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In Coherently-cyclic cluster-matter paradigm of universe, information transfer is the transfer of string-segment from source-string to observer-string that is in continuum, in that the period of time of eigen-rotational cycle of the source-string and that of the observer-string are in reference with the period of time of eigen-rotational cycle of the cluster-matter holon they belong on information transfer. In this paradigm a periodization hierarchy is expressional for quantum information transfer in group waves, in that the difference in emergence of gravity on eigen-rotations of source-string and observer-string is causal for the transfer of information as gravitational mass of string-segment and thus two different time-intervals in temporal sequence is comparable in this paradigm.

With best wishes

Jayakar

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www.CIGTheory.com is a Causal Theory cuz it brings determinism back into quantum.

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