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**Anonymous**: *on* 5/20/20 at 10:12am UTC, wrote Thanks for sharing this. Here they have chosen the topic of the discreet...

**Anonymous**: *on* 6/6/11 at 17:34pm UTC, wrote Peter, Best wishes for the future too! I wish you and all the...

**Peter Jackson**: *on* 6/6/11 at 8:43am UTC, wrote Paul Sincerest commiserations at your undeserved apparent omission from...

**Paul Halpern**: *on* 4/27/11 at 23:05pm UTC, wrote Thanks so much, Peter! I appreciate your comments! All the best, Paul

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FQXi FORUM

September 18, 2021

CATEGORY:
Is Reality Digital or Analog? Essay Contest (2010-2011)
[back]

TOPIC: The Discreet Charm of the Discrete by Paul Halpern [refresh]

TOPIC: The Discreet Charm of the Discrete by Paul Halpern [refresh]

In this essay I argue that the large discrepancy between the calculated vacuum energy density of the universe and the amount corresponding to the observed acceleration of spatial expansion places a lower limit on the wavelengths of elementary fields. I demonstrate how the lowest wavelength, highest-energy fields, which I call holons, could form the basis for a digital system akin to a structurally dynamic cellular automaton. I show how such a system could model the growth of form, and offer an increasing topological entropy corresponding to the forward arrow of time. I examine the points of commonality between the holon hypothesis and the holographic principle, but argue that the two are independent, as the former does not necessitate reference to a boundary. Finally, I comment on the development of interferometry tests for the graininess of space that could also point to a fundamental minimum wavelength.

Paul Halpern is a theoretical physicist specializing in general relativity, complex systems, and the history of physics. He is Professor of Physics at the University of the Sciences in Philadelphia. In 1996, he was a Fulbright Scholar researching evolutionary algorithms at the Humboldt University of Berlin. In 2002, he received a Guggenheim Fellowship to study the history of higher dimensional theories. Halpern has published twelve books, along with more than thirty research articles and forty scholarly presentations. In recognition of his science writing he was the recipient of an Athenaeum Literary Award.

Hi Professor Halpern,

It was a pleasure to read your essay, and thank you for bringing structurally dynamic cellular automata to my attention. My research is in the domain of such models and this was a particular variant of which I was not aware.

Out of curiosity, do you see synchronous update of the sort employed in cellular automata to be central to the success of such a model, or do you think something more like Langton's Ant would suffice if operating over the right structure?

(If you're interested in algorithms of this sort, I would draw your attention to my own essay, which outlines several, which I've used for modeling both particle phenomena and the generation of spacetime geometry.)

Alex

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It was a pleasure to read your essay, and thank you for bringing structurally dynamic cellular automata to my attention. My research is in the domain of such models and this was a particular variant of which I was not aware.

Out of curiosity, do you see synchronous update of the sort employed in cellular automata to be central to the success of such a model, or do you think something more like Langton's Ant would suffice if operating over the right structure?

(If you're interested in algorithms of this sort, I would draw your attention to my own essay, which outlines several, which I've used for modeling both particle phenomena and the generation of spacetime geometry.)

Alex

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Hi Alex,

Thanks for your kind comments. Glad to see that you are interested in structurally dynamic cellular automata. I will certainly have a look at your essay -- sounds very interesting! In answer to your question, one of the advantages of cellular automata is their flexibility, so synchronous updates would not be essential to the model's success. CA that display highly complex structures, resembling universal Turing machines, such as Langton's Ant or a glider gun, represent promising steps forward in trying to link discrete models with the dynamics of nature.

Thanks for your kind comments. Glad to see that you are interested in structurally dynamic cellular automata. I will certainly have a look at your essay -- sounds very interesting! In answer to your question, one of the advantages of cellular automata is their flexibility, so synchronous updates would not be essential to the model's success. CA that display highly complex structures, resembling universal Turing machines, such as Langton's Ant or a glider gun, represent promising steps forward in trying to link discrete models with the dynamics of nature.

Dear Professor Paul Halpern,

Holoarchy of Holon is a good philosophy to elucidate a Hierarchical clustering in, Coherently-cyclic cluster-matter universe model.

Thanking you.

With Best Wishes,

Jayakar Johnson Joseph

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Holoarchy of Holon is a good philosophy to elucidate a Hierarchical clustering in, Coherently-cyclic cluster-matter universe model.

Thanking you.

With Best Wishes,

Jayakar Johnson Joseph

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Hello professor Halpern, I was lost by the complexity of your essay but wondered whether the Archimedes screw is a structurally dynamic cellular automata?

Alan

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Alan

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Hi Paul,

I like the holon idea and your essay, holons are something like my "particles made by their properties" in my essay, so maybe the ideas there are not so strange as it appears to be (and I have to read something more about holons and related stuff :-)

But, in my opinion, holons assumed to be "... a photon (or other fundamental field) of highest energy and lowest wavelength" should be highly "reactive", and a Universe filled up with such particles, permeating everybody and anything, would be an extremely dangerous place. A holon particle stream would be by definition far more destructive than cosmic gamma-ray bursts.

What comes me to mind as a resolution to this problem is an idea of "holon confinement", e.g. in a string ? AFAIK, string confinement of quarks was proposed in the literature sometime ago.

Best regards,

-Joachim.

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I like the holon idea and your essay, holons are something like my "particles made by their properties" in my essay, so maybe the ideas there are not so strange as it appears to be (and I have to read something more about holons and related stuff :-)

But, in my opinion, holons assumed to be "... a photon (or other fundamental field) of highest energy and lowest wavelength" should be highly "reactive", and a Universe filled up with such particles, permeating everybody and anything, would be an extremely dangerous place. A holon particle stream would be by definition far more destructive than cosmic gamma-ray bursts.

What comes me to mind as a resolution to this problem is an idea of "holon confinement", e.g. in a string ? AFAIK, string confinement of quarks was proposed in the literature sometime ago.

Best regards,

-Joachim.

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Hi Joachim,

Glad that you like the holon idea. Interesting point you raise. My intention, however is to suggest these as limiting particle states, meaning that the universe today would be filled with particles spanning a wide range of frequencies (and energies). The spectrum of frequencies would be consistent with the current frigid temperature of space. However, instead of an unlimited range of frequencies, holon states would constitute an upper bound. This would cap the vacuum energy density at a value consistent with the amount needed for the observed acceleration of spatial expansion.

Best regards,

Paul

Glad that you like the holon idea. Interesting point you raise. My intention, however is to suggest these as limiting particle states, meaning that the universe today would be filled with particles spanning a wide range of frequencies (and energies). The spectrum of frequencies would be consistent with the current frigid temperature of space. However, instead of an unlimited range of frequencies, holon states would constitute an upper bound. This would cap the vacuum energy density at a value consistent with the amount needed for the observed acceleration of spatial expansion.

Best regards,

Paul

Dear Paul,

I find your proposal intriguing and intelligent. The analogy you draw, between the ‘ultraviolet catastrophe’ and the discrepancy between theoretical and observed values of the cosmological constant, seems apt. In that context, however, I would point out that Planck’s “solution” (to the former) was purely a mathematical device—the beginning, not the end, of many unresolved issues.

I also liked your “mailbox” metaphor. It might prove helpful in clarifying the nature of ‘information’, which seems to be a glibly misused concept these days. In a number of submitted essays, there is reference to information being ‘stored’ or ‘encoded’, when the author simply means that there is continuity within reality itself, and from one description of reality to another, (at another time, for instance). While organisms explicitly need to model their environment, encoding it in some representation, there is no reason to assume that physical reality in general does this. The information is encoded by physicists, not necessarily by the world they study.

Thanks and best wishes,

Dan

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I find your proposal intriguing and intelligent. The analogy you draw, between the ‘ultraviolet catastrophe’ and the discrepancy between theoretical and observed values of the cosmological constant, seems apt. In that context, however, I would point out that Planck’s “solution” (to the former) was purely a mathematical device—the beginning, not the end, of many unresolved issues.

I also liked your “mailbox” metaphor. It might prove helpful in clarifying the nature of ‘information’, which seems to be a glibly misused concept these days. In a number of submitted essays, there is reference to information being ‘stored’ or ‘encoded’, when the author simply means that there is continuity within reality itself, and from one description of reality to another, (at another time, for instance). While organisms explicitly need to model their environment, encoding it in some representation, there is no reason to assume that physical reality in general does this. The information is encoded by physicists, not necessarily by the world they study.

Thanks and best wishes,

Dan

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Dear Dan,

Thanks for your thoughtful remarks! Yes you are absolutely correct that Planck meant his resolution of the blackbody radiation "ultraviolet catastrophe" as a mathematical device, rather than as a physical quantum. It was Einstein who brilliantly suggested in his theory of the photoelectric effect that the quantum is a physical notion. Glad you like the mailbox metaphor! Interesting what you write about the distinction between encoding information and maintaining continuity within reality.

Many best wishes,

Paul

Thanks for your thoughtful remarks! Yes you are absolutely correct that Planck meant his resolution of the blackbody radiation "ultraviolet catastrophe" as a mathematical device, rather than as a physical quantum. It was Einstein who brilliantly suggested in his theory of the photoelectric effect that the quantum is a physical notion. Glad you like the mailbox metaphor! Interesting what you write about the distinction between encoding information and maintaining continuity within reality.

Many best wishes,

Paul

Hi both,

As part-historian of physics, I feel I have to clear up a myth contained in here. Planck did not introduce the quantum of action (initially written as an epsilon, to be taken to zero) to resolve a problem in the UV part of the spectrum (the bad behaviour predicted by the Rayleigh-Jeans law), but rather with the Wien law, in the infrared part of the spectrum. It was Wien's law that he sought to recover with his own formula for the blackbody energy. It really ought to be called the "infrared catastrophe". The historical evidence points to the fact that Planck was not aware of Rayleigh's analysis when he proposed his idea - Rayleigh's proposal came in June, and Planck's in the October of 1900 - there was no correspondence and no publication at this stage). Also, quite interestingly, the name "ultraviolet catastrophe" wasn't coined until 1911, by Paul Ehrenfest.

Best,

Dean

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As part-historian of physics, I feel I have to clear up a myth contained in here. Planck did not introduce the quantum of action (initially written as an epsilon, to be taken to zero) to resolve a problem in the UV part of the spectrum (the bad behaviour predicted by the Rayleigh-Jeans law), but rather with the Wien law, in the infrared part of the spectrum. It was Wien's law that he sought to recover with his own formula for the blackbody energy. It really ought to be called the "infrared catastrophe". The historical evidence points to the fact that Planck was not aware of Rayleigh's analysis when he proposed his idea - Rayleigh's proposal came in June, and Planck's in the October of 1900 - there was no correspondence and no publication at this stage). Also, quite interestingly, the name "ultraviolet catastrophe" wasn't coined until 1911, by Paul Ehrenfest.

Best,

Dean

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Dean,

Thanks for your comments. I would be indeed be interested in reading such evidence about when Planck became aware of Rayleigh's work. Yes it is interesting that the term "ultraviolet catastrophe" was coined by Ehrenfest, even though the concept was introduced beforehand.

Best regards,

Paul

Thanks for your comments. I would be indeed be interested in reading such evidence about when Planck became aware of Rayleigh's work. Yes it is interesting that the term "ultraviolet catastrophe" was coined by Ehrenfest, even though the concept was introduced beforehand.

Best regards,

Paul

Dear Professor Halpern,

Your essay provides much food for thought. I would like to know how in the scenario of a holon falling into a black hole this idea can be reconciled with the GR prediction that the holon becomes gravitationally blueshifted.

Thank you,

Armin

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Your essay provides much food for thought. I would like to know how in the scenario of a holon falling into a black hole this idea can be reconciled with the GR prediction that the holon becomes gravitationally blueshifted.

Thank you,

Armin

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Dear Armin,

Thanks for your kind comment! That is a fascinating question. It is unclear if GR applies in its classical form down to such minuscule length scales. According to the standard line of reasoning, because of the proximity to the Planck scale, one would need to replace classical GR with quantum gravity. Alternatively, let us consider the discrete approach, with fields emerging from an evolving network of connections similar to structurally dynamic cellular automata. In that case gravitational blueshifts or redshifts would represent the impact of regions with different topologies upon the size (wavelength) of structures within the network. The holon size would remain the lower limit of such distortions, similar to a single stone representing the minimal structure in the game Go.

Thanks for your kind comment! That is a fascinating question. It is unclear if GR applies in its classical form down to such minuscule length scales. According to the standard line of reasoning, because of the proximity to the Planck scale, one would need to replace classical GR with quantum gravity. Alternatively, let us consider the discrete approach, with fields emerging from an evolving network of connections similar to structurally dynamic cellular automata. In that case gravitational blueshifts or redshifts would represent the impact of regions with different topologies upon the size (wavelength) of structures within the network. The holon size would remain the lower limit of such distortions, similar to a single stone representing the minimal structure in the game Go.

Paul,

Incisive argument for holons that led me with the weight of your argument in each direction you took including your holon thrust.

I haven't heard many looks into a dark energy explanation that work.

Quite persuasive and scholarly.

Jim Hoover

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Incisive argument for holons that led me with the weight of your argument in each direction you took including your holon thrust.

I haven't heard many looks into a dark energy explanation that work.

Quite persuasive and scholarly.

Jim Hoover

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Only this Essay and my comment reminding about Holometer

http://www.fqxi.org/community/forum/topic/946

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http://www.fqxi.org/community/forum/topic/946

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Hi dear Prof.Halpern,

Congratulations, the evolution is so important.....quantum spheres.....H....CNO..Hydrospheroids about 3.4billions......CH4 H20 HCN H2C2 NH3....time evolution rotating spinning proprotions.........UNICELLS....differenciation......plurice

lls.....sponges ..mmedusas.......humans................UNIVERSAL SPHERE.

The encoding is rational simply.

Best Regards and good luck

Steve

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Congratulations, the evolution is so important.....quantum spheres.....H....CNO..Hydrospheroids about 3.4billions......CH4 H20 HCN H2C2 NH3....time evolution rotating spinning proprotions.........UNICELLS....differenciation......plurice

lls.....sponges ..mmedusas.......humans................UNIVERSAL SPHERE.

The encoding is rational simply.

Best Regards and good luck

Steve

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Dear Steve,

Thanks for the kind comments and for pointing me to your theory of spinning spheres!

Best regards,

Paul

Thanks for the kind comments and for pointing me to your theory of spinning spheres!

Best regards,

Paul

Dear Paul,

You are welcome.I liked your essay, it's rational, we need that.

Best Regards

Steve

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You are welcome.I liked your essay, it's rational, we need that.

Best Regards

Steve

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Dear Paul Halpern

I thoroughly enjoyed your essay, that started with a reference to the much-maligned Lord Kelvin. He also conjectured that the ether is made up of 'knots' which may well describe holons or twistors or the lattice nodes of my own theory. I have tried to show in my in my earlier 2005 Beautiful Universe paper on which my present fqxi paper is based that if these universal building blocks have dielectric properties and angular momentum, their precise mutual interactions may well account for matter, space, radiation and dark matter. Dark energy will be the natural result of the mutual electrostatic repulsion of these nodes, probably self-assembled in an FCC crystal-like configeration. I also proposed experiments to test the graininess of the vacuum. In a fqxi discussion here with Tommaso Bolognesi I proposed a variation of my experiment in which two parrallel standing waves in vacuum may exhibit moire patterns with a phase much larger than the wavelength of the original universal node (or holon - I like the word and will check Koestler's book) length. I would greatly appreciate your reading my papers and hearing your expert reaction.

With best wishes.

Vladimir Tamari

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I thoroughly enjoyed your essay, that started with a reference to the much-maligned Lord Kelvin. He also conjectured that the ether is made up of 'knots' which may well describe holons or twistors or the lattice nodes of my own theory. I have tried to show in my in my earlier 2005 Beautiful Universe paper on which my present fqxi paper is based that if these universal building blocks have dielectric properties and angular momentum, their precise mutual interactions may well account for matter, space, radiation and dark matter. Dark energy will be the natural result of the mutual electrostatic repulsion of these nodes, probably self-assembled in an FCC crystal-like configeration. I also proposed experiments to test the graininess of the vacuum. In a fqxi discussion here with Tommaso Bolognesi I proposed a variation of my experiment in which two parrallel standing waves in vacuum may exhibit moire patterns with a phase much larger than the wavelength of the original universal node (or holon - I like the word and will check Koestler's book) length. I would greatly appreciate your reading my papers and hearing your expert reaction.

With best wishes.

Vladimir Tamari

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Dear Vladimir,

Thanks for your insightful comments. I'll certainly take a look at your papers -- sounds intriguing!

Best wishes,

Paul

Thanks for your insightful comments. I'll certainly take a look at your papers -- sounds intriguing!

Best wishes,

Paul

For me you are the two best, you merit to win.

Best Regards to both of you.

Steve

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Best Regards to both of you.

Steve

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Dear Paul Halpern,

''Hogan and Chou discover, through their holometer experiment, evidence that light's motion follows discrete steps''.

Because of Heisenberg uncertainty the position of photon is uncertain, so you'll never see evidence that light's motion follows discrete steps.

Since you are interested in discrete spacetime, please look here. The hole model of discontinuous spacetime can explain gravitation, inertia and most of the quantum phenomena. How about vacuum holes in your model?(Don't forget to vote(:

Regards

Constantin

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''Hogan and Chou discover, through their holometer experiment, evidence that light's motion follows discrete steps''.

Because of Heisenberg uncertainty the position of photon is uncertain, so you'll never see evidence that light's motion follows discrete steps.

Since you are interested in discrete spacetime, please look here. The hole model of discontinuous spacetime can explain gravitation, inertia and most of the quantum phenomena. How about vacuum holes in your model?(Don't forget to vote(:

Regards

Constantin

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Dear Constantin,

Interesting point, however I think they are hoping to see these subtle path differences (reflected in the transverse components) through highly precise interferometry. Trying to measure the exact position and momentum of a photon simultaneously (along the same axis) would be ruled out by the uncertainty principle, but that is not the case here.

I look forward to reading your essay. Sounds interesting. Thanks for the link!

Best wishes,

Paul

Interesting point, however I think they are hoping to see these subtle path differences (reflected in the transverse components) through highly precise interferometry. Trying to measure the exact position and momentum of a photon simultaneously (along the same axis) would be ruled out by the uncertainty principle, but that is not the case here.

I look forward to reading your essay. Sounds interesting. Thanks for the link!

Best wishes,

Paul

Dear Professor Halpern,

Let me start by saying that I enjoyed the mix of the historical with modern conjectural views toward physics displayed by your essay. One question. Have you considered the possible role of The Extended Theories of Gravity in which the cosmos possesses an intrinsic curvature as an alternative to the Standard Model with respect to the many open cosmological questions we now face? I would point you toward Christian Corda's excellent essay as well as own. In my own simple approach, I show that the cosmos must have an intrinsic curvature for a very elementary reason. As for the observations that lead to the DE hypothesis, they have to rate as the most exciting discovery since Hubble.

Have a great day,

Dan

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Let me start by saying that I enjoyed the mix of the historical with modern conjectural views toward physics displayed by your essay. One question. Have you considered the possible role of The Extended Theories of Gravity in which the cosmos possesses an intrinsic curvature as an alternative to the Standard Model with respect to the many open cosmological questions we now face? I would point you toward Christian Corda's excellent essay as well as own. In my own simple approach, I show that the cosmos must have an intrinsic curvature for a very elementary reason. As for the observations that lead to the DE hypothesis, they have to rate as the most exciting discovery since Hubble.

Have a great day,

Dan

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Dear Dan,

Glad that you enjoyed my essay. Thanks for pointing me to your essay and Christian Corda's. Looking forward to reading both!

All the best,

Paul

Glad that you enjoyed my essay. Thanks for pointing me to your essay and Christian Corda's. Looking forward to reading both!

All the best,

Paul

Dear Paul,

I enjoyed reading your essay and I like how you use the idea of lowest wavelength fields to discuss discrete aspects of the physical law. Congratulations for the very well-written essay and the profound exploration of the implications of the idea of holons.

Best regards,

Cristi

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I enjoyed reading your essay and I like how you use the idea of lowest wavelength fields to discuss discrete aspects of the physical law. Congratulations for the very well-written essay and the profound exploration of the implications of the idea of holons.

Best regards,

Cristi

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Dear Paul Halpern,

Twenty years ago, when I heard for the first time of CA, they were used almost like FEM by those who model plasma, heat conduction and the like. Since then I did not get aware of reported convincing benefits. Your essay makes understandable to me chains of more or less speculative hope for foundational insight that might be confirmed in the very far future.

Let me frankly admit that I am ready to accept the big bang as an exiting hypothesis but not yet as proven for good. What about the attribute foundational, I prefer to judge it as did you from experience over centuries. I appreciate that you avoided technicalities that would perhaps anyway not be convincing.

Most appealing to me was your question for upper and lower frequencies of in particular electromagnetic waves. You will certainly not need reading my essay in order to understand that discrete frequencies correspond via cosine transform with continuous functions of temporal or spatial distance and nice versa. Cosine transform differs from Fourier transform in that performing it twice yields the original function. In other words, it is its own inverse.

Not just in CA the notion neighbor plays a role. Hausdorff topology does also consider a neighbor each to the left and to the right. I found out that this is based on a non-Euclidean notion of number and at odds with a lot. For instance, it is to be blame for trouble at zero, for the unwillingness to accept R+ as sufficient in case of non negative spatial or temporal distance, and even with the usual unilateral attribution of the increment dx to the direction of x.

Regards,

Eckard

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Twenty years ago, when I heard for the first time of CA, they were used almost like FEM by those who model plasma, heat conduction and the like. Since then I did not get aware of reported convincing benefits. Your essay makes understandable to me chains of more or less speculative hope for foundational insight that might be confirmed in the very far future.

Let me frankly admit that I am ready to accept the big bang as an exiting hypothesis but not yet as proven for good. What about the attribute foundational, I prefer to judge it as did you from experience over centuries. I appreciate that you avoided technicalities that would perhaps anyway not be convincing.

Most appealing to me was your question for upper and lower frequencies of in particular electromagnetic waves. You will certainly not need reading my essay in order to understand that discrete frequencies correspond via cosine transform with continuous functions of temporal or spatial distance and nice versa. Cosine transform differs from Fourier transform in that performing it twice yields the original function. In other words, it is its own inverse.

Not just in CA the notion neighbor plays a role. Hausdorff topology does also consider a neighbor each to the left and to the right. I found out that this is based on a non-Euclidean notion of number and at odds with a lot. For instance, it is to be blame for trouble at zero, for the unwillingness to accept R+ as sufficient in case of non negative spatial or temporal distance, and even with the usual unilateral attribution of the increment dx to the direction of x.

Regards,

Eckard

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Hi Paul,

interesting essay!

You write:

'One measuring of entropy in network theory is the growth of complexity in link structure.'

Are you referring to a specific definition of entropy for networks? Any pointers? Would this be something like the log of the number of graph automorphisms?

You also write:

'Given the promise of simple, discrete algorithms, it is interesting to consider a dynamic digital model of fundamental interactions based on holon states. Because holons would have the minimal wavelength of all fields, they might be thought of as 'cells' in a dynamic grid. It is possible that simple digital rules, akin to SDCA algorithms, could transform both the values (quantum states, such as polarization) and linkage of sites. This would render this stratum geometrically dynamic, offering a digital basis for distortions in spacetime'.

I am interested in SDCA type of models, where interconnection patterns evolve, although I claim that having a dynamic interconnection pattern should suffice for building everything, without need of an additional layer of labels, or cell states. The interconnection pattern could indeed code for local states. In the planar case, for example, one has polygonal faces, each with its size, and this generalizes to simplices in higher dimensions. Depending on whether or not these 'atoms' have and preserve their own identity, one can conceive two different types of field/particle (I see analogies with fermion vs. boson behaviour here).

Did you run computer experiments in which both the background cell structure and the additional layer of state information you place on top of it give rise, separately, to the emergence of solitons or other patterns?

Thanks and good luck!

Tommaso

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interesting essay!

You write:

'One measuring of entropy in network theory is the growth of complexity in link structure.'

Are you referring to a specific definition of entropy for networks? Any pointers? Would this be something like the log of the number of graph automorphisms?

You also write:

'Given the promise of simple, discrete algorithms, it is interesting to consider a dynamic digital model of fundamental interactions based on holon states. Because holons would have the minimal wavelength of all fields, they might be thought of as 'cells' in a dynamic grid. It is possible that simple digital rules, akin to SDCA algorithms, could transform both the values (quantum states, such as polarization) and linkage of sites. This would render this stratum geometrically dynamic, offering a digital basis for distortions in spacetime'.

I am interested in SDCA type of models, where interconnection patterns evolve, although I claim that having a dynamic interconnection pattern should suffice for building everything, without need of an additional layer of labels, or cell states. The interconnection pattern could indeed code for local states. In the planar case, for example, one has polygonal faces, each with its size, and this generalizes to simplices in higher dimensions. Depending on whether or not these 'atoms' have and preserve their own identity, one can conceive two different types of field/particle (I see analogies with fermion vs. boson behaviour here).

Did you run computer experiments in which both the background cell structure and the additional layer of state information you place on top of it give rise, separately, to the emergence of solitons or other patterns?

Thanks and good luck!

Tommaso

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Dear Tommaso,

Thanks for your kind comments and detailed message!

In terms of a type of 'topological entropy' measuring network complexity, a quantity related to the Hausdorff dimension (and defined in the SDCA papers listed in the references of my essay) serves as an effective measure. The ratio of next-nearest neighbors to nearest neighbors tends to rise as the system becomes more complex. The parameter you mentioned, 'log of the number of graph automorphisms,' would be another measure.

We did indeed run experiments looking for a type of 'topological soliton' that could potentially represent particle states.

Your ideas sound very interesting. It would certainly be an important achievement to find evidence of 'fermion'- and 'boson'-like states developing from pure networks.

Best wishes,

Paul

Thanks for your kind comments and detailed message!

In terms of a type of 'topological entropy' measuring network complexity, a quantity related to the Hausdorff dimension (and defined in the SDCA papers listed in the references of my essay) serves as an effective measure. The ratio of next-nearest neighbors to nearest neighbors tends to rise as the system becomes more complex. The parameter you mentioned, 'log of the number of graph automorphisms,' would be another measure.

We did indeed run experiments looking for a type of 'topological soliton' that could potentially represent particle states.

Your ideas sound very interesting. It would certainly be an important achievement to find evidence of 'fermion'- and 'boson'-like states developing from pure networks.

Best wishes,

Paul

Dear Eckard,

Glad you found my essay understandable. Yes, CA offer a great deal of flexibility in modelling a wide range of physical systems. Interesting about Hausdorff topology and the role of neighbors.

I look forward to reading your essay.

Best regards,

Paul

Glad you found my essay understandable. Yes, CA offer a great deal of flexibility in modelling a wide range of physical systems. Interesting about Hausdorff topology and the role of neighbors.

I look forward to reading your essay.

Best regards,

Paul

Paul,

From my perspective you have successfully moved a "holon" from the list of zeroes (could exist but don't exist) to the list of ones (exists). Also from the list of fuzziness to the list of clarity. Now, I am interested in more movement from zero to one. If I pointed to some point in space with my finger...would a holon exist at the end of my point? If not, what would increase the possibility of a holon being there? Expansion of the space pointed to...and what about expansion of the time allowed for observation at the intitial point at the end of my finger? Would expansion of space searched and time observed increase my chances of locating a holon? Why is the possibility increasing with a change in either condition? Or, is there actually only holons everywhere which make my questions mute?

Irvon

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From my perspective you have successfully moved a "holon" from the list of zeroes (could exist but don't exist) to the list of ones (exists). Also from the list of fuzziness to the list of clarity. Now, I am interested in more movement from zero to one. If I pointed to some point in space with my finger...would a holon exist at the end of my point? If not, what would increase the possibility of a holon being there? Expansion of the space pointed to...and what about expansion of the time allowed for observation at the intitial point at the end of my finger? Would expansion of space searched and time observed increase my chances of locating a holon? Why is the possibility increasing with a change in either condition? Or, is there actually only holons everywhere which make my questions mute?

Irvon

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Hi Irvon,

Glad my essay clarified things! The holons would represent the maximum energy fields, and therefore could not be directly detected at present. They would manifest themselves only through their indirect consequences (such as placing an upper limit on the vacuum energy density).

Best wishes,

Paul

Glad my essay clarified things! The holons would represent the maximum energy fields, and therefore could not be directly detected at present. They would manifest themselves only through their indirect consequences (such as placing an upper limit on the vacuum energy density).

Best wishes,

Paul

Paul,

So, are we willing to attach the fuzziness of nothingness to create meaningfulness in the sensory world (sensed objects, forces and relationships that we actually can point to and even get close enough to touch)?

Here I would suggest what I think is an appropriate poem:

V

I don't know which came first

After the chicken

And sex

And the egg

And the empty can of soup

There's no need for

An opinion

Based on observed facts

Not in this day of

Revealing ignorance

What's left for modern man

Isn't even a bone

There's just the opportunity

To scavenge

To catch a glimpse of

A suggestive piece of evidence

An imprint exists

Where it once was

Substance

And now

Even

Ideas are Art

--------------------------

Paul, you have created a great piece of art!

Respectfully,

Irvon Clear

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So, are we willing to attach the fuzziness of nothingness to create meaningfulness in the sensory world (sensed objects, forces and relationships that we actually can point to and even get close enough to touch)?

Here I would suggest what I think is an appropriate poem:

V

I don't know which came first

After the chicken

And sex

And the egg

And the empty can of soup

There's no need for

An opinion

Based on observed facts

Not in this day of

Revealing ignorance

What's left for modern man

Isn't even a bone

There's just the opportunity

To scavenge

To catch a glimpse of

A suggestive piece of evidence

An imprint exists

Where it once was

Substance

And now

Even

Ideas are Art

--------------------------

Paul, you have created a great piece of art!

Respectfully,

Irvon Clear

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Paul,

I was looking forward to your entry in this contest, and I was not disappointed. You are so very expert at drawing a picture of abstract models in sensuous terms. I especially appreciate your comparison of an office tower to the possibility of a finite field theory (in itself a concept to launch a thousand dissertations). I was reminded of Jorge Luis Borges's short story, "The Library of Babel."

Interesting, informative and original. Just excellent.

Good luck in the contest, and I hope you get a chance to visit my essay, which shares in common with yours an emphasis on information theory.

All best,

Tom

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I was looking forward to your entry in this contest, and I was not disappointed. You are so very expert at drawing a picture of abstract models in sensuous terms. I especially appreciate your comparison of an office tower to the possibility of a finite field theory (in itself a concept to launch a thousand dissertations). I was reminded of Jorge Luis Borges's short story, "The Library of Babel."

Interesting, informative and original. Just excellent.

Good luck in the contest, and I hope you get a chance to visit my essay, which shares in common with yours an emphasis on information theory.

All best,

Tom

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Dear Paul,

Thank you for your very kind remarks on my essay. I had also read your essay, some days ago, and very much appreciated your holon idea.

With my best wishes,

Tejinder

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Thank you for your very kind remarks on my essay. I had also read your essay, some days ago, and very much appreciated your holon idea.

With my best wishes,

Tejinder

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Dear Paul,

I liked very much the historical part of your essay, which is much more developed than mine. Also, I liked the analogy of the information contained in an envelope and the size of the characters.

On the other hand, a minimal wavelength seems to me counternatural as this would mean an upper limit of the wavenumber. Intuitively both ends (linear and inverse linear) are unbound.

Best wishes for this contest.

Arjen

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I liked very much the historical part of your essay, which is much more developed than mine. Also, I liked the analogy of the information contained in an envelope and the size of the characters.

On the other hand, a minimal wavelength seems to me counternatural as this would mean an upper limit of the wavenumber. Intuitively both ends (linear and inverse linear) are unbound.

Best wishes for this contest.

Arjen

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Dear Paul Halpern,

Thanks for your opinion.When I saw the heading of the essay contest 'Is it possible to reconcile digital and analog nature of reality' the idea of connecting it to Advaitha dawned on me.Because Advaitha in a literal sense means Non-dualism.If it is possible for us to reconcile both forms of reality,then it must be done only on the concept of Non-dualism (that is Advaitha).Combining digital with analog, in physics means combining QM with GR,leads to QG which is non-dual to both.

Today itself I will go thro' your article and express my opinion.

Good luck and best regards.

Sreenath B N.

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Thanks for your opinion.When I saw the heading of the essay contest 'Is it possible to reconcile digital and analog nature of reality' the idea of connecting it to Advaitha dawned on me.Because Advaitha in a literal sense means Non-dualism.If it is possible for us to reconcile both forms of reality,then it must be done only on the concept of Non-dualism (that is Advaitha).Combining digital with analog, in physics means combining QM with GR,leads to QG which is non-dual to both.

Today itself I will go thro' your article and express my opinion.

Good luck and best regards.

Sreenath B N.

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Dear Sreenath B N.

Great to hear from you. Yes your idea of connecting the notion of digital/analogue with the concept of Advaitha, or non-dualism, is fascinating.

Hope you enjoy my essay.

Best regards,

Paul

Great to hear from you. Yes your idea of connecting the notion of digital/analogue with the concept of Advaitha, or non-dualism, is fascinating.

Hope you enjoy my essay.

Best regards,

Paul

Dear Paul Halpern,

In your intriguing essay,you have argued for the existence of a fundamental particle called,Holon.It is really good if such a particle exists as all of our knowledge of elementary particles can based on it.But you have not mentioned holon's mass and wave-length.I hope you will soon do it as it gives limits to our understanding of the physics.

Anyway your essay is enjoyable.

Best regards and good luck.

Sreenath B N.

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In your intriguing essay,you have argued for the existence of a fundamental particle called,Holon.It is really good if such a particle exists as all of our knowledge of elementary particles can based on it.But you have not mentioned holon's mass and wave-length.I hope you will soon do it as it gives limits to our understanding of the physics.

Anyway your essay is enjoyable.

Best regards and good luck.

Sreenath B N.

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Dear Sreenath B N.

Glad you enjoyed my essay. Thanks so much for your remarks. An excellent question about the value of the wavelength and mass (or, more precisely, energy) of the holon. Those values would be determined by a field theoretic calculation of the vacuum energy density that included an ultraviolet (high energy) cutoff, and a comparison of that vacuum energy density value to that needed to explain the observed acceleration of the cosmological expansion. In other words, the wavelength cutoff would be adjusted to match the observations. I expect that the wavelength would have a value close to the order of the Planck length (approximately 1.6 x 10^{-35} m) and that the cutoff frequency would consequently be somewhat less than 1.8 x 10^{43} Hz. The energy would be that cutoff frequency value multiplied by Planck's constant h . Clearly, under the current low temperature conditions of the universe, such a massive state would be highly unstable. However, its existence would offer field theory a natural maximum energy cutoff.

Best wishes,

Paul

Glad you enjoyed my essay. Thanks so much for your remarks. An excellent question about the value of the wavelength and mass (or, more precisely, energy) of the holon. Those values would be determined by a field theoretic calculation of the vacuum energy density that included an ultraviolet (high energy) cutoff, and a comparison of that vacuum energy density value to that needed to explain the observed acceleration of the cosmological expansion. In other words, the wavelength cutoff would be adjusted to match the observations. I expect that the wavelength would have a value close to the order of the Planck length (approximately 1.6 x 10

Best wishes,

Paul

Paul

I've just re-read your essay carefully. As a non 'professional physicist' I appreciated your knowledge and the latest detail of some current ideas.

I also fully understand the logic of the holon, May this perhaps be somewhat apparent in Cherenkov radiation? and do you consider there may also be any 'lowest' energy for a discrete particle?

I've been studying; .. "the overwhelming discrepancy between the calculated and observed values of the cosmological.." {'constant' I assume}, and the many other discrepancies, anomalies and paradoxes, and appear to have found a logical model which removes them all. This provides a resolution to the 'dark energy enigma' and evaporates the 'murky clouds', where indeed it derives 'exciting times' as you predict. I do hope you'll be able to read my essay. http://fqxi.org/community/forum/topic/803

It is difficult to see beyond the murky clouds using current understandings, so you'd have to temporarily step back from those, use pure logic and focus on improving conceptual dynamic visualisation skills.

You may also wish to see the strings, in which much added explanation lies, and you may see that immediate conceptual understanding has now improved significantly to around 1 in 4 professional physicists and others. It also explains the issues, proofs and gives links. It is simply a fine tuning of SR with a Quantum Mechanism, removing all issues in SR and beyond. (see also the identification of the errors, the logic, and the many thought Gedankens).

I'd be extremely grateful for your thoughts if you have time to read it.

Best of luck in the competition.

Peter Jackson

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I've just re-read your essay carefully. As a non 'professional physicist' I appreciated your knowledge and the latest detail of some current ideas.

I also fully understand the logic of the holon, May this perhaps be somewhat apparent in Cherenkov radiation? and do you consider there may also be any 'lowest' energy for a discrete particle?

I've been studying; .. "the overwhelming discrepancy between the calculated and observed values of the cosmological.." {'constant' I assume}, and the many other discrepancies, anomalies and paradoxes, and appear to have found a logical model which removes them all. This provides a resolution to the 'dark energy enigma' and evaporates the 'murky clouds', where indeed it derives 'exciting times' as you predict. I do hope you'll be able to read my essay. http://fqxi.org/community/forum/topic/803

It is difficult to see beyond the murky clouds using current understandings, so you'd have to temporarily step back from those, use pure logic and focus on improving conceptual dynamic visualisation skills.

You may also wish to see the strings, in which much added explanation lies, and you may see that immediate conceptual understanding has now improved significantly to around 1 in 4 professional physicists and others. It also explains the issues, proofs and gives links. It is simply a fine tuning of SR with a Quantum Mechanism, removing all issues in SR and beyond. (see also the identification of the errors, the logic, and the many thought Gedankens).

I'd be extremely grateful for your thoughts if you have time to read it.

Best of luck in the competition.

Peter Jackson

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Dear Peter,

Thanks for your kind remarks. Cherenkov radiation applies to energetic charged particles, so if there were an effect it would only be very indirect. The theoretical lowest energy of photons would depend on the size of the universe (with a theoretical lower limit of zero for an infinite universe). In practice, because of thermal fluctuations and the Third Law's prohibition against reaching absolute zero, this lowest energy would never be realized.

Looking forward to your essay.

Best wishes,

Paul

Thanks for your kind remarks. Cherenkov radiation applies to energetic charged particles, so if there were an effect it would only be very indirect. The theoretical lowest energy of photons would depend on the size of the universe (with a theoretical lower limit of zero for an infinite universe). In practice, because of thermal fluctuations and the Third Law's prohibition against reaching absolute zero, this lowest energy would never be realized.

Looking forward to your essay.

Best wishes,

Paul

Dear Professor Halpern- I have downloaded, studied, and copied your essay: THE DISCREET CHARM OF THE DISCREET, to my folder of seminal manuscripts. It appears to me that you are very much the heir apparent to Abraham Pais.

You may find my paper: IS REALITY DIGITAL OR ANALOG? somewhat outside of mainstream thinking. I confess that my work, is of a decidedely different 'style' from your work. But the justification for my approach is not that I am right and you or any formally trained physicist is wrong. The virtue of my paper is that my methods allow for a completely mechanical explanation of the process of cell duplication. Coming to point on the subject of how it is that cancer cells duplicate faster than healthy cells. I'm going to make a thorough study of your books and papers. I'm hoping you can find the time to glance at: NEOPLASIA MATHEMATICS.

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You may find my paper: IS REALITY DIGITAL OR ANALOG? somewhat outside of mainstream thinking. I confess that my work, is of a decidedely different 'style' from your work. But the justification for my approach is not that I am right and you or any formally trained physicist is wrong. The virtue of my paper is that my methods allow for a completely mechanical explanation of the process of cell duplication. Coming to point on the subject of how it is that cancer cells duplicate faster than healthy cells. I'm going to make a thorough study of your books and papers. I'm hoping you can find the time to glance at: NEOPLASIA MATHEMATICS.

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Dear Joel,

Thanks so much for your kind words!

I am greatly humbled by your comments, as Abraham Pais is one of my personal heroes, and was a dear friend of my research advisor, Max Dresden. Pais was a brilliant historian of physics, whose books I have very much enjoyed. So, he is a role model for anyone interested in the history of 20th century physics (the history of physics prize is named in his honor).

I appreciate that you are aspiring to a different goal in your work, and that your focus is on cell duplication. I will take a look at your work NEOPLASIA MATHEMATICS. One of the exciting aspects of this contest is encountering a wide range of ideas about science.

Best wishes,

Paul

Thanks so much for your kind words!

I am greatly humbled by your comments, as Abraham Pais is one of my personal heroes, and was a dear friend of my research advisor, Max Dresden. Pais was a brilliant historian of physics, whose books I have very much enjoyed. So, he is a role model for anyone interested in the history of 20th century physics (the history of physics prize is named in his honor).

I appreciate that you are aspiring to a different goal in your work, and that your focus is on cell duplication. I will take a look at your work NEOPLASIA MATHEMATICS. One of the exciting aspects of this contest is encountering a wide range of ideas about science.

Best wishes,

Paul

Dear Paul,

your essay seems very interesting even at a first superficial scanning. It is extremely important to know how the ideas constituting the foundations of modern physics come from.

Best wish,

Donatello

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your essay seems very interesting even at a first superficial scanning. It is extremely important to know how the ideas constituting the foundations of modern physics come from.

Best wish,

Donatello

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Paul,

As you were kind to read and comment favorably on my essay, I feel compelled to respond. Which is difficult, as I am of the dualistic camp and you present a very detailed argument for a discrete model, along with a comprehensive historical foundation for it.

That said, I still think you are missing part of the picture. I don't have the attention to detail required to fully...

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As you were kind to read and comment favorably on my essay, I feel compelled to respond. Which is difficult, as I am of the dualistic camp and you present a very detailed argument for a discrete model, along with a comprehensive historical foundation for it.

That said, I still think you are missing part of the picture. I don't have the attention to detail required to fully...

view entire post

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Dear John,

Thanks for taking the time to write such a detailed response to my essay. The primary focus of my work was to try to suggest a solution to the vacuum energy problem by setting a minimal wavelength, and to examine the implications of having a discrete set of smallest-wavelength building block particles on the most fundamental level (i.e. at the high-energy limit).

However, I do appreciate your point about energy and form. One of the beautiful aspects of this essay contest is the opportunity for each of us to consider different ways of viewing reality, and various aspects of how the natural world fits together. I fully recognize that the origin of consciousness and the modes by which humans interact with the natural world are profound mysteries. Clearly, even if a discrete system could offer one level of description, there are aspects to our experience that require something more. For example, a chemical, physical or mathematical analysis of the components of the Mona Lisa would clearly not reveal why that painting is so captivating--especially since that image could be duplicated through other materials. So I applaud your interest in tackling not only the fundamental aspects of the smallest realm, but also how nature and our perception of it connect. Hope that makes sense! Thanks again for your detailed comments!

All the best,

Paul

Thanks for taking the time to write such a detailed response to my essay. The primary focus of my work was to try to suggest a solution to the vacuum energy problem by setting a minimal wavelength, and to examine the implications of having a discrete set of smallest-wavelength building block particles on the most fundamental level (i.e. at the high-energy limit).

However, I do appreciate your point about energy and form. One of the beautiful aspects of this essay contest is the opportunity for each of us to consider different ways of viewing reality, and various aspects of how the natural world fits together. I fully recognize that the origin of consciousness and the modes by which humans interact with the natural world are profound mysteries. Clearly, even if a discrete system could offer one level of description, there are aspects to our experience that require something more. For example, a chemical, physical or mathematical analysis of the components of the Mona Lisa would clearly not reveal why that painting is so captivating--especially since that image could be duplicated through other materials. So I applaud your interest in tackling not only the fundamental aspects of the smallest realm, but also how nature and our perception of it connect. Hope that makes sense! Thanks again for your detailed comments!

All the best,

Paul

Hello Paul:

After reading your appropriate comments on my essay (obviously you at least perused it) and your bio, what else could I do when I'm deviating in a totally different direction than the majority... but give you a ten?

Good luck,

joseph markell

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After reading your appropriate comments on my essay (obviously you at least perused it) and your bio, what else could I do when I'm deviating in a totally different direction than the majority... but give you a ten?

Good luck,

joseph markell

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John,

Interesting point; however I wouldn't characterize a photon as a "fluctuation of a medium," given that it can travel through the vacuum. Therefore if it has a smallest wavelength, that would represent a kind of minimal unit or discreteness, since there would be no such entity that is more compact. Thanks for your thoughtful questions and comments!

Best regards,

Paul

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Interesting point; however I wouldn't characterize a photon as a "fluctuation of a medium," given that it can travel through the vacuum. Therefore if it has a smallest wavelength, that would represent a kind of minimal unit or discreteness, since there would be no such entity that is more compact. Thanks for your thoughtful questions and comments!

Best regards,

Paul

Paul,

One of my muses on the subject of waves vs. particles, is Carver Mead, one of the godfathers of the computer revolution. This from an old interview, when his book on problemw ith physics came out:

http://freespace.virgin.net/ch.thompson1/People/CarverMe

ad.htm

So early on you knew that electrons were real.

The electrons were real, the voltages were real, the...

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One of my muses on the subject of waves vs. particles, is Carver Mead, one of the godfathers of the computer revolution. This from an old interview, when his book on problemw ith physics came out:

http://freespace.virgin.net/ch.thompson1/People/CarverMe

ad.htm

So early on you knew that electrons were real.

The electrons were real, the voltages were real, the...

view entire post

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Dear Sir,

Special Relativity is not only conceptually, but also mathematically wrong. This is what Einstein describes in his 30-06-1905 paper "On the Electrodynamics of Moving Bodies":

Einstein: We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:

3. If the...

view entire post

Special Relativity is not only conceptually, but also mathematically wrong. This is what Einstein describes in his 30-06-1905 paper "On the Electrodynamics of Moving Bodies":

Einstein: We assume that this definition of synchronism is free from contradictions, and possible for any number of points; and that the following relations are universally valid:

3. If the...

view entire post

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I respectfully disagree with your characterization of special relativity, as it has proven to be one of the most successful theories in modern physics and has been verified again and again.

Best regards,

Paul

Best regards,

Paul

Sir,

Newton's law was also "one of the most successful theories in modern physics and has been verified again and again". Then should we continue with it alone? If not, your reply is not justified. It is not science, but superstition. We expect you to be a scientist and not superstitious.

We may be wrong. But as a scientist you must prove it wrong. Simple denial is no science. Kindly prove where we are wrong.

Incidentally, we are not alone in finding fault with SR. A growing number of scientists the world over are supporting our views. In fact a large number of participants in this competition have accepted our views. You will find it at various threads.

Hence kindly explain which part of our view is wrong and how? Otherwise, kindly accept our views in true scientific spirit.

Regards,

basudeba.

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Newton's law was also "one of the most successful theories in modern physics and has been verified again and again". Then should we continue with it alone? If not, your reply is not justified. It is not science, but superstition. We expect you to be a scientist and not superstitious.

We may be wrong. But as a scientist you must prove it wrong. Simple denial is no science. Kindly prove where we are wrong.

Incidentally, we are not alone in finding fault with SR. A growing number of scientists the world over are supporting our views. In fact a large number of participants in this competition have accepted our views. You will find it at various threads.

Hence kindly explain which part of our view is wrong and how? Otherwise, kindly accept our views in true scientific spirit.

Regards,

basudeba.

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Dear Basudeba,

Clearly SR has limitations (it cannot adequately handle gravitation and accelerating systems), as Einstein recognized, and which motivated him to develop GR. However, the basic predictions of SR such as time dilation, relativistic mass increase, and so forth, have been verified in numerous high energy experiments.

Best regards,

Paul

Clearly SR has limitations (it cannot adequately handle gravitation and accelerating systems), as Einstein recognized, and which motivated him to develop GR. However, the basic predictions of SR such as time dilation, relativistic mass increase, and so forth, have been verified in numerous high energy experiments.

Best regards,

Paul

Dear Paul,

I just wanted to personally thank you for making a concerted effort to read and respond to many of the essays. Many of the authors with similar credentials to yours, didn't seem to make much of an effort. I is always nice to get positive feedback from someone such as yourself. I realize that everyone is busy and have other obligations, that makes your efforts all the more commendable. I didn't realize, until becoming an author, myself, how exhausting a process it is to evaluate the myriad of different ideas contained in the essays. This is an obligation I took seriously regardless of the bio of the author. It is obvious that you considered it seriously also. Congratulations, on making it to the judging, but after reading your essay, I considered it a foregone conclusion.

Have a great day,

Dan

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I just wanted to personally thank you for making a concerted effort to read and respond to many of the essays. Many of the authors with similar credentials to yours, didn't seem to make much of an effort. I is always nice to get positive feedback from someone such as yourself. I realize that everyone is busy and have other obligations, that makes your efforts all the more commendable. I didn't realize, until becoming an author, myself, how exhausting a process it is to evaluate the myriad of different ideas contained in the essays. This is an obligation I took seriously regardless of the bio of the author. It is obvious that you considered it seriously also. Congratulations, on making it to the judging, but after reading your essay, I considered it a foregone conclusion.

Have a great day,

Dan

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Dear Dan,

My pleasure! One of the great things about the internet (when it works well) is the ability to share ideas on forums such as these in a friendly, civil way. I enjoyed reading the many essays, and learned much in the process. Yes I did need to set aside time for reading and thinking about so many different essays, and am now catching up a bit. I appreciate very much your kind remarks!

Best wishes,

Paul

My pleasure! One of the great things about the internet (when it works well) is the ability to share ideas on forums such as these in a friendly, civil way. I enjoyed reading the many essays, and learned much in the process. Yes I did need to set aside time for reading and thinking about so many different essays, and am now catching up a bit. I appreciate very much your kind remarks!

Best wishes,

Paul

Dear Paul,

Congratulations on your dedication to the competition and your much deserved top ten placing. I have a bugging question for you, which I've also posed to all the top front runners btw:

Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

Best wishes,

Alan

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Congratulations on your dedication to the competition and your much deserved top ten placing. I have a bugging question for you, which I've also posed to all the top front runners btw:

Q: Coulomb's Law of electrostatics was modelled by Maxwell by mechanical means after his mathematical deductions as an added verification (thanks for that bit of info Edwin), which I highly admire. To me, this gives his equation some substance. I have a problem with the laws of gravity though, especially the mathematical representation that "every object attracts every other object equally in all directions." The 'fabric' of spacetime model of gravity doesn't lend itself to explain the law of electrostatics. Coulomb's law denotes two types of matter, one 'charged' positive and the opposite type 'charged' negative. An Archimedes screw model for the graviton can explain -both- the gravity law and the electrostatic law, whilst the 'fabric' of spacetime can't. Doesn't this by definition make the helical screw model better than than anything else that has been suggested for the mechanism of the gravity force?? Otherwise the unification of all the forces is an impossiblity imo. Do you have an opinion on my analysis at all?

Best wishes,

Alan

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Hi Alan,

I'm wondering if you mean your helical model as a analogy for a kind of field theory describing the graviton but also incorporating electromagnetism. If so, it would be interesting to see the field equations.

Best wishes,

Paul

I'm wondering if you mean your helical model as a analogy for a kind of field theory describing the graviton but also incorporating electromagnetism. If so, it would be interesting to see the field equations.

Best wishes,

Paul

Hi Paul,

My idea of a field is a pattern of flux density of gravitons. I don't think in terms of a 'fabric' of spacetime at all incidentally. I have the mental picture of p.i.e.s (particles in empty space). The forces of the electric field are due to the mechanical dynamics and internal structure of the proton. The arrangement of protons throughout a larger crystal structure lattice can lead to a field formation of stronger graviton flux density helical pattern. The arrangement of neutrons as well can lead to the magnetic field flux pattern at a larger scale. The equations are to be had, but a visual representation is my ultimate goal.

Kind regards,

Alan

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My idea of a field is a pattern of flux density of gravitons. I don't think in terms of a 'fabric' of spacetime at all incidentally. I have the mental picture of p.i.e.s (particles in empty space). The forces of the electric field are due to the mechanical dynamics and internal structure of the proton. The arrangement of protons throughout a larger crystal structure lattice can lead to a field formation of stronger graviton flux density helical pattern. The arrangement of neutrons as well can lead to the magnetic field flux pattern at a larger scale. The equations are to be had, but a visual representation is my ultimate goal.

Kind regards,

Alan

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Hi Alan,

Thanks for the clarification. It would be interesting to see if your theory matches all the verified predictions of general relativity, such as the procession of Mercury, bending of starlight, gravitational lensing of quasars, Lense-Thirring effect and so forth.

Kind regards,

Paul

Thanks for the clarification. It would be interesting to see if your theory matches all the verified predictions of general relativity, such as the procession of Mercury, bending of starlight, gravitational lensing of quasars, Lense-Thirring effect and so forth.

Kind regards,

Paul

Dear Paul,

Congrats for standing fifth on the list.If you have done that it is bacause of the simplicity and originality with which your essay appealed to the participants.

Thanking you once again

Sreenath.

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Congrats for standing fifth on the list.If you have done that it is bacause of the simplicity and originality with which your essay appealed to the participants.

Thanking you once again

Sreenath.

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Hello,

I was surprised I didn't see a reference to the work of Y. JACK NG in your paper: http://arxiv.org/PS_cache/gr-qc/pdf/0403/0403057v1.pdf

Regard

less, the idea of photons "moving" in steps is peculiar, to say the least. I personally think it is naive. Dr. Baez says:

"If the rest mass of the photon were non-zero, the theory of quantum electrodynamics would be "in trouble" primarily through loss of gauge invariance, which would make it non-renormalisable; also, charge conservation would no longer be absolutely guaranteed, as it is if photons have zero rest mass."

http://math.ucr.edu/home/baez/physics/ParticleAndNucle

ar/photon_mass.html

If the photon has no mass then it can only move continuously. If it turns out that it has a very small, finite mass, then the universe would need virtually infinite energy to accelerate and stop all the photon so that they move in steps, unless this energy comes from somewhere else, in which case your model breaks down.

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I was surprised I didn't see a reference to the work of Y. JACK NG in your paper: http://arxiv.org/PS_cache/gr-qc/pdf/0403/0403057v1.pdf

Regard

less, the idea of photons "moving" in steps is peculiar, to say the least. I personally think it is naive. Dr. Baez says:

"If the rest mass of the photon were non-zero, the theory of quantum electrodynamics would be "in trouble" primarily through loss of gauge invariance, which would make it non-renormalisable; also, charge conservation would no longer be absolutely guaranteed, as it is if photons have zero rest mass."

http://math.ucr.edu/home/baez/physics/ParticleAndNucle

ar/photon_mass.html

If the photon has no mass then it can only move continuously. If it turns out that it has a very small, finite mass, then the universe would need virtually infinite energy to accelerate and stop all the photon so that they move in steps, unless this energy comes from somewhere else, in which case your model breaks down.

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Albert,

Thanks for the reference and comments. Deviations from the expected behavior of photons would occur only at the very highest energy scales, well beyond what has been directly observed. I don't think we can rule out, as of yet, the possibility of holographic noise. I'm excited about Hogan's holometer experiment and looking forward to the results.

Best regards,

Paul

Thanks for the reference and comments. Deviations from the expected behavior of photons would occur only at the very highest energy scales, well beyond what has been directly observed. I don't think we can rule out, as of yet, the possibility of holographic noise. I'm excited about Hogan's holometer experiment and looking forward to the results.

Best regards,

Paul

Gentlemens

I wonder why you did not notice or do not want to notice the radical view that an independent investigator.Remember this name: name,Friedwardt Winterberg

http://bourabai.narod.ru/winter/relativ.htm

http://

bourabai.narod.ru/winter/clouds.htm

Yuri Danoyan

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I wonder why you did not notice or do not want to notice the radical view that an independent investigator.Remember this name: name,Friedwardt Winterberg

http://bourabai.narod.ru/winter/relativ.htm

http://

bourabai.narod.ru/winter/clouds.htm

Yuri Danoyan

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New Measurement of the Earth’s Absolute Velocity with the Help

of the “Coupled Shutters” Experiment

http://www.ptep-online.com/index_files/2007/PP-08-

05.PDF

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of the “Coupled Shutters” Experiment

http://www.ptep-online.com/index_files/2007/PP-08-

05.PDF

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Paul

Sincerest commiserations at your undeserved apparent omission from the final placings. A travesty for a fundamental physics site, as some far less important 'stock' opinion is elevated above some excellent original work and conceptual thinking (and also my own of course!) with seemingly no respect given to the community view and ratings by anonymous judges.

I didn't check to see if you did comment on mine, if you didn't read it I hope you might, except it's now being left behind by exciting progress. I do feel there is commonality to be explored.

Don't be disparaged. Best wishes for the future.

Peter

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Sincerest commiserations at your undeserved apparent omission from the final placings. A travesty for a fundamental physics site, as some far less important 'stock' opinion is elevated above some excellent original work and conceptual thinking (and also my own of course!) with seemingly no respect given to the community view and ratings by anonymous judges.

I didn't check to see if you did comment on mine, if you didn't read it I hope you might, except it's now being left behind by exciting progress. I do feel there is commonality to be explored.

Don't be disparaged. Best wishes for the future.

Peter

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Peter,

Best wishes for the future too! I wish you and all the participants all the best. Best of luck with all of your endeavours!

-Paul

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Best wishes for the future too! I wish you and all the participants all the best. Best of luck with all of your endeavours!

-Paul

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Thanks for sharing this. Here they have chosen the topic of the discreet charm of the discrete and I don't know how effective for writing essays.They have briefly given about the author and also provided the download essay PDF file. Hope it will be helpful

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