• [deleted]

Dan,

The thing is, that taking Mach's principle as Mach formulated it, _does_ undermine general relativity. Since you brought up Smolin, consider this 2005 preprint, particularly p. 8. When Smolin speaks of a relational theory, it is in the context of background independence, not relationalism as a physical principle.

Dynamic physical relations in Mach assumed acceleration as absolute. In Einstein, the roles played by absolute spacetime and the constant speed of light disallow this assumption.

Tom

  • [deleted]

Correction. I meant to say that Mach regarded inertia (motion) as absolute.

Tom,

Thanks, for the information on Smolin's preprint. It looks to be a interesting paper. I'll need some time to read and respond. I was without power for 16 hours due to the "storm of the century" and without the internet longer than that. It was not fun. Hopefully, I'll have a response later today.

Thanks,

Dan

  • [deleted]

You're still in Illinois, I take it. You guys got socked a little harder than those of us in the Detroit area, though I enjoyed my snow day away from work. :-)

16 hours without power! Brrrrr. Hope everyhting is well with you now.

We have quite some common ground in Smolin's relational philosophy.

Tom

Tom,

Thanks, for your concern. I'm in the Peoria area and all is well. We ended up with about 14 inches of snow with a lot of wind. It could have been worse. We could've gotten the 20 inches that they were forecasting. I must say the thunder snow was quite impressive. I've heard of it before, but never experienced it. The first rumble of thunder must have lasted 30-45 seconds. It was quite unnerving, I thought something had blown up!

As for the FPC, I'm still attempting to discern the differences between my working definitions and the conventional definitions described in Smolin's paper, which is quite comprehensive. The conventional definitions are a bit more involved than I was aware, and I won't be able to resolve the issue without additional contemplation and understanding. I appreciate you bringing it to my attention.

It seems to me that motion has the most fundamental part to play w.r.t. the very definition of time. For it seems that no definition of time can exist without motion and motion cannot exist without time, with local time only realizable w.r.t. and constrained by the speed of light. As Emmanuel Moulay so eloquently puts it is his e-print: "The time coordinate ct represents the possibility of motion for the matter relative to the speed of light c along the geodesics defined by a metric g" (see http://cel.archives-ouvertes.fr/cel-00511837) and "then time comes from the time coordinate but it is not a fundamental variable of the General Relativity."

This is why the infinite hierarchy of BHs with their inherent cosmic hypersurfaces is so important. It allows for an underlying motion that defines a cosmic time, and therefore the potential for local time, to exist, always. This is of the utmost importance, since it is my belief, that in order to progress, physics needs to obtain a consensus on the nature of physical time. I believe the HBCS Cosmology along with GR provides the starting point for such a definition.

Dan

  • [deleted]

Hi Dan,

I know what you mean about the lightning and thunder. We had a little of it here. It's eerie!

Back to business, What you call the FPC reminds me a bit of how some physicists apply the (strong) anthropic principle, as a philosophical support to their theories. I don't agree with it, but there are heavy duty theorists such as Leonard Susskind, who do.

Personally, I think that the universe ought to be able to explain itself on its own terms, without invoking a first or final cause. That's just too Aristotelian for my tastes.

I agree with you, without qualification, that the nature of time is the key. Did you read Sean Carroll's book _From Eternity to Here_? I think it's the best non-technical survey of the current state of the physics of time that one can find.

For my own part, if you're interested, my publications and preprints all deal with time. Briefly, if time is n-dimensional continuous, n > 4, the time metric can maintain classical symmetry (reversible trajectory) while as a least action principle in n-dimensions, extend by analytical continuation in an irreversible and dissipative trajectory asymptotic to T = 1. The final conclusion is that time, gravity and information are the same phenomenon.

I also plan to post an essay here in the next day or two.

All best,

Tom

Hello Tom,

It's funny you mentioning Sean Carroll's book. I just received my copy, today, after renewing my membership to Sci. Am. Book Club. I'm looking forward to reading it. I give him kudos for his nature of time essay and his simple and elegant description of his Heraclitean cosmology, but then I have to shake my head when I see him on TV talking seriously about backward time travel. This issue was one of the main reasons that I believe we need something similar to the FPC (one that doesn't undermine Einstein, that is). I'm still trying to work out the details, among other things.

I find it curious that we don't see many of the notable people such as Sean, Julian Barbour, George Ellis, Marcelo Gleiser, David Wilshire, etc. in this contest. What gives? Do you think it was the subject? My essay wasn't an explicit argument, so it looks a little off subject. I just ran out of space. I haven't been keeping up with the new entries. Maybe they're there and I just haven't noticed.

At the moment, I'm trying to learn all I can on Roger Penrose's Conformal Cyclic Cosmology. I think his model and mine are quite compatible. I didn't reference CCC in my essay, because I'd only heard about it while in the process of composing my ideas. From what I've read, the models are similar if for no other reason than his "outrageous proposal" that the Big Bang origin and the remote future are physical identical.

As for your papers, I am always interested in reading everything on the subject of time and will gladly read yours. I also look forward to reading your essay. You are very knowledgeable and I greatly appreciate the feedback you have given to me regarding my ideas, for if you have questions or concerns, they are probably shared by others.

Thanks,

Dan

Dan

Absolutely excellent essay. In fact I had a sense of Deja vu, as the concepts were so close to those of a recent paper of mine (currently being reviewed - still unpublished to date) that it almost made me believe in quantum nonlocality! They follow from but had to be mainly left out of my essay, until published and for space reasons.

My essay, not so well written as yours, argues the case for Locality and Reality, represented by the discrete field around mass (so particularly a smbh), which is in the same frame, moving and rotating with it.

Put simply; em waves change propagation speed between frames to always move at 'c' locally. But all is observer dependent.

Once we work out the implications of that one statement all physics resolves to simple relationships.

I also offer the quantum mechanism, which is established physics and takes us most of the way to quantum gravity, via equivalence.

In the paper, the big bang is indeed a scaled up smbh quasar, but a Tokamak toroid (they have intrinsic rotation) giving a continuous double helix bipolar field. They recycle whole galaxies and spit them out as gas jets (the receding jet red shifted to a radio source). See my HH34 Fig, and also look carefully for the Toroid outlined by the lensing.

This does of course solve the re-ionisation 'epoch' issue, and there are some other very fundamental implications, which I won't mention now. (though I've already touched on them in the blogs and strings.) Please do read my essay first and comment.

There are some parts of yours which are rather different, and I'd need to think on those.

Essentialy I'm convinced we have the correct model, which is also consistent with Edwin's, Georgina's, Willard's etc. and I hope I can contribute the key to making it run, which is CSL wrt receiver, unifying without paradox.

I think the (apparently) hardest bit, conceiving of infinitely many co-moving frames, you may be familiar enough with anyway having already got there.

Best wishes

Peter

PS; Tom; As you said, wisely; "Einstein incorporated the absolute speed of light into Mach's mechanics to show that motion is not primary, but that rest states are relative and therefore ALL PHYSICS IS LOCAL, since relative rest states beg observer dependence."

    • [deleted]

    Peter,

    Thanks, for your kind words. I do think that we are on the verge of being able to supplant the Standard Model of Cosmology with a cyclical model that envelopes many of the current open questions and gives us a better fundamental understanding. The ideas that went into my essay have been stewing for several years. Little did I know that none other than the likes of Anthony Aguirre here, Sean Carroll with his Heraclitian Cosmology (see his essay in the Nature of Time Contest), and Roger Penrose's Conformal Cyclical Cosmology have set a precedence for serious consideration of such an alternative cosmology. I believe that in my simple way (conceptual and graphical), I've given the mechanism for such a cosmology through the primacy of BHs in the overall scheme. The best case scenario is that my ideas would provide the tipping point, but I'm not naive enough to believe that totally. But that's what makes these contests great!

    While I agree that all physics is local and while my FPC may have been worded a little too broadly, some of us need to be reminded that all local spacetimes are a subset of a cosmological spacetime, and all cosmological spacetimes are a superposition of many local spacetimes.

    I've have read your essay, twice now, and will leave on comment there soon.

    Thanks again,

    Dan

    10 days later

    Dear Dan,

    You write in your post at Emmanuel Moulay's thread:

    ---"In this essay we maintain that certain physical properties, originate from the fundamental nature of the universe as a whole and are not independent of it."---

    The 'nature of the universe as a whole' is a meaningless concept as there's nothing outside of with respect to which it can express its 'nature' to: it has no physical reality as a whole. If with 'inside nature' we mean a consistent entirety of rules of behavior (laws of physics) and in a self-creating universe particles create each, then they at the same time create their rules of behavior, so you cannot say that one is the 'origin' of the other. If you agree that it doesn't make sense to ask what is cause of what, the particles or the laws they (force each other to) obey, then this is a tautology.

    ---"As I've shown in my essay, the energy from the Big Bang comes from a previous cycle of the universe"---

    This doesn't solve the problem where all energy came from (if we may use the past tense here, which I don't believe), but only shifts that question to the encompassing whole in which this succession of bangs is supposed to occur.

    ---"Elsewhere, Emmanuel has stated that he believes that the contents rather than the container must be fundamental. I believe they are both fundamental, that's why gravity and the other three forces are so different."---

    I agree: one defines, creates the other as I argue in my essay.

    As to your own essay, you write

    ---"For any event or physical property to be defined as completely as possible within the limits of physical certainty, such an event or property must be defined with respect to the universe as a whole and is never independent of it."---

    Indeed: if in a self-creating universe, particles have to create themselves, each other, then (the properties of) particles are as much the product as the source of their interactions. As they only have reality, exist to each other as far as they interact, they express and preserve their properties by exchanging energy, at the same time creating, preserving spacetime between them, the thing we call 'universe'.

    ---"Is there an ultimate meaning of time in nature?"---

    A universe which manages to create itself out of nothing, can hardly stop creating, so if there's no time before/after/outside the universe, then it must produce time itself if it is to keep creating itself, and contains all time within. The universe doesn't then evolve as a whole, in time, with respect to some independent outside clock, but creates time as it keeps creating itself. So concepts like 'the universe as a whole' and 'cosmic time' ultimately don't mean anything. In a universe which creates itself out of nothing, the sum of everything inside of it, including spacetime and time, has to remain nil, so the universe doesn't exist, evolve as a whole: there is no time outside of it. Statements like "The mass of the Universe is 1.8x10^54 kg. The radius of the Universe is 0.95x10^26 meter." make no sense at all if there's nothing outside of it with respect to which these quantities can be expressed in interactions.

    ---"However, the incompleteness of GR, as currently formulated, has been extremely problematic and resolving this most intractable of primary issues is one of the fundamental goals of an acceptable theory of QG."---

    If in a self-creating universe (the properties of) particles are as much the product as the source of their interactions, then the same holds for the force between them, so a force cannot be either attractive or repulsive. Since they need some kind of backbone to prevent their properties to vary continuously as the circumstances vary, to have properties and a fixed energy, to be stable within a certain energy interval, their properties and rest energy must be quantified. If particles are as much the source as the product of their interactions, then so is the force between them, so a force cannot be either attractive or repulsive. This means that though particles, within the conditions they can exist, are stable, may act as if they either attract or repulse, as their rest energy also is the product of their interactions, they have no 'bare' mass or charge which can give rise to infinite interaction energies at infinitesimal distances, and hence there's no need for string theory. Since the mass of particles similarly is the cause as well as the effect of their interactions, of their energy exchange, we need no Higgs particles either. It is our assumption that particle properties only are the source their fields and interactions which leads to these infinities. If we accept that particles, their properties also are the product of their interactions, of an evolution, then it is easy to see that the unification problem is an artificial, unnecessary problem of our own making. The weak gravity which causes so much problems in present physics is just the effect (or cause) of the continuous creation process of a self-creating universe. The chief culprit of today's mess in physics is the Big Bang fairy tale: the assumption that particles only are the source of their interactions, that they passively have been created by some outside intervention. For details see my essay.

    Regards, Anton.

    Dear Anton,

    Let's see if I can clarify the meaning of the expressions of which you have questions. Some of it comes from the misinterpretation of certain words that may have multiple meanings and were not defined explicitly due to essay constraints.

    By universe as a whole, I am referring to the cosmic spacetime (which has a local nature, this is the realm in which physics is conducted, and it has a nature as a whole which are the intrinsic properties that are separate from the local nature). We know cosmic spacetime to exist because of the direct evidence which is available to us. On cosmic distances, this always comes to us in the form of EM radiation. I have shown that this universe is finite and has an indeterminate but cyclical lifetime in cosmic time. This is opposed to a Universe (capital U), commonly know today as the Multiverse that is everything that physically exists, whether we have direct access to it or not. Thus,

    "certain physical properties, originate from the fundamental nature of the universe as a whole and are not independent of it"

    was meant to emphasize a relational nature between the contents and the properties of the contents to the entirety of cosmic spacetime (universe) as a whole. For example, many consider a particle the source of its own existence and the source of its properties. I consider the source of existence of the particle to be inseparable from cosmic spacetime within the limits of physical certainty. To further clarify, Peter Jackson had a wonderful quote from Einstein that said "Physical objects are not in space, but these objects are spatially extended." Therefore, what we consider a "particle" is normally identified with a local point "source" that has certain properties. I would say that cosmic spacetime is the superposition of local spacetimes that are inseparable from the extended particle; extended in space, therefore extended in time as well. What we normally consider as the point like 'source" is just a local spatial-temporal effect of the extended particle.

    Then you write: "This doesn't solve the problem where all energy came from..."

    In a Steady State Universe or in my case a Evolving Steady State Multiverse, this is never an issue. The Multiverse was never created but has always existed as a set of evolving cosmic spacetimes along with all of their contents, in parallel, or as part of the hierarchy of evolving cosmic spacetimes bounded by their local and cosmic event horizons.

    By: "Is there an ultimate meaning of time in nature?" I should have ask instead: "Is there an ultimate manner in which time in nature can be defined?" This would have better described the question I had intended. Therefore time as a ordered process of change is about as elemental as we can get for a definition. In a nutshell, time is defined by motion, yet motion is defined by time. This is why the infinite hierarchy of evolving cosmic spacetimes is fundamental. Without it or some type of recurrence instead, neither motion nor time could define the other, thus neither would be viable and a paradox would result.

    You write: "The universe doesn't then evolve as a whole, in time, with respect to some independent outside clock, but creates time as it keeps creating itself."

    The universe (cosmic spacetime) does evolve and does create both cosmic time (via its expansion) and local time (via constancy of c in the local frame). The evidence for this should not be an issue. But, the time that we measure locally is defined w.r.t. the velocity of light which *is not* invariant to the evolution of cosmic spacetime, but *is* invariant to local objects in spacetime. Cosmic time and local time therefore both have meaning. As Emmanuel has so eloquently put it "The time coordinate ct (i.e. local time *my emphasis*) represents the possibility of motion for the matter relative to the speed of light c along the geodesics defined by a metric g". But this local time varies as the universe expands, so referring to the universe as 13.7 Billion years old is rather problematical. However, this paradox is resolved in that cosmic time also has meaning in that it describes how the universe evolves (continuously and cyclically) and that it bounds the cycles and thus gives us a reference to determine where (when?) we are presently in the cosmic cycle. This determination must be made by empirical evidence, i.e. redshift, CMB, and luminosity data of standard candles compared to the model.

    I didn't quite understand all of your last paragraph. I will read your essay to see if I can put it into context. I don't think we disagree as much as you originally thought due to poor definitions on my part. What you call a self-creating universe, I call a Evolving Steady State Multiverse which I didn't detail as much as I would have liked due to the constraints of the essay. I will have to read your essay to help clarify your position. If we end up disagreeing on philosophical reasons, so be it. I just don't want to disagree due to misunderstanding and inexact definitions. If you have any other questions, criticisms, or if I missed something, please let me know.

    Best Regards,

    Dan

    • [deleted]

    congratulations,a very creative idea in all case.

    Good luck

    Steve

      Dear Steve,

      Thanks for your kind words. They are very much appreciated.

      Dan

      My apologies to Steve Gratton. He was the co-author with Anthony Aguirre of the paper referred to in this post. His omission was an unintentional oversight. These impressive papers, among others, hopefully will eventually convince the community of cosmologists of inferiority of the Standard Model. Unfortunately, IMO I believe they will not concede until an alternative model definitively explains away dark matter and dark energy. My model is hopefully a small step in this direction.

      Dan

      • [deleted]

      you are welcome, sincerely.

      Steve

      Dear Dan,

      Thank you very much for reading and even comprehending (at least partly) what I'm trying to do! What I do not, however, is saying that the universe doesn't evolve. Though things inside of it certainly evolve with respect to each other, the universe as a whole does not evolve as a whole with respect to some imaginary Outside Observer. My point is that to obey conservation laws, in a universe which creates itself out of noting the sum of everything inside the universe, including spacetime and time must remain nil. If it then cannot have any particular property as a whole, then it doesn't make sense to say that it evolves as a whole. Only a universe which is created by some Outside Intervention can evolve as a whole, with respect to Him/Her/It: only on His/Her/Its watch did He/She/It create our universe 14 billion years ago. A self-creating universe, however, doesn't evolve IN time, but produces and contains all time itself. A statement like "The mass of the Universe is 1.8x10^54 kg and its radius is 0.95x10^26 meter" doesn't mean anything. That we nevertheless cannot get rid of our habit to make just such statements shows that we regard all inside objects as pieces of furniture floating in spacetime, as completely autonomous objects the existence of which is too self-evident to even bother much about their origin, their properties independent from anything, as if they would keep existing if they wouldn't interact, exchange energy at all. However, if particles create each other, if they preserve and express their properties by continuously exchanging energy, then they would vanish if we could cut off this exchange like the image on a TV screen when we pull its plug: particles power each other's existence by this continuous exchange, at the same time forcing each other to obey the same kind of behavior, the same laws of physics. The idea that the universe can have any particular property as a whole ignores or denies this exchange because it is unobservable, because, despite quantum field theory, we dare not let go of the (classical) belief that particles only are the source of their fields and interactions, and hence keep existing even if they wouldn't interact at all, so we regard their properties to have a physical reality even outside their interactions, as if they would be observable, have a physical reality even outside the universe. However, a property like the rest energy of a particle only exist in this exchange, in its expression, and is not something which has a physical reality outside these interactions. If we consider its mass as a property which depends on nothing, then we implicitly say that the particle passively has been created by some Outside Intervention. Similarly, we cannot speak about the mass or energy content of the universe as it has no autonomous, physical existence, as all mass is tied up in the continuous energy exchange between its particles. There's nothing left of their mass to engage an imaginary outside observer in an observation interaction (and which would incorporate the observer into the universe). This is why I insist that the universe as a whole is an intellectual concept, which has no physical reality whatsoever. Without their continuous energy exchange, particles wouldn't even belong to the same universe: particles are wave phenomena because of this exchange. That macroscopic objects have lots of superfluous properties which don't affect their function at all (like the color and shine of a bullet), properties which seem to depend on nothing, does not mean that we may treat quantum particles in the same manner.

      As to the anisotropy in time, I can but speculate. If new galaxies keep being created everywhere, at all distances, but we see on average more young galaxies at larger distances, and (if and when) quasars and GRB's mainly occur in an early phase of the evolution of galaxies, then this might explain why they are more numerous at higher redshifts. Another possibility may be that if the black-hole like objects at the centers of galaxies are more massive in heavier and/or more compact clusters of galaxies, then these hole-like objects may power more violent phenomena. So perhaps the clusters in our near neighborhood as yet aren't massive enough? I don't know. I only know that the big bang scenario doesn't make any sense at all as it treats the universe as an ordinary object which evolves as a whole, at a pace determined by the watch of its creator.

      In your previous reaction you wrote about a cyclical universe: I assume you mean a universe which alternates between big bangs and crunches, so we live 14 billion years after the bang, and x billion years before the next crunch. However, if there's no overarching 'Über Universe' in which a hypothetic observer may witness an alternation of big bangs and crunches, the energy liberated at the crunch being the stuff the universe starts with at the next bang, then this still doesn't answer the question as to its origin, how it was created without violating conservation laws. In my essay I sketch how a universe can create itself out of nothing without violating any conservation law, without needing any kind of bang (see for an alternative explanation for the 2.8 K background radiation my UPDATE 2 post at my thread).

      As to the 2nd law of thermodynamics: if we could isolate the particles within a system completely from any interaction with the outside world, from the energy exchange by means of which they preserve and express their properties, then we would annihilate them, in which case it wouldn't make any sense to speak about the inside entropy. The same holds for the universe as a whole: as it doesn't exist, has no physical reality as a whole, it cannot have any particular entropy as a whole. The 2nd law only holds for systems which are closed to any net energy in- or outflow, but allows the energy exchange between the particles within the system and the outside world to continue. Only of a big bang universe which necessarily, implicitly must have been created by some outside intervention, which exists, has particular properties with respect to that creator, we might ask how much energy it contains, how large or how old it is and what its entropy is. The price we pay for believing in this naïve, religious view on the universe is very high: it affirms our classical, false notion that particles only are the source of their interactions. By clinging to the bigbang tale, to the idea that particle properties are independent from their interactions, we make them incomprehensible. The result is that we condemn ourselves to invent unnecessary, nonsensical hypotheses and theories like cosmic inflation, string theory and fictitious (Higgs) particles. Being the product of fundamental misconceptions, intended to solve or (weep under the carpet) the many problems and inconsistencies of the bang tale, such theories and particles are part of the problem, not of its solution. The result of these misconceptions is that one contradictory theory breeds the next inconsistent theory to appear consistent itself. As the bigbang scenario cannot explain the homogeneity and isotropy of the universe (unlike a self-creating universe which automatically, unavoidably produces this homogeneity and isotropy), it needed an inflation theory to repair this fundamental shortcoming. This theory, in turn, cannot answer fundamental questions as to its mechanism, who/what determined the time to start the inflation, its rate, and when to stop. I'm sure someone will come up with a theory to 'explain' this, a theory which in turn will prove to evoke more questions than it solves, and thus needs another theory to explain its inconsistencies away, etcetera. I like to think that my essay offers a way out of the present stalemate. As to the magnificent Maxwell laws, they certainly remain valid: it is only our present, outdated interpretation of what charge is which needs revision.

      Regards, Anton

      Dear Anton,

      After reading your last comment, I don't believe you fully read my essay.

      You wrote: " if particles create each other, if they preserve and express their properties by continuously exchanging energy, then they would vanish if we could cut off this exchange like the image on a TV screen when we pull its plug".

      I completely agree with this statement. This is why I proposed the FPC, so that particles aren't seen as just their own source. But in that principle, I referred to the universe as a whole, and that is IMO where you must have lost my meaning. By reading the entire essay you missed the most profound part, that is of the role of the BHs in the creation cycles of the universe! The universe doesn't contract in a Big Crunch (that would violate second law), but as it expands the mass-energy that was lost to BHs is eventually recovered in the new cycle. My model actually gives your model a mechanism for self-creation!

      Your statement above is exactly why I proposed that mass-energy doesn't actually "fall into" a BH, as orthodox BH theory indicates, because it ceases to have any distinguishable meaning at the event horizons. This makes it a local boundary of the cosmos. I know it's against your philosophy, that the universe can have boundaries, so how does your model deal with BHs and the mass-energy that is lost to them? The universe can have boundaries *and* can still have the self creating aspects in which you embrace.

      When I was constructing my model, I asked myself, is the universe in a continual mode of creation? I came to the conclusion that it had to be cyclical due to 1) constancy of a finite velocity of light for all observers in the universe, 2) the simplest explanation for redshift is cosmic expansion, 3) the isotropic distribution of unusual astronomical objects only at high red-shift; and I determined that most of the SMBHs in the universe are in a "white hole" mode currently (as in right now), but they only reveal this mode to extremely distant observers (i.e. in the extreme distant future)! This mode is then followed by the quasar/GRB mode and a galaxy forming mode all in the subsequent cycle. This model explains a lot of phenomena. Can your model explain why there are two separate sets of empirical correlations between SMBHs and their galaxies? Does your model give an elegant alternative hypothesis for dark matter? This is what you missed if you didn't read the whole essay.

      Perhaps I didn't word like you would have, but if you re-read my essay and looked past the statements that you disagree with, you may just see the beauty in it.

      Dan

      Dan

      I meant to post a link to a recent preprint of mine underpinning a paper recently accepted for peer review, which I think has some close parallels to your own theories; http://vixra.org/abs/1102.0016

      Thanks for your support on the blog, I've just posted a 2nd debagging of poor and complacent science with a number of Einstein quotes in what seems to be becoming a well supported and (eventually) irresistible assault on the 'tipping point' you refer to. I'm hope you've by now, as well as Johns' James etc, also read the essays of Edwin, Georgina, Constantinos, Robert Spoljaric, Rafeal Castel and others, all with the consistent "new level of awareness" Einstein knew would be needed to solve the problems created by the old level.

      I would like to see all working together, as the power of the whole would certainly still be needed. I see your essay is languishing just below mine a little off the pace, which I shall help with the top score it deserves, and hope you may consider mine (and perhaps the others) worth the same.

      Do also give me your views on the preprint. I'd like to be able to also cite your own work in future.

      Best wishes.

      Peter

        Thanks, Peter.

        I've committed to read five essays a day, and unfortunately having a hard time getting everything done. I do look forward to reading your preprint. I just never realized how exhausting these essays would be. I try to give them equal time. Some are just not worth it, while others are worth 2-3 readings.

        I have read Edwin's, Georgina's, Robert's and I believe I read Rafeal's, but I'll have to double check.

        These essays along with yours and Christian Cordas' essay are all worth high scores. I would suggest Irvin Shirazi's essay as being top notch also. One of those worth a couple readings as it is a little more abstract, but I believe he's onto something both fundamental and profound. I'm quite puzzled by Ayind Mahamba's essay. He comes across as being very intelligent, claims a TOE, and even has 3 equations that relate a lot of the mathematical numbers together, such as e, phi, i, etc. but I don't really know what to make of it.

        I'll try to give feedback on your preprint as soon as possible.

        Dan

        Thanks Dan

        You may like the one from Jarmo I just helped boost to No.1 with a 10 as well - Anothe deja vu. I had to confess about his lost papers! I'll read Irvin Shirazriz's.

        Peter