Fluctuation and Superposition of Digital and Analog Aspects of Spacetime by Willard Mittelman

Willard,

Thanks for the comment on Peter's page. I'm still absorbing that, but I wanted to respond to your last question.

Also, at some point I'd like to discuss black hole entropy and holography with you.

But the immediate issue is to resolve the 'low entropy' problem of a high energy big bang. Recall that my Master equation del (dot) phi = phi (dot) phi has solution phi = 1/r where phi is a radial vector. Since phi is quickly found to be gravity G, with energy proportional to G*G and mass proportional to energy,E=mc**2, then the G-field distribution and hence the G-field energy, and hence the G-field mass is distributed as 1/r, that is the mass is inversely proportional to distance (squared) from the 'origin'.

If we are dealing with a continuous field (as opposed to a smallest finite element of space) then we can obtain as large a mass as we want, since 1/r comes as close as we want to a singularity. We can thus see that the lion's share of the mass is effectively 'at' the origin; r=0.

But if you told me that all of the gaseous energy in a large cube was effectively concentrated 'at' one of the corners of the cube, then I would say that this was very low entropy, since the high entropy distribution would be evenly distributed over the entire volume of the cube. So, in similar fashion, the location of all of the energy/mass of the G-field at the origin or singularity r=0, is a low entropy solution, whereas all of the GR-inspired FLRW 'dust' models are homogeneously distributed over the entire volume of the universe and hence are high entropy solutions. This is why Roger Penrose also tries to engineer a Big Crunch that will somehow lead to a following low entropy big bang.

I hope this is clearer now. You might read the relevant part of my essay again, with the above in mind.

I'm going to think some more on the comments you and Peter left me on his page. I have some ideas and interesting results, but I'm still somewhat confused.

Edwin Eugene Klingman

Willard, You've lost me on both points. Specifying one 'size' in my cube example doesn't determine entropy, with no other data specified, and Penrose is talking baryons which I suspect are evenly distributed inside black holes, while the G-field distribution in a perfect fluid is quite different. But since I haven't done in calculations on the entropy, I can't say. I still believe that the only quantum is Planck's constant and the perfect fluid is a continuum. I'll try to compute the entropy, but it's not at the top of my list of todo's.

Willard, thanks for the additional remarks. One of us is missing something, probably me. I'll read the other pages in Penrose and think about it some more. Entropy is not the main point of my theory, and I may be incorrect there. At the moment a much higher to-do is the topic you and I and Peter were discussing. I hope to offer a new idea there in the next few days, unless I'm fooling myself.

Dear Willard,

I had a glance to your essay and I listed it for a better read. For the present I would stay to your conclusions that are in accordance to the concept of my essay.

"In conclusion, then, spacetime - and, ipso facto, reality itself - has a fundamentally dual nature marked by (i) a superposition of discrete and continuous metrics, and hence of the digital and the analog, and (ii) microstructural fluctuations between digital states and near-analog states. In addition, the "analog component" of the above superposition manifests as a continuum viscous stress tensor, which adds a further analog aspect to reality.":

It is evidence that discreetness can be seen only when we examine the virtual part of our reality (e.g. electron as wave, light as waver). In real part "near-analog" states are seen (Fig. 6 in my essay). However, Is there any evidence that this part is really analogue and not near-analogue?

I always wonder how you can do physics without figures. As a chemist, I have great difficulty in following mathematical formulations. Contrary, I am sure I can grasp any complex theory that has the plain reality (geometry or spirit) as base.

best regards,

narsep (ioannis hadjidakis)

Hello Ioannis,

Thanks for your comments and question. By a "near-analog" state, I mean a global state of the microstructure of spacetime, such that this microstructure is analog "almost everywhere." The fact that it is not totally analog reflects the fact that the cancellation of the random fluctuations of N spacetime elements (where N is approximately equal to the four-volume V of the universe, and hence is a very large number) is not total or exact - specifically, there is always (by the Law of Large Numbers, and the random character of the relevant fluctuations) an uncanceled remnant of approximately square-root-of-N-many elements, a remnant that is very small in comparison with N. The presence of these elements entails that the spacetime microstructure is characterized by a certain discontinuity, and hence a certain (small) deviation from a totally or purely analog state. From my standpoint, the existence of this deviation, and hence the fact that we are dealing with a state that is (only) "near-analog," is crucial to explaining the phenomenon of dark energy. Hence, if one accepts my theoretical perspective on dark energy, the very existence of dark energy represents evidence that spacetime is never totally analog but only "comes close" to being completely analog. Of course, if one opts for a different account of dark energy altogether, then it is possible that one could find evidence that spacetime is really analog; but from my standpoint, at least, this possibility is not available.

One motivation for my account of dark energy, an account which is broadly similar to (and in fact, is inspired by) the treatment of dark energy in causal set theory, is the existence of an analogy between dark energy (or the "cosmological constant") and the surface tension of fluid membranes: this analogy is discussed in R. Katti et al., "The Universe in a Soap Film" [arXiv:0904.1057]. Perhaps, with your background in chemistry, you will find this analogy to be interesting. (Or perhaps not.) In any case, best wishes to you,

Willard

Dear Willard,

I hope you recall the issues we spoke of with respect to Peter Jackson's essay. I've finally posted a brief pdf that I believe relates to these issues (while being based on the ideas in my essay.) I would hope you find time to read it through a few times and then I'd be very interested in your comments.

GEM and the Constant Speed of Light

Edwin Eugene Klingman

Willard,

Thanks for the comments. I have to remember that things that are clear to me must be made clear for others. In GEM (gravito-electro-magnetic) theory, the G-field is the radial analog of the E-field in electro-magnetics, and the C-field is analogous to the magnetic field. And in the same way that in electro-magnetics the circulation of B is dependent on the time rate of change dE/dt, the circulation of the C-field depends on 'mass current' (momentum) and upon dG/dt.

So when I say "ignore gravity" what I meant to say was "assume the gravito-electric field G is not changing". If gravity does change we get red-shift or blue-shift, which I wish to ignore here.

That is what the wavy line ~ represented, as well as suppressing the constants in the equation.

The equation in which I show "2p" is a vector identity, that is meant to show that if C is defined strictly as an angular momentum term r cross p, then the equation is trivially satisfied. Since the C-field has units angular frequency, and other constants play into the equation to make all terms reduce to the same units, the '2p' was meant to be suggestive that C will probably look a lot like angular momentum. I realize that that is confusing, and will probably simply delete that rather than explain it.

I will probably do a little cleanup based on your feedback. I hope the above answers your questions and you can proceed to see if it makes sense to you. I'm pretty happy with it, needless to say. And if you had not put your two cents in, I'm not sure I would have gotten so deeply into Peter's paper.

Edwin Eugene Klingman

It's cleaned up now. -- Edwin Eugene Klingman

Willard,

I really appreciate your efforts to understand my theory, and I'll try to answer.

The primordial field, in my theory, is gravity. It satisfies the Calabi conjecture and, as I understand it, deSitter space, where gravity extends over (defines?) all space, and is generated by its own self energy. This bootstrap is mathematically justified, and since no one knows WHY the universe came into being, I simply assume it existed as one field. The Master equation is perfectly symmetrical and motion invariant, but the formal time derivative makes sense only if a new constant (Planck's constant) appears. Thus the perfect radial symmetry remains until a 'quantum fluctuation' [my second assumption] occurs in an 'off-radial' direction, unlocking the energy of the C-field, which had been suppressed by the perfect symmetry.

We now have the full gravitational field with radial and circulatory aspects.

The fact that both directly interact with mass and both have energy, hence equivalent mass, and the interaction is non-linear, means that a C-field vortex will establish a 'solenoidal' C-field dipole, which strengthens the vortex, which strengthens the dipole, which strengthens the vortex, with the process ending in an infinitely dense point. UNLESS THERE IS A LIMITING CONDITION. I next assume that a limiting condition exists [otherwise the universe would be nothing but one [or more?] infinitely dense points, which doesn't seem to be the case. The condition I impose is a 'limit to the curvature of the C-field. That is, the C-field vortex has a 'minimum radius' that prevents collapse to an infinitely dense point.

But where does that lead? Picture a spinning skater who pulls her arms in. How fast can she spin if she can pull her arms into zero radius? Got that? Is there an answer? On the way to 'zero radius' can her fingertips reach the speed of light? We are not 'boosting' her in any way that requires infinite energy, we're just conserving angular momentum.

Since there is nothing stopping the non-linear vortex-dipole-vortex-dipole--- feedback process, in which the energy-mass of the vortex wall serves as a 'mass current' (momentum) that induces a solenoidal C-field dipole, then the radius of the vortex keeps shrinking and the velocity of the vortex wall continues to speedup to conserve angular momentum. Where does this end? Will the vortex wall reach the speed of light? If it does, then how is it connected to the rest of the world, since, if there was an electromagnetic field, we could not 'look at' the the vortex, because, moving faster than the speed of light, it would have 'moved on'.

I hope you're still with me.

Now, if you work out the equations, it turns out that this radius is basically the Compton wavelength, and I make my next assumption, which is that at this point, electric charge comes into existence. It's probably my weakest assumption in my whole theory, but, I now have mass, charge, gravity and electro-magnetics.

And obviously the charge that is on the vortex 'wall' will resist the shrinking to an infinitely dense point through self-repulsion. So now a true limiting force exists to prevent infinitely dense points of C-field energy.

If one takes the simple equation of the mass of the vortex wall being forced into a smaller orbit, and sets it equal to the self-repulsive force of the electron, then one would hope to find the equilibrium where the inward C-field force and the outward electric force are equal and the particle is stable. And when this equation is worked out, the fine structure constant (1/137) falls out! I put the exclamation sign because I don't believe that there exists another theory that can calculate the fine structure constant.

By the way, the v=c radius is the Compton wavelength of the particle, but the radius where the charge repulsion equals the inward force is about 10^-18 meters which agrees with the best measurements. So the electromagnetic field can see only to the v=c radius, but collision data can see all the way down to the 'real' radius. I find that nice.

So now we have a Z-boson (the C-field vortex) that produces a charged particle and, if charge is conserved, then the remaining vortex (outside of the Compton wavelength radius) has acquired a charge, and become a W-boson, ready to produce an 'anti-particle'.

There's more, but I'll stop here to let you put the picture together in your own mind.

By the way, having left both academia and the government years ago to run my companies, I am not in the loop, and my submissions to Phys Rev Lett were immediately rejected with "don't darken our door again". So, I had the choice of 'start with inconsequential journals and work my way up' (which at my age is not appealing) or simply put this into books and hope someone reads them. Although I have presented the above in several factual books, the most complete presentation is in "The Chromodynamics War", which has the format of a scifi novel, in the hope that graduate physics students, upon reading a scifi novel that explained things better than their QCD textbooks might be induced to look further. Then fqxi came along and gave me another outlet.

Each book has worked out more details and corrected earlier typos and mistakes, but the most complete treatment of particle physics is "The Chromodynamics War". A version that drops the scifi narrative and simply presents this in straight form is in process, to be titled, "Physics of the Chromodynamics War".

Willard, sorry this can't all fit into 9 pages, but it just can't. I do appreciate your interest.

Edwin Eugene Klingman

Willard,

Upon re-reading your last post, I want to be sure that I answered your question completely.

The 'gravity', G, that i mention is the one you are familiar with, from Newton to Einstein to Hawking.

The electro-magnetic fields, E and B, you are also familiar with, from Maxwell to Einstein, etc.

The C-field, which I never heard of in my academic career, is the aspect of gravity that has the same relationship to G as the magnetic field has to B in electrodynamics.

E and B can be considered as 'two' fields, or B can be considered as the relativistic aspect of the 'one' E field. The choice, as far as I can tell, is one of convenience.

Now Maxwell, noticing that Newton's equation and Coulomb's equation had identical form, if we replace G by E and mass by charge, postulated that one could perfom this replacement in ALL of Maxwell's field equations. But this left a 'hole'. What was the analog of the magnetic field? This is the C-field, which he called the gravito-magnetic field. It is either a 4th field or the relativistic aspect of the gravity field. I treat it as a fourth field, because it simplifies things.

So, the short story is: We start with G, which has perfect symmetry. When this 'breaks' we now have G and C **and nothing else**. But the C-field self-interacting vortex will spiral to an infinitely dense point or else something else will happen. I describe the case in which something else happens: electric charge appears at the v=c horizon of the shrinking vortex. Now that we have electric charge, we have the electric and magnetic fields, E and B.

So we now have four fields, G and C, that interact with mass (and hence each other) and E and B, which interact with charge, but are themselves uncharged.

When the term 'electro-magnetic' is applied to gravity, it is an analogy. It is not an equivalence. The G-C mass-based fields are ultimately different from the E-B charge-based fields.

I hope it keeps getting clearer. G and C follow from Einstein's general relativity, I didn't make them up. E and B follow from Maxwell's field equations.

Edwin Eugene Klingman

Willard, thanks for the effort you have put into my theory and for any that you intend to do. I only recently became aware of viXra, and will look into it. I appreciate your suggestion, and your comments, and hope we have occasion to continue this conversation at a time of your choosing.

Good luck in the contest, and thanks again.

Edwin Eugene Klingman

Edwin

I posted back to you on my string.

The above was also very helpful, and rang a steeple full of bells.

In my latest paper (which haven't yet got accepted either) I identify tokamacs as the geometrical solution, which I think is analageous to your field relationships.

The rotation and forces are not only dual axis but helical. It is a torus, with a plasmasphere of 'extended space' translating at rest with it, which spins round it's 'ring' axis, with a force also round it's sectional circumference, giving and endless helix. This is from nuclear physics, but the whole angular momentum of a galaxy is concentrated into one (though not quite ALL at once, hence blazars) because black holes are toroid. (also stellar mass bh's - you must know the Chandra crab nebula core photo). Tokamaks have 'intrinsic' rotational motion. If scaling works how it should quasars even become a prime candidate as a big bang process, which means big 'crunch', and before it was our predecessor galaxy. Then that's the sort of thinking that gets papers rejected of course. Peer review editors will have a lot to answer for come the revolution!

40] J.E. Rice et al 2007 Nucl. Fusion 47 1618 IOP Inter-machine comparison of intrinsic toroidal rotation in tokamaks. http://dx.doi.org/10.1088/0029-5515/47/11/025

And re your note about the vortex wall = a little over 7 x c, which is the max ejection velocity we've found from our frame (but 'c' locally in the 'incentric' graduated stream).

I'm trying to work out precisely how the FSC emerges at 1/137th. I have it increasing with motion, and the fine structure itself as the diffractive medium. (all receivers measure em at c because the receivers fine structure makes it so). Ergo inertial frames.

I'm doing some further revisions to my current paper (on galaxy evolution) and would like to cite something of yours. I'm not quite sure what and where yet but would need to do it quickly, and it would need to be concise - any ideas? peter.jackson53@ymail.com

I really must find one your books!

Any harmonious oscillations there?

Best wishes

Peter

Willard

Sorry about the above for Edwin -I was re-appreciating your paper, then catching up with posts, and forgot it wasn't Edwin's string.

I've also just caught up with Joy Christian blog on her disproof of Bells inequity, and mentioned your essay as well as mine and Edwins. You may like to see it and her papers if you haven't yet.

Best wishes

Peter