Essay Abstract

Motivated by the problem of obtaining a plausible account of dark energy, we describe the microstructure of spacetime as continually fluctuating between discreteness and a generally continuous state, with dark energy taking the form of a quantum potential of spacetime that emerges from this process of fluctuation. In addition, we consider the problem of explaining the initial conditions of our universe, which leads us to entertain the idea that spacetime itself is a superposition of both discrete and continuous metrics.

Author Bio

Graduated from Michigan State University and received a PhD in philosophy from the University of North Carolina (Chapel Hill). Since 1999 has lived in Athens, Georgia, working for the University of Georgia.

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Willard

I enjoyed your essay, and agreed with almost all the content, particularly your preferred frame, and;

"Specifically, we can view this preferred frame as a "gravitational aether"."

You have to sidestep constancy of 'c' (CSL) but I hope I can help your theory with the model my own essay (20-20 vision - a Model of Discretion) which allows the 3rd frame by means of a quantum mechanism for CSL in SR.

I'd be interested in your views.

Best of luck

Peter

Hi Peter,

Thanks for your helpful comment; I like the idea that your theory can ensure peaceful co-existence between CSL and a preferred frame (see also the comment I've attached to your own paper).

Good luck with your work,

Willard

Thanks for your support Willard.

I'm also now quite convinced the model finally fully unifies SR and QM, which Roger Penrose described as the 'Holy Grail' of physics. Unfortunately I'm also quite convinced that most are so indoctrinated with the current paradigm they'll be unable to recognise the way out into the light.

There do however seem to be a slowly growing number who can think like we do, are unhappy with the rut we're in and are willing to follow Bragg's advice. (There are at least 2 more here). Soon the lunatic asylums may be too small for us all to be consigned there as crackpots. But I'm at a loss how to speed up the process, which may still fail, (and with it humanity?) I just hope for the day my thesis is criticised for being 'self evident'! Walter Babin believes we currently lack anyone with the intellect and 'authority' to take a firm stance. I agree it would help. Any ideas or help you can give would be welcome.

In the meantime I hope I can rely on a good ('community') rating from you, as it may at least get the judges to take it seriously. Yours certainly deserves similar.

Best wishes.

Peter

Dear Willard Mittelman,

Thanks for your comment on Peter Jackson's page. You further stimulated my interest in Peter's CSL remarks to me.

I don't claim to understand every detail of your paper, but what little I do understand makes me wonder whether you are looking for discrete length and time elements [the 'causet elements'], and particularly elements that explain "the initial co-existence of high temperature with very low entropy."

My preference is to believe in only one discrete 'element', the action, h, and to allow continuity everywhere else (no minimum length or time) subject to my generalized quantum principle: (dm/dt)(dx)**2 = h.

If you view the single "origin element" as a perfect fluid with continuity, I believe that the high temp-low entropy problem is solved as explained in my essay. The outward radial velocity [temp] at least equals the gravitational potential at the singularity [the zero total energy (free lunch) universe], and the 'shape' of the solution to the Master equation provides low entropy. Only the action is discrete.

I don't know if this makes any sense in your FS framework, but I offer it for what it's worth. It may or may not be consistent with what you're proposing. As a side note, my universe begins with perfect symmetry [again, probably requiring complete continuity] and I don't believe a Big Crunch will ever reproduce the original perfect symmetry, so I don't think we'll see another Big Bang.

Good luck and thanks again,

Edwin Eugene Klingman

    Hello Edwin,

    Thanks for your comments. My interest in the idea of spacetime discreteness is actually motivated by the idea's relevance to the issue of black hole entropy, as well as by its applicability to the problem of dark energy. The existence of such motivation doesn't prove that spacetime is discrete, of course, since (e.g.) there are other possible ways of explaining dark energy; but I believe it does at least indicate that spacetime discreteness is an idea worth exploring. At the same time, it is important to explore other approaches as well, such as your own highly interesting theory.

    A plurality of approaches is also warranted with respectt to the problem of the universe's initial conditions. I actually agree with you that continuity is important in connection with this problem. I'm not sure, though, how the shape of the solution to your Master equation guarantees initial low entropy; any explanation or clarification of this point would be much appreciated.

    Good luck with your ongoing theoretical endeavors,

    Willard

    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

    Edwin,

    Two points: (i) it is unclear what the initial size of the "cube" is in your model; (ii) the "clumping" of matter can indeed be associated with high entropy, e.g. in the case of black holes - see p. 728 of Penrose's "Road to Reality."

    Best Regards,

    Willard

    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.

      Hi Edwin,

      Penrose is not talking specifically about baryons, and in fact the particular nature of the matter or mass here is irrelevant; the key question is simply whether or not gravitational effects are prominent - if they are, then clumping of matter is associated with high entropy (see pp. 706-7, as well as p. 728, of Penrose). Presumably, in your model, gravitational effects are indeed prominent at the origin r=0, since it seems from what you say that the G-field approaches a singularity there. Hence, I'm not sure how you get a low-entropy initial state for the universe. You could perhaps claim that the universe-"cube" is initially very large and has low entropy everywhere except in the vicinity of r=0, in which case the entropy density at least might be low (as it is in Steinhardt & Turok's ekpyrotic model); hence my question about the size of the cube. Judging from your reply, though, you don't seem to be making a specific claim about the size of the cube; and in any case, it's unclear that the overall entropy density can be made sufficiently low here, given the high entropy near r=0.

      Best Wishes,

      Willard

      Edwin,

      I just want to add that it's perfectly okay if you want to leave the question of entropy aside and focus on other aspects of your theory; it's just that your earlier remarks about entropy piqued my curiosity and led me to ask for further details. If there are other things on your "to-do list" that have higher priority, that's fine; we don't need to keep going back and forth about entropy.

      Good Luck,

      Willard

      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.

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      • Post #13

      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)

        • [deleted]

        • Post #14

        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

        "Anonymous" in the above comment was me (Willard Mittelman). Sorry I forgot to login!

        14 days later

        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

          Hi Edwin,

          Thanks for the opportunity to read your new and interesting paper. Here are a few brief initial comments and questions; I apologize in advance if I've misunderstood your ideas. Also, please take these remarks as providing simply an opportunity for providing additional information and/or clarification.

          1.) I'm not sure why, on p. 2, you say "if we ignore gravity..."; since you're dealing with a GRAVITO-magnetic field, it's unclear how gravity can legitimately be ignored here.

          2.) Also on p. 2, you write the equations describing the C-field and its circulation using merely approximate equality (wavy lines for the "equals" sign); on the following pages, however (and once on p. 2), you switch to exact equality, but without any explanation or justification for doing so. This is an important issue, since if the equations here are not exact, it is possible for the value of c to undergo some variation, which of course you don't want.

          3.) Again on p. 2, you give an equation in which the C-field's circulation is equal to 2p, but elsewhere you use "p" for this circulation; so, there seems to be a discrepancy here that needs clearing up.

          I don't know if this is helpful or not; if not, I'm sorry.

          Best Wishes,

          Willard Mittelman

          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

          Hi Edwin,

          Thanks for your helpful remarks; they do help clear things up. At this point, I'll try asking a question; it's possible that this question reflects additional misunderstandings on my part - if so, maybe you can clear things up further with new comments. At any rate, my question is prompted by your remark, at the bottom of p. 5 of your new paper, that the key equation you obtain "couples the electromagnetic field and the gravito-magnetic, or C-field". To me, this suggests that, in addition to the C- and G-fields, there also exists the familiar electromagnetic (EM) field of existing physical theory. My question, then, is this: given the EM field's existence, what theoretical or experimental motivation is there for positing additional electromagnetic fields in the form of your C- and G-fields? Or are you claiming that the EM field is itself derived from the G-field and your master equation? If the latter is the case, then it would be good to have the derivation worked out explicitly, and in detail. (It's important in this connection to avoid simply assuming that the known properties of the EM field apply to the G-field as well, since this just raises the question of why the G-field is needed over and above the EM field.) So far, I haven't been able to find such a derivation in your writings; if you have presented the derivation somewhere, and I missed it, then I apologize.

          Best Wishes,

          Willard