• Cosmology
  • A Self-Gravitational Upper Bound on Localized Energy

Jonathan Dickau has requested a new thread to discuss a recent arXiv paper by Stephen Kenneth Kauffmann, titled: "A Self-Gravitational Upper Bound on Localized Energy, Including that of Virtual Particles and Quantum Fields, which Yields a Passable "Dark Energy" Density Estimate."

From the paper's abstract: "The self-gravitational correction to a localized spherically symmetric static energy distribution is obtained from an upgraded Newtonian model which is energetically self-consistent, and is also obtained from the Birkhoff-theorem extension of the unique "Newtonian" form of the free-space Schwarzschild metric into the interior region of its self-gravitationally corrected source. The two approaches yield identical results, which include a strict prohibition on the gravitational redshift factor ever being other than finite, real and positive. Consequently, the self-gravitationally corrected energy within a sphere of radius r is bounded by r times the "Planck force", namely the fourth power of c divided by G. Even in the absence of spherical symmetry, the same bound, to within a factor of two, is shown to apply. That energy bound rules out any physical singularity at the Schwarzschild radius, and it also cuts off the mass deviation of any interacting quantum virtual particle at the Planck mass. Because quantum uncertainty makes the minimum energy of a quantum field infinite, such a field's self-gravitationally corrected energy essentially attains the Planck force times that field's boundary radius r. Roughly estimating r as c times the age of the universe yields a "dark energy" density of 1.7 joules per cubic kilometer. But if r is put to the Planck length appropriate to the birth of the universe, that energy density changes to the enormous Planck unit value, which could quite conceivably drive primordial "inflation". The density of "dark energy" decreases as the universe expands, but more slowly than the density of ordinary matter decreases. Its evolution suggests "dark energy" has inhomogeneities, which may be "dark matter"."

Jonathan, please let us know why you this paper is of particular interest to you.

    • [deleted]

    Nice.

    No singularity at the Schwarzchild radius not only confirms the quantum nature of the cosmological initial condition, it implies non-quantization of classical spacetime. For if the quantum field does not collapse, the universal wavefunction, which is continuous (Kauffmann concludes, " ... only the universe itself, with its cosmological redshift, is actually capable of 'containing' the arbitrarily high frequencies of a quantum field") is physically real and dark energy isn't.

    The understatement of the century: "It would be a relief if something so elusive ultimately turned out to not have an independent existence."

    Congratulations, S. K. Kauffmann! Good eye, Jonathan!

    Tom

    Thank you Zeeya,

    Frank Wilczek wrote an open letter to the Physics community a few years back, about the centrality of understanding vacuum energy density. If we compare estimates from Quantum Field Theory and the cosmological value from astrophysical measurements, the disparity may be as much as 120 orders of magnitude. While renormalization allows us to still do real Physics at various levels of scale without understanding this matter, it is only by plugging in known values that we are able to obtain a good fit. Gerard 't Hooft has pointed out that there is a need for theories which provide a reasonable model of reality, without a lot of adjusting factors put in by hand. He has suggested, in papers and lectures, that we may need to put gravity back into our formulations in order to obtain the desired result, rather than regarding it as inconsequential to quantum-scale interactions.

    Steven Kenneth Kauffmann does exactly this in the paper Zeeya has cited above. By putting the self-gravitation factor back in to the equation, and running it back to the Planck scale, it is found that those terms become dominant - and are not inconsequential at all! To my mind; this is a profound and significant result, which has broad implications across the field of Physics. It is one of those insights that seems obvious, once you have fully grasped the setup of the problem, and it leaves you wondering why great minds have not seen this before. Perhaps the answer was too simple to be obvious. But the existence of an upper bound on concentrations of energy, due to self-gravitation, removes a lot of thorny problems like the conundrum of an initial singularity, offers a mechanism for inflation, and provides a 'passable' estimate of the cosmological value for dark energy.

    I am gratified for the opportunity to discuss this important work, here on the FQXi Forum.

    Have Fun!

    Jonathan

    Thanks also Tom,

    Your keen insight bespeaks the true potential of this discovery. A profoundly simple result, but it has many implications. I am thinking the difference between the spherically-symmetric formula and the final equation (a factor of two) suggests a geometric analogy. The maximally-asymmetric case is where the instantaneous energy distribution is concentrated in a lobe just to one side of the nominal or overall center. But this concentration cannot itself exceed the spherical bound regardless.

    Anyhow; if lobes to either side of a nominal center are regarded as the first in a progression of spherical harmonics, one can see a possible analogy with electron orbitals in an atom - and so on. This likely leads to a connection via Hartle-Hawking to a modified Wheeler-Dewitt equation. But I have not yet worked that out formally. But since I've spoken of energy spreading as a driver for inflation in several papers already (including my last essay), you can see why I find this to be an appealing result.

    All the Best,

    Jonathan

    Hi Folks,

    I wanted to attach the open letter from Frank Wilczek "Centrality of Understanding Vacuum Energy Density" which I have on file. For the record; I first became aware of this open problem - and its extraordinary severity - at the 2nd Crisis in Cosmology conference, in Port Angeles, WA. This became somewhat of a running joke at that event, as an indicator of how much we don't know for sure.

    I should probably note that one of the speakers at that conference, Phil Mannheim, presented a conformal theory of gravitation addressing this problem, that was featured in 't Hooft's Foundations of Physics paper calling for theories with no adjustments put in by hand - DOI 10.1007/s10701-011-9586-8 - which I mentioned above.

    All the Best,

    JonathanAttachment #1: wilczek.pdf

    Jonathan,

    Congratulations on starting an interesting new topic. I haven't absorbed Kauffmann's paper yet, but I looked at t'Hooft's. While I fully agree that we need elementary particle models without any adjustable real parameters, he says that his 'top-down' theory will have difficulty formulating any firm predictions about physics at energies as low as the TeV domain. That's a problem, as far as I'm concerned. We currently have far too many blue-sky ideas about multiverses, and other metaphorical schemes, usually involving infinity or infinities, yet there are several anomalies for which good data exists that are ignored.

    Last week, at a Stanford physics colloquium on the 'Firewall' problem, Nobelist Laughlin asked Polchinski whether the quantum gravity workers (and similar) were not headed to a place where a number of contradictory theories exist, NONE of which can possibly be backed up by actual data, now or in the foreseeable future. That may make those who like to talk blue sky happy, but I believe that physics still needs to be based on measurements.

    I look forward to understanding what Kauffmann has to say.

    Best,

    Edwin Eugene Klingman

      Thanks Ed,

      I think Laughlin's comments speak to the problem of information silos that have formed because people must focus on the important information within a single discipline or area of specialization, in order to learn it all. And even if one wants to take an interdisciplinary approach, because it is seen to be more likely to bear fruit, one is often compelled to declare a specific focus within an established theoretical branch or community. Ben Dribus communicated to me that he thought it might be better if researchers could pursue the approach that they believe is most likely to bear fruit instead. But this is rare.

      One can make an analogy to the Music business, where it is a rare artist who can create a new genre, because the whole marketing and delivery machine is geared to delivery through specialized channels. There are Country music stations, and Rock and Roll channels. In places that still sell Albums or CDs - there are rows or aisles for different categories and styles. Even if they wanted to sell your music; how would people find you if your album can't be filed in any existing category because your work is so different? But of course; musicians do combine styles - it happens all the time - but until the Internet leveled the playing field, most of that music was never heard by the public.

      Regards,

      Jonathan

      Oh I meant to add..

      Kauffmann's result is obtained specifically because it takes pieces from both inside and outside Quantum Physics, rather than working within that silo. One could argue that anyone who takes the basic tenets of QFT as gospel could never have seen this, where someone with exposure to a broader base of Physics knowledge can grasp Kauffmann's point more immediately. As for myself; it took some time to sink in, before I realized just how profound Steven's main point in this paper is.

      I think Gerard 't Hooft was talking about his CA based QG theory, when he made comments about adding gravity back in to our formulations, in order to obtain the correct result. But it is seen that this is what Steven Kauffmann did here too, as it is putting the self-gravitation term for energy back in that makes things work out.

      Regards,

      Jonathan

      Jonathan,

      I also meant to thank you for the Wilczek letter. I agree with him that the 123 orders of magnitude error in vacuum energy is a really big deal, with significant consequences for 'virtual particles'. It *is* potentially as important for 21st century physics as black body radiation was for 20th century. I've argued with some physicists who seem to think it's no big deal. I think they're whistling past the graveyard. You can't have a change of 123 orders, probably the biggest number in physics, and not have repercussions on theories that depend on this for their basic concepts. This ties in with the fact that almost ALL current theories depended on SUSY, and that's going away too. It's actually a great time to be a physicist, if one is concerned with real things, i.e., things that are measurable.

      Best,

      Edwin Eugene Klingman

      • [deleted]

      Something also worth noting is that Kauffmann's framework solves the universal solvent paradox (i.e., whether there exists a container strong enough to hold a solvent that can dissolve everything).

      For if only the universe itself is capable of containing the arbitrarily high frequencies of a quantum field, the universe is clearly not a black body and the cosmological redshift prescribes a no-boundary condition.

      Furthermore, though, one is compelled to speculate from this point whether a hypothetical observer in an adjacent universe might perceive our universe as a black body -- leading to a deeper paradox answered by the multiverse hypothesis.

      Tom

      • [deleted]

      All,

      What is "self-gravitation"? Do I dare ask! Only physical explanations that make sense, please!

      Constantinos

        • [deleted]

        "What is 'self-gravitation'?"

        I would hazard to guess that it's the coalescing field of all particles possessing nonzero mass toward the center of the greater mass according to the inverse square field law that governs both gravitational and electromagnetic interactions.

        Dare to ask.

        Tom

        Hi Jonathan, all,

        A quick note here. Christoph Schiller had explored some of this about maximum force in nature a few years ago in this paper arXiv:physics/0607090, "General relativity and cosmology derived from principle of maximum power or force". And derives Einstein's field equations from it. I believe that he also talks about it in his comprehensive physics textbook.

        Of course this is all subject to if you believe that Planck length, etc. is some kind of law in nature. I'm still on the fence about that.

        Best,

        Fred

          Hi Constantinos,

          You ask, "What is "self-gravitation"?".

          Einstein said that "there is no space absent of field" and today there are dozens of (supposed) fields, fermion fields, boson fields, gravity and electromagnetic fields, and gauge fields in general ( and if you count the 'multiverse', which I don't, then add several hundred more fields, per Susskind. One question that interests me is whether the universe came into existence (assuming it did) with all of these fields or are some derivative. In my first and second FQXi essays, I make the assumption that the universe began as only ONE field, and ask what can be derived from this assumption. I conclude that if there is only one field (absolutely nothing else) then the only way it can evolve is to interact with itself, which implies the equation I present in these essays, and have developed at length. It quickly becomes clear that Newton's equation for gravity falls out of this, as does a generalized uncertainty principle. Therefore it would appear if there was initially only one field, it must have been the gravitational field. This idea can be pushed quite a long way, and I have done so in several places.

          In 1953 Eugenio Calabi (of Calabi-Yau fame) in effect asked if my equation was valid: "Could there be gravity...even if space is a vacuum totally devoid of matter?" He reasoned: "...being non-linear, gravity can interact with itself and in the process create mass", and he conjectured, "curvature makes gravity without matter possible". The Calabi-Yau manifold confirms my equation--based only on gravity. [He preceded me, of course, I wasn't writing original equations in 1953.]

          The key ideas are "fields have energy" (Maxwell) and "energy has mass-equivalence" (Einstein) and "gravity acts on mass" (Newton), so a gravitational field can and does act on itself. I find it more reasonable to believe that one field initially exists, from which all else evolves, than that dozens or hundreds of fields 'just happened' to come into existence at the same time.

          Anyway, that's how I interpret 'self-gravitation'.

          Edwin Eugene Klingman

          • [deleted]

          Edwin, Tom

          Thank you for your thoughts re:self-gravitation. Pardon my doubting self. I am skeptical of everything! Down to gravity and beyond! But I am more inclined to favor Edwin's view on this, however. Is it mass that produces gravity or gravity that produces mass? Is it the Law of Gravity that produce elliptical orbits or elliptical orbits that produce the Law of Gravity? What if the Universe "just is" as it is. With no universal laws but certain self-similar (self-interacting) patterns that emerge. Just like ripples in the desert sand. And all we say and know about "what is" is what we create in our own minds to fit our own understanding of our experiences. Any problem with that? Just asking!

          In my view, there are no 'physical laws' per se. Only 'mathematical identities' camouflaged as 'physical laws'.

          Constantinos

          • [deleted]

          " ... I am more inclined to favor Edwin's view ..."

          What is that view, exactly?

          Tom

          • [deleted]

          Tom,

          From what I understand, he starts from 'one' to create 'all' in contrast to starting from 'all' to create 'one'. But you better ask him that to be sure!

          "coalescing field of all particles possessing nonzero mass" asks for too many particles. Before, in my view, none exist.

          It's me, Tom. You are probably correct in some 'multiverse' of thinking.

          Constantinos

          Constantinos,

          "What is "self-gravitation" You may well ask. In words of 5 syllables it seems to be;

          The gravitational attraction between individual electrons and protons.

          This seems fair enough as most massive bodies are made of them. But it's the distribution pattern effects that are being considered here. It seems to me it's mainly making some theory consistent with much else, which is an important task when most isn't. i.e. in Astronomy potentials are calculated using very diffuse particle densities over virial radii and modelling the effects. But I recall an excellent astronomical paper was recently shouted down by theorists because theory didn't recognise that very thing. So all grist to the mill.

          The 'correction' quantification seems to be the inverse of the gravitational redshift factor. I find that a very tenuous link so far, but linked none the less. I expect to get my head better round the reasoning once fully assimilated.

          I also by the way disagree with a number of assumptions. i.e. a spherically symmetrical field. That is not reality, but it is easy to calculate so at least gives an approximation. It just quandruples the error bars. One day someone will also catch up wit the fact that the systems are NOT static as assumed! So the Navier Stokes equations are also needed, and subject to gamma appraoching a density limit which I put at of 10^21/cm^3 but which he doesn't consider or derive.

          All in all I think it has value as a step in the right direction. But I would, as it's conceptually consistent with some basics of my own fuller model. The 'energy density' decrease (from the big bang?) is of course identical to that of my AGN based model.

          What I want to know is where did Frank Wiczeck get his numbers from? I agree with him too, except he still ignores the distortion implicit in plasma n = 1, which is ignored by all in correlating curve space time to baryonic matter density. I also missed any discerning of Dark M from Dark E! Do point it out to me if it's there.

          I hope that hasn't confused you even more. It has me! What did that Bohr say? "Never express yourself more clearly than you are able to think"

          Peter

            Thanks Fred,

            I forwarded a copy of Schiller's paper to Steven Kauffmann, along with a few comments. My view, after quickly skimming the Schiller paper, is that it is largely complementary to Kauffmann's work - affirming the existence of a bound but approaching the problem from a different angle. A profound result, how ever you interpret it.

            I'll have to read for detail, before I say too much more.

            Regards,

            Jonathan

            • [deleted]

            Peter,

            Easy for you to say! For me ... more googly-gook!

            Constantinos