If this author was a Mafia gangster (continued)
In other words: What’s the difference? No observer can experience an individual quantum state, but only the sum of said states as a total probability density of states that emerges ultimately as P = 1. So, the quantum quasi-singularity of a black hole must appear as if it is a real singularity. This could be construed as quantum relativistic existentialism. Seeming is being. Or, according to logical positivism, if it walks like a duck, quacks like a duck, flies like a duck and looks like a duck – it’s a duck. And, if it is roasted, it will smell and taste like duck too.
People like to forget the correspondence principle. If general relativity is real, quantum relativity must endorse it and vice versa. In a GUT or TOE, one can never be used to negate the other or else they are both false.
Once again, all that the author is saying
herein is that there is sufficient reason to go right ahead and allow the hyperbolic G field as a postulate. We shall figure out the theoretical justification later. The ideas below are not to be gnawed apart and eaten alive. But, they should still be digested. They are not at all logically necessary and sufficient, so their demolition may be pointless. They are meant merely to illustrate the notion that to allow the hyperbolic field as a simple plain postulate might conceivably make good practical sense.
A 2-D origin of the universe is not inconceivable. And, 2-D components of a non-spherical 3-D gravitational field are not ruled out. One can imagine that 2-D cosmogenesis or galactic orbital motion around a black hole was conceived when such motion or even the entire universe began to unfold or deconvolve from a compactified form, perhaps like opening (or closing) a child’s “pop-up” book. So, the universe may be deconvolving and galactic SMBHs are reconvolving – they are unfolding and refolding exactly as they should*.
The aforementioned rationale would include Guth’s hypothesis of an ultra- energetic hyper-massive “inflaton” point particle in a super-excited “inflaton field” that decomposed, decayed or deconvolved from the a false vacuum, thus forming our universe. It seems unlikely that the inflaton particle would have decayed directly into gazillions** of photons and little fundamental particles directly, all at once. This is not the way short lived excited particles typically decay. It probably split first into several quantum “fields” (but NOT gravity because gravity might have been already present, perhaps as the ground state of the inflaton field at the floor of the false vacuum) then thousands, and then millions of large black holes (the enhanced gravitational fields of which constituted Dark Matter) and simultaneously and/or subsequently into a lot of electromagnetic energy as well as many small particles.
The inflaton gravity-like field itself also surely would not have collapsed or changed all at once. Its time dependent quantum transition might have been a process that may still be going on. If the universe was once a quantum entity, then it still is. Then, the present epoch’s continued breakdown of the residual inflaton field may act like gravity in whatever proper kind of spacetime it may need to give a hyperbolic asymptotic effect for the whole universe (so that it would have a higher potential energy than the ground state inverse square field).
In an infinite array of 2-D slices (if necessary to allow the HBHF) the universe HBHF’s ongoing stacked or packed 2-D asymptotic cross sections might devolve or transform into the lower energy 3-D inverse square gravitational field. This process might then result in acceleration of the expansion of the universe and putative Dark Energy.
Or else, a black hole is a tunnel or portal to another universe (Everett’s “Many Worlds” interpretation of QM) with different physical laws spilling over into our world and which simply do not prohibit the HBHF.
Another avenue might be to say that a super-massive black hole galactic gravitational field can be hyperbolic by virtue of analytic pure geometry in a non-Euclidian space, by an appeal to Schwartzschild’s analysis which certainly includes a potentially non-Euclidian metric and to Kretschmann’s invariance which does not depend on any coordinate system. Then, if proper assumptions are made and correct boundary conditions are set, GR cannot be seen to override these sets of principles, however fundamental GR itself may be.
As well, under the circumstances that would allow F = GMm/kr, GR might not be seen to trump the symmetry argument that is used to extend the asymptotic hyperbolic field to the far right on the ordinate of a gravitational field strength diagram. (Such a diagram needs to be given some latitude because it is a plot in 2-D Euclidian space, LOL). Symmetry representation is one of the most powerful tools available to the quantum physicist.
With additional assumptions or slightly different boundary conditions, the Schwartzschild treatment and Kretschmann’s invariance will still work if the overall geometry of spacetime in the broader galactic zone around a black hole is not Euclidian, such that this whole local space could be strongly hyperbolic. And, there may be a way around the necessity to consider gravity as always operating under an inverse square relation, especially if there are “perturbations” that are really more like very strong distortions (like a train wreck distorts the rail cars) so much so that perturbation principles cannot reliably be used for a mathematical description of any real black hole.
The spacetime geometry in the distortion zone of a galaxy or galactic cluster containing black holes may be so strongly warped and hyperbolic in nature that any type of field, hyperbolic or not, can exist, persist and never cease to desist. Yet the overall hyperbolic or “open” geometry of the universe may be counterbalanced by the mere existence of all the matter and energy that it contains so as to “behave” like it might be flat. But acceleration of Hubble expansion means that, if the universe is not open at present, it “soon” will be.
By the way, the hyperbolic gravitational field, being quantum normalizable, could be characterized, perhaps, as also pertaining to the Higgs field and the Higgs boson.
Therefore, the author thinks that there is something fishy about the way GR is used and Birkhoff’s Theorem and its siblings are cited in order to put the kibosh on the HBHF.
All this author is saying, once again, is that there is sufficient reason to go ahead and allow the HBHF as a postulate. The above notions are not meant to be picked apart by intellectual sharks, however kindly, gentle, articulate, well meaning, gifted and dedicated. These ideas are not logically necessary and sufficient, so their utter demolition may be pointless anyway. They are meant only to illustrate an idea, not to prove it. This is that to allow the HBHF as a postulate might make very good practical sense, eventually.
Let us do this in the same way that Louis DeBroglie promulgated the postulate that the Bohr planetary model of the atom that he defended simply did not and could not undergo an “ultraviolet catastrophe” as classical physicists insisted that it must. DeBroglie almost single handedly invented quantum mechanics by means of his postulate. But, he had a little help from Albert Einstein, Irwin Schrödinger, Werner Heisenberg, P.A.M. Dirac and a few others.
This is what is needed now. Some help. If you or someone you know can collaborate on a paper for the Astrophysical Journal or some other platform, please consider it.
Furthermore, allowing the HBHF may provide yet another link between quantum mechanics and general relativity. There are a number of links already and when we forge enough critical connections we will have a ready-made unified theory of quantum gravity without having made any special fuss. We need not invent seemingly unfalsifiable, incompetently unpredictive, almost infinitely numerous, unmitigated psychedelically novel and inordinately complex hypotheses. The author hopes that he is wrong but, such as these look like a whole boatload of Aristotelian theories of baroque “epicycles” that might accomplish little new that is uniquely proven. That is, except to satisfy the anal retentive urges of some who may otherwise be very fine workers, what purpose is to be served?
Theoretical physicists have long been fascinated by Eastern philosophies. They say that many principles of modern physics, including relativity, are reflected by philosophical concepts therein that are millennia old. The philosophical point that they choose to ignore is the tenet of “Yin & Yang”. Why should we not be satisfied with “two sides to the same coin”? Quantum mechanics and general relativity are not truly in opposition in any way. They do not address the same issues. They may be mathematically incompatible largely because they were assembled by different people who used different symbolic conventions and starkly different initial concepts. But, why should one necessarily be able to express gravity on an exceedingly small quantum scale? What for? Why should we be able to compute the properties of a galactic cluster from quantum principles? Why?
* After Desiderata by Max Ermann
** A gazillion is a number about equal to the total number of massive bodies, tiny fundamental particles and photons that were ever present as the inflationary Big Bang proceeded toward the time of “recombination” and far beyond. It is much larger than a googolplex. LOL