The Nature of Gravitational Singularities and a Heuristic Introduction to HBCS Cosmology by Dan T. Benedict

Tom,

Thanks, for your comments. The two pillars of my model are the FPC and primary role that BH's have in evolution and the very definition of the cosmos. With the FPC, we have a principle with which to define more than just motion, such as the very nature of existence. "A physical property only has meaning only in relation to universe as a whole". It frees us from having to use GR globally, which has only been tested locally.

My graphical method has also freed us from the conventional tools, which are difficult at best to work with, and shows how the nature of BHs from the "cosmic perspective" differs from conventional theory.

I believe the FLRW models fail because they assume that the universe's geometry is simply connected. The HBCS model is neither simply connected nor multiply connected in the traditional sense, but something altogether different. New maths may be needed. Besides as they say "a picture's worth a thousand words" (I'm not sure how many math symbols that equates to).

There was mounting evidence for DM, long before Vera Rubin published her results showing the flat rotation curves of galaxies, which is historically viewed as the definitive evidence in favor of DM. Something about her graphs "leapt to the eye" and caught the attention of the community. Of course, her graphs were empirical evidence, mine are just based on principle and reasoning. I'm the first to admit that this model needs a more rigorous treatment, but I'm fairly satisfied with the results and implications so far. This is just the beginning. The hard work is yet to done.

Dan

Tom,

The FPC limits the interpretation of the equivalence principle to the exterior and ultimately the boundary of the BH. The orthodox interpretation allows a dual existence, at least temporarily, for a test particle that "falls into" the BH. For exterior observers, the test particle ends up and remains at the boundary until the end of the universe. From the test particles' frame of reference, it passes the event horizon and continues falling ultimately ending in an unknown state at the singularity. This is a paradox! The FPC removes the paradox, since the particle's very existence is defined only w.r.t. the rest of universe, which is the exterior of the BH and its boundary. This doesn't negate the equivalence principle, since at the boundary, the test particle remains in a locally timeless state and experiences nothing, that is until it's energy is eventually liberated by a extremely long period of cosmic expansion. Without the FPC, we have dual existence and unknown states. With the FPC, everything has a unique existence and the singularity is understood as just a point in cosmic time. The remains of the star interior to and immediately after the horizon is formed, exists in a new set of expanding spacetimes, with the BH's event horizon equivalent to the cosmic horizon in their infinite future.

Dan

Tom,

Hopefully this helps:

The FPC is an extension of Leibniz's relational philosophy (on which Mach's principle is based) that has fundamental physical implications. It is not a scientific claim, since it cannot be verified directly by experiment, only its implications are verifiable. (BTW continuation across the event horizon cannot be verified either, it's just the accepted interpretation within the current framework.) The FPC is philosophically appealing because it insists that we precisely define physical properties and events and that relationships are logically consistent. It allows us to define cosmic spacetime, without resorting to the a priori global application of GR, which is a local theory, and has only been proven on the local scale. I'm not claiming that GR is wrong (in fact it must be correct for the model to be valid), only the interpretation that allows continuation across the event horizon.

Since the FPC has physical implications and is philosophically more appealing, the resulting HBCS Cosmology deserves our attention and scrutiny. The implications are far reaching and profound as they relate to our conceptual understanding of the formation of structure, DE (which was not covered in the essay), and in particular, DM. DM has been and is currently still thought of (by most of the community) as a particle physics problem. The HBCS model claims that the observations that lead to the DM hypothesis are a general relativistic effect and can be understood using only GR in the given background. This is would be a major breakthrough if it can be proven correct. Thus, the implications of the HBCS model will be the ultimate test of whether the FPC is valid and useful.

So we have a new model, in which singularities can be understood, and if proven correct, will seamlessly resolve many of the open questions in cosmology and astrophysics. I would say that not allowing continuation across the event horizon is a small price to pay, especially since we're not really giving up anything substantial. The equivalence principle is still valid up to the event horizon, which is defined by the model to be a closed (inclusive) local boundary of the universe in the present era. So, if the model's implications hold up to scrutiny after comparison to super computer simulations and the empirical evidence, we have made much progress in our understanding of the universe.

Dan

Tom,

We're in the domain where philosophy meets physics, the playground where truly fundamental physics takes place! FPC leads to a model that has physical consequences, so new physics is required, but not immediate. I don't know if you've read Kip Thorne's "Black Holes and Time Warps". It"s mostly about the history of BH physics, except for the last few chapters, which are worth the price of the entire book. In particular, Ch. 11 entitled "What is Reality?" is a gem. In this chapter, he writes about the the different paradigms physicists use to solve, in this case, problems and questions regarding BH physics.

He defines a paradigm as "a complete set of tools that the community of scientists uses in its research on some topic, and in communicating the results of its research to others." The three paradigms used in BH research are the warped spacetime paradigm (of which most everyone is familiar), the flat spacetime paradigm, and the membrane paradigm. Some problems are more easily solved using one paradigm over the other due to the suitability of the mathematical formalisms or the intuitive pictures that guide the calculations. Each of the paradigms is completely equivalent (here's the kicker) "so long as one restricts attention to the hole's exterior". The mathematical results of the MP differs from that of the WSP on the interior of a BH. This is a clue the something not quite right. Two separate math formalisms, representing the same physical laws, giving consistent results exterior to the hole, but inconsistent results interior the hole.

The FPC is actually aligned philosophically with the FSP. In case your not familiar, the FSP, "is based on three sets of laws: a law describing how matter, in a flat spacetime, generates the gravitational field; laws describing how that field controls the shrinkage of perfect rulers and the dilation of the ticking rates of perfect clocks; and laws describing how the gravitational field controls the motions and fields through flat spacetime." So this paradigm differs from the WSP on the interior of the BH also, since at the horizon the radial dimension of the perfect ruler shrinks to zero and the ticking rate of the perfect clock dilates to infinity.

So where is the new physics required? It is probably required locally at the horizon (this is where QG needs to be developed), but is definitely required at the beginning of the universe (of the present cycle according to HBCS Cosmology), and in the descriptions and understanding of DM and DE, and the icing on the cake is that the singularity is no longer incomprehensible. New physics is compulsory since HBCS Cosmology differs from the Standard Model.

Allowing continuation across the event horizon is based on a belief that the WSP is the true nature of reality, even though it cannot be proven to be. I believe the FSP is the true nature of reality, and I think, I've given compelling reasons why it should be considered as such. More importantly, if the HBCS model aligns with the empirical observations and detailed calculations, that would be evidence for the FSP, validate the evocation of the FPC, and contribute to a vastly more complete picture of our cosmos.

Tom,

Yes, the universe is bounded locally at the black hole horizon. Thus, as a boundary, everything exterior to it, including the boundary itself ( it is a closed boundary) belongs to the universe, everything interior to the boundary is subject to speculation, since there can be no experiment or observation conducted there that can be conveyed to the exterior. One can choose the prevalent view of the WSP, that the horizon is just empty curved space and an observer falling toward a large enough BH would not experience anything unusual, or one can choose to believe the view from the MP, and the the observer would experience an electrically charged membrane at the horizon, or finally one can choose to believe the FSP and that the horizon is where space, time, matter, and energy are poorly defined. So for now, the interior of the BH is a matter for philosophy.

Now, remember that I used the FPC to also define cosmic time and hence cosmic spacetime, which are not really new concepts either, except I was able to define them without reference to GR, a local theory. GR is viewed as fundamental and it is natural to want to use it to understand the global aspects of the universe, but what if it's a false assumption that GR applies globally? It may or may not. This is why I believe the my method is a more fundamental procedure to build a cosmological model. It relies only on simple definitions and relationships and assumes GR is valid on the local scale, the scale of which it has been tested most thoroughly.

Finally, when we allow cosmic time to approach infinity, the null surface through cosmic time approach the surface of the hypersphere. Once again, this is where space, time, matter, and energy are all poorly defined. The cosmic horizon in the infinite future is indistinguishable from the horizon of the interior of the BH. Is this philosophy or a conclusion based on a physical model? You say that the FPC is superfluous. I say it is a guiding principle that lead to a unique model.

If DM is found to be the result of a general relativistic effect and not a particle physics problem, if DE and inflation are better understood, and if the formation of structure is determined to result from the transition of BHs at the singularity and re-transition at the SLS, then I guess I won't care if the FPC is deemed unnecessary. For these are examples where the physics needs to be developed.

Dan

Tom,

Let me quote from the introduction of Lee Smolin's, Life of the Cosmos : "Even the simple act of describing where something is, or when something happened, involves implicit reference to the rest of the world. Because of this, all the theories that describe parts of the world actually need the rest of the world in order to make complete sense." This is the FPC in a nutshell. It is nothing new, it does not undermine GR, I just see the need to elevate this basic concept to the status of a principle, mainly due to the misunderstanding of the nature of time. The warped (no pun intended) view of spacetime has allowed all sorts of "fantasical" unphysical solutions to Einstein's equations and are taken seriously because the physicist that discovered the solution, and those who take it seriously, forgot that "parts of the world actually need the rest of the world in order to make complete sense." They are looking only at the mathematics and not the context. The FPC may be superfluous to the classical explanation of relativistic spacetime effects of Einstein's relativity, but not to the context of that explanation.

Dan

Sridattadev,

Thanks, for your comments. I have a question for you. If our inner most self does not age and has no boundaries, why is it that we find ourselves in our present state? For if we are truly eternal, omniscient, and omnipotent, shouldn't we have progressed to a state of perfection?

Dan

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

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