January 8, 2021

This is a summary of a highly speculative cosmological theory. This summary is intended to guide the development of a more precise simulation model and research program. Please contact whiteholedynamics@gmail.com to share any critiques, papers or ideas relevant to the formal development, simulation and testing of the below ideas.

Cosmological Scaffolding

The White Hole Dynamics (WHD) research program builds and explores the theoretical framework that results from taking seriously the physicality of white holes, negative mass¹, and far-from-equilibrium dynamics. Specifically, the WHD program explores a range of speculative conjectures that might follow from the hypotheses that:

1. our universe is a spacetime region on a 3+1-dimensional exterior boundary surface of a 4+1-dimensional long-lasting white hole;

2. the white hole core initially expels negative mass and positive mass fluids to the interior boundary surface of the 4+1-dimensional bulk spacetime and remains powered by a negative mass core over long timescales;

3. a kind of hydraulic jump forms a weak horizon between the negative/positive mass fluids trapped at the interior boundary surface of the bulk spacetime and the lower-dimensional exterior boundary surface; and

4. the bulk fluids build the local scaffolding on the 3+1-dimensional exterior boundary surface via the pressure they exert against the interior boundary surface, with the positive mass fluid forming regions of primordial black holes and positive mass clustering on the lower-dimensional boundary and the negative mass fluid forming regions of expanding vacuum.

In the WHD program, an arrow of time might begin one of two ways: (i) out of a pure vacuum state of nothingness, or (ii) from a black-to-white-hole transition out of a pre-existing 4+1-dimensional white hole spacetime. In the first scenario, a true vacuum state of nothingness, for instance a scalar field with a zero-valued lowest energy state, could generate the threshold energy density to form the white hole. In the second scenario, a pre-existing white hole spacetime feeds a black hole within that spacetime that transitions into another white hole and creates a new spacetime decoupled from and with no memory of its origin.

In this second scenario, the black-to-white-hole transition could be achieved on time scales much shorter than Hawking evaporation scales because, in the WHD program, supermassive primordial black holes form almost immediately upon creation of the bulk spacetime, i.e., long before positive mass matter has the chance to accumulate on the exterior boundary surface. This is due to the ejection of positive mass fluid from the core that builds up rapidly and inhomogeneously against the interior boundary surface of the bulk spacetime, as discussed further below.

In either of the birthing scenarios, once a threshold energy density is obtained, the excess energy is trapped in a phase transition to a new white hole that produces many positive and negative mass excitations. The negative mass repels both negative and positive masses, resulting in the emergence of a 4-dimensional bulk consisting of a core, an interior horizon and an exterior horizon (with interior and exterior boundary surfaces), as depicted in the below diagram.

This diagram is illustrated in much greater visual detail in the below video.

The positive and negative mass excitations are weakly coupled at only the very earliest times. The negative mass repels both negative mass and positive mass excitations, which begin to run away, forming a fully relational bulk spacetime. Upon the very early formation and expansion of this bulk spacetime, the positive and negative mass excitations phase transition into two strongly coupled fluids that remain held far from equilibrium over extremely long timescales by the negative mass that remains in the white hole core. The two bulk fluids are nearly ideal fluids exhibiting collective behavior and long-range correlations under the slaving influence of the white hole core.

The exterior horizon has an interior and exterior boundary surface separated by a kind of hydraulic jump. The same spin-2 graviton field permeates the entire spacetime – both the higher-dimensional bulk and the lower-dimensional exterior boundary surface. This is typically referred to as the Planck epoch, the first 10^-43 seconds, and can be described on the exterior boundary surface as a separation of gravity from a unified force.

The initial inhomogeneities in the distribution of positive and negative mass fluids are now manifested at the exterior horizon. In regions where a supercritical density of positive mass fluid has aggregated against the interior boundary surface, one or more supermassive primordial black holes form even in the absence of any positive mass matter aggregations on the exterior boundary surface.

In the WHD program, a black hole is a region of partial hydraulic jump collapse. These partial collapses occur when a critical positive energy density threshold obtains that is sufficient to permit wave propagation in the lower-dimensional space to overcome the pressure exerted by the hydraulic jump. The reason the collapse is described as partial is because the hydraulic jump is still present but is not sufficiently strong to prevent waves in the lower-dimensional spacetime from propagating into the higher-dimensional bulk.

The partial collapse of the hydraulic jump occurs when the positive energy density in a boundary region becomes supercritical. This positive energy density is a function of both positive mass matter on the exterior boundary surface (e.g., baryonic matter in our universe) and positive mass fluid pressed against the interior boundary surface on the other side of the hydraulic jump.

Importantly, the qualifier "partial" indicates that black holes do not fully collapse the hydraulic jump. The bulk remains behind a horizon inaccessible to the boundary exterior, which is why we cannot directly detect the white hole and bulk fluids. The hydraulic jump is best characterized as a kind of weak horizon because the horizon is violated in only two circumstances: (i) by matter falling into the black hole, and (ii) by heat radiating out of the black hole.

The interior of the black hole is a region of positive mass fluid trapped against the interior boundary surface of the bulk spacetime, i.e., the bulk side of the hydraulic jump. It is trapped because pressure from negative mass fluid is exerted upon it within the bulk from other near-boundary regions and from the interior horizon and core. In other words, negative mass fluid exerts a repulsive pressure on all sides of the positive mass fluid, and the positive mass fluid in turn exerts a pressure on the boundary in its attempt to run away.

An observer far from the supercritical positive energy region, i.e., the black hole, would perceive the crossing from the 3+1-dimensional boundary exterior into the 4+1-dimensional bulk, i.e., crossing the event horizon of the black hole, as a kind of smearing across the exterior surface of the hydraulic jump (the side of the hydraulic jump on which our universe resides). The object crossing into the positive energy region would pass into the higher-dimensional bulk and eventually hydrodynamize, i.e., the object would first break down into fundamental particle constituents and then phase transition into the positive mass fluid that makes up that local region of the bulk interior, remaining trapped there by the repulsive pressure surrounding it in the bulk.

Over long timescales, these positive energy regions at the interior boundary of the bulk continue to aggregate locally and reach a supercritical density that can trigger another black-to-white-hole transition, beginning an entirely new process of developing the cosmological scaffolding in which it is possible for matter to self-organize and evolve into highly complex structures by virtue of being held far from equilibrium by the white hole powering the higher-dimensional bulk and lower-dimensional boundary exterior.

On this view, black holes can form due to (i) positive mass fluid aggregation trapped against the interior boundary surface of the bulk, (ii) positive mass matter aggregating on the exterior boundary surface, or (iii) a combination of (i) and (ii). In other words, a sufficient density of positive mass fluid on the interior boundary surface can create extremely large primordial black holes in the absence of any matter at all on the exterior boundary surface.

This is precisely what happens in the formation of the white hole during the Planck epoch. One or more black holes are formed almost immediately. Meanwhile, the fluid dynamics in the bulk become highly dissipative under the influence of the white hole core. As the two bulk fluids transition into a strongly coupled regime, the entropy drop in the bulk dissipates a tremendous amount of heat into the exterior boundary surface. The only way for this heat to dissipate is by venting through the primordial black holes that were just formed.

This tremendous dissipation of energy quickly brings the exterior boundary surface to a temperature on the order of 10³² K. The exterior boundary surface in the region near the black hole is now an extremely small, dense, hot 3+1-dimensional spacetime region with positive energy density and high entropy. Because the black holes are the only vents available to dissipate the energy of the far-from-equilibrium dynamics of the bulk, a positive-negative mass symmetry breaking occurs in which, unlike positive energy, negative energy can never "escape" onto the exterior boundary surface.

During the Planck and Grand Unification epochs, the interior boundary of the bulk spacetime is not yet saturated with positive and negative mass fluids. As the positive and negative mass fluids repel to the boundary interior under the repulsive force of the negative mass fluid remaining in the white hole core, a short but massive inflationary period begins.

As the bulk expands, the energy density, temperature and pressure on the exterior boundary surface rapidly decrease, causing the energy on the exterior boundary surface that vented through the black hole to transition from a weakly coupled quark gluon plasma (QGP) to a strongly coupled QGP and ultimately to confinement and hadrons with a mass gap. Each primordial black hole vents the energy dissipation from the bulk into the exterior boundary surface. In other words, each primordial black hole creates its own Big Bang event. The question thus arises whether (i) these Big Bang regions on the exterior boundary surface crossover, or (ii) the bulk expands so quickly that these regions never come into contact.

The bulk smoothly transitions out of the inflationary regime as the repulsive pressure between the fluids at the boundary surface and the negative mass fluid remaining in the core establishes an interior horizon stabilizing the core, thus preventing its rapid depletion. The interior boundary surface and the interior horizon are now fully saturated with an inhomogeneous distribution of positive and negative mass fluid. Thus, the exterior boundary surface most likely expands anistropically, with different expansion rates in different regions on the exterior boundary surface depending on the local distribution of negative mass fluid on the bulk side of the hydraulic jump.

As the bulk continues to expand, surface volume opens up at both the interior horizon and interior boundary. This permits negative mass fluid to continue to be expelled from the core over long timescales at a controlled rate based on the metastable regime that the interior horizon helps establish. In other words, the interior horizon serves as a way station between the core and the interior boundary surface, and the fluid from the core and interior horizon is expelled at a rate determined by the rate at which interior boundary surface volume frees up due to expansion. The spacetime picture of this expansion of bulk and boundary thus resembles a Gabriel's horn with a 4+1-dimensional finite interior volume and a 3+1-dimensional infinite exterior boundary volume.

Both boundary and bulk spacetimes have global negative curvature but local curvature varies due to the anisotropic distribution of the bulk fluids. The fluids running away from the negative mass core and interior horizon expand the bulk spacetime, thereby expanding the lower-dimensional exterior boundary surface on the other side of the hydraulic jump.

There may be many regions on the exterior boundary surface that are causally disconnected, and which have their own Big Bang events and subsequent evolution of complex forms of matter. This is one sense in which the concept of the multiverse might be invoked in the WHD program, i.e., causally disconnected spacetime regions on the same exterior boundary surface. The other sense in which one might invoke the multiverse in the WHD program is in the sequence of black-to-white-hole transitions that can result in entirely new bulk spacetimes and exterior heat sinks being created.

It is important to emphasize that the stabilization of the rate at which negative mass fluid is expelled from the core enables the white hole to thrive in this metastable regime for a very long time. In other words, the core does not deplete at the end of the initial inflationary period because the pressure from the interior boundary surface and interior horizon enable the core to smoothly transition out of inflation and expel at a more controlled rate.

Over the lifetime of our universe, the white hole remains behind a weak extra-dimensional horizon in which it (i) drives the expansion of the universe via negative mass fluid ("dark energy"); (ii) aggregates clusters of positive mass matter in the lower-dimensional exterior surface via positive mass fluid ("dark matter"); and (iii) dissipates energy into the universe via the black hole vents, albeit at a much lower and more stable rate on long timescales. Put simply, we live in a heat sink for a low-entropy fluid dynamics embedded in a higher-dimensional space that remains held far from equilibrium for an extremely long time.

On this view, what we call dark matter and dark energy are the effects of something that perhaps in the broadest possible sense could be described as a kind of holographic encoding of the positive and negative mass fluids, respectively, trapped near the interior boundary surface in the bulk. Dark matter will never be found on our exterior boundary surface, because it isn't there. Rather, the gravitational potential on the exterior boundary surface results from the pressure exerted by the positive mass fluid against the bulk side of the hydraulic jump.

The false vacuum energy of the exterior boundary surface remains constant despite the expanding boundary surface due to the influence of the continuous inflow of negative mass fluid on the bulk side of the hydraulic jump. Thus, for instance, a critical threshold can be obtained after approximately 5 billion years in which expansion stops slowing and begins accelerating because the boundary surface expands to allow more negative mass fluid trapped at the interior horizon to reach the interior boundary surface. Changes in the sign of the derivative of the expansion rate would be expected to happen locally and differ across different regions of the boundary.

Because the positive and negative mass excitations in the bulk behave like nearly perfect fluids held in a metastable regime by the white hole core, it is the pressure between the two fluids that forms the interior boundary surface, i.e., the edge of the bulk spacetime. The fluids remain infinitely far away from the interior boundary surface but exert a pressure on it that forms the weak horizon best characterized as a hydraulic jump.

The question of how the fluids on the bulk side of the hydraulic jump slave the lower-dimensional spacetime on the other side of the hydraulic jump, i.e., the lower-dimensional exterior boundary surface, requires the invocation of something akin to a holographic dictionary. It should be noted that the term "holography" is used in the broadest possible sense here, as the holography invoked in the WHD program differs in a host of fundamental ways from the toy model holography demonstrated, for instance, in large N (many color), supersymmetric Yang Mills theories corresponding to AdS₅ × S₅ string theory where one has an integrable, particle-free theory on the boundary and a weakly interacting supergravity theory in the bulk. More will be said about this in the next chapter.

For now, we note only that the kind of "holography" we develop in the WHD program arises out of a form of slaving mechanism in which the bulk exerts control over the dynamics on the exterior boundary by erecting a scaffolding that drives ordinary matter in a highly non-ergodic journey through its phase space. The bulk slaves the boundary by (i) dissipating energy through black hole vents; (ii) exerting positive and negative pressure through the bulk fluids at the boundary; and (iii) maintaining fundamental fields that span both bulk and boundary, including gravity and the Higgs.

With respect to this third slaving mechanism, like gravity, the scalar field imparting mass also spans the bulk and the boundary. What we observe as the Higgs field are the boundary representations of this higher-dimensional scalar field. This explains why the energy density of our observed boundary-trapped Higgs field is much larger than the observed vacuum energy density. In other words, the negative energy density occupying the bulk cancels most but not quite all of the energy density of the observed Higgs field, resulting in the near-zero but slightly positive value of what is referred to as the cosmological constant.

Thus, for the WHD program to get off the ground, we must find a way to explore an open many-body quantum system dual to a black hole in the bulk and driven from the outside by fields and matter in the bulk. This is no small task given the available mathematical toolkits for exploring dynamics of many body quantum systems held far from equilibrium over long time scales.

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Footnotes

¹ Not to be confused with negative mass squared, i.e., imaginary mass.