Minimal Deterministic Physicality Applied To Cosmology
Transcript Of Minimal Deterministic Physicality Applied To Cosmology
MINIMAL DETERMINISTIC PHYSICALITY APPLIED TO COSMOLOGY
JOHN S VALENTINE
Independent researcher, [email protected]
This report summarizes ongoing research and development since our 2012 foundation paper, including the emergent effects of a deterministic mechanism for fermion interactions: (1) the coherence of black holes and particles using a quantum chaotic model; (2) wide-scale (anti)matter prevalence from exclusion and weak interaction during the fermion reconstitution process; and (3) red-shift due to variations of vacuum energy density. We provide a context for Standard Model fields, and show how gravitation can be accountably unified in the same mechanism, but not as a unified field.
Keywords: unified mechanism, physicality, deterministic, mass-energy, weak interaction, wave-particle duality, collapse, entanglement, spontaneous symmetry breaking, decay, gravitation, field, neutrino, fermion, boson, black hole, redshift, anti-matter asymmetry.
1. Introduction
Our deterministic mechanism has simple foundational rules for emergent physicality [7]: 1) Waves are bound in pairs as oscillators (bosons); 2) Waves propagate radially, and only at light speed,
having equivalence of phase, distance, and time:
= =
3) Waves having the same phase and source are excluded from interactions;
4) A boson’s mass-energy is a function of its phases,
=− (
)
5) Other sources’ waves are phase-modulated by ; 6) Bosons collapse into a fermion where waves from
two different bosons have value –b at a unique point (fig.1, 3.2).
solutions of phase (2); and as a matter–anti-matter duality where structural evolution leads to a prevalence of one sign of matter over large regions, polarizing the other sign into vacuum energy (5).
2. Physicality
At a fermion, the four Dirac phases are present, though two are phase-shifted from being strict ± duals. Radiation resumes immediately from the new point source. Two of the waves emitted from the source have identical phase, so are excluded from interacting with other bosons because they are non-unique in all possible external variables (3.2, fig.4).
2.1. Boson structure: mass, leading to wave collapse
A boson’s mass-energy is its elliptic deviation from a circular phase picture of (cos , cos ); a scalar function of the phase difference between its two waves:
− = − cos( − ) = − (
) (1)
Figure 1. Phase evolution of a fermion’s constituents.
We exploit ± as a matter–vacuum duality, localizing waves in an interference process at unique spatial
Figure 2. Boson structure.
While propagating, mass-energy is a phase operator on the waves of other overlapping bosons:
=
+∑
(2)
Or, in right-to-left operator notation:
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=
(3)
In other words, where a boson overlaps another, its mass-energy widens the phase window for both its own collapse, and that of overlapping bosons, even those of zero mass, creating gravitational force as expected (3.7).
3.2. Emergent localization of mass [7]
Mass can be loosely localized by this mechanism (2.1). ( ) (eq.4) gives us the history-dependent probability
of collapse for a single wave for radius , per wave cycle, incorporating the failure of previous events, and the remaining null-interaction term to infinity:
()
( ) = 1 − (1 − )
(4)
where is the proportion of the phase cycle available for interaction due to mass-energy (eq.1), and
Figure 3. phase-modulates to solutions of = − , advancing or retarding the prospective quantization of fermions by a fraction of Planck length.
This can be integrated to a probability function for decay, propagation, collapse or decoherence (3.12).
(∞) → 0 ;
( ) =1
(5)
3. Emergent Effects
3.1. Particles
1) Fundamental bosons: scalar radiation (2.1). 2) Fundamental fermions: points of locality (2, 3.2).
Particles are fermions or a confined system of fermions and bosons that consistently maintain their constitution (fig.4). Such particles (e.g. quarks, electrons, hadrons), have convenient ontological names while they maintain their constitution.
Figure 5. Probability distribution for single iteration of collapse, with radius : plot of ( ) for = 10 , eq.4.
may be varied over iterations or limits, to incorporate the introduction of waves throughout the life of the wave of interest. Large masses tend to collapse at smaller radius than smaller masses (eqs.1–4, Table 3), localizing the mass-energy of matter near its emission source, with lighter bosons more likely to be radiated away, becoming environmental vacuum energy.
Figure 4. Fermion reconstitution with vacuum: Identical waves from fermion event A are excluded from triggering the next quantization condition until . (a) weak-excluded until B; (b) weak-broken until C.
We should be careful to avoid correcting our imperfect abstract fields using fictitious force carrier ‘particles’; such entities will be prone to nonconservation (3.7).
Why are fermions collapsed, localized states?
To understand wave collapse and localization, we look at which terms are unique as a system evolves.
In Table 1, we have bosons A and B from different sources, each having waves 1 and 2, with ‘wave 1’ being the reference wave at collapse. For the ‘fermion’ column, the interacting waves [A1, B1] at − are identified only by their unique spatial solution. This can be considered dual to the boson state; bosons are distinguished by unique source and phase (but not space), are not coupled with other bosons, and have no unique spatial solution. At a fermion point, two waves of identical phase meet (2), but this does not violate the exclusion principle because they originated from different sources. Thus, similar fermions may exist as matter, only when their spatial identity is unique.
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Table 1: Uniqueness of wave phase and space , for components of a fermion event.
pre- fermion
post-
( = ) ? n/a
Unique
Unique
( = ) ? n/a Non-unique Non-unique
disruptive rather than supportive of constitution. Our approach is powerful in examining such speculative high-energy or early-universe conditions. Indeed, it is possible to treat black holes and particles similarly, and to examine decoherence in context of environmental variables (4).
( = ) ? No ( = ) ? No
as point as point
n-sphere* n-sphere*
3.3. Weak interaction
The symmetry of the excluded waves (2) is broken with the collapse of one of the two bosons radiating from a fermion event: disentangling the collapsed boson, and enabling the other excluded wave sharing the shell (fig.4: AC). We map this to spontaneous symmetry breaking and the weak interaction; ‘spontaneous’ being attributed to vacuum energy as bosons. While this is no different from every other fundamental interaction, its context provides an emergent and measurable effect. How the particle behaves in its environment, depends on the first interaction being collapsed in a confined manner (internally), or a radiated manner (externally). A weak field is then a statistic of the difference between these wavefunctions (3.1, 3.12). This is difficult to distinguish as a conventional observation, because the interaction is inherent to all fermions (being the first event, of three total, required to reconstitute a fermion) but it is not always available to be measured externally.
3.4. Sign of angular momentum
Given any reference wave (fig.1), a boson’s other wave is the vacuum wave (order term). As an oscillator (fig.2), they define its intrinsic angular momentum, with sign dependent on whether the reference wave leads or trails the vacuum wave.
3.5. Decoherence
The environmental vacuum flux provides the only reflection points (fig.4: B,C), external to the confined particle, that prevent bosons escaping to infinite distance. If that process fails, the particle changes its constitution, gaining matter, or becoming decoherent. Decoherence may be caused by: a lack of supporting environmental bosons, the introduction of disruptive bosons, or a composite’s bosons slipping out of critical phase. In high-energy environments, this flux can be
3.6. Particle genesis and unification energies
If the flux density of vacuum energy increases from our background levels, to that of the particle itself, then the particle is likely to become decoherent as it approaches thermal equilibrium with its environment: it will decay into the flux of the vacuum to become part of its plasma [9]. Given that the external bosons are intercepting the particles’ own interactions, we predict that such environments reduce the interaction size of the particles, with pressure-like effect [9], with consequences for emission and absorption of radiation (red-shift) [10].
If we apply this to QED and QCD scales, and increase the environmental vacuum energy (or provide enough incoming matter), then given time, the probability equalizes, between the particle continuing to preserve its constitution, or instead interacting with other bosons. This gives us a context for unifying particles on the common basis that we have described (2). If we know a particle’s make-up, we can approximately identify the energy spectrum for its decay into ‘soup’, or condensation of plasma into conserved particles. Each system (with vacuum) has its own phase diagram, including weak interaction radii.
Traceable constituents
Our constitution-invariant approach offers some explanations where accepted hypotheses allow particles to be changed randomly by fields: we maintain instances of bosons, which themselves determine the type of particles that are maintained or the radiation that is emitted. We remove the ‘dice-rolling’.
In doing so, we have not abandoned quantum field theory, which is a necessary compromise to enable relevant statistical computation of complicated systems. What we have here is a tool that may deliver quantum mechanics, and describe what its fields and interactions are, rather than assuming them to be purely abstract algebraic constructs and concepts.
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3.7. Wave collapse by gravitational sources Vacuum energy will interact with a large body (fig.6: C), and radiate from it as bosons, again as vacuum energy. The more mass-energy body C has, the more vacuum energy it will collapse and re-emit.
Figure 6. Gravitation: a boson from body A is collapsed by radiation from large body C, rather than by vacuum energy (shown here as planar waves, approximate to distant spheres).
As body C’s bosons radiate, some of them will collapse. With increasing radius, their area for interaction increases, giving a higher probability of collapse from vacuum energy, as per eq.4. Some of the bosons available to test particle A will be environmental vacuum energy, and some will have been emitted by body C. Where bosons from particle C are preferred, this results in a gravitational deflection (or ‘force’). The resulting approximation of gravitational deflection [7] is comparable to classical formulations:
( , , ) = 4 (6)
Unification of the gravitational field?
We have reservations about whether a unified field theory can include gravity, instead suggesting that, although we get gravitation ‘gratis’ with our mechanism, it might not be helpful to search for a unified field in the conventional manner. Such a gravitational field would be a fictitious, prone to accountability problems.
The answer might instead lie in our approach, of finding a fundamental mechanism, with uniformlydefined entities, the simplest one-basis algebraic abstraction, and very simple rules (1). The standard interactions and fields are then statistical derivations of the fundamental interaction, with the added benefit of knowing what information is discarded when building such approximations. In fig.7, all bosons overlapping the test particle have the same structure. Fermions 1 and 2 are assumed to be an example sequence of fermion events within the test particle: respectively a virtual vacuum interaction, and (e.g.) a quark. For charged particles, the vacuum provides a flux current that passes through the particle, where bosons in the structure are substituted for like vacuum bosons, before being radiated later by the particle structure.
The mean deflection , independent of the mass of the test particle, is the probability that the test particle (fig.6: A) will interact with the body’s flux , rather than with the environmental vacuum flux , scaled by the mean expected vector between particle events where the particle interacts with the body’s bosons. Stable particles may become decoherent (3.5) in extreme gravitational flux, e.g. near a black hole (4).
The first opportunity for gravitational interaction is a point approximately between the bodies (see arrows meeting, fig.6), in contrast to the uniformly-distributed directionality of vacuum interactions, unless there are some large nearby structures that generate flux. The direction resulting from its own bosons collapsing will depend on its structure, including any structural changes that aggregate to its classical momentum.
Figure 7. Attribution of unified wave sources. C, E: gravitational flux of nearby massive bodies; A: confined bosons; B and D: anonymous vacuum bosons.
3.8. Neutrinos as vacuum energy
We propose that the low mass-energy constituent bosons of neutrinos [7] are presently in a state of plasma or soup, requiring a significantly lower vacuum energy flux before the majority of neutrinos can become conserved particles in their own right.
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Identity of neutrinos
Presently, neutrinos will not maintain their identity: due to their low mass-energy, they extend noncollapsed for great distances, and vast numbers of bosons will overlap and interact with bosons of higher mass-energy (3.2). This makes neutrino oscillations difficult to measure, because we are unable to guarantee that a neutrino has the same identity of bosons at successive detectors. We must instead detect and count the flavor of many instances and statistically infer flavor changes due to intermediate conditions.
Bosons
W and Z bosons are intrinsic to the re-constitution circuit of each fermion. Given our statistical derivation of gravity (3.7), we do not need the spin-2 graviton.
Photons
We model photons as paired boson impulses, absorbed by structures like their emitters, having a frequency that may be derived from a sparse sampling of impulses (6) [7: 6.2.1.2]; compatible with creation and annihilation operators of quantum harmonic oscillators.
Vacuum energy, dark matter, and anti-neutrinos
Neutrino constituents are a good candidate for the vacuum energy that allows fermions to reconstitute. Its plasma creates temporary fermions from vacuum energy [5], with the properties required for dark matter.
Rather than taking a field-based approach, with continuous matter propagation where events seem spontaneous, we instead specify a deterministic process for (anti-images of) fermions to interact with identifiable instances of vacuum energy. This gives us additional detail when exploring vacuum interactions. In the Standard Model, the weak interaction seems only to interact with left-handed matter, because the collapsed boson always has a particular sign for angular momentum at the point of weak interaction, so by definition, it is ‘left-handed’. Doing the same for anti-matter using our mechanism, we find the weak interaction is right-handed for anti-matter. This can be seen in the diagram for fermion decay (5.2: fig.11).
3.9. Constitution of Standard Model entities*
It is controversial enough to suggest that fermions can have sub-structure. The following hypothetical list is highly rudimentary and speculative, based on highenergy decay modes, and the requirements for massenergy when creating fermions from vacuum.
Fermions
Using two boson energies, A (high mass-energy) and B (low mass energy), we compose three types of fermion: Quark (A, A); Lepton (A, B); Neutrino (B, B).
3.10. Generations as n-dimensional solutions
In previous work [7], we suggested that unique phase solutions for a fermion (3.6) may have lower spatial dimensionality than 3. This positions fermions, and by extension, a boson B (Table 2).
Given that the third generation requires a unique 1dimensional solution, and only allows this when no other bosons are overlapping, their effective radius is very small. Should vacuum bosons increase the overlapping boson count for the propagating boson shell, it would introduce more constraints for the unique solution required for the next fermion event, so the bosons will radiate further.
Table 2: Dimensionality of unique fermion solutions.
Generation/Flavor
1 23B
Uniqueness in dimensions 3 2 1 0
Total overlapping bosons
4
3 2 1
Lepton (B, A), (A, B)
–
Neutrino (B, B)
–
Quark (A, A)
d/u c/s b/t –
This introduction of overlapping bosons gives opportunities for the constitutional input required to create the extra fermions of standard weak decay modes (5.2: fig.11). The high mass values of (for example, the third generation of) quarks equate to the energy required to constitute a plasma of similar fermions. In such plasmas, the quarks formed would quickly degrade from t/b, to c/s or u/d quarks, because a dense vacuum flux would cause bosons to overlap more readily, increasing the dimensionality of the unique solution, and decaying the quark when a unique solution is found.
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An artificial scenario where third-generation quarks could persist is difficult to create and maintain: where a plasma of sufficient energy exists, it decreases the probability for one-dimensional solutions because of its high flux density, so its structure must be regular.
The number of overlapping bosons required to create a fermion determines the capability for a fermion to be directional, with generation-1 fermions (u/d quarks, electron-like leptons) being the most directional, due to the availability of more terms for interference.
3.11. Computing solutions: geometry of limits
deterministically by testing whether the newlyoverlapping waves (at the point directly between the sources) would be in the condition required for collapse.
Given that the active phase window of a wave is a tiny proportion of the available phase cycle, then with random phase, most waves will progress from stage 6 to stage 10, to be radiated until a vacuum wave eventually meets it at the phase required to collapse it. Self-correcting phase-coherent structures may allow more instances of state 7 than would be indicated solely by mass-energy values. Stages 8, and stage 9 (which, unlike the other states, repeats every cycle) would occur most frequently in confining structures, as in QCD.
Figure 8. Evolution of wave geometry, in Euclidean space. P , P , P are deterministic fermion events. “Final Geometry” is for two sources to infinity; adding a further source presents more constraints and opportunities for unique solutions.
We may quantitatively solve the unique solutions in Euclidean space, by identifying the limits where each solver equation would apply. Solutions occur only within a wave cycle of the introduction of a new intersection within the system. Fig.8 shows this evolution. The trivial case, of there being no vacuum energy, is the interactions between the known bosons/waves, which can be achieved entirely
Figure 9. Quarks {1, 2, 3} in singlet, with confined RGB bosons, and anti-RGB interacting with vacuum (at grey fermion points). Time: rightwards, compacted space: upwards.
Interactions with environmental vacuum energy makes the chaotic approach non-trivial. If we concede to using statistics rather than instances of vacuum energy, we lose the deterministic view, and must instead branch each possible outcome as part of the total sum of probable events.
3.12. Free fermion in vacuum
We can quantify a free fermion simply by specifying { , } as the mass-energies of its two bosons. To obtain a probability distribution, for the collapse of each wave, we also need a statistic of the vacuum. Assuming this be a scalar mass-energy, we can use eq.4 and map this spherically into the sample volume, for each boson.
The fermion’s first reconstitution is the second collapse of the heavier fermion, combined with either the returning lighter boson, or a substituted boson from vacuum. The result is slightly skewed from the standard
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probability = amplitude
to instead be factors:
probability =
with the terms representing the amplitudes of the two bosons on their respective paths, including decoherence and substitution probabilities. One might want to privilege boson 1, to track the heavier boson, where it is assumed that the lighter boson could be exchanged for vacuum bosons without a macroscopic observer necessarily noticing. Using as reference is equally valid, as the formulation includes the probabilities of either or both bosons failing to collapse; the latter can be considered to be ‘decoherence of the fermion’.
Obtaining a PDF for given time limits is less trivial, because when a collapse occurs, we must ‘branch’ reality in a many-worlds sense, and reintegrate results.
4. Black Hole Cosmology [9]
Recent work by S.W. Hawking [8] has led us to review our work [5, 7]. Both we and Hawking have stated requirements and principles for approaching the poorly-understood physics of black holes. Here we compare the works, and apply our previous principles to find conclusions. We propose that there is no absolute event horizon: bosons of different massenergy value present respective effective probabilistic escape boundaries in a process of distillation that occurs in an evaporation process, driven by the flux of vacuum energy. Our foundational mechanism behaves no differently in low-energy environments than in a black hole environment, and we extract emergent effects without the effective limits of mainstream representations and their transition problems (general relativity, AdS / string / brane, QFT).
We offer our deterministic mechanism to fulfill the requirements and conclusions outlined by Hawking, using simple classical principles to produce quantum effects, in a manner that is constitution invariant, and preserves unitarity and information. We begin by comparing respective principles:
Approximations and statistical methods can fail
Both authors highlight the pitfalls of approximations that discard information and lead to misunderstandings,
H:“…approximation of this chaotic metric by a smooth Kerr metric is responsible for the information loss in gravitational collapse.” [8]
V:“We lose fidelity from the physical mechanism by approximating the actual bosons as a power spectrum of vacuum energy. … We lose even more fidelity by assuming the power spectrum as a scalar flux term. … We also lose the phase coherence of any radiation, and the quantum detail for individual wave collapses.” [7: 2.3, 3.1.1]
V:“Conventional background vacuum energy density and its related statistics assume a uniform [continuous] or non-local field value” [7: 1.1.3]
Boundaries: deterministic mechanisms are required
V:“…it does not conform to a continuous function with radius, and conventional rigidity of Schwarzschild solutions is probabilistically avoided. …The unitary phase operation implies that no quantum field value may exceed unity, and the scenario of a fermion outwardly crossing the event horizon is possible.” [5]
H:“However inside the event horizon, the metric and matter fields will be classically chaotic. … The chaotic collapsed object will radiate deterministically but chaotically. … That is unitary, but chaotic, so there is effective information loss.” [8]
V:“Confinement, entanglement, vacuum statistics, forces, and wavefunction terms emerge from the model’s deterministic foundations.” [7: abstract]
V: “We can assume that, in a massive body, a proportion of radiated bosons will interact with other quanta of radiation from the same body, … in a chaotic system.” [7: 3.1.2]
V:“When two waves … are available …, the solutions … are superimposed: interleaved and ordered.” [7]
V:“The history-dependent radial form of probability distribution incorporating the failure of previous events, and the remaining null term available to infinity tends to zero for infinite r” [7: 2.2]
There is no ‘event horizon’
H:“…gravitational collapse produces apparent horizons but no event horizons behind which information is lost.” [8: abstract]
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V:“The Schwarzschild radius is not privileged, but … achieved by quantum means; our event horizon is a fuzzy probabilistic boundary.” [7: 5.1]
Information loss
We identify with the previous Hawking quote offering a context for matter (2) where no information units are lost when traversing a black hole,
V:“We may resolve the information paradox … the ‘event horizon’ is not a strict barrier, but a probabilistic one, … all bosons may eventually traverse the event horizon, in a different ‘encoding’ than the matter that entered the body.”
[5: 5.7]
V:“This model does not suffer ‘information paradox’ problems, because our matter is encoded as separate bosons, and even within the dense body of a black hole, these bosons interact as normal. However, the encoding of fermions entering a black hole is likely to be significantly scrambled by the interactions within.” [7]
V:“Convention assumes an unchanging constitution of a fermion, and that some vacuum properties are constant, whereas our model … operates on the fundamental information units: the waves of bosons, allowing fermions and the interacting elements of their environment to accountably change their constitution.” [7: 1.1.3]
Representations need interfacing
There is an interface problem between the effective limits of established theories,
V:“…having limited scope as effective methods that degrade at smaller scales and higher energies.” [7]
V:“…the constitution-invariance of the process, free of renormalization, singularity problems, and effective energy limits, is worthy of further study.” [7]
H:“ADS-CFT correspondence indicates that the evaporating black hole is dual to a unitary conformal field theory on the boundary of ADS.” [8]
H:“…the correlation functions from the Schwarzschild anti deSitter metric decay exponentially with real time. … the topologically trivial periodically identified anti deSitter metric is the metric that interpolates between collapse to a black hole and evaporation.” [8]
4.1. There are no event horizons
In even the most extreme scenarios, a boson can collapse further away from the black hole than its own source event, allowing matter or radiation to escape over cosmological timescales (4.5). This agrees with Hawking’s assertion that “gravitational collapse
produces apparent horizons, but no event horizons behind which information is lost” [8], but contrasts with the general relativistic view that the gravitational field overcomes all outward radiation (4.3).
4.2. The re-encoding of matter
Fermions need external bosons to reconstitute (fig.4), but vacuum bosons of similar mass-energy can substitute themselves into the fermion structure (3.5, fig.11), ‘conducting’ vacuum energy, and preserving the ontology of the fermion while changing its identity. Generally though, the probability, that a stable fermion re-encodes with the same constitution, decreases as vacuum energy flux density increases.
4.3. Unitarity and mass-dependent wave collapse
Unitarity is preserved, because interactions continue inside the conventional Schwarzschild radius, albeit intensively and chaotically, in a manner that is difficult to calculate meaningfully for a significant duration. The deterministic calculation process is complete, and without singularities. With sufficient attention to detail, this applies [7: 2.1] to any system or extent, for any desired outcome to occur, with probability 0.0–1.0 (eqs.4,5). To calculate a boson’s probability of collapse using our mechanism, we need to know: (a) The phase interval for which its waves are
receptive to collapse, derived from mass-energy, in turn derived from the phase interval between a boson’s waves: the elliptical skew of the oscillator (2); (b) Its propagation rate, which is universally . (c) Its propagation metric, which is radial, but can be applied to flat space for vacuum interactions. (d) The vacuum energy flux, e.g. count and massenergy values for quanta, see (a), or (less exactly) the mass-energy power spectrum of the vacuum, or (less exactly again) a scalar term. (e) Which of the bosons’ waves are not excluded (2). Where two or more waves are active on a shell, the function is a set of ordered and interleaved trials.
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Taking fig.5 as a trivial example [7: 2.1.1], of one nonexcluded wave propagating through vacuum, having evenly distributed quanta at identical mass-energy values (as ideally close to isotropic as discrete vacuum energy can be), we find that each wave cycle would have a probability of collapse proportional to the width of the interaction window (eq.3, Table 3), and to the flux traversed by the sweep of the growing surface area.
Limits exceeding 1.0
Another aspect of the function is the number of overlapping vacuum bosons, which converges the probability of collapse to 1.0 as the count approaches infinity. This differs from general relativity, which presents no limit to the gravitational field when the flux density approaches infinity, exceeding ‘1.0’ in terms of fundamental effects, generating singularities, and therefore excluding all probability of emission.
4.4. Gravitational fields generated by black holes
Given that we define gravitation as a statistical tendency for fermions to deviate towards sources of vacuum energy flux, i.e. massive objects, (3.7) [7: 3.1], and that gravitation is wholly propagated by our mechanism (and not non-locally), it follows that any gravitational effect imposed by the black hole must be transmitted by escaped bosons. We should therefore ask: in the local context of our mechanism, if very little radiation escapes a black hole, then how does a nearby object feel its gravity?
this in terms of fermionic matter at the interaction points, corresponding to sources of bosons. Starting with the outermost: (a) The light-emitting matter we can see; (b) Gravitationally-interacting dark matter at the
periphery of black holes, which escapes directly, or interacts with vacuum quanta which in turn interacts with external bodies; and (c) The matter of confined mass-energy within black holes that does not directly contribute to the vacuum energy currents outside the body.
Given time, matter evaporates to outer tiers, releasing stored mass-energy to the surrounding space, with correspondingly characteristic spectra.
Black holes as an energy store
A body’s contribution to the gravitational field is derived entirely from its interaction with environmental vacuum energy, the background level (fig.10), except: (1) when it is evaporating (gravitational flux is
higher); (2) when some of its mass is confined (flux is lower
than expected for the mass of the body); (3) when it is absorbing material (flux is lower).
In this respect, a black hole can be viewed as a store of mass-energy, and also of the flux outside the ‘surface’ that contributes to gravitation (3.7), and the dark matter that allows orbits to remain stable at lower velocity.
Confined mass-energy and gravitational field
We envisage sufficiently large black holes where the probability is close to zero for any given boson to escape from far below the conventional event horizon within reasonable time limits. In other words, the boson is confined, traversing fermion events within the body of the black hole. These may eventually evaporate, but while bosons are confined like this, the overall flux contributing to the gravitational field outside the horizon will be lower than expected for the total (hidden) mass within. Objects around a black hole will not feel gravitational interactions from the massenergy confined inside a black hole.
This picture implies that there are three tiers of boson behavior, in terms of effect and observation, which can be loosely mapped radially. We write about
Figure 10. Deterministic black hole evaporation: simplified with all bosons having identical mass-energy value.
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Prediction: radial occlusion effect; EPR variants
A large body, at radius from a radiating source, should collapse some of the waves that would otherwise have radiated beyond the system. This occlusion effect should be a squared order smaller than direct phase modulation interaction and should be testable [7].
4.5. No horizons: equilibrium, and evaporation
As with the thermodynamic approach, we propose that equilibrium is a state of uniform flux density. Any other distribution, where environmental bosons exist, will eventually correct itself towards equilibrium with the vacuum. The vacuum erodes any hard ‘event horizon’ boundary towards an equilibrium state, via a fuzzy quantum boundary. Black holes are a temporary concentration, rather than a final confined singularity state; for there to be an absolute event horizon, there must be no vacuum energy flux outside it [9].
The process of filamentation and accretion will continue until no further matter is available from the environment, and the system is at thermal equilibrium with the environment, followed by the process of evaporation, to approach the background equilibrium state ("heat death").
Final evaporation
If no heavy bosons could escape for a long time, they can still interact with the vacuum quanta, which may themselves escape and interact with the surroundings, softening the flux gradient, and weakening it further. The process for final evaporation requires a gentle slope of flux density, so that bosons can more easily collapse outward. This can be provided by the absorption of lighter bosons, or environmental vacuum quanta.
5. Matter/Anti-matter: Cascading Prevalence of Dirac Images of the Fermion
In standard literature, we accept that in creating a charged particle of the Standard Model from vacuum, we also create its corresponding anti-particle in the same event. Likewise for annihilating a particle: both it and its anti-particle are converted to radiation.
We apply our deterministic physicality mechanism to find an inherent polarizing effect from exclusion in the wavefunction, leading to a prevalence of one sign of Dirac image (matter or anti-matter) as the matter
state for the observable universe. This is limited to the radius of the weak interaction (fig.4). We offer perspectives for current cosmological hypotheses of particle genesis.
In this work, we show how exclusion applies to the waves leaving a fermion event, creating an imbalance in the probability of interaction for each of the Dirac images.
5.1. Vacuum polarization
Given any two matter-state waves, which are excluded from the first interaction of a fermion (fig.4), one of their anti-images will partake in the first collapse event, coupling with waves external to the fermion. For a conserved fermion, this also needs to happen to the remaining wave, making two de-localized collapsing anti-images (usually interacting with vacuum, or they may be confined in a composite structure). This process repeats, such that on their next interaction, we return to the original states interacting with the original constitution (anti-anti-states: the original fermion).
Integrated over any interval, collapse flavors the non-excluded waves, increasing the probability of removing the alternatives from future solutions. This leads to one sign of Dirac state as the matter state, especially in high-energy scenarios where matter nucleates from plasma. In our locality, we have matter (as conserved localized fermions) and anti-matter (nonconserved states, as de-localized anti-images).
The sign (matter or anti-matter state) of the bosons at the massive particles determines the polarity of matter and vacuum in that locality, leaving the lowermass bosons to propagate further out. Because all waves of the remaining bosons on the shell are enabled after the first interaction, they carry an uncollapsed superposition of both signs, as radiation.
With their extended propagation from the source, the lighter bosons are also more likely to be exchanged (interchanged or substituted), losing coherence as they extend from the locality of their fermion sources. With untraceability or a complete loss of coherence and source identity, we may then regard the radiation as vacuum energy.
Applying this to the mechanism for fermion reconstitution (fig.4), if a boson has sign + at event A, then exclusion requires that the same boson’s vacuum wave will be the reference wave at event B (the first interaction of the entangled shell of all bosons leaving
JOHN S VALENTINE
Independent researcher, [email protected]
This report summarizes ongoing research and development since our 2012 foundation paper, including the emergent effects of a deterministic mechanism for fermion interactions: (1) the coherence of black holes and particles using a quantum chaotic model; (2) wide-scale (anti)matter prevalence from exclusion and weak interaction during the fermion reconstitution process; and (3) red-shift due to variations of vacuum energy density. We provide a context for Standard Model fields, and show how gravitation can be accountably unified in the same mechanism, but not as a unified field.
Keywords: unified mechanism, physicality, deterministic, mass-energy, weak interaction, wave-particle duality, collapse, entanglement, spontaneous symmetry breaking, decay, gravitation, field, neutrino, fermion, boson, black hole, redshift, anti-matter asymmetry.
1. Introduction
Our deterministic mechanism has simple foundational rules for emergent physicality [7]: 1) Waves are bound in pairs as oscillators (bosons); 2) Waves propagate radially, and only at light speed,
having equivalence of phase, distance, and time:
= =
3) Waves having the same phase and source are excluded from interactions;
4) A boson’s mass-energy is a function of its phases,
=− (
)
5) Other sources’ waves are phase-modulated by ; 6) Bosons collapse into a fermion where waves from
two different bosons have value –b at a unique point (fig.1, 3.2).
solutions of phase (2); and as a matter–anti-matter duality where structural evolution leads to a prevalence of one sign of matter over large regions, polarizing the other sign into vacuum energy (5).
2. Physicality
At a fermion, the four Dirac phases are present, though two are phase-shifted from being strict ± duals. Radiation resumes immediately from the new point source. Two of the waves emitted from the source have identical phase, so are excluded from interacting with other bosons because they are non-unique in all possible external variables (3.2, fig.4).
2.1. Boson structure: mass, leading to wave collapse
A boson’s mass-energy is its elliptic deviation from a circular phase picture of (cos , cos ); a scalar function of the phase difference between its two waves:
− = − cos( − ) = − (
) (1)
Figure 1. Phase evolution of a fermion’s constituents.
We exploit ± as a matter–vacuum duality, localizing waves in an interference process at unique spatial
Figure 2. Boson structure.
While propagating, mass-energy is a phase operator on the waves of other overlapping bosons:
=
+∑
(2)
Or, in right-to-left operator notation:
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John Valentine
=
(3)
In other words, where a boson overlaps another, its mass-energy widens the phase window for both its own collapse, and that of overlapping bosons, even those of zero mass, creating gravitational force as expected (3.7).
3.2. Emergent localization of mass [7]
Mass can be loosely localized by this mechanism (2.1). ( ) (eq.4) gives us the history-dependent probability
of collapse for a single wave for radius , per wave cycle, incorporating the failure of previous events, and the remaining null-interaction term to infinity:
()
( ) = 1 − (1 − )
(4)
where is the proportion of the phase cycle available for interaction due to mass-energy (eq.1), and
Figure 3. phase-modulates to solutions of = − , advancing or retarding the prospective quantization of fermions by a fraction of Planck length.
This can be integrated to a probability function for decay, propagation, collapse or decoherence (3.12).
(∞) → 0 ;
( ) =1
(5)
3. Emergent Effects
3.1. Particles
1) Fundamental bosons: scalar radiation (2.1). 2) Fundamental fermions: points of locality (2, 3.2).
Particles are fermions or a confined system of fermions and bosons that consistently maintain their constitution (fig.4). Such particles (e.g. quarks, electrons, hadrons), have convenient ontological names while they maintain their constitution.
Figure 5. Probability distribution for single iteration of collapse, with radius : plot of ( ) for = 10 , eq.4.
may be varied over iterations or limits, to incorporate the introduction of waves throughout the life of the wave of interest. Large masses tend to collapse at smaller radius than smaller masses (eqs.1–4, Table 3), localizing the mass-energy of matter near its emission source, with lighter bosons more likely to be radiated away, becoming environmental vacuum energy.
Figure 4. Fermion reconstitution with vacuum: Identical waves from fermion event A are excluded from triggering the next quantization condition until . (a) weak-excluded until B; (b) weak-broken until C.
We should be careful to avoid correcting our imperfect abstract fields using fictitious force carrier ‘particles’; such entities will be prone to nonconservation (3.7).
Why are fermions collapsed, localized states?
To understand wave collapse and localization, we look at which terms are unique as a system evolves.
In Table 1, we have bosons A and B from different sources, each having waves 1 and 2, with ‘wave 1’ being the reference wave at collapse. For the ‘fermion’ column, the interacting waves [A1, B1] at − are identified only by their unique spatial solution. This can be considered dual to the boson state; bosons are distinguished by unique source and phase (but not space), are not coupled with other bosons, and have no unique spatial solution. At a fermion point, two waves of identical phase meet (2), but this does not violate the exclusion principle because they originated from different sources. Thus, similar fermions may exist as matter, only when their spatial identity is unique.
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Table 1: Uniqueness of wave phase and space , for components of a fermion event.
pre- fermion
post-
( = ) ? n/a
Unique
Unique
( = ) ? n/a Non-unique Non-unique
disruptive rather than supportive of constitution. Our approach is powerful in examining such speculative high-energy or early-universe conditions. Indeed, it is possible to treat black holes and particles similarly, and to examine decoherence in context of environmental variables (4).
( = ) ? No ( = ) ? No
as point as point
n-sphere* n-sphere*
3.3. Weak interaction
The symmetry of the excluded waves (2) is broken with the collapse of one of the two bosons radiating from a fermion event: disentangling the collapsed boson, and enabling the other excluded wave sharing the shell (fig.4: AC). We map this to spontaneous symmetry breaking and the weak interaction; ‘spontaneous’ being attributed to vacuum energy as bosons. While this is no different from every other fundamental interaction, its context provides an emergent and measurable effect. How the particle behaves in its environment, depends on the first interaction being collapsed in a confined manner (internally), or a radiated manner (externally). A weak field is then a statistic of the difference between these wavefunctions (3.1, 3.12). This is difficult to distinguish as a conventional observation, because the interaction is inherent to all fermions (being the first event, of three total, required to reconstitute a fermion) but it is not always available to be measured externally.
3.4. Sign of angular momentum
Given any reference wave (fig.1), a boson’s other wave is the vacuum wave (order term). As an oscillator (fig.2), they define its intrinsic angular momentum, with sign dependent on whether the reference wave leads or trails the vacuum wave.
3.5. Decoherence
The environmental vacuum flux provides the only reflection points (fig.4: B,C), external to the confined particle, that prevent bosons escaping to infinite distance. If that process fails, the particle changes its constitution, gaining matter, or becoming decoherent. Decoherence may be caused by: a lack of supporting environmental bosons, the introduction of disruptive bosons, or a composite’s bosons slipping out of critical phase. In high-energy environments, this flux can be
3.6. Particle genesis and unification energies
If the flux density of vacuum energy increases from our background levels, to that of the particle itself, then the particle is likely to become decoherent as it approaches thermal equilibrium with its environment: it will decay into the flux of the vacuum to become part of its plasma [9]. Given that the external bosons are intercepting the particles’ own interactions, we predict that such environments reduce the interaction size of the particles, with pressure-like effect [9], with consequences for emission and absorption of radiation (red-shift) [10].
If we apply this to QED and QCD scales, and increase the environmental vacuum energy (or provide enough incoming matter), then given time, the probability equalizes, between the particle continuing to preserve its constitution, or instead interacting with other bosons. This gives us a context for unifying particles on the common basis that we have described (2). If we know a particle’s make-up, we can approximately identify the energy spectrum for its decay into ‘soup’, or condensation of plasma into conserved particles. Each system (with vacuum) has its own phase diagram, including weak interaction radii.
Traceable constituents
Our constitution-invariant approach offers some explanations where accepted hypotheses allow particles to be changed randomly by fields: we maintain instances of bosons, which themselves determine the type of particles that are maintained or the radiation that is emitted. We remove the ‘dice-rolling’.
In doing so, we have not abandoned quantum field theory, which is a necessary compromise to enable relevant statistical computation of complicated systems. What we have here is a tool that may deliver quantum mechanics, and describe what its fields and interactions are, rather than assuming them to be purely abstract algebraic constructs and concepts.
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3.7. Wave collapse by gravitational sources Vacuum energy will interact with a large body (fig.6: C), and radiate from it as bosons, again as vacuum energy. The more mass-energy body C has, the more vacuum energy it will collapse and re-emit.
Figure 6. Gravitation: a boson from body A is collapsed by radiation from large body C, rather than by vacuum energy (shown here as planar waves, approximate to distant spheres).
As body C’s bosons radiate, some of them will collapse. With increasing radius, their area for interaction increases, giving a higher probability of collapse from vacuum energy, as per eq.4. Some of the bosons available to test particle A will be environmental vacuum energy, and some will have been emitted by body C. Where bosons from particle C are preferred, this results in a gravitational deflection (or ‘force’). The resulting approximation of gravitational deflection [7] is comparable to classical formulations:
( , , ) = 4 (6)
Unification of the gravitational field?
We have reservations about whether a unified field theory can include gravity, instead suggesting that, although we get gravitation ‘gratis’ with our mechanism, it might not be helpful to search for a unified field in the conventional manner. Such a gravitational field would be a fictitious, prone to accountability problems.
The answer might instead lie in our approach, of finding a fundamental mechanism, with uniformlydefined entities, the simplest one-basis algebraic abstraction, and very simple rules (1). The standard interactions and fields are then statistical derivations of the fundamental interaction, with the added benefit of knowing what information is discarded when building such approximations. In fig.7, all bosons overlapping the test particle have the same structure. Fermions 1 and 2 are assumed to be an example sequence of fermion events within the test particle: respectively a virtual vacuum interaction, and (e.g.) a quark. For charged particles, the vacuum provides a flux current that passes through the particle, where bosons in the structure are substituted for like vacuum bosons, before being radiated later by the particle structure.
The mean deflection , independent of the mass of the test particle, is the probability that the test particle (fig.6: A) will interact with the body’s flux , rather than with the environmental vacuum flux , scaled by the mean expected vector between particle events where the particle interacts with the body’s bosons. Stable particles may become decoherent (3.5) in extreme gravitational flux, e.g. near a black hole (4).
The first opportunity for gravitational interaction is a point approximately between the bodies (see arrows meeting, fig.6), in contrast to the uniformly-distributed directionality of vacuum interactions, unless there are some large nearby structures that generate flux. The direction resulting from its own bosons collapsing will depend on its structure, including any structural changes that aggregate to its classical momentum.
Figure 7. Attribution of unified wave sources. C, E: gravitational flux of nearby massive bodies; A: confined bosons; B and D: anonymous vacuum bosons.
3.8. Neutrinos as vacuum energy
We propose that the low mass-energy constituent bosons of neutrinos [7] are presently in a state of plasma or soup, requiring a significantly lower vacuum energy flux before the majority of neutrinos can become conserved particles in their own right.
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Identity of neutrinos
Presently, neutrinos will not maintain their identity: due to their low mass-energy, they extend noncollapsed for great distances, and vast numbers of bosons will overlap and interact with bosons of higher mass-energy (3.2). This makes neutrino oscillations difficult to measure, because we are unable to guarantee that a neutrino has the same identity of bosons at successive detectors. We must instead detect and count the flavor of many instances and statistically infer flavor changes due to intermediate conditions.
Bosons
W and Z bosons are intrinsic to the re-constitution circuit of each fermion. Given our statistical derivation of gravity (3.7), we do not need the spin-2 graviton.
Photons
We model photons as paired boson impulses, absorbed by structures like their emitters, having a frequency that may be derived from a sparse sampling of impulses (6) [7: 6.2.1.2]; compatible with creation and annihilation operators of quantum harmonic oscillators.
Vacuum energy, dark matter, and anti-neutrinos
Neutrino constituents are a good candidate for the vacuum energy that allows fermions to reconstitute. Its plasma creates temporary fermions from vacuum energy [5], with the properties required for dark matter.
Rather than taking a field-based approach, with continuous matter propagation where events seem spontaneous, we instead specify a deterministic process for (anti-images of) fermions to interact with identifiable instances of vacuum energy. This gives us additional detail when exploring vacuum interactions. In the Standard Model, the weak interaction seems only to interact with left-handed matter, because the collapsed boson always has a particular sign for angular momentum at the point of weak interaction, so by definition, it is ‘left-handed’. Doing the same for anti-matter using our mechanism, we find the weak interaction is right-handed for anti-matter. This can be seen in the diagram for fermion decay (5.2: fig.11).
3.9. Constitution of Standard Model entities*
It is controversial enough to suggest that fermions can have sub-structure. The following hypothetical list is highly rudimentary and speculative, based on highenergy decay modes, and the requirements for massenergy when creating fermions from vacuum.
Fermions
Using two boson energies, A (high mass-energy) and B (low mass energy), we compose three types of fermion: Quark (A, A); Lepton (A, B); Neutrino (B, B).
3.10. Generations as n-dimensional solutions
In previous work [7], we suggested that unique phase solutions for a fermion (3.6) may have lower spatial dimensionality than 3. This positions fermions, and by extension, a boson B (Table 2).
Given that the third generation requires a unique 1dimensional solution, and only allows this when no other bosons are overlapping, their effective radius is very small. Should vacuum bosons increase the overlapping boson count for the propagating boson shell, it would introduce more constraints for the unique solution required for the next fermion event, so the bosons will radiate further.
Table 2: Dimensionality of unique fermion solutions.
Generation/Flavor
1 23B
Uniqueness in dimensions 3 2 1 0
Total overlapping bosons
4
3 2 1
Lepton (B, A), (A, B)
–
Neutrino (B, B)
–
Quark (A, A)
d/u c/s b/t –
This introduction of overlapping bosons gives opportunities for the constitutional input required to create the extra fermions of standard weak decay modes (5.2: fig.11). The high mass values of (for example, the third generation of) quarks equate to the energy required to constitute a plasma of similar fermions. In such plasmas, the quarks formed would quickly degrade from t/b, to c/s or u/d quarks, because a dense vacuum flux would cause bosons to overlap more readily, increasing the dimensionality of the unique solution, and decaying the quark when a unique solution is found.
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An artificial scenario where third-generation quarks could persist is difficult to create and maintain: where a plasma of sufficient energy exists, it decreases the probability for one-dimensional solutions because of its high flux density, so its structure must be regular.
The number of overlapping bosons required to create a fermion determines the capability for a fermion to be directional, with generation-1 fermions (u/d quarks, electron-like leptons) being the most directional, due to the availability of more terms for interference.
3.11. Computing solutions: geometry of limits
deterministically by testing whether the newlyoverlapping waves (at the point directly between the sources) would be in the condition required for collapse.
Given that the active phase window of a wave is a tiny proportion of the available phase cycle, then with random phase, most waves will progress from stage 6 to stage 10, to be radiated until a vacuum wave eventually meets it at the phase required to collapse it. Self-correcting phase-coherent structures may allow more instances of state 7 than would be indicated solely by mass-energy values. Stages 8, and stage 9 (which, unlike the other states, repeats every cycle) would occur most frequently in confining structures, as in QCD.
Figure 8. Evolution of wave geometry, in Euclidean space. P , P , P are deterministic fermion events. “Final Geometry” is for two sources to infinity; adding a further source presents more constraints and opportunities for unique solutions.
We may quantitatively solve the unique solutions in Euclidean space, by identifying the limits where each solver equation would apply. Solutions occur only within a wave cycle of the introduction of a new intersection within the system. Fig.8 shows this evolution. The trivial case, of there being no vacuum energy, is the interactions between the known bosons/waves, which can be achieved entirely
Figure 9. Quarks {1, 2, 3} in singlet, with confined RGB bosons, and anti-RGB interacting with vacuum (at grey fermion points). Time: rightwards, compacted space: upwards.
Interactions with environmental vacuum energy makes the chaotic approach non-trivial. If we concede to using statistics rather than instances of vacuum energy, we lose the deterministic view, and must instead branch each possible outcome as part of the total sum of probable events.
3.12. Free fermion in vacuum
We can quantify a free fermion simply by specifying { , } as the mass-energies of its two bosons. To obtain a probability distribution, for the collapse of each wave, we also need a statistic of the vacuum. Assuming this be a scalar mass-energy, we can use eq.4 and map this spherically into the sample volume, for each boson.
The fermion’s first reconstitution is the second collapse of the heavier fermion, combined with either the returning lighter boson, or a substituted boson from vacuum. The result is slightly skewed from the standard
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probability = amplitude
to instead be factors:
probability =
with the terms representing the amplitudes of the two bosons on their respective paths, including decoherence and substitution probabilities. One might want to privilege boson 1, to track the heavier boson, where it is assumed that the lighter boson could be exchanged for vacuum bosons without a macroscopic observer necessarily noticing. Using as reference is equally valid, as the formulation includes the probabilities of either or both bosons failing to collapse; the latter can be considered to be ‘decoherence of the fermion’.
Obtaining a PDF for given time limits is less trivial, because when a collapse occurs, we must ‘branch’ reality in a many-worlds sense, and reintegrate results.
4. Black Hole Cosmology [9]
Recent work by S.W. Hawking [8] has led us to review our work [5, 7]. Both we and Hawking have stated requirements and principles for approaching the poorly-understood physics of black holes. Here we compare the works, and apply our previous principles to find conclusions. We propose that there is no absolute event horizon: bosons of different massenergy value present respective effective probabilistic escape boundaries in a process of distillation that occurs in an evaporation process, driven by the flux of vacuum energy. Our foundational mechanism behaves no differently in low-energy environments than in a black hole environment, and we extract emergent effects without the effective limits of mainstream representations and their transition problems (general relativity, AdS / string / brane, QFT).
We offer our deterministic mechanism to fulfill the requirements and conclusions outlined by Hawking, using simple classical principles to produce quantum effects, in a manner that is constitution invariant, and preserves unitarity and information. We begin by comparing respective principles:
Approximations and statistical methods can fail
Both authors highlight the pitfalls of approximations that discard information and lead to misunderstandings,
H:“…approximation of this chaotic metric by a smooth Kerr metric is responsible for the information loss in gravitational collapse.” [8]
V:“We lose fidelity from the physical mechanism by approximating the actual bosons as a power spectrum of vacuum energy. … We lose even more fidelity by assuming the power spectrum as a scalar flux term. … We also lose the phase coherence of any radiation, and the quantum detail for individual wave collapses.” [7: 2.3, 3.1.1]
V:“Conventional background vacuum energy density and its related statistics assume a uniform [continuous] or non-local field value” [7: 1.1.3]
Boundaries: deterministic mechanisms are required
V:“…it does not conform to a continuous function with radius, and conventional rigidity of Schwarzschild solutions is probabilistically avoided. …The unitary phase operation implies that no quantum field value may exceed unity, and the scenario of a fermion outwardly crossing the event horizon is possible.” [5]
H:“However inside the event horizon, the metric and matter fields will be classically chaotic. … The chaotic collapsed object will radiate deterministically but chaotically. … That is unitary, but chaotic, so there is effective information loss.” [8]
V:“Confinement, entanglement, vacuum statistics, forces, and wavefunction terms emerge from the model’s deterministic foundations.” [7: abstract]
V: “We can assume that, in a massive body, a proportion of radiated bosons will interact with other quanta of radiation from the same body, … in a chaotic system.” [7: 3.1.2]
V:“When two waves … are available …, the solutions … are superimposed: interleaved and ordered.” [7]
V:“The history-dependent radial form of probability distribution incorporating the failure of previous events, and the remaining null term available to infinity tends to zero for infinite r” [7: 2.2]
There is no ‘event horizon’
H:“…gravitational collapse produces apparent horizons but no event horizons behind which information is lost.” [8: abstract]
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V:“The Schwarzschild radius is not privileged, but … achieved by quantum means; our event horizon is a fuzzy probabilistic boundary.” [7: 5.1]
Information loss
We identify with the previous Hawking quote offering a context for matter (2) where no information units are lost when traversing a black hole,
V:“We may resolve the information paradox … the ‘event horizon’ is not a strict barrier, but a probabilistic one, … all bosons may eventually traverse the event horizon, in a different ‘encoding’ than the matter that entered the body.”
[5: 5.7]
V:“This model does not suffer ‘information paradox’ problems, because our matter is encoded as separate bosons, and even within the dense body of a black hole, these bosons interact as normal. However, the encoding of fermions entering a black hole is likely to be significantly scrambled by the interactions within.” [7]
V:“Convention assumes an unchanging constitution of a fermion, and that some vacuum properties are constant, whereas our model … operates on the fundamental information units: the waves of bosons, allowing fermions and the interacting elements of their environment to accountably change their constitution.” [7: 1.1.3]
Representations need interfacing
There is an interface problem between the effective limits of established theories,
V:“…having limited scope as effective methods that degrade at smaller scales and higher energies.” [7]
V:“…the constitution-invariance of the process, free of renormalization, singularity problems, and effective energy limits, is worthy of further study.” [7]
H:“ADS-CFT correspondence indicates that the evaporating black hole is dual to a unitary conformal field theory on the boundary of ADS.” [8]
H:“…the correlation functions from the Schwarzschild anti deSitter metric decay exponentially with real time. … the topologically trivial periodically identified anti deSitter metric is the metric that interpolates between collapse to a black hole and evaporation.” [8]
4.1. There are no event horizons
In even the most extreme scenarios, a boson can collapse further away from the black hole than its own source event, allowing matter or radiation to escape over cosmological timescales (4.5). This agrees with Hawking’s assertion that “gravitational collapse
produces apparent horizons, but no event horizons behind which information is lost” [8], but contrasts with the general relativistic view that the gravitational field overcomes all outward radiation (4.3).
4.2. The re-encoding of matter
Fermions need external bosons to reconstitute (fig.4), but vacuum bosons of similar mass-energy can substitute themselves into the fermion structure (3.5, fig.11), ‘conducting’ vacuum energy, and preserving the ontology of the fermion while changing its identity. Generally though, the probability, that a stable fermion re-encodes with the same constitution, decreases as vacuum energy flux density increases.
4.3. Unitarity and mass-dependent wave collapse
Unitarity is preserved, because interactions continue inside the conventional Schwarzschild radius, albeit intensively and chaotically, in a manner that is difficult to calculate meaningfully for a significant duration. The deterministic calculation process is complete, and without singularities. With sufficient attention to detail, this applies [7: 2.1] to any system or extent, for any desired outcome to occur, with probability 0.0–1.0 (eqs.4,5). To calculate a boson’s probability of collapse using our mechanism, we need to know: (a) The phase interval for which its waves are
receptive to collapse, derived from mass-energy, in turn derived from the phase interval between a boson’s waves: the elliptical skew of the oscillator (2); (b) Its propagation rate, which is universally . (c) Its propagation metric, which is radial, but can be applied to flat space for vacuum interactions. (d) The vacuum energy flux, e.g. count and massenergy values for quanta, see (a), or (less exactly) the mass-energy power spectrum of the vacuum, or (less exactly again) a scalar term. (e) Which of the bosons’ waves are not excluded (2). Where two or more waves are active on a shell, the function is a set of ordered and interleaved trials.
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Taking fig.5 as a trivial example [7: 2.1.1], of one nonexcluded wave propagating through vacuum, having evenly distributed quanta at identical mass-energy values (as ideally close to isotropic as discrete vacuum energy can be), we find that each wave cycle would have a probability of collapse proportional to the width of the interaction window (eq.3, Table 3), and to the flux traversed by the sweep of the growing surface area.
Limits exceeding 1.0
Another aspect of the function is the number of overlapping vacuum bosons, which converges the probability of collapse to 1.0 as the count approaches infinity. This differs from general relativity, which presents no limit to the gravitational field when the flux density approaches infinity, exceeding ‘1.0’ in terms of fundamental effects, generating singularities, and therefore excluding all probability of emission.
4.4. Gravitational fields generated by black holes
Given that we define gravitation as a statistical tendency for fermions to deviate towards sources of vacuum energy flux, i.e. massive objects, (3.7) [7: 3.1], and that gravitation is wholly propagated by our mechanism (and not non-locally), it follows that any gravitational effect imposed by the black hole must be transmitted by escaped bosons. We should therefore ask: in the local context of our mechanism, if very little radiation escapes a black hole, then how does a nearby object feel its gravity?
this in terms of fermionic matter at the interaction points, corresponding to sources of bosons. Starting with the outermost: (a) The light-emitting matter we can see; (b) Gravitationally-interacting dark matter at the
periphery of black holes, which escapes directly, or interacts with vacuum quanta which in turn interacts with external bodies; and (c) The matter of confined mass-energy within black holes that does not directly contribute to the vacuum energy currents outside the body.
Given time, matter evaporates to outer tiers, releasing stored mass-energy to the surrounding space, with correspondingly characteristic spectra.
Black holes as an energy store
A body’s contribution to the gravitational field is derived entirely from its interaction with environmental vacuum energy, the background level (fig.10), except: (1) when it is evaporating (gravitational flux is
higher); (2) when some of its mass is confined (flux is lower
than expected for the mass of the body); (3) when it is absorbing material (flux is lower).
In this respect, a black hole can be viewed as a store of mass-energy, and also of the flux outside the ‘surface’ that contributes to gravitation (3.7), and the dark matter that allows orbits to remain stable at lower velocity.
Confined mass-energy and gravitational field
We envisage sufficiently large black holes where the probability is close to zero for any given boson to escape from far below the conventional event horizon within reasonable time limits. In other words, the boson is confined, traversing fermion events within the body of the black hole. These may eventually evaporate, but while bosons are confined like this, the overall flux contributing to the gravitational field outside the horizon will be lower than expected for the total (hidden) mass within. Objects around a black hole will not feel gravitational interactions from the massenergy confined inside a black hole.
This picture implies that there are three tiers of boson behavior, in terms of effect and observation, which can be loosely mapped radially. We write about
Figure 10. Deterministic black hole evaporation: simplified with all bosons having identical mass-energy value.
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Prediction: radial occlusion effect; EPR variants
A large body, at radius from a radiating source, should collapse some of the waves that would otherwise have radiated beyond the system. This occlusion effect should be a squared order smaller than direct phase modulation interaction and should be testable [7].
4.5. No horizons: equilibrium, and evaporation
As with the thermodynamic approach, we propose that equilibrium is a state of uniform flux density. Any other distribution, where environmental bosons exist, will eventually correct itself towards equilibrium with the vacuum. The vacuum erodes any hard ‘event horizon’ boundary towards an equilibrium state, via a fuzzy quantum boundary. Black holes are a temporary concentration, rather than a final confined singularity state; for there to be an absolute event horizon, there must be no vacuum energy flux outside it [9].
The process of filamentation and accretion will continue until no further matter is available from the environment, and the system is at thermal equilibrium with the environment, followed by the process of evaporation, to approach the background equilibrium state ("heat death").
Final evaporation
If no heavy bosons could escape for a long time, they can still interact with the vacuum quanta, which may themselves escape and interact with the surroundings, softening the flux gradient, and weakening it further. The process for final evaporation requires a gentle slope of flux density, so that bosons can more easily collapse outward. This can be provided by the absorption of lighter bosons, or environmental vacuum quanta.
5. Matter/Anti-matter: Cascading Prevalence of Dirac Images of the Fermion
In standard literature, we accept that in creating a charged particle of the Standard Model from vacuum, we also create its corresponding anti-particle in the same event. Likewise for annihilating a particle: both it and its anti-particle are converted to radiation.
We apply our deterministic physicality mechanism to find an inherent polarizing effect from exclusion in the wavefunction, leading to a prevalence of one sign of Dirac image (matter or anti-matter) as the matter
state for the observable universe. This is limited to the radius of the weak interaction (fig.4). We offer perspectives for current cosmological hypotheses of particle genesis.
In this work, we show how exclusion applies to the waves leaving a fermion event, creating an imbalance in the probability of interaction for each of the Dirac images.
5.1. Vacuum polarization
Given any two matter-state waves, which are excluded from the first interaction of a fermion (fig.4), one of their anti-images will partake in the first collapse event, coupling with waves external to the fermion. For a conserved fermion, this also needs to happen to the remaining wave, making two de-localized collapsing anti-images (usually interacting with vacuum, or they may be confined in a composite structure). This process repeats, such that on their next interaction, we return to the original states interacting with the original constitution (anti-anti-states: the original fermion).
Integrated over any interval, collapse flavors the non-excluded waves, increasing the probability of removing the alternatives from future solutions. This leads to one sign of Dirac state as the matter state, especially in high-energy scenarios where matter nucleates from plasma. In our locality, we have matter (as conserved localized fermions) and anti-matter (nonconserved states, as de-localized anti-images).
The sign (matter or anti-matter state) of the bosons at the massive particles determines the polarity of matter and vacuum in that locality, leaving the lowermass bosons to propagate further out. Because all waves of the remaining bosons on the shell are enabled after the first interaction, they carry an uncollapsed superposition of both signs, as radiation.
With their extended propagation from the source, the lighter bosons are also more likely to be exchanged (interchanged or substituted), losing coherence as they extend from the locality of their fermion sources. With untraceability or a complete loss of coherence and source identity, we may then regard the radiation as vacuum energy.
Applying this to the mechanism for fermion reconstitution (fig.4), if a boson has sign + at event A, then exclusion requires that the same boson’s vacuum wave will be the reference wave at event B (the first interaction of the entangled shell of all bosons leaving