**6. General relativity and black holes**

Finally, there is General Relativity. This theory must be regarded as just an other theme of the general concept of local gauge theories. It represents a non compact gauge group of curved coordinate transformations and it may well be that it can be handled similarly. It is important to remember that this theory is not renormalizable when presented in its usual form. We do observe that the addition of one further interaction term, the square of the conformal Weyl curvature term *Cμναβ*, restores renormalisability at the cost of negative energy modes [19]. Perhaps this mode can serve as a fast variable, but much more work will be needed to remedy various difficulties.

Theories for quantum mechanics that also aspire to include General Relativity, must address the fundamental black hole question. Black holes that are sufficiently large and heavy compared to the Planck scale of units, can be perfectly well described by classical, *i.e.* unquantised Einsteinian laws. However many researchers appear to arrive at the conclusion that there is something wrong with the black hole horizon, which might even involve the larger black holes. The origin of this suspicion is the emergence of 'firewalls' forming a curtain of destruction against particles entering (or leaving) the horizon. The firewalls originate from the Hawking particles that are expected to emerge in the more distant future.

The present author found that there exists a unique procedure to neutralise the firewalls, but it does not happen automatically. To see what may well happen, one should compute the effects that particles entering a black hole have on the Hawking particles leaving. It is not an act of destruction but a precisely calculable effect of repositioning those rays of out going material. The bottom line is that the *positions* of the out going particles are effected by the *momenta* of the in-going ones, and, because of quantum duality relating position to momentum, the same relation is found when going backwards in time: the momenta of the out-going particles are linked to the positions of the in-going ones.

These findings allow one to construct a unique expression for the *black hole evolution matrix*, only requiring very basic knowledge of the mathematics of GR and QM.

However, we also hit upon a more sobering difficulty, The region behind the horizon has to be used to describe the *time reverse* of the region normally visible, otherwise the evolution matrix (actually a quantum evolution matrix) fails completely to be unitary. For someone familiar with the Schwarzschild metric and its generalisations that have charge and angular momentum, there is no surprise here, but for the quantum physicist, this presents a problem. If we reverse the time direction, we also change the signs of all energies of the matter particles. Yet quantum field theories became successful precisely because they ensure the positivity of the energy of all particles. Can we allow ourselves a theory with such apparently conflicting properties?

The only answer that we could find is that we should act in a way similar to what P.A.M. Dirac did in order to overcome the negative energy problem in the Dirac equation. Now in a black hole, we have bosons and electrons alike, but we can achieve the same result by assuming that the entire band of energy eigenstates in a

field theory should be bounded from below *and from above!* In that case, we can interpret the energy states beyond the horizon to be filled with particles completely, if the region at our side of the horizon is empty, and the other way around. The name *anti-vacuum* was coined, describing the completely filled state.

The region beyond the vacuum then represents a CPT inversion of the region at our side of the horizon. This picture appears to make perfectly sense, and we believe it to be likely that it resolves the energy inversion problem in black hole physics.

This solution of the energy inversion problem replaces the infinite energy spectrum of all harmonic oscillators generated by the fields outside the horizon, with a spectrum of evenly separated energy levels that have both a beginning and an end, the end being the highest possible energy level. We note that this is not only the energy spectrum of an atom with finite spin inside a homogeneous magnetic field (the Zeeman atom), but it also represents the energy levels of a periodic system with finite time steps *δt* in its evolution law, see the beginning of Section 2.

Indeed, we find that black holes may be telling us something about the origin of quantum mechanics.

## **7. Conclusions**

Our aim was to rescue the concept of ontology as opposed to epistemology in quantum mechanics. This tells us that the atoms, molecules, electrons and other tiny entities are features of things that really exist. They evolve into different states or objects that also exist, according to universal physical laws. We find that this makes perfect sense if what we now perceive as quantum mechanics is understood as a vector representation of the states as they exist and evolve. Vector representations themselves allow superposition, and one finds that the superpositions of 'ontological'states evolve through the same Schrödinger equations as the original states themselves. This in turn implies that one may ignore everything that is said about ontological existence as long as we use Born's dictum that the absolute squares of the superposition coefficients represent probabilities. The reason why we nevertheless attach much importance to our ontological interpretation is that it implies a severe restriction for the evolution laws; asking for the existence of an ontological representation forces us to redesign the set of elementary basis elements of Hilbert space, which might implicate new constraints on what kinds of Standard Model we may suspect to describe our world.

An ontological interpretation is also of great help in resolving the numerous 'paradoxes' that have been around confusing scientists as well as young students as to what 'reality' really is about. Questions such as the physical process that seems to be associated to the 'collapse of the wave function', the 'measurement problem', as well as the difficulties raised in the EPR paper as well as Bell's theorem, questions surrounding the features of entanglement, and the Greenberger - Horne - Zeilinger (GHZ) paradox, all become much less counter intuitive and mysterious than what they look like in their original quantum settings.

The explanation of these features is that the real thing that is happening is the classically evolving collection of microscopic objects, of which the fastest periodically moving things automatically enter into a completely featureless, even distribution over all of their possible states.

Remarkably, the reason why the states of the fastest moving objects stay in an even distribution is better understood in the quantum formalism than when using the original classical picture: the highest energy excitations are difficult or almost impossible to excite, simply because the energy needed for that is usually unavailable to us: in our accelerators we can only reach a dozen or so TeVs, and in

### *Ontology in Quantum Mechanics DOI: http://dx.doi.org/10.5772/intechopen.99852*

cosmic rays the highest detectable energies are still well below the Planck scale. Therefore, the excited modes are only virtually present, and may well be ignored in practice. And, since all superposition coefficients for the ground state are equal, the distribution is featureless, in practice – according to Born.

Thus, what we really find is that the lowest energy states of the slow variables become entangled due to their interactions with the fastest variables. Quantum mechanics ensues; it is mathematically inevitable.

Our work is far from finished. Fresh young minds should probe the remaining mysteries; in particular, the Standard Model is built from fundamental symmetry principles. There are more symmetries than one might have expected from 'just any' classical system: there are many continuous symmetries, and also non-compact symmetries such as Lorentz invariance and general coordinate transformation invariance, and there are exact local gauge invariances as dictated by the gauge fields in the Standard Model.

Finally, a natural place must be found where we can put and understand the black hole solutions of Einstein's equations. They too must obey the laws of quantum mechanics, before we can embrace these remarkable systems in our overall picture of nature. Data obtained from the observations of cosmologists must also be incorporated. What we are searching for is nothing less than a grand picture of the evolution laws shaping our physical world.
