arXiv subjects

Gerard t Hooft

Publications and source records attributed to Gerard t Hooft.

At least 19 recordsLinked to original sources

arXiv2025

Alternative theory for the quantum black hole and the temperature of its quantum radiation

A mechanism is found that explains how matter falling into the future event horizon of a black hole leaves information there, which it sends to the past event horizon, and there it determines how particles are emitted. This way information must be conserved. The mechanism is a calculable gravitational effect. We also show how it is avoided that the "hidden region" of the black hole gets involved, which has been standing out as a problem ever since Hawking found that particles must be emitted. The most striking consequence of our mechanism is that the radiation temperature is not what Hawking calculated, but twice that value. This is a direct consequence of the fact that the hidden region is not there.

gr-qc↗

arXiv2024

The Hidden Ontological Variable in Quantum Harmonic Oscillators

The standard quantum mechanical harmonic oscillator has an exact, dual relationship with a completely classical system: a classical particle running along a circle. Duality here means that there is a one-to-one relation between all observables in one model, and the observables of the other model. Thus the duality we find, appears to be in conflict with the usual assertion that classical theories can never reproduce quantum effects as observed in many quantum models. We suggest that there must be more of such relationships, but we study only this one as a prototype. It reveals how classical "hidden variables" may work. The classical states can form the basis of Hilbert space that can be adopted in describing the quantum model. Wave functions in the quantum system generate probability distributions in the classical one. One finds that, where the classical system always obeys the rule "probability in = probability out", the same probabilities are quantum probabilities in the quantum system. It is shown how the quantum x and p operators in a quantum oscillator can be given a classical meaning. It is explained how an apparent clash with quantum logic can be explained away.

quant-ph↗

arXiv2024

The sounds of science a symphony for many instruments and voices part II

Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine the future of the Universe. It is clearly prohibitive for the general reader, and even the best informed physicists, to follow the vast number of technical papers published in the thousands of specialized journals. For this reason, we have asked the leading experts across many of the most important areas of physics to summarise their global assessment of some of the most important issues. In lieu of an extremely long abstract summarising the contents, we invite the reader to look at the section headings and their authors, and then to indulge in a feast of stimulating topics spanning the current frontiers of fundamental physics from The Future of Physics by William D Phillips and What characterises topological effects in physics? by Gerard t Hooft through the contributions of the widest imaginable range of world leaders in their respective areas. This paper is presented as a preface to exciting developments by senior and young scientists in the years that lie ahead, and a complement to the less authoritative popular accounts by journalists.

physics.soc-ph↗

arXiv2024

Black Hole Firewalls and Quantum Mechanics

Firewalls in black holes are easiest to understand by imposing time reversal invariance, together with a unitary evolution law. The best approach seems to be to split up the time span of a black hole into short periods, during which no firewalls can be detected by any observer. Then, gluing together subsequent time periods, firewalls seem to appear, but they can always be transformed away. At all times we need a Hilbert space of a finite dimension, as long as particles far separated from the black hole are ignored. Our conclusion contradicts other findings, particularly a recent paper by Strauss and Whiting. Indeed, the firewall transformation removes the entanglement between very early and very late in- and out-particles, in a far-from-trivial way.

gr-qc↗

arXiv2023

Quantum Foundations as a Guide for Refining Particle Theories

All quantum field theories that describe interacting bosonic elementary particles, share the feature that the zeroth order perturbation expansion describes non-interacting harmonic oscillators. This is explained in the paper. We then indicate that introducing interactions still leads to classical theories that can be compared with the quantum theories, but only if we terminate the expansion somewhere. `Quantum effects' typically occur when some of the classical variables fluctuate too rapidly to allow a conventional description, so that these are described exclusively in terms of their energy eigen modes; these do not commute with the standard classical variables. Perturbation expansions are not fundamentally required in classical theories, and this is why classical theories are more precisely defined than the quantum theories. Since the expansion parameters involve the fundamental constants of nature, such as the finestructure constant, we suggest that research in these classical models may lead to new clues concerning the origin of these constants.

hep-th↗

arXiv2023

An ontological description for relativistic, massive bosons

Relativistic, scalar particles are considered, contained in a box with periodic boundary conditions. Although interactions are not expected to be a fundamental problem, we concentrate on free particles. By considering them to be harmonic oscillators, it is found that their dynamical variables can be replaced by a completely ontological set, which means that, here, quantum mechanics does not deviate from a purely geometric, ontological particle system. The effects of the mass terms are included. Locality holds for the quantum theory, and seems to be fully obeyed also by the classical treatment, although further discussion will be needed. Quantised interactions are briefly speculated on, but mostly postponed to later. We do discuss extensively the distinction between the quantum treatment and the classical one, even though they produce exactly the same equations mathematically. We briefly explain how this result can be squared with the usual quantum no-go theorems. It is suggested to apply this theory for real time quantum model simulations.

quant-ph↗

arXiv2023

How an exact discrete symmetry can preserve black hole information or Turning a black hole inside out

To apply the laws of General Relativity to quantum black holes, one first needs to remove the horizon singularity by means of Kruskal-Szekeres coordinates. This however doubles spacetime, which thereby is equipped with an exact binary symmetry. All particles near a black hole share the same symmetry, and conservation of this symmetry may completely remove the information paradox: the quantum black hole has no interior, or equivalently, the black hole interior is a quantum clone of the exterior region. These observations, totally overlooked in most of the literature on quantum black holes, resolve some issues concerning conservation of information. Some other problems do remain.

gr-qc↗

arXiv2022

How studying black hole theory may help us to quantise gravity

Black holes are more than just odd-looking curiosities in gravity theory. They uniquely intertwine the basic principles of General Relativity with those of Quantum Theory. Just by demanding that they nevertheless obey acceptable laws of dynamics, just like stars and planets, we hit upon strange structures that must play key roles in the quantum effects that we expect in the gravitational force at ultrashort distance scales. It is explained why, in our approach to address the problem of information conservation, the usual expression for the temperature of Hawking's radiation is off by a factor 2.

gr-qc↗

arXiv2022

The Black Hole Firewall Transformation and Realism in Quantum Mechanics

A procedure to derive a unitary evolution law for a quantised black hole, has been proposed by the author. The proposal requires that one starts off with the entire Penrose diagram for the eternal black hole as the background metric, after which a procedure was proposed to identify the two asymptotic domains of this metric, such that they both refer to the same outside world. In this paper we focus on the need to include time reversal in applying this identification. This forces us to postulate the existence of an 'anti-vacuum' state in our world, which is the state where energy density reaches a maximal value. We find that this squares well with the deterministic interpretation of quantum mechanics, according to which quantum Hilbert space is to be regarded as the 'vector representation' of a real world. One has to understand how to deal with gravity in such considerations. The non-perturbative component of the gravitational force seems to involve cut-and-paste procedures as dynamical features of space and time, of which the re-arrangement of space-time into two connected domains in the Penrose diagram is a primary example. Thus we attempt to obtain new insights in the nature of particle interactions at the Planck scale, as well as quantum mechanics itself. In this newer version of the paper an important correction is made concerning the antipodal transformation: applying more insight in the situation, as explained in newer publications by the author, we now regard region II of the Penrose diagram as an exact quantum copy of region I , still with time being reversed, but interchanging a region of spacetime with its antipodes is now seen to be incorrect.

gr-qc↗

arXiv2022

Quantum clones inside black holes

A systematic procedure is proposed for better understanding the evolution laws of black holes in terms of pure quantum states. We start with the two opposed regions I and II in the Penrose diagram, and study the evolution of matter in these regions, using the algebra derived earlier from the Shapiro effect in quantum particles. Since this spacetime has two distinct asymptotic regions, one must assume that there is a mechanism that reduces the number of states. In earlier work we proposed that region II describes the angular antipodes of region I, the `antipodal identification', but this eventually leads to contradictions. Our much simpler proposal is now that all states defined in region II are exact quantum clones of those in region I. This indicates more precisely how to restore unitarity by making all quantum states observable, and in addition suggests that generalisations towards other black hole structures will be possible. An apparent complication is that the wave function must evolve with a purely antisymmetric, imaginary-valued Hamiltonian, but this complication can be well-understood in a realistic interpretation of quantum mechanics.

gr-qc↗

arXiv2022

Projecting local and global symmetries to the Planck scale

The Standard Model of the elementary particles is controlled by more than 20 parameters, of which it is not known today how they can be linked to deeper principles. Any attempt to clean up this theory, in general results in producing more such parameters rather than less. Yet it is clear that, at distance scales of the order of the Planck length, the gravitational force presents itself in such a way that the need for new physical principles is evident. A stand-in-the-way is then quantum mechanics, a theory that demands the occurrence of superpositions of physical states in such a way that, when combined with general relativity, space and time themselves may require new formalisms for being used as primary frames for the descriptions of events. In previous papers the author proposed that quantum mechanics as a theory for the elementary particles should be rephrased as originating from a combination of deterministic evolution laws and discreteness at the Planck scale. This may well have a drastic effect on the symmetry structures and algebras. Local, discrete and continuous symmetries do not emerge without a cause, and we suggest that the symmetries can tell us more about fundamental constants, among which the Higgs mass is the most peculiar and the most challenging one.

hep-th↗

arXiv2021

Explicit construction of Local Hidden Variables for any quantum theory up to any desired accuracy

The machinery of quantum mechanics is fully capable of describing a single realistic world. Here we discuss the converse: in spite of appearances, and indeed numerous claims to the contrary, any quantum mechanical model can be mimicked, up to any finite accuracy, by a completely classical system of equations. An implication of this observation is that Bell's theorem is not applicable in the cases considered. This is explained by scrutinising Bell's assumptions concerning causality, retrocausality, statistical (in-)dependence, and his fear of `conspiracy' (there is no conspiracy in the language used to describe the deterministic models). The most crucial mechanism for the counter intuitive Bell/CHSH violation is the fact that, regardless the settings chosen by Alice and Bob, the initial state of the system should be a realistic one. The potential importance of our construction in model building is discussed.

quant-ph↗

arXiv2021

Ontology in quantum mechanics

It is suspected that the quantum evolution equations describing the micro-world as we know it are of a special kind that allows transformations to a special set of basis states in Hilbert space, such that, in this basis, the evolution is given by elements of the permutation group. This would restore an ontological interpretation. It is shown how, at low energies per particle degree of freedom, almost any quantum system allows for such a transformation. This contradicts Bell's theorem, and we emphasise why some of the assumptions made by Bell to prove his theorem cannot hold for the models studied here. We speculate how an approach of this kind may become helpful in isolating the most likely version of the Standard Model, combined with General Relativity. A link is suggested with black hole physics.

quant-ph↗

arXiv2021

Fast Vacuum Fluctuations and the Emergence of Quantum Mechanics

Fast moving classical variables can generate quantum mechanical behavior. We demonstrate how this can happen in a model. The key point is that in classically (ontologically) evolving systems one can still define a conserved quantum energy. For the fast variables, the energy levels are far separated, such that one may assume these variables to stay in their ground state. This forces them to be entangled, so that, consequently, the slow variables are entangled as well. The fast variables could be the vacuum fluctuations caused by unknown super heavy particles. The emerging quantum effects in the light particles are expressed by a Hamiltonian that can have almost any form. The entire system is ontological, and yet allows one to generate interference effects in computer models. This seemed to lead to an unsolvable paradox, which is now resolved: exactly what happens in our models if we run a quantum interference experiment in a classical computer is explained. The restriction that very fast variables stay predominantly in their ground state appears to be due to smearing of the physical states in the time direction, preventing their direct detection. Discussions are added of the emergence of quantum mechanics, and the ontology of an EPR/Bell Gedanken experiment.

quant-ph↗

arXiv2020

Deterministic Quantum Mechanics: the Mathematical Equations

Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the equations to be considered. Special attention is given to the notion of 'locality'. Various examples are worked out, followed by a systematic procedure to generate classical evolution laws and quantum Hamiltonians that are exactly equivalent. What is new here is that we consider interactions, keeping them as general as we can. The quantum systems found, form a dense set if we limit ourselves to sufficiently low energy states. The class is discrete, just because the set of deterministic models containing a finite number of classical states, is discrete. In contrast with earlier suspicions, the gravitational force turns out not to be needed for this; it suffices that the classical system act at a time scale much smaller than the inverse of the maximum scattering energies considered.

quant-ph↗

arXiv2019

The Ontology Conservation Law as an Alternative to the Many World Interpretation of Quantum Mechanics

A sharper formulation is presented for an interpretation of quantum mechanics advocated by author. As an essential element we put forward conservation laws concerning the ontological nature of a variable, and the uncertainties concerning the realisation of states. Quantum mechanics can then be treated as a device that combines statistics with mechanical, deterministic laws, such that uncertainties are passed on from initial states to final states.

quant-ph↗

arXiv2019

The quantum black hole as a theoretical lab, a pedagogical treatment of a new approach

Getting the mathematical rules for quantised black holes correctly is far from straightforward. Many earlier treatises got it not quite correctly. The general relativistic transformation linking the distant observer (who only detects particles outside the hole) with the observations of a local observer (who falls into a black hole) must map the quantum states in a one-to-one way. This does not come out right if one follows text book rules. Here it is advocated that demanding very strict logic leads to new insights, such as the non-triviality of space-time topology near a black hole. This way one may attempt to make up for the lack of direct experimental evidence concerning gravitation at the Planck scale. It is noted that this approach does not require assumptions such as string theories or AdS/CFT conjectures. All we need to assume is the validity of quantum field theory wherever the Schwarzschild metric is regular, combined with the requirement that only those general coordinate transformations apply that map pure quantum states one-to-one onto pure quantum states.

gr-qc↗

arXiv2018

What happens in a black hole when a particle meets its antipode

The notion of antipodal identification on the black hole horizon is further explained and elaborated. Contrasting with numerous attempts in the literature to make fuzzy, poorly motivated models for black holes, we explain how, with an absolute minimum of assumptions, known laws of local physics suffice to calculate the unitary evolution law for a Schwarzschild black hole. Earlier work by the author, which explains how firewalls can and must be avoided, while also the information paradox disappears, ran into its one remaining problem: how to explain it better to the community. Antipodal identification is a natural way to replace thermally mixed states by pure quantum states, without the need to hide our ignorance in "chaos". We do encounter a strange looking sign switch in the relation of particles to their antipodes near the horizon. This sign switch is necessary to recover complete unitarity without any loss of information anywhere, while restoring locality. Although there are some important remaining problems, we advertise our approach as a healthy alternative to the reliance on AdS/CFT conjectures, which, we claim, do not guarantee to provide reliable answers.

gr-qc↗