Micro-cosmos model of a nucleon

Many Dimensions in Gravity Theory

About a century ago, Albert Einstein realized how the Theory of Newton's Universal Gravitation was inadequate to describe nature and needed to be revised in order to be neatly incorporated into the relativistic scheme with its undesirable instantaneous force shortcomings. Since then we have come to adopt the relativistic high energy tensor theory of General Relativity, which saw its inception into mainstream physics in the year 1916. General Relativity has stood firm against varied tests, such as: gravitational lensing, perihelion of mercury, gravitational time dilation, PSR1913+16 etc, but with the steady advancement of Quantum Mechanics, and its overwhelming experimental success, we are yet again faced with the same problem that was faced a century ago, but this time, the problem is much worse, and the elephant in the room is General Relativity. The fact that General relativity and Quantum mechanics, share different views in the description of space and time or space-time, with quantum mechanics in favor of the latter and general relativity of the former; does not allow one to have a smooth transition from one representation to the other. This automatically implies that for scenarios where both quantum mechanics and gravity / general relativity are required, then that scenario is unsolvable with our current model of physics (hence either General Relativity or Quantum Mechanics is flawed). It becomes clear from the microscopic realm of quantum mechanics and the cosmological problems associated with General Relativity, such as dark energy, dark matter, the inflation force... perhaps a bit closer to home for general relativity being the singularities inherent in its own equations, and the very nature of General Relativity, allowing mostly approximate solutions (reason why most physicist, even today still cling to Newtonian dynamics), because of this and more a new theory of gravity is required – the much anticipated “Quantum Gravity” – just as it was required those many years ago. In the theory that I propose, we will see how from the most basic concepts of quantum mechanics, a theory of gravity can emerge that has the power to not only be mathematically simpler than General Relativity, explain dark energy, dark matter and inflation without any ad-hoc mechanisms, but also have the power to unify all the forces of nature into a single unified theory of everything.

Optomechanics has made great strides in theory and experiments over the past decade, which culminated in the first direct detection of gravitational waves in 2015 by LIGO. This thesis explores how optomechanics can be used to test fundamental physics other than the theory of general relativity. Our emphasis will be on falsifiable theories (ultimately, only experiments can decide whether a theory is correct) that address two outstanding issues in quantum mechanics: the measurement problem, and reconciling quantum mechanics with the theory of general relativity. In particular, we show that the space experiment LISA pathfinder places aggressive bounds on two objective collapse models, which are non-linear stochastic modifications of the Schroedinger equation that can resolve the measurement problem. Moreover, we show that state-of-the-art torsion pendulum experiments can test the Schroedinger-Newton theory, which is the non-relativistic limit of a non-linear theory combining quantum mechanics with a fundamentally classical spacetime. Along the way, we propose how to resolve two major difficulties with determining the predictions of non-linear quantum mechanics in an actual experiment. First, we cannot use the density matrix formalism in non-linear quantum mechanics and so we have to suggest and justify a particular ensemble for the thermal bath. Separating out quantum and classical fluctuations helped us propose a reasonable ensemble. Second, most researchers believe that deterministic non-linear quantum mechanics must violate the no-signaling condition. We show this isn't necessarily the case because different interpretations of quantum mechanics make different predictions in non-linear quantum mechanics. We propose an interpretation, the causal-conditional prescription, that doesn't violate causality by noticing that once we fix an initial state, the evolution of a system under many non-linear theories is equivalent to evolution under a linear Hamiltonian with feedback. The mapping allows us to leverage the tools of quantum control, and it tells us that if the non-linear parameters of a non-linear Hamiltonian respond causally (i.e. with an appropriate delay) to measurement results, then the theory can be made causal. We also contribute to the theory of quantum optomechanics. We introduce two new bases that one can view environment modes with. In linear optomechanics a system interacts with an infinite number of bath modes. We show that the interaction can be reduced to one with finite degrees of freedom. Moreover, at any particular time, the system is correlated with only a finite number of bath modes. We show that if we make the assumption that we can measure any commuting environment modes, then this basis allows us to understand the one-shot quantum Cramer-Rao bound in a simple way, and allows us to sweep large parameter regimes and so find promising optomechanics topologies for quantum state preparation tasks that we can then analyze without the assumption of being able to measure any observable of the environment. We also use this basis to show that when we are interested in the conditional dynamics of a test mass, we can only adiabatically eliminate a lossy cavity when we measure the optomechanical system at a slow enough rate. Finally, we develop an analytic filter for obtaining the state of a generic optomechanical system that interacts linearly with its environment and is driven by Gaussian states, and where the outgoing light is measured with a non-linear photon-counting measurement. We hope that our work will help researchers explore optomechanics topologies that make use of photon counters.

RETRACTED: On the same origin of quantum physics and general relativity from Riemannian geometry and Planck scale formalism

Science sets itself apart from other paths to truth by recognizing that even its greate practitioners sometimes err.

The aim of this chapter is to introduce the general ideas on which this book is based and to present the picture of quantum spacetime that emerges from loop quantum gravity, in a heuristic and intuitive manner. The style of the chapter is therefore conversational, with little regard for precision and completeness. In the course of the book the ideas and notions introduced here will be made precise, and the claims will be justified and formally derived. The problem of quantum gravity Unfinished revolution Quantum mechanics (QM) and general relativity (GR) have greatly widened our understanding of the physical world. A large part of the physics of the last century has been a triumphant march of exploration of new worlds opened up by these two theories. QM led to atomic physics, nuclear physics, particle physics, condensed matter physics, semiconductors, lasers, computers, quantum optics … GR led to relativistic astrophysics, cosmology, GPS technology … and is today leading us, hopefully, towards gravitational wave astronomy. But QM and GR have destroyed the coherent picture of the world provided by prerelativistic classical physics: each was formulated in terms of assumptions contradicted by the other theory. QM was formulated using an external time variable (the t of the Schrodinger equation) or a fixed, nondynamical background spacetime (the spacetime on which quantum field theory is defined). But this external time variable and this fixed background spacetime are incompatible with GR. In turn, GR was formulated in terms of riemannian geometry, assuming that the metric is a smooth and deterministic dynamical field.

I. In general, time is used in quantum theory as an external ('classical') concept. So it is assumed, as in classical physics, to exist as a controller of all motion – either as absolute time or in the form of proper times defined by a classical spacetime metric. In the latter case it is applicable to local quantum systems along their world lines. According to this assumption, time can be read from appropriate classical or quasi-classical 'clocks'. This conception has to be revised only when general relativity, where one regards the spatial metric as a dynamical object, is itself quantized [1] – as required for consistency (see IV). The thereby achieved 'quantization of time' does not necessarily lead to a discretization of time – just as the quantization of free motion does not require a discretization of space. On the other hand, the introduction of a fundamental gravitational constant in addition to Planck's constant and the speed of light leads to a natural Planck time unit, corresponding to 5.40 10 sec. This may signal the need for an entirely novel conceptual framework – to be based on as yet missing empirical evidence. A formal (canonical) quantization of time would also be required in non-relativistic Machian ('relational') dynamical theories [4], which consistently replace the concept of time by some reference motion. If quantum theory is universally valid, all dynamical processes (including those that may serve as clocks or definers of time) must in principle be affected by quantum theory. What does this mean for the notion of time? Historically, the dynamics of quantum systems seemed to consist of individually undetermined stochastic 'quantum jumps' between otherwise 'stationary' states (energy eigenstates) – see [2] for an early review of the formalism and the attempt of an interpretation. Such stochastic events are observed in quantum measurements, in particular. For this reason, von Neumann [3] referred to the time-dependent →Schrodinger equation as a 'second intervention', since Schrodinger had invented it solely to describe consequences of time-dependent external 'perturbations' of a quantum system. Note, however, that atomic clocks are not based on any stochastic quantum events, even though they have to be designed as open systems in order to allow their permanent reading (representing 'measurements' of the clock – see IV). In a consistent →Schrodinger picture, all dynamics is described as a time dependence of the quantum states, while the observables are fixed formal kinematical concepts (see also Sect. 2.2 of [5]). The time dependence according to the Schrodinger equation can be completely understood as an interference phenomenon between different stationary states |m>, which possess individually meaningless phase factors exp(iωmt). Their →superpositions are able to describe time-dependent quantum states |α(t)> in the form |α(t)> := ∫dq ψα(q,t)|q> = Σmcmexp(iωmt)|m> . The wave function ψα(q,t) is here used to define the time-dependent state |α(t)> in abstract →Hilbert space. The Hilbert space basis |q> diagonalizes an appropriate observable Q. The time dependence of a quantum state is in fact meaningful only relative to such a fixed basis, as demonstrated by means of the wave function in the above definition. In non-relativistic quantum mechanics, the time parameter t that appears in the Schrodinger wave function ψ(q,t) is identified with Newton's absolute time. So it is presumed to exist regardless of how or whether it is measured. The letter q represents all variables qi (i=1...I) that span the required configuration space. The special case of a point mass, where q

Einstein’s theory of general relativity has passed all precision tests to date. At some length scale, however, general relativity (GR) must break down and be reconciled with quantum mechanics in a quantum theory of gravity (a beyond-GR theory). Binary black hole mergers probe the non-linear, highly dynamical regime of gravity, and gravitational waves from these systems may contain signatures of such a theory. In this thesis, we seek to make gravitational wave predictions for binary black hole mergers in a beyond-GR theory. These predictions can then be used to perform model-dependent tests of GR with gravitational wave detections. We make predictions using numerical relativity, the practice of precisely numerically solving the equations governing spacetime. This allows us to probe the behavior of a binary black hole system through full inspiral, merger, and ringdown. We choose to work in dynamical Chern-Simons gravity (dCS), a higher-curvature beyond-GR effective field theory that couples spacetime curvature to a scalar field, and has motivations in string theory and loop quantum gravity. In order to obtain a well-posed initial value formalism, we perturb this theory around GR. We compute the leading-order behavior of the dCS scalar field in a binary black hole merger, as well as the leading-order dCS correction to the spacetime metric and hence gravitational radiation. We produce the first numerical relativity beyond-GR waveforms in a higher-curvature theory of gravity. This thesis contains additional results, all of which harness the power of numerical relativity to test GR. We compute black hole shadows in dCS gravity, numerically prove the leading-order stability of rotating black holes in dCS gravity, and lay out a formalism for determining the start time of binary black hole ringdown using information from the strong-field region of a binary black hole simulation.

We show that the precision of an angular measurement or rotation (e.g., on the orientation of a qubit or spin state) is limited by fundamental constraints arising from quantum mechanics and general relativity (gravitational collapse). The limiting precision is r−1 in Planck units, where r is the physical extent of the (possibly macroscopic) device used to manipulate the spin state. This fundamental limitation means that spin states S1 and S2 cannot be experimentally distinguished from each other if they differ by a sufficiently small rotation. Experiments cannot exclude the possibility that the space of quantum state vectors (i.e., Hilbert space) is fundamentally discrete, rather than continuous. We discuss the implications for finitism: does physics require infinity or a continuum?

Quantum Gravity (Cambridge Monographs on Mathematical Physics)

In the last century two revolutionary new concepts have enriched the field of theoretical physics: the theory of quantum mechanics and the general theory of relativity. The latter one has predicted the existence of gravitational waves, which can be emitted from massive astrophysical objects. The most promising detector design for the first direct observation of gravitational waves is given by large-scale laser interferometers. These interferometers are large in terms of the extension of their arms as well as in terms of the size and the weight of their mirror-endowed test masses. Due to a vast choice of possible technological improvements the sensitivity of those interferometers will be increased more and more. It is expected that the sensitivity of the planned next generation of laser interferometer gravitational-wave detectors already becomes limited by quantum effects in the measurement process. This certainly raises the question about the existence of quantum effects in the dynamics of the test masses of the detector. This thesis will theoretically provide a link between the increase of the sensitivity of gravitational-wave detectors and the possibility of preparing macroscopic quantum states in such detectors. In the first part of this thesis, we theoretically explore the quantum measurement noise of an optical speed meter topology, the Sagnac interferometer, equipped with an additional detuned cavity at the output port. This detuned signal-recycling technique was already investigated when applying it to a Michelson interferometer and is used in the gravitationalwave detector GEO600. Together with the quantum noise analysis of the simple Sagnac interferometer, it is the basis of our study: we optimize the Sagnac interferometer’s sensitivity towards the detection of a certain gravitational-wave source in the vicinity of a realistic classical noise environment. Motivated by the fact that the Michelson interferometer, as a position meter, with detuned signal-recycling can transduce the gravitational-wave strain into real mirror motion, we compare the transducer effect in a speed and in a position meter. Furthermore, we theoretically investigate the conditional output squeezing of a cavity which is detuned with respect to its carrier and its subcarrier. Therewith we pursue the theoretical analysis of the ponderomotive squeezer. With the knowledge gained in the first part about the quantum measurement process in laser interferometers, the second part of this thesis comprises a theoretical analysis of the conditional state in position and momentum of the interferometer’s test masses. We motivate not to obtain the conditional states from a stochastic master equation but with the help of the so-called Wiener filtering method. Using this method, we calculate the most general expression for the conditional covariance matrix of the Gaussian state of a test mass under any linear Markovian measurement process. Then we specify to the interferometry and theoretically show under which circumstances the conditional states of the test masses in a Michelson interferometer become close to pure quantum states, showing quantum features as squeezing or even entanglement. This certainly depends on the level of the classical noise. But we quantify this by giving a necessary relation between the spectrum of the classical noise and a standard reference in interferometric experiments, the standard quantum limit.

The aim of this work is to review the concepts of time in quantum mechanics and general relativity to show their incompatibility. We show that the absolute character of Newtonian time is present in quantum mechanics and also partially in quantum field theories which consider the Minkowski metric as the background spacetime. We discuss the problems which this non‐dynamical concept of time causes in general relativity that is characterized by a dynamical spacetime.

Re-examination of the work of Max Karl Planck has revealed hidden variables in his famous quantum work, consistent with Einstein's famous sentiment that quantum mechanics is incomplete due to the existence of hidden variables. The recent discovery of these previously hidden variables, which have been missing from the foundational equations of quantum theory for more than one hundred years, has important implications for all the sciences as well as for understanding the interactions of electromagnetic radiation with matter. Planck's quantum formula, E = hν, is missing the variable for measurement time. Planck had included the missing time variable in his earlier electromagnetic work, but omitted it in his famous work that sparked the quantum revolution. Restoration of measurement time to Planck's quantum formula produces the more complete, E = ν t. The numerical value Planck calculated for his action constant h takes on new meaning as an energy constant h~ for light. Planck's energy constant is the mean energy of a single oscillation of light, namely 6.626 X 10 -34 J/oscillation. The mean oscillation energy of light is constant , and does not vary with frequency or wavelength. The photon, as historically defined, is a time dependent packet of energy, based on the arbitrary measurement time of one second. An arbitrary, one second increment of energy cannot be a truly indivisible and elementary particle of nature. Omission of the time variable from Planck's quantum formula contributed to numerous paradoxes in quantum mechanics, such as uncertainty relating to formulations involving time, wave-particle duality, the need for normalization of wave functions, lack of dimensions for the fine structure constant, and irreconcilability of quantum mechanics and general relativity (Einstein's gravitational theory). Many of these paradoxes are simplified or eliminated altogether with a re-interpretation of quantum mechanics with Planck's hidden time variable and energy constant.

The two pillars of modern physics are general relativity and quantum field theory, the former describes the large scale structure and dynamics of space-time, the latter, the microscopic constituents of matter. Combining the two yields quantum field theory in curved space-time, which is needed to understand quantum field processes in the early universe and black holes, such as the well-known Hawking effect. This book examines the effects of quantum field processes back-reacting on the background space-time which become important near the Planck time (10-43 sec). It explores the self-consistent description of both space-time and matter via the semiclassical Einstein equation of semiclassical gravity theory, exemplified by the inflationary cosmology, and fluctuations of quantum fields which underpin stochastic gravity, necessary for the description of metric fluctuations (space-time foams). Covering over four decades of thematic development, this book is a valuable resource for researchers interested in quantum field theory, gravitation and cosmology.

Many of the most exciting open problems in high-energy physics are related to the behavior and ultimate nature of gravity and spacetime. In this dissertation, several categories of new results in quantum and classical gravity are presented, with applications to our understanding of both quantum field theory and cosmology. A fundamental open question in quantum field theory is related to ultraviolet completion: Which low-energy effective field theories can be consistently combined with quantum gravity? A celebrated example of the swampland program---the investigation of this question---is the weak gravity conjecture, which mandates, for a U(1) gauge field coupled consistently to gravity, the existence of a state with charge-to-mass ratio greater than unity. In this thesis, we demonstrate the tension between the weak gravity conjecture and the naturalness principle in quantum field theory, generalize the weak gravity conjecture to multiple gauge fields, and exhibit a model in which the weak gravity conjecture solves the standard model hierarchy problem. Next, we demonstrate that gravitational effective field theories can be constrained by infrared physics principles alone, namely, analyticity, unitarity, and causality. In particular, we derive bounds related to the weak gravity conjecture by placing such infrared constraints on higher-dimension operators in a photon-graviton effective theory. We furthermore place bounds on higher-curvature corrections to the Einstein equations, first using analyticity of graviton scattering amplitudes and later using unitarity of an arbitrary tree-level completion, as well as constrain the couplings in models of massive gravity. Completing our treatment of perturbative quantum gravity, outside of the swampland program, we also reformulate graviton perturbation theory itself, finding a field redefinition and gauge-fixing of the Einstein-Hilbert action that drastically simplifies the Feynman diagram expansion. Furthermore, our reformulation also exhibits a hidden symmetry of general relativity that corresponds to the double copy relations equating gravity amplitudes to sums of squares of gluon amplitudes in Yang-Mills theory, a surprising correspondence that yields insights into the structure of quantum field theories. Moving beyond perturbation theory into nonperturbative questions in quantum gravity, we consider the deep relation between spacetime geometry and properties of the quantum state. In the context of holography and the anti-de Sitter/conformal field theory correspondence, we test the proposed ER=EPR correspondence equating quantum entanglement with wormholes in spacetime. In particular, we demonstrate that the no-cloning theorem in quantum mechanics and the no-go theorem for topology change of spacetime are dual under the ER=EPR correspondence. Furthermore, we prove that the presence of a wormhole is not an observable in quantum gravity, rescuing ER=EPR from potential violation of linearity of quantum mechanics. Excitingly, we also prove a new area theorem within classical general relativity for arbitrary dynamics of two collections of wormholes and black holes; this area theorem is the ER=EPR analogue of entanglement conservation. We next turn our attention to the emergence of spacetime itself, placing consistency conditions on the proposed correspondence between anti-de Sitter space and the Multiscale Entanglement Renormalization Ansatz, a special tensor network that constitutes a computational tool for finding the ground state of certain quantum systems. Further examining the role of quantum entanglement entropy in the emergence of general relativity, we ask whether there is a consistent microscopic formulation of the entropy in theories of entropic gravity; we find that our results weaken equation-of-state proposals for entropic gravity while strengthening those more akin to holography, guiding future investigation of theories of emergent gravity. Finally, we examine the consequences of the Hamiltonian constraint in classical gravity for the early universe. The Hamiltonian constraint allows for the Liouville measure on the phase space of cosmological parameters for homogeneous, isotropic universes to be converted into a probability distribution on trajectories, or equivalently, on initial conditions. However, this measure diverges on the set of spacetimes that are spatially flat, like the observable universe. In this thesis, we derive the unique, classical, Hamiltonian-conserved measure for the subset of flat universes. This result allows for distinction between different models of cosmic inflation with similar observable predictions; for example, we find that the measure favors models of large-scale inflation, as such potentials more naturally produce the number of e-folds necessary to match cosmological observations.