Quantum Gravity and Quantum Cosmology

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Wood, J. The microstates of the system evolve via information transfer mechanisms on dynamic complete graphs built upon substitution networks developed in the latter stated paper.

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Using the positive integer edge weights as measures of distance, the system is artificially embedded in R n by treating the flat space violations as stress resulting in a curved geometry figure 1. This stress then effects a force on the vertices. In this paper light cone dynamics of the motion of the minima of this stress is observed, along with superluminal motion of the vertices. We argue that this superluminal velocity corresponds to the quantum mechanical discontinuous motion of particles and provides possibilities for descriptions of entanglement and particle spin within the system.

Further to this, that the compatibility of this type of dynamics with relativistic behaviour makes this system non-trivial and worthy of further investigation. Gravity of a irregular mass and curvature of space. For gravity, we have two important theories. One was presented by Isaac Newton and the other was by Albert Einstein. Newton proposed in his theory, gravity as a pulling force. Einstein proposed gravity as the curvature of space time Einstein proposed gravity as the curvature of space time caused by the mass and energy. On his theory, I was realized gravity as a pushing force towards the space time.

In his equation he showed us that, the left hand side is about the curvature of space time and the right hand side as the energy. Everything in our universe is depends upon the energy. So gravity must be a force of attraction or repulsion. Newton shows us gravity as an attractive pulling force. Both of these theories explain the gravity of a system. Here I am not bothering, while gravity is a pulling force or a pushing force, I don't care, whatever it is, I wish to recognize the characteristics of gravity.

I am considering the curved space time of each mass, so this model is explaining about the curvature of both masses in a collaborated system. By this, the distortion of the curvature of space time of any mass will lead to a gravitational collision. In our present concept, the massive object is the center of a gravitational system; the other masses are secondary in the system and are obeyed to orbit the huge mass. Here I am trying describing more about the curved space time of the secondary mass. Naturally we cannot observe the advantage of this concept every system, but we can find it when two massive objects like two stars or two black holes are orbiting together.

The SERD network is a discrete system that emerges out of a philosophical idea related to the question of what caused the universe to exist in the first place. It has great depth, diverse structure and has shown, through direct It has great depth, diverse structure and has shown, through direct simulation, evidence of physically comparable behaviour. Philosophical first principle "Why does the universe exist in the first place?

In classical mechanics, the state of matter in space in a moment of time is entirely determined by the state of matter in space the instant before it. In quantum mechanics the wave function is in a quantum state due to the cumulation of information transferred from other unseen quantum states in other points in space-time. Through observations of the CMB and of galactic recessional velocities we can deduce that the universe came from a hot dense plasma that expanded out of a singularity. That singularity representing the first instance in time. Even if we consider the idea of existing in a multiverse and the multiverse is an infinite loop of big bangs, this still doesn't answer our initial question.

This then leads to another question. Matter wave explorer of gravity MWXG. Development of a high-sensitivity torsional balance for the study of the Casimir force in the 1—10 micrometre range. Unitarity violates relativity [Updated version with a new experiment and an analysis of many worlds]. Unitary quantum theory permits that a local measurement can be undone locally in the EPR situation. This may have an interesting implication for the incompatibility between quantum theory and relativity.

In this paper, we propose a In this paper, we propose a variant of the EPR-Bohm experiment. We find that when a measurement on one particle can be undone locally, the correlation between the results of spacelike separated measurements may depend on the time order of these measurements.

This violates relativity, which requires that relativistically non-invariant relations such as the time order of spacelike separated events have no physical significance. General Asymmetric Fields of Ontology and Cosmology. By discovering Asymmetric World Equations, this manuscript formulates astonishing results to represent a consequence of the laws of asymmetric conservations and commutations, and characterize universal evolutions and motion dynamics of As a result, it reveals that the virtual world supplies energy resources and modulates the messaging secrets of the intrinsic operations, beyond General Relativity.

As another major part of the unification theory, the quantum fields give rise to a symmetric environment and bring together all field entanglements of the flux conservation and continuity. Remarkably, it reveals the natural secrets of Remarkably, it reveals the natural secrets of: 1 General Symmetric Fields-A set of generic fluxions unifying electromagnetism, gravitation, and thermodynamics. Conclusively, this manuscript presents the unification and compliance with the principal theories of classical and contemporary physics in terms of Symmetric dynamics.

As a result, the hierarchy topology inaugurates mass acquisition for the classical or contemporary physics, unifying the mathematical models of quantum electrodynamics, spontaneous field breaking, chromodynamics, gauge theory, perturbation theory, standard model, etc. The scope of this manuscript is at where a set of mathematical formulae is constituted of, given rise to and conserved for the field formations and evolutions at ontological horizons.

Through the events of the Yin and Yang actions, laws of creation, reproduction, conservation and continuity determine the physical properties or particle fields of interruptive transformations, dynamic transportations, entangle commutations and fundamental forces. Framework of Natural Cosmology. Consequently, we are revealed exceptionally secrets of the Natural Cosmology with horizon infrastructure, superphase modulation, entropy of dark energy, and lightwave or gravitation fields in the forms of dispersive or non-dispersive wave-packets, which orchestrate all types of life events essential to the operations and processes of creation, annihilations, reproduction and communication for natural formations and evolutions.

For the first time in mankind, Universal and Unified Field Theory is philosophically, mathematically and empirically revealed the workings of Universal Topology and Laws of YinYang Conservations. The nature of dark energies unfolds its The nature of dark energies unfolds its Event Operations systematically on the origin of physical states. It prompts the entire discipline of physics, from Newtonian to spacetime relativity to quantum mechanics, to look back to the future: Virtumanity - Dialectical Nature of Virtual and Physical Reality.

Intuitively following the system of yinyang philosophy, this holistic theory is concisely accessible and replicable by readers with a basic background in mathematical derivation and theoretical physics. As a summary, this manuscript completes and unifies all of the principal equations, important assumptions, and essential laws, discovered and described by the classical and modern physics. The Incomplete Revolutions of String Theory. If one tried to get a palatable picture of Electromagnetism, it would be natural to hear from an expert about charges, flux lines, potentials and waves.

These are subtle concepts, and yet they can convey some valuable intuition on these These are subtle concepts, and yet they can convey some valuable intuition on these phenomena, despite the intricacies of the underlying Mathematics. Similar questions about General Relativity would probably bring up falling bodies, the Equivalence Principle and deformations of the fabric of spacetime where planets slide along their orbits. String Theory, however, is still a very different matter, and experts have a hard time defining it.

One could say that strings replace particles, as we shall try to explain, but in our current view particles emerge from fields, whose geometry underlies their interactions. As we shall see, appealing to such geometrical principles within the low-energy Supergravity has provided unprecedented glimpses of a unified view of Nature that transcends not only strings but our very picture of spacetime. Yet, we lack somehow satisfactory answers to some basic questions, which ought to have preceded all this.

What replaces the principles of General Relativity in String Theory? What do strings tell us about spacetime at short distances? Why is our Universe the way it seems? String Theory is today an awesome unfinished monument, whose roots remain elusive despite decades of intense effort. While this brings about some distress, it also makes the subject mysterious, challenging and highly fascinating. In the following, I shall describe the origin of this unusual situation, while also trying to address some future prospects.

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The multiple realizability of general relativity in quantum gravity. Must a theory of quantum gravity have some truth to it if it can recover general relativity in some limit of the theory? This paper answers this question in the negative by indicating that general relativity is multiply realizable in This paper answers this question in the negative by indicating that general relativity is multiply realizable in quantum gravity.

The argument is inspired by spacetime functionalism—multiple realizability being a central tenet of functionalism—and proceeds via three case studies: induced gravity, thermodynamic gravity, and entanglement gravity.

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In these, general relativity in the form of the Einstein field equations can be recovered from elements that are either manifestly multiply realizable or at least of the generic nature that is suggestive of functions. If general relativity, as argued here, can inherit this multiple realizability, then a theory of quantum gravity can recover general relativity while being completely wrong about the posited microstructure. As a consequence, the recovery of general relativity cannot serve as the ultimate arbiter that decides which theory of quantum gravity that is worthy of pursuit, even though it is of course not irrelevant either qua quantum gravity.

Various definitions of what a singularity could mean have been explored 2 , 3 , 4 , 5 , 8 , 9 : that the wave function has support on singular metrics, that the wave function is peaked around singular metrics, that the expectation value of the metric operator is singular, etc. Although these definitions may have something so say about the occurrence or non-occurrence singularities, neither of these is completely satisfactory. In fact, since there is merely the wave function, one might even consider the question about space-time singularities as off-target, since it is the dynamics of the wave function that needs to be well-defined.

Various possible solutions have been explored to solve some of these problems. In particular, a number of solutions to the measurement problem exist, such as for example the Many Worlds theory, spontaneous collapse models and Bohmian mechanics. There also exist a number of approaches to solving the problem of time, for a recent overview see ref. Solving one problem may also lead to the solution of another one. For example, in spontaneous collapse models the collapses are objective processes. But the collapses entail change and hence may solve the problem of time. The question of singularities in the context of both the Wheeler-DeWitt theory and LQC has been discussed in great detail for the Consistent Histories approach to quantum mechanics 11 , 12 , 13 , In this paper, we consider Bohmian mechanics.

Bohmian mechanics is an alternative to standard quantum mechanics that solves the aforementioned problems. In non-relativistic Bohmian mechanics there are particles in addition to the wave function 15 , 16 , The wave function determines the motion of the particles in a way that is similar to the way the Hamiltonian determines the motion of classical particles. There is no measurement problem since there is no collapse of the wave function. Outcomes of measurements are determined by the positions of the actual particles. We explore the question of singularities in the mini-superspace model of a FLRW space-time coupled to a homogeneous scalar field in the context of Bohmian mechanics.

In the Bohmian versions of the Wheeler-DeWitt theory there is an actual FLRW metric and scalar field whose dynamics is determined by the wave function in a deterministic way 18 , 19 , 20 , In the Bohmian version of LQC, which is developed here, there are also an actual FLRW metric and scalar field, but now the dynamics of the metric is stochastic rather than deterministic. While the wave function is static, the actual metric and scalar field generically evolve in time.

The wave function does not collapse, although it may at an effective level, so that there is no measurement problem. Finally, it is also clear in this case what is meant by a singularity: there are singularities whenever the actual metric becomes singular. In previous work 11 , 22 , the question of singularities was studied for the Bohmian version of the Wheeler-DeWitt theory for mini-superspace. It was found that there may or may not be singularities; it depends on the wave function and the initial conditions of the actual fields.

In particular, there are wave functions for which there are no singularities for any of the initial conditions and there wave functions for which there are always singularities. In this paper, we develop a Bohmian theory for LQC and consider the question of singularities. We consider some common models for LQC which correspond to different wave equations arising from operator ordering ambiguities and find that big bang or big crunch singularities do not occur for any value of the spatial curvature and cosmological constant.

The outline of the paper is as follows. First, we consider the Wheeler-DeWitt quantization of the mini-superspace model, the corresponding Bohmian theory and the results for singularities. Then in section 3, we present some common models for LQC. In section 4, we present their Bohmian versions and show that there is no big bang or big crunch singularity.

In section 5, we discuss how the problem of time is usually addressed in LQC and compare it to the Bohmian solution. Finally, in section 6, we consider a modified Wheeler-DeWitt equation inspired by loop quantum cosmology which also has the potential to eliminate singularities. The classical equations of motion are.

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The latter equation is the Friedmann equation. The Friedmann acceleration equation follows from 3 and 4. N remains an arbitrary function of time.

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This implies that the dynamics is time reparameterization invariant. In the context of standard quantum theory, this equation is hard to interpret due to the problem of time 1 , 6 , 7. Namely, the wave function is static. So how can the apparent time evolution of the universe be accounted for? The function N is again the lapse function, which is arbitrary, and, just as in the classical case, implies that the dynamics is time reparameterization invariant.

Cosmology and Quantum Gravity: Loops and Spinfoams (Carlo Rovelli)

As such, the classical equations are obtained, with addition of the quantum potentials to the classical potentials. Even though the wave function is static, the Bohmian scale factor generically depends on time. As such there is no problem of time. We will discuss this further in section 5. This measure is preserved by the Bohmian dynamics. However, it is non-normalizable i. Probabilities are only secondary, with the primary role of the wave function to determine the evolution of the metric and the scalar field.

For that reason, it is also not important to introduce a Hilbert space. We just need to assume that the wave function is such that the Bohmian dynamics is well-defined. Since it is rather unclear what the Wheeler-DeWitt equation means in the context of standard quantum mechanics, there is also no straightforward comparison between the Bohmian predictions and those of standard quantum theory possible.

This is unlike the situation in non-relativistic quantum mechanics, where it can be shown that Bohmian mechanics reproduces the predictions of standard quantum theory provided the latter are unambiguous. For example, the Hartle-Hawking wave function which is studied in great detail is empirically inadequate from the Bohmian point of view since it is a real wave function and implies a stationary universe Let us now turn to the question of singularities.

This singularity is obtained for generic solutions. In this case there is no singularity. This means that the universe reaches the singularity in finite proper time. In the standard quantum mechanical approach to the Wheeler-DeWitt theory, the complete description is given by the wave function and as such, as mentioned in the introduction, the notion of a singularity becomes ambiguous. Not so in the Bohmian theory.

The Bohmian theory describes the evolution of an actual metric and hence there are singularities whenever this metric is singular. In this case, the Wheeler-DeWitt equation is. The actual metric might be singular; it depends on the wave function and on the initial conditions. Ochner that the only wave functions for which there are no singularities are of the form. In comparison we note that in the context of the consistent histories approach to quantum mechanics, it was shown that singularities are always obtained for this system 11 , 12 , 13 , The Wheeler-DeWitt equation then reads.

Loop quantization is a different way to quantize general relativity 27 , Application of this quantization method to the mini-superspace model considered here results in the following. As usual, the quantization is not unique. Because of operator ordering ambiguities different wave equations may be obtained.

A comparison of these models can be found in ref. Unlike the earlier version, the APS model tends to yield a bounce when the matter density enters the Planck regime rather than higher energies. The Bohmian singularity analysis of this model would not differ much from that of the APS model. The gravitational part, determined by K , is not a differential equation but a difference equation. For now, we do not consider a non-zero curvature or a cosmological constant. This will be done at the end of this section. Just as in the case of the Wheeler-DeWitt theory, we will not worry about a suitable Hilbert space for the wave equation.

One choice is 4 :. Another one is 5 :. This is a simplification that was introduced to make the model exactly solvable. This results in the wave equation. In the Bohmian theory there is again an actual scalar field and an actual metric of the form 1. Since the gravitational part of the wave equation 22 is now a difference operator, rather than a differential operator, we need to develop a Bohmian theory which results in a jump process rather than a deterministic process. Such processes have been introduced in the context of quantum field theory to account for particle creation and annihilation 34 , 35 , The wave equation 22 implies the continuity equation.

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The scalar field satisfies the guidance equation. Just as in the classical case and the Bohmian Wheeler-DeWitt theory, the lapse function is arbitrary, which guarantees time-reparameterization invariance. Since the evolution of the scale factor is no longer deterministic like in the Wheeler-DeWitt theory, but stochastic, the metric is no longer Lorentzian.

Namely, once there is a jump, the metric becomes discontinuous. In any case, the sLQC model is considered only as a simplification of the APS model; it does not follow from applying the loop quantization techniques to mini-superspace. Importantly, no boundary conditions need to be assumed. For other possible solutions, the wave equation needs to be solved first. This is rather hard, but can perhaps be done in sLQC since the eigenstates of the gravitational part of the Hamiltonian are known in this case.

Something can be said about the asymptotic behaviour however. This implies an expanding or contracting or static universe. We expect that a bouncing universe will be the generic solution. In each case, the extra term is merely a potential term so that it does not contribute to the Bohmian jump process.

So the same results hold concerning singularities as in the free case. An actual clock should be modeled in terms of the other variables. One can then express the evolution of the other variable in terms of the clock variable. In the case of LQC, the same is true, except if the scale factor is taken as a clock variable, then it will be a discrete one. The situation is different in the standard quantum mechanical approach to the Wheeler-DeWitt theory and loop quantum theory. There one has to deal with the notorious problem of time 1 , 6 , 7.

In both cases, the wave equation does not depend on time and hence the wave function is static. So how does one account for apparent time evolution? However, also the scale factor could be taken as clock variable. However, we believe that the classical behaviour of some variables should have no implications concerning the suitability to act as time variables in the quantum case. Different time variables also lead to different theories characterized by different Hilbert spaces and in particular to different conclusions concerning the presence of singularities.

In the Bohmian treatments no such ambiguities arise. In particular, whether variables act as clock variables depends on their quantum behaviour, not on their classical behaviour. So on the fundamental level, the scalar field is not regarded as a time variable in the Bohmian theory. So, just as in the fundamental Bohmian theory, singularities may or may not exist depending on the wave function and the initial conditions. One can do a similar analysis for LQC. Let us first consider the Hilbert space. This point is not really emphasized in refs 2 — 5.

There, the issue of singularities is analyzed by considering whether the wave function is peaked around the singularity 2 , 3 , 4 or whether the expectation value of the volume operator becomes zero 5.

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