Is the Cosmological Constant, a “Vacuum” Field? We Explore This by Squeezing Early Universe “Coherent-Semi Classical States”, and Compare This to Energy from the Early Universe Heisenberg Uncertainty Principle

Our question delves into the nature of early universe vacuum fields, and if this initial vacuum field corresponds to a configuration of early universe space-time at the start of inflation. The answer as to this came out due to wanting to know if a cosmological constant, as given in the Einstein field equations is commensurate with the byproduct of squeezed states. We compare our answer, with the influx of energy as given by a modified Heinsenberg uncertainty principle, at the start of the inflationary era. The so called influx of energy is tied into the squeezed state phenomena as written up in the onset of this article. The impetus to writing this document came from Dr. Karim, in an e mail which the author relates to, in the introduction. Our claim is that the smallness of is what is driving the existence of the squeezed states.

Heisenberg Uncertainty Principle for n-Dimen-sional Linear Canonical Transforms

The uncertainty principle proposed by German physicist Heisenberg in 1927 is a basic principle of quantum mechanics and signal processing.Since linear canonical transformation has been widely used in various fields of signal processing recently and Heisenberg uncertainty principle has been endowed with new expressive meaning in linear canonical transforms domain,in this manuscript,an improved Heisenberg uncertainty principle is obtained in linear canonical trans-forms domain.

Squaring the Circle Is Possible When Taking into Consideration the Heisenberg Uncertainty Principle

Squaring the circle is one of the oldest challenges in mathematical geometry. In 1882, it was proven that π was transcendental, and the task of squaring the circle was considered impossible. Demonstrating that squaring the circle was not possible took place before discovering quantum mechanics. The purpose of this paper is to show that it is actually possible to square the circle when taking into account the Heisenberg uncertainty principle. The conclusion is clear: it is possible to square the circle when taking into account the Heisenberg uncertainty principle.

The Absolute Certainty Principle (ACP) Revolutionizes Quantum Physics

When the ubiquitous quantum, acting as an active principle, generates meteons in the System of the World, the Absolute Certainty Principle (ACP) regulates the characteristics of their motion. This newly uncovered law of Nature suggests that the cosmos is filled with an “aether”, as Newton and others—even Einstein!—called it in their days, and explains quite simply why we stand erect vertically on the surface of the Earth and why the universe is in expansion.

Unruh Metric Tensor HUP via Planckian Space-Time Compared to HUP Based Complexity of Measured System Results to Obtain Inflaton Potential Magnitude

First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δgtt. The metric tensor variations given by δgrr, δgθθand δgϕϕare negligible, as compared to the variation δgtt. Afterwards, what is referred to by Barbour as emergent duration of time δtis from the Heisenberg Uncertainty principle (HUP) applied to δgttin such a way as to be compared with ΔxΔp≥ℏ2+γ˜∂C∂Vwith V here a volume spatial term and γ˜a complexification strength term and ∂C∂Vinfluence of complexity of physical system being measured in order to obtain a parameterized value for the initial value of an inflaton which we call V0.

Heuristic Estimation of the Vacuum Energy Density of the Universe: Part II-Analysis Based on Frequency Domain Electromagnetic Radiation

In Part I of this paper, an inequality satisfied by the vacuum energy density of the universe was derived using an indirect and heuristic procedure. The derivation is based on a proposed thought experiment, according to which an electron is accelerated to a constant and relativistic speed at a distance L from a perfectly conducting plane. The charge of the electron was represented by a spherical charge distribution located within the Compton wavelength of the electron. Subsequently, the electron is incident on the perfect conductor giving rise to transition radiation. The energy associated with the transition radiation depends on the parameter L. It was shown that an inequality satisfied by the vacuum energy density will emerge when the length L is pushed to cosmological dimensions and the product of the radiated energy, and the time duration of emission is constrained by Heisenberg’s uncertainty principle. In this paper, a similar analysis is conducted with a chain of electrons oscillating sinusoidally and located above a conducting plane. In the thought experiment presented in this paper, the behavior of the energy radiated by the chain of oscillating electrons is studied in the frequency domain as a function of the length L of the chain. It is shown that when the length L is pushed to cosmological dimensions and the energy radiated within a single burst of duration of half a period of oscillation is constrained by the fact that electromagnetic energy consists of photons, an inequality satisfied by the vacuum energy density emerges as a result. The derived inequality is given by where is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 5.38 × 10-10 J/m. The result obtained here is in better agreement with experimental data than the one obtained in Part I of this paper with time domain radiation.

How 5 Dimensions May Fix a Deterministic Background Spatially as to Be Inserted for HUP in 3 + 1 Dimensions, and Its Relevance to the Early Universe

We will first of all reference a value of momentum, in the early universe. This is for 3 + 1 dimensions and is important since Wesson has an integration of this momentum with regards to a 5 dimensional parameter included in an integration of momentum over space which equals a ration of L divided by small l (length) and all these times a constant. The ratio of L over small l is a way of making deterministic inputs from 5 dimensions into the 3 + 1 dimensional HUP. In doing so, we come up with a very small radial component for reasons which due to an argument from Wesson is a way to deterministically fix one of the variables placed into the 3 + 1 HUP. This is a deterministic input into a derivation which is then First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δgtt. The metric tensor variations are given by δgrr, δgθθ and δgφφ are negligible, as compared to the variation δgtt. From there the expression for the HUP and its applications into certain cases in the early universe are strictly affected after we take into consideration a vanishingly small r spatial value in how we define δgtt.

On the Quantization of Time, Space and Gravity

We combine the de Broglie Matter Wave Equation with the Heisenberg Uncertainty Principle to derive an equation for time as a wave. This happens to be the first time that these two statements have been combined in this manner to derive an equation for time. The result is astounding. Time turns out to be a minuscule blob of quantum electromagnetic energy in perpetual angular momentum. From this time equation, we derive an equation for space which turns out to also predict a string (like the string of string theory). We then combine the time equation with the space equation to derive an equation for the inverse of quantum gravity which is also surprisingly electromagnetic in nature. This last statement implies that space is multidimensional and gravity in multidimensional space is not quantized, but its inverse (which is single-dimensional) is.

How 5 Dimensions May Fix a Deterministic Background Spatially as to Be Inserted for HUP in 3 + 1 Dimensions, and Its Relevance to the Early Universe? Criteria for Massive Graviton Detection from Relic Conditions Mentioned

We will first of all reference a value of momentum, in the early universe. This is for 3 + 1 dimensions and is important since Wesson has an integration of this momentum with regards to a 5 dimensional parameter included in an integration of momentum over space which equals a ration of L divided by small l (length) and all these times a constant. The ratio of L over small l is a way of making deterministic inputs from 5 dimensions into the 3 + 1 dimensional HUP. In doing so, we come up with a very small radial component for reasons which due to an argument from Wesson is a way to deterministically fix one of the variables placed into the 3 + 1 HUP. This is a deterministic input into a derivation which is then, first of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining is variation in δgtt. We state that the metric tensor variations are given by δgrr, δgθθ and δgφφ are negligible contributions, as compared to the variation δgtt. From there the expression for the HUP and its applications into certain cases in the early universe are strictly affected after we take into consideration a vanishingly small r spatial value in how we define δgtt.

Gedanken Experiment for Refining the Unruh Metric Tensor Uncertainty Principle via Schwarzschild Geometry and Planckian Space-Time with Initial Nonzero Entropy and Applying the Riemannian-Penrose Inequality and Initial Kinetic Energy for a Lower Bound to Graviton Mass (Massive Gravity)

This paper is with the permission of Stepan Moskaliuk similar to what he will put in the confer-ence proceedings of the summer teaching school and workshop for Ukrainian PhD physics stu-dents as given in Bratislava, as of summer 2015. With his permission, this paper will be in part reproduced here for this journal. First of all, we restate a proof of a highly localized special case of a metric tensor uncertainty principle first written up by Unruh. Unruh did not use the Roberson-Walker geometry which we do, and it so happens that the dominant metric tensor we will be examining, is variation in δgtt. The metric tensor variations given by δgrr, and are negligible, as compared to the variation δgtt. Afterwards, what is referred to by Barbour as emergent duration of time is from the Heisenberg Uncertainty principle (HUP) applied to δgtt in such a way as to give, in the Planckian space-time regime a nonzero minimum non zero lower ground to a massive graviton, mgraviton. The lower bound to the massive graviton is influenced by δgtt and kinetic energy which is in the Planckian emergent duration of time δt as (E-V) . We find from δgtt version of the Heisenberg Uncertainty Principle (HUP), that the quantum value of the Δt·ΔE Heisenberg Uncertainty Principle (HUP) is likely not recoverable due to δgtt ≠ Ο(1)~gtt ≡ 1. i.e. δgtt≠ Ο(1) . i.e. is consistent with non-curved space, so Δt · ΔE ≥ no longer holds. This even if we take the stress energy tensor approximation Tii= diag (ρ ,-p,-p,-p) where the fluid approximation is used. Our treatment of the inflaton is via Handley et al., where we consider the lower mass limits of the graviton as due to when the inflaton is many times larger than a Potential energy, with a kinetic energy (KE) proportional to ρw ∝ a-3(1-w) ~ g*T4 , with g* initial degrees of freedom, and T initial temperature. Leading to non-zero initial entropy as stated in Appendix A. In addition we also examine a Ricci scalar value at the boundary between Pre Planckian to Planckian regime of space-time, setting the magnitude of k as approaching flat space conditions right after the Planck regime. Furthermore, we have an approximation as to initial entropy production N~Sinitial(graviton)~1037. Finally, this entropy is N, and we get an initial version of the cosmological “constant” as Appendix D which is linked to initial value of a graviton mass. Appendix E is for the Riemannian-Penrose inequality, which is either a nonzero NLED scale factor or quantum bounce as of LQG. Note that, Appendix F gives conditions so that a pre Planckian kinetic energy (inflaton) value greater than Potential energy occurs, which is foundational to the lower bound to Graviton mass. We will in the future add more structure to this calculation so as to confirm via a precise calculation that the lower bound to the graviton mass, is about 10-70 grams. Our lower bound is a dimensional approximation so far. We will make it exact. We conclude in this document with Appendix G, which is comparing our Pre Planckian space-time metric Heisenberg Uncertainty Principle with the generalized uncertainty principle in quantum gravity. Our result is different from the one given by Ali, Khali and Vagenas, in which our energy fluctuation is not proportional to that of processes of energy connected to Black hole physics, and we also allow for the possibility of Pre Planckian time. Whereas their result (and the generalized string theory Heisenberg Uncertainty principle) have a more limited regime of interpolation of final results. We do come up with equivalent bounds to recover δgtt ~ small-value ≠ O(1) and the deviation of fluctuations of energy, but with very specific bounds upon the parameters of Ali, Khali, and Vegenas, but this has to be more fully explored. Finally, we close with a comparison of what this new Metric tensor uncertainty principle presages as far as avoiding the Bicep 2 mistake, and the different theories of gravity, as reviewed in Appendix H.

Quantum-Classical Algorithm for an Instantaneous Spectral Analysis of Signals:A Complement to Fourier Theory

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.

Hints of the Photonic Nature of the Electromagnetic Fields in Classical Electrodynamics

Several recent publications show that the electromagnetic radiation generated by transmitting antennas satisfy the following universal conditions: The time domain radiation fields satisfy the condition A ≥ h/4π ⇒q ≥ e where A is the action of the radiation field, which is defined as the product of the radiated energy and the duration of the radiation, h is the Planck constant, e is the electronic charge and q is the charge associated with the radiating system. The frequency domain radiation fields satisfy the condition U ≥ hv ⇒q ≥ e where U is the energy radiated in a single burst of radiation of duration T/2 and v is the frequency of oscillation. The goal of this paper is to show that these conditions, which indeed are expressions of the photonic nature of the electromagnetic fields, are satisfied not only by the radiation fields generated by physical antennas but also by the radiation fields generated by accelerating or decelerating electric charges. The results presented here together with the results obtained in previous studies show that hints of the photonic nature of the electromagnetic radiation remain hidden in the field equations of classical electrodynamics, and they become apparent when the dimension of the radiating system is pushed to the extreme limits as allowed by nature.

Heuristic Estimation of the Vacuum Energy Density of the Universe: Part I—Analysis Based on Time Domain Electromagnetic Radiation

In this paper, an inequality satisfied by the vacuum energy density of the universe is derived using an indirect and heuristic procedure. The derivation is based on a proposed thought experiment, according to which an electron is accelerated to a constant and relativistic speed at a distance L from a perfectly conducting plane. The charge of the electron is represented by a spherical charge distribution located within the Compton wavelength of the electron. Subsequently, the electron is incident on the perfect conductor giving rise to transition radiation. The energy associated with the transition radiation depends on the parameter L. It is shown that an inequality satisfied by the vacuum energy density will emerge when the length L is pushed to cosmological dimensions and the product of the radiated energy and the time duration of emission are constrained by Heisenberg’s uncertainty principle. The inequality derived is given by ρΛ ≤ 9.9×10-9J/m3 where ρΛ is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 0.538 × 10-9J/m. Since there is a direct relationship between the vacuum energy density and the Einstein’s cosmological constant, the inequality can be converted directly to that of the cosmological constant.

Physical Kinetics, Relativism and Nonlocal Physics

The old classical problems of theoretical physics are revisited from the point of view of nonlocal physics. Nonlocal physics leads to very complicated mathematical apparatus. Here, we explain the main principles of nonlocal physics using transparent considerations and animations.