Uncertainty relations are of profound significance in quantum mechanics and quantum information theory.The well-known Heisenberg-Robertson uncertainty relation presents the constraints on the spread of measurement out...Uncertainty relations are of profound significance in quantum mechanics and quantum information theory.The well-known Heisenberg-Robertson uncertainty relation presents the constraints on the spread of measurement outcomes caused by the non-commutability of a pair of observables.In this article,we study the uncertainty relation of triple observables to explore the relationship between the standard deviations and the commutators of the observables.We derive and tighten the multiplicative form and weighted summation form uncertainty relations,which are found to be dependent not only on the commutation relations of each pair of the observables but also on a newly defined commutator in terms of all the three observables.We experimentally test the uncertainty relations in a linear optical setup.The experimental and numerical results agree well and show that the uncer-tainty relations derived by us successfully present tight lower bounds in the cases of high-dimensional observables and the cases of mixed states.Our method of deriving the uncertainty relation can be extended to more than three observables.展开更多
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 t...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.展开更多
It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in t...It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.展开更多
Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. ...Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.展开更多
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...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.展开更多
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, a...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 δg<sub>tt</sub>. The metric tensor variations given by δg<sub>rr</sub>, and are negligible, as compared to the variation δg<sub>tt</sub>. Afterwards, what is referred to by Barbour as emergent duration of time is from the Heisenberg Uncertainty principle (HUP) applied to δg<sub>tt </sub>in such a way as to give, in the Planckian space-time regime a nonzero minimum non zero lower ground to a massive graviton, m<sub>graviton</sub>. The lower bound to the massive graviton is influenced by δg<sub>tt </sub>and kinetic energy which is in the Planckian emergent duration of time δt as (E-V) . We find from δg<sub>tt </sub>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 δg<sub>tt </sub>≠ Ο(1)~g<sub>tt</sub> ≡ 1. i.e. δg<sub>tt</sub>≠ 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 T<sub>ii</sub>= 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 ρ<sub>w</sub> ∝ a<sup>-3(1-w)</sup> ~ g*T<sup>4</sup> , with g* initial degrees of freedom, and T initial temperature. Leading t展开更多
The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are ...The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.展开更多
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 ...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<sup>-10</sup> 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.展开更多
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 inclu...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 δg<sub>tt</sub>. The metric tensor variations are given by δg<sub>rr</sub>, δg<sub>θθ</sub> and δg<sub>φφ</sub> are negligible, as compared to the variation δg<sub>tt</sub>. 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 δg<sub>tt</sub>.展开更多
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 &...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.展开更多
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...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 ρ<sub>Λ</sub> ≤ 9.9×10<sup>-9</sup>J/m<sup>3</sup> where ρ<sub>Λ </sub>is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 0.538 × 10<sup>-9</sup>J/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.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.12175052,11775065,62105086,and 11935012).
文摘Uncertainty relations are of profound significance in quantum mechanics and quantum information theory.The well-known Heisenberg-Robertson uncertainty relation presents the constraints on the spread of measurement outcomes caused by the non-commutability of a pair of observables.In this article,we study the uncertainty relation of triple observables to explore the relationship between the standard deviations and the commutators of the observables.We derive and tighten the multiplicative form and weighted summation form uncertainty relations,which are found to be dependent not only on the commutation relations of each pair of the observables but also on a newly defined commutator in terms of all the three observables.We experimentally test the uncertainty relations in a linear optical setup.The experimental and numerical results agree well and show that the uncer-tainty relations derived by us successfully present tight lower bounds in the cases of high-dimensional observables and the cases of mixed states.Our method of deriving the uncertainty relation can be extended to more than three observables.
文摘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.
文摘It is shown that in Euclidean space with any number of spatial dimensions more than three, the Lorentz transform holds true if the proper time of each elementary particle is proportional to the length of its path in the extra-dimensional subspace, and all elementary particles move at the speed of light in the complete space. The six-dimensional treatment of the Coulomb force of interaction between two charges is given. The electric force is due to the motion of charges in the extra-dimensional subspace and is equal to the corresponding Lorentz force.
文摘Review of the irreversibility problem in modern physics with new researches is given. Some characteristics of the Markov chains are specified and the important property of monotonicity of a probability is formulated. Using one thin inequality, the behavior of relative entropy in the classical case is considered. Further we pass to studying of the irreversibility phenomena in quantum problems. By new method is received the Lindblad’s equation and its physical essence is explained. Deep analogy between the classical Markov processes and development described by the Lindblad’s equation is conducted. Using method of comparison of the Lind-blad’s equation with the linear Langevin equation we receive a system of differential equations, which are more general, than the Caldeira-Leggett equation. Here we consider quantum systems without inverse influ-ence on a surrounding background with high temperature. Quantum diffusion of a single particle is consid-ered and possible ways of the permission of the Schr?dinger’s cat paradox and the role of an external world for the phenomena with quantum irreversibility are discussed. In spite of previous opinion we conclude that in the equilibrium environment is not necessary to postulate the processes with collapses of wave functions. Besides, we draw attention to the fact that the Heisenberg’s uncertainty relation does not always mean the restriction is usually the product of the average values of commuting variables. At last, some prospects in the problem of quantum irreversibility are discussed.
文摘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.
文摘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 δg<sub>tt</sub>. The metric tensor variations given by δg<sub>rr</sub>, and are negligible, as compared to the variation δg<sub>tt</sub>. Afterwards, what is referred to by Barbour as emergent duration of time is from the Heisenberg Uncertainty principle (HUP) applied to δg<sub>tt </sub>in such a way as to give, in the Planckian space-time regime a nonzero minimum non zero lower ground to a massive graviton, m<sub>graviton</sub>. The lower bound to the massive graviton is influenced by δg<sub>tt </sub>and kinetic energy which is in the Planckian emergent duration of time δt as (E-V) . We find from δg<sub>tt </sub>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 δg<sub>tt </sub>≠ Ο(1)~g<sub>tt</sub> ≡ 1. i.e. δg<sub>tt</sub>≠ 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 T<sub>ii</sub>= 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 ρ<sub>w</sub> ∝ a<sup>-3(1-w)</sup> ~ g*T<sup>4</sup> , with g* initial degrees of freedom, and T initial temperature. Leading t
文摘The breakdown of the Heisenberg Uncertainty Principle occurs when energies approach the Planck scale, and the corresponding Schwarzschild radius becomes similar to the Compton wavelength. Both of these quantities are approximately equal to the Planck length. In this context, we have introduced a model that utilizes a combination of Schwarzschild’s radius and Compton length to quantify the gravitational length of an object. This model has provided a novel perspective in generalizing the uncertainty principle. Furthermore, it has elucidated the significance of the deforming linear parameter β and its range of variation from unity to its maximum value.
文摘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<sup>-10</sup> 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.
文摘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 δg<sub>tt</sub>. The metric tensor variations are given by δg<sub>rr</sub>, δg<sub>θθ</sub> and δg<sub>φφ</sub> are negligible, as compared to the variation δg<sub>tt</sub>. 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 δg<sub>tt</sub>.
文摘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.
文摘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 ρ<sub>Λ</sub> ≤ 9.9×10<sup>-9</sup>J/m<sup>3</sup> where ρ<sub>Λ </sub>is the vacuum energy density. This result is consistent with the measured value of the vacuum energy density, which is 0.538 × 10<sup>-9</sup>J/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.
