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Quantum optics with Rydberg superatoms Rydberg超原子的量子光学
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-05-12 DOI: 10.1088/2399-6528/acd51d
J. Kumlin, C. Braun, C. Tresp, N. Stiesdal, S. Hofferberth, A. Paris-Mandoki
Quantum optics based on highly excited atoms, also known as Rydberg atoms, has cemented itself as a powerful platform for the manipulation of light at the few-photon level. The Rydberg blockade, resulting from the strong interaction between individual Rydberg atoms, can turn a large ensemble of atoms into a system which collectively resembles a single two-level emitter, a so-called Rydberg superatom. The coupling of this artificial emitter to a driving photonic mode is collectively enhanced by Rydberg interactions, enabling strong coherent coupling at the few-photon level in free-space. The exquisite level of control achievable through this has already demonstrated its utility in applications of quantum computing and information processing. Here, we review the derivation of the collective coupling between a Rydberg superatom and a single light mode and discuss the similarity of this free-space setup to waveguide quantum electrodynamics systems of quantum emitters coupled to photonic waveguides. We also briefly review applications of Rydberg superatoms to quantum optics such as single-photon generation and single-photon subtraction.
基于高度激发原子(也称为里德伯原子)的量子光学已经巩固了其作为在少光子水平上操纵光的强大平台的地位。由单个里德伯原子之间的强相互作用产生的里德伯阻断可以将一个大的原子系综变成一个整体类似于单个两能级发射极的系统,即所谓的里德伯超原子。Rydberg相互作用共同增强了这种人造发射器与驱动光子模式的耦合,从而在自由空间中实现了少光子级的强相干耦合。通过这种方式可以实现的精细控制水平已经证明了它在量子计算和信息处理应用中的实用性。在这里,我们回顾了里德堡超原子和单光模式之间集体耦合的推导,并讨论了这种自由空间设置与耦合到光子波导的量子发射器的波导量子电动力学系统的相似性。我们还简要回顾了里德伯超原子在量子光学中的应用,如单光子产生和单光子相减。
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引用次数: 0
Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves 海森堡反铁磁体在边与角共用三角形晶格上的热特性:来自自旋波的讯息
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-05-05 DOI: 10.1088/2399-6528/acd320
Shoji Yamamoto, J. Ohara
We propose a new scheme of modifying spin waves so as to describe the thermodynamic properties of various noncollinear antiferromagnets with particular interest in a comparison between edge- versus corner-sharing triangular-based lattices. The well-known modified spin-wave theory for collinear antiferromagnets diagonalizes a bosonic Hamiltonian subject to the constraint that the total staggered magnetization be zero. Applying this scheme to frustrated noncollinear antiferromagnets ends in a poor thermodynamics, missing the optimal ground state and breaking the local U(1) rotational symmetry. We find such a plausible double-constraint condition for spin spirals as to spontaneously go back to the traditional single-constraint condition at the onset of a collinear Néel-ordered classical ground state. We first diagonalize only the bilinear terms in Holstein-Primakoff boson operators on the order of spin magnitude S and then bring these linear spin waves into interaction in a perturbative rather than variational manner. We demonstrate specific-heat calculations in terms of thus-modified interacting spin waves on various triangular-based lattices. In zero dimension, modified-spin-wave findings in comparison with finite-temperature Lanczos calculations turn out so successful as to reproduce the monomodal and bimodal specific-heat temperature profiles of the triangular-based edge-sharing Platonic and corner-sharing Archimedean polyhedral-lattice antiferromagnets, respectively. In two dimensions, high-temperature series expansions and tensor-network-based renormalization-group calculations are still controversial especially at low temperatures, and under such circumstances, modified spin waves interestingly predict that the specific heat of the kagome-lattice antiferromagnet in the corner-sharing geometry remains having both mid-temperature broad maximum and low-temperature narrow peak in the thermodynamic limit, while the specific heat of the triangular-lattice antiferromagnet in the edge-sharing geometry retains a low-temperature sharp peak followed by a mid-temperature weak anormaly in the thermodynamic limit. By further calculating one-magnon spectral functions in terms of our newly developed double-constraint modified spin-wave theory, we reveal that not only the elaborate modification scheme but also quantum corrections, especially those caused by the O(S 0) primary self-energies, are key ingredients in the successful description of triangular-based-lattice noncollinear antiferromagnets over the whole temperature range of absolute zero to infinity.
我们提出了一种修改自旋波的新方案,以描述各种非共线反铁磁体的热力学性质,并特别感兴趣的是边缘与角共享三角晶格之间的比较。众所周知的共线反铁磁体的修正自旋波理论对角化了一个受总交错磁化为零约束的玻色子哈密顿量。将该方案应用于受挫的非共线反铁磁体的结果是热力学差,错过了最佳基态并破坏了局部U(1)旋转对称。我们发现了这样一个似是而非的双约束条件,使得自旋螺旋在共线nsamel有序经典基态开始时可以自发地回到传统的单约束条件。我们首先对角化荷尔斯坦-普里马科夫玻色子算子中自旋量级为S的双线性项,然后以微扰而非变分的方式将这些线性自旋波引入相互作用。我们演示了在各种基于三角形的晶格上根据这样修改的相互作用自旋波的比热计算。在零维,修正自旋波的发现与有限温度的Lanczos计算相比较,结果非常成功,可以分别再现基于三角形的共享边柏拉图式和共享角阿基米德多面体晶格反铁磁体的单峰和双峰比热温度分布。在二维中,高温系列展开和基于张量网络的重整化群计算仍然存在争议,特别是在低温下,在这种情况下,修正自旋波有趣地预测了kagome-晶格反铁磁体在共享角几何中的比热在热力学极限下仍然具有中温宽最大值和低温窄峰值。而三角形晶格反铁磁体的比热在共边几何结构中保持低温尖峰,随后在热力学极限处出现中温弱异常。通过用我们新开发的双约束修正自旋波理论进一步计算一磁振子谱函数,我们揭示了在绝对零度到无穷远的整个温度范围内,不仅精细的修正方案,而且量子修正,特别是由0 (s0)主要自能引起的量子修正,是成功描述三角晶格非共线反铁磁体的关键因素。
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引用次数: 0
Quantum advantage of Monte Carlo option pricing 蒙特卡罗期权定价的量子优势
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-05-04 DOI: 10.1088/2399-6528/acd2a4
Zoltán Udvarnoki, G. Fáth, N. Fogarasi
Quantum computers have the potential to provide quadratic speedup for Monte Carlo methods currently used in various classical applications. In this work, we examine the advantage of quantum computers for financial option pricing with the Monte Carlo method. Systematic and statistical errors are handled in a joint framework, and a relationship to quantum gate error is established. New metrics are introduced for the assessment of quantum advantage based on sample count and optimized error handling. We implement and analyze a Fourier series based approach and demonstrate its benefit over the more traditional rescaling method in function approximation. Our numerical calculations reveal the unpredictable nature of systematic errors, making consistent quantum advantage difficult with current quantum hardware. Our results indicate that very low noise levels, a two-qubit gate error rate below 10−6, are necessary for the quantum method to outperform the classical one, but a low number of logical qubits (ca. 20) may be sufficient to see quantum advantage already.
量子计算机有潜力为目前在各种经典应用中使用的蒙特卡罗方法提供二次加速。在这项工作中,我们用蒙特卡洛方法研究了量子计算机在金融期权定价中的优势。系统误差和统计误差在一个联合框架中处理,并建立了与量子门误差的关系。引入了基于样本计数和优化错误处理的量子优势评估新指标。我们实现并分析了一种基于傅立叶级数的方法,并证明了它在函数近似中优于传统的重标度方法。我们的数值计算揭示了系统误差的不可预测性,使得当前量子硬件难以保持一致的量子优势。我们的研究结果表明,非常低的噪声水平,两个量子比特的门错误率低于10−6,是量子方法优于经典方法所必需的,但是低数量的逻辑量子比特(约20)可能已经足以看到量子优势。
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引用次数: 0
3D printed variable aperture horn with modular ridges 3D打印可变孔径喇叭与模块化脊
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-04-28 DOI: 10.1088/2399-6528/acd167
I. Goode, C. Saavedra
3D printing technology has significant potential to modernize the student laboratory experience in the area of electromagnetic wave propagation and scattering. In this contribution, a fast and low-cost method to 3D print and metallize a variable aperture horn and waveguide launcher are presented. The launcher converts a SubMiniature version A (SMA) coaxial connector to WR 187 waveguide (standard size of waveguide for 3.95 GHz to 5.85 GHz) and is printed from plastic while being metallized with aluminum tape. The launcher provided similar performance to an off the shelf launcher at one 40th the cost. As a teachable extension to this launcher a variable aperture horn is 3D printed and metallized with aluminum tape. The aperture area of the horn is changed by rotating the E⃗ walls of the horn away from each other by use of pivot in the transition between the launcher and the horn. This horn showed the expected decrease in beamwidth and increase in peak gain as the aperture area was increased while maintaining a usable impedance match. Modular center ridges were also printed to demonstrate the utility of center ridges in a horn antenna without H⃗ walls. Overall, a modular, inexpensive, and easy to construct waveguide system is presented that is useful for teaching electromagnetics specifically the relationship between aperture area and antenna gain, as well as providing a platform for waveguide experiments.
3D打印技术在电磁波传播和散射领域具有使学生实验室体验现代化的巨大潜力。在这一贡献中,提出了一种快速、低成本的方法来3D打印和金属化可变孔径喇叭和波导发射器。发射器将SubMiniature版本a(SMA)同轴连接器转换为WR 187波导(3.95 GHz至5.85 GHz的标准尺寸波导),并用塑料印刷,同时用铝带进行金属化。该发射器提供了与现成发射器类似的性能,成本为其40分之一。作为该发射器的可教扩展,可变孔径喇叭是3D打印的,并用铝带进行金属化。喇叭的孔径面积通过旋转E而改变⃗ 通过在发射器和喇叭之间的过渡中使用枢轴使喇叭的壁彼此远离。随着孔径面积的增加,该喇叭显示出波束宽度的预期减小和峰值增益的增加,同时保持可用的阻抗匹配。模块化的中心脊也被打印出来,以证明中心脊在没有H的喇叭天线中的实用性⃗ 墙壁。总之,提出了一种模块化、廉价且易于构建的波导系统,该系统有助于教授电磁学,特别是孔径面积和天线增益之间的关系,并为波导实验提供平台。
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引用次数: 0
Relativistic probability densities for location 位置的相对论概率密度
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-04-17 DOI: 10.1088/2399-6528/acddcc
Joshua G. Fenwick, R. Dick
Imposing the Born rule as a fundamental principle of quantum mechanics would require the existence of normalizable wave functions ψ( x , t) also for relativistic particles. Indeed, the Fourier transforms of normalized k -space amplitudes ψ(k,t)=ψ(k)exp(−iωkt) yield normalized functions ψ( x , t) which reproduce the standard k -space expectation values for energy and momentum from local momentum (pseudo-)densities ℘ μ ( x , t) = (ℏ/2i)[ψ +( x , t)∂ μ ψ( x , t) − ∂ μ ψ +( x , t) · ψ( x , t)]. However, in the case of bosonic fields, the wave packets ψ( x , t) are nonlocally related to the corresponding relativistic quantum fields ϕ( x , t), and therefore the canonical local energy-momentum densities (x,t)=c0(x,t) and (x,t) differ from ℘ μ ( x , t) and appear nonlocal in terms of the wave packets ψ( x , t). We examine the relation between the canonical energy density (x,t) , the canonical charge density ϱ( x , t), the energy pseudo-density ˜(x,t)=c℘0(x,t) , and the Born density ∣ψ( x , t)∣2 for the massless free Klein–Gordon field. We find that those four proxies for particle location are tantalizingly close even in this extremely relativistic case: in spite of their nonlocal mathematical relations, they are mutually local in the sense that their maxima do not deviate beyond a common position uncertainty Δx. Indeed, they are practically indistinguishable in cases where we would expect a normalized quantum state to produce particle-like position signals, viz. if we are observing quanta with momenta p ≫ Δp ≥ ℏ/2Δx. We also translate our results to massless Dirac fields. Our results confirm and illustrate that the normalized energy density (x,t)/E provides a suitable measure for positions of bosons, whereas normalized charge density ϱ( x , t)/q provides a suitable measure for fermions.
将玻恩规则作为量子力学的基本原理,需要相对论粒子也存在可归一化波函数ψ(x,t)。事实上,归一化k空间振幅ψ(k,t)=ψ(k)exp(−iωkt)的傅立叶变换产生归一化函数ψ(x,t),该函数再现了来自局部动量(伪)密度的能量和动量的标准k空间期望值℘ μ(x,t)=(ℏ/2i)[ψ+(x,t。然而,在玻色子场的情况下,波包ψ(x,t(x,t)=c0(x,t)和(x,t)不同于℘ μ(x,t),并且根据波包ψ(x,t)表现为非局部的。我们检验了正则能量密度之间的关系(x,t),规范电荷密度ϱ(x,t),能量伪密度~(x,t)=c℘0(x,t),以及无质量自由Klein-Gordon场的Born密度Şψ。我们发现,即使在这种极端相对论的情况下,粒子位置的这四个指标也非常接近:尽管它们之间存在非局部数学关系,但它们是相互局部的,因为它们的最大值不会偏离共同的位置不确定性Δx。事实上,在我们期望归一化量子态产生类似粒子的位置信号的情况下,它们实际上是不可区分的,即,如果我们观察到动量ṕΔp≥ℏ/2Δx。我们还将结果转化为无质量狄拉克场。我们的结果证实并说明了归一化能量密度(x,t)/E为玻色子的位置提供了一个合适的度量,而归一化电荷密度ϱ(x,t)/q为费米子提供了一种合适的度量。
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引用次数: 0
Investigation of Coulomb’s law and the nature of the electric charge 库仑定律与电荷性质的研究
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-04-17 DOI: 10.1088/2399-6528/accdb4
Saqer M Darwish
This theoretical work investigates spin-spin energy in the hydrogen atom and its relation to Coulomb’s force law. Most elementary particles are assigned intrinsic properties of carrying electric charges, which leave us blundering about the essence of electric charge. The perplexity originated in Coulomb’s force law when the proportionality constant is expressed using the free vacuum electric permittivity constant ε 0 in units of. C2m−2. N−1. Introducing these units by the proportionality constant canceled any direct role for the electric charge. In this research, a genuine suggestion based on energy conservation redefines Coulomb’s force law. A new formula has been suggested for the force between two spinning particles. The results of energy and force calculations agreed with Coulomb’s law evaluations. The spin-spin energy is related to the electric potential energy, and the electric charge is found to be connected to the rotational energy of the mass.
这项理论工作研究了氢原子中的自旋-自旋能量及其与库仑力定律的关系。大多数基本粒子都具有携带电荷的固有性质,这让我们对电荷的本质产生了误解。当比例常数用自由真空介电常数ε0表示时,困惑源于库仑力定律,单位为。C2m−2.N−1。通过比例常数引入这些单位抵消了电荷的任何直接作用。在这项研究中,一个基于能量守恒的真实建议重新定义了库仑力定律。对于两个自旋粒子之间的力,提出了一个新的公式。能量和力的计算结果与库仑定律的评估结果一致。自旋-自旋能量与势能有关,电荷与质量的旋转能量有关。
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引用次数: 0
One-dimensional pseudoharmonic oscillator: classical remarks and quantum-information theory 一维伪谐振子:经典评述与量子信息论
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-04-13 DOI: 10.1088/2399-6528/acce20
O. Olendski
Motion along semi-infinite straight line in a potential that is a combination of positive quadratic and inverse quadratic functions of the position is considered with the emphasis on the analysis of its quantum-information properties. Classical measure of symmetry of the potential is proposed and its dependence on the particle energy and the factor a describing a relative strength of its constituents is described; in particular, it is shown that a variation of the parameter a alters the shape from the half-harmonic oscillator (HHO) at a=0 to the perfectly symmetric one of the double frequency oscillator (DFO) in the limit of huge a . Quantum consideration focuses on the analysis of information-theoretical measures, such as standard deviations, Shannon, Rényi and Tsallis entropies together with Fisher information, Onicescu energy and non–Gaussianity. For doing this, among others, a method of calculating momentum waveforms is proposed that results in their analytic expressions in form of the confluent hypergeometric functions. Increasing parameter a modifies the measures in such a way that they gradually transform into those corresponding to the DFO what, in particular, means that the lowest orbital saturates Heisenberg, Shannon, Rényi and Tsallis uncertainty relations with the corresponding position and momentum non–Gaussianities turning to zero. A simple expression is derived of the orbital-independent lower threshold of the semi-infinite range of the dimensionless Rényi/Tsallis coefficient where momentum components of these one-parameter entropies exist which shows that it varies between 1/4 at HHO and zero when a tends to infinity. Physical interpretation of obtained mathematical results is provided.
考虑了由位置的正二次函数和反二次函数组合而成的势中沿半无限直线的运动,重点分析了其量子信息性质。提出了电势对称性的经典度量,并描述了它对粒子能量和描述其成分相对强度的因子a的依赖性;特别地,参数a的变化改变了从a=0的半谐振荡器(HHO)到在巨大a的极限下的双频振荡器(DFO)的完全对称振荡器的形状。量子考虑侧重于分析信息理论度量,如标准差、Shannon、Rényi和Tsallis熵,以及Fisher信息、Onicescu能量和非高斯性。为了做到这一点,除其他外,提出了一种计算动量波形的方法,该方法得到了它们以合流超几何函数形式的解析表达式。增加参数a以这样一种方式修改度量,即它们逐渐转变为与DFO相对应的度量,特别是,这意味着最低轨道饱和了海森堡、香农、雷尼和Tsallis的不确定性关系,相应的位置和动量非高斯变为零。导出了无量纲Rényi/Tsallis系数半无限范围的轨道无关下阈值的一个简单表达式,其中存在这些单参数熵的动量分量,这表明当A趋于无穷大时,它在HHO的1/4和0之间变化。提供了对所获得的数学结果的物理解释。
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引用次数: 1
Accessing radiation damage to biomolecules on the nanoscale by particle-scattering simulations 通过粒子散射模拟在纳米尺度上获取对生物分子的辐射损伤
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-04-06 DOI: 10.1088/2399-6528/accb3f
M. B. Hahn
Radiation damage to DNA plays a central role in radiation therapy to cure cancer. The physico-chemical and biological processes involved encompass huge time and spatial scales. To obtain a comprehensive understanding on the nano and the macro scale is a very challenging tasks for experimental techniques alone. Therefore particle-scattering simulations are often applied to complement measurements and aide their interpretation, to help in the planning of experiments, to predict their outcome and to test damage models. In the last years, powerful multipurpose particle-scattering framework based on the Monte-Carlo simulation (MCS) method, such as Geant4 and Geant4-DNA, were extended by user friendly interfaces such as TOPAS and TOPAS-nBio. This shifts their applicability from the realm of dedicated specialists to a broader range of scientists. In the present review we aim to give an overview over MCS based approaches to understand radiation interaction on a broad scale, ranging from cancerous tissue, cells and their organelles including the nucleus, mitochondria and membranes, over radiosensitizer such as metallic nanoparticles, and water with additional radical scavenger, down to isolated biomolecules in the form of DNA, RNA, proteins and DNA-protein complexes. Hereby the degradation of biomolecules by direct damage from inelastic scattering processes during the physical stage, and the indirect damage caused by radicals during the chemical stage as well as some parts of the early biological response is covered. Due to their high abundance the action of hydroxyl radicals (•OH) and secondary low energy electrons (LEE) as well as prehydrated electrons are covered in additional detail. Applications in the prediction of DNA damage, DNA repair processes, cell survival and apoptosis, influence of radiosensitizer on the dose distribution within cells and their organelles, the study of linear energy transfer (LET), the relative biological effectiveness (RBE), ion beam cancer therapy, microbeam radiation therapy (MRT), the FLASH effect, and the radiation induced bystander effect are reviewed.
辐射对DNA的损伤在治疗癌症的放射治疗中起着核心作用。所涉及的物理化学和生物过程涵盖了巨大的时间和空间尺度。对实验技术而言,全面了解纳米和宏观尺度是一项非常具有挑战性的任务。因此,粒子散射模拟通常用于补充测量和辅助解释,帮助规划实验,预测结果和测试损伤模型。近年来,基于蒙特卡罗模拟(MCS)方法的强大的多用途粒子散射框架,如Geant4和Geant4- dna,通过友好的用户界面如TOPAS和TOPAS- nbio进行了扩展。这使得它们的适用性从专门的专家领域扩展到更广泛的科学家领域。在本综述中,我们旨在概述基于MCS的方法来理解辐射相互作用的广泛范围,从癌组织、细胞及其细胞器(包括细胞核、线粒体和膜),到放射增敏剂(如金属纳米颗粒)和含有额外自由基清除剂的水,再到以DNA、RNA、蛋白质和DNA-蛋白质复合物形式存在的分离生物分子。从而涵盖了生物分子在物理阶段由非弹性散射过程的直接损伤引起的降解,以及化学阶段由自由基引起的间接损伤以及早期生物反应的某些部分。由于它们的高丰度,羟基自由基(•OH)和次级低能电子(LEE)以及预水合电子的作用将被详细介绍。本文综述了辐射敏化剂在预测DNA损伤、DNA修复过程、细胞存活和凋亡、辐射敏化剂对细胞及其细胞器内剂量分布的影响、线性能量传递(LET)研究、相对生物效应(RBE)、离子束癌症治疗、微束放射治疗(MRT)、FLASH效应和辐射诱导旁观者效应等方面的应用。
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引用次数: 1
Reply to Comment on: ‘Experimental indications of non-classical brain function’ (2022 Journal of Physics Communications 6 105001) 回复关于“非经典脑功能的实验适应症”的评论(2022物理通讯6 105001)
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-03-21 DOI: 10.1088/2399-6528/acc636
C. Kerskens, David López Pérez
We have recently suggested a proposal to explore non-classicality in the brain, for which we developed an entanglement witness protocol using MRI. The witness protocol intended to find spin interactions which could not be explained by classical interactions, based on intermolecular multiple quantum coherence (iMQC). As for Warren’s comments, we show in more detail that this was indeed the case; our observations were certainly not generated by interactions based on the iMQC model. Further, we discuss some additional details not present in the original paper.
我们最近提出了一项探索大脑非经典性的建议,为此我们开发了一种使用MRI的纠缠见证协议。基于分子间多重量子相干(iMQC)的见证协议旨在寻找经典相互作用无法解释的自旋相互作用。至于沃伦的评论,我们更详细地说明了事实确实如此;我们的观察结果当然不是基于iMQC模型的相互作用产生的。此外,我们还讨论了一些原始论文中没有出现的其他细节。
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引用次数: 0
Comment on: ‘Experimental indications of non-classical brain function’ 2022 Journal of Physics Communications 6 105001 评论:“非经典脑功能的实验迹象”,2022年物理通讯杂志6 105001
IF 1.2 Q3 PHYSICS, MULTIDISCIPLINARY Pub Date : 2023-03-01 DOI: 10.1088/2399-6528/acc4a8
Warren S. Warren
A recent paper in this journal presents magnetic resonance imaging (MRI) data on humans which are asserted to ‘suggest that we may have witnessed entanglement mediated by consciousness-related brain functions. Those brain functions must then operate non-classically, which would mean that consciousness is non-classical.’ Unfortunately, the article provides no evidence to justify this claim. In fact, the paper only provides evidence for what we already knew: the brain (and any other living tissue) is complex, multicompartmental, and imprecisely characterized by MRI.
该杂志最近发表的一篇论文展示了人类的磁共振成像(MRI)数据,这些数据声称“表明我们可能已经目睹了由意识相关的大脑功能介导的纠缠”。这些大脑功能必须是非经典的,这就意味着意识是非经典的。不幸的是,这篇文章没有提供任何证据来证明这一说法。事实上,这篇论文只是为我们已经知道的东西提供了证据:大脑(和任何其他活组织)是复杂的,多室的,并且通过MRI无法精确表征。
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引用次数: 0
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