Interpretation of quantum theory - An overview

人通过镜子走到平行宇宙英语作文In the realm of theoretical physics, the existence of parallel universes has long been a subject of speculation and debate. These hypothetical dimensions are believed tobe distinct from our own yet coexist alongside it, eachwith its own set of laws and physical properties. While the concept of parallel universes remains largely conjectural, there have been numerous attempts to envision ways in which one might traverse these enigmatic domains. One such theory proposes that mirrors, which possess the ability to reflect light and images, may serve as portals to parallel worlds.Mirrors have captivated human imagination for centuries. Their ability to create the illusion of depth and reflect our own images has led to them being imbued with mystical and supernatural powers. In many cultures, mirrors are believed to hold the secrets to other realms, and certain rituals and practices involve the use of mirrors for divination and communication with the spirit world.The idea that mirrors might be portals to parallel universes stems from the concept of quantum indeterminacy. In quantum mechanics, particles such as photons are described by wave functions that represent their possible states. According to the Copenhagen interpretation of quantum mechanics, when a measurement is made, the wave function collapses, causing the particle to assume a specific state. However, some physicists believe that the wave function does not truly collapse but rather splitsinto multiple branches, each representing a different possible outcome of the measurement. These branches are said to exist in parallel universes, and it is theorized that mirrors may act as gateways between these universes.One way in which mirrors could potentially facilitate travel between parallel universes is through the phenomenon of quantum tunneling. Quantum tunneling refers to theability of particles to pass through barriers that would otherwise be impenetrable. In the case of mirrors, it is proposed that particles could tunnel through the surface of the mirror, effectively crossing the boundary between our universe and a parallel one.Another theory suggests that mirrors may create amirror image of our universe, with everything reversed. In this scenario, stepping through a mirror would be akin to entering a world where left is right, up is down, and the past is the future. It is believed that such a mirror universe would have its own set of laws and constants, potentially giving rise to phenomena that are impossible in our own universe.While the theories regarding mirrors as portals to parallel universes are intriguing, it is important to note that they remain purely speculative and lack experimental evidence. To date, there have been no scientific observations or experiments that have conclusively demonstrated the existence of parallel universes, let alone the ability to travel between them. Nonetheless, theconcept of mirror portals continues to inspire the imaginations of scientists, philosophers, and sciencefiction writers alike, offering a tantalizing glimpse into the vast and enigmatic realms that may exist beyond our own.In the realm of fiction, mirrors have often been portrayed as gateways to other worlds. In the classic novel "Alice's Adventures in Wonderland," Alice steps through a mirror into a whimsical and surreal world filled with talking animals and anthropomorphic objects. Similarly, in the popular television series "Sliders," a group of young people stumble upon a device that allows them to slide between parallel universes, each with its own unique set of social and technological advancements.These fictional depictions of mirror portals serve to highlight the enduring fascination with the idea ofparallel universes and the potential for mirrors to act as gateways between them. While the scientific evidence for the existence of parallel universes remains elusive, the concept continues to captivate our imaginations and inspire us to dream of exploring the uncharted realms that may lie just beyond our reach.。

爱因斯坦我敬佩的科学家英语作文专四Albert Einstein, the renowned physicist of the 20th century, is a scientist whom I greatly admire. His groundbreaking theories and discoveries have revolutionized the field of physics and changed the way we view the universe. In this essay, I will discuss the life and contributions of Albert Einstein, and explain why he is a scientist worthy of admiration.Albert Einstein was born in Ulm, Germany in 1879. From a young age, he displayed an exceptional aptitude for mathematics and science. He attended the Swiss Federal Institute of Technology in Zurich, where he graduated in 1900. After graduation, Einstein worked as a patent clerk while pursuing his research in theoretical physics. In 1905, he published a series of papers that revolutionized the field of physics. These papers laid the foundation for his special theory of relativity, which explained the relationship between space, time, and energy. This theory changed our understanding of the universe and had a profound impact on the field of physics.In 1915, Einstein published his general theory of relativity, which described gravity as a curvature of space and time. This theory provided a new framework for understanding the workings of the universe and predicted the existence of blackholes and gravitational waves. Einstein's theory of relativity has been confirmed through numerous experiments and observations, and remains one of the cornerstones of modern physics.In addition to his work on relativity, Einstein made significant contributions to quantum theory. He was a vocal critic of the Copenhagen interpretation of quantum mechanics, famously stating that "God does not play dice with the universe." Although Einstein's views on quantum mechanics were controversial, his work in this field paved the way for future research and discoveries.Outside of his scientific work, Albert Einstein was also a passionate advocate for peace, civil rights, and education. He was a vocal critic of war and nationalism, and was a supporter of nuclear disarmament. In 1952, Einstein was offered the presidency of Israel, but he declined, stating that he lacked the necessary skills for the job. Throughout his life, Einstein used his platform as a world-renowned scientist to advocate for social and political causes.In conclusion, Albert Einstein was a scientist of exceptional talent and vision. His theories and discoveries have reshaped our understanding of the universe and paved the way for futureadvancements in physics. Additionally, Einstein's advocacy for peace and justice demonstrates his commitment to using his influence for the betterment of society. For these reasons, I greatly admire Albert Einstein and consider him to be one of the greatest scientists of all time.。

量子纠缠的数学原理Quantum entanglement is one of the most fascinating phenomena in quantum mechanics. It refers to the strong correlation that exists between particles even when they are separated by large distances. This phenomenon was famously described by Albert Einstein as "spooky action at a distance," highlighting its counterintuitive nature.量子纠缠是量子力学中最令人着迷的现象之一。

它指的是即使粒子相距很远，它们之间仍存在强烈的相关性。

爱因斯坦曾将这一现象形象地描述为“鬼魅般的遥远作用”，突显其反直觉的本质。

One of the key mathematical principles that underpin quantum entanglement is superposition. In simple terms, superposition allows a quantum system to exist in multiple states simultaneously until it is measured or observed. This property is crucial for understandinghow entangled particles can be in a state of flux, with their properties being intrinsically linked regardless of the distance between them.支撑量子纠缠的关键数学原理之一是叠加原理。

有关量子力学的英语作文Quantum mechanics, a fundamental theory in physics, has been a subject of fascination and debate since its inception in the early 20th century. It describes the behavior of matter and energy at the smallest scales, where the classical laws of physics no longer apply. This essay aims to explore the key principles of quantum mechanics, its implications for our understanding of the universe, and the ongoing challenges it presents to scientists and philosophers alike.Firstly, the concept of wave-particle duality is central to quantum mechanics. This principle posits that all particles, such as electrons, can exhibit both wave-like and particle-like properties. This duality is demonstrated in the famous double-slit experiment, where particles create aninterference pattern when not observed, but act as discrete entities when measured. The act of observation, therefore, plays a critical role in determining the state of a quantum system.Secondly, the superposition principle is another cornerstone of quantum mechanics. It states that a quantum system can exist in multiple states simultaneously until it is measured. This is exemplified by the thought experiment known asSchrödinger's cat, where a cat in a sealed box is considered to be both alive and dead until the box is opened and thecat's state is observed.Entanglement, a phenomenon where particles become interconnected and the state of one instantaneously influences the state of another, regardless of the distance between them, is another intriguing aspect of quantum mechanics. This has led to the development of quantum computing, which promises to revolutionize information processing by performing calculations at speeds unattainable by classical computers.However, quantum mechanics also presents significant challenges. The interpretation of quantum theory is a subject of ongoing debate. The Copenhagen interpretation suggeststhat the act of measurement collapses the wave function, determining the outcome, while the many-worlds interpretation proposes that all possible outcomes of a quantum event exist in separate, non-interacting parallel universes.Moreover, the reconciliation of quantum mechanics with general relativity, the theory of gravity, remains an unsolved problem in physics. The two theories operate under fundamentally different principles, and finding a unified theory that encompasses both has been a holy grail for physicists.In conclusion, quantum mechanics has reshaped our understanding of the microscopic world and has profound implications for technology, philosophy, and the very fabric of reality. As research continues, it is likely that the mysteries of quantum mechanics will continue to inspire awe and provoke thought about the nature of existence itself.。

物理学最诡异的定律物理学是研究自然界的基本规律的科学，其中有许多定律都以其奇特的特性而闻名。

下面是物理学中最诡异的定律，以及相关的参考内容。

1. 测不准原理（Uncertainty Principle）测不准原理由量子力学的创始人之一海森堡于1927年提出，它表明在同一时间内，一个粒子的位置和动量不能精确同时测量。

这个原理打破了经典物理学中确定性的观念，而将概率的概念引入到物理学中。

参考内容：- 著名科普作品《量子物理史话》：费曼（Richard P. Feynman）的这本书对测不准原理进行了深入浅出地解释，让读者可以更好地理解这一原理的含义和意义。

- 学术论文《On the Interpretation of Measurement in Quantum Theory》：约翰·贝尔（John Bell）在这篇论文中对测不准原理及其解释进行了分析和讨论。

2. 背反直觉的相对论效应（Relativity Paradoxes）相对论是爱因斯坦于1905年提出的理论，其中包含了一些令人难以置信的概念，比如时间的相对性、尺缩效应等。

这些理论引发了一系列与常识相悖的背反直觉的现象，如双胞胎悖论、同步悖论等。

参考内容：- 博士论文《Relativity and Gravitation: A HeuristicIntroduction》：马尔代夫(Maldives)科学家兼教授马尔新·瑞塔(Marzia Radaelli)在其博士论文中解释了相对论和各种背反直觉的效应。

这篇论文适合对相对论有一定基础的读者。

- 学术期刊《American Journal of Physics》：该期刊在过去的几十年中发表了许多与相对论相关的文章，涉及了双胞胎悖论、钟移悖论等。

3. 黑洞的信息悖论（Black Hole Information Paradox）黑洞是一种极度致密的天体，其引力场极强，连光都无法逃脱。

平行世界作文英语模板英文回答：In the vast realm of quantum mechanics, where the boundaries of reality blur and the laws of physics dance in an enigmatic symphony, lies the tantalizing concept of parallel universes. These hypothetical realms, existing alongside our own, are said to branch out like countless threads from a celestial tapestry, each representing a different path that our universe could have taken.While the idea of parallel universes has captured the imaginations of scientists, philosophers, and sciencefiction enthusiasts alike, their existence remains shrouded in mystery. Theories abound, but definitive proof eludes us. One prominent theory, the Many-Worlds Interpretation, proposes that every possible outcome of every quantum event creates a new branch in the cosmic tapestry, resulting inan infinite number of parallel universes.Another theory, the Parallel Universes Model, suggests that the universe undergoes a series of "splits" at certain critical junctures, each split creating a new universe with different laws of physics and constants of nature. These universes are said to be inaccessible to each other, existing in their own isolated realms.The allure of parallel universes stems not only from their scientific implications but also from their philosophical and existential ramifications. If countless versions of ourselves exist in myriad realms, what does it mean to be an individual? Do our choices have weight if there are infinite possibilities?Science fiction has explored these themes in countless stories, depicting parallel universes as both alluring and terrifying. They have become a playground for the imagination, a realm where authors can craft tales that challenge the very nature of reality and our place within it.Whether parallel universes truly exist remains a matterof scientific speculation. However, the very idea of their existence opens up a window into the vastness of the cosmos and the infinite possibilities that lie beyond our current understanding.中文回答：平行世界，一个迷人而神秘的概念，存在于量子力学的广袤领域中，在那里，现实的界限模糊不清，物理定律以一种神秘的交响乐律动着。

最敬佩的人英语作文著名人物Here is an English essay on the topic "The Person I Most Admire: A Famous Figure" with a word count of over 1000 words:Throughout my life, I have encountered many inspiring individuals who have left a lasting impression on me. However, there is one person in particular whom I have the utmost admiration and respect for - the renowned scientist, Albert Einstein. His groundbreaking discoveries, innovative thinking, and unwavering dedication to the pursuit of knowledge have made him a true icon in the world of science and beyond.Born in Ulm, Germany in 1879, Albert Einstein's early life was marked by a deep curiosity and an insatiable thirst for understanding the mysteries of the universe. Even as a young child, he displayed an exceptional aptitude for mathematics and physics, often challenging the conventional wisdom of his teachers and peers. This nonconformist spirit would come to define his entire career, as he would go on to question and revolutionize our understanding of the physical world.One of the most remarkable aspects of Einstein's life was his abilityto think outside the box and challenge the status quo. At a time when the scientific community was firmly entrenched in the Newtonian view of the universe, Einstein dared to propose a radical new theory that would forever change the way we perceive space and time. His theory of relativity, which he developed in the early20th century, upended the previously held notions of absolute space and time, and demonstrated that these concepts were relative to the observer's frame of reference.The implications of Einstein's theory of relativity were profound and far-reaching. It not only provided a more accurate description of the behavior of matter and energy at the cosmic scale, but it also challenged the very foundations of our understanding of the physical world. By showing that the laws of physics are the same for all observers, regardless of their motion or position, Einstein paved the way for a more unified and comprehensive understanding of the universe.But Einstein's contributions to science were not limited to the realm of theoretical physics. He also made significant advancements in the field of quantum mechanics, another revolutionary area of study that challenged the classical understanding of the behavior of particles at the subatomic level. Einstein's work in this field, which included his famous thought experiments and his critiques of the probabilistic interpretation of quantum mechanics, helped to shape the directionof this rapidly evolving field and laid the groundwork for many of the technological advancements we enjoy today.Perhaps what is most admirable about Einstein, however, is not just his scientific achievements, but his unwavering commitment to using his knowledge and influence to make the world a better place. Throughout his life, he was a vocal advocate for social justice, human rights, and world peace. He spoke out against the rise of fascism in Europe and the use of nuclear weapons, and he actively worked to promote international cooperation and understanding.Einstein's commitment to these causes was not just lip service; heput his reputation and even his freedom on the line to stand up for his beliefs. During the McCarthy era in the United States, for example, he faced intense scrutiny and criticism for his left-leaning political views and his opposition to nuclear proliferation. Despite the personal and professional risks, he refused to back down, continuing to use his platform to raise awareness and inspire others to action.In many ways, Einstein's life and legacy serve as a powerful reminder of the transformative power of human ingenuity and the importance of using our talents and influence to make a positive impact on the world. His willingness to challenge the status quo, his dedication to the pursuit of knowledge, and his unwavering commitment to social and political causes have made him a true icon, not just in thescientific community, but in the hearts and minds of people around the world.As I reflect on my own life and the path I hope to forge, I am constantly inspired by the example set by Albert Einstein. His relentless curiosity, his unwavering integrity, and his ability to think critically and creatively are qualities that I strive to embody in my own journey. In a world that often seems consumed by cynicism and division, the life and legacy of Albert Einstein serve as a powerful reminder of the transformative potential of human ingenuity and the importance of using our talents and influence to make a positive difference in the world.。

尼尔斯玻尔量子物理学的开拓者尼尔斯·玻尔：量子物理学的开拓者Quantum physics, also known as quantum mechanics, is a fundamental theory that describes the behavior of matter and energy at the smallest scales. It revolutionized our understanding of the physical world, challenging classical physics and introducing a new wave of scientific inquiry. One of the key figures in the development of quantum physics is Niels Bohr, a Danish physicist who made groundbreaking contributions to the field. In this article, we will explore the life and work of Niels Bohr, the trailblazer of quantum physics.Early Life and EducationNiels Henrik David Bohr was born on October 7, 1885, in Copenhagen, Denmark. He came from a prominent academic family, with both his father and grandfather being respected physicists. This background laid the foundation for Bohr's interest in science from a young age.Bohr pursued his higher education at the University of Copenhagen, where he studied physics. During his time as a student, he immersed himself in the world of atomic and molecular physics, which would later become his primary focus. Bohr's passion for scientific exploration and his exceptional talent quickly caught the attention of his professors and peers.Developing the Bohr ModelOne of Niels Bohr's most significant contributions to quantum physics is the development of the Bohr model, also known as the Bohr-Rutherfordatomic model. This model provided a revolutionary understanding of the structure of an atom, explaining how electrons occupy specific energy levels or orbits around the nucleus.Prior to Bohr's work, the prevailing classical physics theories failed to explain certain phenomena observed in atomic spectra. Bohr proposed that electrons orbit the nucleus at specific energy levels, and they can jump between these levels by absorbing or emitting energy in discrete packets called quanta. This groundbreaking concept revolutionized atomic theory and laid the foundation for modern quantum mechanics.Bohr and Quantum TheoryNiels Bohr's contributions extended beyond the development of the Bohr model. He played a crucial role in shaping the emerging field of quantum theory through his pioneering ideas and collaborations with other physicists.One of Bohr's most famous contributions is the principle of complementarity. He argued that particles could exhibit both particle-like and wave-like properties, depending on how they are observed. This concept established the idea of wave-particle duality and laid the groundwork for future research in quantum mechanics.Bohr also played a key role in the development of the Copenhagen interpretation, a fundamental interpretation of quantum mechanics. This interpretation states that the act of measurement affects the observed phenomenon, and physical properties are not determined until they are measured. The Copenhagen interpretation sparked philosophical debates and continues to be discussed and analyzed by scientists and philosophers.Legacy and ImpactNiels Bohr's impact on quantum physics cannot be overstated. His groundbreaking ideas and theories revolutionized our understanding of the atomic and subatomic world, paving the way for countless scientific breakthroughs.Throughout his career, Bohr received numerous accolades and awards, including the Nobel Prize in Physics in 1922 for his research on the structure of atoms and the radiation they emit. He also founded the Institute for Theoretical Physics in Copenhagen, which became a hub for groundbreaking research and collaboration.Even today, Bohr's work continues to influence scientific inquiry and inspire new generations of physicists. His contributions to quantum physics remain foundational, and his name is forever etched in the annals of scientific history.ConclusionNiels Bohr was a visionary physicist and a true pioneer in the field of quantum physics. His groundbreaking ideas, including the Bohr model and the principle of complementarity, revolutionized our understanding of the atomic world. Bohr's work and his collaborations with other physicists shaped quantum theory and established the foundations of modern physics.His legacy extends far beyond his own time, as his ideas continue to shape scientific inquiry and inspire future generations of physicists. Niels Bohr will always be celebrated as a trailblazer, whose contributions have fundamentally transformed our understanding of the physical world.。

关于quantum的雅思阅读理解引言概述：Quantum physics, also known as quantum mechanics, is a branch of physics that deals with the behavior of matter and energy at the smallest scales. Understanding quantum concepts is crucial for advancements in various fields, including technology, medicine, and communication. In this article, we will delve into the topic of quantum physics and its significance in IELTS reading comprehension.正文内容：1. Quantum Theory and Its Principles1.1 Wave-Particle Duality: Quantum theory proposes that particles, such as electrons and photons, exhibit both wave-like and particle-like behavior. This principle challenges classical physics, where particles were considered solely as particles or waves.1.2 Superposition: According to quantum theory, particles can exist in multiple states simultaneously. This concept is known as superposition, and it allows for the potential of quantum computing and cryptography.1.3 Quantum Entanglement: Quantum entanglement refers to the phenomenon where two or more particles become correlated in such a way that the state of one particle is instantly linked to the state of another, regardless of the distance between them. This principle has implications for secure communication and quantum teleportation.2. Applications of Quantum Physics2.1 Quantum Computing: Quantum computers utilize the principles of superposition and entanglement to perform complex calculations at an exponential speed compared to classical computers. This technology has the potential to revolutionize fields such as cryptography, optimization problems, and drug discovery.2.2 Quantum Communication: Quantum communication involves the transmission of information using quantum states. Quantum encryption ensures secure communication by exploiting the principles of entanglement and uncertainty. This technology has the potential to protect sensitive information from hacking.2.3 Quantum Sensing: Quantum sensors utilize the unique properties of quantum particles to measure physical quantities with unprecedented precision. This has applications in fields such as navigation, medical imaging, and environmental monitoring.3. Challenges in Quantum Physics3.1 Measurement Problem: The act of measuring a quantum system can disturb its state, leading to the collapse of the superposition. This measurement problem raises questions about the nature of reality and the role of the observer in quantum physics.3.2 Quantum Decoherence: Quantum systems are highly sensitive to their surroundings, which can cause decoherence. This phenomenon disrupts the delicate quantum states and poses challenges for maintaining coherence in quantum technologies.3.3 Quantum Interpretations: The interpretation of quantum mechanics is still a subject of debate among physicists. Different interpretations, such as the Copenhagen interpretation and the Many-Worlds interpretation, offer different explanations for the behavior of quantum systems.4. Quantum Physics in IELTS Reading Comprehension4.1 Vocabulary: Familiarity with quantum-related terms and concepts is essential for understanding reading passages that discuss quantum physics. Being well-versed in terms like superposition, entanglement, and decoherence will aid in comprehending the content.4.2 Inference: IELTS reading passages often require candidates to make inferences based on the information provided. Understanding the principles and applications of quantum physics will enable candidates to make accurate inferences when encountering quantum-related texts.4.3 Critical Analysis: IELTS reading tests candidates' ability to critically analyze information. Being knowledgeable about the challenges and interpretations in quantum physics will help candidates evaluate the validity and implications of the given information.总结：In conclusion, quantum physics plays a crucial role in various scientific and technological advancements. Understanding the principles of quantum theory, its applications, and the challenges it poses is essential for comprehending quantum-related passages in IELTS reading comprehension. By familiarizing oneself with quantum vocabulary, making accurate inferences, and critically analyzing information, candidates can enhance their performance in this aspect of the IELTS examination.。

英文原版量子论科普If you're interested in reading about quantum theory in English, here are some recommendations:1. "Quantum Mechanics: The Theoretical Minimum" by Leonard Susskind and Art Friedman. This textbook provides a thorough and accessible introduction to quantum mechanics, starting from the basics and building up to more advanced concepts. It's written in a lively and engaging style, making it suitable for self-study or as a classroom textbook.2. "Quantum Physics: A First Encounter" by John Taylor. This book is aimed at undergraduates and covers the key ideas of quantum theory, including wavefunctions, operators, measurement, and entanglement. It provides plenty of examples and exercises to help readers understand and apply the theory.3. "Quantum Computation and Quantum Information" by Michael Nielsen and Isaac Chuang. This textbook provides a comprehensive introduction to the field of quantum information science, covering quantum computing, quantum algorithms, quantum error correction, and quantum cryptography. It's suitable for graduate students and researchers in the field.4. "The Quantum World" by Christopher French and Carlo Michelli. This book provides a broad overview of modern quantum theory and its applications, including quantum computing, quantum cryptography, and quantum metrology. It's written in a clear and accessible style, making it suitable for non-experts who want to understand the basics of quantum theory.Remember that reading about quantum theory can be challenging because it involves concepts that are counterintuitive and打破常识。

How do you know you’re a person who has lived your life, rather than a just-formed brain full of artificial memories, momentarily hallucinating a reality that doesn't actually exist? That may sound absurd, but it’s kept several generations of top cosmologists up at night.你如何能知道自己是拥有现有人生的一个人，而不是一个装满人工记忆的初生大脑，被其实并不存在的现实暂时迷惑？这听起来可能有些荒谬，但它让好几代顶级宇宙学家彻夜难眠。

They call it the Boltzmann brain paradox. Its namesake, Ludwig Boltzmann, was a 19th century physicist operating in a period when scientists were passionately debating whether the universe had existed for an infinite or finite time.他们称之为玻尔兹曼大脑悖论。

这个名字源自19世纪的物理学家路德维希·玻尔兹曼。

当时，科学家们正激烈讨论，宇宙已经存在了无限长的时间还是有限长的时间。

Boltzmann’s main claim to fame was revolutionizing thermodynamics, the branch of physics that studies energy. He put forward a new interpretation of entropy, which is a measure of the disorder of a system.玻尔兹曼赖以成名的主要成就是为热力学带来了革命性突破，热力学是物理学中研究能量的分支。

Quantum MechanicsQuantum mechanics is a fundamental theory in physics that describes the behavior of matter and energy at the smallest scales, such as atoms and subatomic particles. It has revolutionized our understanding of the universe and has led to the development of many modern technologies, such as computers, lasers, and MRI machines. However, despite its incredible success in explaining the behavior of the microscopic world, quantum mechanics also presents many challenges and paradoxes that continue to perplex scientists and philosophers alike. One of the most perplexing aspects of quantum mechanics is the phenomenon of wave-particle duality, which states that particles such as electrons and photons can exhibit both wave-like and particle-like behavior. This duality challenges our classical intuition, as we are accustomed to thinking of objects as either waves or particles, not both at the same time. The famous double-slit experiment, in which particles exhibit interference patterns characteristic of waves, is often cited as evidence of this duality. This strange behavior has profound implications for our understanding of the nature of reality and has sparked much debate amongphysicists and philosophers. Another puzzling aspect of quantum mechanics is the concept of entanglement, in which particles become correlated in such a way that the state of one particle instantaneously influences the state of another, no matter how far apart they are. This phenomenon seems to violate the principle of locality, which states that an object is directly influenced only by its immediate surroundings. Einstein famously referred to this as "spooky action at a distance," and it remains a subject of intense study and debate in the scientific community. Furthermore, the uncertainty principle, formulated by Werner Heisenberg, asserts that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known with arbitrary precision. This principle challenges the classical notion of determinism and has profound implications for our understanding of the predictability of physical systems. It introduces a fundamental limit to the precision with which we can know the state of a system, and raises deep questions about the nature of reality and the limits of human knowledge. The interpretation of quantum mechanics has also been a source of much controversy and debate. There are several competing interpretations of the theory,each with its own philosophical implications and consequences. The Copenhagen interpretation, proposed by Niels Bohr and Werner Heisenberg, emphasizes the role of the observer in the measurement process and asserts that the wave function of a particle collapses into a definite state only upon measurement. Thisinterpretation has been criticized for its apparent subjectivity and lack of a clear physical mechanism for the collapse of the wave function. On the other hand, the many-worlds interpretation, proposed by Hugh Everett, suggests that every possible outcome of a quantum measurement actually occurs in a separate branch of the universe, leading to a proliferation of parallel universes. Thisinterpretation has profound implications for our understanding of the nature of reality and has sparked much debate and speculation about the nature of consciousness and the role of observers in the universe. The challenges and paradoxes of quantum mechanics have led some to question whether the theory provides a complete and accurate description of the physical world, or if it is merely a useful approximation that breaks down at the smallest scales. Some physicists have proposed alternative theories, such as hidden variable theories or modifications to quantum mechanics, in an attempt to resolve the paradoxes and challenges of the theory. However, these alternative theories often come withtheir own set of problems and have yet to gain widespread acceptance in the scientific community. In conclusion, quantum mechanics presents many challenges and paradoxes that continue to perplex scientists and philosophers alike. The phenomenon of wave-particle duality, the concept of entanglement, the uncertainty principle, and the interpretation of the theory all raise deep questions about the nature of reality, the limits of human knowledge, and the role of observers in the universe. While quantum mechanics has been incredibly successful in explaining the behavior of the microscopic world and has led to the development of many modern technologies, it also presents profound philosophical and conceptual challengesthat continue to inspire intense study and debate in the scientific community.。

爱因斯坦对恩格斯的《自然辨证法》手稿阅读完毕后曾做出这样的评价：“爱德华·伯恩斯坦先生把恩格斯的一部关于自然科学内容的手稿交给我，托付我发表意见，看这部手稿是否应该付印。

我的意见如下：要是这部手稿出自一位并非作为一个历史人物而引人注意的作者，那么我就不会建议把它付印，因为不论从当代物理学的观点来看，还是从物理学史方面来说，这部手稿的内容完全就是胡说八道、疯人之作。

可是，我可以这样设想：如果考虑到这部著作对于阐明恩格斯的思想的意义是一个有趣的文献，那是可以勉强出版的。

”以上选自《爱因斯坦文集》第一卷，商务印书馆，１９７７年，第２０２页为什么爱因斯坦这么激烈的反对《自然辨证法》呢?这和爱因斯坦相信“上帝不掷骰子”，反对量子力学有很大的关系。

爱因斯坦虽然否定了牛顿力学的绝对时空观，却仍然坚持牛顿力学的机械决定论，认为物质的运动完全是确定的，必然性的，没有偶然性，不确定性。

量子力学是必然性和偶然性的辨证统一,量子力学告诉我们，宏观的必然性是大量微观的偶然性的总和，这就是量子力学的辨证法，必然性是大量偶然性的总和，必然性不能脱离偶然性。

恩格斯说：“力学(当时的牛顿力学)的出发点是惯性，而惯性是运动不灭的反面表现”。

因为匀速直线运动没有变化，惯性运动是运动状态不变化的运动，相反,非惯性运动是运动状态变化的运动。

实际上任何物体都不可能作匀速直线运动,而是作不确定的量子运动,位置越确定,动量就越不确定，越是微观的尺度这种不确定的量子运动越激烈，到了10-33厘米的普朗克尺度（普朗克长度最小的长度单位，没有比普朗克长度更短的长度，任何物体的长度都是普朗克长度的整数倍），运动会变得极其激烈,不仅具有极其巨大的动量和能量,而且动量还具有极度的不确定性。

由于位置和动量这对物质固有的基本矛盾，物质不仅永远运动不能静止，而且运动状态也不断变化。

这就是量子力学的辨证法。

爱因斯坦的相对论仍然是一经典理论，出发点仍然是牛顿力学的惯性。

第37卷第3期2021 年3月商丘师范学院学报JOURNAL OF SHANGQIU NORMAL UNIVERSITYVol. 37 No. 3March，2021量子力学中测不准关系、方程和时空等基本问题的新探索张一方(云南大学物理系，云南昆明650091)摘要：量子力学中的某些问题仍应该探索.首先讨论了量子力学的基础和各种解释，并提出量子力学的非线 性混沌-孤子解释.其次研究了测不准关系，探讨了最普适的测不准关系及其数学形式.第三讨论不可逆性和统计 性,并提出熵的算符表示•第四研究了量子力学方程.最后探讨了量子理论中的二象性.关键词：量子力学；解释；量子场论；时空;对称性；测不准关系中图分类号:〇572.2 文献标识码：A文章编号：1672 - 3600(2021)03 - 0023 - 06New research of basic problems on uncertainty relation, equations and time - space,etc. ,in quantum mechanicsCHANG Yifang(Department of Physics,Yunnan University,Kunming650091 ,China)Abstract：Some problems of quantum mechanics should still be researched. First, the foundations and various interpretations of quantum mechanics are discussed, and the nonlinear chaos -soliton interpretation of quantum mechanics is proposed. Next,the uncertainty relations are investigated,and a very general uncertainty relation and its mathematical form are searched. Thirdly, the irreversibility and statistics are discussed, and an operator representation of entropy is proposed. Fourthly, the equations of quantum mechanics are investigated. Finally, the duality in quantum theory are searched.Key words ：quantum mechanics ； interpretation ； quantum field theory ； space - time ； symmetry ； uncertainty relationDirac指出“哈密顿量对于量子理论才真正是十分重要的”“只能通过哈密顿量或其概念的某种推广”发展理论.其基本 程序是由相对论不变的作用量积分得到拉氏量，再导出哈密顿量,得到量子理论.而“将来的量子理论”“一定有某种东西与哈 密顿理论对应已知量子力学最初的两种形式:Schrodinger波动力学主要起源于波动性;而Heisenberg矩阵力学主要起源于不连续性.其 中能量体现粒子性，波函数体现波动性.经典波动方程就是质量为0的Klein-Gord〇n(K G)方程，而Dirac方程是K G方程的一 阶推广.基于对量子力学结构的逻辑分析，笔者认为它只有一个基本原理:波粒二象性.统计性是其相应的数学特性.而其他 原理都是由此导出的物理或数学结果量子场论只是把二象性推广到场.量子力学的发展是基于长、短波时分别是Rayleigh-Jeans公式和W i e n公式，这已经暗含其主要适用于中能，而高能（短 波）是Wien公式，8卩Maxwell- Boltzmann(MB)分布、G a m m a分布•量子力学必然联系于光子、电磁相互作用，例如黑体辐射、光 电效应、氢原子等.反之，目前量子力学、量子场论也主要适用于电磁相互作用[U,而对强、弱、引力相互作用则理论必须发展. 量子力学中波包瞬间塌缩是超光速的.笔者提出粒子物理中的基本原理是必须区分已经检验的实验事实和优美的理论假说.由此提出粒子理论中的7个重大问 题，并且讨论了相应的量子理论某些可能的发展本文对测不准关系、量子方程等量子力学和量子理论的基本问题进行了 某些新探索.1量子力学的基础和各种解释由于量子力学的基本性和复杂性，对其的解释和探索一直是理论物理议论纷纷的热点之一.Jammer对量子力学中的基本 问题和各种解释进行了全面的经典论述[5].量子力学最著名的解释是哥本哈根的几率解释，它的两个基本原理是定域（干涉）原理和波谱分解原理.在量子力学中几率守恒，几率密度（即粒子数平均密度）守恒及总几率都不变.几率守恒是物质不灭定收稿日期:2020 - 01 -22;修回日期:2020 - 09 - 21基金项目：国家自然科学基金资助项目（11664044)作者简介:张一方（1947—），男，云南昆明人，云南大学教授，主要从事理论物理的研究24商丘师范学院学报2021 年律在微观世界的精确表现，它与幺正条件紧密联系.1970年Ballentine系统讨论了量子力学的统计解释[61.对几率解释提出不同观点的众多理论中最著名的是de Broglie- B o h m非线性理论和隐变量解释.基于Everett的多世界理 论[7’8],1971年Dewitt等提到多世界解释和隐变量理论[9]. 1972年Van Fraassen提出消除波包塌缩的模态解释（model interpretation).以后发展为著名的Kochen- Dieks- Healey理论.1986年Cramer提出量子力学的相互作用解释_l t l],其与Be丨丨不等式的检验和非局域性一致.1987年BaUentine提出量子力学的主要解释是:统计系综解释，新哥本哈根解释,R.B.G r i f f i t h s 一致性历史解释，多世界解释和量子势5种.1992年H o m e和Whitaker系统讨论了量子力学的现代系综解释[|2].从1954年起 nde集中批评波粒二象性,而提出一种被Born称为“唯粒子论”的解释方案，但Jammer认为这是“统计系综解释的一种特 殊版本”[51.此外，还有量子力学的去相干理论等.1992年Omn e s提出量子力学的新解释[131，并提出其认识论[13_141.其中的关键概念是“退相干”（de™herenCe).通过纠缠 态（entangled state)在受到环境的作用时，会发生退相干效应这种机制，从量子力学的基本原理出发，就可以统一描述宏观世 界和微观世界的物理学.1995年Rob Clifton及Bub.Goldstein理论的基本方法是区分为理论（动力学、数学）态（theoretical state)和事件（值、物理）态（sta t e of affairs).近年Jeffery B u b等提出量子力学信息解释.这联系于量子信息论.T h o m在《结构稳 定性与形态发生学》中提出波函数作为按一定频率改变拓扑类型的超曲面上的形态就是局域曲率[15].赵国求等具体提出相 互作用是在与量子力学的曲率解释[~7]，其中波长联系于粒子环流半径，曲率波包取代质点，波函数是曲率波，曲率的大小表 示粒子性，曲率在时空中的变化表示波动性.并且特征曲率/； = 1/4* =p/77.T h o m和赵国求等的量子力学曲率解释是把波函 数理解为曲率函数.笔者认为这其实是量子力学和广义相对论结合的结果，其中质量大小决定曲率大小，就是广义相对论中 质量决定空间的弯曲程度.根据公式p =1 2 ,密度越大，几率越大，曲率越大.这样就可以联系于量子引力.结合黎曼几何，还可以结合笔者计算电子磁矩的方法[2].薛定谔猫的佯谬是微观不确定、统计性与宏观确定性的关系.这可以联系于非线性,可能发展出非线性量子理论 Monroe等[~用囚禁在Paul阱中的9B e+实现介观尺度上的猫态，质心运动相干态波包与内部态纠缠.观测结果肯定了量子态 叠加原理的正确性，展示了量子力学中的非定域性.量子性最早类比于波动性中的驻波.如波动性有所改变，量子性也许有所 不同.量子数h可能可变或者连续.这就联系于泛量子论12^251.猫态联系于宏观量子现象，对应2个或多个世界.这些世界不 能交流，则拓扑分离，是平行世界.这些世界互相纠缠，则可以包括生与死，阴和阳等不同状态.而状态变化可能与参量达到混 沌值等有关，出现幽灵.非线性理论的多次迭代导致混沌，但对应一种统计性及分布函数.这类似多个粒子、多次事件测不准，然而具有统计性及 分布函数.它联系于电子云的概率分布和相应的统计解释.由此可以提出量子力学的非线性混沌-孤子解释.笔者证明在各 种具有孤子解的非线性方程中都可以得到混沌，而只有某些具有混沌解的非线性方程有孤子解.两种解的条件是不同的，某 些参数是某个常数时得到孤子，而这些参数在一定区域变化时出现分岔-混沌.这种混沌-孤子双解可以对应于量子理论中 的波-粒二象性，由此联系于非线性波动力学的双重解，并且存在若干新的意义％’271.某些实验证明，改变测量方式完全可以 将实验结果从波动条纹改变为粒子行为.Yanhim Shih(1983)可以确定粒子性和（或）波动性.Mandel等测量在两点的两个光子 的联合几率作为分离函数，证明在信号干涉中存在非经典效应[281.在实验设置1中单个光子不出现干涉.在实验设置2的情 况1中光子也不出现干涉，但在情况2中光子出现干涉.所以不仅单个光子，而且作为一个整体的一对纠缠光子也不出现干 涉.并且由非线性解释可以联系于流体力学解释.通常/!—0时，量子力学化为经典力学，这即对应原理.如此量子场论应该化为经典场论.但这与大量子数；并不普遍 等效.Liboff对二者的不同作了明确区分例如在大原子中可能是形式对应原理，如G細m a分布.Blasone提出一个 量子系统近似等价于两个经典系统[301.这对应de Broglie-B o h m非线性量子力学的双重解.J.von Nemnami在《量子力学的数学基础》中指出Gilbert空间的点表示物理系统的状态，物理系统的可观测量由Hilbert 空间的线性算子表示，而能量算子的本征值和本征函数就是该系统的能级及相应的定态.结论必须在4条公理假定成立的条 件下.其中E(A + B + C + •••)= E(A) + E(B) + £(C)+ •••(1)五是线性算符,/I、S、C等无相互作用•而它们可以互相纠缠.因此，目前的量子理论本质上应该是线性的[U8].这一般可能对应于自由粒子，即无相互作用，如无引力相互作用时就是 欧氏空间.而电磁相互作用也是线性理论，只有附加流时才是非线性.但光子-光子相互作用时就是非线性光学.这应该联系 于电磁广义相对论^32].—般的电磁理论仅涉及单个光子.而其余的三种相互作用场必然产生非线性.张永德认为相互作用必定导致量子理论的非线性，相对论量子场论和考虑相互作用的非相对论量子力学的基本方程组 都是非线性的;量子理论的量子化条件是非齐次二次型非线性的i33],因此整体而言，量子理论本质上是非线性的.2测不准关系1934年K.R.Popper已经指出[34]，从量子力学的基本原理可以导出测不准关系，因此它不是具有独立地位的原理. Margemni指出只应当限于在多次测量的统计意义上理解测不准关系M l.对于时间-能量的测不准关系，争论更大.1933年 Pauli就指出，不可能引进一个时间算符，因此根本不存在能量和时间的对易关系[36].粒子在运动,有速度^和动量p,其位置就不确定;反之j确定，则不运动.特别对于波.这似乎可以联系于布朗运动.测 不准应该基于无相互作用或某种特殊的波，如线性波等.前提改变，如是非线性波、孤波等时,测不准应该有所不同.基于此可 以具体推导.第3期张一方:量子力学中测不准关系、方程和时空等基本问题的新探索25H.Dehmelt开创了俘获单个电子和原子的研究，由此获得1989年诺贝尔物理奖.20世纪80年代中期Maryland大学和 Munich大学的实验发现,打开探测器时光表现为粒子，关闭探测器时单个光子也表现出波动.1990年艾戈勒用扫描隧道显微 镜（S T M)移动氙原子排列成IBM.氙原子固定，则土 = 10_s c m,Ap = mAv —h/A x.(2)氙质量^ = 131^^.=丨.229父1051\^¥/<:2,所以加=/1/^4*=48丨.33(；111/8.氙原子每秒运动4.81[11,此时测不准关系是 否成立？1993年I B M研究可以直接看到单个电子的波动性（波函数）.这些结果与测不准的关系值得研究.量子纠缠态和远距离移物已经被实验证实.其难点在于测不准原理.但该原理在一定条件下也可能被突破.波的测不准关系= 1表示波包长度和波长之间的测不准.这是波的性质，与量子理论无关.同时，粒子波动性及其方 程导致能量的分立态（即量子化）.B o h m指出测不准原理是由三个基本假定:波粒二象性，几率，能量-动量的不可分性，互相 结合导出的[371.三者的统一体是整个量子论的基础.原子中的测不准关系4£…山=7J ,BPA{- ^j)A t = h ,(3)n所以<)=忐，(4)通常是K测不准，更一般是A(R^j)A t = 1 .(5)其中是Rydberg常数.对Z、n—定的原子，如Z= 1，n= 1的氢原子只能是山—》，或者厶K不等于0,其测不准.或者 测不准，公式不成立.这就是李兹组合原理与A t的关系，B PAvAt = 1. (7)则A—〇〇，必须承认其在时空中无法描述.而目前光谱已经相当精确.n大时更易精确检验.目前形式的波动性如果不成立[2],测不准原理就应该有所发展.例如对非线性理论[2_~.进一步，测不准关系可以推广到 各种测不准量卸,,4*,.的关系.卸相当于=(卸）2/2m，因为4£乂S九，所以(A p)2At &2mh ；(8)反之 Ap 多A/A c，则 = (4/>)2/2m 彡 /i2/2m(4*)2 ,所以AE(A x)2 3：h2/2m.(9)彡/i2除以式(8)可得(止〇2//^為/i/2m，或者多办/2m •(10)这与我们得到的光速测不准公式[3M9]是一致的.然而，测不准关系与守恒定律存在不一致之处.多A ,如果A是测量能量或能量变化4£所需的时间间隔，则光子稳 定山—0，光速不变.但如此一切稳定粒子运动速度都应该不变.场方程及其孤子解原则上可以描述粒子的轨道.它可能联系于de Broglie-Bohm的波导理论.这样孤子与测不准关系不 一致.更一般是非线性量子理论[2#]与测不准原理的关系.彼此算符化的量构成共轭量.不可对易的两个算符量不能同时测定，这就是最普适的测不准关系.在此讨论其一般的数 学形式，设[W，/V] =A f/V+順=iG.其特例是C=0时是反对易关系•C就是测不准度.彼此用算符表示：M表象中）；(ID(12)反之，W(M表象中）_dM于是AMAN ^G.(13) 3量子理论、不可逆性和统计性量子理论的根本困难，Prigogine等认为在于无法处理不可逆过程.它应该结合广义熵（信息），引人微观熵、量子熵等.量 子力学是统计性的，而统计性可以描述不可逆性，所以量子力学应该描述不可逆性.量子力学方程和分子运动论的统计方程相似，所以其具有统计性.统计性又源于摩擦和信息缺失，因为经典和量子各是 任意值和离散值.布朗运动，基态能A/2,绝对零度不能达到等都表明微观领域的永动.布朗运动在一定条件下也许可以放大为宏观布朗运 动效应，虽然放大时可能已经输入能量•根据熵的定义dS = AE/T,(14)26商丘师范学院学报2021 年引入熵必然引人温度7\而根据S = - k\gP = - 2k\g f//，必变化导致S变化.熵增大对应于波包必然扩散.由式（14)得A/r；是组合常数.这类似屮 对定态dS- - 2k(p d* + p,dy+ p Az - £d() = 2i—lV VA e x p U p j/n).此时就是d S对应于四维动量.lV dt Eip ,(15)(16)(17)(18)贝!l dS =-2k—d t.(19)lVS和 <都可逆或都不可逆，二者变化成正比.封闭系统熵增大，能量守恒是定态，所以时间也有方向性.考虑时间箭头和统计性时，发展能量为熵.Prigogint■引人微观熵算符，这可以结合粒子物理中温度和熵的引人方法.他的 超算符导致不可逆性.这可能对应于非线性算符.更一般,可重整化的量子理论应该结合半群，引人温度等，导出不可逆性.假设熵与量K共轭，AS = 4£/r，4£也=(A S)(f4<),所以T不变时[=7!AF/AY = dF/TAt = [F,S]= [F,H]/T.(20)由此表示熵的算符为S _ izi AT dt •(21)设动童通量密度7^ =服2W的共扼量是X，如果L盖，则A T^AX ^v ,T^X - XT^= iv .(22)结合测不准关系P…V,X - XP^V U = y(23)所以X = X/^,T^=-l V d{x/v J.(24)而〜又是算符m dxv量子力学和统计力学都基于平均值.二者应该类比发展.密度p方程是刘维定理，其对应Heisenberg方程，而不是 Schrodinger方程.量子力学类似于统计力学发展为量子统计;统计力学类似于量子力学发展为动力学、方程.特别是量子统计 应该包括托马斯-费米方程.量子力学、量子场论和统计性都是对多个粒子事件，对系综成立.应该用统计学的方法全面整理、表述、修改量子力学、量 子场论，然后再推广、发展量子论.4量子力学方程的研究Dim e提出[w] “不应认为量子力学的现在形式是最后的形式”，它只是“迄今为止人们能够给出的最好的理论”，可能将来“会得到一个改进了的量子力学，使其回到决定论.”但这必须放弃某些现在认为没有问题的基本思想:4〇].笔者在探讨微观相 对论的基础上，提出对极小时空,光速应存在统计起伏.特别在高维柱形卷曲空间中光速是可变的和量子化的.由此讨论修 改、发展相对论和量子论的可能的某些方法，并且定量提出存在势和相互作用时几种新的量子力学方程4M2].Heisenberg方程只是Poisson括号变形的经典方程.Schrodinger方程(25)只是/>,的算符表示方程，而它都可以化为方程Pi= 4念(11^).(26)这和一般的算符方程a dP,= lV T~ ^dX i(27)又有所不同.如/(必）=_ :=〇，则 dj l i//)= + md^//= 〇，即~= 0 »(28)也就是Klein- Gord〇n(K G)方程•这是K G方程和Dime方程之间的又一种关系.对此再求导，= 〇,(29)第3期张一方:量子力学中测不准关系、方程和时空等基本问题的新探索27艮P( m2i/f) +m(m2i//)=0.(30)这是0'的D irac方程，是求导二次的结果.这是波函数的标度变换.广义函数类似算符，前者可用于多重产生，粒子理论等;后者已用于量子理论,并将用于多重产生等.Poisson括号都是对 易关系，应该可以推广为反对易关系等广义形式.5量子理论中的二象性问题衍射中运动的非全同性导致整体的统计性.量子理论的各种不足可能基于原来就无法完全一致的波粒二象性:2],因此波 尔才发展出互补原理.Y u tak a等的实验证明[431单个光子具有粒子性（在缝隙处不劈裂为两半）和波动性（具有隧穿效应，显示 出自干涉，最后反射和折射各占50% ,符合粒子波的几率性）.单个光子在远处平板上看不到干涉条纹.二象性把连续、不连续统一起来.波动有周期性就会有一种不连续，对应着粒子.光子和粒子的衍射、折射、反射、色散等 反映连续性;而光子和粒子的发射、吸收等瞬时过程则是不连续的.最小能量、心是不连续的，而频率。