In the early decades of this century physics was revolutionised by the advent of quantum mechanics. Observed atomic spectra could only be explained if the seemingly unshakeable concept of a particle moving along a path (trajectory), sharply defined and uniquely determined by the initial position and momentum coordinates, was dropped in favour of a description of electrons as standing waves or wave packets, whose position and momentum carry inherent uncertainties. In the course of the quantum revolution, generations of physicists were taught that the concept of classical paths is wrong on the atomic scale.
In the early decades of this century physics was revolutionised by the advent of quantum mechanics. Observed atomic spectra could only be explained if the seemingly unshakeable concept of a particle moving along a path (trajectory), sharply defined and uniquely determined by the initial position and momentum coordinates, was dropped in favour of a description of electrons as standing waves or wave packets, whose position and momentum carry inherent uncertainties. In the course of the quantum revolution, generations of physicists were taught that the concept of classical paths is wrong on the atomic scale.
By now the “chaos revolution” has reached nearly every branch of the natural sciences. In fact, chaos is everywhere. To name but a few examples, we talk about chaotic weather patterns, chaotic chemical reactions and the chaotic evolution of insect populations. Atomic and molecular physics are no exceptions. At first glance this is surprising since atoms and molecules are well described by the linear laws of quantum mechanics, while an essential ingredient of chaos is nonlinearity in the dynamic equations. Thus, chaos and atomic physics seem to have little to do with each other. But recently, atomic and molecular physicists have pushed the limits of their experiments to such high quantum numbers that it starts to make sense, in the spirit of Bohr's correspondence principle, to compare the results of atomic physics experiments with the predictions of classical mechanics, which, for the most part, show complexity and chaos. The most striking observation in recent years has been that quantum systems seem to “know” whether their classical counterparts display regular or chaotic motion. This fact can be understood intuitively on the basis of Feynman's version of quantum mechanics. In 1948 Feynman showed that quantum mechanics can be formulated on the basis of classical mechanics with the help of path integrals. Therefore it is expected that the quantum mechanics of an atom or molecule is profoundly influenced, but of course not completely determined, by the qualitative behaviour of its underlying classical mechanics.
For nearly a century, the orthodox Copenhagen interpretation of quantum mechanics has asserted that physical reality is fundamentally non-deterministic at the subatomic scale. Central to this view is the idea that a particle's position and momentum cannot be simultaneously known to arbitrary precision, and that particles exist only as abstract probability waves until observed. This paper proposes a profound alternative. Following the recently developed seven-dimensional torus electron model, we demonstrate that quantum uncertainty is not a metaphysical limitation, but rather the direct, classical Fourier transform limit of a localized, self-confined wave packet of light. By lifting the wave's trajectory into a compactified seven-dimensional torus, we show that the particle's internal state is fully deterministic and governed by local wave geometry. We show how the long-standing debate between Albert Einstein and Niels Bohr is resolved by treating the quantum probability cloud as the time-averaged spatial projection of a deterministic higher-dimensional path, restoring local realism and coordinate-based determinism to quantum foundations.
A philosopher once said ‘It is necessary for the very existence of science that the same conditions always produce the same results’. Well, they don't! Richard Feynman Watching electrons We have seen that quantum mechanics does not allow us the comfort of being able to visualize the motion of a quantum particle. In a normal game of billiards we can imagine the paths taken by the individual balls (Fig. 1.1). Figure 2.1 shows the physicist George Gamow's attempt to give some impression of how the same game might look if played with quantum particles. Besides illustrating that the notion of a path is no longer valid in quantum mechanics, this cartoon also illustrates another significant difference between the quantum and classical worlds: the exact position of the white ball is not known. Uncertainty has entered physics and replaced the determinism of Newtonian mechanics. By the nineteenth century, physicists had been able to explain vast amounts of experimental observations on objects as different as planets and billiard balls. If an observation differed from the predictions of classical physics, they looked for something they had overlooked to explain the deviation. In 1864, physicists' confidence in the whole edifice of classical physics seemed to be spectacularly verified by an analysis of some irregularities in the orbit of Uranus. These were attributed to the existence of a then undiscovered planet – the subsequent discovery of Neptune was a triumph for Newtonian physics.
Abstract In the first quarter of this century physicists were slowly and somewhat reluctantly forced to realize that the view of the physical world, so painstakingly built up over the preceding four centuries, was in serious need of revision. In particular, the laws that governed the motion of particles on the atomic scale were not those of classical mechanics. Physics found itself catapulted into the strange new world of quantum theory in which the very notion of position or velocity of a particle became blurred and statistical laws dominated everything.
For a century, quantum mechanics has been hailed as both the most profound revolution in physics and the ultimate failure of human reason. Wave-particle duality, superposition, collapse, the uncertainty principle, quantum entanglement—these concepts have been enshrined as fundamental laws of the microscopic world, yet no one has ever truly understood them. Feynman said, "Nobody understands quantum mechanics." Dirac said, "Shut up and calculate." Where does this century-old dream come from? Not from any mystery inherent in the world, but from wearing the wrong lens. We tried to understand waves using the concept of "particles." A wave spreading through space was described as "a particle being in many places at once." A traveling wave forming a standing wave at a boundary was described as "a particle suddenly collapsing." Quantum entanglement was described as "spooky action at a distance between particles." Every mysterious concept in quantum mechanics is a distorted image—a wave's true nature seen through the funhouse mirror of the particle perspective. This series of twelve papers declares: the dream is over. There are only two things in the universe—traveling waves and standing waves. Light is a traveling wave. The electron is a photon confined as a ring-shaped standing wave. A moving electron is a standing wave carrying a traveling wave. That a wave spreads through space is its nature—not superposition. That a traveling wave forms a standing wave at a boundary is ordinary physics—not collapse. That waves obey the Fourier relation is a mathematical theorem—not the uncertainty principle. Quantum entanglement is phase memory—not nonlocal connection. Return to the world of waves, speak the language of waves, and all phantoms vanish instantly. This is not a denial of quantum mechanics. It is the disenchantment of quantum mechanics. The mathematics survives. The interpretation dies. The particle perspective ends. The era of waves begins. --- 一百年来,量子力学被视为物理学最深刻的革命,也被视为人类理性最彻底的失败。波粒二象性、叠加态、坍缩、不确定性原理、量子纠缠——这些概念被奉为微观世界的基本法则,却从未被真正理解。费曼说:“没有人理解量子力学。”狄拉克说:“闭嘴计算。” 百年梦幻的根源是什么?不是世界本身神秘,而是我们戴错了眼镜。我们用“粒子”的概念去理解波——波覆盖空间,被说成“粒子同时处于多处”;波在边界处形成驻波,被说成“粒子突然坍缩”;量子纠缠被说成“粒子间有超距作用”。量子力学的所有神秘概念,都是波的本性在粒子观这面哈哈镜中的扭曲像。 本系列十二篇论文宣告:梦幻结束了。宇宙中只有两种东西——行波与驻波。光是行波,电子是光子环形驻波,运动电子是驻波携带着行波。波覆盖空间是本性,不是叠加态;行波在边界处形成驻波是普通物理,不是坍缩;波的傅里叶性质是数学定理,不是不确定性原理;量子纠缠是相位记忆,不是非定域关联。回到波的世界,用波的语言说话,所有幻象瞬间消失。 这不是对量子力学的否定,而是对量子力学的祛魅。数学幸存,解释死亡。粒子观终结,波的时代开始。