Length Contraction Research Articles

Schwarz-Pick type inequalities from an operator theoretical point of view

We use (versions of) the von Neumann inequality for Hilbert space contractions to prove several Schwarz-Pick type inequalities. Specifically, we derive an alternate proof for a multi-point Schwarz-Pick inequality by Beardon and Minda, along with a generalized version for operators. Connections with model spaces and Peschl's invariant derivatives are established. Finally, Schwarz-Pick inequalities for analytic functions on polydisks and for higher order derivatives are discussed. An enhanced version of the Schwarz-Pick lemma, using the notion of distinguished variety, is obtained for the bidisk.

The length contraction paradox

Reciprocal length contraction and time dilation, as enshrined in the Lorentz transformation, are the bulwark of the special relativity theory. Reciprocal time dilation is typically discussed (in the context of its apparent contradiction) and usually explained away as the result of differing synchronization in inertial reference frames and the relativity of simultaneity. Further, it is generally suggested that time is an abstract concept, and its perceptions may differ with context. However, we suggest that regarding length measurements no such abstraction can be envisaged. In this manuscript, we examine the reciprocal length contraction in detail to assess whether it leads to any contradiction.

Theory of Everything

Our Theory of Everything is made possible by the discovery of a closed fluid dynamic principle, working in a closed fluid space-time system, (the universe). Through the principle of fluid space-time, almost all of the unexplained mysteries of the universe are revealed. How the universe came into being, with matter and the most basic force, Gravity. Newton’s law of gravity in particular, the inverse square law with distance. (the reason is for appearance of the inverse square law, simultaneously in gravitation and electromagnetism, not a coincidence). Special Relativity is an account of how space contracts, time dilates and mass increases, with velocity. General Relativity is an account of how space-time curves. According to Muhammad’s closed fluid dynamic principle, space actually consists of an extremely fluid substance which we call aether. It is therefore fitting that through the closed fluid dynamic principle, we can arrive at an explanation for one major thorn in the side of Special Relativity, the twin paradox. The problem is, it is the twin who accelerates that gets it wrong. Because his assessment of the age of his brother was done without consideration of the fact that when he turned around, made the return journey, he felt his acceleration but did not employ this in Einstein’s time dilation, which was based on inertial reference frames. The task we are confronted with in this paper is to find out how the time dilation addressed in special relativity comes into proceedings in an accelerated frame. We achieve this.

On Bell's dynamical route to special relativity

This paper develops the approach to special relativity put forward by John S. Bell. The classical dynamics of an electron orbiting a nucleus in uniform motion is solved analytically and compared to numerical simulations for an accelerated nucleus. The relativistic phenomena of length contraction and time dilation are shown to result from the electric and magnetic forces on the electron when its motion is analyzed in a single frame of reference. The relevance of these results for understanding the theory of special relativity is discussed.

Using Rotations to Control Observable Relativistic Effects

This paper examines the possibility of controlling the outcome of measured (flat space-time) relativistic effects, such as time dilation or length contractions, using pure rotations and their nontrivial interactions with Lorentz boosts in the isometry group SO+(3,1). In particular, boost contributions may annihilate leaving only a geometric phase (Wigner rotation), which we see in the complex solutions of the generalized Euler decomposition problem in R3. We consider numerical examples involving specific matrix factorizations, along with possible applications in special relativity, electrodynamics and quantum scattering. For clearer interpretation and simplified calculations we use a convenient projective biquaternion parametrization which emphasizes the geometric phases and for a large class of problems allows for closed-form solutions in terms of only rational functions.

SPECIAL THEORY OF RELATIVITY IS ALSO FAILED TO EXPLAIN NULL RESULT OF MICHELSON AND MORLEY EXPERIMENT

Michelson and Morley conducted an experiment in the year 1887 to measure the speed of earth in luminiferous aether. In this experiment Michelson’s interferometer was used in which two waves are superimposed to generate interference fringes. Keeping in view known velocity of earth around the sun a fringe shift of 0.44 fringe was expected on the rotation of interferometer at an angle of 900, but surprisingly no fringe shift was observed. The experiment was conducted so many times and at so many places but always null results were obtained. The null result of MMX could not be explained by classical mechanics. A number of explanations for null results were submitted but no one was found to be correct. George Fitzerald and Hendrick Lorentz proposed length contraction hypothesis in the direction of motion of earth, but it was also rejected being an adhoc hypothesis. Albert Einstein submitted his famous theory “The special theory of relativity” in the year 1905. The second postulate of the STR states that speed of light is constant in all directions of inertial frames of reference irrespective of motion of source of light or the observer and states that no luminiferous aether exist as a medium, light waves do not require any medium to propagate. As light travels with constant velocity in both the arms of interferometer irrespective of motion of interferometer and there involves no time difference between the two rays hence null results of MMX were explained by special theory of relativity. Michelson and Morley experiment is based on the wave nature of light. In such experiments wavefront of light plays very important role but behaviour of wavefront of light was not taken into consideration while deriving the time taken by the light rays in the arms of interferometer due to motion of earth resulting into wrong derivation of time. The present article describes the principle and realization of role of wavefront of light in MMX. The time taken by light rays in the arms of the interferometer due to motion of earth depends upon the behaviour of wavefront of light. It has been established by results of Fizeau experiment and steller aberration of light that speed of light is not effected by velocity of moving medium. The derivation of time has been worked out keeping in view constancy of speed of light, wavefront of light and laws of reflection of light according to Huygen’s principle. Contrary to earlier beliefs the Lorentz length contraction hypothesis is not able to explain the null results of MMX. In the light of new facts it is established that there is no difference between theorectical results derived by classical mechanics and special theory of relativity. Special theory of relativity is also failed to explain the null result of MMX. The null result of Michelson and Morley experiment has again become a perplexing question for physicists.

Spatial Contraction Based on Velocity Variation for Natural Walking in Virtual Reality.

Virtual Reality (VR) offers an immersive 3D digital environment, but enabling natural walking sensations without the constraints of physical space remains a technological challenge. Previous VR locomotion methods, including game controller, teleportation, treadmills, walking-in-place, and redirected walking (RDW), have made strides towards overcoming this challenge. However, these methods also face limitations such as possible unnaturalness, additional hardware requirements, or motion sickness risks. This paper introduces "Spatial Contraction (SC)", an innovative VR locomotion method inspired by the phenomenon of Lorentz contraction in Special Relativity. Similar to the Lorentz contraction, our SC contracts the virtual space along the user's velocity direction in response to velocity variation. The virtual space contracts more when the user's speed is high, whereas minimal or no contraction happens at low speeds. We provide a virtual space transformation method for spatial contraction and optimize the user experience in smoothness and stability. Through SC, VR users can effectively traverse a longer virtual distance with a shorter physical walking. Different from locomotion gains, the spatial contraction effect is observable by the user and aligns with their intentions, so there is no inconsistency between the user's proprioception and visual perception. SC is a general locomotion method that has no special requirements for VR scenes. The experimental results of our live user studies in various virtual scenarios demonstrate that SC has a significant effect in reducing both the number of resets and the physical walking distance users need to cover. Furthermore, experiments have also demonstrated that SC has the potential for integration with existing locomotion techniques such as RDW.

Conversion Factors for Physical Property Measurements in different Rest Frames Using a Revised Version of Relativity Theory Based on the Uniform Scaling Method

The history of the development of the Uniform Scaling Method is reviewed. It has its beginning with the Law of Causality and Newton’s First Law of Kinetics (Law of Inertia). On this basis it can be concluded that the rates of clocks do not change spontaneously, i.e. without the application of some external force. Since the ratio Q of the rates of any two such (inertial) clocks must therefore itself be a constant, it follows that whenever they are used to measure a specific time difference between two events, their respective results must always be in the same ratio: Δt’=Δt/Q. This relationship is referred to as Newtonian Simultaneity since it guarantees that if one of the clocks finds that the events occurred simultaneously (Δt’=0), the other must do so as well (Δt=0). A useful way to interpret Q is as a conversion factor between the different units of time employed in the two rest frames. If we assume that the value of the speed of light is the same in both rest frames, it follows that they must agree on the unit of speed, i.e. the conversion factor in this case is unity (Q0 ). It therefore follows that the conversion factor for the unit of distance must be exactly the same as that for time, namely also Q. This claim of the Uniform Scaling Method is thus seen to be in direct contradiction to the length contraction tenet of Einstein’s theory of relativity introduced in 1905. Experiments with accelerated electrons carried out by Bucherer in 1909 indicate that their inertial mass increase in direct proportion to γ (v) = (1-v2 c-2)-0.5 (v is the speed of the electrons and c = 299792458 ms-1 is the speed of light in free space), the same ratio as observed for the periods of atomic lines by Ives and Stilwell in 1938. Consistency therefore requires that the conversion factor for inertial mass is the same (Q) as for time. Since inertial mass, time and distance are the three fundamental quantities on which all other physical properties are defined (mks system), it follows that the conversion factor for any other property must be an integral multiple of Q. An analogous set of definitions can also be justified for the corresponding conversion factors in the same two rest frames caused by gravitational effects. In this case the conversion factors are always integral multiples of the quantity S, which therefore plays as analogous role as Q in kinetic scaling. Since experiments with circumnavigating atomic clocks carried out in 1971 by Hafele and Keating found that the two types of effects are completely independent of one another, it is therefore useful to define a product Z of the corresponding Q and S factors for each physical property, including those that are used to define the results of electromagnetic measurements. These total conversion factors are stored in Tables 1 and 2 of the manuscript. They are shown to guarantee that if a physical law is valid in one of the rest frames, it will also hold in the other. This relationship allows for an Addendum to Galileo’s Relativity Principle: The laws of physics are the same in all inertial rest frames, but the units in which their results are expressed can differ from one rest frame to another.

Research on 3D Visualization of Drone Scenes Based on Neural Radiance Fields

Neural Radiance Fields (NeRFs), as an innovative method employing neural networks for the implicit representation of 3D scenes, have been able to synthesize images from arbitrary viewpoints and successfully apply them to the visualization of objects and room-level scenes (<50 m2). However, due to the capacity limitations of neural networks, the rendering of drone-captured scenes (>10,000 m2) often appears blurry and lacks detail. Merely increasing the model’s capacity or the number of sample points can significantly raise training costs. Existing space contraction methods, designed for forward-facing trajectory or the 360° object-centric trajectory, are not suitable for the unique trajectories of drone footage. Furthermore, anomalies and cloud fog artifacts, resulting from complex lighting conditions and sparse data acquisition, can significantly degrade the quality of rendering. To address these challenges, we propose a framework specifically designed for drone-captured scenes. Within this framework, while using a feature grid and multi-layer perceptron (MLP) to jointly represent 3D scenes, we introduce a Space Boundary Compression method and a Ground-Optimized Sampling strategy to streamline spatial structure and enhance sampling performance. Moreover, we propose an anti-aliasing neural rendering model based on Cluster Sampling and Integrated Hash Encoding to optimize distant details and incorporate an L1 norm penalty for outliers, as well as entropy regularization loss to reduce fluffy artifacts. To verify the effectiveness of the algorithm, experiments were conducted on four drone-captured scenes. The results show that, with only a single GPU and less than two hours of training time, photorealistic visualization can be achieved, significantly improving upon the performance of the existing NeRF approaches.

Space Viscosity and Fundamental Constants

Fundamental constants in physics, such as the speed of light and the gravitational constant, are usually considered to be constant over time and space. This means that their value does not change with the expansion of the universe. Constants determine all the properties and behaviors of the cosmos, and any change in them would lead to the formation of a universe with new physical characteristics. The constants of physics in an expanding universe have always been a research challenge. In this context, some models suggest these constants may vary over time due to changes in the conditions of the cosmos; however, these theories have not yet been widely accepted by the scientific community. Fundamental forces in the universe are interactions that govern the behavior of matter and energy at the most elementary level. For example, the gravitational field, which follows the universal constant of gravity, clearly demonstrates its effect on large cosmic structures. According to the theory of general relativity, gravity is the result of distortions in space-time created by mass and energy. Moreover, gravity interacts with a specific type of matter in the universe known as dark matter. In fact, from the perspective of cosmologists, it is believed that this type of matter consists of hypothetical fundamental particles that do not emit electromagnetic radiation, such as light, and can be detected through their gravitational effects on visible matter and the large-scale structure of the universe. In conventional cosmology, dark energy can also be considered as a cosmological constant, is fundamentally a characteristic of space itself, which possesses a constant negative pressure and, contrary to gravity, causes the universe to expand at an accelerating rate. Dark energy is a dynamic quantity that can vary over time and space. However, T-Consciousness Cosmology posits that space has viscosity, and does not consider it constant. In other words, this viewpoint sees gravity as a result of the contraction of space (space viscosity) caused by the mass of light matter (ordinary matter). Additionally, this perspective introduces different types of dark matter (solid-like, liquid-like, gas-like), stating that dark matter is representative of high levels of space viscosity that envelopes massive objects or galaxies. Consequently, dark matter corresponds to high space viscosity and dark energy to low space viscosity. Moreover, both dark matter and dark energy not only possess gravitational properties but also act as the glue that holds massive cosmic objects and structures together. Due to the positive pressure it exerts within the isolated spherical cosmos, dark energy is recognized as one of the factors that drive cosmic expansion, effectively counteracting gravity. T-Consciousness Cosmology introduces a viscosity coefficient of space, ranging from infinity in the Cosmic Black Hole to zero at the Terminal Edge of the Cosmos (the final stage of space Rebound). Furthermore, this perspective argues that the speed of light varies in different viscosities of space, such that in areas of high viscosity, light's frequency increases and its wavelength decreases, slowing down the speed of light, and the opposite occurs in areas of low viscosity. Consequently, the speed of light is not constant throughout the cosmos due to the variability of space viscosity. The speed of light increases significantly higher than its currently calculated speed as the cosmos approaches its final stage of Rebound. It is important to note that while the notion of variable light speed is present in mainstream science, the approach taken by T-Consciousness Cosmology is distinctively different from these theories.

Relativistic Formulation in Dual Minkowski Spacetime

The objective of this work is to derive the structure of Minkowski spacetime using a Hermitian spin basis. This Hermitian spin basis is analogous to the Pauli spin basis. The derived Minkowski metric is then employed to obtain the corresponding Lorentz factors, potential Lie algebra, effects on gamma matrices and complex representations of relativistic time dilation and length contraction. The main results, a discussion of the potential applications and future research directions are provided.

Novel results for separate families of fuzzy-dominated mappings satisfying advanced locally contractions in b-multiplicative metric spaces with applications

The objective of this research is to present new fixed point theorems for two separate families of fuzzy-dominated mappings. These mappings must satisfy a unique locally contraction in a complete b-multiplicative metric space. Also, we have obtained novel results for families of fuzzy-dominated mappings on a closed ball that meet the requirements of a generalized locally contraction. This research introduces new and challenging fixed-point problems for families of ordered fuzzy-dominated mappings in ordered complete b-multiplicative metric spaces. Moreover, we demonstrate a new concept for families of fuzzy graph-dominated mappings on a closed ball in these spaces. Additionally, we present novel findings for graphic contraction endowed with graphic structure. These findings are groundbreaking and provide a strong foundation for future research in this field. To demonstrate the uniqueness of our novel findings, we provide evidence of their applicability in obtaining the common solution of integral and fractional differential equations. Our findings have resulted in modifications to several contemporary and classical results in the research literature. This provides further evidence of the originality and impact of our work.

Origami‐Inspired Modular Electro‐Ribbon Actuator for Multi‐Degrees of Freedom Motion

Origami robots, inspired by an ancient form of paper folding art, are capable of achieving high displacement in a lightweight and compact design that conventional robots can hardly attain. It, however, remains a challenge to drive origami robots with in situ active materials that imply minimal added mass and complexity and can be easily controlled to achieve multiple actuation modalities. Herein, inspired by the Twisted Tower origami structure, dielectrophoretic liquid zipping actuation concept is employed to develop a modular architecture, capable of achieving complicated motions with multiple degrees of freedom (DoF). The experimental results show a maximum of 3.9 degrees tilting per layer toward any desired direction, a 56.1% contraction of the original length, and 5.4 degrees twisting per layer. Each layer can generate a maximum contractile force of 1.03 N with a maximum 64.7% power efficiency and 2.775 W kg−1 power‐to‐weight ratio. A modified heterochiral arrangement of this modular actuator is proposed to enhance controllability across various movement modes. Its use in robotic‐wrist‐like actuation has been demonstrated, highlighting its significant potential for integration into soft robotic multi‐DoF structures, such as continuum arms.

Energy-Space-Time Plateau-Rayleigh Instability, Quantum Phenomenon & the Fundamental Interactions

In general, fluids in motion or at rest tend to minimize their surface area due to their surface tension. It is shown that kinetic energy flow through space-time experience the same Plateau-Rayleigh instability observed in fluid dynamics. Energy, space-time act like fluids, and the space-time reaction to the energy action is the equivalent of an interface tension between energy and space-time. Energy cannot continuously flow through space-time due to an energy-space-time Plateau-Rayleigh instability, space-time compression (contraction) on kinetic energy direction of motion induces an energy wave like motion (a space-time compression wave acting as kinetic energy waveguide), the particle or energy packet must follow when moving through space-time, the reason for the observed wave - particle duality. Quantum phenomenon is simply a consequence of the space-time compression on kinetic energy direction of motion. Kinetic energy and space-time are fluids and energy quanta can reach a critical point when energy quanta can change from linear to circular motion and assume a spherically symmetrical shape (the minimum surface area possible to minimize the tension at the space-time energy interface) and so it condensates as mass energy. It is shown that energy quanta to mass transformation occurs via Plateau–Rayleigh energyspace-time instability and it is governed by an energy-space-time Young-Laplace equation. Electric field lines are described as space contraction energy shock waves induced by a dynamic space-time phase transition at maximum kinetic energy space- time interface tension which is the “charge”. Space-time always reacts to the presence of energy and that reaction is the interface tension at the energy-space-time boundary: gravitational & electric energy fields are consequences of energyspace-time interface tension (at either rest or kinetic energy boundary) also governed by an energy-space-time instability Young-Laplace equation. Gravitational constant G and the fine structure constant ∝ are respectively, the energy interface field’s interaction constants. The Strong force is a consequence of a direct contact between the nucleon's energy-space-time interface tension fields and has no interaction constant. The range and variation in the strength of the Strong force is due to Heisenberg’s uncertainty principle

Existence and approximation of fixed points of enriched contractions in quasi-Banach spaces

Existence and approximation of fixed points of enriched contractions in quasi-Banach spaces

Dilation and Birkhoff-James orthogonality

For any two elements x and y in a normed space X, x is said to be Birkhoff-James orthogonal to y, denoted by x⊥By, if ‖x+λy‖≥‖x‖ for every scalar λ. Also, for any ε∈[0,1), x is said to be ε-approximate Birkhoff-James orthogonal to y, denoted by x⊥Bεy, if‖x+λy‖2≥‖x‖2−2ε‖x‖‖λy‖,for all scalarsλ. For any ρ>0, a unitary operator U acting on a Hilbert space K is said to be a unitary ρ-dilation of an operator T on a Hilbert space H if H⊆K and Tn=ρPHUn|H for every nonnegative integer n, where PH:K→H is the orthogonal projection. Also, when ρ=1 and T is a contraction, U is called a unitary dilation of T. We obtain the following main results.(1)We find necessary and sufficient conditions such that for any two contractions T,A on H, their Schäffer unitary dilations UT˜ and UA˜ on the space ⊕−∞∞H are Birkhoff-James orthogonal. Also, counter example shows that in general UT˜⊥̸BUA˜ even if T⊥BA.(2)For any ρ>0 and for two Hilbert space operators T,A with T⊥BA, we show that if ‖T‖=ρ then UT⊥BUA for any unitary ρ-dilations UT of T and UA of A acting on a common Hilbert space. Also, we show by an example that the condition that ‖T‖=ρ cannot be ignored.(3)For any ρ>0, we explicitly construct examples of Hilbert space operators T,A such that T⊥̸BA but any of their unitary ρ-dilations UT,UA acting on a common Hilbert space are Birkhoff-James orthogonal.(4)We find a characterization for the ε-approximate Birkhoff-James orthogonality of operators on complex Hilbert spaces.(5)For any ρ>0 and for any Hilbert space operators T,A, we find a sharp bound on ε such that T⊥BA implies UT⊥BεUA for any unitary ρ-dilations UT of T and UA of A acting on a common space. Also, we show by an example that in general the bound on ε cannot be improved.(6)We construct families of generalized Schäffer-type unitary dilations for a Hilbert space contraction in two different ways. Then we show that one of them preserves Birkhoff-James orthogonality while any two members UT,UA from the other family are always Birkhoff-James orthogonal irrespective of the orthogonality of T and A.(7)We show that Andô dilation of a pair of commuting contractions of the form (T,ST), where S is a unitary that commutes with T, are orthogonal. Also, we explore orthogonality of regular unitary dilation of a pair of commuting contractions. However, Birkhoff-James orthogonality is independent of commutativity of operators.

Correcting Common Misunderstandings of Lorentz-Fitzgerald Length Contraction: A Guide to Accurate Measurements

Correcting Common Misunderstandings of Lorentz-Fitzgerald Length Contraction: A Guide to Accurate Measurements

A fixed point theorem for nonself nonlinear contractions in length spaces

In 1988 N.A. Assad showed that a nonself nonlinear contraction taking a closed subset of a complete metrically convex space into the space so that the boundary of this subset is mapped back into the subset itself has a unique fixed point. In the present paper we extend this result by replacing the complete metrically convex space with a complete metric space which is a length space.

Fixed Point Theorems for Kannan Interpolative, Riech Interpolative and Dass-Gupta Interpolative Rational type Contractions in A-Metric Spaces

(\(\lambda\), \(\alpha\))- interpolative Kannan contraction, (\(\lambda\), \(\alpha\), \(\beta\))- interpolative Kannan contraction, (\(\lambda\), \(\alpha\), \(\beta\), \(\gamma\))- interpolative Riech contraction and (\(\lambda\), \(\alpha\), \(\beta\))- interpolative Dass-Gupta rational contraction are presented in this study. Furthermore, we prove a few fixed-point theorems for interpolative contractions in complete A-metric spaces. These theorems also extend and apply to an A-metric setting several interesting results from metric fixed-point theory.

Solving large-scale combined heat and power economic dispatch problems by using deep reinforcement learning based crisscross optimization algorithm

The extensive interconnection in bulk power systems brings great challenges in the economic dispatch problems, especially the large-scale combined heat and power economic dispatch (CHPED), which is quite intractable due to complex thermal and electrical couplings in cogeneration units. Most meta-heuristic algorithms cannot work well while considering non-convexity, discontinuity, and non-differentiability. Particularly, when it comes to the high dimensional and large-scale CHPED problems, these algorithms are either easy to trap in the local optimum or quite time-consuming. To address these issues, a novel deep reinforcement learning (DRL) based crisscross optimization (CSO) algorithm is proposed for the first time, which can (1) improve the searching ability of CSO, (2) enhance the overall searching efficiency, and (3) perform extraordinarily well for the large-scale CHPED problems. Firstly, to further improve the global search ability, DRL is employed to reduce dimensionality and narrow the search space of the initial population of the CSO algorithm. Then, DRL is updated by the deep deterministic policy gradient (DDPG) strategy, which can facilitate an instantaneous decision in accelerating CSO. Thereafter, by adopting each decision provided by DRL, a great difference may occur in the same scenario to speed up the crossover procedure and guide the upcoming search round. On this basis, the enhanced CSO algorithm could quickly carry out crossovers with search space contraction and dimensionality reduction. Finally, experiments on four test systems have substantiated the effectiveness of the proposed algorithm, especially the superiority over other state-of-the-art techniques in solving large-scale CHPED problems.