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A novel axially symmetric metric is proposed to solve the Einstein field equations. This provides an analytical solution within the matter in the equatorial plane for any galaxy density profile. The solution predicts the observed increase in rotational velocity up to the edge of the galaxy's bulge. However, beyond the bulge, the rotational velocity remains constant, which contradicts the observed peak curves. The existence of the Universe is then considered by approximating the gravitational fields within the galaxy as the sum of those generated by the galaxy and the Universe. The resulting solution explicitly includes a Universe frame-dragging term, aligning with the sixth version of Mach's principle proposed by Bondi and Samuel: "inertial mass is affected by the global distribution of matter". Neglecting the presence of the Universe, stars only have a relative rotation to the bulge, and their rotational velocities monotonically increase with the radial distance r to balance the increasing mass contained in distances < r. At larger distances, the bulge's attraction and its frame-dragging effect decrease, resulting in a constant rotational velocity. When the Universe is considered, stars also have a relative rotation to the non-rotating Universe and experience an additional centrifugal force at any distance from the bulge. This component induces a decrease in rotational velocity as the gravitational influence of the bulge diminishes with r. This model predicts the observed rotational velocity curves for the galaxies M31, M101, and M81 without requiring any dark matter halo or adjustable parameters. This success substantiates Mach's idea as an alternative to the dark matter halo theory. [ABSTRACT FROM AUTHOR]

The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction with the rest of the universe. This idea is known today as Mach's principle. We discuss Mach's principle based on transactional gravity, the recently developed connection of entropic gravity to the physics of quantum events, induced by transactions. It is shown that Mach's principle holds and that there is a fundamental relation between the gravitational constant G and the total mass in the causal universe. This relationship, derived by means of entropic principles, is rigorously proven. [ABSTRACT FROM AUTHOR]

A novel axially symmetric metric is proposed to solve the Einstein field equations. This provides an analytical solution within the matter in the equatorial plane for any galaxy density profile. The solution predicts the observed increase in rotational velocity up to the edge of the galaxy’s bulge. However, beyond the bulge, the rotational velocity remains constant, which contradicts the observed peak curves. The existence of the Universe is then considered by approximating the gravitational fields within the galaxy as the sum of those generated by the galaxy and the Universe. The resulting solution explicitly includes a Universe frame-dragging term, aligning with the sixth version of Mach’s principle proposed by Bondi and Samuel: “inertial mass is affected by the global distribution of matter”. Neglecting the presence of the Universe, stars only have a relative rotation to the bulge, and their rotational velocities monotonically increase with the radial distance r to balance the increasing mass contained in distances < r. At larger distances, the bulge’s attraction and its frame-dragging effect decrease, resulting in a constant rotational velocity. When the Universe is considered, stars also have a relative rotation to the non-rotating Universe and experience an additional centrifugal force at any distance from the bulge. This component induces a decrease in rotational velocity as the gravitational influence of the bulge diminishes with r. This model predicts the observed rotational velocity curves for the galaxies M31, M101, and M81 without requiring any dark matter halo or adjustable parameters. This success substantiates Mach’s idea as an alternative to the dark matter halo theory.

The question of where the inertial properties of matter come from has been open for a long time. Isaac Newton considered inertia an intrinsic property of matter. Ernst Mach held a different view whereby the inertia of a body comes from its interaction with the rest of the universe. This idea is known today as Mach’s principle. We discuss Mach’s principle based on transactional gravity, the recently developed connection of entropic gravity to the physics of quantum events, induced by transactions. It is shown that Mach’s principle holds and that there is a fundamental relation between the gravitational constant G and the total mass in the causal universe. This relationship, derived by means of entropic principles, is rigorously proven.

After examining the Schwarzschild solution, Nobel prize winner Richard Feynman concluded that it contains three problems: the constant 1, the negative sign, and the singularity. These three problems do not manifest themselves in the case of a weak gravitational field but can lead to misinterpretation of processes near black holes and in cosmology. As a working hypothesis, we consider a corrected Schwarzschild solution: the constant 1 is expressed in terms of the distribution of all masses in the universe, positive sign instead of a negative sign, and no singularity. In a weak gravitational field, the new solution leads to the same effects as the usual solution. The choice between the two solutions can be made if the accuracy of gravitational experiments in the solar system is increased by 1–2 orders of magnitude. The new solution implies that black holes do not have an event horizon. Therefore, the new solution can also be tested using future, more accurate observations of black holes. If it is confirmed, our ideas about cosmogonic processes can change in the most radical way.

Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Albert Einstein visited Spain only once, precisely one hundred years ago. The circumstances, of a very different kind, of this visit will be explained here. In special, some important events happened to Einstein during that period, which, eventually, were key for converting modern cosmology into a genuine physical theory. Among them is the famous Einstein-Friedmann controversy, first, on the mathematical validity of Friedmann's equations and, later, their possible usefulness as a reliable tool to describe the real world. A summary of the deepest ideas underlying Einstein's contributions to the theory of relativity, which he had already completed before his visit, will precede the discussion, also supplemented with a description, in very simple terms, of the three main relativistic theories, namely Galileo's one, and Einstein's special and general theory. They pave the way towards a definitive theory of total relativity, so far unattainable. It will be recalled that the most general relativity principle, faithfully reflecting Ernst Mach's far-reaching ideas, might have much to do with the symmetry-breaking paradigm, a most crucial tool in quantum field theory and high energy physics. [ABSTRACT FROM AUTHOR]

In axistationary, asymptotically flat spacetimes, zero angular momentum observers (ZAMOs) define an absolute standard of non-rotation locally, as can be verified by the absence of any Sagnac effect for these observers. Nevertheless, we argue that on a global scale the only physically meaningful concept is that of relative rotation. The argument is substantiated by solving Einstein's equations for an approximate thin shell model, where we maintain a degree of freedom, by relaxing the natural assumption of vanishing rotation at asymptotic infinity, at the outset of the analysis. The solution reveals that Einstein's equations only determine differences in the rotation rate of ZAMOs, thereby establishing the concept of relative rotation globally. The interpretation of rotation as relative in a global context is inherently linked to the freedom to transform between coordinate systems rotating relative to each other, implying that an arbitrary ZAMO located at any radius may claim to be the one that is non-rotating on a global scale, and that the notion of an asymptotic Lorentz frame relative to which one may measure absolute rotation is devoid of any meaning. The concept of rotation in Kerr spacetime is then briefly discussed in the context of this interpretation. [ABSTRACT FROM AUTHOR]

A modeling of natural phenomena based on the principle of 100% efficiency of mathematics is presented. The fundamental distinction between abstract and material entities is discussed and the probabilistic nature of natural phenomena is explained. The paper provides explanations for many observed phenomena. A general definition of the virtual state of matter, the concept of entropic interaction, and the phenomenon of quantum entanglement is given. An additional interpretation of the Hubble law is considered. It is shown how local entropy changes in world space lead to the bifurcation of its state and subsequent “Big Bangs” with the formation of an infinite number of parallel universes that do not interact with each other. The correlation between the change in entropy and the rhythm of time, which is valid for isolated non-equilibrium thermodynamic systems, including our Universe, is presented. The fundamental principles of thermodynamics, quantum mechanics, quantum field theory and the theory of relativity, as well as the origin and evolution of our Universe are discussed. An alternative explanation for the curvature of space is given for the effects of deflection of a light beam towards the sun, the shift of the perihelion of Mercury, the periastron of binary stars, and the gravitational slowing of the rhythm of time. The interference pattern is considered as the result of small-angle scattering in a weak potential field without using the wave mechanism and is interpreted as the result of the entropic interaction of photons or particles passing through the corresponding slots. The presented paper applies equally to both living and non-living nature objects, and contains information about the laws of dialectics. [ABSTRACT FROM AUTHOR]

Albert Einstein visited Spain only once, precisely one hundred years ago. The circumstances, of a very different kind, of this visit will be explained here. In special, some important events happened to Einstein during that period, which, eventually, were key for converting modern cosmology into a genuine physical theory. Among them is the famous Einstein-Friedmann controversy, first, on the mathematical validity of Friedmann’s equations and, later, their possible usefulness as a reliable tool to describe the real world. A summary of the deepest ideas underlying Einstein’s contributions to the theory of relativity, which he had already completed before his visit, will precede the discussion, also supplemented with a description, in very simple terms, of the three main relativistic theories, namely Galileo’s one, and Einstein’s special and general theory. They pave the way towards a definitive theory of total relativity, so far unattainable. It will be recalled that the most general relativity principle, faithfully reflecting Ernst Mach’s far-reaching ideas, might have much to do with the symmetry-breaking paradigm, a most crucial tool in quantum field theory and high energy physics.

The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of ‘absolute space’. When applied to classical mechanics, under the guise of an extended symmetry group, this procedure is known to lead to an equation of motion with inertial-like forces that are sourced by the mass distribution of the system itself. In this paper we follow a similar procedure and reformulate the Schrödinger equation of non-relativistic quantum mechanics in a fully Machian way. Just like its classical counterpart, the resulting quantum theory is fully relational in the positions and momenta of the bodies comprising a given physical system, leaving no room for the notion of absolute space. [ABSTRACT FROM AUTHOR]

Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

After examining the Schwarzschild solution, Nobel prize winner Richard Feynman concluded that it contains three problems: the constant 1, the negative sign, and the singularity. These three problems do not manifest themselves in the case of a weak gravitational field but can lead to misinterpretation of processes near black holes and in cosmology. As a working hypothesis, we consider a corrected Schwarzschild solution: the constant 1 is expressed in terms of the distribution of all masses in the universe, positive sign instead of a negative sign, and no singularity. In a weak gravitational field, the new solution leads to the same effects as the usual solution. The choice between the two solutions can be made if the accuracy of gravitational experiments in the solar system is increased by 1–2 orders of magnitude. The new solution implies that black holes do not have an event horizon. Therefore, the new solution can also be tested using future, more accurate observations of black holes. If it is confirmed, our ideas about cosmogonic processes can change in the most radical way. [ABSTRACT FROM AUTHOR]

An evolutionary scenario of processes, especially of the thermodynamic processes, in a perpetually mass-generating Planckian model universe has been studied. This is a Milne-type flat-space, R = ct, model with steady radial mass flow as recently described by us. In this ‘Broadcasting TV’ model universe the rest-mass particles are moving practically with light speed and the neutrinos and photons, both in thermal equilibrium and decoupled states, are moving in (almost) perpendicular directions along the light cones as the frozen-in particles. Therewith the density of radiation has the same dilutional dependence as for the radially squared lowering density of rest-mass particles. In such model universe the horizon problem is avoided automatically, whereas the light-cone photons are moving relative to atomic matter along the logarithmic Archimedes spiral around the mass-generating Planckian source, covering during evolution about 22 cycles. Crucially, the cosmic ‘dark ages’ start at 33.2 times younger age and about 103 times greater densities of matter, leading to much earlier formation of stars and galaxies than in the traditional LCDM cosmology. In the Planckian universe the cosmological principle holds for every epoch, thus removing the anthropocentric principle. The modified critical density in the model is ρ = 8.6·10–31g·cm–3. The needed dark matter contribution ρv = 3·10–31g· cm–3 can be provided by neutrinos if their rest energy is 0:16 eV. These correspond to degenerated cooled neutrinos at velocities of the order vF = 104 km/s.

In a recent issue of this journal, Rodal (Gen Relativ Gravit 51:61–84, 2019) has written an extensive critique of a novel propulsion scheme devised nearly 30 years ago (Woodward in Found Phys Lett 6:1–39, 1995; Making starships and stargates: the science of interstellar transport and absurdly benign wormholes, Springer, New York, 2012). That scheme depends on the production of rest mass fluctuations, driven in special systems, that arise when the systems are accelerated, through the interaction of the systems with the field that produces inertial forces. Following Einstein, the field that produces inertial forces is taken to be the gravitational field due chiefly to the most distant matter (everything that gravitates) in the universe. Such rest mass fluctuations in local accelerating objects, predicted using the relativistic Newtonian approximation to general relativity, are now called "Mach effects" since they depend on inertial forces in fact being gravitational forces as Ernst Mach hinted might be the case. Rodal claims that such rest mass fluctuations with significant magnitude, save in the vicinity of black holes, are not to be found in general relativity notwithstanding that they appear in the relativistic Newtonian approximation. Rodal is mistaken in this claim, as I have already explained at some length (Woodward in J Br Interplanet Soc 70:354–364, 2018). Here I recapitulate some of that material and expand some material with specific reference to his now published claims. [ABSTRACT FROM AUTHOR]

The paper presents the study of quantum mechanics of a free particle with the constraints in the phase space, the canonical equations, which are the geometrical constraints of Friedmann type. It has been proved that the constraints can imitate force. As well as in quantum geometrodynamics with Logunov constraints, in quantum mechanics with constraints time does not vanish

Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Proceedings of the Estonian Academy of Sciences is the property of Teaduste Akadeemia Kirjastus and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In many circumstances the perfect fluid conservation equations can be directly integrated to give a geometric-thermodynamic equation: typically that the lapse N is the reciprocal of the enthalphy h, (N = 1/h). This result is aesthetically appealing as it depends only on the fluid conservation equations and does not depend on specific field equations such as Einstein's. Here the form of the geometric-thermodynamic equation is derived subject to spherical symmetry and also for the shift-free ADM formalism. There at least three applications of the geometric-thermodynamic equation, the most important being to the notion of asymptotic flatness and hence to spacetime exterior to a star. For asymptotic flatness one wants h → 0 and N → 1 simultaneously, but this is incompatible with the geometric-thermodynamic equation. Observational data and asymptotic flatness are discussed. It is argued that a version of Mach's principle does not allow asymptotic flatness.

As gravitation and electromagnetism are closely analogous long-range interactions, and the current formulation of gravitation is given in terms of geometry, we expect the latter also to appear through the geometry. This unification has however, remained an unfulfilled goal. The goal is achieved here in a new theory, which results from the principles of equivalence and Mach supplemented with a novel insight that the field tensors in a geometric theory of gravitation and electromagnetism must be traceless, since these long-range interactions are mediated by virtual exchange of massless particles whose mass is expected to be related to the trace of the field tensors. Hence, the Riemann tensor, like the analogous electromagnetic field tensor, must be traceless. Thence emerges a scale-invariant, Machian theory of gravitation and electrodynamics unified, wherein the vanishing of the Ricci tensor appears as a boundary condition. While the field equations of the theory are given by the vanishing divergence of the respective field tensors and their duals, the matter and charge emerge from the spacetime. A quantitative formulation thereof, embodied in "energy-momentum super tensors", follows from the respective Bianchi identities for the two fields. The resulting theory is valid at all scales and explains the observations without invoking the non-baryonic dark matter, dark energy or inflation. Moreover, it answers the questions that the general relativity-based standard paradigm could not address. [ABSTRACT FROM AUTHOR]

Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A technique for making probe measurements of the parameters of a plasma rotating in crossed radial electric and axial magnetic fields is described. Unlike the commonly used method, the processing of readings of the Langmuir triple probe was carried out using the results of measurements based on a Mach plasma probe. When using a magnetic field produced in a solenoid without end-to-end magnetic plugs, a positive potential with respect to the grounded anode and outer metal tube is observed in the plasma that arrives from the electric discharge source with the thermoemission cathode and the annular anode. It is shown that the speed of azimuthal electron drift in the crossed-fields system under investigation is much higher than the ion rotation speed. [ABSTRACT FROM AUTHOR]

Copyright of Physics Essays is the property of Physics Essays Publication and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

For a high-speed rotor in a magnetically suspended control moment gyroscope (MSCMG), the gyroscopic effect is one of its prominent characteristics. To improve the control stability of this kind of high-speed rotor in an MSCMG, an extremely important parameter of the rotor named the inertia ratio is defined originally and its effects on the rotor's gyroscopic effect are analysed theoretically by simplifying the rotor into a standard model during its mechanical design precessing. This research indicates that the inertia ratio of a rotor is determined not only by the rotor's mass and material density, but also by its generalized stiffness and shape coefficient. For an MSCMG with speed 12,000 rev/min and angular momentum 200 Nms, the optimized range of the rotor's inertia ratio can be selected as 1.780-1.9, which is more accurate than the experimental one (1.4-2.0). In this case, the precession frequency is reduced by 19.2%, the mass is reduced by 4.63% and angular momentum is increased by 24.45%. This paper will provide helpful hints for the design and optimization of a high-speed rotor. [ABSTRACT FROM AUTHOR]

A non-relativistic theory of inertia based on Mach’s principle is presented as has been envisaged, but not achieved, by Ernst Mach in 1872. The central feature is a space-dependent, anisotropic, symmetric inert mass tensor. The contribution of a mass element d m to the inertia of a particle m 0 experiencing an acceleration from rest is proportional to cos 2 α , where α is the angle between the line connecting m 0 and d m and the direction of the acceleration. Apsidal precession for planets circling around a central star is not a consequence of this theory, thereby avoiding the prediction of an apsidal precession with the wrong sign as is done by Mach-like theories with isotropic inert mass.

Mach's principle asserts that the inertial mass of a body is related to the distribution of other distant bodies. This means that in the absence of other bodies, a single body has no mass. In this case, talking about motion is not possible, because the detection of motion is possible only relative to other bodies. But in physics we are faced with situations that are not fully Machian. As in the case of general theory of relativity where geodesics exist in the absence of any matter, the motion has meaning. Another example which is the main topic of our discussion, refers to Bohmian quantum mechanics, where the inertial mass of a single particle does not vanish, but is modified. We can call such situations in which motion or mass of a single particle has meaning, pseudo-Machian situations. In this paper, we use the Machian or pseudo-Machian considerations to clarify under what circumstances and how a Machian effect leads us to Bohmian quantum mechanics. Then, we shall get the Bohmian quantum potential and its higher order terms for the Klein-Gordon particle through Machian considerations, without using any quantum mechanical postulate or operator formalism. [ABSTRACT FROM AUTHOR]

The experimental study of gravity became much more active in the late 1950s, a change pronounced enough be termed the birth, or naissance, of experimental gravity physics. I present a review of developments in this subject since 1915, through the broad range of new approaches that commenced in the late 1950s, and up to the transition of experimental gravity physics to what might be termed a normal and accepted part of physical science in the late 1960s. This review shows the importance of advances in technology, here as in all branches of natural science. The role of contingency is illustrated by Robert Dicke's decision in the mid-1950s to change directions in mid-career, to lead a research group dedicated to the experimental study of gravity. The review also shows the power of nonempirical evidence. Some in the 1950s felt that general relativity theory is so logically sound as to be scarcely worth the testing. But Dicke and others argued that a poorly tested theory is only that, and that other nonempirical arguments, based on Mach's Principle and Dirac's Large Numbers hypothesis, suggested it would be worth looking for a better theory of gravity. I conclude by offering lessons from this history, some peculiar to the study of gravity physics during the naissance, some of more general relevance. The central lesson, which is familiar but not always well advertised, is that physical theories can be empirically established, sometimes with surprising results. [ABSTRACT FROM AUTHOR]

Relational mechanics is a gauge theory of classical mechanics whose laws do not govern the motion of individual particles but the evolution of the distances between particles. Its formulation gives a satisfactory answer to Leibniz's and Mach's criticisms of Newton's mechanics: relational mechanics does not rely on the idea of an absolute space. When describing the behavior of small subsystems with respect to the so called 'fixed stars', relational mechanics basically agrees with Newtonian mechanics. However, those subsystems having huge angular momentum will deviate from the Newtonian behavior if they are described in the frame of fixed stars. Such subsystems naturally belong to the field of astronomy; they can be used to test the relational theory. [ABSTRACT FROM AUTHOR]

A novel, highly sensitive double-parameter sensor based on the composite interference structure has been designed and implemented in this paper. It can be regarded as a cascade of the traditional single-mode fiber (SMF)–hollow-core fiber (HCF)–photonic crystal fiber (PCF)-SMF structure, which forms a reflected Fabry–Perot interferometer and a transmitted Mach–Zehnder interferometer at the same time. The HCF is filled with ethanol, which is sensitive to temperature. Then the simultaneous measurement of the temperature and the refractive index (RI) can be achieved by monitoring the reflected spectrum and transmitted spectrum. The fact that these two spectrums do not interfere with each other makes it easier to obtain a demodulation method for simultaneous temperature and RI measurement that does not involve complex fast Fourier transform and matrix computation. The sensitivities of the temperature and the RI can reach up to 0.454 nm/°C and 178.7 nm/RIU, respectively. [ABSTRACT FROM AUTHOR]

In a cosmological perspective, gravitational induction is explored as a source to mechanical inertia in line with Mach’s principle. Within the standard model of cosmos, considering the expansion of the universe and the necessity of retarded interactions, it is found that the assumed dynamics may account for a significant part of an object’s inertia.

The equivalence principle is the conceptual basis for general relativity. In contrast, Mach's principle, although said to have been influential on Einstein in his formulation of general relativity, has not been shown to be central to the structure of general relativity. In this paper, we suggest that the quantum effects of Hawking and Unruh radiation are a manifestation of a thermal Mach's principle, where the local thermodynamic properties of the system are determined by the nonlocal structure of the quantum fields which determine the vacuum of a given spacetime. By comparing Hawking and Unruh temperatures for the same local acceleration we find a violation of the Einstein elevator version of the equivalence principle, which vanishes in the limit that the horizon is approached. [ABSTRACT FROM AUTHOR]

The article discusses the history of the debates on relativistic cosmology from 1917-1924. Topics mentioned include the gravitation theory of scientist Albert Einstein, the plan in 1917 to launch eclipse expeditions that will test the light bending in vicinity of the sun, and the articulation on the three assumptions such as principle of equivalence, principle of relativity and Mach's principle.

A new solution of Einstein's vacuum field equations is discovered which appears as a generalization of the well-known Ozsváth-Schücking solution and explains its source of curvature which has otherwise remained hidden. Curiously, the new solution has a vanishing Kretschmann scalar and is singularity-free despite being curved. The discovery of the new solution is facilitated by a new insight which reveals that it is always possible to define the source of curvature in a vacuum solution in terms of some dimensional parameters. As the parameters vanish, so does the curvature. The new insight also helps to make the vacuum solutions the Machian solutions. [ABSTRACT FROM AUTHOR]