## No full-text available

To read the full-text of this research,

you can request a copy directly from the authors.

Basic foundational aspects of both quantum theory and relativity might induce
to represent the physical vacuum as an underlying highly turbulent fluid. By
explicit numerical simulations, we show that a form of statistically isotropic
and homogeneous vacuum turbulence is entirely consistent with the present
ether-drift experiments. In particular, after subtracting known forms of
disturbances, the observed stochastic signal requires velocity fluctuations
whose absolute scale is well described by the average Earth's motion with
respect to the Cosmic Microwave Background. We emphasize that the existence of
a genuine stochastic ether drift could be crucial for the emergence of forms of
self-organization in matter and thus for the whole approach to complexity.

To read the full-text of this research,

you can request a copy directly from the authors.

... By comparing with the motion of a body in a fluid, this traditional view corresponds to the form of regular ("laminar") flow in which global and local velocity fields coincide. Some general arguments (see [41,42]) suggest instead that the physical vacuum might behave as a stochastic medium that resembles a turbulent fluid in which large-scale and small-scale flows are only indirectly related. This means that the projection of the global velocity field at the site of the experiment, sayṽ µ (t), could differ non-trivially from the local field v µ (t), which determines the direction and magnitude of the drift in the plane of the interferometer. ...

... However, in principle, a definite instantaneous value ∆c θ (t) c = 0 could also coexist with a vanishing statistical average. This possibility was considered in [37][38][39][40][41][42] by assuming that the observed signal is determined by a local velocity field, say v µ (t), which does not coincide with the projection of the global Earth motion, sayṽ µ (t), at the observation site. By comparing with the motion of a body in a fluid, the equality v µ (t) =ṽ µ (t) amounts to the assumption of a form of regular, laminar flow where global and local velocity fields coincide. ...

The dominant CMB dipole anisotropy is a Doppler effect due to a particular motion of the solar system with a velocity of 370 km/s. Since this derives from peculiar motions and local inhomogeneities, one could meaningfully consider a fundamental frame of rest Σ associated with the Universe as a whole. From the group properties of Lorentz transformations, two observers, individually moving within Σ, would still be connected by the relativistic composition rules. However, the ultimate implications could be substantial. Physical interpretation is thus traditionally demanded in order to correlate some of the dragging of light observed in the laboratory with the direct CMB observations. Today, the small residuals—from those of Michelson–Morley to present experiments with optical resonators—are just considered instrumental artifacts. However, if the velocity of light in the interferometers is not the same parameter “c” of Lorentz transformations, nothing would prevent a non-zero dragging. Furthermore, the observable effects would be much smaller than what is classically expected and would most likely be of an irregular nature. We review an alternative reading of experiments that leads to remarkable correlations with the CMB observations. Notably, we explain the irregular 10−15 fractional frequency shift presently measured with optical resonators operating in vacuum and solid dielectrics. For integration times of about 1 s and a typical Central European latitude, we also predict daily variations of the Allan variance in the range (5÷12)·10−16.

... In his long scientific activity Blinov offers a concept of gravity as a form of energy transfer from space to objects [34], a concept similar to that proposed [35] by Petry. Cahill identifies aether with flowing space [36], while Consoli and coauthors prefer a flowing aether in the form of a Bose-Einstein condensate [37]. ...

... Therefore, to explain the irregular character of the data, the original idea of refs. [69,70] was to model this vacuum as a turbulent fluid or, more precisely, as a fluid in the limit of zero viscosity 14 . Then, the simple picture of a laminar flow is no more obvious due to the subtlety of the infinite-Reynolds-number limit, see e.g. ...

"Non-Locality is most naturally incorporated into a theory in which there is a special frame of reference. One possible candidate for this special frame of reference is the one in which the Cosmic Microwave Background (CMB) is isotropic. However, other than the fact that a realistic interpretation of quantum mechanics requires a preferred frame and the CMB provides us with one, there is no readily apparent reason why the two should be linked" (L. Hardy). Starting from this remark we first argue that, given the present view of the vacuum, the basic tenets of Quantum Field Theory cannot guarantee that Einstein Special Relativity, with no preferred frame, is the physically realized version of relativity. Then, to try to understand the nature of the hypothetical preferred $\Sigma-$frame, we consider the so called ether-drift experiments, those precise optical measurements that try to detect in laboratory a small angular dependence of the two-way velocity of light and then to correlate this angular dependence with the direct CMB observations with satellites in space. By considering all experiments performed so far, from Michelson-Morley to the present experiments with optical resonators, and analyzing the small observed residuals in a modern theoretical framework, the long sought $\Sigma-$ frame tight to the CMB naturally emerges. Finally, if quantum non-locality reflects some effect propagating at vastly superluminal speed $v_{QI} \to \infty $, its ultimate origin could be hidden somewhere in the infinitely large speed $c_s \to \infty$ of the vacuum density fluctuations.

... Therefore, to explain the irregular character of the data, the original idea of refs. [63,64] was to model this vacuum as a turbulent fluid or, more precisely, as a fluid in the limit of zero viscosity 14 . Then, the simple picture of a laminar flow is no more obvious due to the subtlety of the infinite-Reynolds-number limit; see, e.g., Section 41.5 in Vol. ...

“Non-locality is most naturally incorporated into a theory in which there is a special frame of reference. One possible candidate for this special frame of reference is the one in which the Cosmic Microwave Background (CMB) is isotropic. However, other than the fact that a realistic interpretation of quantum mechanics requires a preferred frame and the CMB provides us with one, there is no readily apparent reason why the two should be linked” (L. Hardy). Starting from this remark, we first argue that, given the present view of the vacuum, the basic tenets of Quantum Field Theory cannot guarantee that Einstein Special Relativity, with no preferred frame, is the physically realized version of relativity. Then, to try to understand the nature of the hypothetical preferred Σ−frame, we consider the so-called ether drift experiments, those precise optical measurements that try to detect, in the laboratory, a small angular dependence of the two-way velocity of light and then to correlate this angular dependence with the direct CMB observations with satellites in space. By considering all experiments performed so far, from Michelson–Morley to the present experiments with optical resonators, and analyzing the small observed residuals in a modern theoretical framework, the long-sought Σ− frame tight to the CMB naturally emerges. Finally, if quantum non-locality reflects some effect propagating at vastly superluminal speed vQI→∞, its ultimate origin could be hidden somewhere in the infinite speed cs→∞ of vacuum density fluctuations.

... In his master thesis Ngucho (2019) is aware that the existence of a thin material field can lead to a slow kinetics energy loss of the planets along their orbits. In his long activity Blinov (2012) has a concept of gravity acting as a transfer of energy from space to objects, and Cahill (2009) identifies the aether with a flowing space, while Consoli et al. (2014) prefer a flowing aether constituted by a Bose-Einstein condensate. Also the concept of Euler of an aether causing gravity by pressure gradient is cultivated today (Arminjon, 2004). ...

From Earth Sciences and geoneutrino experiments Borexino and KamLAND come clues on a role of the aether in the geological evolution of Earth and planets, and of all the structures of the universe. Through the problem of the storage of the aether arriving into the heavenly bodies, hydrodynamic explanation of gravitation is found closely related to the concept of the expanding Earth. Variable radius paleogeography allows a rough evaluation of the amount of ordinary matter that is added to the planet in the time unity, and the statement of some inferences on the Earth's inner energy balance. With the help of astrophysics the aether's density, flow rate, and velocity are computed. The origin of the cosmological redshift and the gravitational redshift is unified to the cause of gravitation, with a concept similar, but not coincident, with that of tired light, considered very plausible by cosmologists such as Edwin Hubble and Fritz Zwicky. A superluminal aether's speed at the Earth's surface is found. INFN experiments confirm hydrodynamic gravitation and superluminal velocities, and it is possible to highlight an interrelations of aether parameters with the actually known cosmological parameters H 0 , G, c. The unification of the hydrodynamic gravitation and the expansion of the heavenly bodies, through the existence of a little dissipative force, a non-Newtonian concept, is linked to a revision of the theories of physics and cosmology, in which the actually accepted physics laws are only good approximations of a more complex reality.

... Some have already been carried out, others are ongoing in both small and large scale physics. In small scale physics there have been experiments attempting to reveal a privileged Lorentz' reference system, as proposed by a group of the Catania INFN (Consoli et al., 2014), and studies conducted at the Flinders University of Adelaide in Australia (Cahill, 2009). Ether has been a stone-guest of science for a long time and even initial deniers were and are now forced to take it seriously (Kostro, 2001; see also the text of Einstein's lecture of 1922, dedicated to this physical entity). ...

In the March 2019 issue of the Rendiconti Online of the
SGI, a geologist continued his attack on the theory of terrestrial
expansion (Sudiro, 2019), this time focusing on the implications that
paleomagnetic data, particularly the paleopoles, have as evidence for
the expanding Earth concept. An initial more general publication
on the subject by the same author appeared in the EGU History of
the Earth Sciences journal in 2014 (Sudiro, 2014). The present paper
demonstrates the inadequacy of many of the criticisms formulated
in the above publications, making it clear that the expanding Earth
is not an out-dated idea from the historical-scientific contingencies
of the past, but instead a scientific concept that is very much alive
and with very interesting future prospects. The evidential value of the
paleopole data and catalogues is specifically defended here, together
with the TPW and its link to the opening of the Pacific Ocean.
The numerous lines of research that have emerged on the basis of
expanding Earth are briefly described in a non-exhaustive review. The
failure to recognise the expansion of celestial bodies as a phenomenon
could be a contributing factor to the current state of crisis in Physics
and Cosmology.

... Questi esperimenti sono stati già effettuati, e continuano ad essere in corso, sia nella piccola che nella grande fisica. Nella piccola fisica ricordo gli esperimenti per tentare di rivelare un sistema di riferimento privilegiato Lorentziano progettati da un gruppo dell'INFN di Catania (Consoli et al., 2014) e quelli condotti alla Flinders University di Adelaide in Australia (Cahill, 2009). Il grande convitato di pietra della scienza, non solo contemporanea, si chiama etere e a lui ha dovuto inchinarsi anche chi inizialmente lo aveva escluso (Kostro, 2001; si veda anche il testo della conferenza di Einstein del 1922, dedicato a questa entità fisica). ...

Una risposta ad articoli negazionisti della espansione terrestre

... It has not yet been possible to choose between the various types of ether, mainly because experimental data are lacking. The experiments of Cahill and Consoli (Cahill 2009;Consoli et al. 2014) reveal the existence of an ether background, but not its characteristics. Returning to Newton's difficulties in theorising different ethers, could it be that their multiplicity is real? ...

This article is written in honor of my mentor Franco Selleri who has helped to consolidate my awareness of the existence of a medium subtended to ordinary matter, and from which everything comes. From my field, the Earth Sciences, come clues converging on an important role of the ether in the geological evolution of Earth and planets, as well as all the structures of the universe. Paleogeographic reconstructions allow a rough quantitative evaluation of the amount of new ordinary matter that is added to the planet in the unity of time, and the consequent statement of some cosmological consequences and on the inner energy balance of the Earth. The concept of central flow of ether defended here is different from the Lorentian stationary ether, but the two concepts could be made compatible.

... Other effects. A third option in explaining the experimental results of Dai is to consider them caused by (i) the "anisotropy of space" (as experimentally investigated over decades by Shnoll et al. [12][13][14][15][16][17]), interaction with (ii) the (quantum) vacuum (which, according to experimental findings of Graham and Lahoz, can be regarded as "something in motion" [18]), (iii) a "cosmological vector potential" [19], or (iv) a fundamental medium [20][21][22][23][24][25][26][27][28][29][30][31], also regarded as a "complex tension field" [32]. In this context, a relation of the observed anisotropic diffusion to the Saganc effect [33][34][35][36] should be considered too. ...

Anisotropic diffusion patterns of a toluidine blue colloid solution in water were recently reported by J. Dai (Nat. Sci., 2014, v. 6 (2), 54–58). According to Dai's observations the fluctuation of anisotropy showed a diurnal and annual periodicity. Since these obser-vations were only qualitatively described in the original manuscript, the data was re-assessed by performing a detailed statistical analysis. The analysis revealed that indeed (i) the diffusion patterns exhibit a non-random characteristic (i.e. the maximum diffu-sion trend is not uniformly distributed), and (ii) a diurnal as well as an annual oscillation could be extracted and modeled with a sinusoidal function. In conclusion, the present analysis supports Dai's findings about anisotropy in diffusion of colloids in water with a daily and annual periodicity. Possible explanations of the observed effect are discussed and suggestions for further experiments are given.

The possibility to correlate ether-drift measurements in laboratory and direct CMB observations with satellites in space would definitely confirm the existence of a fundamental preferred frame for relativity. Today, the small residuals observed so far (from Michelson-Morley onward) are just considered typical instrumental effects in experiments with better and better sensitivity. Though, if the velocity of light propagating in the various interferometers is not exactly the same parameter c of Lorentz transformations, nothing would really prevent to observe an ether drift. Thus, for the Earth cosmic velocity v = 370 km/s, we argue that a fundamental 10-15 light anisotropy, as presently observed in vacuum and in solid dielectrics, is revealing a 10-9 difference in the vacuum effective refractivity between an apparatus in an ideal freely falling frame and an apparatus on the Earth surface. In this perspective, the stochastic nature of the physical vacuum could also explain the irregular character of the signal and the observed substantial reduction from its instantaneous 10-15 value to its statistical average 10-18 (or smaller). For the same v = 370 km/s the different refractivities, respectively, O(10-4) and O(10-5) for air or helium at atmospheric pressure, could also explain the observed light anisotropy, respectively O(10-10) and O(10-11) . However, for consistency, one should also understand the physical mechanism which enhances the signal in weakly bound gaseous matter but remains ineffective in solid dielectrics where the refractivity is O(1) . This mechanism is naturally identified in a non-local, tiny temperature gradient of a fraction of millikelvin which is found in all classical experiments and might ultimately be related to the CMB temperature dipole of ±3 mK or reflect the fundamental energy flow associated with a Lorentz-non-invariant vacuum state. The importance of the issue would deserve more stringent tests with dedicated experiments and significant improvements in the data analysis.-1

This this article is written in honor of my mentor Franco Selleri who has helped to consolidate my awareness of the existence of a medium subtended to ordinary matter, and from which everything comes. From my field, the Earth Sciences, come clues converging on an important role of the ether in the geological evolution of Earth and planets, as well as all the structures of the universe. Paleogeographic reconstructions allow a rough quantitative evaluation of the amount of new ordinary matter that is added to the planet in the unity of time, and the consequent statement of some co-smological consequences and on the inner energy balance of the Earth. The concept of central flow of ether defended here is different from the Lorentian stationary ether, but the two concepts could be made compatible.

"Ether-drift" experiments have played a crucial role for the origin of relativity. Though, a recent re-analysis shows that those original measurements where light was still propagating in gaseous systems, differently from the modern experiments in vacuum and in solid dielectrics, indicate a small universal anisotropy which is naturally interpreted in terms of a non-local thermal gradient. We argue that this could possibly be the effect, on weakly bound gaseous matter, of the temperature gradient due to the Earth's motion within the Cosmic Background Radiation (CBR). Therefore, a check with modern laser interferometers is needed to reproduce the conditions of those early measurements with today's much greater accuracy. We emphasize that an unambiguous confirmation of our interpretation would have far-reaching consequences. For instance, it would imply that all physical systems on the moving Earth are exposed to a tiny energy flow, an effect which, in principle, could also induce forms of self-organization in matter.

The discovery of the Higgs boson at LHC confirms that what we experience as empty space should actually be thought as a condensate of elementary quanta. This condensate characterizes the physically realized form of relativity and could play the role of preferred reference frame in a modern Lorentzian approach. This observation suggests a new interpretative scheme to understand the unexplained residuals in the old ether-drift experiments where light was still propagating in gaseous systems. Differently from present vacuum experiments, where anyhow deviations from Special Relativity are expected to be at the limit of visibility, these now acquire a crucial importance and become consistent with the Earth’s velocity of 370 km/s which characterizes the CMB anisotropy. In the same scheme, one can also understand the difference with the other experiments where light propagates in strongly bound systems such as solid or liquid transparent media. This non-trivial level of consistency motivates a new generation of precise laser interferometry experiments which explore the same particle physics vacuum and, in this sense, are complementary to those with high-energy accelerators.

The velocity field of homogeneous isotropic turbulence is simulated by a large number (38–1200) of random Fourier modes varying in space and time over a large number (> 100) of realizations. They are chosen so that the flow field has certain properties, namely (i) it satisfies continuity, (ii) the two-point Eulerian spatial spectra have a known form (e.g. the Kolmogorov inertial subrange), (iii) the time dependence is modelled by dividing the turbulence into large- and small-scales eddies, and by assuming that the large eddies advect the small eddies which also decorrelate as they are advected, (iv) the amplitudes of the large- and small-scale Fourier modes are each statistically independent and each Gaussian. The structure of the velocity field is found to be similar to that computed by direct numerical simulation with the same spectrum, although this simulation underestimates the lengths of tubes of intense vorticity.

The problem of the propagation of small disturbances of the averaged field of velocities, Reynolds stresses and the pressure in an incompressible turbulent medium, with negligible molecular and turbulent diffusions, is considered. The availability of a limit velocity of such a propagation and the existence of a characteristic cone similar to the Mach cone are discussed. A characteristic equation analogous to the equation of ``C+/--characteristics'' in gas dynamics is derived. The calculation of the geometry of the initial part of a plane turbulent jet running out of the channel into a rest liquid is carried out. Angles of slopes of straight lines of internal and external boundaries of the mixing layer of a jet near the exit section of a channel are related to distributions of steady velocity and Reynolds stresses in the channel. The formal analogy existing between waves of small disturbances of an inviscous and incompressible turbulent medium and electromagnetic waves is established.

We show that the special relativistic dynamics when combined with quantum
mechanics and the concept of superstatistics can be interpreted as arising from
two interlocked non-relativistic stochastic processes that operate at different
energy scales. This interpretation leads to Feynman amplitudes that are in the
Euclidean regime identical to transition probability of a Brownian particle
propagating through a granular space. Some kind of spacetime granularity could
be held responsible for the emergence at larger scales of various symmetries.
For illustration we consider also the dynamics and the propagator of a spinless
relativistic particle. Implications for doubly special relativity, quantum
field theory, quantum gravity and cosmology are discussed.

We examine the interplay between recent advances in quantum gravity and the problem of turbulence. In particular, we argue that in the gravitational context the phenomenon of turbulence is intimately related to the properties of spacetime foam. In this framework we discuss the relation of turbulence and holography and the interpretation of the Kolmogorov scaling in the quantum gravitational setting.

We demonstrate that the emergence of a curved spacetime `effective Lorentzian geometry' is a common and generic result of linearizing a classical scalar field theory around some non-trivial background configuration. This investigation is motivated by considering the large number of `analogue models' of general relativity that have recently been developed based on condensed matter physics, and asking whether there is something more fundamental going on. Indeed, linearization of a classical field theory (that is, a field-theoretic `normal-mode analysis') results in fluctuations whose propagation is governed by a Lorentzian-signature curved spacetime `effective metric'. In the simple situation considered in this paper (a single classical scalar field), this procedure results in a unique effective metric, which is quite sufficient for simulating kinematic aspects of general relativity (up to and including Hawking radiation). Upon quantizing the linearized fluctuations around this background geometry, the one-loop effective action is guaranteed to contain a term proportional to the Einstein-Hilbert action of general relativity, suggesting that while classical physics is responsible for generating an `effective geometry', quantum physics can be argued to induce an `effective dynamics'. The situation is strongly reminiscent of, though not identical to, Sakharov's `induced-gravity' scenario, and suggests that Einstein gravity is an emergent low-energy long-distance phenomenon that is insensitive to the details of the high-energy short-distance physics. (We mean this in the same sense that hydrodynamics is a long-distance emergent phenomenon, many of whose predictions are insensitive to the short-distance cut-off implicit in molecular dynamics.)

Using a density matrix description in space we study the evolution of wavepackets in a fluctuating spacetime background. We assume that spacetime fluctuations manifest as classical fluctuations of the metric. From the non-relativistic limit of a non-minimally coupled Klein–Gordon equation, we derive a Schrödinger equation with an additive Gaussian random potential. This is transformed into an effective master equation for the density matrix. The solutions of this master equation allow us to study the dynamics of wavepackets in a fluctuating spacetime, depending on the fluctuation scenario. We show how different scenarios alter the diffusion properties of wavepackets.

We report on a test of the isotropy of light propagation performed by comparing the resonance frequencies of two orthogonal cryogenic optical resonators subject to Earths rotation over 1yr. The technical aspects of the experiment are discussed and the analysis of the data is presented in detail. For a possible anisotropy of the speed of light c, we obtain c/c0=(2.61.7)10-15. Within the general extension of the standard model of particle physics, we extract limits on seven parameters at accuracies down to 10-15, improving the best previous result by about two orders of magnitude. Within the Robertson–Mansouri–Sexl test theory, this implies an isotropy-violation parameter --1/2=(2.21.5)10-9, about three times lower than the best previous result.

With the use of a quantity normally scaled in multifractals, a generalized form is postulated for entropy, namelyS
q
k [1 –
i=1
W
p
i
q
]/(q-1), whereq characterizes the generalization andp
i are the probabilities associated withW (microscopic) configurations (W). The main properties associated with this entropy are established, particularly those corresponding to the microcanonical and canonical ensembles. The Boltzmann-Gibbs statistics is recovered as theq1 limit.

The role of convention in various definitions of clock synchronization and simultaneity is investigated. We show that two principal methods of synchronization can be considered: system internal and system external synchronization. Synchronization by the Einstein procedure and by slow clock transport turn out to be equivalent if and only if the time dilatation factor is given by the Einstein result (1–v
2)1/2. An ether theory is constructed that maintains absolute simultaneity and is kinematically equivalent to special relativity.

During the last 30 years Kip Thorne has had the joy of participating in a great quest. The quest to understand Einstein's general theory of relativity and its predictions about the universe, and the quest to discern where and how Einstein's theory fails and what then replaces it. This quest has lead him through the labyrinths of exotic objects: black holes, white dwarfs, neutron stars, singularities, gravitational waves, worm-holes and yes, even time machines. The quest, with its hundreds of participants scattered over the globe has led him to appreciate the international character of science, the different ways that scientific enterprise is organized in different societies, and the inexorable manner in which science bas been intertwined with political currents, especially the Soviet/American conflict. This book is the author's attempts to share these insights with lay readers, and the scientists who work in fields other than his. A book of many interlocking themes held together by a thread of history; the history of the development of our times about curved space and warped time, and most especially black holes.

This book focuses on nonextensive statistical mechanics, a current generalization of Boltzmann-Gibbs (BG) statistical mechanics, one of the greatest monuments of contemporary physics. Conceived more than 130 years ago by Maxwell, Boltzmann and Gibbs, the BG theory exhibits many impressive successes in physics, chemistry, mathematics, and computational sciences. Presently, several thousands of publications by scientists around the world have been dedicated to its nonextensive generalization. A variety of applications have emerged in complex systems and its mathematical grounding is by now well advanced. A pedagogical introduction to its concepts - nonlinear dynamics, extensivity of the nonadditive entropy, global correlations, and extensions of the standard central limit theorems, among others - is presented in this book, as well as a selection of paradigmatic applications in various sciences and diversified experimental verifications of some of its predictions. Introduction to Nonextensive Statistical Mechanics is suitable for students and researchers with an interest in complex systems and statistical physics. © Springer Science+Business Media, LLC 2009. All rights reserved.

In some classical contexts, Lorentz symmetry emerges from a microscopic
Lorentz non-symmetric framework represented as an underlying turbulent
fluid. I argue that, with some approximations and in a certain range of
the basic parameters, the same intuitive representation is obtained from
Landau's original form of quantum hydrodynamics. This general picture of
the vacuum, where the observed space-time symmetries have a
kinetic basis, suggests an alternative reading of the stochastic signal
observed in the present ether-drift experiments and, as such, is not a
pure speculative issue but might have non-trivial physical implications.

We examine the hypothesis that every particle of mass m is subject to a Brownian motion with diffusion coefficient ℏ/2m and no friction. The influence of an external field is expressed by means of Newton's law F=ma, as in the Ornstein-Uhlenbeck theory of macroscopic Brownian motion with friction. The hypothesis leads in a natural way to the Schrödinger equation, but the physical interpretation is entirely classical. Particles have continuous trajectories and the wave function is not a complete description of the state. Despite this opposition to quantum mechanics, an examination of the measurement process suggests that, within a limited framework, the two theories are equivalent.

The Einstein Lagrangian allows large fluctuations of the metric and topology of spacetime on scales of order of the Planck length. This foam-like structure can be described by introducing a Λ term as a Lagrange multiplier for the 4-volume. The dominant contribution to the path integral seems to come from metrics which have about one unit of topology per Planck volume.

We present an improved laboratory test of Lorentz invariance in electrodynamics by testing the isotropy of the speed of light. Our measurement compares the resonance frequencies of two orthogonal optical resonators that are implemented in a single block of fused silica and are rotated continuously on a precision air bearing turntable. An analysis of data recorded over the course of one year sets a limit on an anisotropy of the speed of light of c/c1x10¹. This constitutes the most accurate laboratory test of the isotropy of c to date and allows to constrain parameters of a Lorentz violating extension of the standard model of particle physics down to a level of 10¹.

I show that it is possible to formulate the Relativity postulates in a way that does not lead to inconsistencies in the case of spacetimes whose short-distance structure is governed by an observer-independent length scale. The consistency of these postulates proves incorrect the expectation that modifications of the rules of kinematics involving the Planck length would necessarily require the introduction of a preferred class of inertial observers. In particular, it is possible for every inertial observer to agree on physical laws supporting deformed dispersion relations of the type E2-c2 p2-c4m2 + f(E, p, m; Lp) =0, at least for certain types of f.

The swirling motion of fluids that occurs irregularly in space and time is called turbulence. However, this randomness, apparent from a casual observation, is not without some order. Turbulent flows are as abundant in nature as life itself, and are pervasive in technology. They are a paradigm for spatially extended nonlinear dissipative systems in which many length scales are excited simultaneously and coupled strongly. The phenomenon has been studied extensively in engineering and in diverse fields such as astrophysics, oceanography, and meteorology. A few aspects of turbulence research in this century are briefly reviewed, and a partial assessment is made of the present directions.

This paper is a Russian translation by M. L. Gorodetskij of Chapter 7 of the English version. For the monography see 61.003.008.

The Planck radiation law for the blackbody radiation spectrum is derived without the formalism of quantum theory. The hypotheses assume (a) the existence, at the absolute zero of temperature, of classical homogeneous fluctuating electromagnetic radiation with a Lorentz-invariant spectrum; (b) that classical electrodynamics holds for a dipole oscillator; (c) that a free particle in equilibrium with blackbody radiation has the classical mean kinetic energy 12kT per degree of freedom. The Lorentz invariance of the spectrum of zero-temperature radiation is used to derive the zero-point electromagnetic energy-density spectrum, found to be linear in frequency, 12ℏω per normal mode. The procedures based on classical theory employed by Einstein and Hopf, which were formerly regarded as giving a rigorous derivation of the Rayleigh-Jeans radiation law, are modified and corrected for electromagnetic zero-point energy to allow a rigorous derivation of the full blackbody spectrum from classical theory without any assumptions of discrete or discontinuous processes.

This paper is a study of a statistical ensemble of classical harmonic oscillators which is stationary in time, and whose position and momentum distribution functions are those of the corresponding quantum-mechanical oscillator in its ground state. If the oscillating particle is charged, then in order to maintain the distribution stationary a certain random electromagnetic field must be present. The intensity distribution of the radiation field is calculated, and it is found to be identical with the 'photon vacuum' of quantum electrodynamics. It is suggested, therefore, that this radiation field, which in quantum field theory is treated entirely formally, might exist in the classical sense. The method is extended to the excited states. It is found that the classical ensembles corresponding to these have probability distributions which may be negative. However, when attention is shifted to the quantum-mechanical 'mixture', this is no longer the case. Furthermore, the intensity distribution of the radiation field at temperature T is shown to be simply the sum of the Planck distribution and the previously obtained zero-temperature field. The application of these results to statistical mechanics is discussed. In this paper the treatment is non-relativistic throughout, but radiative corrections of the type which give rise to the Lamb shift are an integral part of the theory.

A novel apparatus for a sensitive test of the independence of the speed of optical waves from the propagation direction has been developed. It employs a monolithic ULE glass structure containing two orthogonal, crossing Fabry–Perot cavities which enable common mode rejection of certain disturbances. Highly accurate locking and cavity frequency read-out are achieved using laser frequency modulation at audio frequencies. Several systematic effects were characterized. Without rotation the root Allan variance (RAV) of the beat frequency reaches a minimum of 0.5Hz (2×10−15) close to the thermal noise floor of the cavities. The performance of the apparatus under rotation is demonstrated by determining with improved accuracy one parameter of the standard model extension test theory, (κ˜e-)ZZ=(−1.0±2.3)×10−15, under simplifying assumptions.

We report on the results of a strongly improved test of local Lorentz invariance, consisting of a search for an anisotropy of the resonance frequencies of electromagnetic cavities. The apparatus comprises two orthogonal standing-wave optical cavities interrogated by a laser, which were rotated approximately 175 000 times over the duration of 13 months. The measurements are interpreted as a search for an anisotropy of the speed of light, within the Robertson-Mansouri-Sexl (RMS) and the standard model extension (SME) photon sector test theories. We find no evidence for an isotropy violation at a 1sigma uncertainty level of 0.6 parts in 10¹ (RMS) and 2 parts in 10¹ for seven of eight coefficients of the SME.

A gravitational theory compatible with Mach's principle was published recently by Brans and Dicke. It is characterized by a gravitational field of the Jordan type, tensor plus scalar field. It is shown here that a coordinate-dependent transformation of the units of measure can be used to throw the theory into a form for which the gravitational field appears in the conventional form, as a metric tensor, such that the Einstein field equation is satisfied. The scalar field appears then as a "matter field" in the theory. The invariance of physical laws under coordinate-dependent transformations of units is discussed.

Classical statistical thermodynamics in the presence of electromagnetic radiation is reanalyzed, and is reformulated to give a natural classical description of the phenomena which originally led to the introduction of the idea of quanta. The traditional classical ideal gas fails to exist in principle for particles of finite mass which have electromagnetic interactions, and hence the classical proofs of energy equipartition are all erroneous. A consistently classical treatment of thermal radiation leads to the natural introduction of temperature-independent fluctuating radiation in the universe. The spectrum of this electromagnetic zero-point radiation may be obtained from the arguments for Wien's displacement law or from the requirement of Lorentz invariance of the radiation spectrum; this zero-point spectrum agrees with the 12ℏomega per normal mode familiar in quantum theory. The presence of temperature-independent disordered energy from zero-point radiation leads to a contribution to the entropy connected with thermodynamic probability distinct from the contribution of caloric entropy. The use of quanta in calculations of the thermodynamic probability is seen as a subterfuge to account for this mismatch between caloric entropy and probability. Several examples of statistical thermodynamics, which are generally regarded as having their explanation in terms of quanta, allow natural explanations within the context of classical theory with classical electromagnetic zero-point radiation.

A pair of optical cavities are designed and set up so as to be insensitive to both temperature fluctuations and mechanical vibrations. With the influence of these perturbations removed, a fundamental limit to the frequency stability of the optical cavity is revealed. The stability of a laser locked to the cavity reaches a floor $<2\ifmmode\times\else\texttimes\fi{}{10}^{$-${}15}$ for averaging times in the range $0.5$-${}100$ s. This limit is attributed to Brownian motion of the mirror substrates and coatings.

A general comparison is presented between random electrodynamics and quantum electrodynamics for the two systems which can be solved exactly in both theories, free electromagnetic fields and point dipole oscillators. The N-point correlation functions of the fields are computed in both theories and are found to differ in general because of the dependence upon the order of the quantum operators within products of operators. However, if all products of quantum operators are symmetrized by taking all permutations of the operator order, then the two theories give identical results for the correlation functions. Analogous results hold to all orders in the fine-structure constant for dipole oscllators in quantum and random electrodynamics. The theories agree only if the quantum operator products are symmetrized. In the limit that the oscillator couplings to the radiation fields vanish, th oscllators can be regarded as mechanical oscillators in quantum mechanics and in random mechanics. The theory of random mechanics is defined in terms of this limit which uncouples a mechanical oscillator from the radiation field. The average values of oscillator variables in random mechanics agree with those of symmetrized products in quantum mechanics. The question is then raised as to the physical significance of the many quantum operators which differ only in the order of their factors. It is pointed out that some operator products which are regarded as physically important, such as the square of the angular momentum, indeed involve unsymmetrized products of operators. On this account the average values of the angular momentum squared in the ground state of an isotropic three-dimensional harmonic oscillator differ between the random-mechanical and quantum-mechanical descriptions. However, there seems to be no case in which experiments have shown that the (unsymmetrized) quantum operator value is to be preferred to that provided by random mechanics. The presence of thermal radiation is next treated for free electromagnetic fields and for dipole-oscillator systems. Despite extraordinary differences in the points of view toward thermal radiation taken by the two theories, the conclusion is the same as that found for zero temperature; the two theories agree in their average values if all products of quantum operators are symmetrized. Finally, as a further example of the power of random electrodynamics to give an account of phenomena where Lorentz's classical electron theory failed, we investigate the diamagnetism of a charged three-dimensional isotropic oscillator. The mathematical descriptions at finite temperature are developed in full random electrodynamics and quantum electrodynamics and in second-order perturbation theory in quantum mechanics.

DOI:https://doi.org/10.1103/RevModPhys.5.203

Applying simultaneously the principles of quantum mechanics and general
relativity we find an intrinsic limitation to quantum measurements of
space-time distances. The intrinsic uncertainty of a length is shown to
be proportional to the one third power of the length itself. This
uncertainty in space-time measurements implies an intrinsic uncertainty
of the space-time metric and yields quantum decoherence for particles
heavier than the Planck mass.

The detection of cosmic rays with unexpectedly high energies has
prompted a rethink of Einstein's theory of special relativity. A new
formulation, called 'doubly special relativity', might be the answer.

An expression is derived for the displacements in an isotropic elastic medium which contains an edge dislocation moving with uniform velocity c. When c=0 the solution reduces to that given by Burgers for a stationary edge dislocation. The energy density in the medium becomes infinite as c approaches c2, the velocity of shear waves in the medium; this velocity therefore sets a limit beyond which the dislocation cannot be accelerated by applied stresses. The atomic structure of the medium is next partly taken into account, following the method already used by Peierls and Nabarro for the stationary dislocation. The solution found in this way differs from the one in which the atomic structure is neglected only within a region of width ζ which extends not more than a few atomic distances from the centre. ζ varies with c and vanishes when c=cr, the velocity of Rayleigh waves. It becomes negative when cr< c<c2. Thus cr rather than c2 appears to be the limiting velocity when the atomic nature of the medium is taken into account. Since cr similar, equals 0.9c2 the difference is not of much importance.
The same method applied to a screw dislocation gives, in the purely elastic case, the expression already derived by Frank. The corresponding Peierls-Nabarro calculation shows that the width ζ is proportional to (1 - c2/c22)½. This "relativistic" behaviour is analogous to Frenkel and Kontorowa's results for their one-dimensional dislocation model.

Soliton properties of kinks on dislocations allow a definition of natural standards for the measurement of length and time which are inherently related to the lattice structure. If dynamical processes such as wave propagation and the motion of screw dislocations are expressed in terms of standards of such a kind, Lorentz symmetries associated with sound propagation become evident.Solitoneneigenschaften von Kinken auf Versetzungen erlauben eine Definition von Normalmaßstäben für die Längen- und Zeitmessung, die an die Gitterstruktur gebunden ist. Bezieht man dynamische Prozesse wie die Wellenausbreitung und die Bewegung von Schraubenversetzungen auf Maßstäbe dieser Art, so werden Lorentz-Symmetrien auf der Grundlage der Schallgeschwindigkeit sichtbar.

We prove that, when linearized, the governing equations of an incompressible viscoelastic continuum can be rendered into a form identical to that of Maxwell’s equations of electrodynamics. The divergence of deviator stress tensor is analogous to the electric field, while the vorticity (the curl of velocity field) is interpreted as the magnetic field. The elastic part of constitutive relation explains Maxwell’s displacement current, and is responsible for the propagation of gradient (shear) waves. In turn, the viscous part is associated with the Ampere’s and Ohm’s laws for the current. This analogy is extended further and the nonlinearity of the material time derivative (the advective part of acceleration) is interpreted as the Lorentz force. The classical wave equations of electrodynamics are also derived as corollaries. Thus an interesting and far reaching analogy between the viscoelastic continuum and the electrodynamics is established.

Modern ether-drift experiments look for a preferred frame by measuring the difference Δν in the relative frequencies of two cavity-stabilized lasers, upon local rotations of the apparatus or under the Earth's rotation. If the small deviations observed in the classical ether-drift experiments were not mere instrumental artifacts, by replacing the high vacuum in the resonating cavities with a dielectric gaseous medium (e.g., air), the typical measured Δν∼1 Hz should increase by orders of magnitude. This prediction is consistent with the characteristic modulation of a few kHz observed in the original experiment with He–Ne masers. However, if such enhancement would not be confirmed by new and more precise data, the existence of a preferred frame can be definitely ruled out.

The behavior of a classical charged point particle under the influence of
only a Coulombic binding potential and classical electromagnetic zero-point
radiation, is shown to yield agreement with the probability density
distribution of Schroedinger's wave equation for the ground state of hydrogen.
These results, obtained without any fitting parameters, again raise the
possibility that the main tenets of stochastic electrodynamics (SED) are
correct, thereby potentially providing a more fundamental basis of quantum
mechanics. The present methods should help propel yet deeper investigations
into SED.

We consider nonequilibrium systems with complex dynamics in stationary states with large fluctuations of intensive quantities (e.g. the temperature, chemical potential or energy dissipation) on long time scales. Depending on the statistical properties of the fluctuations, we obtain different effective statistical mechanical descriptions. Tsallis statistics follows from a χ2-distribution of an intensive variable, but other classes of generalized statistics are obtained as well. We show that for small variance of the fluctuations all these different statistics behave in a universal way.

(1) A wave equation is derived from the kinetic equations governing media with rotational as well as translational degrees of freedom. In this wave the fluctuating quantity is a vector, the bulk spin. The transmission is similar to compressive waves but propagation is possible even in the limit of incompressibility, where such disturbances could become dominant. (2) In this context a kinetic theory of space–time is introduced, in which hypothetical constituents of the space–time manifold possess such a rotational degree of freedom (spin). Physical fields (i.e., electromagnetic or gravitational) in such a theory are represented as moments of a statistical distribution of these constituents, as in the techniques of fluid mechanics. The spin wave equation from (1) is treated as a candidate for governing light and metric. Such a theory duplicates to first order Maxwell's equations of electromagnetism, Schrödinger's equation for the electron, and the Lorentz transformations of special relativity. Slight deviations from the classical approach are predicted and should be experimentally verifiable.