The geodesics and the curvature of a metric representing an isolated tachyon are investigated. It is argued that the properties are unphysical and inconsistent with observation, thus providing further evidence against the existence of tachyons.

Although the existence of tachyons is not ruled out by special relativity, it appears that causal paradoxes will arise if there are tachyons. The usual solutions to these paradoxes employ some form of the reinterpretation principle. In this paper it is argued first that the principle is incoherent, second that even if it is not, some causal paradoxes remain, and third, the most plausible “solution,” which appeals to boundary conditions of the universe, will conflict with special relativity.

Tachyon paradoxes, including causality paradoxes, have persisted within tachyon theories and left little hope for the existence of observable tachyons. This paper presents a way to solve the causality paradoxes, along with two other paradoxes, by the introduction of an absolute frame of reference in which a tachyon effect may never precede its cause. Relativity for ordinary matter is unaffected by this, even if the tachyons couple to ordinary particles. Violations of the principle of relativity due to the (...) absolute frame would appear only in the case of free tachyons. (shrink)

Some elementary properties of tachyons are described and then it is argued that the claim that (T) Tachyons exist, is incompatible with the truth of the Special Theory of Relativity (STR). First it is argued that from T, STR, and the negation of the principle that (Pl) Effect never precedes cause, one can derive a paradoxical conclusion, one of the so-called "causal paradoxes". An obvious response is to affirm (Pl), but then it is argued that (Pl) and (T) (...) entail that STR is false. (shrink)

An apparent inadequacy of the velocity addition theorem in handling a Fizeau (like) experiment beyond the resonance frequence is shown not to be a true failing. The proof consists in showing that the invariance of the signal velocity is unrelated to its maximality. Next, Lorentz transformations which connect frames moving with supersignal velocity to those of subsignal velocity are derived, taking a cue from the acoustic case. Methods are also suggested for laboratory verification of the theory.

Recent attempts to explain the dark matter and energy content of the universe have involved some radical extensions of standard physics, including quintessence, phantom energy, additional space dimensions, and variations in the speed of light. In this paper I consider the possibility that some dark matter might be in the form of tachyons. I show that, subject to some reasonable assumptions, a tachyonic cosmological fluid would produce distinctive effects, such as a surge in quantum vacuum energy and particle creation, (...) and a change in the conventional temperature–time relation for the normal cosmological material. Possible observational consequences are discussed. (shrink)

In the approximation that every inertial observer experiences a homogeneous, uniform flow of time and sees a space that is Euclidean, the arena of physics is Minkowskian and one speed is the same in all intertial frames. If a given intertial observer finds an infinitesimal source or particle traveling faster than this fundamental speed near a given event, the source must appear in some inertial frame spread over neighboring positions at a given time as a spacelike structure. If this structure (...) persists over a period of proper time, it can be interpreted as a wave group. If it is conserved, it can be interpreted as a line or tube of force. (shrink)

Tolman's paradox arises in Lorentz-invariant theories of superluminal particles. In this paper we first try to clarify the nature of the paradox and what it means to solve it. We then analyze the various attempts made to either solve or eliminate it. We show that general consequences can be drawn which hold in essentially all paradox-free schemes proposed so far.

The chronological order of the events along a spacelike path is not invariant under Lorentz transformations, as is well known. This led to an early conviction that tachyons would give rise to causal anomalies. A relativistic version of the Stückelberg-Feynman “switching procedure” (SWP) has been invoked as the suitable tool to eliminate those anomalies. The application of the SWP does eliminate the motions backwards in time, but interchanges the roles ofsource anddetector. This fact triggered the proposal of a host (...) of causal “paradoxes.” Till now, however, it has not been recognized that such paradoxes can be sensibly discussed (and completely solved, at least “in microphysics”)only after the tachyon relativistic mechanics has been properly developed. We start by showing how to apply the SWP, both in the case ofordinary special relativity and in the case with tachyons. Then we carefully exploit the kinematics of the tachyon exchange between to (ordinary) bodies. Being finally able to tackle the tachyon causality problem, we successively solve the paradoxes of : (i) Tolman-Regge, (ii) Pirani, (iii) Edmonds, and (iv) Bell. Finally, we discuss a further, new paradox associated with the transmission of signals by modulated tachyon beams. (shrink)

Light speed, c = 3 × 108 meters per second, is the ultimate speed limit of the universe. The welltested physics orthodoxy of special relativity tells us that nothing can go faster than c. When any massive object with rest mass M (taken to be in energy units) has velocity v=c (or relativistic velocity ß = v/c = 1), the object's mass-energy becomes infinite. This is because the relativistic..

We comment on the previous paper by L. Basano. In particular, we show that its Section 2 is kinematically incorrect (the dynamics of a two-body interaction through tachyon exchange, incidentally, has already been thoroughly expounded in one paper of ours). Its Section 1 is simply a rather subjective introduction. As to its Section 3, containing indeed interesting problems, we again briefly refer to our earlier work. Our conclusions are still in favor of “au revoir to tachyons!,” even if it (...) is known that inside our cosmos tachyons are more likely to have a role in physics (e.g., in elementary particle and black-hole physics) as “exchanged objects” rather than as “asymptotically free” objects. (shrink)

It is shown that in addition to the usual difficulties related to causality, the theory of superluminal particles also exhibits paradoxical symmetry violations. In the second part of the paper a conventional paradox is revisited: causality violations at the macroscopic level follow from simple statistical arguments.

A formalism is developed which admits particles faster than light and reference frames faster than light and as fast as light. It is fully consistent with the physical principles of special relativity. The necessity of introducing imaginary quantities does not arise. It does not encounter any difficulties with the principle of causality if it is reasonably interpreted.

Physical arguments stemming from the theory of black-hole thermodynamics are used to put constraints on the dynamics of closed-string tachyon condensation in Scherk–Schwarz compactifications. A geometrical interpretation of the tachyon condensation involves an effective capping of a noncontractible cycle, thus removing the very topology that supports the tachyons. A semiclassical regime is identified in which the matching between the tachyon condensation and the black-hole instability flow is possible. We formulate a generalized correspondence principle and illustrate it in several different (...) circumstances: an Euclidean interpretation of the transition from strings to black holes across the Hagedorn temperature and instabilities in the brane-antibrane system. (shrink)

In this paper we explain why and how tachyons do not imply any causality violation within relativistic theories. Particular emphasis is given to the role of the Stückelberg-Feynman reinterpretation principle, both in ordinary physics and in tachyon physics.

This book provides the reader with an analysis of backward causation. The notion of backward causation faces many different paradoxes that threaten to make the notion inconsistent or incoherent. The book denies that these pose a real threat. It developed a theory of causation according to which the orientation of causation is not dependent on the direction of time. In this process it takes issues with David Lewis' contrafactual analysis of causation, and denies that the direction of time is determined (...) by irreversible processes . Likewise the book argues that the conceptual possibility of backward causation requires that the future is just as real as the past and present. Finally the book considers what the physical processes may look like if backward causation not only a a conceptual possibility but also a physical possibility. The conclusion is that no normal matter can possibly participate in backward causal processes. Instead objects moving backwards in time seem to posses negative mass and energy, a kind of objects that would be different from both ordinary objects and hypothetical tachyons. (shrink)

This chapter contains sections titled: The State of Play Particles and Relativistic Mass Increase Tachyons.

A tachyon or a superluminal wave group appears as a spacelike structure through a region in the reference frame in which it is at rest. Such a structure can arise from residue left (a) by a particle or wave group traveling at fundamental speed c or less, or (b) in the creation or separation of particles. Thus, Maund's argument does not prove that tachyons cannot exist. Creation may include lepton-quark production as well as particle-antiparticle production.

Quantum theory of Lorentz invariant local scalar fields without restrictions on 4-momentum spectrum is considered. The mass spectrum may be both discrete and continues and the square of mass as well as the energy may be positive or negative. One may assume the existence of such fields only if they interact with ordinary fields very weakly. Generalization of Kallen-Lehmann representation for propagators of these fields is found. The considered generalized fields may violate CPT-invariance. Restrictions on mass-spectrum of CPT-violating fields are (...) found. Local fields that annihilate vacuum state and violate CPT-invariance are constructed in this scope. Correct local relativistic generalization of Lindblad equation for density matrix is written for such fields. This generalization is particularly needed to describe the evolution of quantum system and measurement process in a unique way. Difficulties arising when the field annihilating the vacuum interacts with ordinary fields are discussed. (shrink)

Those who think of some aspects of the world as "physically necessary" usually think of this kind of necessity as being confined to the general law of nature, initial conditions being "contingent." Tachyon theory and general relativity provide independent but related reasons for thinking that some initial states are, however, "impossible." And statistical mechanics seems to lead us to conclude that some initial conditions are, if not impossible, "highly improbable." We are then, led from these aspects of physics to wonder (...) if initial conditions are always "freely specifiable" and in the domain of physical contingency. (shrink)

In this paper, we review a general technique for converting the standard Lagrangian description of a classical system into a formulation that puts time on an equal footing with the system's degrees of freedom. We show how the resulting framework anticipates key features of special relativity, including the signature of the Minkowski metric tensor and the special role played by theories that are invariant under a generalized notion of Lorentz transformations. We then use this technique to revisit a classification of (...) classical particle-types that mirrors Wigner's classification of quantum particle-types in terms of irreducible representations of the Poincaré group, including the cases of massive particles, massless particles, and tachyons. Along the way, we see gauge invariance naturally emerge in the context of classical massless particles with nonzero spin, as well as study the massless limit of a massive particle and derive a classical-particle version of the Higgs mechanism. (shrink)

Superluminal particles are studied within the framework of the Extended Relativity theory in Clifford spaces (C-spaces). In the simplest scenario, it is found that it is the contribution of the Clifford scalar component π of the poly-vector-valued momentum which is responsible for the superluminal behavior in ordinary spacetime due to the fact that the effective mass $\mathcal{M} = \sqrt{ M^{2} - \pi^{2} }$ is imaginary (tachyonic). However, from the point of view of C-space, there is no superluminal (tachyonic) behavior because (...) the true physical mass still obeys M 2>0. Therefore, there are no violations of the Clifford-extended Lorentz invariance and the extended Relativity principle in C-spaces. It is also explained why the charged muons (leptons) are subluminal while its chargeless neutrinos may admit superluminal propagation. A Born’s Reciprocal Relativity theory in Phase Spaces leads to modified dispersion relations involving both coordinates and momenta, and whose truncations furnish Lorentz-violating dispersion relations which appear in Finsler Geometry, rainbow-metrics models and Double (deformed) Special Relativity. These models also admit superluminal particles. A numerical analysis based on the recent OPERA experimental findings on alleged superluminal muon neutrinos is made. For the average muon neutrino energy of 17 GeV, we find a value for the magnitude $|\mathcal{M } | = 119.7\mbox{~MeV}$ that, coincidentally, is close to the mass of the muon m μ =105.7 MeV. (shrink)

Non-commuting quantities and hidden parameters – Wave-corpuscular dualism and hidden parameters – Local or nonlocal hidden parameters – Phase space in quantum mechanics – Weyl, Wigner, and Moyal – Von Neumann’s theorem about the absence of hidden parameters in quantum mechanics and Hermann – Bell’s objection – Quantum-mechanical and mathematical incommeasurability – Kochen – Specker’s idea about their equivalence – The notion of partial algebra – Embeddability of a qubit into a bit – Quantum computer is not Turing machine – (...) Is continuality universal? – Diffeomorphism and velocity – Einstein’s general principle of relativity – „Mach’s principle“ – The Skolemian relativity of the discrete and the continuous – The counterexample in § 6 of their paper – About the classical tautology which is untrue being replaced by the statements about commeasurable quantum-mechanical quantities – Logical hidden parameters – The undecidability of the hypothesis about hidden parameters – Wigner’s work and и Weyl’s previous one – Lie groups, representations, and psi-function – From a qualitative to a quantitative expression of relativity − psi-function, or the discrete by the random – Bartlett’s approach − psi-function as the characteristic function of random quantity – Discrete and/ or continual description – Quantity and its “digitalized projection“ – The idea of „velocity−probability“ – The notion of probability and the light speed postulate – Generalized probability and its physical interpretation – A quantum description of macro-world – The period of the as-sociated de Broglie wave and the length of now – Causality equivalently replaced by chance – The philosophy of quantum information and religion – Einstein’s thesis about “the consubstantiality of inertia ant weight“ – Again about the interpretation of complex velocity – The speed of time – Newton’s law of inertia and Lagrange’s formulation of mechanics – Force and effect – The theory of tachyons and general relativity – Riesz’s representation theorem – The notion of covariant world line – Encoding a world line by psi-function – Spacetime and qubit − psi-function by qubits – About the physical interpretation of both the complex axes of a qubit – The interpretation of the self-adjoint operators components – The world line of an arbitrary quantity – The invariance of the physical laws towards quantum object and apparatus – Hilbert space and that of Minkowski – The relationship between the coefficients of -function and the qubits – World line = psi-function + self-adjoint operator – Reality and description – Does a „curved“ Hilbert space exist? – The axiom of choice, or when is possible a flattening of Hilbert space? – But why not to flatten also pseudo-Riemannian space? – The commutator of conjugate quantities – Relative mass – The strokes of self-movement and its philosophical interpretation – The self-perfection of the universe – The generalization of quantity in quantum physics – An analogy of the Feynman formalism – Feynman and many-world interpretation – The psi-function of various objects – Countable and uncountable basis – Generalized continuum and arithmetization – Field and entanglement – Function as coding – The idea of „curved“ Descartes product – The environment of a function – Another view to the notion of velocity-probability – Reality and description – Hilbert space as a model both of object and description – The notion of holistic logic – Physical quantity as the information about it – Cross-temporal correlations – The forecasting of future – Description in separable and inseparable Hilbert space – „Forces“ or „miracles“ – Velocity or time – The notion of non-finite set – Dasein or Dazeit – The trajectory of the whole – Ontological and onto-theological difference – An analogy of the Feynman and many-world interpretation − psi-function as physical quantity – Things in the world and instances in time – The generation of the physi-cal by mathematical – The generalized notion of observer – Subjective or objective probability – Energy as the change of probability per the unite of time – The generalized principle of least action from a new view-point – The exception of two dimensions and Fermat’s last theorem. (shrink)

While it has often been proposed that, fundamentally, Lorentz-invariance is not respected in a quantum theory of gravity, it has been difficult to reconcile deviations from Lorentz-invariance with quantum field theory. The most commonly used mechanisms either break Lorentz-invariance explicitly or deform it at high energies. However, the former option is very tightly constrained by experiment already, the latter generically leads to problems with locality. We show here that there exists a third way to integrate deviations from Lorentz-invariance into quantum (...) field theory that circumvents the problems of the other approaches. The way this is achieved is an extension of the standard model in which photons can have different speeds without singling out a preferred restframe, but only as long as they are in a quantum superposition. Once a measurement has been made, observables are subject to the laws of special relativity, and the process of measurement introduces a preferred frame. The speed of light can take on different values, both superluminal and subluminal (with respect to the usual value of the speed of light), without the need for Lorentz-invariance violating operators and without tachyons. We briefly discuss the relation to deformations of special relativity and phenomenological consequences. (shrink)

We investigate particular cosmological models, based either on tachyon fields or on perfect fluids, for which soft future singularities arise in a natural way. Our main result is the description of a smooth crossing of the soft singularity in models with an anti-Chaplygin gas or with a particular tachyon field in the presence of dust. Such a crossing is made possible by certain transformations of matter properties. We discuss and compare also different approaches to the problem of crossing of the (...) Big Bang–Big Crunch singularities. (shrink)

Explains relativity--matter and energy, anti-matter, tachyon, etc.--tracing from discovery to discovery the steps that led to the next development in the field.

An elementary presentation is given of classical and relativistic collision dynamics based upon the principle of conservation of momentum. The concepts of mass are shown to be implicitly defined and their basic properties are rigorously derived and discussed. Luxons and tachyons are treated on the same footing as material particles.

A theoretical and experimental search for the so-called Weyssenhof behavior of a spinning particle, due to the noncollinearity of its velocity and momentum, has been undertaken. Z-independent solutions of Maxwell's equations had previously been produced with a nonzeros z component of the Poynting vector; indeed, Imbert emphasized that the spatial exponential damping of Fresnel's evanescent wave would entail a nonzero value for the integral ε εs z dx dy. Excellent experimental verifications of this point have been obtained by Imbert. Besides (...) having noz component of their momentum, the energy-momentum quanta inside Fresnel's evanescent wave have typical tachyon properties, the imaginary character of theiry component (normal to the reflecting surface) entailing that (in units such thatc=1) theirx component islarger than the energy quanta. Imbert is now planning experiments to test these interesting properties. Thus, the two main aspects of noncollinearity of velocity and momentum of spinning particles would be displayed. (shrink)

In a series of quantum experiments performed in 1935-1986 a validity of the quantum theory has been tested. The results obtained have changed the viewpoints of physicists and philosophers on the nature of the Universe and physical reality. In particular, they have changed the traditional West view on the relationship between micro- and macro- level, between a part and the wholeness and between the system and its constituents. From the distinguishing quantum experiments a brief description of the Einstein-Podolsky- Rosen paradox, (...) the Bell\'s inequality and the Aspect-Dalibard-Roger experiment is made. The results obtained are important for the concept of the bioplasmatic transfer of information in the living systems, developed by Włodzimierz Sedlak. According to the Sedlak\'s idea, the bioplasma is a local concept, so it does not take into account the possibility of a faster then light signaling. Because in the living systems the long-range quantum correlations should appear, the concept of bioplasma should be generalized to include the non-local quantum effects. As a consequence - such a dynamic quantum system as bioplasma has to be non-local - all its elements are connected because of quantum correlations, regardless of the distance between them. A model of the biocoherence for the systems described by the Gompertz function is presented. In this approach, the Gompertz function is a solution of the space-like (tachyonic) Horodecki- Feinberg equation with the time-analog of the Morse potential function. It is shown that Gompertzian systems evolve coherently and non-locally in the space. The presented model admits a continuous and instantaneous transfer of \"influences\" between micro- level represented by the single cell and the macro-level represented by the biosystem (tissue, organ, organism) as a whole. A consequence is the integration of organism and its coherent development on all levels of the bio-existence. (shrink)

A new four-component spin-1/2 wave equation for ordinary mass is discussed. It is shown that this equation has a conserved current not easily identified with a transition probability, only pure imaginary energy states, and is covariant. A tachyon-like Klein-Gordon equation is satisfied by this equation, but rest states are explicitly constructed.

In this paper we investigate a number of analytical solutions to the polynomial class of nonlinear Klein-Gordon equations in multidimensional spacetime. This is done in the context of classical φ4 and φ6 field theory, the former with and without the inclusion of an external force field conjugate to φ. Both massive (m≠0) and massless (m=0) cases are considered, as well as tachyonic solutions allowed (v>c). We first present a complete set of translationally invariant solutions for the φ4 model and demonstrate (...) the role of external force fields in altering the form of these solutions. Next, spherically symmetric solutions are discussed in both φ4 and φ6 cases since they provide the most realistic models of elementary particles. (shrink)

Friedmann–Robertson–Walker (FRW) space–time with bulk viscosity in the context of f(R) gravity is considered. The field equations are solved for the Power and Exponential volumetric expansion. Two types of functional relationship i.e. f(R) = R + bRm and f(R)=R-λ4R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \,f(R) = R - \frac{{\lambda^{4} }}{R} $$\end{document} are investigated. The Phantom, Chaplygin gas and Tachyon fields are discussed. It is observed that the universe is open and inflationary.

We calculate the mixing of real and imaginary components of space and time under the influence of superluminal boosts in thex direction. A unique mixing is determined for this superluminal Lorentz transformation when we consider the symmetry properties afforded by the inclusion of three temporal directions. Superluminal transformations in complex six-dimensional space exhibit unique tachyonic connections which have both remote and local space-time event connections.

Alternate View Column AV-70 Keywords: Casimir effect negative energy quantum nonlocality tachyons extra dimensions Published in the February-1995 issue of Analog Science Fiction & Fact Magazine ; This column was written and submitted 7/13/94 and is copyrighted ©1994 by John G. Cramer. All rights reserved. No part may be reproduced in any form without the explicit permission of the author.

* Solar Neutrinos are Up - My column about recent results in neutrino physics Analog - September-1992 ] (no neutrino counts at SAGE and negative mass-squared data suggesting that the e-neutrino may be a tachyon) prompted more reader response than any other column in recent memory . Two months after I wrote it, a new result from GALLEX, the European gallium neutrino-detection experiment housed in the Grand Sasso underground laboratory in Italy, was announced. GALLEX uses the same technique as the (...) SAGE neutrino experiment described in my September column: many million dollars worth of elemental gallium (element 31) is purified and placed in underground tanks where solar neutrinos transmute stable gallium 71 to radioactive germanium 71 (half life 11.4 days). A chemical process separates the new radioactive germanium atoms from the bulk gallium and transports them to a sensitive detector where their decays are counted. (shrink)

Science fiction writers, to avoid undue delays in the story's plot line, need a way of beating the speed of light speed limit of the universe. Most readers of this magazine are familiar with the gimmicks that have been used for faster than light travel: warp drives, detours through hyperspace, matter to tachyon conversion, trans spatial jumps, and dives past the singularity of a rotating black hole. But perhaps the faster than light mechanism which has the best credentials in orthodox (...) physics is the wormhole, also known as a Schwartzschild wormhole or an Einstein Rosen bridge. (shrink)

It continues to be alleged that superluminal in uences of any sort would be inconsistent with special relativity for the following three reasons: they would imply the existence of a ‘distinguished’ frame; they would allow the detection of absolute motion; and they would violate the relativity of simultaneity. This paper shows that the first two objections rest upon very elementary misunderstandings of Minkowski geometry and on lingering Newtonian intuitions about instantaneity. The third objection has a basis, but rather than invalidating (...) the notion of faster-than-light influences it points the way to more general conceptions of simultaneity that could allow for quantum nonlocality in a natural way. (shrink)

We revisit the introduction of the Superluminal Lorentz transformations which carry from “bradyonic” inertial frames to “tachyonic” inertial frames, i.e., which transform time-like objects into space-like objects, andvice versa. It has long been known that special relativity can be extended to Superluminal observers only by increasing the number of dimensions of the space-time or—which is in a sense equivalent—by releasing the reality condition (i.e., introducing also imaginary quantities). In the past we always adopted the latter procedure. Here we show the (...) connection between that procedure and the former one. In other words, in order to clarify the physical meaning of the imaginary units entering the classical theory of tachyons, we have temporarily to call into play anauxiliary six-dimensional space-time M(3, 3); however, we are eventually able to go back to the four-dimensional Minkowski space-time. We revisit the introduction of the Superluminal Lorentz transformations also under another aspect. In fact, the generalized Lorentz transformations had been previously written down in a form suited only for the simple case of collinear boosts (e.g., they formed a group just for collinear boosts). We express now the Superluminal Lorentz transformations in a more general form, so that they constitute a group together with the ordinary—orthochronousand antichronous—Lorentz transformations, and reduce to the previous form in the case of collinear boosts. Our approach introduces either real or imaginary quantities, with exclusion of (generic) complex quantities. In the present context, a procedure—in two steps—for interpreting the imaginary quantities is put forth and discussed. In the case of a chain of generalized Lorentz transformations, such a procedure (when necessary) is to be applied only at the end of the chain. Finally, we justify why we call “transformations” also the Superluminal ones. (shrink)