A warp drive with predominantly positive invariant energy density and global Hawking–Ellis Type I

Dark energy with negative pressure and positive energy density is believed to be responsible for the accelerated expansion of the universe. Quite a few theoretical models of dark energy are based on tachyonic fields interacting with itself and normal (bradyonic) matter. Here, we propose an experimental model of tachyonic dark energy based on hyperbolic metamaterials. Wave equation describing propagation of extraordinary light inside hyperbolic metamaterials exhibits 2 + 1 dimensional Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski spacetime is played by the spatial coordinate aligned with the optical axis of the metamaterial. Nonlinear optical Kerr effect bends this spacetime resulting in effective gravitational force between extraordinary photons. We demonstrate that this model has a self-interacting tachyonic sector having negative effective pressure and positive effective energy density. Moreover, a composite multilayer SiC-Si hyperbolic metamaterial exhibits closely separated tachyonic and bradyonic sectors in the long wavelength infrared range. This system may be used as a laboratory model of inflation and late time acceleration of the universe.

Three recent articles have claimed that it is possible to, at least in theory, either set up positive energy warp drives satisfying the weak energy condition (WEC), or at the very least, to minimize the WEC violations. These claims are, at best, incomplete since the arguments as presented only assert but do not prove the existence of one set of timelike observers, the comoving Eulerian observers, who see relatively ``nice'' physics. While these particular observers might arguably see a positive energy density, the WEC requires all timelike observers to see positive energy density. Therefore, one should carefully revisit this issue. A more careful analysis shows that the situation is actually much grimmer than advertised---within the framework adopted by those three papers all physically reasonable warp drives will certainly violate the WEC, and both the strong and dominant energy conditions. Under plausible subsidiary conditions the null energy condition is also violated. While warp drives are certainly interesting examples of speculative physics, the violation of the energy conditions, at least within the framework of standard general relativity, is unavoidable. Even in modified gravity, physically reasonable warp drives will still violate the purely geometrical null convergence condition and the timelike convergence condition which, in turn, will place very strong constraints on any modified-gravity warp drive.

Space and time traveling is one of the humanity’s most fascinating and challenging topics. The speed limitation makes space traveling highly difficult. Therefore, discovering the warp drive mechanism intrigued humanity to travel in space and time. Miguel Alcubierre proposed a model for warp drive. However, the energy density driven from the Alcubierre warp drive model turns to be negative everywhere. Erik Lentz proposed a shifting vector field in which we shall show that shifting vector field with appropriate spaceship geometry may provide positive energy density for warp drive. Further, we suggest looking at the spaceship geometry as a mother wavelet function with shifting, scaling, and rotation operations that may provide additional positive energy density. This sort of design requires a flexible fuselage that can be stretched and rotated.

We investigate the brane models in arbitrary dimensional critical gravity presented in Lu and Pope (Phys Rev Lett 106:181302, 2011). For the models of the thin branes with codimension one, the Gibbons–Hawking surface term and the junction conditions are derived, with which the analytical solutions for the flat, AdS, and dS branes are obtained at the critical point of the critical gravity. It is found that all these branes are embedded in an AdS $$_{n}$$ spacetime, but, in general, the effective cosmological constant $$\varLambda $$ of the AdS $$_{n}$$ spacetime is not equal to the naked one $$\varLambda _0$$ in the critical gravity, which can be positive, zero, and negative. Another interesting result is that the brane tension can also be positive, zero, or negative, depending on the symmetry of the thin brane and the values of the parameters of the theory, which is very different from the case in general relativity. It is shown that the mass hierarchy problem can be solved in the braneworld model in the higher-derivative critical gravity. We also study the thick brane model and find analytical and numerical solutions of the flat, AdS, and dS branes. It is found that some branes will have inner structure when some parameters of the theory are larger than their critical values, which may result in resonant KK modes for some bulk matter fields. The flat branes with positive energy density and AdS branes with negative energy density are embedded in an $$n$$ -dimensional AdS spacetime, while the dS branes with positive energy density are embedded in an $$n$$ -dimensional Minkowski one.

Minimum size of radiation with spin

Neutrino-gravitational fields with positive energy density are considered. A special case of these fields appeared to introduce some compli- cations. It is shown here that this case may be removed by a simple transformation.

We develop a new, mathematically precise framework for treating the effects of nonlinear phenomena occurring on small scales in general relativity. Our approach is an adaptation of Burnett's formulation of the shortwave approximation, which we generalize to analyze the effects of matter inhomogeneities as well as gravitational radiation. Our framework requires the metric to be close to a background metric, but allows arbitrarily large stress-energy fluctuations on small scales. We prove that, within our framework, if the matter stress-energy tensor satisfies the weak energy condition (i.e., positivity of energy density in all frames), then the only effect that small-scale inhomogeneities can have on the dynamics of the background metric is to provide an effective stress-energy tensor that is traceless and has positive energy density---corresponding to the presence of gravitational radiation. In particular, nonlinear effects produced by small-scale inhomogeneities cannot mimic the effects of dark energy. We also develop perturbation theory off of the background metric. We derive an equation for the long-wavelength part of the leading order deviation of the metric from the background metric, which contains the usual terms occurring in linearized perturbation theory plus additional contributions from the small-scale inhomogeneities. Under various assumptions concerning the absence of gravitational radiation and the nonrelativistic behavior of the matter, we argue that the short-wavelength deviations of the metric from the background metric near a point $x$ should be accurately described by Newtonian gravity, taking into account only the matter lying within a homogeneity length scale of $x$. Finally, we argue that our framework should provide an accurate description of the actual universe.

The general world model for homogeneous and isotropic universe has been roposed. For this purpose, we introduce a global and fiducial system of reference (world reference frame) constructed on a 5-dimensional space-time that is embedding the universe, and define the line element as the separation between two neighboring events that are distinct in space and time, as viewed in the world reference frame. The effect of cosmic expansion on the measurement of physical distance has been correctly included in the new metric, which differs from the Friedmann-Robertson-Walker metric where the spatial separation is measured for events on the hypersurface at a constant time while the temporal separation is measured for events at different time epochs. The Einstein's field equations with the new metric imply that closed, flat, and open universes are filled with positive, zero, and negative energy, respectively. We have demonstrated that the flat universe is empty and stationary, equivalent to the Minkowski space-time, and that the universe with positive energy density is always spatially closed and finite. In the closed universe, the proper time of a comoving observer does not elapse uniformly as judged in the world reference frame, in which both cosmic expansion and time-varying light speeds cannot exceed the limiting speed of the special relativity. We have also reconstructed cosmic evolution histories of the closed world models that are consistent with recent astronomical observations, and derived useful formulas such as energy-momentum relation of particles, redshift, total energy in the universe, cosmic distance and time scales, and so forth. It has also been shown that the inflation with positive acceleration at the earliest epoch is improbable.

Quantum consistency suggests that any de Sitter patch that lasts a number of Hubble times that exceeds its Gibbons‐Hawking entropy divided by the number of light particle species suffers an effect of quantum breaking. Inclusion of other interactions makes the quantum break‐time shorter. The requirement that this must not happen puts severe constraints on scalar potentials, essentially suppressing the self‐reproduction regimes. In particular, it eliminates both local and global minima with positive energy densities and imposes a general upper bound on the number of e‐foldings in any given Hubble patch. Consequently, maxima and other tachyonic directions must be curved stronger than the corresponding Hubble parameter. We show that the key relations of the recently‐proposed de Sitter swampland conjecture follow from the de Sitter quantum breaking bound. We give a general derivation and also illustrate this on a concrete example of D‐brane inflation. We can say that string theory as a consistent theory of quantum gravity nullifies a positive vacuum energy in self‐defense against quantum breaking.

Warp drives in Einstein’s general theory of relativity provide a unique mechanism for manned interstellar travel. It is well-known that the classical superluminal soliton spacetimes require negative energy densities, likely sourced by quantum processes of the uncertainty principle. It has even been claimed by few that negative energy densities are a requirement of superluminal motion. However, recent studies suggest this may not be the case. A general decomposition of the defining variables and the corresponding decomposition of the Eulerian energy are studied. A geometrical interpretation of the Eulerian energy is found, shedding new light on superluminal solitons generated by realistic energy distributions. With this new interpretation, it becomes a relatively simple matter to generate solitonic configurations, within a certain subclass, that respect the positive energy constraint. Using this newfound interpretation, a superluminal solitonic spacetime is presented that possesses positive semi-definite energy. A modest numerical analysis is carried out on a set of example configurations, finding total energy requirements four orders of magnitude smaller than the solar mass. Extraordinarily, the example configurations are generated by purely positive energy densities, a tremendous improvement on the classical configurations. The geometrical interpretation of the Eulerian energy thus opens new doors to generating realistic warp fields for laboratory study and potential future manned interstellar travel.

Alcubierre introduced the warp drive model in 1994. However, Alcubierre warp drive model resulted in negative energy density everywhere. The purpose of this paper is to show that with a small modification in the Alcubierre warp drive geometry, while keeping the warp drive bubble shape unchanged, we achieved a total positive energy density.

Alfvén wave mixing equations used in locally incompressible turbulence transport equations in the solar wind contain as a special case, non-Jeffreys–Wentzel–Kramers–Brouillon (non-JWKB) wave equations used in models of Alfvén wave driven winds. We discuss the canonical wave energy equation; the physical wave energy equation, and the JWKB limit of the wave interaction equations. Lagrangian and Hamiltonian variational principles for the waves are developed. Noether’s theorem is used to derive the canonical wave energy equation which is associated with the linearity symmetry of the equations. A further conservation law associated with time translation invariance of the action, applicable for steady background wind flows is also derived. In the latter case, the conserved density is the Hamiltonian density for the waves, which is distinct from the canonical wave energy density. The canonical wave energy conservation law is a special case of a wider class of conservation laws associated with Green’s theorem for the wave mixing system and the adjoint wave mixing system, which are related to Noether’s second theorem. In the sub-Alfvénic flow, inside the Alfvén point of the wind, the backward and forward waves have positive canonical energy densities, but in the super-Alfvénic flow outside the Alfvén critical point, the backward Alfvén waves are negative canonical energy waves, and the forward Alfvén waves are positive canonical energy waves. Reflection and transmission coefficients for the backward and forward waves in both the sub-Alfvénic and super-Alfvénic regions of the flow are discussed.

Two infinite parallel uncharged conducting planes experience an attractive force between them (called the Casimir force) due to the alteration of the zero point electromagnetic field between the plates. Similarly, there are forces on the surfaces of a rectangular cavity with conductive walls of dimension a1,a2,a3. Recently a paradox was published describing a method for the extraction of mechanical energy from the zero point fluctuations of the electromagnetic field in a rectangular conductive cavity by cyclical changes in the dimensions of the walls without doing any work (Forward, 1998). The validity of the analysis depends on the implicit assumption that the energy density within the cavity is approximately isotropic, so that positive average energy densities within the cavity result in outward forces, and negative average energy densities result in attractive forces. However, detailed computations of the forces on the cavity walls show this assumption is not valid, and that there are positive energy regions in which there are outward forces on some faces and inward forces on other faces (Hacyan, 1993). Specifically, for a cavity with a1=a2=1 the energy is positive for 0.4<a3<3.3, however, the average pressure P1 on the 1×1 faces and the average pressure P3 on the 1×a3 faces are both positive only if 0.7<a3<1.6. For all other values of a3, P1 and P3 have opposite signs. Specifically, for a3>1.6, P3>0, P1<0 and for a3<0.7, P3<0, P1>0. The implications of these and other unusual features of rectangular cavities in the vacuum are discussed.

The Poynting vector, energy density and energy velocity of light pulses propagating in anomalous dispersion medium (used in WKD-like experiments) are calculated. Results show that a negative energy density in the medium propagates along opposite of incident direction with such a velocity similar to the negative group velocity while the direction of the Poynting vector is positive. In other words, one might say that a positive energy density in the medium would propagate along the positive direction with a speed having approximately the absolute valueof the group velocity. We further point out that neither energy velocity nor group velocity is a good concept to describe the propagation process of light pulse inside the medium in WKD experiment owing to the strong accumulation and dissipation effects.

Example of negative energy density in a classical electron model