Теріс масса және физикалық модельдер

Concept in physical models
In theoretical physics, negative mass is a hypothetical type of exotic matter whose mass is of opposite sign to the mass of normal matter, e. g. −1 kg. Such matter would violate one or more energy conditions and exhibit strange properties such as the oppositely oriented acceleration for an applied force orientation. It is used in certain speculative hypothetical technologies such as time travel to the past and future, construction of traversable artificial wormholes, which may also allow for time travel, Krasnikov tubes, the Alcubierre drive, and potentially other types of faster than light warp drives. Currently, the closest known real representative of such exotic matter is a region of negative pressure density produced by the Casimir effect.

In December 2018, astrophysicist Jamie Farnes from the University of Oxford proposed a "dark fluid" theory, related, in part, to notions of gravitationally repulsive negative masses, presented earlier by Albert Einstein, that may help better understand, in a testable manner, the considerable amounts of unknown dark matter and dark energy in the cosmos.

Negative mass is any region of space in which for some observers the mass density is measured to be negative. This may occur due to a region of space in which the sum of the three normal stress components (pressure on each of three axes) of the Einstein stress–energy tensor is larger in magnitude than the mass density. All of these are violations of one or another variant of the positive energy condition of Einstein's general theory of relativity; however, the positive energy condition is not a required condition for the mathematical consistency of the theory.

In general relativity, the universe is described as a Riemannian manifold associated to a metric tensor solution of Einstein's field equations. In such a framework, the runaway motion forbids the existence of negative matter. The universe is then described as a manifold associated to two Riemannian metrics (one with positive mass matter and the other with negative mass matter). According to group theory, the matter of the conjugated metric would appear to the matter of the other metric as having opposite mass and arrow of time (though its proper time would remain positive). The coupled metrics have their own geodesics and are solutions of two coupled field equations. The negative matter of the coupled metric, interacting with the matter of the other metric via gravity, could be an alternative candidate for the explanation of dark matter, dark energy, cosmic inflation and an accelerating universe. As was the consensus among physicists previously, it was experimentally confirmed that gravity attracts both matter and antimatter at the same rate within experimental error. Bubble chamber experiments provide further evidence that antiparticles have the same inertial mass as their normal counterparts. In these experiments, the chamber is subjected to a constant magnetic field that causes charged particles to travel in helical paths, the radius and direction of which correspond to the ratio of electric charge to inertial mass. Particle–antiparticle pairs are seen to travel in helices with opposite directions but identical radii, implying that the ratios differ only in sign; but this does not indicate whether it is the charge or the inertial mass that is inverted. However, particle–antiparticle pairs are observed to electrically attract one another. This behavior implies that both have positive inertial mass and opposite charges; if the reverse were true, then the particle with positive inertial mass would be repelled from its antiparticle partner.

In 1928, Paul Dirac's theory of elementary particles, now part of the Standard Model, already included negative solutions. The Standard Model is a generalization of quantum electrodynamics (QED) and negative mass is already built into the theory. Morris, Thorne and Yurtsever pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally mass negative region of space–time. In this article, and subsequent work by others, they showed that negative matter could be used to stabilize a wormhole. Cramer et al. argue that such wormholes might have been created in the early universe, stabilized by negative mass loops of cosmic string. Stephen Hawking has argued that negative energy is a necessary condition for the creation of a closed timelike curve by manipulation of gravitational fields within a finite region of space; this implies, for example, that a finite Tipler cylinder cannot be used as a time machine.

For energy eigenstates of the Schrödinger equation, the wavefunction is wavelike wherever the particle's energy is greater than the local potential, and exponential like (evanescent) wherever it is less. Naively, this would imply kinetic energy is negative in evanescent regions (to cancel the local potential). However, kinetic energy is an operator in quantum mechanics, and its expectation value is always positive, summing with the expectation value of the potential energy to yield the energy eigenvalue. For wavefunctions of particles with zero rest mass (such as photons), this means that any evanescent portions of the wavefunction would be associated with a local negative mass–energy. However, the Schrödinger equation does not apply to massless particles; instead the Klein–Gordon equation is required.