Negative mass

It is used in certain speculative hypothetical technologies such as time travel to the past and future,[3] 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.

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.

In his 4th-prize essay for the 1951 Gravity Research Foundation competition, Joaquin Mazdak Luttinger considered the possibility of negative mass and how it would behave under gravitational and other forces.

[6] In 1957, following Luttinger's idea, Hermann Bondi suggested in a paper in Reviews of Modern Physics that mass might be negative as well as positive.

For example, an object with negative inertial mass would be expected to accelerate in the opposite direction to that in which it was pushed (non-gravitationally).

Indeed, the Schwarzschild solution for negative mass parameter has a naked singularity at a fixed spatial position.

The question that immediately comes up is, would it not be possible to smooth out the singularity with some kind of negative mass density.

[9][10] However, it was noticed by Belletête and Paranjape that since the positive energy theorem does not apply to asymptotic de Sitter spacetime, it would actually be possible to smooth out, with energy–momentum that does satisfy the dominant energy condition, the singularity of the corresponding exact solution of negative mass Schwarzschild–de Sitter, which is the singular, exact solution of Einstein's equations with cosmological constant.

[11] In a subsequent article, Mbarek and Paranjape showed that it is in fact possible to obtain the required deformation through the introduction of the energy–momentum of a perfect fluid.

The interaction laws are then:For two positive masses, nothing changes and there is a gravitational pull on each other causing an attraction.

Hence Bondi pointed out that two objects of equal and opposite mass would produce a constant acceleration of the system towards the positive-mass object,[7] an effect called "runaway motion" by Bonnor who disregarded its physical existence, stating: I regard the runaway (or self-accelerating) motion […] so preposterous that I prefer to rule it out by supposing that inertial mass is all positive or all negative.Such a couple of objects would accelerate without limit (except a relativistic one); however, the total mass, momentum and energy of the system would remain zero.

This is incompatible with general relativity, for the device gets more massive.But Forward showed that the phenomenon is mathematically consistent and introduces no violation of conservation laws.

[15] If the masses are equal in magnitude but opposite in sign, then the momentum of the system remains zero if they both travel together and accelerate together, no matter what their speed: And equivalently for the kinetic energy: However, this is perhaps not exactly valid if the energy in the gravitational field is taken into account.

Forward extended Bondi's analysis to additional cases, and showed that even if the two masses m(−) and m(+) are not the same, the conservation laws remain unbroken.

Geoffrey A. Landis pointed out other implications of Forward's analysis,[17] including noting that although negative mass particles would repel each other gravitationally, the electrostatic force would be attractive for like charges and repulsive for opposite charges.

Forward used the properties of negative-mass matter to create the concept of diametric drive, a design for spacecraft propulsion using negative mass that requires no energy input and no reaction mass to achieve arbitrarily high acceleration.

In general relativity, the universe is described as a Riemannian manifold associated to a metric tensor solution of Einstein's field equations.

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.

In 1928, Paul Dirac's theory of elementary particles, now part of the Standard Model, already included negative solutions.

[22] The Standard Model is a generalization of quantum electrodynamics (QED) and negative mass is already built into the theory.

Morris, Thorne and Yurtsever[23] pointed out that the quantum mechanics of the Casimir effect can be used to produce a locally energy-negative region of space–time.

Cramer et al. argue that such wormholes might have been created in the early universe, stabilized by negative-mass loops of cosmic string.

[24] 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;[25] this implies, for example, that a finite Tipler cylinder cannot be used as a time machine.

Naively, this would imply kinetic energy is negative in evanescent regions (to cancel the local potential).

[26][27][28][29] The negative effective mass (density) becomes also possible based on the electro-mechanical coupling exploiting plasma oscillations of a free electron gas (see Figure 2).

[30][31] The negative mass appears as a result of vibration of a metallic particle with a frequency of

Metamaterials exploiting the effect of the negative mass in the vicinity of the plasma frequency were reported.