Exotic matter

Exotic matter is matter with physical properties that violate the conditions standard physics associates with ordinary matter — specifically matter with negative energy density or negative mass — required by general relativity as a mathematical ingredient in traversable wormholes, the Alcubierre drive, and certain other faster-than-light or spacetime-manipulation solutions. The Casimir effect provides the only confirmed laboratory-scale demonstration of negative energy density; whether macroscopic quantities can be produced or stabilised remains an open question in physics.

Definition

In general relativity, a stress-energy tensor T μ ν {\displaystyle T_{\mu \nu }} satisfying the Null Energy Condition (NEC) obeys:

T μ ν k μ k ν ≥ 0 {\displaystyle T_{\mu \nu },k^{\mu }k^{\nu }\geq 0}

for all null vectors k μ {\displaystyle k^{\mu }}. Exotic matter is defined as matter that violates the NEC — i.e., for which T μ ν k μ k ν < 0 {\displaystyle T_{\mu \nu },k^{\mu }k^{\nu }<0} along some null direction. Equivalently, in a local orthonormal frame, exotic matter has energy density ρ {\displaystyle \rho } and radial pressure p r {\displaystyle p_{r}} satisfying ρ + p r < 0 {\displaystyle \rho +p_{r}<0}. This condition is required at the throat of a Morris–Thorne traversable wormhole and in the negative-energy shell needed to stabilise an Alcubierre drive bubble.

Casimir effect as evidence

The Casimir effect — the attractive force between two uncharged conducting plates arising from quantum vacuum fluctuations — produces a region of negative energy density between the plates relative to the ambient vacuum:

ρ Casimir = − π 2 ℏ c 720 d 4 {\displaystyle \rho _{\text{Casimir}}=-{\frac {\pi ^{2}\hbar c}{720,d^{4}}}}

where d {\displaystyle d} is the plate separation. This is the only macroscopically observable instance of negative energy density reported by experiment. Michio Kaku and Hal Puthoff have both cited the Casimir effect as proof-of-concept that exotic matter satisfying the NEC-violation condition physically exists — removing it from purely speculative status.

Energy requirements

For the original 1994 Alcubierre warp bubble of radius R {\displaystyle R} and wall thickness Δ {\displaystyle \Delta }, the required exotic energy is approximately:

E ∼ − c 4 G R 2 Δ v s 2 {\displaystyle E\sim -{\frac {c^{4}}{G}},{\frac {R^{2}}{\Delta }},v_{s}^{2}}

For a 10-metre bubble travelling at v s = c {\displaystyle v_{s}=c} with wall thickness 1 metre, this amounts to negative energy equivalent to roughly the total mass-energy of Jupiter — approximately − 1.8 × 10 30 kg ⋅ c 2 {\displaystyle -1.8\times 10^{30},{\text{kg}}\cdot c^{2}}. Harold White's 2011 reformulation using a dynamic toroidal bubble shape reduced the estimate by many orders of magnitude, though the requirement remains far beyond current laboratory production of Casimir-scale negative energy.

Warp drive without macroscopic exotic matter

Physicist Jack Sarfatti, in a presentation hosted by Ashton Forbes, argued that genuine warp drive does not require the enormous quantities of exotic matter posited by the original Alcubierre metric. Sarfatti described warp drive as "motion without motion — it's the actual controlled tilting of light cones, of neighboring light cones, the relative tilting that is controlling the curvature field directly with small amounts of energy. That's the key. Small amounts of energy." He attributed this insight to work he first presented at the DARPA-NASA 100 Year Starship symposium in Orlando in October 2011.

Recovered craft and exotic matter

C. Ron Garner's interview subjects described recovered element 115-derived material that, when bombarded with sufficient electromagnetism, "repels gravity and transforms into a form of exotic matter" — an account interpreted by some researchers as describing a technology for producing macroscopic quantities of NEC-violating matter using superheavy-element interactions unavailable to terrestrial physics.

See also

• Zero-point energy

References