Historical research guide · 0386 · 2023
Alcubierre warp drive in Bohmian Quantum Gravity
Sijo K. Joseph
In one minute
Alcubierre’s warp metric has always come with one bill attached: to hold the bubble open you need matter with negative energy density, and nobody has a jar of it. Sijo K. Joseph takes a different route to paying that bill. Instead of hunting for exotic matter, he works in Bohmian quantum gravity, where a quantum matter field enters geometry as a conformal factor — a stretching of lengths that is literally the exponential of Bohm’s quantum potential. In that setting spacetime is rigid in the ordinary Riemannian sense but not in the Weyl sense, so a quantum field can rescale it far more cheaply than mass-energy can bend it. Joseph shows that the exotic-matter requirement then turns into a wave equation for the conformal factor, and finally into a fourth-order differential equation for the quantum probability density. The exotic matter problem becomes a search for the right quantum density. His toy version already produces solutions ordinary quantum theory cannot have.
Connection
Chapter 4 is where the warp metric is treated as an engineering object rather than a curiosity, and the recurring blocker is the negative-energy requirement. This paper is one of the cleanest attempts to move that requirement out of the matter column and into the quantum column, where a density profile — not a substance — is the thing you have to find.
From the source
Coupling the Alcubierre metric to a quantum mechanical scalar matter field in the Bohmian, de Broglie-Bohm manner turns the exotic matter requirement into a Klein-Gordon type conformal wave equation, in which the Alcubierre exotic function enters exactly where a positive mass term would sit.Section ’Alcubierre warp drive’, Equations 21 to 23
The conformal factor of the theory is not a free parameter but the exponential of the Bohmian quantum potential, which is itself fixed by the square root of the quantum mechanical matter density — so the geometry of the bubble and the shape of a wavefunction are the same variable seen twice.Section ’Bohmian quantum gravity’, Equation 4; Section ’Alcubierre warp drive’, Equation 24
Because the theory is Weyl rather than strictly Riemannian, the length of a vector changes under parallel transport, and the quantum potential plays the role of the Weyl scalar field; the quantum contribution to the energy condition carries no factor of the inverse gravitational constant, which is why Joseph argues quantum manipulation of spacetime structure is easier than ordinary gravitational bending.Section ’Alcubierre warp drive’, the Weyl geometry passage, Equations 17 to 20
Dropping terms of fourth order in Planck’s constant reduces the requirement to a single fourth-order partial differential equation for the square root of the quantum density on the warp spacetime, with the Alcubierre shape function and the bubble velocity as its source term.Section ’Alcubierre warp drive’, Equations 27 to 31
A flat-space toy version of that fourth-order equation admits hyperbolic solutions for the quantum density alongside the usual trigonometric ones — solutions that cannot appear in standard quantum theory, whose wave equation is only second order — and Joseph identifies these extra solutions as where the new physics of the scheme would live.Section ’Alcubierre warp drive’, Equation 32 and the paragraph that follows it
The open item is the exact solution: finding a viable distribution of quantum mechanical density that obeys the fourth-order equation on the warp spacetime would resolve the exotic matter problem for the Alcubierre drive in this framework, and Joseph leaves that solution to further work.Conclusions, final two sentences
The way in
https://doi.org/10.1088/1402-4896/aceb9eHow to cite it
Sijo K. Joseph (2023) Alcubierre warp drive in Bohmian Quantum Gravity doi:10.1088/1402-4896/aceb9e