Historical research guide · 0702 · 2007
Supersymmetry Breaking Casimir Warp Drive
Richard K. Obousy · Gerald B. Cleaver
In one minute
Richard Obousy and Gerald Cleaver of Baylor University take a piece of string-inspired cosmology and ask what it would let a ship do. In brane-world models our universe is a three-dimensional sheet sitting in a higher-dimensional bulk, and supersymmetry — the pairing of every particle with a partner — is broken on our sheet while surviving in the bulk. That mismatch leaves a residual Casimir energy in the small curled-up extra dimensions, and Obousy shows the size of that energy is fixed by one number: the radius of the curled-up dimension. Because that energy feeds straight into the cosmological constant term of Einstein’s equation, changing the radius locally changes the local expansion rate of space. A craft that could shrink the radius ahead of itself and grow it behind would contract space in front and expand it behind — moving without ever exceeding light speed through the space around it, because the distance itself is what changes.
Connection
Chapter 4 is built on the idea that the metric is an engineering variable rather than a fixed backdrop, and this paper supplies an unusually direct handle on it: one geometric parameter setting the local value of the cosmological constant. Chapter 2 gains the same point from the other side, because the quantity doing the work here is Casimir energy, the vacuum’s own bookkeeping, promoted from a laboratory curiosity to a term in the field equations.
From the source
In a brane-world where supersymmetry is broken on our three-brane but preserved in the bulk, the resulting mass-squared splitting between a scalar field and its superpartner leaves a non-trivial Casimir energy in the extra-dimensional volume around the brane, and that energy has the features needed to account for the cosmological constant.Abstract and Section I, arXiv gr-qc/0512152v1, following Chen and Gu, astro-ph/0409238
The renormalised shift in Casimir energy density scales as the brane thickness over the extra-dimensional radius raised to the number of extra dimensions, divided by the radius squared — so the vacuum energy is tied immutably to the radius of the compactified dimension.Section II, equations 3 to 5, arXiv gr-qc/0512152v1
Although the Casimir energy sits in the extra dimension, it contributes to the four-dimensional energy density of the universe and appears as the cosmological constant term in Einstein’s field equation.Section II, equation 8, arXiv gr-qc/0512152v1
It follows that a local change in the radius of the extra dimension produces a local shift in the cosmological constant, given explicitly as the difference between the original and modified radii each raised to the power of the number of extra dimensions.Section II, equation 9, arXiv gr-qc/0512152v1
A craft able to increase the radius at its rear and decrease it at its front would create a bubble of local expansion behind and contraction ahead, analogous to the Alcubierre top-hat metric. The craft stays inside its own light cone throughout; what changes is the proper distance to the destination.Abstract and Section II, Figure 2, arXiv gr-qc/0512152v1
The mechanism for locally adjusting the radius of an extra dimension is the open question. Obousy assumes an arbitrarily advanced civilisation has one and asks what physics then permits, which makes the size and controllability of the compactification radius the measurement the whole proposal waits on.Section II, closing paragraph, arXiv gr-qc/0512152v1
The way in
https://doi.org/10.1063/1.2437563How to cite it
Richard K. Obousy, Gerald B. Cleaver (2007) Supersymmetry Breaking Casimir Warp Drive doi:10.1063/1.2437563