Warp Drive Basics

Warp drive is a name borrowed from science-fiction and applied to theoretical propulsion mechanisms which have the remarkable ability to propel a spacecraft faster than the speed of light. I have long been interested in this concept and have had the privilidge to spend some time working on a novel form of warp drive. I published a paper on the internet in 2005 – the Supersymmetry Breaking Casimir Warp Drive. I did not submit the paper for peer review as I felt there were still a lot of details to be worked out. However, the paper caught the attention of the organizers of the STAIF conference and I was invited to speak. You can watch my STAIF presentation here. Late in 2007 I was invited to talk at the British Interplanetary society at the Warp Drive Symposium. The conference encouraged me to divert some time from my PhD research to developing the warp drive concept I had had two years earlier. As a result of this I wrote a more refined paper that has been accepted for publication in a peer reviewed journal.

The rest of this page is laymans review of warp drive theory.

What is a Warp Drive?

The term ‘warp drive’ originates from science fiction, and for many people it conjures images of Captain Kirk and the starship Enterprise. However, a 1994 paper by the theoretical physicist Miguel Alcubierre placed the concept of a warp drive on a more scientific foundation. Alcubierre’s paper demonstrated that a certain class of solution to the equations of general relativity could “stretch” space in a way such that space itself would expand behind a hypothetical spacecraft, while contract in front of the craft, creating the effect of motion.

One motivation for creating a warp drive is that the universe huge, and the todays propulsion technology restricts us to the exploration of our own solar system. Visiting even the nearest star systems would take us many tens of thousands of years at best. A persuasive reason for why we might actually want to visit other stars is the recent evidence of “extrasolar planets,” which are planets orbiting stars other than our sun. To date, we know of at least 250 extrasolar planets. Even more exciting is the possibility that some of these planets may be “Earth-like.” If we wanted to visit extrasolar worlds in time-frames on the order of a human lifespan a warp drive would need to be developed.

One particularly appealing aspect of this approach to propulsion is that a spacecraft could theoretically travel faster than the speed of light. Although Special relativity forbids objects from moving through space at or above the speed of light, the fabric of space is not restricted in any way. Indeed, it is believed that during the inflationary period of the universe immediately after the big bang, that spacetime inflated at many thousands of times the speed of light.

Negative Energy and the Quantum Vacuum

The warp drive concept is based on Einstein’s general theory of relativity (GR), an accepted and well-tested physical theory. One of the necessary components of a warp drive is a form of energy called negative energy, which would have to be produced in large amounts for propulsion of a spacecraft to occur. Negative energy has been experimentally verified in a famous experiment called the “Casimir Effect”.

The Casimir Effect is one of the most exciting physical manifestations of quantum vacuum fluctuations. In its simplest form, it is the interaction between a pair of neutral, parallel conducting planes which modifies the ground state of the quantum vacuum in the interior portion of the plates, creating a force which attracts the plates to each other.

The interpretation of this phenomenon is that a negative energy state exists in the interior region of the plates. In theory, the Casimir Effect could be used to create the negative energy required for a warp drive. From this perspective, there is nothing that prevents the creation of warp drive.

Even if we could generate the required negative energies, how could we interact directly with spacetime to cause the required expansion and contraction? In this case nature herself can provide a level of insight. Spacetime is already expanding, albeit very slowly. In 1929, Hubble’s observation of galactic redshifting cemented the paradigm of an expanding spacetime in physical cosmology.

The energy responsible for the current expansion of spacetime is usually termed the “cosmological constant,” or equivalently, the “quantum vacuum energy” (both terms will be used interchangeably in this article). On a local scale, space is expanding incredibly slowly: around a billion billionth of a meter per second per meter. Clearly, to build a warp drive would require spacetime to be stimulated in some way to expand (and contract) at a far higher rate, but the fact that it is already expanding gives us a primitive research direction.

Understanding the cosmological constant could be the key to warp drive. However, there are currently several models which attempt to explain the physical origin of this phenomenon. One model suggests that the vacuum energy of graviton fluctuations in the extra dimensions may ultimately be responsible.

Extra Dimensions

The concept of extra dimensions may sound fantastical, but the idea is not new. It was originally introduced by the physicist Theodore Kaluza in 1919, in an effort to unify the laws of gravitation and electromagnetism. Although the theory did contain flaws, it was the first hint that extra-spatial dimensions may play an important role in physics.

One way to envisage an extra dimension of spacetime is to imagine a hosepipe. From a long distance it looks like a one dimensional line but a closer inspection reveals that every point on the line is in fact a circle.

Extra dimensions have now become an accepted component of contemporary theoretical physics. M-theory is a theory that attempts to unify all known physics under a single mathematical and conceptual framework, and predicts the existence of extra spatial dimensions. Another other popular extra-dimensional model is the Arkani-Hamed-Dimopoulos-Dvali (ADD) theory of large extra dimensions. The theory attempts to explain the observation that gravity is far weaker than the other known forces. One way to think about the ADD model is to picture gravity as being free to propagate in all dimensions (including the extra ones), while other forces are restricted to our familiar three spatial dimensions. Thus, gravity is, in a sense, diluted, which results in its being much weaker than the other forces.

How are higher dimensions and the vacuum energy related to the cosmological constant? Well, the vacuum energy is precisely the energy that causes the plates in the Casimir effect to attract one another, as discussed earlier. This vacuum energy should also exist in higher dimensions In the ADD model it is the size (or radius) of the extra dimension that directly effects the higher dimensional vacuum energy which ultimately regulates the magnitude of the cosmological constant, and therefore the expansion of spacetime.

Higher Dimensional Warp Drive

I recently investigated the plausibility of locally adjusting the size of the extra dimension to locally adjust the cosmological constant (by local, we mean in the vicinity of a spacecraft); this would theoretically modify spacetime around a craft and could be tuned to acquire the characteristics of the Alcubierre warp bubble. The basic idea is that by altering the radius of an extra dimension, it would be possible, in principle, to adjust the energy density of spacetime which relates directly to the cosmological constant which ultimately controls the inflation/contraction of space itself. The laymens version of the paper can be found here, of for the more mathematically minded please click here (note, when you follow the links you will then need to download the pdf file in the top right of the page).

We studied the idea from two angles. The first approach involved utilizing the physics of quantum field theory, and the another involved the physics of Einstein’s theory of general relativity. The equations of both theories gave complimentary results indicated that the physics of the extra dimensional space effects the expansion rate of “normal” space by a “dimensional shearing” effect. The equations of GR demonstrated that shrinking the extra dimension would inflate our space, and that expanding the extra dimension would contract our space. In this way, a bubble of expanding/contracting spacetime could be created at the rear/front of a spacecraft.

Preliminary calculations using quantum field theory indicated that superluminal propulsion could be achieved at an estimated energy cost of 10E45 Joules, or roughly the total mass-energy contained within the planet Jupiter after using the famous relation E=mc2. Although this number may appear enormous, it is certainly an improvement on earlier calculations, which indicated that the warp drive would require more mass-energy than is contained in the entire observable universe.

Further calculations revealed an upper bound on the velocity a warp drive might obtain. If the cosmological constant is indeed a consequence of the size of the extra dimension, then there would be a minimum size to this dimension; this would be the Planck length, which is the believed to be the smallest length possible. If the extra dimension were shrunk to the Planck length, then our calculations reveal the limit on warp drive velocity to be 10E32c (where c is the speed of light). This number is a theoretical bound, as our calculations regarding the energy required to reach this velocity indicate that significantly more mass-energy than is available in the observable universe would be required.

One important aspect of future research would have to involve studying how to locally manipulate an extra dimension. String theory suggests that dimensions are globally held compact by strings wrapping around them; if this is the case, then it may be possible to locally modify the string tension, or perhaps even counter the effects of some of the string winding modes. This would achieve the desired effect of changing the size of the extra dimensions, which would theoretically lead to propulsion at greater than lightspeed.

This novel approach to warp drive, although only theoretical at this stage, gives us a glimpse as to how we might address the problems associated with the vast distances involved in interstellar travel, and how we may one day reach the stars.