Paul Titze, who somehow finds time to write the excellent Captain InterStellar blog when not preoccupied with his maritime duties in Sydney, passed along a 2009 paper on warp drives yesterday that I want to be sure to consider before the year is over. Warp drives as in Miguel Alcubierre’s notion of a method of reaching speeds that are faster than light. The Star Trek echo in the choice of names was playful and intentional on Alcubierre’s part, and the physicist kicked off a cottage industry in exotic spacetimes and their geometries when he used it in a 1994 paper on superluminal flight.
Specifically, Alcubierre noted that although nothing can move faster than the speed of light through spacetime, spacetime itself has no such restriction. That notion is more or less built into the theory of inflation, which demands a vast expansion of the infant cosmos that would have far outstripped any lightspeed restriction. And Alcubierre saw that if spacetime could be made to contract in front of a vehicle while being expanded behind it, the craft would remain within a conventional spacetime ‘bubble’ while being carried to its destination at speeds that would allow fast human transport among the stars.
There’s always a catch, of course, and the first to be noticed was the huge demand for negative energy to support the warp drive. While that issue has been kicked around in the literature for some time (and various solutions introduced to lower the requirements), it is also necessary to take quantum effects into account, which is what Stefano Finazzi (International School for Advanced Studies, Trieste) and colleagues have done in their paper. In particular, Finazzi’s team finds that the quantum field known as the renormalized stress-energy tensor (RSET) becomes a problem. From the paper:
…it was noticed that to an observer within the warp-drive bubble, the backward and forward walls (along the direction of motion) look, respectively, like the horizon of a black hole and of a white hole. By imposing over the spacetime a quantum state which is vacuum at the null infinities… it was found that the renormalized stress-energy tensor (RSET) diverges at the horizons. Independently of the availability of exotic matter to build the warp drive in the first place, the existence of a divergence of the RSET at the horizons would be telling us that it is not possible to create a warp-drive geometry within the context of semiclassical GR: Semiclassical effects would destroy any superluminal warp drive.
The ‘bubble’ housing our starship, in other words, becomes unstable under these conditions. But this is hardly the last of our problems. Assuming that this instability could be avoided by some kind of external action on the warp drive bubble, Finazzi’s team argues that Hawking radiation at the center of the bubble will burn the occupants to a crisp with temperatures in the area of 1032 K. If this highly detailed argument is correct, the Alcubierre warp drive will remain what it has been up to this point, a useful way to study general relativity and quantum field theory in curved spacetimes, with little possibility of being translated into technology.
Is there any hope for warp drive? Perhaps, says Finazzi, though not on the level of Star Trek-style vessels making interstellar journeys in mere days:
…we think that this work is casting strong doubts about the semiclassical stability of superluminal warp drives. Of course, all the aforementioned problems disappear when the bubble remains subluminal. In that case no horizons form, no Hawking radiation is created, and neither strong temperature nor white horizon instability is found. The only remaining problem is that one would still need the presence of some amount of exotic matter to maintain the subluminal drive.
A subluminal warp drive may not sound quite the exotic note of the classic Alcubierre drive, but in any other circumstances attaining a substantial percentage of the speed of light would seize the imagination. So perhaps a subluminal warp drive will continue to play a role in interstellar thinking, even if its energy demands remain hugely problematic. The paper is Finazzi et al., “Semiclassical instability of dynamical warp drives,” Physical Review D 79, 124017 (2009). Abstract and preprint available.