Alcubierre Drive without FTL?

The Alcubierre drive works by distorting space around a bubble: expanding space behind it and contracting space in front of it. It's a nice way to get faster-than-light travel without, well, technically traveling faster than light. But the basic mechanism behind it can, it works out, work at any speed. Nothing in the equations forbids sub-light speed travel.

The Alcubierre drive is one of a more general class of spacetimes (Natario 2001), and the metric describing how space curves around it is defined partly by an arbitrary choice of a function $x_s(t)$, from which we get the speed $v_s$ by differentiating:$$v_s=\frac{d{x}_s(t)}{dt}$$ While there are constraints on certain other parameters of the metric (such as the function defining the shape of the bubble), there's no mandate that $v_s. We have some freedom there.

Unfortunately, even sub-light speed travel falls prey to one of the classic problems with Alcubierre's original idea: it still requires a negative energy density. The energy density inside the bubble, as seen by an outsider observer, is $\rho \propto -v_s^2$, and while this goes to $0$ as $v_s$ goes to $0$, it is still negative. It would be nice if traveling slower than light got us out of that little kink, but it doesn't.

However, traveling slower than light is an improvement in other ways. For example, particular horizons form (see Finazzi et al. 2009) when the drive reaches $v_s=c$; those horizons are absent at sub-light speeds. This enables communication (a term I use loosely here) between the bubble and the outside universe. The horizons have historically been regarded as another one of the practical problems with a classic Alcubierre drive, alongside the negative energy density.

All that said, yes, you can use an Alcubierre drive subluminally. Let me know how that goes for you.

posted almost 5 years ago

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