Using the starship Enterprise (NCC1701D) as an example, every time it accelerates to 0.5c (half impulse) and then stops, it burns a mass of matter-antimatter fuel equal to 170% of its payload!

Fuel requirements are somewhat smaller for a multi-stage rocket. But most conceivable interstellar probes will not be multi-stage vehicles.

Accelerating slowly takes more time, but does not save fuel.

In any event, it takes a lot of fuel to reach any reasonable velocity. One way around this is by using a Bussard Ramjet, which scoops up fuel (hydrogen) from the interstellar medium. While the idea of gathering fuel along the trip is attractive, there are many practical problems, among them that the low density of the interstellar medium will require a scoop about the sie of a small planet, and the problem of stopping protons coming at you at close to the speed of light. See for a more detailed description of a Bussard Ramjet.

It has been suggested, by R. Edgars of the University of Wisconsin, that the reason there are no aliens visiting us is because we live in a low density part of the interstellar medium, the local bubble, and that keeps the aliens with their Bussard Ramjets away.

A site that goes into space travel in quite a bit of detail, including some unconventional solutions, is the Warp Drive, When site.

The Fermi Paradox

Once you begin to colonize the Galaxy, no matter how slowly, you can visit everywhere in a small time (relative to the age of the Galaxy). If you can travel at 1/10 the speed of light, it takes about 1 million years to cross the 100,000 light year-wide Milky Way Galaxy. If you stop at each star on the way, and construct probes to send to other stars (to the side), and each of these probes then constructs other probes, the length of time needed to visit every star in the Galaxy is the time it takes to cross the Galaxy, or about a million years (10 million if you only go at 1/100 the speed of light).

One need not send humans (or aliens) on these probes: they could be robots which can build replicas of themselves (von Neumann probes), which send back their data to the home world.

So, a space-faring civilization will be able to visit every star in a time much shorter than the age of the galaxy, and perhaps much less than the survival time of that civilization. If that is true, then why aren't they here?

Some possibilities are:

• We are the only (or first) spacefaring species. The principle of mediocrity suggests that we should not be the first.
• Space travel is not possible for biological beings. Recent data from the Mars Odyssey shows a higher than expected radiation level in interplanetary space. See this site for more specifics. Outside the heliosphere, cosmic ray levels will be even higher. However, this won't account for the lack of von Neumann probes.
• Space travel is possible, but advanced civilizations stay home.
• We are in quarantine. This could be to protect us, and let us advance at our own rate (e.g., Star Trek's Prime Directive), or to protect us, an immature species, from the psychological shock of knowing that we are not alone.
• We are an exhibit in a cosmic zoo.
• They are here: we just don't know it.
• They are here: UFOs are alien spacecraft.

A good article about the Fermi paradox and some possible resolutions is in the July 2000 issue of Scientific American.