What are the most realistic ways of high speed space propulsion? Liquid and solid chemical fuels in rockets are very expensive and inefficient. I have heard of solar sails but what are the most realistic space travel fuels that will be used in the future to get close to the speed of light?
 A: In a lot of ways this is a technology---rather than physics---question, but lets look at some limits imposed by physics.


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*For rockets there are two numbers that matter: the velocity relative the spacecraft with which the fuel can be expelled (called the specific impulse) and the fraction of the original mass that is fuel. For very high mass fractions the spacecraft can have delta V equal to several times the specific impulse. That means that if you plan to stop at the other end your maximum velocity perhaps twice is the specific impulse. If you need to come home without refueling it is around the specific impulse.


That's the killer for fast burn rockets. We still use them for launch from the surface because they can develop the necessary thrust (our high efficiency engines (ion drives and the like) are all low thrust at the present time).
That suggests one of two strategies:


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*Leave your engine behind. This is the mechanism used by laser sails, star wisps, etc.

*Pick up your fuel as you go. The strategy of ram-scoops.


Sail technology is--at least in principle--within reach of our current competence, but building and running one capable of efficient interstellar travel is beyond the current Gross Planetary Product. Star wisps are a subset of sails, but require considerable expertise in nanotechnology before they are useful even for exploration.
A second disadvantage of sails for traveling to other start in person, is that you're counting on politicians and policy makers you left behind to continue funding your trip...
Ram-scoops are a big unknown, as we don't know how to build them as yet. A BOTE calculation for a minimal, naive hydrogen fusion ram-scoop limits their top speed to about 14% of c (under the maximum drag assumption that the fuel must be brought to rest relative the craft). 
A: I wrote a semi-popular book on this subject a couple of years ago:
http://www.amazon.com/Can-Star-Systems-Be-Explored/dp/9812706178/ref=sr_1_3?ie=UTF8&s=books&qid=1297567209&sr=8-3
A lot of this was worked out.  I illustrate the relativistic rocket and the photon sail.  The photon sail is clearly the most reasonable of these two.  I also suggest using electromagnetically accelerated nano-probes, where millions of tiny probes are sent towards another star, with the prospect that a few might set up shop there and build up a robotic colony of sorts.  The solar sail is capable of reaching a $\gamma~=~1.4$, or .$69c$, though a more realistic figure is $\gamma~=~1.15$ or about $v~=~.5c$.  This analysis involve the redshifting of light on the frame of the sail craft and so forth.  To accomplish this requires placing large Fresnel lenses in space which collimate light towards the sail.
There is not much point in sending probes towards extrasolar systems faster than $\gamma~=~2$, or $v~=~.86c$.  The time saved becomes smaller and the energy costs enormous.  A $\gamma~=~2$ probe has as much kinetic energy as its rest mass, which would be a considerable feat to achieve.  At $.5c,~.7c$, and $.86c$ probes could be send within the interstellar neighborhood and signals returned in reasonable time.
The ramjet concept is useful IMO from one main reason.  Suppose various instruments were packed onto a spacecraft with an acceleration of one gravity, or larger.  These instruments look at the CMB and maybe particle detectors.  The machine reaches a high $\gamma$ in order to probe the universe as it appeared earlier on.  The CMB would be blue shifted into the IR, and maybe other detectors which can detect weakly interacting particles which pass through the early radiation dominated period of the universe.  This is pretty speculative, but maybe not impossible in principle.
A: The most realistic way is to get rid of humans, and let robots travel. They don't eat and can spend 1'000'000 years in flight without being bored too much. This way is achievable even with current tech. ;-)
A: In order to make space travel truly affordable, the only realistic way is using thermonuclear explosions. The technology is relatively cheap and available, but it is dangerous, and must be strictly controlled by large stable governments. This puts it out of reach of commercial development, and there are well known issues with government controlled projects regarding efficiency. This makes it implausible that we will see such a thing realized soon or realized well. Since this is a problem of human political organization, not of technology, I won't discuss it further.
Ignoring politics and economics, the orion project proposed a ship propelled by thermonuclear explosion products, which produces ablation pressures from products at temperatures which are simply unreachable with any chemical fuel. This technology is not speculative in any way, and it certainly allows feasable economic travel to any point in the solar system in a time-scale of a few weeks. A large Orion can be the size of an office building, it can be shielded from cosmic ray radiation, and it could be built in a few years at a cost of a few billion dollars, with no technological innovation required.
The idea that further scientific discovery is going to do better than orion is not very realistic. It is actually remarkable that we know how to make Teller-Ulam devices. When people consider orion type things today, they are dreaming of an inertial confinement fusion, but even if this works, it will require an enormous laser in the ship, which is going to be heavy and require the ship to carry a ridiculously heavy power-source. Inertial confinement is also a dream. But plutonium triggered explosions are a reality, and it seems a waste to reject the peaceful applications of this technology because of the  cold war nightmares everyone used to have.
A: I suppose that one could develop some sort of slingshot-like approach along side of some other approach using gravitaional pull of stars. My best guess is to look at technolgies that has yet to be discovered or developed. The current discussion seems limited to existing theory. Consider if similar discussion occurred 100 years ago about placing all of my phonograph records into a single device that I could carry with me and listen at whim to the different selection therein. We could very easily be discussing mini records, stacked in a tube with multiple needles to each disc. The techology of what would become an MP3 player would never occur to any in the discussion. This is why I enjoy - good - science fiction that tries to propose theory that is far beyond current and conventional understanding. I'm not sure but I would imagine that a better understanding of light itself may lead to a propulsion approach that far superior that what most consider.
A: A fun question for science fiction fans. Ever since strings started to look like the Theory Of Everything I have been fascinated by the extra dimensions. It is the analogy of an ant in a two dimensional maze. If it sees the third dimension it can climb over and be million of ant miles away from his two dimensional path to that point.
So the TOE will be great fun once it is found and established. Even if all extra dimensions are curled, each particle in our four dimensions exists also in those curled dimensions. Who knows what the future may bring in technology. The best bet then is to go full steam ahead and find the TOE, before starting on these journeys worrying about fuel.
