The fundamental problem of manned space exploration

Mankind is trapped in the solar system. At least that's what our current status on propulsion-, protection- and communication- technology dictates.

Propulsion

Reaching the second nearest planet to us (Mars) already takes half a year and that's by the short route. It took the Voyager 1 probe 36 years to leave our solar system while travelling at 61k km/h and even the fastest available ion thrusters do not generate enough acceleration to make extra-solar space travel feasible. 4.2 light years to reach the nearest solar system Alpha Centauri C would take even at 10% of lightspeed 42 years. This number of course isn't considering the time needed to accelerate to this speed and the fact that you'll need to decelerate as well at some point of the journey to avoid rushing right through the system.

Protection

Rushing through space -as vast as it may be- does not turn spaceships magically invincible. Flying multiple times faster than a bullet we have movies like "Gravity" illustrating the destructive capabilities of space projectiles. Without protection but the ships hull itself any man-made interstellar object will be extremely vulnerable and most probably doomed in attempting such a journey. We simply don't have any material strong (or cheap) enough to protect a ship from impacts at these velocities and the probability to encounter objects large enough to harm the ship is very high. especially at such distances.
And it gets worse: Physical matter isn't the only danger. Cosmic radiation is an omnipresent hazard outside Earth's magnetosphere.

Communication

At distances of lightyears communication becomes pointless. Even if we had a station on something as near as Mars, one-way communiques would require several minutes to reach the recipient and we'd have to wait just as long for an answer. So the problem with intersolar communication becomes immediately apparent.

Are there solutions?

Propulsion

NASA's Jet Propulsion Laboratory (JPL) is actively researching the possibility of realizing an Alcubierre drive. A technology which theoretically enables apparent faster-than-light travel, i. e. obeying the laws of special relativity. Current reports on results are "inconclusive" but in my opinion it's a simple matter of funding. The theoretical groundwork is done, all we need is the political will to make it a reality.

Protection

To protect a crew from cosmic radiation it was proven by British and Portugese scientists that an emulation of Earth's magnetosphere can be generated, another matter of funding to make it real. As for protection from physical objects the technology of a plasma window exists: It may be a flat kind of "force field" but at temperatures of 15k Kelvin it would literally sizzle anything to dust. Provided with power from a fusion reactor a window of feasible size could be created and projected in front of the ship rendering it into a bulldozer safe from physical hazards throught its journey.

Communication

Nothing really. In Star Trek we have subspace communication which has nothing to do with the real world whatsoever. But we know of no way to send signals faster than light. This most probably contributes to the fact that we haven't heard from any aliens yet. Our signals may have travelled only around 40-50 light years in all directions and considering how huge space is, this is nothing. Currently it seems we'd have to bite the bullet and surrender to the size of space, abstaining from communication with our pioneers. But maybe we wouldn't even want to contact them, since they'll be in suspended animation during their journey and if they find a habitable planet to colonize any news from Earth will seem irrelevant to them anyway.