Some people on the internet are getting very excited at the (unconfirmed) reports of an "Earth-like" exoplanet orbiting Proxima Centauri, a mere 4.25 light-years away from Earth. If correct, the planet is orbiting in the liquid water zone around our nearest stellar neighbour and is of the same order of mass as the Earth. (Note that this could mean anything from Mercury to Neptune in scale: it's very approximate at this stage. Earth-like in exoplanetography does not mean it's a habitable new eden suitable for colonization, it just means "not a gas giant like Jupiter or a tiny dwarf like Pluto".)
So here's a reality check.
The report allegedly comes, not from the Kepler planet-finder space telescope, but the La Silla Observatory. It hasn't been confirmed yet and ESO aren't commenting. If confirmed it'll be big news for exoplanetography, but there's a huge caveat attached to it which you can bet your bottom dollar the regular news media will miss completely in the aforementioned excitement:
4.25 light years is roughly 40 trillion kilometers (or 25 trillion miles, if you're American).
I don't want to minimize the significance of the discovery; it's certainly a good addition to the list of potentially habitable exoplanets here, but you will note that 4.25 light years isn't an order-of-magnitude improvement over the previous winners for Earthlike proximity, such as Wolf 1061c (13.8 light years away) or Kapteyn B* (12.76 light years away). We're talking about the difference between 40 arbitrarily-huge-units and 100 arbitrarily-huge-units. So how should we contextualize these arbitrarily-huge-units?
Currently, the most distant visited body in the solar system is Pluto, at 7.5 billion kilometers. The New Horizons probe flew past Pluto on July 14, 2015. It was launched on January 19th 2006 by a booster and upper stage combination that blasted it straight up to solar escape velocity, with a speed of 16.26 km/sec (58,536 km/h), making it the fastest human-made vehicle ever: it then executed a Jupiter gravity-assist flyby to slingshot it out past Pluto, where it arrived nine and a half years after departure.
This veritable speed racer of an interplanetary probe would thus require a mere 31,600 years to reach Proxima Centauri (if indeed it was pointed in the right direction, which it isn't).
Yes, but what if we sent a probe using (wave hands) some vastly better propulsion system that exists only as a series of paper studies, you may ask? For example, use an M2P2 plasma sail to hitch a ride on the solar wind? Well, that might reach the dizzy speed of 500km/s, in which case it might actually get to Proxima Centauri in less than a thousand years (just). This seems, from my reading, to be the best we can hope for in the near future—nuclear-thermal rockets don't offer anything like as much of a performance boost over chemical rockets as one might naively think, and it's kind of dumb to postulate a spacegoing fusion reactor until we can get one to work on Earth (and figure out what to do with the gigawatts of waste heat it'd be spewing out when mounted on a spacecraft in vacuum, which as you know is a rather good insulator).
What if we leave the engine back home? Put an M2P2 sail on a probe, but instead of relying on the solar wind, point a plasma beam at it in order to maintain thrust throughout the voyage (this is called a MagBeam propulsion system)? Now we're talking ... but such a beam generator is going to have to be constructed and operated in space (down here there's too much atmosphere in the way), and it's going to take a lot of power to generate significant thrust, much less to ensure enough of the plasma beam reaches the probe to continue generating thrust once the probe is significantly far away from home. NB: when I say lots of power, I'm talking of the same ball-park as the entire electricity production of the USA to keep pushing a probe of the same sort of size as New Horizons for a few years.
We might get a small probe up to arbitrarily high velocities if we cheat by using an engine that stays back home where we can keep it running, but then we run into other problems. Space is not empty and vacuum is not perfect. There are gas molecules (mostly neutral hydrogen) sitting around in deep space; on the order of 102 to 106 atoms per cm3. This is vastly more tenuous than the best vacuum we can produce on Earth, but it's still going to be intensely damaging to any spacecraft we can design that would have to traverse it at speed. Roughly 1% of the ISM consists of helium atoms, and we have a technical term for an ionized helium nucleus travelling at roughly 2% of the speed of light—6000km/sec—we call it an alpha particle. At a notional 6000km/sec interstellar cruise speed (2% of lightspeed), a space probe is going to encounter up to 10,000 alpha particles per centimeter of distance travelled, or 6 trillion alpha particles per square meter of frontal area per second. That's 6 TBq of radiation; or in old money, 160-odd Curies. To get a feel for what this means, note that the Fukushima Daiichi reactor meltdowns released about 100 million Curies, so the front of our one-meter-square-frontal-area probe would receive that amount of irradiation every eight days from alpha particles alone (the situation is undoubtedly worse when you factor in proton and gamma radiation bombardment). It might be better by 2-3 orders of magnitude if I've over-estimated the density of helium atoms in the stellar vicinity ... but then you can simply change the bottom line from 3 nuclear reactor meltdowns per week per square meter to 3 nuclear reactor meltdowns per year per square meter.
It still doesn't make much difference: at 2% of lightspeed, Proxima Centauri is 212 years away.
Anyway, the point I'd like you to take away from this is that while it's really hard to say "sending an interstellar probe is absolutely impossible", the smart money says that it's extremely difficult to do it using any technology currently existing or in development. We'd need a whole raft of breathroughs, including radiation shielding techniques to kick the interstellar medium out of the way of the probe as well as some sort of beam propulsion system and then some way of getting data back home across interstellar distances ... and that's for a flyby mission like New Horizons that would take not significantly less than a human lifetime to get there.