Is it possible to get to get to Proxima B in 30 years? This morning I read about the discovery of an earth-like planet, Proxima B, being 'just' 4.22 light years away from us. This is quite interesting since the planet is oribiting our closest neighbour.
I read on a Dutch news site something which roughly translates to:

Scientists have been investigating whether a mission to our 'space neighbour' is possible. It would leave in about 20 years. Thanks to new technologies a probe would be able to fly very fast and only need 30 years to reach the star.

http://www.rtlnieuws.nl/buitenland/nieuwe-planeet-ontdekt-buitenaards-leven-dichterbij-dan-we-denken
This sounds very unlikely to me. I calculated that you'd have to fly at about 0.14c. Our current fastest space probe (New Horizons) achieves around 0.00001c.
How likely is it that, within the next 20 years, we can launch a probe that can reach Proxima B in 30 years?
 A: I wrote a little book on this topic, that was meant to be more of a way of presenting some elementary physics than as a serious proposal for interstellar spacecraft. The main approach that I discuss is the photon sail, which is similar to these latest proposals. These proposals involve high powered lasers, while I discussed large space-based Fresnel lenses that concentrate and columate solar radiation. The underlying physics is much the same. I also discuss how you might want your spacecraft to slow down as it approaches the target star. 
A photon sail I think could be pushed to $\gamma~=~2$, or more plausibly $1.15$ or $v~=~.5c$. That is one advantage I think that space-based Fresnel lenses might have. There is little need to push a photon sail any faster, for $\gamma~=~2$ is $v~=~.87c$ and there is little advantage for Earth based observers to send it much faster. That upper “limit” is probably an ideal. There is also the problem of accelerating to the final speed of the craft and so forth. 
A photon sail craft that reaches $v~=~.2c$ is certainly possible. This is $\gamma~=~1.02$ which means one must generate energy equivalent to $2\%$ the mass of the probe. If the system has $1000kg$ of mass this would require about $1.8\times 10^{18}j$ of energy. The entire world energy generating capacity is about $10^{13}w$. It would then take $.6%$ of a year's worth of electrical generation to impart that much energy to the probe. This is one reason I think the solar based Fresnel lens might be preferable. Yet, it is still possible that some high powered laser system could push this craft to this final velocity.
As for whether this can be done in $20$ years, that I think is a stretch. For one thing I see a number of “dragons” that we will need to fight in the future for our very survival. These problems will require our resources, mental and physical labor and considerable wealth available. I think that interstellar probes might be a project for the late $21^{st}$ century.
A: The likelihood of this isn't something that I can comment on, but the project is definitely on the books.
This would involve tiny 'nano-probes'. Being so small, it would be relatively easy to accelerate them. This would be done with lasers, which would be fired at a sail. This would act as the propulsion system for these craft.See here for a description of how solar sails work. 
The craft would accelerate to around $.2c$, which is sufficient, as you have already shown, to reach Proxima B in around 20 years.
