As recent research has been started by a team around Stephen Hawking under the name Breakthrough Starshot they are going for accelerating little probes up to 0.2~0.25$c$. There isn't that much information about it available yet, but they say there will be different obstacles before they really can start launching the probes. While I read it as its questionable the accelaration method will even work as expected, it seems no one else is having any doubt about it.
Even critics just see problems in challenges like:
How they want to make probes the size of 1cm3 be traveling for 30 years through space, while not hitting any particles at said 0.25$c$ or other stuff from that region.
But no one (or at least I was not able to find) was stating:
They will never ever be able to accelerate the probes to that speed because of [$reason]".
So is it really that certain, that we have knowledge available how to accelerate microcontroller like electronics of that size to a quarter of speed of light?