Rockets need to eject particles to generate force. And to eject 1 kg of fuel, its photo synthesis system has to lose 1 km of mass in one way or another.
The solution is to find a way to generate thrust without rocket fuel ejection.
There's been a number of pure electric propulsion proposals or prototypes, but they've all turned out to be a hoax; the latest one I recall was the EmDrive [0], where any paper claiming it produced positive thrust was debunked with the measurements having been influenced by outside forces.
The TL;DR is that reactionless drives are not possible due to Newton's third law. This page / this website is always a great resource for things like this, it's in the context of writing science fiction but it has tons of research: [1]
[0] https://en.wikipedia.org/wiki/EmDrive
[1] https://www.projectrho.com/public_html/rocket/reactionlessdr...