What is the fastest thing in The Three-Body Problem universe?
Sophon quantum communication. It is the single fastest thing in the trilogy, and it is not a ship at all. The Trisolarans entangle two sophons at the quantum level, keep one at home and hide the other in the Solar System, and changes in one are mirrored in the other instantaneously, regardless of distance. A fleet four light-years out can talk to its homeworld in real time, while a human radio signal would take over four years to cross the same gap.
There is an important caveat: quantum entanglement here transmits information, not matter or energy, so it does not break relativity's speed limit on physical objects. But as "the fastest thing that can reach the other side," it sits unchallenged at the top. The rest of what these unfolded protons can do is covered in the sophon entry.
How fast are the lightspeed ships?
They approach the speed of light, c, which is the hard ceiling of this universe. In Death's End, humanity and other civilizations master curvature propulsion, which pushes a ship by altering the curvature of the space behind it and can in theory accelerate a vessel arbitrarily close to c.
These ships are not faster-than-light; nothing physical in the story is. They simply take "infinitely close to c" to its limit, which makes them the fastest physical objects in the universe. The cost is a trail of reduced lightspeed left in their wake, and that side effect later becomes the basis of the defensive black domain. The reason c works as an absolute wall is laid out in why the speed of light matters in the trilogy.
How fast is the Trisolaran fleet?
The First Trisolaran Fleet cruises at one percent of light speed, and even at that pace its journey from Trisolaris to the Solar System takes more than four hundred years. One percent of c was the practical ceiling for a sustained interstellar fleet before curvature drive existed. By the time the First Fleet neared Earth, a single probe had already decided the war.
Is the droplet really the slowest?
Among these contenders, yes. The droplet's first strike in the Doomsday Battle comes in at 31.7 km/s and later doubles to about 60 km/s, which is roughly one ten-thousandth of light speed, two orders of magnitude slower than the Trisolaran fleet. The full breakdown of the droplet's speed and its impossible turns shows that its terror comes from inertia-defying acceleration, not velocity. The most hopeless weapon humanity ever faced was also the slowest mover on this list, which is the coldest lesson of the dark forest: a technology gap is not measured in percentages of speed but in whether the enemy plays by your physics at all.