I looked and listened to the video, it was very interesting and it also brought up an interesting question in the laws of physics.

He mentions that the exhaust velocity of the plasma was the same as the speed of light, then he mentioned that the engine could travel at the same speed.

The question is about the theory of action/reaction propulsion in a space environment.

If you have a chemical rocket that has a exhaust velocity of “x“ number of kilometres per second when the rocket is stationary compared to an external reference, then when the rocket is flying at half the speed of “x” the exhaust is being expelled at the speed of “x” if referenced to the rocket.
The rocket then only receives half the speed of “x” compared to the external reference. Right?

Now consider if the exhaust was made up of photons of electromagnetic energy same as light.

According to the modern theories of photon propagation, their speed is constant regardless of the motion of their source, in other words, even if the source (rocket) was moving at the speed of light, the photons would still exit the rocket at the speed of light.

Not taking into consideration Lorentz-Fitzgerald contraction or the increase in mass, what would prevent the rocket from going faster than light speed?