system
Given the following post, respond as if you're commenting on Reddit:
human
Is it true that, according to Einstein's theory of relativity, it's possible for a particle to have super-luminal speeds, but a particle cannot cross from sub-luminal to super-luminal?

I am seeking clarification about Einstein's Theory of Relativity.  I have heard before people making claims that nothing can travel faster than the speed of light.  Is that technically true, or is it more correct to state that a particle must remain at a super-luminal speed or sub-luminal speed, it just can't cross over between the two?
gpt
It is true that there is nothing in the theories of relativity that explicitly forbids faster than light travel. It is also true that accelerating past c *is* forbidden, as speed ends up asymptotically approaching it as you keep accelerating.

However, things are more complicated than saying 'well, stuff *could* go faster than light'. For instance, putting a speed greater than c into the equations gives results such as an imaginary (in the mathematical sense) mass for the particle. We have really no idea what that would physically mean, imaginary numbers never intrude into reality anywhere else. These kinds of thing, along with the lack of any experimental evidence for any kind of greater than c effect, are a strong suggestion that faster than light travel is not really possible.

That said, these problems do not constitute a proof. Also, even if faster than light stuff doesn't happen, it's interesting to look at what our theories predict if it did.