Time Travel in Star Trek: Discovery (DIS)
"As days go, this is a weird one." (Stamets, DIS: "Magic to Make the Sanest Man Go Mad")
DIS: Magic to Make the Sanest Man Go Mad
A time crystal gives Harry Mudd the ability to rewind time by 30 minutes, with him being the only one who is aware of the effect. Everyone else experiences those 30 minutes without noticing that everything happens again and again. Using this tactical advantage, Harry Mudd gradually learns to evade his pursuers and to operate the systems of the Discovery with the goal of handing the ship over to the Klingons. Lt. Stamets is the only other person who knows what is going on, thanks to his connection to the spore network. It takes at least 56 loops for Stamets and his crew to stop Mudd.
The idea behind this story is very similar as that of TNG: "Cause and Effect". The difference in a physical and logical sense is that in the TNG episode time was reset in a causality loop, which may have lasted forever without human interference. In the Discovery episode, Mudd triggers the reset on purpose in each loop (or it is triggered by his death). There is no causality loop in "Magic to Make the Sanest Man Go Mad" but "only" someone playing with the "time controls".
It is clear that Mudd's crystal does not reset time in the whole galaxy or universe but just in a limited space around the Discovery. He wears a wrist device that seems to control the time displacements and obviously protects him against the effect. The displacement is triggered by Mudd pressing a button or by his death as it seems. The actual crystal is located in his ship that is hidden inside the Gormagander. This readily explains why it is necessary each time for him to get the "space whale" aboard the Discovery in order to pursue his plan, although he might have found better ways once he knew all controls of the ship he wants to capture. Yet, it also aggravates the problem of why the creature was beamed aboard each time, although Stamets knew what was going on. Had he managed to convince Lorca not to do it in just one of the many loops, Mudd may not have been able to carry on.
Classification: time reset in an isolated region of space-time
DIS: What's Past Is Prologue
After the escape from the Mirror Universe through the spore network the USS Discovery arrives in its own universe nine months late. It is not the first time that the time is a variable in the crossover from one universe to another. Something similar already happened in ENT: "In a Mirror, Darkly", except that the USS Defiant of our universe crossed over in the opposite direction, and wound up in the past of the Mirror Universe.
Classification: travel to the future of another universe