Summary: The geometry of spacetime in Einstein’s general relativity allows for wormholes that connect arbitrary points of spacetime, making it possible to travel to a point in the past or future (faster than the usual 1 second per second). Very few time travel movies actually get the mechanics of this correct (or even attempt to), although others do explore the implications of time travel in meaningful ways.
I think Seigal’s analysis of the films he mentions is largely similar to my own, although I have a higher opinion of Bill & Ted’s Excellent Adventure than he does. While he’s right that the movie has little interest in the physics of spacetime, I think the film uses the concept of time travel to clever effect in a few points–especially the jail escape sequence.
I’d add Primer and Timecrimes to the list of movies with well-crafted depictions of fixed time scenarios (i.e. all the activity of the time travelers in the past only contribute to what was already their own history). And I’d include Frequency as a movie that makes interesting use of a changing timeline while only allowing information (via radio wave) to actually travel through time. Interstellar does something similar, only using gravitational waves instead of electromagnetic waves to carry the information; also, Interstellar depicts a fixed time scenario and also explores the time-dilation implications of special relativity.
The article also mentions closed time loops, which can be fun story devices. The TV show Lost has a good one; as you watch, ask yourself where the compass comes from. The X-Factor Investigations volume of the comic X-Factor also does fun things with closed time loops.
I did mention Groundhog Day when discussing the idea of a multiverse and all the possible variations of ourselves and the choices we can make. While the main character of the film experiences a linear sequence of events, since that is within the context of a repeated day we can think of it as a search through all the possible versions of how he can live out that day to find the optimal one. ‘Optimal’ being relative to particular optimality criteria, in this case related to kindness and self-discovery as mentioned above. In this way, the movie has been compared to certain concepts of reincarnation.
Edge of Tomorrow (rebranded as Live. Die. Repeat. for the home video release) has a similar structure, albeit within the context of a more standard men-on-a-mission story. There are aspects of personal growth, and also optimality criteria in the form of military mission objectives. In this way, it is more directly comparable to a video game where you have to keep repeating a level until you make it through the whole level successfully. The cause and rules of the time loop are more clearly spelled out than in Groundhog Day. The story also does some clever things with audience expectations, probably because it can rely on many audience members being familiar with the Groundhog Day setup.
I’d also include the German film Lola rennt (Run Lola Run) as another well done film with a similar conceit, just with fewer repetitions.