[Coldplay] The Scientist is about being stuck in a time travel loop.
Taking evidence from lyrics and video.
The protagonist lost his lover in the car accident we see in the video. He wanders back into town in shock and passes out on a mattress. Then he uses science to create some method of time travel, he is the eponymous scientist. This might be years or decades later or maybe he was already a scientist and had the potion in his pocket and he drank it, that doesn't matter for my theory.
So at some point he uses the time travel technology, maybe it's a pod he enters and pulls a switch or a chemical reaction in his own body from a drug infusion orally or intravenously, it's science, he is the scientist. At this point, the way the technology works, he starts experiencing his own life backwards. He is just traveling backwards in time at normal speed.
So the beginning of the video, what we see is the start of him "waking up/falling asleep" on the day he made it back to see his lover again. He is still moving backwards, and may continue to do so until being unborn, exemplified by the repeated lyric "going back to the start." I don't think he can stop this, and will eventually be reborn and live his life exactly the same way and get to the moment he started the time travel and loop back again.
"I had to find you, tell you I need you"
This is the impetus, he will do anything to find her, even break time itself.
"Runnin' in circles, chasin' our tails, Coming back as we are...Runnin' in circles, comin' up tails, Heads on a science apart"
This sounds like a time loop to me.
"I was just guessing at numbers and figures, Pulling the puzzles apart, Questions of science, science and progress, Do not speak as loud as my heart"
People probably interpret this proverbially but I think it could easily be taken to mean doing risky and experimental science without proper safety rails, not asking those questions because the heart is guiding him, which leads to the time loop problem.
"Nobody said it was easy, No one ever said it would be so hard"
Reference to media depiction of time travel, it is obviously considered a difficult or impossible task, no one says it is easy, but it is also glorified in the media and seems like an amazing awesome thing, not a curse to loop through time.
tl;dr: Chris Martin got stuck in a time loop trying to reconnect with his dead lover.