Roland Michel Tremblay

Sci-Fi Helper

This report on the Net: www.themarginal.com/timeloop.htm

Download a doc version: www.themarginal.com/timeloop.doc

  rm@themarginal.com     www.themarginal.com

Groundhog Day – Temporal Causality Loop Introduction

Star Trek - The Next Generation – Cause and Effect

Comments - Star Trek - Cause and Effect

Stargate SG-1 - Window of Opportunity

Comments – Stargate SG-1 - Window of Opportunity

The X-Files - Monday

Comments - X-Files - Monday

Overall Comments

Star Trek Voyager – Future’s End

Comments - Voyager - Future's End

Overall Solutions

     Solution 1 - It is not explained but it is happening

     Solution 2 – An explosion or something like a magnetic storm

     Solution 3 – Travel in the future, do something wrong, travel in the past to

                       prevent the departure but causing that very departure (time

                       paradox causality loop)

     Solution 4 – A fluctuating timeline

           Unusual gravity influencing the timeline

         The Moon gravitational pull influencing the timeline

           How to end the loop?

           Mind and Mood Influencing the Timeline

           No need for the moon or artificial gravity field like a wormhole

           Star Trek - The Next Generation - Time Squared

           Comments – Star Trek – Time Squared

This is going to be a long analysis as I think it is important to understand the principles beyond Groundhog Day in order to write something more interesting. You might forget all this and keep it simple, but at least I would have made you aware of the potential of that story.

It is important to note that the movie Groundhog Day has not tried to explain the phenomenon of the day repeating itself. The movie starts with clouds, which suggests that God is involved somehow. Well, this does not do good sci-fi, so no help there. Fortunately the movie has spawned some monsters and the people inspired by it tried to explain it (the fools!).

Groundhog Day is one of my favorite movies of all time. As it happens the episodes of the X-Files, Star Trek and Stargate SG-1, that I will be talking about here, are all my favorite episodes in their respective series. It is not only me, many fans of those series said the same thing. Cause and Effect is an all time favorite episode of all Star Trek series. So this story has a great potential from the start.

Why? Because of the subject and the possibility that this is happening right now in our lives even though we don't realize it. How many times have we heard: I had a hunch, I had a feeling, I feel I have already done that, I had an intuition, and the classic I just had a déjà vu? So many times that there must be something underlying these phenomena. Something that can be exploited and amplified in a story after, for example, an initial explosion wrecked normal space-time in the area and perhaps the normal linearity of the timeline.

It is important to know what the others did so you don't do the same thing and you can do better. So please read the short descriptions of these episodes and then my comments following each description. My four identified solutions are at the end. Here is a shortcut to the Overall Solutions.

www.startrek.com/library/tng_episodes/episodes_tng_detail_68542.asp

While playing poker with Riker, Data and Worf, a strange feeling of déjà vu helps Beverly successfully call Riker's bluff. She is then summoned to sickbay to examine a dizzy Geordi, and once again experiences this sensation. When she goes to bed that evening, she is haunted by strange voices in her quarters. The ship continues to chart the Typhon Expanse, a previously unexplored region of space, until the distortion field suddenly fluctuates, the main propulsion systems collapse, and the Enterprise is thrown into red alert on a collision course with an older starship. Riker recommends decompressing the main shuttlebay, but Picard follows Data's advice and uses the tractor beam to alter the other ship's trajectory. Unfortunately, this course fails, the ships collide and the Enterprise explodes and is completely destroyed.

Later, Riker, Data, Worf and Beverly are playing cards again, and both Riker and Beverly realize they know what is coming next. Beverly is again summoned to Sickbay, where she and Geordi both experience feelings of déjà vu. When she hears the voices in her room, she immediately goes to Picard and tells him that something strange is going on. He decides to run a diagnostic. The next morning, while discussing the results of that diagnostic, the older ship mysteriously appears and the Enterprise is again destroyed.

The card game is in full swing again, but this time, all four players realize they know what cards are coming next. Beverly anticipates being called to Sickbay, and when Geordi again shows up feeling dizzy, she goes to Picard and repeats their previous exchange. She hears the voices in her room again, but this time Beverly turns on her tape recorder. The recording is studied, and Data deduces that the strange voices are the voices of the crew.

Beverly and Geordi realize that they are trapped in a causality loop — a time warp that dooms them to endlessly repeat the same fragment of time. This phenomenon is causing Geordi's dizziness, and Data discovers that it also explains the voices on the tape, which are "echoes" from a previous loop. He isolates pieces of dialogue that indicate that the Enterprise collided with another ship, exploded, and got stuck in the time warp. Realizing that whatever they do to avoid the collision will probably be the same thing they have done before, Data decides the only hope is to send a deliberate message into the next loop. They prepare to send the message, the red alert begins again, and the ship is destroyed.

Another card game is in progress, but this time, the cards are different, with everything occurring in threes. Things continue to happen in sets of three, and the number three is seen everywhere for no explicable reason. Other than this difference everything occurs as before. When the red alert begins, Picard again chooses Data's advice over Riker's. At the last minute, however, Data notices the three pipes on Riker's uniform and, realizing "three" was the message he planted for himself, takes Riker's advice and leads the ship to safety. The collision avoided, the crew is hailed by the older ship, the U.S.S. Bozeman. The Enterprise contacts Starfleet Command, who reports that they have been caught in a time warp for seventeen days, while the other ship has been stuck for 90 years.

Here is the script of act 4: http://home.att.net/~que/qstce.htm

In the series Star Trek they talk about being caught in a time loop or a temporal causality loop. They have to remember it themselves, with feelings of déjà vu that get stronger and stronger with the days passing by. They get to understand that they are stuck in a specific fragment in time that they are experiencing over and over again. So they try to find a way out but they forget all about it the next day. They have to find a way to remember and do things differently. They don't call it déjà vu anymore because it is more than a feeling, they are actually reliving the same day again and again.

They hear voices from previous loops that they can record and analyze, especially one that says that there is a highly localized distortion of the space-time continuum (a distortion field created by another ship coming towards them). The whole thing was very well thought.

How they get this temporal distortion? With a big explosion that ruptured the space-time continuum, the explosion of their anti-matter propulsion system. Also, they are in a previously unexplored region of space called the Typhon Expanse (that always helps, to be somewhere spooky that nobody explored before, except that other ship colliding with them).

Their solution is to send a message into the next loop on how to avoid the collision and prevent the explosion. The echoes or after images of the previous loops received through Geordi's visors appear in the distortion of the Tachyon Field (a tachyon is a particle going faster than the speed of light). To send a deliberate echo in the next loop, they will enhance a Tachyon emission to create a specific pattern and send to themselves a very short message, like the word 3. If the Tachyon emission is modulated correctly, it will set up a resonance in the positronic subprocessors of Data. He will receive the message on a subconscious level and they don't know how data will perceive that information, it could be like a post hypnotic suggestion.

I will continue my analysis in the overall comments later on.

www.stargate-sg1.com/home/episodes/s4.html

Synopsis : While exploring planet P4X 639, the SG-1 team meets Malikai, a human explorer from another world who shares Daniel's interest in an alien computer covered in a strange Latin-like script. As solar flares flash from the red sun overhead, Malikai warns Daniel that the geomagnetic disturbance may be dangerous to the SG-1 team and tells him to leave. When Daniel ignores him, Malikai zaps him with a weapon and begins to program the alien computer. O'Neill and Teal'c rush to Daniel's aid and are caught, with Malikai, in a mysterious blue light. Suddenly, they find themselves back at Stargate command, ten hours earlier, preparing to head off on the mission they've just returned from. And then it happens again. And again. And again. As O'Neill returns to eat the same plate of Fruit Loops over and over again, it becomes clear that they've been caught in a time loop and that only he and Teal'c retain their memories through each ten-hour cycle. It's up to them to decode the message on the mysterious machine and figure out a way to break the loop.

In Stargate, interesting enough, they found a different way of exploiting the idea. Two characters remember everything clearly, the last 10 hours, after which they go back in time to the beginning of the time loop. They have a very big familiarity with the events and remember clearly what happened the first time. It is the funniest and most intelligent episode they did. I wonder who thought about the Fruit Loops in an episode about time loops. Note that only the three characters caught in the beam remember everything, they others don't.

They need two things for the loop to happen. First, a solar storm: a coronal mass emission (giant solar flare) on a weird planet creating a geomagnetic field (geomagnetic disturbances) - disrupting the planet's magnetic field and creating dangerous radiation. The second element is a strange and old alien device with some weird scriptures on it: "conqueror of time" is a first suggestion, but the right translation is "masters of the uncertain past". The device is activated by drawing energy from the ionization in the atmosphere (electric field) and sends a huge energy beam in the wormhole of the Stargate, causing 14 different worlds to relive the same 10 hours over and over again.

An interesting question asked in the episode: do they remember future events or have they been sent back in time? An explanation: could this beam from the alien device be a mean to access the gate's subspace field in order to create some kind of time inversion outside of subspace? (Some people must have had headaches thinking of that one!)

An interesting thing is that since nobody else remembers what happened in the previous loops, O'Neill and Teal'c can do whatever they want without consequences. Very funny what they do…

Monday morning and Mulder awakes to find his water bed has leaked, shorting out his alarm clock making him late. Water has seeped through the floor to the apartment below and the resident calls to complain. On arrival at the X-files basement office in the FBI building Scully informs him he is late for a meeting with Assistant Director Skinner, but Mulder has to make a bank deposit to cover the cheque he wrote to his landlord for the damages. Mulder goes to the Cradock Marine Bank down the street from the FBI offices. In a car outside a woman, Pam, and a man, Bernard, sit talking. Bernard tells Pam he has to run an errand but when he gets inside the bank he starts a robbery. Moments later Scully enters the bank looking for Mulder and draws her gun, in all the commotion Mulder is shot. As Scully tries to help Mulder, who lies bleeding, riot police alerted by the silent alarm storm the bank. Bernard knowing he is trapped detonates the explosives strapped to his chest destroying the bank....

Monday morning and Mulder awakes to find his water bed has leaked, shorting out his alarm clock making him late.....and so it goes on, time appears to be repeating itself in a loop, forcing Mulder and Scully to continually relive the experience with small variations but always the same result, the bank is blown up. Only the woman Pam appears conscious of the time loop, of the events repeating themselves and tries in vain to alert the two agents to their shared predicament.

Noteworthy Quote

Mulder: "Scully, did you ever have one of those days you wish you could rewind and start all over again from the beginning?"

Scully: "Yes, frequently. But I mean, who's to say that if you did rewind it and start over again that it wouldn't end up exactly the same way?"

Again in the X-Files, like in Star Trek, an explosion in the teaser is the catalyst for going back to a point in time that is the beginning of the time loop. In Star Trek they go back to a poker game where they can easily remember the cards. In the X-Files they have chosen to start with Mulder waking up on a Monday morning like in Groundhog Day when Bill Murray wakes up in the bed of the hotel. This time the radio clock is fried so we don't have to suffer Mulder trying to destroy it dozens of times.

The explosion of a bank (and quite an explosion for a TV show) is the cause of the time loop, and only the girlfriend of the guy with a bomb can remember everything from a loop to another. She has tried everything to break the loop except being shot, freeing everybody from the loop.

Though there is absolutely nothing that could explain that loop in the X-Files, they have developed a very nice philosophic way of looking at it. Mulder is having a horrible Monday with his bed dripping on the neighbors downstairs and being late for work. His terrible day continues when he arrives in the bank where a mad guy shoots him and blows the bank. The girlfriend remembering everything realizes with time that the others start remembering glimpses of the other loops. And it is only this fate in the truth that will save them all, because then Mulder will believe her enough to work with her into a workable solution.

The interesting philosophical ideas: destiny, cause and effect. If you did not buy a water bed, you would not have been late, you would have not met Scully, your whole life would have been different. If you could change fate, do something differently, are the things that are meant to be still happening? Can you change it? The main question is: how to end this in a different way, or should you?

Yes you can change the events, the girlfriend got killed ending the loop. But any other change from the others like Scully going to the bank instead of Mulder (Mulder has to go to the bank anyway in the end), or Mulder using the ATM machine because the girlfriend warned them (the ATM machine turns out to be out of order and Mulder goes into the bank), has little effect on the turn of events. They cannot tempt fate, they cannot change the turn of events. Only the girl remembering the loops appears to be able to do that, and then again, only with the help of Mulder once he starts to remember as well.

The main question is: how to end this in a different way? It appears that something went wrong in the mechanisms of the existence, something happened that was not supposed to happen. And that is why they keep reliving the day until things are right, that they are the way they are supposed to be. And that is: the girlfriend needs to die in the robbery. She is the only one remembering, she is the one supposed to die, she is the element that is wrong in the picture causing the time loop.

Mulder keeps repeating to himself: he's got a bomb, he's got a bomb, right before they blow up. Like in Star Trek he is trying to convey a message into the next loop. This is how for once they will avoid the explosion, because remembering that the guy's got a bomb brings back all the memory of the previous loops to Mulder.

Explanation of a déjà vu by Mulder: Some Freudians believe that the déjà vu phenomenon is a repressed memory escaping the unconscious. It represents a desire to have a second chance, to set things right. Scully’s explanation (more scientific): it's more likely that we are talking about neurochemistry, a glitch in the brain's ability to process recognition and memory. It does not mean that the memory is authentic. (They certainly did their research! An explanation that has nothing to do with physics to explain a time loop! Using psychoanalyst studies and medical science.) Then Mulder asks: “What if it was authentic memory, what if he was reliving the moment for real?” And in that case, none of the explanations given make sense. Because then it is not psychological and it cannot be explained by a glitch in the brain. Unless this whole episode was happening in the head of someone, in a dream.

What we can learn from this is that to explain the events from the point of view of science, you don’t need to have it spot on or really believable. Offering some explanations without them being plausible is also acceptable. This episode of the X-Files shows you that even without a sci-fi series you can have very interesting ideas borrowed from the sci-fi arena. And you don’t even have to explain or justify the events from a physics point of view.

As you can see the idea is not new. Even Jett Jackson has its own Groundhog Day episode, but I have not seen it and I could not find an episode’s description on the Internet. The episode is called: The Perfect Day (Originally aired 12/29/2000), Season 3, Episode 17. Synopsis: Jett relives a miserable day, over and over, until he gets it right.

In Groundhog Day and the X-Files, it appears that fate, destiny and/or God are involved. Truly we cannot do this, we need to explain it in terms of physics. In Star Trek we have the perfect solution, but they are on a ship and they need the positronic brain of Data to get the message from the previous loop. They are also using subspace signals (signals travelling outside the fabric of space) and tachyon emissions (sending a message with tachyon particles means with particles going faster than the speed of light) in order to send a message in subspace where time is nor fixed nor linear. Clearly we cannot follow that course. In Stargate, again we are confronted with subspace fields that cannot be proven. Both subspace and tachyon particles are theoretical ideas very far from reality. So, we need something else.

In the X-files and Star Trek, a message needs to be sent into the next loop in order to prevent the explosion. In Stargate, since they know about the time loops and can remember events from one loop to the next, they only need to learn how to stop the machine in order to prevent the energy beam to cause the time loop. In Groundhog Day there are no such things. Bill Murray only needs to be a better person to win the woman and wake up outside of the loop.

Well, if in the real science temporal causality loop could happen, and I believe it could, then you would need to learn what will happen next, what is the cause of the loop in order to prevent it. Now, do you keep your memory or not? In theory you would not. Why would you? Everything goes back to how it was some time ago. The only way you could remember everything is if you keep my fourth solution described at the end. In solution 4 you could remember what has happened if the timeline was fluctuating and the frontier between past, present and future was not fixed in a linear time frame. You could still not remember anything and use solution 4.

www.startrek.com/library/voy_episodes/episodes_voy_detail_68934.asp

In Star Trek Voyager there is an interesting episode called Future's End:

The U.S.S. Voyager is fired upon by the 29th-century Federation "Timeship" Aeon commanded by Captain Braxton, who has time-traveled through a spatial rift to destroy Janeway's ship. Braxton claims that Voyager is responsible for a temporal explosion that will obliterate Earth's solar system in his era. Although equipped with only 24th-century technology, the crew manages to deflect Braxton's blasts and damage his ship, but then both the timeship and Voyager get sucked through the rift. The starship winds up in orbit around Earth in 1996.

Knowing Braxton's ship holds the key to returning to their own era, the crew begins searching for it, and an Away Team beams down to Los Angeles to investigate subspace readings that seem out of place in the 20th century. Meanwhile, at Griffith Observatory in the Hollywood Hills, astronomer Rain Robinson picks up Voyager's warp emission on her instruments and reports the finding to computer mogul Henry Starling, who funds her lab. Against Starling's instructions, Rain transmits a greeting to Voyager, and the crew tracks her to the Observatory. While Paris and Tuvok head for the site, Chakotay and Janeway identify a homeless man as Captain Braxton. He explains that he emerged from the time rift in 1967 and crash-landed in the desert, where a young Henry Starling found the timeship and utilized its technology to start a high-tech empire. Starling is now planning to use Braxton's vessel to time travel, and, according to Braxton, that will cause the explosion in the future.

Fearing that Rain is a security risk, Starling sends a henchman to kill her. But Paris and Tuvok spirit her away before she can be harmed. When Rain questions what they're up to, Paris tells her that they're secret agents tracking a Soviet KGB spy operation. She sees through his story, though, because the Soviet Union and the KGB no longer exist.

Chakotay and Janeway sneak into Starling's office, where they discover Braxton's timeship just as Starling walks in and confronts them. Janeway warns Starling not to launch the ship, explaining it will unleash disaster. Undaunted, Starling tries to kill Chakotay and Janeway, but they're transported to Voyager in the nick of time. They try to beam up the timeship, but Starling uses their transporter beam to access Voyager's computer and study its systems. Minutes later, the wily Starling steals the Doctor's program from Sickbay. To complicate things even further, Voyager's presence is disclosed on the evening news!

Janeway's attempts to beam up 20th-century computer mogul Henry Starling and the timeship in his possession are stymied because Voyager's long-range transporters aren't working. As a result, brilliant astronomer Rain Robinson lures Starling to a meeting where the crew hopes to hijack him. Starling shows up with the Doctor, whom he's supplied with a 29th-century portable holo-emitter that allows him to exist in environments without standard holographic emitters.

Having reconfigured the shields on a shuttlecraft to disguise it from 20th-century radar, Chakotay and Torres try to beam up Starling from the rendezvous. Starling has a device that interferes with the attempt, but Voyager is able to redirect the transporter signal to beam him directly to the starship. Unfortunately, Starling's attempt to disrupt the beam-out damages the shuttle's controls. It goes down in the desert, where Chakotay and Torres are taken hostage by a paramilitary group. Voyager traces the crash site to Arizona, and the Doctor and Tuvok travel there to find them.

On Voyager, Starling admits to Janeway that he wants to travel into the future to steal more advanced technology. Although Janeway thinks she's put an end to those plans, one of Starling's henchmen uses his scavenged 29th-century technology to transport Starling back to his office. Outside Starling's headquarters, Paris spots a truck that appears to be moving the timeship to another location. In Arizona, Tuvok and the Doctor manage to free Chakotay and Torres. Torres repairs the damaged shuttle, which they use to track the truck and destroy it. However, they discover the truck was a ruse; the timeship is back in Starling's office, and he's just launched it.

Retrieving Paris and Tuvok, the shuttle returns to Voyager, where Janeway hails Starling, who refuses to abort his mission. She has no choice but to destroy the timeship. Seconds later, a time rift opens and Braxton appears in his timeship. With his previous timeline altered by the destruction of Starling, this Braxton has come from the future to lead Voyager back to the 24th century, where it belongs. Janeway implores Braxton to place them at Earth, but Braxton cites the Temporal Prime Directive, which Janeway cannot argue with. Back in the Delta Quadrant, the crew finds that they've gained one particular advantage from their journey: the Doctor has retained the 29th-century mobile holo-emitter, freeing him from the confines of Sickbay.

Voyager is the cause of an accident that happened in the 29th century, but they are not really the cause. They were involved somehow. A cause "A" (Voyager gets involved) leads to a consequence "B" (they are thrown in the past in 1996 with the timeship) which leads to another result "C" (the timeship and Voyager go in the 29th Century and cause a temporal explosion destroying the planet). This brings us back to "A" because the timeline police with the timeship tries to stop Voyager to ever get involved, which gives Voyager the chance to get involved in the first place. Like a time loop Voyager would have created by getting involved in all of this.

The real question is: what was the cause of the explosion since Voyager would have not got involved in the first place if the timeline police had not gone back in the past to destroy Voyager before it can get involved? Something else, another cause originally created the explosion. And with the changes in time, Voyager became the cause by getting involved. That is an explanation. Or perhaps it is another one of those episodes about the effect can precede the cause (like in Star Trek Voyager Parallax and Time and Again, Season 1, episodes 3 & 4).

My point in all of this is that you need an initial cause to the effect, something that leads to an event that causes the loop. In time another event can become the cause, and that is what you would need to find out and prevent. In order to break the loop you will need to know about the new cause and the effect, then you could devise a plan. We are already very far from Groundhog Day.

What could be our cause (in any of the four solutions described below)? An explosion, perhaps the explosion of a machine, or a science experience that went horribly wrong (getting mixed up with different liquids in order to create a nitroglycerin bomb or something similar). Then, you need to learn about that consequence and prevent it. Now, you could be prevented from preventing it (by fate or predestination) or you could easily do it once you get to know about it. How do you get to know about it? By sending a message into the next loop, intuition, guesses, déjà vu.

As for explaining how this is possible, an explosion creates a rupture in the space-time continuum bringing everything back to the way it was some time ago. But we can be more imaginative, like in Voyager, and involve time travel. By going in the past or the future, someone can actually create a cause that will create a time loop. Like Voyager receiving the visit of a timeship, which brings them in the past, then they go to the future and destroy everything. That leads the timeship from another timeline to go back to Voyager in order to prevent it from going in the past. Get your imagination running if you wish to create a time paradox like this!

Of course, if you just want someone to live his or her day all over again without getting too much involved in time paradoxes, you can just have what could be a natural phenomenon related to the weird things happening around the area.

And why would only one person or two persons remember the previous loops? Perhaps because they are more sensitive to the déjà-vu phenomenon. Or like in Stargate they were in the field of the beam that caused the time loop.

Someone wakes up remembering doing the same day over and over again and the others don't remember anything. Perhaps in time they will remember more (like in the X-Files) or they will never (like in Groundhog Day and Stargate). We don't know exactly how, we give some suppositions or hypothesis that you can find in all my previous comments, and eventually by doing something special you will break the loop. Something obvious, like trying to correct everything in order to make the day the perfect day (like in Jett Jackson). Or prevent something from happening that appears to be the cause or starting point of the loop.

An explosion or something else like a magnetic storm (or geomagnetic fields like in Stargate) creates a rupture in space and time (in the space-time continuum) creating the loop. Now you need to learn about the cause and the effect and prevent the explosion from causing the rupture (like in Star Trek - The Next Generation and the X-Files).

Note that if you don’t have someone remembering everything, like in Stargate, the X-Files and Groundhog Day, you will need someone more aware of the phenomena in order to get people to realize that they are in a time loop. In Star Trek it is Doctor Crusher who appears to be the most aware of the phenomena. She has clues to follow: Geordi’s Visor, feelings of déjà vu with her flowers, premonitions about which cards will come next at the poker game, and intuition about Riker’s bluff.

Someone goes in the future and there he does something (perhaps just by being there) that kills someone or destroys something (perhaps the planet like in Voyager). So now we need to prevent him from going in the future in the first place. How do you do this? You go back in the past but by going in the past, you create the cause of his departure. You open a vortex or something for him to go in the future. You need to find a way to prevent him from going in order to stop the time loop.

Note: this is not very Groundhog Day and could be another story all by itself. To make it more like Groundhog Day you could have many times your character going in the future and trying to prevent whatever it is he is causing. And you could have many times the people going in the past trying to stop his departure in the first place, trying different things every time but not succeeding in stopping him. 

So far I have only brought you what the others did and how you could do it. If I had to think of a solution myself though, I would have something much closer to reality and the relativity of Einstein. This does not need explosions, magnetic fields or time paradoxes.

It is a fluctuating timeline and the hypothesis to explain how the day can be repeating itself would go something like this: there is an obscure theory that states that the timeline is fluctuating due to the fact that we travel in space at different and relative speed each day. Depending on our speed and the gravity surrounding the Earth, time runs at different rates every seconds of our existence. Therefore the timeline is not as linear as we may have thought. The timeline could be fluctuating to such an extent that future events can happen before the present, and past events can happen in the future.

Therefore something we do in the future might have happened in the past and it has somehow caused a time loop in which we are trapped. This is why we usually have feelings of déjà vu, but this time it appears to be a very strong feeling, like if it was more than on a subconscious level. The question is: what is the cause of the time loop, why do we go back in time like this?

A reason could be that the gravity around the area is unusually strong. A ball falls faster than normal and the usual gravitational force of 9.8 Newton. A bit like if a wormhole was around here. As a consequence, when gravity reaches a certain point, we go back in time and relive the day.

For example, when gravity reaches a lighter level, bringing the gravity force back to normal (during the full moon), we go back in time and relive the day. Therefore something someone does in the present might be happening in the past because of the strong gravity forces that slow his time down considerably. And when the moon reaches the top, gravity sort of goes back to normal and he finds himself back in the past. If gravity gets lighter, if you could weight less, then you could free yourself and wake up the next day in a new day.

The timeline is not as linear as you may think, the future can actually happen in the past. The higher the gravity, the slower time goes. If gravity becomes super-high, then you could get stuck into the present and not move forward in time anymore. 

The moon is important (but not essential) because the force of gravity exerted on your character is very high, keeping him in the present with no way of moving forward. When the moon reaches its peak, gravity is lighter and this is how the Loop happens, he goes back into the past (his present moves back into the past).

We need to find out where the gravity is coming from and prevent it from reaching the point when the loop starts again. It could be a huge Vortex opened somewhere and we could close it with an energy device. Instead of a wormhole or a vortex, it could also be a meteorite fallen from the sky, exhibiting strange gravitational forces. You could just find a weird rock made of an unknown metal that is very heavy and a lot of gravity could emanate from it. That could be the problem about too much gravity. You could then just have to get that rock out of here. Arrange to have it send in the polar caps or at the bottom of the ocean, or the US government could come and pick it up in order to study it further and then we would get rid of the rock and gravity will be back to normal, stopping the day from happening over and over again. Letting you to wonder if those government officials know what they are getting into and if they will take appropriate actions to make certain they will not get trapped into a time loop themselves.

When gravity is high, people should feel heavier, weight heavier and that should affect their mood as well.

Another solution to the cause of the time loop could be that there is a full moon and strange things happen on a full moon. In this case, the gravity is less than usual and affects the timeline, making things done in the present affect the future and the past. It is that very thing that someone does during the full moon that needs to be prevented. So the future or the past will not be changed and there would be no time loops trapping us.

Check this website, it shows you the Moon phases for each day of the month: http://www.googol.com/moon/

Now you want to explain how this loop ends. Well, if you look carefully at the website mentioned above, the Moon phases slowly turning to full and getting smaller again last a few days. Perhaps the day could be repeating itself, but the Moon could change like if it was a normal Moon phase. It would show that time is somehow distorted and a different "same day" is not exactly the same since the Moon would change a little bit every day. The loop would finish as the Moon gets smaller. I think this would be perfect.

So in theory, the day would have not repeated itself forever, only for the few days that the Moon was influencing the timeline. Once the Moon does not have a significant effect anymore on the gravity here on Earth, the normal gravitational force of 9.8 Newton will be back to normal, as well for the apparent linearity of the timeline. The Moon phases remained normal. The days are not exactly the same, somehow the Moon affects the gravity and the timeline in an unusual way. There is a way out of this time loop once the full Moon is gone. (And then, even though it will take a few more “same days” as the Moon becomes smaller, the theory is still OK. It is just that the Moon, even though is not full, still has a strong gravitational pull on the Earth).

In certain solutions, your character must influence reality around him, he must be the cause of the loop. In which case the whole universe could be imagined from one mind’s point of view. The gravity that is too high and gets you back in time could be the gravity surrounding your own mind because your mood is really too deep, it affects your surrounding universe.

That is why sometimes the Déjà Vu phenomena is about very strong events like accident, death of someone close to you, or the Titanic that hundreds of people foresaw. They were events heavy in consequences and in our minds, that could be part of the shift back in the past. And they are highly localized events, like if the gravity needed to foresee the future and create a time fluctuation (future happening before the past) was instead closer to our brain or in our minds. 

And the way to break the loop would be to alleviate the mood, the negativity, the deepness and heaviness of the day and how it affects you mentally. This solution does not need the gravity of a big body like a wormhole. And the full moon could help to alleviate some of the gravity affecting all this if necessary (but it is not necessary). If you use the full moon, perhaps it can always stay full until your character realizes the influence of the full moon, and then the next day once outside the loop, the moon would be smaller. 

In this case, whatever your character does, it has to have an effect on the loop. He must somehow control the loop just by his actions. So basically, the more he keeps it the way reality should be, the more he will get out of the loop. Of course he might want the reality to be something else, keeping him in the loop. At this stage, an explanation you could give on top of everything as to how his action might influence the whole thing is what they used in the X-File: destiny, fate, predestination.

Unless somehow his mood, his negativity, was connected with the actual distortion of the space-time continuum. Like if he was ultimately in a dream but affecting everyone around him. We don't know exactly how, we give some suppositions or hypothesis like somehow his moods and emotions are so strong, they are somehow affecting the timeline. Perhaps it adds to the gravity around him, it destroys the right balance of energy or gravity around and it causes the loop.

These are only some ideas, the loop could still end with something else then the moon phases, and the cause of the loop could also be something else than the gravitational pull of the Moon or a wormhole.

Again, here is how you would explain living the same day over and over again: The timeline is always fluctuating since we travel in space at different and relative speeds each day. Depending on our speed and the gravity surrounding the Earth, time runs at different rates every seconds of our existence. Therefore the timeline is not as linear as we may have thought. The timeline could be fluctuating to such an extent that future events can happen before the present. Therefore something we do in the future might have happened in the past and it has somehow caused a time loop in which we cannot get out of.

This is sufficient in itself, you don’t need the moon or another gravitational force on Earth. In fact, the gravity that somehow wrecks the timeline is perhaps in space and the result of a natural cause, more or less gravity suddenly exerted on the Earth, affecting our speed in space. In that case stopping the loop has nothing to do with the moon passing by or closing a wormhole around or any other gravity field. It would have something to do with changing your behavior right to the point of causing the causality loop. You need to find the cause to the effect and prevent it. For example, if you do something in the future that is somehow moved to the past, changing the behavior of some other people that will lead you to do that very action creating a time loop, you need to prevent that key action that creates the causality loop.

There is an interesting episode about that in Star Trek the Next Generation, it is called Time Squared:

Riker discovers that the shuttlecraft belongs to the U.S.S. Enterprise, and Dr. Pulaski finds an unconscious double of Picard inside. Captain Picard accompanies his double to sickbay, where Troi explains that the double really is Picard, but from another time. Data tells Picard that the shuttle's on-board clock shows it to be just six hours ahead of the U.S.S. Enterprise.

Scenes taken by the shuttle camera as it departed show the U.S.S. Enterprise surrounded by a whirlpool of energy. The double, frightened and confused in a nightmare world of his own, is unable to convey any information about the impending danger, and a scan of the area reveals nothing similar to the force filmed by the shuttle camera. Picard begins to doubt himself and worries that the judgment he made, as his double in the future, may have left him and his crew in a never-ending cycle of torment.

Suddenly, the whirlpool is upon them. Picard orders Geordi to take the U.S.S. Enterprise away at warp speed, but when it is unable to move, the U.S.S. Enterprise is forced to shut down before it is torn apart by the strain. The whirlpool lashes a tongue of energy which strikes each Picard, leading Troi to explain to Picard that the energy only wants him. Learning of his double's resolve to again leave the ship, Picard decides that they will never be able to move forward until the cycle is broken. He orders the U.S.S. Enterprise to charge directly into the vortex. After a tense moment, the double, the shuttle and the whirlpool disappear, leaving the Enterprise alone and on course again.

As you can see, even though they are not mentioning anything like in my solution 4, they still managed to create a similar time loop. Something happens in the future that makes Captain Picard to get out alone in a shuttle, making him the only survivor of a big explosion in which the Enterprise is destroyed. That explosion appears to have created a time loop, also the fact that they are again in a strange area of space, bringing the Picard of the future to the Enterprise hours before it is destroyed. They are caught in a causality loop because Picard still goes out of the ship. It is the only way, it is believed, to save the Enterprise, because there are two of him on the ship, bringing instability to the space-time continuum. Only by killing one of the Picard can they finally escape the time loop.

Something remains unanswered: if the problem right now is the fact that there are two Picard, what was the original cause of the problem? Why would Picard leave the ship the very first time? Another cause was at the origin, and in those cases, you don’t need to mention what that other cause was, it is no longer important. You could not know anyway, your characters could not find out. It is the source of the paradox that can easily be explained. Something else made Picard get out of the ship the first time. We don’t know what, but in the second and subsequent loops, it is the presence of Picard on the ship that is now the cause that makes Picard leave the ship. Sometimes the cause of time paradoxes is when an initial cause has been replaced by another one.

Like the ship Voyager going into the future with the other timeship in order to blow up the planet. Since this is the event that leads the timeship to go get Voyager, how could Voyager be involved in the explosion in the first place? Something else caused that explosion originally. Somehow, when changing the timelines to prevent the explosion, it was necessary to go get Voyager. This is how Voyager got involved and even became the cause of the explosion with the timeship, creating the time loop.

Another example, someone invents a time machine and goes in the past with his time machine. Someone steals his time machine, goes in the future and kills the inventor before he invents his time machine. So, how can the time machine exist, who invented it? Simple, the time machine has been invented by our guy on a certain timeline. When he was killed, this has created a new timeline that does not cancel the original one. He is still the inventor, but to find out about it you would need to understand all the different timelines and that may be almost impossible.

Good luck in deciding what is the best solution for your story! All of it is quite fine and easy to justify (not!).

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