On The Axioms & Corollaries Of Temporal Transforms

[ZeaLitY]

Notes on Time Bastard to be used later:

Zeality and I have expanded on the aptly named Time Bastard theory.

In its original form, Time Bastard described the version Serge who was born in the ideal timeline, after the dimensional unification of Chrono Cross, and was subsequently eliminated when the old Serge returned from the Darkness Beyond Time.  It was supposed that the new Serge was sent in to DBT or otherwise discarded by the direct actions of some agency.

However, all time travelers who change the past would also produce duplicates.  For example, if Crono warps back in time, a new timeline is created, containing a new version of himself.  Evidently, when Crono returns home, the duplicate is nowhere to be found.  Presuming that the new Crono also travels through time doesn't solve the problem, because it doesn't eliminate the copy, and introduces some trouble with cause and effect.

There has to be some universal mechanism which removes these redundant copies, so that time travelers can return home.  The duplication of matter in this fashion may also violate the laws of thermodynamics.  We surmise the Time Bastard theory to operate like the Missing Piece theory in reverse.  If a dimension contains an excess of a particular entity, the extra one is pushed out.  When Crono travels back in time, and creates a new timeline, the instant the old Crono stepped into the Gate, the new Crono is sent into the Darkness Beyond Time.  If this event coincides with the new Crono entering a Time Gate, then it is only an added bonus

For the record, bringing Robo to 600 AD while his past self if still reseeding the forest is not an example of duplicate travelers existing.  Past, present and future, there is only one version of Robo in the universe.  He has a single, uninterrupted world line, which is viewed from different time frames.

This is the official submission to the Axiom and Corollaries article.

Time Bastard Theorem
ZeaLitY, GrayLensman

Suppose an entity X exists on timeline Y.  

If X time travels from time A to time B, such that B < A; for time > B, Y is sent into the DBT, and Y' is created, containing X'.  

For time > A, two identical entities X and X' will exist in Y'.

Conservation of Energy requires that only one entity X or X' exist.  

Therefore, X' will be expunged from Y' at time A, and sent into the DBT.

Expanding a little bit upon the Time Bastard theory...

This popped up in my mind during an AIM chat with ZeaLitY and GrayLensman...

(NOTE:  Possessive apostrophes are omitted so as not to confuse them with the mark for "prime")

If Traveler X from Timeline Y executes actions that cause Character X' (Traveler Xs counterpart in Timeline Y', the new timeline caused by Event or Action T) to die or otherwise cease to exist prior to Point Z, at which Traveler X enters Timeline Y', rather than replace Character X' in the grave (or whatever), Traveler X will exist independently.  This will give others in Timeline Y' the impression that Character X' has been given a new lease on life, while Traveler X will retain only his memories and history.

This allows for, among other things, Robo to exist in A.D. 2300 after the defeat of Lavos.  In CT's ending, Robo himself worried that, due to any unforseeable result of Lavos's defeat and the possibly radically different future that event could cause, he would not have a counterpart in the new future.  This subtheorem of the Time Bastard theorem states that if there was a Robo' he was replaced by Robo, and if there was not a Robo' then Robo simply came into existence as a true Time Bastard, that is one without an origin in the timeline in which he resided.

Some TB clarification by GrayLensman:

TB states that the mechanics of time travel cannot be used to create duplicate entities. If you warp back in time and create a new future where you did not time travel at all, you cannot meet the new, non-time traveling, version of yourself because that person will disappear at the instant of your original departure. This would be the same for any material object.

For all time and space, only one version of any entity may exist. However, an entity's world line may loop back onto itself so that the past and future version of an entity may exist in the same space-time. Magus can warp back to Zeal and encounter his past self, Janus, but there is no duplication. Robo can meet himself in Fiona's Forest. The articles taken from the sealed boxes can co-exist in the exact same way.

If the travelers retrieve a Red Mail from a sealed box in 1000 AD and then seemingly remove the same article from a box in 600 AD, they have not duplicated the item. For all space and time, only one item containing the physical matter of the Red Mail exists. But, the travelers possess versions of that item from two different times. The world line of the Armor has looped in on itself just like Magus and Robo.

This is not a free lunch, however. Once the Red Vest experiences a passage of time such that it reaches 2300 AD, it will cease to exist.

~

A traveler exiting a time warp is a “time bastard” with no relationship to the causality of that timeline whatsoever. That traveler’s past world line cannot be affected by any event within that timeline, and thus no change can prevent the traveler’s arrival from taking place. The traveler’s arrival is not dependant on his departure from another time or his historical existence in that timeline. I see this as a requirement for time travel to function in the Chrono universe as it does.

When Magus was warped to the Dark Ages, his actions significantly changed the events of the Ocean Palace disaster, but his memories were unaffected. The historical events involving Magus in 600 AD did not appear to change either. Magus changed the timeline prior to his original departure in 12000 BC, and this did not cause a new Janus to warp to 600 AD, or a new Magus to warp to 12000 BC.

TIME BASTARD - A REVIEW

The premise behind Time Bastard is that time travel cannot be used to create duplicates of entities.  It is possible for past and future versions of entities to exist in the same point in space-time, but duplicate entities from the same time period cannot coexist.  The doubles in Chrono Cross do not violate this because Home and Another are separate dimensions.

Consider this scenario:

At the Millennial Fair Crono warps 400 years into the past.  His presence in 600 AD creates a new timeline, and the original is sent to the Darkness Beyond Time.  In the new timeline, a new version of Crono will exist, but the original version of Crono in 600 AD is not affected because he has time traveller immunity.

In 1000 AD, the new version of Crono may enter the warp to 600 AD, but where does he go?  He cannot arrive in 600 AD, because the original version of Crono, who is protected by time traveller immunity already exists there.  Based on evidence in Chrono Trigger, time periods do not fill up with duplicate time travellers.  Thus, the new version of Crono is eliminated from the timeline and sent to the DBT.

Basically, if changes to the timeline result in the version of a time traveller entering a time-warp not being identical to the same traveller exiting the warp, the traveller entering the time-warp is sent to the DBT.

And if Crono continued time travelling:

The original version of Crono warps from 600 AD to 12,000 BC, creating another timeline.  Yet another version of Crono would enters the warp in 1000 AD, and is sent to the DBT.  The original version of Crono, protected by time traveller immunity, arrives in 600 AD.  However, due to the new timeline, when this version Crono warps to 12,000 BC, he is not identical to the original Crono, and is sent to the DBT.

Another case:

Perhaps if the changes to the timeline are severe, the new version of Crono would not enter the warp in 1000 AD (or the version of Crono in 600 AD).  Would the original version of Crono return to the present to find a duplicate of himself?  Since there are no duplicates, the new version of Crono must have been sent to the DBT at the same time the original Crono left.

The Theory in a Nutshell

Duplicates of entities cannot be created through time travel because this would violate the conservation of energy in the universe.  If a time travel scenario would cause a duplicate entity to exist, the entity with the least seniority of time traveller immunity would be sent to the DBT.

Examples

Robo encounters the past version of himself in 600 AD

After Fiona's Forest is replanted, Robo warps from 1000 AD to 600 AD and encounters his past self.  They are not duplicates because the versions of Robos are not the same age.  They are the same version of Robo looped in time.  When the "past" version of Robo reaches 1000 AD, he will be sent into the DBT at the time the "present" version of Robo originally warped out.

Magus encounters Janus in 12,000 BC

After the encounter with the time travellers in 600 AD, Magus is warped to 12,000 BC.  Magus encounters his past self (Janus), but they are not duplicates because they are not the same age.  During the destruction of Zeal, the new version of Janus will be sent to the DBT at the time the original Janus was warped to the middle ages.  The new version of Magus will be sent to the DBT when the original warped to 12,000 BC, and so on.

Pretty good explanation there. Just an alternate interpretation here:

Each entity has its own personal time, measuring the point in their existence . When a group of entities exit a gate, the new timeline created (assuming they went to the past) starts to run again from that point, with the new versions of the travelers acting completely naturally until their personal times reach the same time as the old travelers had when they exited the gate. At this point, the new versions are sent to the DBT to uphold conservation of energy.

Another little point of temporal mechanics:

Let's say on their second trip to 65,000,000 BC, Crono and crew screw up badly, allowing the Reptites to rule the earth. This would mean that the new timeline would start from here, and Crono would never exist to time travel and eventually make the first trip to 65,000,000 BC. Would this cause a new timeline to overwrite the changes Crono just made in 65,000,000 BC?

If it does, a new timeline starts from when they would have first traveled to 65,000,000 BC. This timeline contains no intervention, and would turn out to be the same as the original timeline. This would then lead to the same set of events happening once again, leading into what's known as a reciprocal causalty loop--one set of circumstances causing the other which then causes the first, and so on infinitely.

Since the Chrono universe has the mechanics set up to avoid paradoxes such as these, we can pretty safely assume that this is not what happens. Instead, this set of circumstances seems most likely:

The new future may contain travels to the past, and these exist as normal for anyone in this new timeline. But, once the personal clocks of the travelers run out and no more changes would take place (at least at a Time-Error lower than the travelers' arrival), this new past is shunted to the DBT and the old past remains as part of the timeline. This results in the travelers not having their actions overwrite themselves accidentally. It still is possible for something to happen after this (speaking in terms of Time-Error) that could go back and overwrite the past (assuming a Gate that can go back far enough), as this wouldn't result in a paradox or infinite loop.

Then again... a reciprocal causalty loop may be just the thing needed to split the timeline in two. If it's possible, I'm sure Balthasar could have figured out how.

But the Time Bastard theory itself it really scary.

1) The new being of any original being will always be sent to the DBT without ever even having the chance to become something. How f***ing sad is that! I doubt the entity would allow such butchering.

2)What would happen if for instance Norric from another world went to Home world and killed the Norris there and lived as if he was the Home Norris?

Time Bastard does not apply to dimensional travel.  It is simply a hypothetical way to resolve time paradoxes.  Norris could switch places with his counterpart without consequence.

The concept does seem cruel, but it is no worse that the millions of people sent into the DBT every time Crono time travels, which is canon!

Plus people who are erased and sent to the DBT don't exist anymore at all, so they don't really suffer or even become conscious of their erasing. On the contrary, people who were killed becaused of Lavos (for example) did suffer physically and were conscious of their death afterwards since, apparently, ghosts exist in the Chrono world.

[ZeaLitY]

Lastly, the Doan situation needs some attention. It is #3 two posts up; please read it.

[DBoruta]

Regarding the original Ocean Palace Disaster, the gates there were not created by the Entity, but by Lavos.  In Magus' flashback, Lavos' head moves each time someone is gated, which is, at the very least, strongly implying that Lavos did create those gates.  Also, both Magus and Belthasar state that it was Lavos that gated them from 12,000 B.C.  As for the gates that open during the new disaster, I would agree that it is Time Bastard in action.  


I'll give the Doan situation more thought - that is really odd...  The only thing I could think of at the moment is that Lucca informed the new Doan of everything that had transpired, or maybe Crono & co.'s actions were recorded in history books.  I'm not convinced that's really the case though...

[Sentenal]

1. Why do Gates sometimes lead to their other end and sometimes directly to the End of Time?

At first, the gates you enter lead to their other end.  Then, they lead to the End of Time.  Its possible that Gaspar has done something to make the End of Time as a cross-roads for Gates, with him being the Guru of Life.

2. Who really caused the Ocean Palace Incident and other anomalistic distortions?

Ocean Palace Disaster: I believe it was simply a side effect of the Mamon Machine overreacting due to the Red Knife being stuck into it.  It caused Lavos' powers to create gates, which gated the Guru's and Janus.  The Entity may have had a hand in deciding where those gates lead, due to the gates wouldn't have been a conscious decision by Lavos to make them (they would have been made by the Mamon Machine, techincally).

Marle's Pendant Reacting with the Telepod:  The Entity created a gate at Leene Square, to try and prevent its death by use of Crono.  The Telepod energizes the Pendant just enough to produce some sort of magical reaction, opening the gate.

Magus' Summoning, and the gating:  Lavos was awoke, and used his power to smit Magus.  Originally, Magus was able to complete his summoning properly, without disurbance.  But when Crono and Frog assualted him, the summoning cerimony was thrown into chaos, and resulted in a situtation similar to the Ocean Palace Disaster, though a bit different.  The Entity may have taken advantage of this situation as well.

Melchior and Janus' disappearance in 12000bc:  I'll go with the Time Bastard here.

3. How does Lucca get the original version of Doan from ruined 2300 A.D. after defeating Lavos?

Plot.  Hole.

[ZeaLitY]

Yeah, it's looking that way. Thanks for the contributions so far; that's an excellent piece of observation on Lavos's head, DBoruta, and I like the theory of the Entity deciding destination as a possible remedy for the sheer coincidence of the Gurus going to those eras. I'll think of something else in a minute.

[Mystik3eb]

About the gates: I think that the first time the travellers go through one of a pair of gates, they arrive at the other end. Once oneof the gates have been travelled through once, they go to the End of Time from then on. This, of course, takes effect after the party arrives at the End of Time the first time once they've broken the law of Time Conservation.

Doan. Yeah. Plot hole.

[SilentMartyr]

1. Why do Gates sometimes lead to their other end and sometimes directly to the End of Time?

Basically this has been stated, but anytime someone goes through a gate that they had already gone through after previously visiting the End of Time then it automatically brings them there. This works in all cases except for when the group went from 12,000 to 65,000,000 but that can be disregarded due to the fact that the gate was in the process of being sealed when the group was traveling through the gate.

2. Who really caused the Ocean Palace Incident and other anomalistic distortions?

Entity, every time. Every time there is a time anomaly in the events of Trigger it helps the Entity. This is assuming the Entity is either the planet itself, or is some form of god that watches over the planet. It makes no real sense for Lavos to be responsible, since every action seems to counter Lavos's nature. (If you want I can go over each instance, but I figure until the general theory is accepted it makes little sense to go into great detail)

The theory that Lavos's energy caused the gates but the Entity made the selection of where the gates end up really doesn't make any sense to me. Why didn't the gates reappear when Crono and co showed up at the Ocean Palace? They stuck the same knife in the same Mammon Machine, so gates should have appeared in the same fashion.  

3. How does Lucca get the original version of Doan from ruined 2300 A.D. after defeating Lavos?

A plot hole...for now.

[AuraTwilight]

As for Doan....

Maybe Lucca accidently went to the DBT and thought it was 2300 AD XD