On The Axioms & Corollaries Of Temporal Transforms

[GrayLensman]

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.

[YbrikMetaknight]

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.

[Swordmaster]

about the missing piece theory:

Before Serge cross to another world he hear someone or something calling for him: "Serge... Serge... Serge..."
So i wonder if beside the already stated, for  the missing piece cross the dimension it need a second entity to help open the portal.

[ZeaLitY]

about the missing piece theory:

Before Serge cross to another world he hear someone or something calling for him: "Serge... Serge... Serge..."
So i wonder if beside the already stated, for  the missing piece cross the dimension it need a second entity to help open the portal.

Good point; Serge had to have the amulet to do switch dimensions unless Kid called him into the other one, probably by using the amulet.

[Swordmaster]

[quote="ZeaLitY
Good point; Serge had to have the amulet to do switch dimensions unless Kid called him into the other one, probably by using the amulet.[/quote]

If was Kid to Summon Serge, Belthasar said a half truth about the missing piece.

Now other question:
if serge is a Missing Piece to Another World and cross the dimensions its possible that Serge  become a Working Piece in Another and a missing piece in Home while out of it?

[doulifee]

or maybe the two dimension tend to gather themeselves.

[Swordmaster]

or maybe the two dimension tend to gather themeselves.

I believe that the two Realitys atract Serge in both sides of the dimensions, so to Serge cross, he need a a interference of a third entity,device or effect, like the astral amulet, to unbalance the forces.Without it Serge will be atracted, but will not cross the dimensions.

Or it possible that he can cross half way and get lost in time...

[The Unknowuser_]

I haven’t been here for a while. I wrote this a few days ago but maybe now it’s irrelevant because I haven’t read the new posts. Anyway, hope this helps a bit…
__________

1)

There's also the issue of the gate at Proto Dome... where, or when, does that Gate REALLY lead? All the other Gates found by the party have some counterpart at another point in time, except for the one at the Proto Dome.

I think that the sister door of the gate at Proto Dome is the one that leads you to the Day of Lavos, but we have the problem that it always leads you to a few moments before Lavos appears. Maybe the large amounts of radiation/energy that came from Lavos in that moment (after all, he is going to “destroy” the planet) makes the gate hyper-stable so it is “frozen in time”.

This theory could explain this to:

2)

Then, there's the matter of, after Lavos crashed down in 65 million BC, the Gate left behind leads DIRECTLY to 12,000 BC, WITHOUT taking the party to the End of Time like all the other Gates did.

If radiation/energy makes gates stable, the energy that Lavos left behind after the crash could easily make the gate stable enough to “jump” directly to 12,000 BC and vice-versa, this due to the fact that large amounts of energy takes a while to disappear/dissipate or maybe it’s because Shala’s pendant (that was used to open the gate) has a lot of energy within it.

3)

Can anybody help with this?

Gaspar wrote:
When 4 or more beings step into a time warp, the Conservation of Time theorem states that they will turn up at the space-time coordinates of least resistance. Here. [End of Time]
Then, why after you visit the End of Time for the first time every gate leads you there even if in your party there are only 3 “beings”?

When you arrive to the [EoF] you have to left a party member there, right? After that, when you have to go back to 600 A.D. (from 1000 A.D.) you have only 3 party members but you still end on the [EoT], no matter which gate you use. (Why!!)

Theory: When anyone gets to The End of Time, they start to live “outside time” (WHERE is really the End of Time? Is it everywhere and everywhen? Or is it just there, actually at the End of Time, when the universe finally collapses?) and a switch within them is turned on that tell this to the gates so every time someone of them steps into a gate it’s automatically sent to The End of Time, no matter who and how many people stepped on the gate. This explains why Frog and Ayla are sent to the [EoT] on their first time travel.
__________

It’s far from perfect but I’m not who decides that. Any comments?

[doulifee]

or maybe it's a pocket dimension with particular effect. that why you land there with four characters the first time. that why lavos' gate don't allow you /or interfere/ to land there sometimes. and maybe you need a consciousness of it to allow a character (or party) to land there whenever they want

[ZeaLitY]

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.

[Leebot]

Just noticed this thread; copied from the article's thread:

I've developed a theory of my own which I believe adequately describes how gates work and how time "flows" at the End of Time:

I'll first introduce a concept I call "Time-Error." This is essentially a second time axis, which governs how time travel through gates and the Epoch works, and at which point on the time axis travelers will arrive.

Principles of Time-Error:

-Only time portals and locations outside the axis of time (such as the End of Time, the inside of the Black Omen, or the Tesseract) exhibit a flow of Time-Error.

-Time portals within the standard time axis flow through time and Time-Error at equal rates.

Example: A time portal is created at time X, and Time-Error 0. At time X+T, the Time-Error of the Portal is T.

-The perception of time in locations outside the time axis is actually a flow of Time-Error.

Example: A traveler enters the End of Time at Time-Error T. He spends a length of time U at the End of Time. He exits at Time-Error T+U.

-When a traveler enters a time portal, the Time-Error of the location at which they exit is the same as the Time-Error at which they enter, and the time at which they exit is determined by the Time-Error.

Example: Two time portals exist, one at time X at Time-Error 0, one at time Y at Time-Error 0. A traveler enters the latter portal at time Y+T. Since the Time-Error of this portal is T at time Y+T, the traveler arrives at Time-Error T of the former portal. Since this Time-Error corresponds to time X+T, the traveler arrives at time X+T.

-When a traveler travels to a time portal from a point outside the axis of time, they arrive at the same Time-Error as the Time-Error from which they left, and the corresponding time.

-When a time-traveling device (such as Epoch) is used to travel through time from within the time axis, the Time-Error of one of the portals existing at the exit point is recorded. The exit location can only be a time when a portal exists. The recorded Time-Error is used to determine the exact time of arrival.

Example: Two time portals exist, one at time X at Time-Error 0, one at time Y at Time-Error 0. A time-traveling device is used to travel to the former portal's time at time Y+T. The Time-Error of T is recorded from the latter portal. The time-traveling device arrives at time X+T.

-When a time-traveling device is used to travel through time from a point outside the time axis, it can only reach a time when some portal exists. The exact time it arrives is determined by the Time-Error at which it left.

-Whenever a time-traveler reenters the timeline, a new timeline is written from that point on, with the Time-Error at which the traveler exited. The old timeline is sent to the DBT.

I'm pretty sure this theory is solid. I've got a few more ideas I'll add later. Please reply with comments and suggestions on this theory.

[Leebot]

Sorry, but I didn't realise that this subject was already discussed here, so I'm CPing this from a separate post. This just boils down to a different way of looking at worldlines, but I believe the tie-in to Conservation of Energy bears mentioning.

My theory: Conservation of Energy would have to be revised if time-travel were possible. Let's say that every "piece" of energy has its own timer, tracking the time of its existence from the Big Bang. In the continuity of 5 dimensions (three spatial, one time, and one to accomodate new timelines created via time travel), each piece of energy will exist at exactly one point for each time on its own timer. So, yes, that's the same Robo with mostly the same energy making up him if you go back to 600 AD after Fiona's sidequest, but the energy is 400 years older/younger.

Just a thought: while Robo is cultivating the forest, give him a Red Vest (for example), and have its future version, the Red Mail in your inventory. When Robo comes back you'll have a Red Vest that's at the same "time" as its Red Mail counterpart. Can anyone say "incredibly obscure plothole that's best left unmentioned?"

[Leebot]

One theorem necessary to resolve the Guardia Royal Line Paradox:

Future Travel Theorem
When a time traveler travels to a point in time in the future of their time period of origin, they travel to the future that would occur had they instead returned to (or remained in) their time period of origin and lived out their life naturally.

Evidence: Marle travels from 1000 AD to 2300 AD and meets Doan, who turns out to be her descendent. Doan could not have existed if Marle had disappeared from the timeline in 1000 AD. This 2300 AD must be the one that would have existed if Marle had remained in 1000 AD.

On another note, should some of the information here be put into the actual article?

[Daggart]

Perhaps I missed it, but does the Time Bastard theory take into account Serge's party members? When a party member enters another world where they also exist, what prevents one of them from be pushed out?

[GrayLensman]

That may or may not be a problem with the theory.  During a normal time travel event, the timeline fissions into two segments:  the original timeline, having zero energy, is sent into the DBT; the new timeline, having X energy becomes reality.  However time traveling mixes up objects world lines, the total energy of the universe (for all time and space) may not exceed X.  The dimensional split in 2010 AD was an aberration.  Somehow a complete copy of all the matter and energy in the universe was created.  This is a real mystery.

Home and Another behave like other separate space-times, such as the Reptite dimension.  For example, Time Bastard does not eliminate Home Norris and Another Norris because they are distinct people who exist on separate world lines.  Our rationale for Time Bastard was conservation of energy and it would not be violated in this case.  This is a highly theoretical topic, which required a great deal more development.