Author Topic: On The Axioms, Corollaries Governing Temporal Transforms  (Read 4953 times)

ZeaLitY

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On The Axioms, Corollaries Governing Temporal Transforms
« on: January 18, 2004, 06:31:32 pm »
On The Axioms & Corollaries Governing Temporal Transforms
by the Chrono Compendium

The Chrono series is composed of an infinite number of dimensions that are all a matter of possibility. Time travel conducted within dimensions and there effects thereof are limited to the parent dimension, except in certain cases. These are supported by the following:

On what we shall limit our concern to, and on the basic reasons for certain dimensions existing:

Relevant Dimensions Theory
ZeaLitY


When considering the Chronopolis computer's statement -- that in other timelines, Lavos's data (or implications) in spacetime were extremely volatile -- the others can be regarded as fragmentary, incomplete, or otherwise possible but nonexistent and unrelated dimensions; the only we should truly focus on and recognize as existent are those seen from the perception of the Keystone Dimension; if other worlds are to be viewed, then let us go by the Chronopolis statement -- the world is only stabilized by the viewpoint of the one who observes it -- and base our vantagepoint in this dimension, home to the series and for all intents and purposes, complete. This stated, I propose that dimensionally, Home/Another splitting was caused by Kid's time traveling and the gravity of Serge's life/death on the continued existence of reality, and the splitting of Prehistory into the Reptite Dimension and Keystone Dimension was a matter of possibility, as stated by Chronopolis; that the Reptite Dimension is simply the most logical choice by which the planet pulled a counterbalance for Chronopolis from; finally, that the Radical Dreamers Dimension is another matter of possibility and does not directly stem from the Keystone Dimension.

Support:

Computer in Chronopolis: ...However,
in the distant past humans could have been defeated in the contest of evolution, and the Reptites could have continued to develop... It is not unthinkable that such a time line could exist in other dimensions. Everything is purely a problem of possibilities, and the world is only stabilized by the viewpoint of the one who observes it.


Computer in Chronopolis: All the data on Lavos that was obtained from tracing different parallel world possibilities has proven to be volatile, with fluctuating discrepencies.

Third Party Member: Radical Dreamers...!? What does this mean?
Second Party Member: ...... This seems to be an archive from a different time than our own.
Third Party Member: Aside from the two worlds we already know about... other worlds and times may
also exist...


On time traveling being limited to parent dimensions, known as the Singular Worlds Theory

warmgun: (The Tesseract's) existence proves that timelines do, in fact, disappear. If timelines disappear, then dimension creation is not an insignificant event. Every change (in time) does not lead to a new dimension. If it did, then the Tesseract would have no use. I believe the time mechanincs in Chrono Trigger are exactly as they appear and aren't the illusion of time travel via dimensional travel. Singular worlds all the way. The Time Devourer was going to destroy all of reality, correct? That was the impression I was under. Under the Singular Worlds theory, there aren't an infinite number of dimensions. So perhaps its not such an absurd task after all.

Note: There are an infinite number of dimensions; however, the Singular Worlds Theory proposes that time traveling does not cause new dimensions with every instance of change.

GrayLensman: I agree, warmgun, but there are other dimensions (Dragonian, Radical Dreamers, etc.), possibly an infinite number. With singular worlds, these other space times would not have fissioned off the main Chrono dimension due to time travel or random chance. They originated from separate creation events (big bang?) and developed independently of each other. Different initial conditions and chaotic randomness would account for the variation between these worlds.

Aitrus:
That could be the best explanation. Let us assume that the Chrono Universe works on the Singular worlds theory. However, at the beginning of the universe, the quantum indeterminancy would be so great as to cause the formation of many universes, one of which eventually becomes the Chrono universe, while others become the various others like the RD world and the Reptite Universe. Since a big bang causing infinite universes would allow for many to be very similar to each other, this would allow for the similarities between these and "ours," while also allowing us to have a world bounded by the Singular World theory.


ZeaLitY: If new dimensions were created with every instance of time traveling, the series would lose much purpose and meaning. Also, the game suggests, as warmgun alluded, that in truth only two timelines existed after the events of Chrono Trigger, which incorporate several instances of time travel. One may reason that everything in between the start (world before Crono entered the Millennial Fair) and end (the defeat of Lavos) are bastard dimensions and aren't allowed existence; whether this is true or not, it has no real effect and confirms Singular Worlds; it can thus be disregarded.

These are the known dimensions:

http://www.chronocompendium.com/images/Articles/dimensions2.png

Lastly, in regard to dimensions, we have the following axioms:
 
On the formation of Angelus Errare points and the resulting possibility of dimensional travel therein
ZeaLitY


If event X at point Y in dimension Z causes a dimension Z' to form, travel between dimensions will be most probably at point Y in dimension Z or Y' in Z'.

Missing Piece Theorem
ZeaLitY


If item X causes dimension Y to split and form Y' at point Z in space, and item X does not exist in Y but retains existence in Y', item X will feel pressure to enter Y if X is in close proximity to point Z'.  

On the ability of non-missing pieces to travel dimensions
ZeaLitY


If item X, a missing piece, travels dimensions at an Angelus Errare point, accompanying persons must maintain close proximity to also be transferred.  

Under dimensions, we have the rules of time travel itself. First let us establish the known timelines:


http://www.chronocompendium.com/images/timelines2-warmgun.png


The following principles govern time travel in various aspects.

Principle of Discarded Timelines
GrayLensman


Whenever a timeline is altered by a time traveler, a new timeline is created as a result of these changes.  The original timeline from that point onward is sent into the Darkness Beyond Time, a realm of frozen non-existense containing all discarded timelines.

Support:

ZeaLitY: This is how the Dead Sea operates; the timeline after 1999 AD in which Lavos destroyed the world was ressurrected upon the nullification of Crono's quest. Likewise, this expounds upon the notion of those who suffer a change to time not having any memory of the past timeline; the last timeline is discarded, a new is created.

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.

Conservation of Time Theorem
Gaspar


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]

Support:

When Crono, Marle, Lucca, and Robo travel through an Entity-made Gate, they arrive at the End of Time.

ZeaLitY: Note that this applies to Entity-made Gates only. The warp effect at Magus' Lair brought about by Lavos did not send Crono's party and Magus to the End of Time, and likewise the Ocean Palace disaster disperses several beings through time-

65000000 BC: Nu at Laruba Ruins
600 AD: Janus
1000 AD: Melchior
2300 AD: Belthasar
End of Time: Gaspar


How Changing the Past Affects Those in the Present and Future
warmgun


If a certain time, X, is altered to to become a new time, X', due to new events in a prior time, Y, where Y<X, every person in time X' will have no recollection of time X or that time X ever existed. This rule applies to EVERYONE in time X when the change occurs, including time travelers who happen to be at time X.

Support:

TandeM: For example, the collected population of the 1000 A.D. CT world doesn't flip out when the Black Omen suddenly "appears" in their time, rather, they seem surprised in the least to a giant fortress hovering in the sky.

ZeaLitY: This also may prove true for dimensional edits; the residents of the merged/split dimensions would have no recollection of the split or subsequent resealing. Perhaps this is why Serge forgets the events of Cross, though this would conflict with the ability of time travelers to remember the state of the world before their own changing actions are brought.

Determining the Destination of Time Travel via Epoch and Time Gates
warmgun, TheUnknowuser_


Time Gates and Epoch have the unique ability of knowing a person's personal time. These things know how long a person has spent in certain times. These devices work under the following principle:

“At time X, a person enters Epoch and chooses a certain time, Y, on Epoch's dial, where |X-Y| = Z. In time Y, the person stays for a certain duration, T so now Y=Y+T. When he chooses time X from Epoch's dial, it does not take him to time X. It takes him to time Y+Z. So the total amount of time this person just traveled from time Y is Z. This quantity, Z, is constant. Likewise, when this person enters a time gate, the same rules apply. The only difference is that Z cannot be chosen from a dial, it is inherent to the time gate and is constant.”

Granted, this may seem overly technical, but it provides great insight. For example, this rule proves that time MUST flow a the End of Time. While Epoch has it listed as infinity(inf), the time gates and Epoch treat time travel to and from it as inf-Z and inf+Z. In other words, time flows.

Support:

TandeM: Consider that when making a return visit to an era, any effects wrought on it still pertain. Let's take the sequence of events in 12000 B.C.

-Crono and co. arrive in 12000 B.C. via timegate for first time

-The party spends time T completing the initial quest (up until they are banished and Schala seals the gate). The time is now -12000+T years.

-The party spends time U in the quest for the Epoch. When they use it to warp to 12000 B.C., they aren't actually taken to -12000 years, they're taken to -12000+T+U years!

If they simply went to -12000 years, the gate wouldn't have been sealed yet, and the warp pods would still work. But since the effects of the previous trip to 12000 B.C. still pertain, it follows that the party re-arrives in a time after that trip.

(Think of the consequences if this weren't true. For one, Queen Leene would need rescuing upon every trip to 600 A.D. In fact, Crono and co. would have to start from scratch every time they revisited a time period!)


This axiom formerly operated on a variable known as 'T'. Reasoning behind Unk's revising and mostly eliminating T:

TheUnknow_user: Think on the first trip to 600AD: Marle warps to 600AD. Then, a few minutes later, Chrono goes too and later on (some hours, I think) Lucca enters the gate, right? So, we have three DIFFERENT personal times to each character, because Marle spent more time in 600AD than Chrono, and Chrono spent more time than Lucca (Marle > Chrono > Lucca)

When they came back to 1000AD Lucca should arrive first, later on should arrive Chrono and then Marle (because T is different for each one), but we see them arriving at the same time  . So, the time gates only works with the Z variant that, we know, is constant:

 The gate in Leene Square goes 400 years in the past or (the gate on 600AD goes 400 years in the future) so, Z=400.
 At any point in time, if you enter to the gate, it’ll always take you to X-Z or X+Z instead of X±Z+T because T doesn’t have any relevance to the gate.
ie. You are in 1004 AD. You take the gate in Leene Square. That gate won’t take you to 600AD because Z=400, X-Z=Y => 1004-400=604, Y=604 <= you’ll arrive in this year. Now, say you stay there 3 years (why? I don’t know) so now X=607. lets go inside the gate!: X+Z=Y => 607+400=1007, Y=1007 <= you arrive in this year. Note that the gate doesn’t remembers your “personal time” (T), it only applies the Z variant (that is constant) to the actual time period.


Flow Principle
ZeaLitY


In timeline X, if event Y shall rewrite certain events to form X', even if event Y surely shall occur, time must flow until reaching Z, the time of Y's occurrence, until X can be rewritten to X'.

Support:

TandeM: Let's make this simple and apply it to the Ocean Palace incident.

Timeline X = 1000 A.D.
X' = 1000 A.D. w/Black Omen
Event Y = Ocean Palace disaster, raising of Black Omen
Z = Time of Ocean Palace disaster (12000 B.C.)

So, to rephrase:

Due to the Ocean Palace disaster, the 1000 A.D. timeline is rewritten to include the hovering Black Omen. The rising of the Omen is unpreventable in the "correct" version of the plot (the one that nets New Game+ and the normal ending), but until the Ocean Palace disaster actually occurs in 12000 B.C., the Omen does not appear in the other time periods.

We can make another example out of Ending #1:

Timeline X = Ruined 2300 A.D.
X' = Bright and Happy 2300 A.D.
Event Y = Defeat of Lavos
Z = Time of Lavos' fall - 1999 A.D. (You could argue 12,000 B.C., or say that Lavos exists in some kind of pocket dimension, or that it's a temporal anamoly... but as long as it's before 2300 A.D. we're good.)

Crono and co. defeat Lavos in 1999 A.D., averting the apocalypse and making the future bright and happy. While its defeat is predestined in CT's course of events, until Lavos has actually been vanquished, the ruined 2300 A.D. future still exists.


Reletavistic Time Flow Principle
GrayLensman


The rate of time in each time period should not be the same. Relativistic effects produced by changes in the earth and sun's velocity would result in minute time dilations. Thus, each time period would have its own relative time rate, dependent on relativistic factors.

This introduces a further complexity to the "Determining the Destination of Time Travel" axiom. Time Gate apertures and Epoch destinations follow the natural flow of time in their era, but since the time rate of each time period is unique, there would be a discrepancy in the translation of both ends of a Gate into the future.

For example, if Crono were to warp from 1000 AD to 400 years in the past, the time he spent in 600 AD is not necessarily the same as the time he was away from 1000 AD. Luckily, Crono could not return to 1000 AD before he left, so there is no worry about causality.

For most time periods this discrepancy should be very small, perhaps on the order of seconds. However, 65 million BC might experience a significant time dilation.

Support:

Aitrus: Motion and mass have affects on the speed of time.  As a simple example, a ball bounced on a train takes longer to bounce to someone on the station platform than to someone on the train with it.

GrayLensman: Crono could never return to 1000 AD before he left, so there is no worry about causality.

How Changing the Past Affects Those Time Travelers whose Past Now No Longer Exists
warmgun


Assume there is a man that by a time, X, has experienced a certain set of events, {E1, E2, E3, E4...E(inf)}. Assume an event, E4, occurs at a time Y. Suppose the man travels to a time T, where T<Y. If time is altered at a time A, where T<A<Y, so as to eliminate E4, the man remains exactly the same as though the time change at A never happened and the causal effects leading the man to time T remain.

Support:

warmgun: Crono takes the jerky to the Porre mayor of 600AD to make his 1000AD counterpart give up the sun stone. So Crono's past now reflows through the new timeline. Crono has no need to go to the past now to give the 600AD mayor the jerkey because his 1000AD descendent is now generous and gives him the sun stone. If Crono doesn't go back, the 600AD mayor won't get the jerkey. The grandfather paradox is conveniently brushed aside.

Crono defeats Lavos in 1999AD, making the future bright and happy. In this new timeline, Crono's past is now forced to reflow. The future he must warp to now is not derelict and ruined. So does he still find an Epoch just waiting for him there? There won't be one, so he can't do half the stuff he's supposed to in order to kill Lavos!

You can take this idea and apply it to nearly every single instance of changing time in the game!


~

These principles are current. If you disagree with them or wish to support them with commentary, please use the Comment function on this article.

Thanks for this article-

Warmgun for initiating discussion,
Everyone who has participated in discussion over these subjects,
Everyone who has read work on the Compendium or has joined the ranks of its members. Without you, the Compendium would not exist.

Cliftor

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On The Axioms, Corollaries Governing Temporal Transforms
« Reply #1 on: January 19, 2004, 12:01:20 am »
I am of the opinion that time travel, dimension travel, and all related phenomena and oddities in the Chrono Trigger game universe are not governed by any set of axioms. My support for this opinion is the assumption that game creators and storywriters, while aware of how complex a story they were creating, did NOT have any inkling of the need for laws and axioms their complex universe would require to be paradox-less. What I'm saying is: "They made up the story as they went along." There is no rhyme or reason to the phenomena of the Chrono Trigger universe, except as pertaining to making the story enjoyable, coherent, and "plausible." In that vein, I suggest we NOT spend our time formulating laws to govern the game universe, for the formation of such laws makes the incorrect assumption that the game does (or needs to) make sense. Time travel and demension travel are NOT axiomatic, scientific, discussible topics. They are story and plot devices. With that in mind, I suggest that the ONLY demension of ANY signifigance is the True Demension (split buy Kid's actions and reunified by Serge and the Chrono Cross), any demension that anything of note originated from (the Dino-demension), and the Tesseract. All superfulous demensions are meaningless and therefor non-existent unless the struggles of the True demension require them to exist (the Dino-demension). And finally, I suggest that at the conclusion of Chrono Cross's story, there is only one timeline, the True Demension, the world of Chrono, Marle, and Lucca, of Schala and Magus, and so on. Chrono Break will, hopefully, take place in a unified timeline without any need for more conjecture and inference.

doulifee

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About the end of time
« Reply #2 on: January 31, 2004, 07:49:30 am »
i just want to understand how you can apply usual space-time continuum rule to the end of time because these rules don't appply here. if there is no time, time can't flow. so you can and can't be there at the same point (i am not using "time" here because he is not there) it's a dimension were only space rule (or something like that...)

ZeaLitY

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On The Axioms, Corollaries Governing Temporal Transforms
« Reply #3 on: February 04, 2004, 09:43:10 am »
GrayLensman has elaborated on this in the Analysis board:

Quote from: GrayLensman
The End of Time seems to have a timeless, unchanging quality. I introduce the possibility that the EoT behaves like Lavos' pocket dimension. That is, time passes, but not relative to any other time period.

The EoT is often considered to be an actual space-time co-ordinate. Considering the infinite time designation, I consider this to be an impossibility. The End of Time appears to be a state of existence. It is describes as the point of least resistance during time travel, which would indicate that the EoT has the lowest energy level of space-time. This is analogous to the absolute zero energy level of molecular motion; the End of Time is the state where time comes to a halt. If time is quantized, the EoT would be the base energy state of time. The End of Time would exist as a single infinitesimal moment for all time.

YbrikMetaknight

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On The Axioms, Corollaries Governing Temporal Transforms
« Reply #4 on: February 04, 2004, 11:24:46 am »
Cliftor, man....you're really in the wrong place if you don't want to discuss this subject.  This kind of thing is what the Chrono Compendium is all about.  If you don't really like that, I suggest you not hang around.  Or at the very least simply don't read the threads on topics you don't enjoy discussing.

I don't take well to people telling us what we do is stupid (not your words, I know, but the inference can be made, even if you didn't mean it) on other boards, but I tolerate it because those are not boards dedicated to doing what we do here, and usually such comments come after we've already brought the subject up (usually...and I'm talking about OCR for those of you who don't know).  However, I really, REALLY don't like people suggesting this on boards dedicated to the subject.  Don't keep this up, Cliftor, or you'll be met harshly, at least by me.

Sorry if this seems a little extreme...but this kind of thing really annoys me, ESPECIALLY on our own boards.  Please, anyone that has a problem with discussing any of the things we discuss, at least for reasons of "They were imperfect writers and therefore did not follow any set of rules," please just don't bring it up.

doulifee

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On The Axioms, Corollaries Governing Temporal Transforms
« Reply #5 on: February 05, 2004, 11:41:54 am »
that what i'am thinking too Zeality. and that explain why 4 people land there.. if there is no time it's the lesser resistant point in the continuum. it's the shore on the flow of time.

OathoftheTimeTraveler

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On The Axioms, Corollaries Governing Temporal Transforms
« Reply #6 on: February 05, 2004, 07:58:06 pm »
However, literally, there is time flow there. What significant temporal aspect is missing from there?

doulifee

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On The Axioms, Corollaries Governing Temporal Transforms
« Reply #7 on: February 06, 2004, 12:25:28 pm »
Quote
TandeM: Consider that when making a return visit to an era, any effects wrought on it still pertain. Let's take the sequence of events in 12000 B.C.

-Crono and co. arrive in 12000 B.C. via timegate for first time

-The party spends time T completing the initial quest (up until they are banished and Schala seals the gate). The time is now -12000+T years.

-The party spends time U in the quest for the Epoch. When they use it to warp to 12000 B.C., they aren't actually taken to -12000 years, they're taken to -12000+T+U years!

If they simply went to -12000 years, the gate wouldn't have been sealed yet, and the warp pods would still work. But since the effects of the previous trip to 12000 B.C. still pertain, it follows that the party re-arrives in a time after that trip.


It look like the entity and the creator of epoch himself was wise enough to add a security system that forbid the time traveller to cross his own time travel.

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Time-Error Theory
« Reply #8 on: June 10, 2004, 04:24:37 pm »
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.

Please reply with comments and suggestions on this theory.

Dalton

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Re: On The Axioms, Corollaries Governing Temporal Transforms
« Reply #9 on: December 05, 2013, 02:49:12 pm »
Time devourer can travel from dimensions only if he have Chrono Trigger\Cross