Temporal Relativity

[Eske]

This theory exists to address the Telepod Paradox (and the Ayla Paradox, in a sense). Enjoy.

The main idea is that changes to the timeline do not affect everything in the future all at once - the changes move at the same pace as the march of time.  So, when Crono changes something in 600AD, it will take 400 years for that change to affect 1000AD. But by then, all things in 1000AD will now exist in 1400AD, so they will never be able to experience the change.

Temporal Relativity.

"Changes to the timeline move at the same rate as time. Therefore, changes at Point A on a timeline will take N amount of time to reach Point B, but all bodies previously at Point B are now at Point B+N, and will remain unaffected indefinitely."

The Compendium has long held that any change to the timeline will result in an instantaneous change across all points on the timeline beyond the point of change.

This has been accepted because of the observation that making changes to the past and immediately time traveling allows the observer to see the effects of his change to the timeline.

There is a special example in Chrono Trigger that makes this conclusion impossible: The Telepod Paradox. If you are not familiar with this, it can be found in the Articles under "Principles of Time and Dimensional Travel". The Ayla Paradox also suggests this view of time is flawed.

Just because Crono can make 5D movements and witness his changes to the past immediately after he time travels back to 1000AD does not mean that the changes manifest instantly. It just means that he is able to skip ahead to after the changes have manifest - much like the way he can skip thousands of years in seconds.

Temporal Relativity at work:

First, recall Time Error:  Crono spends one day in 600AD and returns to 1000AD.  There, he will see that one day has also passed. 
Using this, I will give you an example of Temporal Relativity.

Marle uses the Telepod, which interacts with her pendant and sends her to 600AD.  Crono and Lucca are just standing there, bewildered, wondering what to do.

For them, 5 minutes pass before Crono decides to follow Marle.  For Marle in 600AD, 5 minutes have also passed.  Crono and Lucca can choose to do nothing and get on with their lives, and the changes to the Guardia line (death of Leene) in the past will never ever catch up to them.

Why? Because...

Those 400 years don't just instantly occur. The changes cannot possibly move that fast because time itself only moves at a certain rate.  Furthermore, the changes are "in dimension" - they are not 5D events like time traveling.  That means that the rate at which time passes acts as a speed limit for changes to the timeline as well.

Here is a 3D space analogy:

If I were some cosmic godlike being and I reach in and pull the Sun away from the Earth, Earth would still continue to orbit as if the Sun were there for a few minutes because the effects of the change cannot move faster than the speed of light and light from the Sun does not reach us instantly.
I would think the same concept works for changes to the timeline.

Let's look at a hypothetical using Temporal Relativity.

Imagine if the we, the gamers, were looking at 1001AD "before" (Time Error-wise) the Entity opened the gates in 1000AD.  We would see Crono chatting with his mother or Lucca.  Now, it is still 1001AD but the Entity has opened the first gate in 1000AD, and Crono has entered it.   What happens to  1001AD??

The Compendium says it will be cast to the wind in the Darkness Beyond Time, replaced by a new 1001AD where Crono is absent.

But the Telepod example shows that is bogus.  1001AD Crono is just fine and dandy, living out his life.  The changes to the timeline that collapse the causality leading to this lifestyle will never ever ever catch up to him. He is moving away from the Point of Change at the same rate the wave of change is moving toward him.

Conclusion:  It's all relative.  To "Time Traveler Crono", he is married in 1001AD to Marle and is living the prince lifestyle, but to "1001AD Crono", he is enjoying long summer days with Lucca, just like he always does.


What about the Marle Paradox?  I'll get to that later with Part 2. But I only really addressed the Telepod Paradox here.  So,

I've only covered how non-time travelers experience changes to the timeline:  they don't.

For Time Travelers it is a completely different story,  more on that later... 

[Thought]

Time only moves forward at a certain pace, true, but Crono & Co's effects on the timeline are not limited to the same dimension. The very fact that they have time traveled means that they are applying a 5th dimensional force to a 4 dimensional object. To use a lesser dimensional example, imagine a line (a foot long) existing in a single dimension. It can move forwards and backwards but never up and down or side to side; it can't even perceive those dimensions. When moving in a direction, one end of the line will always precede the other end of the line, no matter what. That is essentially what you seem to be saying: point A can never overtake point B.  However, apply a 2D force to it so that it moves from side to side and suddenly everything moves at once and equally in a new direction. Both A and B end at the exact same 2 dimensional endpoint at the exact same time, something impossible on a 1d scale.

While certainly this isn't dictate as to how time travel behaves, it fits with the available data.

[Daniel Krispin]

Actually, Thought, Time does not move forward at a certain pace. It can be measured relativistically, but has no absolute measure of movement. To speak of things like '1000 years' and the like is rather irrelivant when one thinks about it, because it really doesn't matter. Basically... hmm... okay, think about it this way, the earth goes around the sun once a year. 1 iteration per year, right? Well, what would it matter if things went 1 iteration every 'two years', if everything else were doubled in that way? It's difficult to put into words at the moment, but it's something I was mulling over earlier. Time does not have a 'speed', and I do not think it logically can, as the very definition of a speed is (change)/(time).... if you were to make (time) the (change), you would get (time)/(time), which really doesn't work.

I'll have to give this some thought, but I think the whole concept of time error is, well, in error.

Nb. I'll consider what you're saying, Though, I think you may be right on that. But this concept that time 'moves' does not seem to work out very well. We move, because our actions are dictated by the relative relation of space and time, which is what movement is, but just as space, pure 'space' can't move, neither can time move. It just 'is'.

[Thought]

Time does not have a 'speed', and I do not think it logically can, as the very definition of a speed is (change)/(time).... if you were to make (time) the (change), you would get (time)/(time), which really doesn't work.

Depends on how one wants to look at it. Parts of time might have speed, just as parts of "space" might have a speed (for example, a car, with in part of the entire 3rd dimension). So time as the whole doesn't have a speed, true, but things moving through it do. Which is what you said, but is also what I was originally getting at and just used confusing terminology to define. A fragement of "time" (the one foot line I mentioned, here representing a specific "car-like" fragment of the whole) is moving in the wider dimension of time, but is fixed in only a few directions of movement ("forward" and "backwards" in the larger dimension, aka "Forward and backwards" in time). The back of the car can never overtake the front of the car in those limited means of movement because the two are directly connected by the mass between them. But add a different direction, and the two points reach a destination at the same time.

I have an odd means of looking at time. Personally, I would say that time is merely our perception of moving through a higher dimension while perceiving lesser dimensions. That is, "Time" isn't a fourth dimension, rather it is our movement through the 4th dimension while only being able to experience 3. A being moving through 3 dimensions while only perceiving 2 would likewise experience "time." Indeed, if we could give "life" to a figure on a reel of film, that figure would experience "time" much in the same way we view it on the screen (but without the perceived depth of the sceen).

[Daniel Krispin]

Eh, but in that case, in speaking of the car, you are speaking not an object in 3d, but in 4 or greater dimensions. The reason you can speak of a car's speed is because it exists spacially relative to temporally. An object can have a speed through time, but time itself cannot have a speed.

However, I think you're still mistaking. You're speaking of a 'fragment' of time moving thought the larger dimension, but that simply cannot be. Yes, you can speak of a discrete element in the temporal dimension, but it doesn't move. Objects move through the temporal dimension, and in part will move through that fragment, but the fragment is neccessarially unmoving and static. Plot these things on a space-time grid, with time in the horizontal and space in the vertical. The slope is therefore velocity. What you end up getting is that even a segment along the horizontal line cannot 'move', it simply is. But a plotted line on the graph can move through both dimensions. Nonetheless, there is no inherent 'speed' to the line on the graph, the line simply is. We only perceive this movement because our frame of reference views the relative interaction of the two axes.

[Thought]

I think semantics is throwing us off. As such, allow me to attempt to be overly careful.

When I compare time to a car, I am not speaking of time-the-dimension, but rather time-the-bit-between-600ad-and-1000-ad. That is, I am comparing that period of "time" as an object in a dimension, not a dimension itself. I see no difference between a car and a span of 400 years except in that one is a 3rd dimensional object and the other is a 4th dimensional object.

So yes, I am speaking of an object in 4 or greater dimensions. But I say that "time" can have a speed (which is rather sloppy of me; as you pointed out, velocity would be more accurate) because I would reject the notion that temporality is objective to anything. As mentioned, I maintain that temporality is merely the function of movement through a higher dimension as perceived through a lower dimension (I’m rejecting Euclidean mechanics in favor of relativistic mechanics). Therefore, time-the-dimension doesn't exist, only time-the-relation-between-two-dimensions. Or, in other words, Velocity.

The 4th dimensional time-as-an-object-comprising-400-years itself could move through a 5th dimension at a certain time-the-relation-between-two-dimensions (aka, Velocity).

The original model is limited to the X and Y axis (that is, space and time). We take the point 32, 600 on a line with a slop of 1, and say that we want to find a point on X at Y = 1000 to see if it is possible for that point to be greater than a point at Y. Given the slope of the line, X can only be 432 when Y = 1000. X can never be equal to or greater than Y.

But add a Z axis (a higher dimension, with which both X and Y can relate to form a different perspective of time-the-relation-between-two-dimensions), the point on X can indeed be equal to (or greater), but only along the Z axis (that point being at X= 432 Z= 2850 while the other point is at Y= 1000 and Z=1).

This relates back to the original post in that in a limited number of dimensions (in this particular case, 4), a time traveler could indeed never overtake their own changes to the timeline. But if a greater dimension is added, a time traveler could indeed overtake such changes. It just depends on which axis one is referring to, the comparative velocity of that axis, and one’s perspective.

[Daniel Krispin]

The problem is, Thought, is that it is, I think, logically impossible to even speak of a segment of time as moving along at a certain velocity. Movement, as we know it, is a derivative of something relative to time. You simply can't take time relative to itself that way and come up with anything meaningful.

Maybe I'm still not getting what you're saying. However, this is not semantics. I think you are making certain assumptions that you cannot make. For example, you say you are comparing a period of time an an object in a dimension... this you cannot do. In fact, I think with that first bit you are making evident your error on the whole affair. You say 'I see no difference...' when in fact you should see a difference. Or, if you hold that both are merely objects in their respective dimensions (which might be true), then you must also understand the fact that an object in a spacial dimension cannot move either, and cannot have velocity. That only appears when you take its position relative to its temporal coordinates. If you would want to perform an analogous type of effect on a temporal element you would have to take it relative to spacial changes, and even this would be something altogether different. The point is, I don't think you're accounting for derivatives with respect to something.

Time simply cannot have a velocity. Nor can a segement of time, nor a 4th dimentional object. Even an object that exists in all four dimensions does not have velocity unless one takes the comparitive change of all four of these dimensions. Velocity is change in a direction over time. Speed is a change over time. But what can you possibly say of the movement of time? It is change alone, change without either direction or magnitude (unless you put in an 'object' that exists in all these dimensions as a frame of reference, which is not what we are talking about)... hence, time cannot, simply cannot, have either velocity or speed.

Now yes, there might be a movement laterally, but not of some segment. I think you are making a grave mistake in assuming that time acts as a sort of piece of something that moves. Things might move through it, from our perspective, but if you take a step back, the space-time continuum is in fact static, and it is only our frame of reference that moves through it, indeed it is our very comparison between the two that we consider movement. As attractive as it might sound, pieces of the timeline can't move laterally in the way you're speaking of, because you cannot speak of 'pieces' of the timeline. I think the problem is you're approaching this with analogies that don't fit and are misleading you.

Anyway, the thing you have to remember is just to be careful in using the word 'velocity'. That word, and that concept, can only be applied in things relative to the temporal dimension. Not to the dimension itself. Time is NOT a river along which things flow. You're thinking that the space-time continuum can 'change' without realising that the concept of 'change' is internal, not external, to said continuum.

I think it might be more telling to consider time apart from space by taking space apart from time.

[Thought]

But what can you possibly say of the movement of time? It is change alone, change without either direction or magnitude (unless you put in an 'object' that exists in all these dimensions as a frame of reference, which is not what we are talking about)... hence, time cannot, simply cannot, have either velocity or speed.

Perhaps you are understanding what I am saying better than I think, but it appears that I still haven't made myself clear. I think this is due to the word "time" having too many definitions and uses.

Consider these two statements and labels.

A = Time is change
B = Time is the span of years between 600AD and 1000AD

A does not equal B. Time defined in A is not equal to time defined in B. They are two totally different concepts. You are correct in that Time is change and as such cannot move, cannot have velocity, etc. But that isn't the time I am referring to.

Perhaps thinking on the different definitions of "dimensions" might help illustrate my point, as the confusion between various forms of dimensions is similar to the confusion it appears we have between the various forms of time. A dimension is a single direction of measurement. A dimension is also a different reality. Length is not analogous to Home World, nor is Width similar to Another World, even though all of those can be defined as dimensions.

The "time" that I am claiming could move is not the same "time" that is allowing change to occur. A ball exists in 3 dimensions, the arc of a bouncing ball in 4 dimensions, but time-as-change is neither of those dimensions. The directed distance between two points on that arc in 4 dimensions, as perceived through 3 dimensions, gives us the perception of movement (and the colloquial sense of time), because of time-as-change. Let us call one end of the arc 600AD and the other end 1000AD. That arc is what I am referring to when I say "time-as-an-object," as that arc, from a 3 dimensional perspective, represents the course of events from 600AD to 1000AD. It is representing "time," in a colloquial sense, but is not "time-as-change.” The arc can be moved (though that would require itself a higher dimension, I'd argue) because time-as-change is still untouched.

Did that make any more sense?