Multiple Time Dimensions

[Secret]

Here's what i think about multiple dimensions of time

Assume time is fundamental but not a phenomenon/illusion derived from random movements of particles
Assume parallel universes of dimensions 3 exists and the resultant flow rate of time is fixed to n

Time will be like space flowing in one direction, i.e. a vector in space
If the space which contains the universes is 4D+t while our universe is 3D+t, we will have two directions for time to point to
So our universe will have time with flow rate n while in a neighbouring universe the flow rate will be -n

Now expanding the space which contains the universes to 5D+2t. We can have universes with its time vector pointing in any direction on the 'time plane'. this result in the vector placed at some angles [theta] away from t₁ axis. Therefore if we resolve the orthogonal components of this vector. We'll get the following:
Flow rate at t₁ axis: ncos[theta]
Flow rate at t₂ axis: nsin[theta]

For organisms such as us who can only sense time in 1D only within such a universe, we will sense the flow rate of either ncos[theta] or nsin[theta]
For organisms who can sense 2D time, they will sense the flow rate of n and with an extra parameter to indicate the 'direction'
,however i've no idea what will the extra parameter will be like if we can sense it.

The above can be generalized to arbitary no. of time dimensions
Combining with the P/F theory of probability as a continuum, this will result in splitting of timelines

These are my thoughts after reading serval sci fi stuffs in describing timelines, correct me if I'm wrong

Edit:
Another idea is that time is flexible
Assume the time travel and history altering event below does not lead to grandfather paradox
http://img90.imageshack.us/img90/1053/22236642.png

Assume the actual 1st building is built on 1898
Time travel back to e.g. year 1846 and another building is built.
1. From the perspective of past and future, it seems the 1846 building is built earlier than the 1898 one

2. But after knowing there is a time travel event and that time still flows forward before and after time travel
we will know that the 1846 building is built later than the 1898.

If we consider the 2nd case, the timeline is like bending back to 1846 and then continue to the future as usual.
This gives us something like 'time displacement' and 'time distance'. Time here is sort of 2D
And this arguement gives us a theory that time is space like with a unidirectional 'flow' like component

P.S. For the grandfather paradox case, this result in 1t+1p(robability)+3D, according to the P/F theory

[PWrong]

You need to be pretty careful and rigorous when talking about this stuff. It's far too easy to sound like you're talking crap.

Extra time dimensions is distinct from time travel, unless the 2nd time dimension is extremely restricted.

These are my thoughts after reading serval sci fi stuffs in describing timelines, correct me if I'm wrong

Hitch-hiker's Guide?

[Secret]

You need to be pretty careful and rigorous when talking about this stuff. It's far too easy to sound like you're talking crap. Extra time dimensions is distinct from time travel, unless the 2nd time dimension is extremely restricted.

In that case might need your help to guide me to the right direction of interpretation of time as a dimension

btw what about the 'flow rate' theory? it sounds more reasonable than the time travel stuff (although I might be wrong)

Hitch-hiker's Guide?

Star Trek, Star Wars

For the 'fluid time' theory, however it is not inspired from a sci fi but rather from this:
http://www.pastelforum.com/topic.php?id ... post-89556
Which from one of the users comments , found this:
http://www.eblong.com/zarf/nosgoth/timeline.html

[PWrong]

In that case might need your help to guide me to the right direction of interpretation of time as a dimension

It's not easy. The first step is to separate our 1T universe into those concepts that we could possibly to extend to 2T, and those we can't. That means throwing out concepts like "organism" and "flow rate", and talking about things like velocity and force. These are extremely complicated already in 2T. Understanding 2T is an ambitious project, to say the least. I have a couple of ideas about where to begin, but I have no idea where this could lead.

For organisms such as us who can only sense time in 1D only within such a universe, we will sense the flow rate of either ncos[theta] or nsin[theta]
For organisms who can sense 2D time, they will sense the flow rate of n and with an extra parameter to indicate the 'direction'

btw what about the 'flow rate' theory? it sounds more reasonable than the time travel stuff (although I might be wrong)

I don't really get what you were trying to say. You're right about the time plane. To talk about some organisms that can sense the extra dimension and some that can't is way too ambitious at the moment. I think what we need is a symmetry in the time plane, so that you wouldn't be able to tell the axes apart in principle without entropy. Like I said before though, you would get entropy increasing mostly in one direction locally. So that direction would be special, and the perpendicular direction would be different. For a simple system like one ball orbiting another, entropy isn't an issue and there's no way to tell the directions apart.

[Secret]

It's not easy. The first step is to separate our 1T universe into those concepts that we could possibly to extend to 2T, and those we can't. That means throwing out concepts like "organism" and "flow rate", and talking about things like velocity and force. These are extremely complicated already in 2T. Understanding 2T is an ambitious project, to say the least. I have a couple of ideas about where to begin, but I have no idea where this could lead.

[Most important] 1. Do you mean 'throwing out' as in 'suggest', or 'throwing out' as in 'discard,reject'?
2. Need some insights on force and velocity in 2T (Better in graphical or visual form)

Also the concept of 'flow rate' is similar to the 'velocity of time' as said by keiji

The problem with counting time as a dimension is it makes everything have multiple positions, probably infinite. Suppose you have a particle moving in the positive x direction in a 3-dimensional space, then it exists at all the positions [x,y,z,t]:

[k,0,0,0], [k+1,0,0,1], [k+2,0,0,2], etc.

Now if you were to have two time dimensions and simply said that this particle existed at the positions [x,y,z,t1,t2]:

[k,0,0,0,0], [k+1,0,0,1,0], [k+2,0,0,2,0], etc

then it would exist only for a single moment of the other time dimension...

--------------------------------------------

Alternatively, one can give the movement of time a "velocity". In one-time-dimensional-space, time would have a velocity of k, where if k was positive time would be going forwards and if k was negative time would be going backwards. Due to time dilation, the velocity of time would be different for any given object.

In two-time-dimensional-space, time would have a velocity of ai + bj, where i is a "time vector" of k in the t₁ dimension and j is a "time vector" of k in the t₂ dimension.

If this was the case, there should be some way for time dilation to affect the velocity of time in such a way that not only its magnitude was changed. Assuming this was possible, it would be possible for objects to disappear and reappear from the viewpoint of another object.

*shrug* It doesn't really make much sense, but time dimensions are confusing anyway. >.<

But both terms aren't really accurate ,as rate is defined as the change per unit time (d(change)/dt), and velocity is change of displacement per unit time (dS/dt)
We need a term to describe the constant unidirectional "drag" of time acted onto things (i.e. the 'something' that make us can only go forward involuntarily in the time dimension)

I don't really get what you were trying to say. You're right about the time plane. To talk about some organisms that can sense the extra dimension and some that can't is way too ambitious at the moment.

1. The idea is similar to Eric B's 'statue scenario' somewhere in page 1 of this thread
Pics:
http://img717.imageshack.us/img717/1269/74057236.png (Note that all axes are mutually orthogonal)
For different Δt1 and Δt2 there will be a resultant time vector marking an angle Θ away from one of the axis. If Δt1 = Δt2, then Θ = 45^o (Δ means the rate of change of the 'position' or entrophy of the time axes)
But is it correct to say so?

EDIT: Just notice a misconception in the 'flow rate' theory, i treated the time axes as 'space-like', that's why universes that are placed one side in the origin of the time axis will have time flow backwards and universes placed on the other side will have time flows normally, which should never happened as entrophy only tend to increases but not going both directions. The theory will be more accurate when this misconception is removed

2. Ok

I think what we need is a symmetry in the time plane, so that you wouldn't be able to tell the axes apart in principle without entropy. Like I said before though, you would get entropy increasing mostly in one direction locally. So that direction would be special, and the perpendicular direction would be different. For a simple system like one ball orbiting another, entropy isn't an issue and there's no way to tell the directions apart.

Do you mean in 2T there'll be two distinct types of entrophy acting on the same object or space?
Also does the concept of "arrow of time" important in 2T discussions?

[PWrong]

[Most important] 1. Do you mean 'throwing out' as in 'suggest', or 'throwing out' as in 'discard,reject'?

Discard. Maybe not the flow rate idea, although I'm still not sure what that means. There's certainly no point talking about organisms, because life implies things like growing, thinking, being born, which might make no sense at all when time is so radically different. You can still talk about observations and reference frames, if you're careful.

Do you mean in 2T there'll be two distinct types of entrophy acting on the same object or space?

No, I don't think so. Entropy is just a number based on the arrangement of objects in space. So it's a scalar function E(t_1, t_2). The "arrow of time" will be very important here. What you find with any scalar function is that there's a direction in which the function increases more than in any other direction. This direction is called the gradient. It's like if you're climbing a hill, and you find the hardest possible direction in which to climb (or the opposite direction, I cant remember).

I'll talk a bit about velocity. How much do you know about vectors and calculus?

A point in 3D2T looks like x = (x(t1,t2) , y(t1,t2) , z(t1,t2)). Because we have two times, we have two velocities.
v_1 = (dx/dt_1 , dy/dt_1 , dz/dt_1)
v_2 = (dx/dt_2 , dy/dt_2 , dz/dt_2)

Suppose you start at a point x_0. Then at time (t1, t2) you'll be at x(t1, t2) = x_0 + t1 v1 + t2 v2.

Acceleration will be difficult because you end up with a big table of numbers. Gravity might be a bad place to start, I'm thinking maybe we should do a simple 1D spring system with Hooke's law.

[Secret]

Discard. Maybe not the flow rate idea, although I'm still not sure what that means. There's certainly no point talking about organisms, because life implies things like growing, thinking, being born, which might make no sense at all when time is so radically different. You can still talk about observations and reference frames, if you're careful.

The 'flow rate' (or 'velocity of time' used by keiji and some others) is a term trying to illustrate that we move in time involuntarily in one direction (arrow of time) at a constant "speed", rather than moving freely in both directions in space.
imagine that the time axis is a conveyor belt, and that matter is a box on the belt. The speed of the belt is the 'flow rate'
In short, it is the measure of how fast the value of time coordinate changes, i.e. how fast does t1 turns into t2 then t3 etc., anologues to velocity is the measure of how fast the displacement changes
A smaller value of flow rate means that time flows slower in a particular time axis, a negative value means that time flows backwards, a zero value makes the time becomes space-like
Trying to explain the meaning of 'flow rate' is difficult as you'll make use of the terms like rate, which requires time to define. (Also this kind of thing appears frequently in sci fi so that the author can put things like 'a slower time' or 'a faster time' in their sci fi. However this has no relation with time travel)
Although this might be wrong in the context of relativity or maybe science in general but idk, cause i'm still quite confused after reading relativity articles

i hope this can clarify so that you can decide whether to discard it or not, if yes then i'll just focus on the equations

No, I don't think so. Entropy is just a number based on the arrangement of objects in space. So it's a scalar function E(t_1, t_2). The "arrow of time" will be very important here. What you find with any scalar function is that there's a direction in which the function increases more than in any other direction. This direction is called the gradient. It's like if you're climbing a hill, and you find the hardest possible direction in which to climb (or the opposite direction, I cant remember).

According to wikipedia, the gradient is the vector field of a scalar field/function where all its vectors points in the direction of the greatest rate of increase in the scalar field, with its magnitute the greatest change. (Actually i 've never come across with gradient before)
So do you mean here for a Entrophy scalar field S(t1,t2 ... tn), its gradient is the arrow of time?

I'll talk a bit about velocity. How much do you know about vectors and calculus?

A point in 3D2T looks like x = (x(t1,t2) , y(t1,t2) , z(t1,t2)). Because we have two times, we have two velocities.
v_1 = (dx/dt_1 , dy/dt_1 , dz/dt_1)
v_2 = (dx/dt_2 , dy/dt_2 , dz/dt_2)

Suppose you start at a point x_0. Then at time (t1, t2) you'll be at x(t1, t2) = x_0 + t1 v1 + t2 v2.

Acceleration will be difficult because you end up with a big table of numbers. Gravity might be a bad place to start, I'm thinking maybe we should do a simple 1D spring system with Hooke's law.

Hooke's Law
F = -kx

For the F, it can be either -d(mv)/dt or -ma
The unit of k is kgs^-2

So where to start?

P.S. I learnt some basic rules of differentiation such as the chain rule, limits and derivative, and some basic rules of integration such as definite integral, indefinite integral at grade 10
I also know about matrix, determinants and linear transformation at grade 12 (basic matrix operations, row vector , column vector), though not much (especially the latter two, which usually get me confused)
I learnt vectors at grade 10, i've learnt about the dot product, unit vector, vector components and vector operations (additon, scalar multiplication) etc.
I've some concepts on gradient, scalar field, vector space and vector field via wikipedia, but i don't know much besides the basic concepts
I know nothing about the del operator, tensor, partial differentiation, pseudovectors and pseudo scalars, eigenvalue, lie group
And i never learnt matrix calculus before
If something in your maths requires things that i might not understand, i'll try to digest them. If unsucessful i'll maybe ask for clarifications

[A-L-E-X]

Some branches of string theory include multiple temporal dimensions. It makes sense when you think about it-- especially if the universe is cyclic, there would have to be another time dimension to resolve the big bang singularity problem. Hawking came up with the idea of Imaginary Time.

Im my Origin series, I use the idea of multiple temporal dimensions to argue for parallel time lines emerging at each Big Bounce when inflation occurs and converging again as gravity increases at deflation before the next big bounce. A second or even third temporal dimension allows us to have time travel, forward and reverse, as (as I picture it) multiple time lines would be parallel lines on a graph with time extending in two or three axes and a hypothetical time machine being able to navigate these other time axes, perhaps making use of wormholes. There is also Linde's idea that universes exist inside Kerr black holes, in which case those universes would have a different form of time than ours. Ours might be inside one also. I believe the generation of these might me possible inside a particle collider like LHC at some point and, as Linde has stated, the universe would expand into its own space time. Who knows, maybe that's where ours came from

I believe Aharanov takes time even further and argues for retrocausation, that is, the future can affect the present in quantum mechanics. Two way time is an interesting idea and opens up the idea of stuff like precognition, which I have been reading about that a professor at Cornell has published some research about.

Anyway, here is more stuff on Aharanov:
Here is the discovery article about post-selection:
http://discovermagazine.com/2010/apr/01-back-from-the-future

One more:
http://physicsandphysicists.blogspot.com/2011/01/yakir-aharonovs-world.html

Please don't copy and paste large walls of text, we can click on the link. - Pwrong

[PWrong]

Ok the flow rate idea sounds similar or related to the gradient thing.

So do you mean here for a Entrophy scalar field S(t1,t2 ... tn), its gradient is the arrow of time?

Exactly. This is the direction in which eggs break, things get more disordered, and memories can be made.
There is another arrow of time perpendicular to the gradient. In this direction not much really changes. Things can move, but eggs neither break nor repair themselves, disorder (entropy) stays constant, and you can neither make memories nor forget them.

Hooke's Law
F = -kx

See this is the main problem. In 1T, F is a scalar and x is a scalar. But in 2T, F has at least 3 numbers in it. The equation doesn't work. I'm thinking about starting with what we'd like the spring to do, and then deriving a simple force law that gives us this outcome and looks a bit like F = -kx.

So the length of the spring should be given by x(s,t), where x is symmetric in s and t (because there's no change in entropy for an ideal spring). It should look pretty much like simple harmonic motion. For example:

x(s,t) = A cos(ω t + φ) cos(ω s + φ)

dx/dt = - ω A sin(ω t + φ) cos(ω s + φ)
dx/ds = - ω A cos(ω t + φ) sin(ω s + φ)

d^2x/dt^2 = - ω^2 A cos(ω t + φ) cos(ω s + φ)
d^2x/dtds = ω^2 A sin(ω t + φ) sin(ω s + φ)
d^2x/ds^2 = - ω^2 A cos(ω t + φ) sin(ω s + φ)

I guess we could have a t-force and an s-force and have a law like:
F_t = - k x
F_s = - k x

That would probably allow more solutions than the one I chose.

[rickfieldrj]

Three mutually orthogonal time dimensions, along each of which three spatial dimensions expanded at time zero of the Big Bang would mean that in our three dimensions the other spatial dimensions would still appear to be unexpanded and tightly wrapped up, as each of their time dimensions would appear to be at time zero permanently to us. Each of the three possible sets of matter, up/down quarks and electron, strange/charm quarks and muon, top/bottom quarks and tau could exist as the only form of matter in each of the three universes, each 90 degrees out of phase with the others, expanding from the Big Bang along their own independent time axis. However, as gravity operates through all the dimensions, the effect of the matter in the other two universes would be felt in ours as dark matter and energy, explaining the non-Keplerian rotation of galaxies and missing mass-energy in ours. Just a thought!

[Halfbaker]

Really, (at least as far as I can tell) the difference between space dimensions and time dimensions is that time dimensions get special treatment from the laws of physics, the laws thermodynamics, for a major example. A universe with multiple time dimensions would essentially be a precession of gradually changing timelines as far as I can tell. You wouldn't even notice if you where living in one of these because your whole timeline would just be a moment in the other dimension of time, save that the previous timeline would almost always leave an impact on your timeline.

[Mrrl]

Ok the flow rate idea sounds similar or related to the gradient thing.

Hooke's Law
F = -kx

x(s,t) = A cos(ω t + φ) cos(ω s + φ)
I guess we could have a t-force and an s-force and have a law like:
F_t = - k x
F_s = - k x

That would probably allow more solutions than the one I chose.

So we have equations
d²x/dt²=-k/m x
d²x/ds²=-k/m x
and say nothing about d²x/dsdt

In this case all solutions have form x(s,t) = A cos(ω t + φ1) cos(ω s + φ2)
It's not bad, but we have special time directions (t,0) and (0,s).

If we add equation d²x/dsdt=0, we'll get equation system that is invariant to time basis selection, but it has no non-zero solutions.
Also we can take system

d²x/dt²=-k/m x
d²x/ds²=0
d²x/dsdt=0

with solutions x(s,t)=A cos(ω t + φ) - and our clock will work only in one time direction and show nothing in another.

May be there is another way - to work in terms of energy instead of force... What are solutions of q(s,t)²+(dq/ds)²+(dq/dt)²=1 ?

[hosj]

That's interesting. Reading this forum has opened my eyes to something unexpected. i thought multiple time dimensions referred to the idea that every time a quantum event occurs, time branches off, (pretty much Everett's many worlds interpretation.)and these branching time lines create a 2-D "plane" of time.

[hcesarcastro]

That's interesting. Reading this forum has opened my eyes to something unexpected. i thought multiple time dimensions referred to the idea that every time a quantum event occurs, time branches off, (pretty much Everett's many worlds interpretation.)and these branching time lines create a 2-D "plane" of time.

Yes, hosj, that was also my idea. Metaphorically, if one decides to go to the right time goes one way, if he/she decides to go to the left it goes another, and if he/she stays in the same place time goes in a yet another way, thus creating a time plane.

I thought of something even more strange that there were no smaller unit of time than the Planck time and no smaller unit of length than the Planck length. I thought that everything is discete, but in such a tiny scale that seems to be continuous.

[Prashantkrishnan]

MultiDimensional Time?

I'm now posting on a very old post in this topic.... but I felt that there was something worth mentioning.
If the statues actually existed in a different timeline which intersected our timeline, isn't it true that we would view their universe only at the instant of intersection? At all other instants, we should not be able to see them at all.

Let the intersecting timelines be x and y axes. For the x timeline, t = 0 at the point of intersection. Same goes for the y timeline. So the people of the x timeline would not be able to see the statues when t = -1 or t = 1.

[Eric B]

I was basing it on those two fictional productions I mentioned. This would assume that each timeline has a temporal "hyperthickness" where the objects are still in place in the spatial dimensions in the new time dimension. The point was to show what two (or more) time dimensions would be like, which could be futile if the frozen time dimension only existed in an instant of the perpendicular dimension.

I've since added the concept of an entirely new continuum (in addition to space and time) called "chance" (viewtopic.php?f=4&t=1318) which is about parallel realities, and would figure in this, since in both of those fictional portrayals, the people in the perpendicular time dimension could change things in the frozen time dimension (I remember in one of them, swapping a man and woman's swimwear!)

[logicxtreme]

The universe in which we are, has 24 dimensions. 4 + 4 space. 8 + 8 time. The fourth dimension is a two-dimensional complex which lies on the border between matter and antimatter.Each geometric dimension has two temporal dimensions. The fourth dimension is primarily responsible for the forces of attraction and rejection, including gravity. So infinity is zero. So all you are right.

[Teragon]

logicxtreme that's your belief. Sources?

[Teragon]

The more I think about it, the more fascinating the idea of mulitple time dimensions becomes. I'm going to share my thoughts about it, they might be awkward and vague, because this is all well beyond what I can grasp.

There seem to be different views on the issue of multiple time dimensions. According to one view, experienced time is only 1D and we can choose the time direction of a time plane at any moment. That's a good starting point and easier to visualize, but essentially, what we do has to take place in two time dimensions as well, because we're also part of the universe and every observer could choose and explore a different path in time. So I'm going to refer to the more radical view.

Let's talk about two time dimensions for now. Time is not a line anymore, but at plane. Multiple time dimensions are giving hard constraints to what can happen in any time direction between them. As on a spatial plane there are many different ways to reach the same object, there are many different "time paths" (sequences of events) to reach exactly the same state of the universe. What your free will does in one time direction, puts constraints on what can possibly happen in another time direction.

If you start at (t1, t2) = (0, 0) at position (x, y) = (0, 0), for example and choose to walk two steps forward within one second of t1, at (t1, t2) = (1, 0) you're at (x, y) = (2, 0). From there you go one step to the right within one second of t2. Now your position at (t1, t2) = (1, 1) is determined, it's (2, 1). Where can you possibly go from time (0, 0) to time (0, 1) ? If you go one step to the right (0, -1), your body has to move two steps forward and two steps to the right in just 1 second of t2 in order to be consistent with your other "line of action" and reach the location (2, 1) at time (1, 1). This also applies for any possible path on the time plane reaching time (1, 1) or any predefined point on the time plane (as long as the movement is always towards the direction of the first quadrant).

Now that propably wouldn't be what a beeing living in a universe with 2 time dimensions would feel. The language I'm using is one of linear, one dimensional time. There's no distinguished time direction for a beeing in multiple time dimensions, time would be passing uniformly in each future time direction. Like space, the time plane would be smooth and interrelated. Movement has to be seen not as a sum of independent times lines, but as a whole process with two time dimensions in nature. Two actions on two linear time paths leeding to two different outcomes at the same point of time would seem as impossible for beeings living in two time dimensions as it seems to us to be at two places at once.

The consequences are very bizarre. The present, where the beeing is making decisions, seems to be splitting into muliple presents, again and again. Some of these presents reunify in later presents. Those presents are interrelated in a way that choice somehow is "blurred" throughout them. They seem to know about each other. Still it is not clear how such a universe could be possibly perceived. What two time directions actually mean is that there are two completely independent lives one can live "at once" (or in general things that can happen). The number of time dimensions is equal to the number of independent "linear lives" one can live. Even more interesting is that this applies for any point in life and that also everything in between those different lifes becomes realized.

There is not one past and one future anymore. For any point in life there are two futures independent of each other as well as linear combinations of both of them. Both of those two principal futures are dependent on the past, which consists of two pasts and linear combinations of them, but in addition, one of them is dependent on the past-future, and the other one is dependent on the future-past. For one present moment, the past-future lies in the past in t1, but in the future in t2 and vice versa for the future-past. That's an interesting structure of causality!

[Teragon]

I see there have been efforts to develop some physics in a universe with two dimensions of time. Propably it won't work with our conceptions of interactions, potentials and forces. The problem arises even with at first place freely moving particles without any forces, as soon as the interact. Below you see the structure of two time dimensions in a discretized form. Black dots indicate the points on the time plane, which are all crossings of different paths. There is a number of possibilities to get from the bottom left point to the top right point (462 to be precise, in accordance with Pascal's triangle).

Concerning a freely moving particle with velocity v1 in t1 and v2 in t2, the time plane also corresponds to a plane in space that is traced out with time(s), if v1 and v2 point in different directions. So the different realized paths in time also correspond to different paths in space. If at any one location there is another particle, an obstacle, an interaction we have a problem, because both velocities have to stay the same in order for the particle to reach the point in space corresponding to the top right point at the given time. Another possibility would be that somehow all the paths communicate, therefore non-local physics. However it's unclear to me if there is a consistent way to satisfy the constraints of all pairs of points on the time plane and still allow for interactions. In other words: Order must never matter.



There seems to be a way to avoid all these troubles, namely if the time-structure is in a way that different pasts never cross. Conflicting paths in the classical time-structure are just two different branches that have no common future. While hard to imagine continuously, this would be a tree-like structure if discretized. For every point on the classical time plane there is now one point for every possible path from the starting point. Physics is no problem any more, but different branches do have more the character of parallel universes/scenarios. The structure reminds me of chance/choice space (discussed here: http://hi.gher.space/forum/viewtopic.php?f=4&t=1318), but its meaning is quite different.



The whole continuum seems to have effectively more than 2 dimensions, but obviously it's not possible to define the dimensionality as a power. The number of time points x points into the future (t = t1 + t2 - no diagonal movement is allowed in the discrete case) from one time point isn't x² or anything like that. It's 2^x! (The sum of row number x in Pascal's triangle/pyramid.) If we take into account the past and can't move to parallel branches, it's 3^x. So for this kind of structure, the size doesn't grow with distance^{dimensionality}, but with dimensionality^distance! Does anyone know where I can find information about such structures?

[PatrickPowers]

I have, for the past several months, been captivated by the idea of a universe with two separate dimensions of time. Despite having tried numerous methods of visualizing such a universe -- comparing it to a two-variable parametric equation seems to help a bit -- I remain unable to do so. Has anybody else thought about this before, and if so, have you been successful?

The first thing to do is look at Einstein's relativity. Every particle has its own clock. This is a big hassle for chemists, who have to deal with electrons moving at relativistic speeds. Each electron has its own clock. Each electron has its own [x,y,z,t] tuple. The number of dimensions increases by 4 when each electron is added. The dimensions of the problem increase linearly, which means that the complexity increases exponentially. The biggest system ever simulated is something like a gold atom. Big molecules with hundreds of electrons are forever out of reach for traditional computers. That is why they are working on quantum computers to solve these problems.

If you are interested, the place to look is the Minkowski geometry of spacetime. Essentially what it says is that relative velocity is a rotation in 3+1 spacetime. Weird, huh? Each particle observes a different past and different future.

Let me cook up something inspired by this but with two dimensions of time. No going backward in either dimension. No standing still. My time vector has a constant length, so I'm always moving forward in time by the same amount. I can move forward in either time dimension or in both at the same time, with the condition that t1^2+t2^2 = 1, with t1 and t2 >= 0.

Well, how can anyone distinguish this from what we see now? The difference is that the past is two-dimensional instead of one. Two particles colliding could have different paths through that 2D time, so could have different pasts.

So suppose you have an automobile accident with someone. Whose fault is it? You both have dashboard cameras. But since you have different pasts, each record might conclusively show that the other party was at fault. Or one record might show the weather was to blame while the other shows a pedestrian caused it, or whatever. There is no longer any reason the two records should agree, because there are multiple pasts. Introducing a third party won't help, because he/she/it has yet another past.

That is a bit too anarchic for me. Here is another possibility. Everyone has a different past, but everyone at the same angle of time observes the same past. That is, a particle might take any sort of path it likes though the 2D space of time, but the past it observes depends on t1/t2. It is a more natural to use arctan(t1/t2) to get an angle from 0 to 90 degrees: that's the angle of time. Every particle for which t1/t2 has the same value observes the same past, but the path each particle actually experienced may be quite different. On the other hand, any group that maintains a constant angle through time will experience and observe the same past. Individuals that do not maintain a constant angle through time experienced a different past than they now observe.

The two parties had to be at almost the same angle of time in order to collide. In the time before the collision they must have had almost the same angle, so discrepancies between their dash cam recordings in, say, the minute before the crash should almost always be insignificant.

[Teragon]

PatrickPowers, in theory this is all nice, but a universe with two time dimensions that work this way would either be so exotic that I can't think of one at the time or very boring. The universe we live in is made up from interactions. If you consider the air for example, the properties of the gas are a result of many individual particles moving at high speeds and colliding all the time. In a universe with two time dimensions, if any timeline on the timeplane leeds to a collision (interaction), each other timeline through the same point must lead to the same collision, both particles must arrive at the same location at the same time respectively. So all the pasts of the particles must be consistent with all of those collisions. It turns out that as soon as the velocity is different for different time directions there are always paths that don't lead to collisions creating inconsistencies on the time plane. For example we start at (0,0) in time and a collision occurs at the point (1, 0). At the point (1,1) there only paths running through (1,0) involve a collision in their past (because other paths involve slightly different velocities so the involved particles move past each other). As all paths have to be consistent with the universe at (1,1), there are two possibilities:

(1) Velocity is independend on the time direction so that the same collision occurs at the same time intervall sqrt(t1²+t2²) in any time direction. Such a universe would not make use of its additional time dimension looking the same as a universe with only one time dimension.
(2) Local interactions do not occur. There would just be linear movement of a chaotic sea of particles that don't take notice of each other.

It doesn't work with the physical laws we have. Adding a second time dimension is very restricting to possible universes. There might be very different rule sets that are consistent with two time dimensions, where the time plane looks as smooth and consistent as a landscape. A landscape on the other hand is not causally connected (only via time), but a timeplane is. Because an action is something that leads to a different outcome, taking an action at a point on the time plane is not possible. Actions would have to stretch from one point infinately into both present-futures to have a lasting effect.

[Teragon]

Another way to picture the problem: Starting from one point in spacetime, going a little step from (t1, t2) to (t1, t2+Δt) should result in a small change in a resonable universe. A small step from (t1, t2) to (t1+Δt, t2) should result in another small change. If the universe behaves in a chaotic way, small changes in the parameters result in totally different outcomes sooner or later. Therefore when some time t1 has passed, a small change in t2 would result in a totally different outcome - smoothness and causality would get lost in this time direction.

So chaotic processes are not possible in a universe with two time dimensions, if different paths on the time plane meet. Our universe is governed by chaotic processes: Diffusion at the scale of fractions of a second, the state of the atmosphere at the scale of several days, the evolution of galaxies and star at long time scales...

[PatrickPowers]

PatrickPowers, in theory this is all nice, but a universe with two time dimensions that work this way would either be so exotic that I can't think of one at the time or very boring.

Quite so. Pure science fiction, that. Not meant to be a realistic physical possibility.

[Teragon]

PatrickPowers, in theory this is all nice, but a universe with two time dimensions that work this way would either be so exotic that I can't think of one at the time or very boring.

Quite so. Pure science fiction, that. Not meant to be a realistic physical possibility.

I didn't intend to make a point here and to shut down the discussion, rather I hoped to provoke thoughts about how it could still work. It seems that while adding spatial dimensions adds new possibilities, adding time dimensions imposes unequally stronger restrictions on what is possible.

[Teragon]

Two time dimensions are consistent if causality is not involved or only involved in one time direction.

One possibility is a spacelike time dimension. Let's call it s. It seems to be a necessity that information can travel in s-direction, so that the universe can stay smooth and neighbouring places in s don't develop into completely different scenarios at the same t, x, y and z. If signals can travel in both s-directions with time, another characteristic of a temporal dimension is dropped and the universe would behave just like a universe with four spatial dimensions and one temporal dimension.

Another possibility is a mixture of spatial and temporal. Allowing signals only to travel in positive s-direction has strange consequences. Particles would travel in s as in a spatial dimension, but they couldn't move back. They would feel the forces of everything in -s direction (the quasi-past), but the particles in the quasi-future would be invisible to them. Beings would be able to see the quasi-past, but they couldn't ever go back and the quasi-future would be invisible to them. Maby living beings could not exist at all in such a universe. Might also be that there are contradictions with some principles physics. Thoughts anyone?

Yet another possibility are phenomena that occur in time but that are not actually causally related in t. An example would be a wave with an amplitude that's a function of x and y travelling in x-direction with t and y-direction with s with no interactions occuring. Might not be interesting physically, but as a possibility for experience. A piece of music could be thought of a wave with two time dimensions. Would be very interesting to experience such a piece of music.

[PatrickPowers]

So let's say that we have two dimensions of time. Let's say that two particles collide if dx^2+dy^2+dz^2+dt^2+dt'^2 = r^2. What are the consequences of this.

Particle A could move into the past of particle B and collide with it. So what? Any observer of particle B is not in the past. So neither the observer nor particle B would know about it. It would make no difference.

Another way to look at it is that there are a very great number of pasts that would result in the present. We will never have enough information to determine which is the correct one. Why should we believe that the past is unique? I don't. I see no reason at all to believe this. If the present is indeterminate, then surely the past is as well.

How do we know that this is not happening already? I'm entertaining myself by saying that it is. The quantum realm is indeterminate, and there is good reason to think that it is largely time-symmetric. Who is to say that it is causal?

As far as we know the quantum realm is largely acausal. Things happen one way instead of the other for no apparent reason. It is easy to imagine that there is a causal reality behind it, but Simon Kochen and John Conway with their 1-0-1 theorem seem to have shown that assuming this leads to a contradiction. (More precisely, either there is no causal reality, or the observer's measurements are also caused and the observer's free will is an illusion.)

[ICN5D]

Perhaps we live in an infinite-dimensional time universe, intersected by a 3-plane of space. Our worldline (path integral) is the zig-zagging 3-plane, tracing out poly-helical (helices within helices) patterns on the large scale (planets going around stars going around galaxies) , and cyclical, semi-random (work, home, grocery store, occasional trips to other cities) on the 'human' scale.

Each axis of the time universe represents a choice or event: it either happens or it doesn't, a yes/no answer equal to + or - directions along the axis, away from origin. So, time becomes more of a quantized event-space, where our path precisely records everywhere we've been, everything we've done, and all possible choices ahead of us.

The light-cone of future choices would be multi-dimensional, with some kind of physical shape that represents the most probable outcomes of our current state of being. Sharply-defined light-cone regions are the habitual behaviors, highly predictable and most likely to occur. A fuzzy, widespread region is more undecided or unknown. We're literally spot-lighting our way through the dark caverns of reality, and repeat what we know. It reveals itself only so much.

Maybe it's not infinite dimensional, but extremely high, like 10^128 (which is virtually infinite) . Maybe the number of particles in the universe has something to do with it, like some kind of max potential collision probability, from one to all the rest. Perhaps the exact, precise rules that govern individual particle worldlines are entirely different to those that govern humans living together, and building a city over time.

Where, both are deeply inter-related in some unknown mathematical way. In the ways that living beings, societies and ecosystems are the physical representation of some super-advanced harmonic math function, of particles in space-time. A highly predictable emergent system, based on a simple set of rules and trillions of iterations of time. Anyways, just putting it out there.

[PatrickPowers]

Is anyone doing serious work with two or more time dimensions? I'm having fun with science fiction, but I'm curious what they have come up with.

[quickfur]

The fundamental problem with more than one time dimension is that time loses one of its defining qualities, that is, its unidirectionality. Then it becomes arguable whether it's actually a time dimension, or just another spatial dimension in disguise. Conceptually it's not so easy to come up with a workable concept of multiple time dimensions that retains the defining qualities of being a time dimension.

The closest model I've come up with to a workable concept of 2D time is the writer's model. That is, a writer (conceptually!) writes a novel which somehow captures all the events of some fictional universe in which the story is set. Let's call this the "internal history", or time as seen from within the fictional universe's point-of-view. Now, the writer himself exists in his own time, that is, in the "real" universe, in which time passes independently of the timeline in the fictional universe. So we may say that there are two dimensions of time: internal time, and external time. However, thus far, they aren't bound together, so this doesn't really get us anywhere in terms of 2D time...

... until we posit the linking idea, which is that the story that the writer wrote was merely a first draft. In this first draft, certain events took place in the fictional universe, but the writer, at a later point (in external time) decides to revise his novel so that certain events take place differently. This new version of the novel essentially represents a different timeline in the fictional universe, related to the original timeline, but some things happen differently. Now, suppose over the course of writing, the writer makes many revisions to his novel, such that for each given moment M in external time, there is an associated version of the story in internal time that's distinct from any other version. Imagine if we lay out all versions of the internal timelines in sequence, according to the corresponding external time. If we interpolate between each version of the novel, we can in theory create a smooth change from one (internal) timeline to the next, such that putting them all together forms a 2D manifold that, if you go along one axis, represents the progression of internal time, and if you go along another axis, represents the progression of external time.

Something interesting happens when you go along both axes at the same time: you get a story in which the beginning events are the ones described in the first version of the story, but as you progress the sequence of events slowly morph across the different versions of the story until at the end, you end up with the final events in the final story. We may call this "diagonal time". In theory, it's possible to interpolate all the versions of the story such that given any path through the 2D manifold that's non-decreasing in both time dimensions, a coherent story results. This, then, would represent a model of 2D time.

But we're not quite done yet. Our model, as we've currently constructed it, still has a discontinuous relationship between external time and internal time. As such, the two timelines aren't really symmetric to each other -- the writer acts as an external agent that generates the different versions of the internal timeline, but there is no entity in the internal timeline that influences events in the external timeline. What's needed is a kind of mutual, reciprocal relationship, a further refinement of our model, in which events in internal time have an effect on events in external time. Perhaps one way to imagine this would be a kind of mutually-linked pair of universes, let's call them universe V and universe W, and in universe V there's a writer that's writing the history of universe W, but in universe W, there's another writer that's simultaneously writing the history of universe V. Each time the first writer rewrites the story, he generates a new version of the history of universe W, but somehow, by fiat, each version of the history of universe W also has a writer who is revising the history of universe V. Eventually, what the first writer writes about what the second writer writes, is what he himself becomes.

Once we have such a mutually-reciprocal model, we're ready to launch the full model of 2D time. The two writers are, of course, metaphors; in the actual model there aren't separate entities that are writing each other, but a single universe which evolves along two simultaneous time dimensions, but with events along each dimension interlinked with events in the other dimension. Past time (0,0), there are actually infinitely many versions of the universe (i.e., timelines of events) which smoothly integrate with each other into a 2D manifold. This manifold is constructed such that when you're moving in one time dimension, the entire history along the other dimension is evolving; and vice versa. The interesting thing is that when you're moving diagonally, both histories are evolving. In fact, there are an arbitrary number of paths that start from (0,0) and progress "forwards" (except that "forward" is not well-defined, it can refer to any one of an arbitrary number of directions you can go in). Summing all these paths together give you an expanding quarter circle that starts with time (0,0) and fans outwards, sweeping out a quarter-circle shaped area of 2D time.

The resulting universe, of course, is one that's probably extremely difficult for us to comprehend. There is causality along either time dimension, but there is no unique successor state to any given state; in fact, there are an infinite number of states of the universe at any given moment (whatever "moment" even means... since time is non-linear). There is no unique timeline, but a 2D area representing all possible timelines, yet, taken together, these timelines themselves follow some kind of causality that's internally consistent. Any given object will have not a single future, but an infinite number of actual futures, all of which will happen, each along its own trajectory, yet every future version of the object also represents a single continuous arc of development along the orthogonal time dimension. Furthermore, the exact way a sequence of events will unfold changes depending on which direction you're following across the 2D sheet of time. Perhaps even the laws of physics themselves morph as you change the angle at which you trace 2D time from the origin, such that along one time axis, one set of laws hold, and along the other axis, another set holds, and angles in between will see intermediate interpolations between these two sets of laws, all of them self-consistent and mutually-consistent.