# Multidimensional Time-Lines

Ever since grade school, we have been taught to visualize time in the form of a time-line. This model works particularly well considering the fact that, according to widely accepted scientific theory, time exhibits the same dimensions as a line, with movement across this dimension being constrained to a linear progression.

So, what would the universe look like if time had more than one dimension?

For the sake of this particular question, I'd like to focus on 2-dimensional time, and how our universe might express this second temporal-dimension in contrast to linear time.

My Interpretation:
While I'm not by any means certain as to what 2D-time would look like, I imagine that it would look something like what would happen if the entire quantum-miltiverse merged into one universe. I.E: every possible iteration of the time-line would exist simultaneously, occupying the same space.

Questions:

1. Is the conclusion which I have drawn correct, or am I barking up the wrong tree?

2. Are there any (other) scientifically valid interpretations of my question that might make for a more unique and/or interesting setting?

• I don't know if I will get time to put together a full answer. Such conceptualizing is quite a broad topic. I will however, recommend studying the philosophy of "identity." Its a brutally hard concept to pin down, once you try to depart from the simplest of day to day cases, but in particular, the concepts of perdurable vs. endurable would be very applicable. Those who believe in perdurable identity talk about a 4 dimensional identity, so it may be extended to 5 dimensions. Feb 12, 2016 at 21:27
• Would there be any was for an object or information to move along the second time axis? Time is also weird because we only can move in one direction along it, were x, y ,z we can go either way. Feb 12, 2016 at 23:29
• "People assume that time is a strict progression of cause to effect. But actually from a non-linear, non-subjective viewpoint it’s more like a big ball of wibbly-wobbly timey-wimey… stuff." Sorry it had to be done. Feb 13, 2016 at 0:41
• Read Greg Egan's Orthogonal trilogy, which goes into far more detail than can be managed in a Stackexchange answer. It's set in a universe where there are four dimensions, any of which can act as a space or time dimension. en.wikipedia.org/wiki/Orthogonal_(novel) Feb 13, 2016 at 19:23
• If one-dimensional time is plotted as a one-dimensional shape, why shouldn't two-dimensional time be plotted as an infinitely large plane, starting at some point/line?
– user21719
Aug 16, 2016 at 18:16

People commonly interpret this as being multiple timelines, or the meta-time in which history may be changed.

But more seriously, you would have physics defined in 5 or more dimensions with 2 or more being "time like". (Oh look, It's in Wikipedia!)

Special relativity describes spacetime as a manifold whose metric tensor has a negative eigenvalue. This corresponds to the existence of a "time-like" direction. A metric with multiple negative eigenvalues would correspondingly imply several timelike directions, i.e. multiple time dimensions, but there is no consensus regarding the relationship of these extra "times" to time as conventionally understood.

You would have events plotted in 5 dimensions with rules explaining the allowed relationships between them. These rules may be different along the different kinds of time. But, like space dimensions are all the same, I like the symmetry of two time dimensions being the same too.

How this would seem to someone inside it, I'm not prepared to say. The common wisdom is that it would not be "interesting" like our universe.
(I'd copy the illustration but it doesn't like SVG it seems. See the link in the paragraph above, please.)

But another idea would be, not a branching universe, but a 2D plane on which the world line of an object can choose a line. Just as forces change the direction of motion in 3 spacial dimensions to pick out one possible line, the time direction might be one chosen line out of infinite possibilities. A different kind of force would alter the trajectory. That would leave the world behind, as everything else continues on the old time direction. This describes what's normally considered parallel universe, and logically that's indeed what a parallel universe is. Perhaps you can combine separate history and branching history by having specific things cause splitting rather than everything causing splitting.

update: Greg Egan is writing a novel set in a universe with two space dimensions and two time dimensions. See his page for material including the mathematics of spacetime in his universe! This material was made available in December 2016. The novel will be out in mid 2017.

It might be tempting to think that with two dimensions of time, the history of any particle, or person, would cease to be linear and would take on some kind of planar aspect. But in fact, there is no reason why objects shouldn’t trace out essentially one-dimensional world lines through space-time, much as they do in our own universe. The difference that arises from having a second dimension of time is that of all the straight lines that pass through a given point, more of them would count as possible world lines.

• Regarding Egan's Dichronauts: while the signature of their universe is ++--, only one of the direction is interpreted as entropic/thermodynamic (i.e. "the normal") time, the other coordinate is a spatial one. So the novel describes a 3D universe with hyperbolic (not Euclidean) distances (and that is the cause of much of the weirdness), but a very mundane linear time. Jul 17, 2017 at 12:52

You would have to have another form of input in order to look sideways across time.
Our eyes see what is around us in this space and time. You'd have to have a time2D vision organ to allow you to see across the time space to the other timelines.
Or maybe a different structure inside the eye, like rods, cones, and Penrose triangles.

To normal eyes you'd see the time and place you are now, but to the other eye I think you're right that you'd see all the possible timelines stretching out beside you.

I imagine them being flatish and layered, blurring as they overlap each other.

The timelines closest to you would be the most similar with only minor differences. The differences might not even be anything near you. Maybe on the other side of the planet (a bird almost got grabbed by a hawk/became a hawks supper), and that caused a new timeline to branch.

If you were able to step sideways across them your normal eyes would see the world flicker as you passed by.

• And, looking forward (along the timeline) would let you see your own future, while looking just left or right of forward would let you see what the future could be if you did one thing or another. Feb 12, 2016 at 21:13
• @Samuel Which could be a weird kind of hell in a way... Or maybe make you very grateful. If you were to look "over" and see the person you lost to an accident, or see people mourning for the person you almost lost... Feb 12, 2016 at 21:25
• I'm not sure that that's how two dimensions of time would work as you would be able to move across that second dimension somewhat at will (your total space-time velocity would have a fixed magnitude, but you could move at different time rates on each of the time axis). Feb 12, 2016 at 21:55
• @Draco18s I guess it kind of depends on if you can cross lines, or just look across them. And if you can cross them, can you alter your "forward" momentum to be other than 1 second per second? OP doesn't actually mention moving, just looking... Feb 12, 2016 at 22:03
• A universe with two dimensions of time (ours doesn't have it) would have to have movement across it. The "one second per second" thing, is of course, relative. Feb 12, 2016 at 22:07

IF you are thinking about how to draw or visualize this, perhaps you should envision a loaf of sliced bread.

If you imagine the time moving from the (infinitely distant) back of the loaf to the (infinitely distant) end, and crossing the loaf with "slices" provides a way to envision the different events across the multiple time lines.

Another way might be to envision a grid with multiple light cones all pointing in the same direction. As your world line moves, you are moving in parallel with multiple other world lines (in a true multiverse, an infinite number). Your light cones might intersect in the distant past or future (or even the near past or future if the world lines are close enough), allowing you to "see" events in otherwhen. It is not clear to me if you will be able to influence events in other when, although since you can see them and gain information, it will certainly "bend" casualty.

The standard interpretation of the multiverse is that each universe is independent and isolated from the other universes (which explains why you can't see into them).

This is pretty mind boggling as is, so I will leave you with an image of a sliced bread timeline or an infinite grid of light cones, while I make a sandwich and break out the Go set.....

• Your examples seem to describe normal spacetime. How does that apply to multiple dimensions of time? Feb 13, 2016 at 18:57
• I really am having a difficult time trying to describe this. Going crosswise on the "slices of bread" or moving from one light cone to another where they intersect (and thus moving among separate world lines) is the best I can do with this concept. Feb 13, 2016 at 20:49
• Slicing the bread at a different angle is just special relativity. Light cones are separated by space and all the nul vectors relate to the same (single) timelike dimension. Feb 14, 2016 at 6:34
• Hmmmmmm.......Maybe 2D time is more difficult than I thought. If there was only another dimension of time to move to and think about it.... Feb 14, 2016 at 23:43

Currently there are 4 dimensions w,x,y,z if w' is your speed through the w dimension then the current rules of space time are w'^2>x'^2+y'^2+z'^2 and w'^2+x'^2+y'^2+z'^2=1 this means that the speed you move through through time is greater than the speed you move through space. With 2 time dimensions to maneuver in it would be possible to loop around and go back in either time direction w'^2+x'^2>y'^2+z'^2

• That depends on how you express the current rules. The 4-velocity is constant but w can't be negative because the speed limit of lightspeed is taken as a separate rule. It's better to suppose that the time direction can't be negative as the principle rule, and this causes the speed limit. So "the same" with multiple time dimensions allows you to trade off between them but not reverse. Note that w isn't an absolute direction but gets mixed up with space directions; so this formulation is more natural. May 2, 2016 at 5:39