It’s
common to think of “dimensions” of space and the “dimension” of time, but what
if there was more than one dimension of time? I’m not going to present any real
theory about this, but just some idea that I’ve been thinking about that offer
some interesting possibilities.

First
of all, what is a dimension, really? It’s easy to see for space: we live in a
three-dimensional world, the three dimensions corresponding to length, width,
and height. Everything, from cats to particles, can be located in space with
three coordinates (x, y, z). If there was a fourth spatial dimension, we would
be unable to perceive it because we are three dimensional beings and so don’t
have the capacity to interact with it directly. However, higher dimensions can
still have effects upon us (see my previous article on multiple worlds
here).

If
we were 4-dimensional beings, it would be perfectly normal for us to use 4
coordinates to locate objects in space, so we would have something like a cat
at point (x, y, z, *) where * is the coordinate in the fourth
dimension. Of course, this can be extended to many more dimensions, as is
common in string theory and other physics theories.

So
how does time fit into this? We can’t think of it in exactly the same sense as spatial
dimensions, because, first of all, there is just one dimension, so it would be
a line rather than a 3D grid. Second, we can’t move back and forth along it or
even forward along it at any speed we want, but everything moves along it at
the same rate. In space, we can stop at a certain point, go forward, backward,
change our speed, but time is restricted to forward motion at a constant
“speed” along the inevitable conveyor belt of time.

From
Einstein, we have learned that it is possible to alter our perceptions of time
and the rate at which we pass through time (as seen in his special and general
theories of relativity), but it still isn’t possible to truly reverse time. We
can’t just stop and head backwards in time like we can stop on a path and
reverse our direction. It is possible to greatly alter the rate at which we
pass through time by travelling at high speeds or going close to a massive
object (massive as in black hole massive), and perhaps even to go to a
different time entirely via a wormhole that cuts through the fabric of
space-time, but in our general lives, these things don’t happen often, if at
all (I’m still waiting for a TARDIS to land in my backyard though…), so we
won’t consider that here.

So
if time is indeed a dimension, it isn’t at all like the ones of space. Indeed,
in physics, time is treated differently than space for other reasons as well.
For example, we can characterize motion through space and time with a “metric”
that describes an interval of space-time. For example, the metric in flat non-expanding
space-time is

where c is the speed of light, ds is the interval in both time and space, dt is the change in time, and dr is the change in space coordinates (x, y, and z). It’s basically just saying that moving in time and space can be written in a combined manner to give the total “interval” that you moved. We can see that space and time are treated differently just by a quick look at the equation: the interval of time is multiplied by c, and it doesn’t have a negative sign like the spatial interval does.

where c is the speed of light, ds is the interval in both time and space, dt is the change in time, and dr is the change in space coordinates (x, y, and z). It’s basically just saying that moving in time and space can be written in a combined manner to give the total “interval” that you moved. We can see that space and time are treated differently just by a quick look at the equation: the interval of time is multiplied by c, and it doesn’t have a negative sign like the spatial interval does.

However,
we know that space-time is not stationary: our universe is expanding. This
doesn’t change the time part of the metric, but it does change the spatial part
because every point is moving further away from every other point. It’s like
blowing up a balloon with gridlines on it: as the balloon expands, the distance
between the gridlines enlarges. In this scenario, the metric is

where a(t) is
the scale factor, a function that describes the expansion of space. Already, we
see that space and time, even if they figure into the same metric, act very
differently (since time doesn’t “expand” as space does).

All this is to say that it isn’t obvious
what would happen if there are multiple dimensions of time. If there are more
dimensions of space, we just add coordinates to Dr that will also expand with the
expansion of space. We can also add additional coordinates of time to the
metric, but what would the scale factor be? What is the preferred direction to
move in time if there are two time dimensions? It was easy when we had a
straight time-line: everything just moves forward along it. But if you have two
dimensions, you no longer have a time-line, but a time-

*grid*(see picture). Let’s say we can only move forward along each dimension of time (into the future). So for time 2, t_{2}, time must move up (that is the forward direction) and for time 1, t_{1}, time must move to the right (also the forward direction). But if the times are*combined*, where can you move? There are plenty of options depending on how fast you go, for example, see the lines on the grid. In each case, you’re moving forward in t_{1}and t_{2}, but for some, you’re going faster in t_{1},_{ }and for others, you’re going faster in t_{2}. Only the blue arrow has you going forward in time at the same speed in each time.
But
what is this “speed” at which we go through time? After all, speed is defined
by as the rate at which we cover a certain distance (with “rate” corresponding
to a passage through time). So what can we compare the speed of time to? Unless
there is a more fundamental time to compare our time to, it doesn’t make sense
to talk about a “speed” of time. You can talk about the relative speed of time
of one person compared to another (as in special relativity, when one person
can appear to age more slowly than another because they’re travelling close to
the speed of light), but it doesn’t make sense to talk about the speed of time
itself.

However,
when we have two times, we can specify the relative speed of the two times with
each other: we can have t

_{1 }passing more quickly than t_{2}, or vice versa. The orange line in the picture has t_{2 }passing more quickly, since for every step through t_{1}, you go forward 2 steps in t_{2}. The green one is the opposite: for every step in t_{2}, you go forward 2 steps in t_{1}. But you could also have more fanciful patterns on the grid like the pink line: here, although you’re going forward in both times, the speeds at which you move forward in each time keeps changing.
What
this would be like for someone experiencing two times is hard to say. Assuming
that you can only move forward in both of the directions and at a certain speed
(since that is what our one-dimensional time is like now. If not, everything is
more complicated!), you probably wouldn’t even notice it unless there were some
things that only moved in one dimension of time rather than two. In that case,
how would an object just moving along t

_{2}(call it O2) appear to someone two travels through both t_{1}and t_{2 }(call them P12)? I think there are a few options. The first is that O2 appears stationary for P12: the object would appear to be “locked” in one direction. Since it doesn’t travel along t_{1}, it could be just stationary at all points in t_{1. }This is hard to imagine: what would an object travelling along one time appear to someone travelling in two times? Would it appear “blurred” in part, or somehow less substantial? I really don’t know. This requires a great stretch of the imagination!
Another
option is that O2 appears at a single moment in P12’s time. It’s like you have
a straight line to represent O2 on the grid and a slanted line to represent
P12, like this:

They
only cross at one point, so they would both see each other for only an instant,
or more likely, not at all, because it would correspond to an infinitesimally
small interval when they cross each other, which wouldn’t be perceptible for
living beings. If we make an analogy with space, it’s as if you had a 2D object
that had no height (see image to the left). It’s located at a certain height in 3D
space, but it doesn’t have height itself. Though the problem with this option
is explaining why O2 appears at a particular instant of t

_{1}. Why not shifted to another time? Since it isn’t travelling in the t_{1}direction, that time is meaningless to it, so it shouldn’t prefer to be at one time rather than another.
Here’s
another scenario that’s easier to understand. Let’s say you’re confined to one
dimension of time, but that there are really two dimensions in the world around
you. This would mean that things that can travel in both time dimensions could
appear to come in and out of existence. Making another analogy with space, it’s
as if you were on a 2D sheet and a sphere was passing through you. You wouldn’t
see it as a sphere, but as a series of disks that start out small, become
larger as the centre of the sphere passes through you, and become small again
as the sphere finishes passing through your sheet.

And
if there were things that travelled in t

_{2 }while you only travelled in t_{1}, they would either appear to you to be stationary, since you can’t perceive their motion in the other dimension, or you just wouldn’t see them at all (like in the first example).
You
could also have three dimensions of time, and then you’d get a 3D grid of time
like you do in space. There will be many more possible directions of travel
through this grid, leading to much stranger things! But whether any of these are
really possible isn’t that clear. After all, could someone even exist in
multiple dimensions of time? Our bodies function in one dimension of time,
relying on cause and effect for our bodily systems to function, and this wouldn’t
be straightforward in more time dimensions. Our thoughts are also sequential:
we think one thing after another (“discursive thinking”). Yet introducing more dimensions
of time might actually correspond to what philosophers and mystics have strived
toward throughout the centuries, namely, “noetic thinking,” where we can grasp
multiple concepts at once without having them being fragmented them due to the
restricted nature of our thoughts. This, however, might only be possible if we
can travel anywhere on the “grid” of time: forward and backward, which
encompasses a more complete view of existence. Though whether or not this is
possible is another matter entirely.

So,
having more than one dimension of time is certainly not as clear as adding more
dimensions of space. But there’s nothing that says it’s impossible. It’s
possible that we already live in two dimensions of time, or three, or ten, and
that things that we’re unable to explain with our current science could be due
to the fact that there are multiple times.

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