Got permission from Dereck.
Geor beat me to it, although I was trying to make a comprehensive post on time in general. Here is my draft although it is incomplete, the basics are there. The title of my thread is "How time works"
Based on recent revisions disguised as clarifying a confusing word in the FAQ, a very wrong standard has been passed.
Namely the standard where spaces that contains universes are now said to have 2 axes of time i.e. any space that contains 2 universes can now becomes low 1-C, which is why I am making this thread. So we can clarify on our universe page how time works.
For anyone who would like to know how a universe with 2 dimension of time will be like, they should watch Tenet.
First, what is time?
In physics, the definition of time is simple—time is
change, or the interval over which change occurs.
the measured or measurable period during which an action, process, or condition exists or continues : duration. b. : a nonspatial continuum that is measured in terms of events which succeed one another from past through present to future.
To put it simply, it is the rate at which change is measured.
How does time flow in a universe?
The modern understanding of time is based on Einstein's theory of relativity, in which rates of time run differently depending on relative motion, and space and time are merged into spacetime, where we live on a world line rather than a timeline. In this view time is a coordinate.
A world line of an object (generally approximated as a point in space, e.g., a particle or observer) is the sequence of spacetime events corresponding to the history of the object. A world line is a time-like curve in spacetime. Each point of a world line is an event that can be labeled with the time and the spatial position of the object at that time.
The world line (yellow path) of an object, which is at location
x = 0 at time
ct = 0.
One common way to describe it is through the arrow of time, which points from the past to the future of an object. This arrow of time is related to the second law of thermodynamics, which states that entropy/change (disorder) tends to increase over time. In our universe, time is a one-way progression from earlier events to later events for objects in it.
Based on the above explanation, we can see time/timelines of an object is simply a world line. Now a universe world line, is a record of all the changes that has occurred in the universe from the past to the present and into the future, in essence the world line or an object or universe is called the time dimension.
why time is referred to as a coordinate?
Change is an attribute of matter and space. Time helps us point out what change or what state an object is. A popular example used to explain this, is this
X and Y agreed to meet for a cup of coffee. X said to Y, "Walk 5 kms straight from your house(x- oordinate). Take a left and keep on walking for 2 kms(y-coordinate). You'll find a coffee house there. Go to the third floor of the coffee house(z-coordinate). I'll be there." Y did so. But he didn't find X there.
Why?
Because X didn't mention the time when he will be there. He needs to specify the exact time when he will be present at the coffee house else they cant meet. If only he would have told that I'll be there on Friday or any other time, Y would have met him. Time acts as a coordinate which specifies,along with x,y and z, the position of X.
In this way, I hope you get why time is referred to as a coordinate.
Time is regarded as a dimension because it fits the definition of the word dimension perfectly. It is “a measurable extent of some kind, such as length, breadth, depth, or height”.
We do not live in a static universe. While it is true that at this moment, everything that is happening is happening at a location that can be mapped to three spatial coordinates, those coordinates are changing constantly relative to everything else in the universe. The universe is in motion. That makes mapping pointless unless we also account for that movement, which we can measure in units of time.
The time axis or dimension.
the time axis is a used to represent and measure the progression of time. It is typically depicted on a one-dimensional axis (the world line). The time axis is typically drawn from left to right, indicating the past on the left side and the future on the right side. This direction reflects the natural flow of time from earlier events to later events. This order is essential for understanding the sequence of events.
To illustrate it, the time axis is combined with other axes, of the spatial dimensions (x, y, z), to create spacetime diagrams. In these diagrams, events are located at specific coordinates in both space and time.
These space-time illustrations are popularly called the Minkowski diagrams.
To put everything I have said so far simply, time as a dimension is simply the direction in which changes flow and in a 4-D space-time model, it is depicted as a single line direction to illustrate the direction of change or the flow of it.
It means a space can only have time in one direction, i.e. nothing like two time dimensions both flowing forward, that is like having a 3D space comprising of 1 length dimension and 2 width dimensions.
Now for the last part.
Multiple time dimension.
Niels Nielsen answers the question of multiple dimensions of time by saying, in part, "Thank god it's impossible."
What does it mean to have two dimensions of time?
The trivial answer is that it just means "you have two dimensions with inverted sign in your spacetime metric". But the perceptual result of that kind of choice doesn't actually look qualitatively different from our universe.
Consider the 4D case; our 4 dimensional spacetime has a a +,+,+,- metric--
according to one convention. If we decide we want two time dimensions, we get +,+,-,-. But, because the choice of which dimensions count as negative and which as positive is in fact purely conventional, this is physically equivalent to a metric with signs -,-,+,+. In other words, physics cannot uniquely distinguish spacelike dimensions from timelike ones. And in fact, Greg Egan wrote a novel in a universe with such a metric (
Dichronauts), in which perceptual proper time is still distinctly one dimensional--just as in our universe, time is the length of your (one-dimensional) worldline.
Go the other way and give all dimensions in you metric the same sign, so there are formally zero time dimensions, and you don't get a static universe without time--you get another Greg Egan novel (actually a trilogy,
Orthogonal), again with normal one-dimensional proper time as measured along worldlines.
It would seem that actually having two dimensions in a practical perceptual sense would require either
- Converting proper time into a vector quantity somehow, or
- Replacing worldlines with worldsheets, such that proper time is proportional to area(2-D).
a question like "when were you born ?" could have an answer like "Dec 1965, January 1831". A question like "which came first ?" might be meaningless and you might need to say "which came first-first ?" or "Which came anytime-last ?".
Multiple time dimensions are theories in physics and not proven, either way some fiction uses it. Here are two major theories of it.
The F-Theory.
F-theory, a branch of modern
string theory, describes a 12-dimensional spacetime having two dimensions of time, giving it the metric signature (10,2)
In 1996, Vafa introduced F-theory as a geometric formulation of Type IIB string theory which automatically incorporates the non-trivial profile of the axio-dilaton τ := C0 + igs−1
in the presence of seven-branes [20]. Such a formulation involves necessarily strongly coupled type IIB theory, as the back-reaction of seven-branes generates a holomorphically varying profile of τ which inevitably attains large gs in certain regions. By noting that the axio-dilaton τ in the presence of seven-branes exhibits the same transformation as the complex structure moduli of a torus T2
(or more technically, an elliptic curve), the main idea of such geometric formulation is
to introduce an extra torus T2 attached to each point in the 10D spacetime of type IIB. Its
complex structure moduli τ encodes the axio-dilaton of Type IIB theory. Thus in F-theory,
we have, formally, a 12-dimensional spacetime.10 By allowing the axio-dilaton τ to vary over the type IIB spacetime, such a 12-dimensional spacetime attains the structure of an elliptic fibration, where the torus (or the elliptic curve) plays the role of the fiber. In order to obtain a low-dimensional supersymmetric theory from an F-theory compactification, the elliptic fibration should be an elliptically fibered Calabi-Yau manifold.
However, in some sense, a more accurate description of F-theory should involve M-theory through a T-duality over the fiber T2
together with certain limits. Such duality naturally passes to F/M-theory compactifications. And more importantly, by going to the M-theory side, one can use well-studied tools such as geometric engineering to analyze various aspects of the effective
theories from the compactifications, such as gauge structures, matter spectra and couplings even though F-theory typically involves a regime non-perturbative in the string coupling gs.
Remarkably, such information is almost entirely encoded in the geometry of elliptic fibrations and one can read off this crucial physical information by studying and analyzing these geometries with well-studied tools in the algebraic geometry. As summarized in the table 1.1 in [21], there is a clear dictionary between the physics of F-theory compactifications and the geometries
of elliptic fibrations. By further studies, the lists in this dictionary would be expected to be
refined and extended. Concerning model building, F-theory naturally incorporates exceptional gauge groups in typical regions of its moduli space, while at the same time it inherits beneficial properties of Type IIB theory, including its ingredients to address moduli stabilization, at least in principle. In some sense, F-theory thus inherits both the attractive properties of Heterotic string compactifications and Type II string compactifications.
Tldr: F-theory adopts duality, which is largely due to it 2 time dimensions.
What does this means, it means it can be and not be, not two it can be at the same time.
Max Tegmark Model.
Max Tegmark
On the Dimensionality of Spacetime.
He argued that, if there is more than one time dimension, then the behavior of physical systems could not be predicted reliably from knowledge of the relevant
partial differential equations. In such a universe, intelligent life capable of manipulating technology could not emerge.
His paper boils down (under gross simplification) to the 4 main areas of the diagram:
- Unpredictable (elliptical)
- Unpredictable (ultrahyperbolic)
- Too simple
- Unstable
The first unpredictable region has a spacetime with elliptical geometry. This mainly means that it is a closed, finite manifold. The unpredictable part comes from the fact that there’s no clear “arrow of time” anywhere: no spatial dimension (unitary base vector) is distinguished as a unidirectional dimension, and therefore there is no clear and unambiguous “before” and “after” under any frame of reference. Without such unambiguous before/after there’s no consistent ability to predict what a system will do given what it has already done.
The second unpredictable region has an “ultrahyperbolic” geometry. This mainly means that it is an open, infinite manifold whose metric grows faster than constant times the measured distance. (Our universe, for instance, has hyperbolic geometry and its metric grows at constant times the measured distance—this constant is
Hubble's constant.) This region always has 2 or more “time arrows”, which interact in non-linear ways and which could be swapped via simple rotations: that is, you could freely rotate between time dimensions as easily as you can rotate between space dimensions. This means that you could rotate away from your friend’s time arrow into another time arrow (orthogonal to the first one) and proceed on that one while they keep moving ahead on theirs—in effect, you would have achieved “infinite velocity” with respect to your friends, as you would now be moving in space without moving in their time arrow. Once you have infinite velocities, causality goes (mostly) out the window. Hence the “unpredictable”.
There are then two other unstable regions: the lower unstable one has 4 or more space dimensions, while the upper unstable one has 4 or more time dimensions. The analysis is more complex but boils down to the fact that not even the simple electromagnetic field equations produce results without “blowing up” to infinities every time. (In our universe, for instance, electromagnetism doesn’t “blow up”—it is quite stable since its field equations are at worst quadratic on their first approximation, and their higher-order factors vanish very quickly.) It would be even worse for space-time itself: the universe would expand much faster than gravity would be able to keep it together, diffusing everything away to a random gas long before large gravitational-bound structures could form. Hence the “unstable”.
Finally, the last two regions; or, actually, spots: the “you are here” spot and the “tachyons only” spot. The first spot is obvious: 3 spacelike dimensions plus one timelike dimension—that’s us (as far as we have been able to find out; note that the other dimensions required by string theory, if they exist at all, while space-like, are curled up to macroscopic insignificance).
The “tachyons only” spot corresponds to our universe, with a “speed-limit” and all, but with every particle always moving faster than light—that is, the “speed limit” is not an upper limit, but a lower limit. While such universe could, in principle exist and work, it would be very different from ours in its detailed day-to-day operation—none of its inhabitants (if it has any) would confuse it with our kind of universe, or think that our universe can be made coherent with theirs under some kind of metric/physics conversion. Bradyons (like ourselves and all matter in our universe) would be impossible—or at least “spontaneously non-existent”—in their universe, as much as tachyons are impossible in ours. The only thing in common between the two would be the electromagnetic phenomenon called light: photons would work exactly the same in both universes, except that they would be the slowest particles in theirs, while they are the fastest ones in ours.
TL;DR
Ours might be the only “easily reachable” parameter-space spot where the universe doesn’t dissipate too quickly to sustain any complexity at all before it is diluted to non-interacting bits and pieces; or where the universe doesn’t become so unstable that everything achieves its highest entropy level long before any complexity and structure can self-organize; or where the only way it can even exist is by collapsing to its lowest possible entropy as fast as it can before it “blows up”.
The other “easily reachable” spot would be the “tachyonic universe”—a sort of dual to our own—where what’s spacelike to us is timelike to them, and vice versa. Why our universe is bradyonic and theirs is tachyonic? Can the tachyonic universe actually exist and be self-consistent? Is our kind of universe the only kind that can exist and contain complexity? Nobody knows. Not yet.
Those are two major theories on multiple time dimensions, and they both have some things in common.
1. Time as a dimension can only move in one direction, and for a space to be said to have two different dimensions of time, those two time dimensions must move in two different directions.
2. With two dimensions of time in a single universe, everything becomes unpredictable. To put it simply, I know that if I put my ice cubes out in the open, it will melt due to time passing. I can definitely say without doubt that it will melt, but if it was 2 or more dimensions of time, I cannot say for certain what sort of change would be recorded on the ice cube, hence nothing is predictable in such a universe.
3. You don't get to have normal causality anymore.
Time as a dimension in a multiverse.
We can apply a world line also to a multiverse i.e. time flowing in its direction.
All universe in a multiverse in which all of them flow with one time direction, operates under a single time axis. If different universes have different time directions, then such a multiverse will have multiple world lines and can be said to have multiple temporal dimensions.
Having two dimensions of time in the physical realm would mean that in addition to being able to go forward and backward in time, you could also move sideways in time onto a different world line, then back sideways to join up again with one's original world line or any other world line in any other universe.
This means that one's sudden appearance on a new world line would occur with no history on that world line, and one's disappearance from it would then result in no future on it either. Occupants of those other universes containing those alternate world lines would also be able to pop into and out of our universe as well.
How does all this epistles relates to us in vs wiki? (TL;DR).
We tier fictional verses and what fictional verses do is break physics, but at the same time we try to find a common ground for these things.
I see things like overarching time dimension getting thrown around, there is no such thing as overarching time. It is like saying overarching height, overarching breadth e.t.c. maybe a correct word will be "overarching causality"
Moving on.
Most times in fiction when a space is said to have different time, it is not different time direction but rather time moving or flowing at a different rate or not flowing at all. Time flowing faster or slower does not mean a different time dimension since that time is still flowing in the same direction. In our universe, time flows at different pace for different parts of it, this does not equate to us living in a multi-temporal universe.
Well as usual here is my proposal for how we should treat time on the wiki. Anyone is welcome to make it more grammatically correct so far as it does not lose the original message I am trying to pass across.
1. Time flowing faster or slower in different universes does not qualify for different time dimension. The same goes for spaces said to have different time due to the virtue of their time flows.
2. For a space to be considered to have multiple temporal dimensions, this time dimensions must have different directions.
3. For a space containing multiple universes to qualify for multiple time dimensions, one or more universe in this space must have a different time direction.