(w,x,y,z,t)

[gonegahgah]

Just exploring time as interchangeable with space again as a fun exercise...

Interesting reading in another thread here about multiple time dimensions and spatial dimensions.
If we were to make - for the sake of argument - the pillar that time is represented by linear motion then this would make matter and multiple dimensions a player.

As discussed before different numbers of dimensions gives us a different expression of gravity.
0D - singularity
1D - constant gravity
2D - dissipating gravity at constant rate
3D - dissipating gravity at square-root rate
4D - dissipating gravity at cube-root rate

Resulting in:
0D - no acceleration (and no motion)
1D - things fall at a constant acceleration
2D - things fall at increasing liner acceleration with closeness
3D - things fall at increasing squared acceleration with closeness
4D - things fall at increasing cubed acceleration with closeness

By closeness I mean how close an object is to another object.
With both objects falling towards each other this accelerates the process even faster above 1D.
The only thing that tends to offset gravity is spin; whether that is two objects orbiting around a common centre or the actual objects themselves rotating...

So things fall faster from further in lesser spatial dimensions than in higher spatial dimensions.

Time to make breakfast...

[gonegahgah]

So only in 1D do objects fall with constant acceleration.
With there being only up/down it would appear that the only motion of an object in this 1D universe is falling and that all vector movement is at a non-linear rate.
All 'gaps' between matter close at the same increasing rate (not percentage).
So each gap between matter (void) decreases by the same distance each moment and each gap decreases by a greater and greater equal amount each consecutive moment.

That's pretty cool.
So without linear motion they don't get to have linear time clocks.

Once we step up passed 1D we begin to have a direction other than down. So, to a degree, we can then have linear motion along one axis.
This lateral/down motion creates the curved motion of falling objects whether in 2D or greater.
With 2D we finally also get to have weight. There probably is no weight in 1D with everything in free fall with constant gravity acting on all objects equally.

So in 2D it is perhaps possible to have a clock that moves back and forth somehow (perhaps a valley floor with a rolling ball).
You can tell each tick as the ball is closest to you.
In 3D of course it is much easier and we can have our suspended pendulums.

[gonegahgah]

Let's just quickly look at a simpler example of force (instead of gravity).
Like gravity, force can be in a vector direction.

If an object has lateral movement then adding a constant force to the side of the object will give it a curved path in a similar fashion to gravity.
Being constant (like 1D) the change in speed is at a constant rate.

We can compare the speeds both laterally and in the direction of the force relative to a 'stationary' observer.
What we see is that the objects experience a change in the two perpendicular directions that are not equivalent.

Without the vector force the objects will change distance to us along both vectors at an unchanging rate.
As soon as we add the vector force the rate of change along the two axis becomes at variance.

So without the force we can use the object as a clock along both axis.
With the force it becomes harder to use the object as a clock along the direction of the force vector as it moves at an increasing rate...

[gonegahgah]

The interesting thing with science, to me, is something I call goal post shifting.
So whereas we, standing on the ground that prevents us from falling, see an object as falling; science tells us it is travelling in a straight line.
Under equivalence, if you were also falling, the object would appear to be moving, relative to you, "along both vectors at an unchanging rate" just as when there are no forces.
So if we were falling we could use the falling object as a clock.

But for those of us standing on the ground as the object falls (or has a vector force) then it will be more difficult for us to use the object as a clock in the falling direction...

[gonegahgah]

So what does this have to do with the relationship between time dimensions and gravity?
Not a lot I suppose except that it might show a relationship between the number of dimensions and the exponential nature of the gravity time dimension if it is to be considered as such...

You get the following relationships:
1D - the second time dimension is factored by mass
2D - the second time dimension is factored by mass over distance
3D - the second time dimension is factored by mass over distance squared
4D - the second time dimension is factored by mass over distance cubed

So an object in a 3D universe falls at a constant rate to itself whereby it can measure its clock at an even rate.
However a gravitation-free parallel universe would watch and measure our 3D object's clock as falling with an increasing rate that increases by an an amount along a squared curve.
The time dimension in the downward direction changes as an amount along a square curve by a distance factor from the mass focus.

So the gravitational dimension is a curved time dimension for all dimensions over 1D.
In 1D the gravitation dimension is simply a straight time dimension.

As I say science has done in other things, I am simply moving the goal posts and expressing gravity as a form of time dimension.
Objects without visual reference (like being inside a enclosed falling box) regard themselves as moving in a straight line but a planet bound observer sees them moving in a increasing deeper curve.
To the in box observer the objects have a constant movement and time rate but to the planet bound observer the objects have a curved movement/accelerating approach (or what I would call curved time).

So if we were to consider that we have 'gravity free' linear time above 1D (sideways or forwards) and gravity curved time (downwards) then this would constitute us having two separate time dimensions.
Just as latitude, longitude, altitude dimensions are tied to each individual space object (like planets); so would linear (sideways) space and gravity (downwards) be time dimensions tied to each of those same space objects.

Gravity changes the path of objects to the grounded observer so I don't see why it can't be considered to be a second time dimension.
In the same respect I am happy for force too to have some equivalence to gravity and also be considered as adding a time dimension that changes the relative path of an object to a non-forced object.
Constant force however applies a straight extra time dimension which is a multiplication field of the normal time dimension.

In this respect you can also create different angles between the different time dimensions by having different forces applied to different multiple objects.
Forward in time can then be considered as more than just a simple figure of 1 and you can even have negative time by considering a particular force (or gravity) vector as the base amount.
Lesser forces (or gravity) would then figure as negative time relative to us... Though it would be hard to tell as they would also appear to be accelerating away from us...

In our existing Universe we are constantly somewhere in a multi-directional gravity well but egocentrically we take our position as time = 1; though as we have seen even we get variances across our accessible area.

[gonegahgah]

I guess what I am saying is that we can basically represent a position as:
(x,y,z,t_xy,t_z)
where t_xy is based on a linear clock and t_z is based on a squared interval clock in the 3D universe.

Where we can take:
(x₁,y₁,z₁,t₁) and,
(x₂,y₂,z₂,t₂)
and basically work out any:
(x_n,y_n,z_n,t_n),
we should be also able to take:
(x₁,y₁,z₁,t1₁,t2₁) and,
(x₂,y₂,z₂,t1₂,t2₂)
and basically work out any:
(x_n,y_n,z_n,t1_n,t2_n).

For different numbers of spatial dimensions we would still have just one linear time plus one gravity direction time.
The gravity time would just have particular intervals related to how many spatial dimensions there are...

In this way we can represent an object's position (except for tumble and collision) as a series of 5 dimension positions relative to us in gravitational space; including before and after.
This takes into account you being relatively fixed (due to the planet's surface, etc.) while the object is not relatively affixed and is in a dropping curve motion relative to us.