Spatial and temporal dimensions

[namespace]

I was reading the spacetime article on Wikipedia and saw this amazing illustration, more like a graph:

We live in a tri-dimensional world, governed by an uni-directional time axis: past-present-future. According to this, time travel will imply two time dimensions which will lead to chaos, because it is unpredictable, as the photo says.

Now, if we think about a tri-dimensional time, this will mean that we can perceive world the same way we interpret a tri-dimensional Cartesian system (x, y, z coordinates). Thus, any point on this graph can't certainly lead to the absolute next one (just as in one-dimension time), so present doesn't interfere with future nor with past.

 

What do you think about this? How would you perceive the world in multi temporal dimensions?

Edited January 28, 2014 by namespace

[Strange]

We live in a tri-dimensional world, governed by an uni-directional time axis: past-present-future.

 

No, we live in a four dimensional world (3+1). It isn't "governed" by the time axis.

 

 

According to this, time travel will imply two time dimensions

 

I don't see why. Time travel, as normally understood, means travelling to different positions on the single time axis. If you travelled in a different time dimension then you wouldn't be travelling into your past. I don't know what you would be doing: travelling sideways in a different present?

 

 

so present doesn't interfere with future nor with past

 

Cause and effect would appear to contradict that. For example, you wrote your post and then, in the future, I wrote mine.

 

But it is a great diagram!

Edited January 28, 2014 by Strange

[davidivad]

that is a great way to express positions at a given point in time. i see you like computers. here is einstein's version.

 

[swansont]

How can you have time coordinates/dimensions that are orthogonal?

[namespace]

1. No, we live in a four dimensional world (3+1). It isn't "governed" by the time axis.

 

2. I don't see why. Time travel, as normally understood, means travelling to different positions on the single time axis. If you travelled in a different time dimension then you wouldn't be travelling into your past. I don't know what you would be doing: travelling sideways in a different present?

 

3. Cause and effect would appear to contradict that. For example, you wrote your post and then, in the future, I wrote mine.

 

But it is a great diagram!

1. We live in a three dimensional world, but we are also governed by the time's one way (past->present->future). This 4th dimension is abstract while the other three are more concrete.

 

2. By "time travel implies two temporal dimensions" I mean that if we will ever be able to travel back in time, then we can think about the time axis (time dimension) as a two-way route: left to right and right to left.

 

3. Of course cause and effect contradicts that example, because this principle is only available in a uni-dimensional time world. If we think with more dimensions, then this idea may become unsteady.

 

How can you have time coordinates/dimensions that are orthogonal?

This is exactly what I wanted to say. If you represent cause and effect in x, y, z coordinates (rather than on a single, straight, one-way line: past-present-future) there will be no actual link between two points in this system (a cause that leads to a specific effect, just some randomness and abstractness). Also, it is unpredictable and impossible to represent them, that's why the idea is kinda forced.

Edited January 28, 2014 by namespace

[swansont]

 

2. By "time travel implies two temporal dimensions" I mean that if we will ever be able to travel back in time, then we can think about the time axis (time dimension) as a two-way route: left to right and right to left.

 

 

That's still a single dimension, but now the time axis is not constrained.

[namespace]

Oh, yea. That was what I was missing. I felt like it was kinda incomplete, but now it's all clear. Haha, thanks!

 

We're talking about the constraints.

[Strange]

This is exactly what I wanted to say. If you represent cause and effect in x, y, z coordinates (rather than on a single, straight, one-way line: past-present-future) there will be no actual link between two points in this system (a cause that leads to a specific effect, just some randomness and abstractness). Also, it is unpredictable and impossible to represent them, that's why the idea is kinda forced.

 

That is what the diagram in post #3 represents; i.e. things within the light cone are those that can be linked by cause and effect.

[namespace]

Yes, that representation is really accurate and very logical, also. It makes such an abstract idea very clear. The symmetry and the mathematic model behind the illustration is wonderful.

[Schneibster]

I have a few concepts that help me when I deal with dimensionality.

 

The first concept I find really helpful when talking about dimensionality is, never mistake an axis of rotation for a "dimension." In one dimension, rotation is impossible. "Axis of rotation" is meaningless, like 1/0. In two dimensions, rotation is possible in only one plane: x-y. Note however that the "axis of rotation" points in a direction that does not exist, and is again meaningless. In three dimensions, rotation is possible in three planes: x-y, x-z, and y-z. Now, it's common to imagine the "fourth dimension" as allowing one to rotate out of sight. And it's common to imagine it does so about a "fourth axis." And it is completely wrong. Actually, adding a fourth dimension adds not one but three planes of rotation: x-t, y-t, and z-t. And again, these three extra degrees of freedom have "axes of rotation" that point in directions that do not exist. "Axis of rotation" is fuzzy thinking when it's used in talking about dimensionality. Use "plane of rotation" instead and remember that only in this way is the definition of rotation meaningful in the system containing the rotating component.

 

Second, the shapes of the past and future are the two branches of a hyperboloid of revolution; and this is far more accurate since the math that describes rotations in real 4d spacetime is hyperbolic trig. You can actually substitute degrees of rotation in hyperbolic geometry for meters per second in 3d space + time formulations and get the same answers. You can represent the Lorentz transform as rotations in 4d spacetime, as the sinh and cosh of the angle. You can find references to this in the literature and on the Internet by searching on "rapidity," which is what relativists call that type of rotation. Baez has a page on it. When you realize that such a rotation results in a second observer means seeing time and space directly convert into one another, you will stop making this unphysical mistake of thinking time is "different." The result of this is that one realizes that the relations of the 3 space dimensions to one another are circular and involve circular trig; but the relation of time to the space dimensions is hyperbolic. That's why the Lorentz Transform works; and that's why you can also do it completely in hyperbolic trig as rotations. When relativists speak of rotations in spacetime being equal to velocity, it's not a model, and it's not a tool. It's an actual statement of physical reality.

 

I hope these ideas help you.