Higher Dimensional Time Implications?

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In summary, higher dimensional time could allow more that seems forbidden currently. Closed timelike curves would be possible in flat spacetime. The laws of physics therefore would be acausal.
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LightningInAJar
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If time were 2 or 3 dimensional what implications are there?
I have read that nothing in math makes time having more than 1 dimension impossible. But if time had 2 dimensions or even 3 dimensions on its own, what would that mean? Could time travel and time travel paradoxes be allowed without destroying the universe or creating branch realities?

I think in 3 dimensional space you can ties your shoes, but in 4 dimensional space a knot can't exist.

Would higher dimensional time allow more that seems forbidden currently?
 
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With more than one dimension of time there would be no more distinction between future and past. Closed timelike curves would be possible in flat spacetime. The laws of physics therefore would be acausal.
 
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Time as 1 dimensional is a line? What about that makes time causal? Who says the arrow doesn't go both ways, or that lines can't bipass between future and past?

What about a plane makes physics acasual? Couldn't it be limited to rightward and upward directions so it doesn't circle back around?
 
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LightningInAJar said:
Time as 1 dimensional is a line? What about that makes time causal? Who says the arrow doesn't go both ways, or that lines can't bipass between future and past?

What about a plane makes physics acasual? Couldn't it be limited to rightward and upward directions so it doesn't circle back around?
Traveling from point A to point C on a 1D spatial line requires passing through midpoint B.
Traveling from point A to point C on a 2D spatial plane allows one to sidestep midpoint B.

The same holds for time dimensions.
Moving from 2020 to 2022 requires passing through 2021.
In 2D time, you could go from 2020 directly to 2022 without passing through 2021.


On second thought, that's a crummy explanation. I'll leave it to the experts.
 
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LightningInAJar said:
Time as 1 dimensional is a line?
No. Time (in this sense) is a direction in spacetime, like the x direction on a plane. You cannot draw a smooth curve on the plane that starts pointing in the +x direction and ends up pointing in the -x direction without it pointing in the y direction inbetween. Similarly, you can't draw a line in spacetime that is advancing in the +t direction (as we all do) and end up advancing in the -t direction without pointing in the x, y, or z direction inbetween. And the physics won't let a worldline advancing in time turn into one advancing only in space.

However, if you had two timelike dimensions you could move smoothly from advancing in the +t direction to the -t direction passing through the t' direction. So there would no longer be a distinction between past and future, so there's no causality.
 
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LightningInAJar said:
Time as 1 dimensional is a line? What about that makes time causal?
The spacetime interval in flat spacetime is ##ds^2 = - dt^2 + dx^2 + dy^2 + dz^2##. If you look at the surface formed by all vectors formed with a fixed ##ds^2=const.## then if ##0<ds^2## you have a hyperboloid of one sheet. Any such spacelike vector can be smoothly mapped to any other. In contrast, if ##ds^2<0## you have a hyperboloid of two sheets. We call one sheet the future sheet and the other the past sheet. A future directed timelike vector can be smoothly mapped to any other future directed timelike vector, but it cannot be smoothly mapped to any past directed timelike vector. The future and the past are topologically disconnected sets, unlike with spatial vectors.

If you add a second timelike vector ##dS^2 = - dt^2 -du^2 + dx^2 + dy^2 + dz^2## then timelike vectors with constant ##dS^2<0## form a hyperboloid of one sheet. Then any timelike vector can be smoothly mapped to any other timelike vector. There is then no more distinction between future and past than there is between left and right. You can turn around in time just like you can in space.

LightningInAJar said:
What about a plane makes physics acasual?
The future and the past would no longer be distinct sets.

LightningInAJar said:
Couldn't it be limited to rightward and upward directions so it doesn't circle back around?
If you did that then you would actually have a single direction of time but just written in a non-orthonormal basis with two timelike basis vectors. It would still be a single time dimension in the right+up direction. You would still have the same hyperboloids.
 
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LightningInAJar said:
I think in 3 dimensional space you can ties your shoes, but in 4 dimensional space a knot can't exist.
The word "knot" is used for two different things. The mathematical knots that can't exist in 4D are closed curves. The practical knot you use to tie your shoes is not a closed curve. Strings are immobilized by friction. Friction knots of strings could exist in any number of dimensions. If the strings are immobilized then it doesn't matter what it might do if they could move freely.

Mathematical knots can exist in N dimensions. They are any closed N-2 dimensional object. In 4D the simplest knot would be a 2-sphere.
 
  • #8
Hawking used what he called "imaginary time." I don't know what it was/is.
 
  • #9
Hornbein said:
Hawking used what he called "imaginary time." I don't know what it was/is.
A bad idea. In Euclidean geometry, the distance between two points is ##\Delta s## where ##\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2##. In Minkowski geometry the "distance" between two events is given by ##\Delta s^2=\Delta x^2+\Delta y^2+\Delta z^2-c^2\Delta t^2## and you can write that last term as ##+(ic\Delta t)^2##. It used to be popular to teach this to try to make Minkowski geometry more familiar to students and hide the concept of a metric tensor (Feynman does it in his lectures), but it generalises badly to curved spacetime where you need the metric tensor explicitly so current thinking is that it makes learning general relativity harder. The modern approach is to be upfront about the role of the metric and introduce the importance of geometry in special relativity (and do undergrads the courtesy of assuming they can deal with one minus sign without bursting into tears) before you get to the added fun of the full machinery of pseudo-Riemannian geometry in general relativity.
 
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FAQ: Higher Dimensional Time Implications?

1. What are higher dimensional time implications?

Higher dimensional time implications refer to the concept of time existing in more than just the three dimensions (length, width, and height) that we experience in our daily lives. It suggests that time could also exist in additional dimensions beyond our perception.

2. How do higher dimensions affect our understanding of time?

Higher dimensions can greatly impact our understanding of time. For example, if time exists in a fourth dimension, it could mean that events in the past, present, and future all exist simultaneously. This challenges our traditional linear understanding of time and raises questions about the nature of causality.

3. Is there evidence for higher dimensional time?

While there is no concrete evidence for higher dimensional time, some theories in physics, such as string theory, suggest the existence of multiple dimensions. Additionally, some scientists believe that phenomena like deja vu and precognition could be explained by our consciousness tapping into higher dimensions of time.

4. How do scientists study higher dimensional time?

Studying higher dimensional time is a complex and ongoing area of research. Scientists use mathematical models and simulations to explore the implications of higher dimensions on our understanding of time. They also conduct experiments and observations to look for any evidence that supports the existence of these dimensions.

5. What are the practical applications of understanding higher dimensional time?

Understanding higher dimensional time could have significant implications in fields such as physics, cosmology, and philosophy. It could also lead to advancements in technology, as some theories suggest that higher dimensions could be used for faster-than-light travel or communication. However, much more research and understanding is needed before any practical applications can be realized.

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