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Why is Space a THREE DIMENSIONAL ENTITY?

I know that In physics and mathematics, the dimension of a mathematical space is informally defined as the minimum number of coordinates needed to specify any point within it

I'm a student and I have tried to find the answer to this question but I probably didn't get any answer that I understand...

So pls help me with this as I'm still a beginner here!

Thanks!

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    $\begingroup$ I believe this is an open question that remains unknown, though there are proposals for additional dimensions over very small distances that so far, have not been backed up by any experiments at CERN. Maybe Physics would give you a better answer than Astronomy. $\endgroup$ – userLTK Feb 23 at 4:29
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    $\begingroup$ There are various conjectures (I am not going to call them "theories") that 3 spatial dimensions plus one time dimension is the only configuration that provides enough stability to enable the very long time span needed for intelligent life to arise. This is partly based on solid mathematical theory (e.g., Bertrand's theorem), but also may partly be due to a lack of multidimensional thinking. If those conjectures are valid, we are here to observe a 3D+1 universe because any universe other than 3D+1 would not given rise to intelligent beings who could ask "why is space 3D?" $\endgroup$ – David Hammen Feb 23 at 10:14
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    $\begingroup$ See also: physics.stackexchange.com/q/10651 $\endgroup$ – Jean-Marie Prival Feb 23 at 14:36
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    $\begingroup$ One should perhaps add that spacetime is 4-dimensional. $\endgroup$ – Jonas Feb 23 at 17:25
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    $\begingroup$ While there are strong arguments making the 3D space special, somehow I think, if it would be 4D, we would have similarly strong arguments for a 4D space. The laws of the physics could work in a different count of space dimensions as well (multiple time dimensions are more problematic but also that could work). $\endgroup$ – peterh Feb 23 at 19:45
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Using the anthropic principle, we can effectively "determine" that a 3D world is most suitable for life and other objects in the universe.

0-dimensional universe

The universe is just a point, and nothing really exists. It's just a singularity.

1-dimensional universe

The universe's objects are line segments. The space between them are also empty line segments. They can move, but only between the empty segments. They will join together if they touch. They cannot go over or pass each other, only collide. Life cannot exist here. There are no celestial objects either.

2-dimensional universe

Case 1: Celestial bodies are large circles or ellipsoids. Stuff on those bodies are on the circumference of these objects. To pass each other, they must go over each other.

Case 2: There is only one ground. Pretty much Flatland. Objects are 2D and see in 1D if they are alive. But if an organism eats something, the waste must come out the same way it went in, otherwise the organism would be split in two.

Gravity is twice as powerful here.

3-dimensional universe

That's us! We know everything (mostly) about our universe and how life goes.

4-dimensional universe

Gravity is half as powerful here. Objects orbiting other objects will have twice the orbital radius. Most 3D systems will fall apart if transformed into a 4D universe. Living objects will see in 3D, meaning that if there is a ball in a box, then the 4D being can see inside the box and all sides of the box. Nevertheless, life probably can't exist here because gravity is not as strong, meaning that many gravitational systems will be unbound.

I hope this helps. If there is anything wrong with my post, please notify me via a comment.

Note: Most of this information was sourced from Stephen Hawking's A Brief History of Time.

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The question of why space is three dimensional has a long history, going back to Kant and Ehrenfest. For an excellent overview see Barrow & Tipler's The Anthropic Cosmological Principle (1986) which also discusses how this fits with the weak anthropic principle: the laws of nature (or properties like dimensionality) needs to allow observers to exist. A common line of argument is that universes with the wrong number of dimensions rule out intelligent life. They might exist "somewhere", but there is nobody to see them.

For example, if the force of gravity is proportional to $r^{1-D}$ (i.e. what you can derive from the divergence theorem) then generically stable and closed orbits are only possible for $D=3$. Indeed, the Schrödinger equation for a hydrogen atom is commonly said to be unstable in higher dimensions (the story is actually more complex, see Caruso, Martins & Oguri 2012). With less than three space dimensions general relativity does not predict any gravity because of the number of independent tensor components is too small. See also Max Tegmark's paper where he also considers different number of time dimensions.

How much should one believe arguments like this? Some physicists get annoyed by anthropic arguments since they seem to be very different from normal evidence (yet, "I observe an apparently 3D universe" is usually seen as fine, despite the fact that there is an easily overlooked "I" inside the statement) and are often used in sloppy ways. It is also possible if you are creative to make higher-dimensional model universes work by tweaking the laws of physics (e.g. see Greg Egan's work on 5D physics for his novel Diaspora).

Another way of answering the question would be for some law to rule out $D\neq 3$ spatial dimensions for some other, observer-independent reason. Unfortunately there is no such law known. Plus, in superstring theory there are "rolled up" spatial dimensions that are too small to matter for our macroscopic physics yet important for particle physics: the dimensionality of spacetime may not be scale-independent.

So in the end, the honest answer is that we do not know. It is a tough problem for physics and philosophy to work on.

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