Why is space-time 3+1 dimensional?

[bchui]

"Why is our space-time 3+1 dimensional?"
The question had been raised by Kant and Hegel for more than 100 years

Could there be any possibility of "simple explanation" within the framework of Relativity or Quantum Theory:shy:

 

[robphy]

It seems to me that both Relativity and Quantum Theory are dimensionally-independent theories of nature. So, I think the answer to your question is no.

[Pardon the following sentence... after finally writing it down, it sounds a little playful.] Dimensionality seems to appear in the relationship among the choice of underlying spaces (the "arena"), the choice of fields (the "players"), and the choice of equations, boundary conditions, and additional requirements [like stability, nontriviality, etc] (their "rules") imposed upon them.

One of the most popular examples is the role of dimensionality in Huygens' Principle. Another is the stability of orbits. These appear in:

P. Ehrenfest, “In what way does it become manifest in the fundamental laws of physics that space has three dimensions?” Kon. Akad. Wetens. Amsterdam. Proc. Sec. Sci. 20 (1918), 200–209; reprinted in Collected Scientific Papers, ed. Martin J. Klein (Amsterdam: North-Holland, 1959), pp. 400–409.

See also my posts in
https://www.physicsforums.com/showthread.php?t=89853&highlight=ehrenfest
https://www.physicsforums.com/showthread.php?t=97776&highlight=ehrenfest

There have been some interesting studies, like
http://adsabs.harvard.edu/abs/1985GReGr..17..545N

 

[Entropia]

The reason why space-time is considered to be 3+1 dimensional is because of our observations and experiments in physics. In classical mechanics, space and time were considered to be separate entities, with three dimensions of space (length, width, and height) and one dimension of time. However, with the development of Einstein's theory of relativity, space and time were found to be interconnected and could not be treated separately. This led to the concept of space-time, where space and time are combined into a four-dimensional continuum.

In relativity, space-time is described as a four-dimensional manifold, with three dimensions of space and one dimension of time. This is also supported by observations and experiments, such as the fact that objects in motion experience time dilation and length contraction. These phenomena can only be explained in a four-dimensional space-time.

Similarly, in quantum theory, the concept of space-time is crucial in understanding the behavior of particles and their interactions. The equations of quantum mechanics also require a four-dimensional space-time in order to accurately describe the behavior of particles.

Moreover, the concept of space-time being 3+1 dimensional is also supported by the fact that we can only perceive and measure three dimensions of space and one dimension of time. Our human brains are limited in their ability to comprehend higher dimensions, making it difficult to imagine a space-time with more than three dimensions of space.

In conclusion, the reason why our space-time is considered to be 3+1 dimensional is due to the observations and experiments in physics, as well as the mathematical frameworks of relativity and quantum theory. While it may be difficult to fully comprehend, the 3+1 dimensional nature of space-time has been consistently supported by scientific evidence.