Geometry in theoretical physics: alternatives having been tried ?

[lalbatros]

String theory opened the barrier of 4 dimensions up to 11.
This is a step outside common sense that apparently opened new horizons.

I would be interrested to know if larger steps have already been tried and if papers are available on these attempts.

For example, I have the feeling that challenging the triangular inequality would be the most audacious.
Did some physicist try to imagine the consequences of such hypothesis?

By the way, I would find it much more interresting to break such an axiom, than adding up new dimensions ...

 

[Crosson]

In mathematics, a metric space is a space in which the triangle equality holds (which is the only thing needed in order to sensibly define distance). Many people believe that on some "quantum foam" level, spacetime is not a metric space.

 

[sir-pinski]

Geometry has played a crucial role in theoretical physics for centuries, from the geometric laws of motion proposed by Isaac Newton to the curved spacetime of Einstein's general relativity. In recent decades, the concept of geometry has been pushed even further with the development of string theory.

String theory proposes that the fundamental building blocks of the universe are not particles, but rather tiny, vibrating strings. These strings exist in a space with more than the traditional three dimensions of length, width, and height. In fact, string theory proposes that there could be up to 11 dimensions, opening up new possibilities for understanding the nature of our universe.

However, string theory is not the only alternative that has been explored in theoretical physics. Other theories, such as loop quantum gravity and brane-world scenarios, have also attempted to reconcile the laws of quantum mechanics with those of general relativity by incorporating higher dimensions.

As for breaking the triangular inequality, this idea has been explored in the field of noncommutative geometry. This theory proposes that the traditional rules of geometry, such as the Pythagorean theorem and the triangular inequality, may not hold true at the smallest scales of the universe. However, this approach has not gained as much traction as string theory and other alternatives.

While it is important for physicists to continue exploring new ideas and alternative theories, it is also crucial to remember that these theories must be supported by evidence and experimentation. String theory, for example, has yet to be proven by experimental data, and it is still a subject of much debate and discussion in the scientific community.

In conclusion, geometry in theoretical physics is constantly evolving and being challenged by new ideas and alternatives. While string theory has opened up new possibilities with its incorporation of higher dimensions, it is important to continue exploring and questioning other fundamental assumptions and axioms in order to deepen our understanding of the universe.