Engineers, mathematicians, and physicists get together and give them the task of answering the question: How dimensional is the world?
Engineers are best at dealing with the world of our daily lives, showing protractors and rulers and spelling out three directions at right angles, that is, length, width and height. "The world is three-dimensional." Three-dimensional is also our most intuitive understanding.
The mathematicians took out notebooks, and they went into the realm of abstraction, creating a list of geometric patterns with regular symmetry with vertical edges. They write that the square has 4 sides and the cube has 6 square faces. Extrapolated, a hypercube has faces made up of 8 cubes. And so on, and this law will continue forever. "Infinite." This is the answer from mathematics.
Now, it's physicist's turn. In order to explain the origin of the universe, many physical theories require the existence of space in higher dimensions, and many popular theories still hold outside the three dimensions. Some physicists (and, of course, mathematicians) insist that more physical dimensions must exist outside of the world we can see, a world that is not just the up, down, left, and backward that we are used to.
Similar to time, the "birth of science" in space is also due to one of the greatest scientists in history, Newton. In 1687, Newton formally proposed the concept of "space" when introducing his theory of gravity. For Newton, space and time were real, but it was just that space was a cold backdrop in which more interesting things were happening, such as apples falling from trees and planets orbiting in orbit.
At the end of the 19th century, the British mathematician Charles Howard Hinton proposed that the different objects we perceive moving against each other can be considered as solid objects in four-dimensional space, passing through our three-dimensional world. To understand what this means, imagine what a ball looks like when it passes through a two-dimensional plane, and it looks like a circle with changing radius, and the size of the circle increases and then decreases over time.
A ball passes through a two-dimensional plane. | Reference: NewScientist
Einstein and the relativistic system prompted a critical shift in our understanding of the world. At the beginning of the 20th century, Einstein proposed special relativity. Subsequently, in 1908, the mathematician Hermann Minkowski distilled the basic concepts of special relativity into an extraordinary four-dimensional geometry, Minkovsky's four-dimensional space-time.
A breakdown of Minkowski's space-time. | Image credit: MissMJ/Wikicommons
Minkowski's geometric view of space-time is of great significance. His four-dimensional space-time consists of standard three-dimensional space and a fourth dimension that describes the flow of time. The greatest revolutionary aspect of Minkowski's thought was that it integrated time and space into an inseparable whole, and thus had a more profound impact. It was precisely because Einstein recognized this extraordinary view of space-time by Minkowski and popularized this idea that it constituted Einstein's concept of the curvature of space-time in his general theory of relativity.
In general relativity, space becomes a dynamic entity. It is intertwined with time into a four-dimensional space-time, bent by mass, producing fundamental forces that we call "gravity."
The increase in dimensions is far from over. In 1919, the mathematician Theodor Kaluza proposed the existence of a fourth dimension of space that might link general relativity to electromagnetic theory. Subsequently, the mathematician Oskar Klein refined on the basis of Karuza's thought. Klein argues that space includes both extended and curled dimensions. Those extended dimensions are the three-dimensional space we are familiar with, and in the depths of the extended dimension, the curled dimension appears, which can be regarded as a very small circle.
Curly Dimensions. | Image source: New Principles Institute
Although subsequent studies have shown that The curly dimensions of Karuza and Klein did not combine general relativity and electromagnetic theory as desired, decades later it inspired later scientists. String theorists found the idea useful, even arguably necessary.
Although string theory is controversial, it is still the path that many physicists have chosen to lead to the unification of gravity and the quantum world, and it is also one of the most promising theories that currently seem to combine general relativity and quantum mechanics into a "theory of everything.".
The mathematics used in superstring theory requires at least ten dimensions. That is, to use equations that describe superstring theory, be sure to take advantage of additional dimensions. String theorists believe that these dimensions are wrapped up in the curly space that Karusa and Klein first described.
To accommodate more dimensions, we also need to expand the extra dimensions of that curl. For ease of understanding, we can do some simplified versions of the imagination.
In The theory of Karuzza and Klein, the dimensions of space consist of three dimensions of standard space, as well as the extra dimensions of a circle. Now, we can first imagine replacing the Karuza Klein circle with the ball. If we only consider the surface of the ball, then there are two extra dimensions, and if we count the interior space of the ball, there are three extra dimensions. So far, these three additional dimensions, plus the original three-dimensional standard dimension (the three-dimensional space we are familiar with), have a total of 6 dimensions.
But this does not seem to be enough for superstring theory. Where do the other dimensions needed come from?
To the excitement of physicists, double mathematicians had paved the way for them before superstring theory. Eugenio Calabi and the Chinese mathematician Chengtong Yau described a six-dimensional geometry. Superstring theorists have found that the Calabi-Chu manifold fits the type of structure required by their equations.
Two-dimensional cross-section of a six-dimensional Calabi-Yau manifold. | Image credit: LUNCH/Wikicommons
If we further replace the previous balls with these Calabi-Chu manifolds, we end up with 10 dimensions – 3 spatial dimensions, plus 6 dimensions in the Calabi-Chu manifold, plus a time dimension.
If superstring theory proves correct (which is difficult, of course), we have to accept a world of ten dimensions, although we may not be directly aware of all its dimensions.
It's easy to add extra dimensions to the world, at least in theory, you just need to add extra items to the coordinate system. The question is, how do we perceive them? How do we find evidence of their existence?
At least the current answer is still somewhat disappointing. As "three-dimensional creatures," we may never be able to see the higher dimensions directly, but that doesn't mean we can't scientifically prove their existence. It's as if we can't directly observe quarks, but that doesn't stop scientists from still agreeing on the existence of quarks.
From the perspective of scientific experiments, whether it is the Large Hadron Collider or gravitational wave detection, there is no evidence of the existence of additional dimensions. But we also have no reason to rush to dismiss the idea of extra dimensions.
If the extra dimension is shown to exist, it may also lead to some strange results, for example, it may mean a multiverse world, with different universes next to each other. However, not everyone likes this result. Physicist Erik Verlinde said in an interview: "I don't like the multiverse. The universe with which we can't communicate is less interesting to me. I think we'd be happy if we could explain the universe we live in. ”
References:
https://www.pbs.org/wgbh/nova/article/how-many-dimensions-does-the-universe-really-have/
https://www.newscientist.com/article/mg23331150-500-cosmic-uncertainty-are-there-really-just-three-dimensions/
https://www.pbs.org/wgbh/nova/article/imagining-other-dimensions/
Roger Penrose, "The Reincarnation of the Universe," Hunan Science and Technology Press, January 2018
Cover image by national institute of technology Tiruchirappalli
Source: Principles
EDIT: He and the cat