Language
Country/Area
No result found
The Secret of the Fifth Dimension: Do You Know How It Changes Our Understanding of the Universe?
Humanity's understanding of space is mostly based on three-dimensional space, but in the fields of physics and mathematics, the concept of five-dimensional space is gradually receiving attention. The exploration of five-dimensional space not only allows us to rethink the foundations of physics, but also challenges our traditional understanding of the universe.
Theoretical background of five-dimensional space
In mathematics, a five-dimensional space is a space with five dimensions. In physics, this is an attempt to unify the four basic interactions of nature - the strong and weak nuclear forces, gravity and electromagnetic forces. German mathematician Theodor Kaluza and Swedish physicist Oskar Klein proposed the famous Kaluza-Klein theory in 1921, which used the fifth dimension to combine gravity and electromagnetism The functions are unified.
Klein speculated that the fifth dimension should be curled into a very small ring, with a size of about 10^-33 centimeters.
Although their theory later turned out to be inaccurate in at least some aspects, the concept laid the foundation for further research over the past century. Their thinking is likened to: light is like a disturbance caused by fluctuations in high dimensions, which cannot be directly observed by humans, but indirectly shows the subtle connection between different forces.
From Kaluza-Klein theory to string theory
The Kaluza-Klein theory received renewed attention in the 1970s due to the rise of string theory and supergravity. String theory proposes that reality consists of vibrating strings of energy, a hypothesis that is only mathematically feasible in environments of ten dimensions or more. As string theory developed further, it evolved into a more general theory called M-theory, which predicted a potentially observable extra dimension in addition to the ten basic dimensions.
This extra dimension predicted by M theory may reveal the mystery of the weakness of gravity relative to other fundamental forces.
This fits with phenomena we experience every day, such as using a magnet to easily lift a pin off a table, suggesting that magnetism is in some ways capable of overcoming the entire Earth's gravitational pull.
The intersection of mathematics and physics
In the early 20th century, mathematicians began to regard the fifth dimension as a theoretical construct and constructed mathematical frameworks such as Hilbert space to allow an infinite number of quantum states. Einstein and his colleagues tried to expand the four-dimensional space-time in general relativity to include electromagnetism as an additional physical dimension and strive to unify all interactions.
In their 1938 paper, they first proposed the four-dimensional theory as a natural extension of the five-dimensional theory. The new theory is consistent with the Einstein-Maxwell theory at long distances.
In the process, physicist Gerard 't Hooft proposed the holographic principle in 1993. He points out that information about the extra dimensions can be visualized as a kind of curvature that occurs in fewer dimensions.
Five-dimensional geometry
According to Klein's definition, "Geometry is the study of the invariant properties of a space-time under internal transformation." Therefore, five-dimensional geometry studies the various invariant properties of such space-time in space, usually Use five coordinate values (x, y, z, w, v) to express.
In a five-dimensional or higher-dimensional space, there are only three regular polyhedrons, including five simple shapes, five cubes, and five squares.
These polyhedra are of mathematical and physical importance, and their number and properties are increasingly attracting attention as our understanding of multidimensional space deepens.
Summary and reflection
The exploration of five-dimensional space not only promotes the theoretical development of mathematics and physics, but also opens up new ideas for our understanding of the nature of the universe. Although direct observation of five-dimensional space is currently not possible, and evidence still relies on indirect detection, all this undoubtedly pushes the boundaries of science. Have you ever thought about the impact these seemingly abstract theories will have on our future?
