I went out for a walk last night and saw two primary school students arguing fiercely in the elevator. When one of the boys saw me, he anxiously asked me to be the referee and asked: "Uncle, do you think there are really points and straight lines in the universe?" "Is it a plane?" I told him: "No. Points, lines, and planes are primitive concepts in mathematics. There is no point, a straight line, or a plane object in the universe."
It can be seen that the two children are a little confused. : Since there are no points, lines and surfaces in reality, why are there lines and surfaces in mathematics?
Are there really no points, straight lines and planes in the universe? This really doesn’t exist!
Is there a point in the universe?
In geometry, "point" is used to simulate a precise position in space. It has no length, width, height, or size. The point is " zero-dimensional ". In other words, we can poke a dot of any size on the paper and call it a "dot", but in the brain it is just a mark that replaces the "infinitely small" location.
In the universe, what thing has no length, width, height, or size?
In the earliest times, scientists believed that atoms were the smallest elements making up matter. With the development of science and technology, we have discovered that the atom can be further divided. It contains a nucleus and extranuclear electrons. Most of the "atom" pictures you see in books are just schematics. If we enlarge an atom to the size of a stadium, the nucleus is only the size of a soybean in the center of the stadium. You can't find electrons. It may be in any corner of the stadium. , but smaller than dust!
The nucleus is larger than the electron, so it obviously cannot be called a "point". In fact, the electron cannot be called a "point" because the static mass of the electron is 9.11×10⁻³¹kg. Although no one knows the volume of the electron, the electron is also a "body" with length, width and height.
Schematic diagram of an atom
Some people will say that the volume of the "singularity" at the center of the black hole is 0 and the gravity is infinite. It is just a "point"! In fact, this is also a problem that scientists need to solve. According to the calculations of Einstein general relativity, there may indeed be such a singularity in the center of the black hole, but this singularity cannot be observed, so we cannot confirm or Falsify .
How big is the singularity of a black hole? Does anyone know that straight lines exist in the
universe?
In geometry, a straight line is the trajectory of point movement. It is composed of an infinite number of "points" and is used to represent a one-dimensional object without width and curvature. A straight line segment has a length, and the length of a straight line is infinite.
Usually we describe plumb line as a straight line. The plumb line is very thick, while the silk pulled by the spider is much thinner. Even if it is spider silk , it still has width. When we magnify it under the electron microscope , we can see that it is actually a long bundle of "cylinder"-like things.
Spider filament is a cylinder under the microscope
So, if you use laser to emit a beam of light into space, will it be a straight line?
According to Einstein's theory of relativity, an object with mass will bend the space-time around it, so when light passes through it, it will also bend because space is bent. The universe is filled with all kinds of massive objects, large and small, so theoretically light does not travel in a straight line.
Those who have studied high school physics will tell you that the various lights we see are actually electromagnetic waves . College friends say that they are energy beams carried by light energy quanta, so light is not a "straight-line object".
Laser is a beam of energy wave, it is not straight
Next, let’s talk about planes - is there a perfect plane in the universe? The answer is still no.
Even if we polish a mirror extremely smooth, its surface will still not be a "perfect" plane.This is because from a microscopic perspective, any mirror must be a surface composed of atoms densely arranged. The shape of the atoms and their relationship to each other determines the surface of the mirror like rolling hills.
The surface of the mirror is actually uneven.
Therefore, we say that there are actually no zero-dimensional "points", one-dimensional "lines" and two-dimensional "planes" in the universe. All objects in the universe are three-dimensional "volumes". ”, they all have length, width and height. The " two-way foil " in the science fiction novel " three-body " is just an imagination of the "high-dimensional world" and does not exist in reality.
But this does not mean that points, lines and surfaces are not important.
In geometry, point-line-plane is a set of axioms and is the basic element of geometry. They are not only abstract definitions of spatial elements in mathematics, but also the most practical tools for physicists to explore the world. It can be said that without points, lines, and surfaces, there would be no physics and most science today.
