Let's start with the conclusion that the four-dimensional space-time (X, Y, Z, T), composed of three-dimensional space and one-dimensional time, can only describe our world approximately and is not complete.

The reasoning is the same as that of Newtonian mechanics, which describes the world as an approximation.

The reason is: our universe cannot be fully described by a set of coordinate systems (X1, X2, X3 ......Xn) in this form.

Let's start with the reason why we use four dimensional space-time (X, Y, Z, T).

Ignoring time for a moment, in practice we found that in order to determine what position an object is in we need to use at least three numbers to describe it.

For example, if we use gps to locate our position, we need the longitude, latitude, and altitude numbers to locate our position.

So, you can create a three-dimensional coordinate system (X, Y, Z) with yourself as the origin and choose three mutually perpendicular directions as axes, which is equivalent to having a map of the world to describe the location of any object in the world.

But the other person, Red, she can also take himself as the origin and create a coordinate system (X1, Y1, Z1), and that map of hers he can also use to describe the world. The equivalent of this world has two different maps.

The same object, A, can have two different coordinates to be described.

But it's okay, we are able to use our own maps to read the coordinates on the little red map.

For example, when Xiao Hong's position on our map is (a, b, c), and if Xiao Ming and we choose the same axis direction.

When an object Red says is located at (X1, Y1, Z1) then we immediately know that the object is located on our map is located at (X, Y, Z) where X=X1+a, Y=Y1+b, Z=Z1+c.

We can call: X=X1+a, Y=Y1+b, Z=Z1+c, the transformation T from Xiao Ming's map to our map

In this way, even if the world has a little green map, a little blue map, and so on, we can read them all by converting them to each other.

For example, we call and ask Hong to go out and say: Let's meet at (X, Y, Z)! Hong immediately knows that the location we said is (X1, Y1, Z1) on her map by converting coordinates between maps. This way she won't get lost.

Okay, now onto the troublesome stuff.

The premise of our previous so to establish three-dimensional coordinates is that the space of our world is flat. For any point on the coordinate system (X, Y, Z), its distance L to the origin has the formula as shown. (Expressing numeric symbols is a damned nuisance)

But the problem is that this universe of ours is not completely flat, but has a shape.

Suppose you and Red live in are two-dimensional organisms living on a two-dimensional sphere.

You can still create a two-dimensional (X, Y) coordinate system with yourself as the origin to represent all points in the world. Red can also create a coordinate system of his own (X1, Y1).

But the problem arises, in this world, you can no longer find a conversion T so that you can read the coordinates of Xiaohong, so that even if Xiaohong tells you which coordinates to meet, you do not know where she said, you two have no way to understand each other, you can no longer find a date with Xiaohong location.

The good thing is that there is a solution, which is that you create not a two-dimensional, but a three-dimensional coordinate system (X, Y, Z), and Red creates a three-dimensional coordinate system (X1, Y1, Z1). This way you and Red can understand each other's language again.

And this universe of ours, (although there is no evidence yet, most physicists believe) also has a shape and is not perfectly flat. This means that in order to describe it accurately, we need to establish at least a four-dimensional spatial coordinate system (X, Y, Z, W). (If the universe had a stranger shape, it would need to be described in more dimensions)

We don't feel this extra dimension because the universe is just too big, just like on the surface of the earth, we would feel that the earth is flat.

But there is something even more troublesome, and that is those things with mass inside this universe of ours. According to general relativity, objects with mass have a distortion of the space-time around them.

And the key thing is that this distortion is nonlinear.

Non-linear!

Non-linear, which means that it is impossible to describe this distortion with a coordinate system (X, Y, Z). (There are other mathematical forms to describe it, but it cannot be represented by coordinates alone)

The story is over, the end of the sprinkles.

This means that we use something like a coordinate system to describe this universe, which is naturally incomplete. No matter how many sets of numbers you use (X1, X2, X3 ......Xn), you can't fully describe a single point in the universe.

So, we use the space (X, Y, Z) to describe the space, which is just an approximation to facilitate the calculation.

Now let's discuss time.

You asked Xiaohong to meet you in front of the cinema. But after waiting for 3 three hours she did not appear, it turns out that you forgot to say the meeting time, at this time she is still at home make-up it.

Because there is motion of objects in our universe, time is also added to spatial coordinates in order to describe an object more clearly. A four-dimensional space-time coordinate system (X, Y, Z, T) is formed.

Little Red came by train from another city, you know, which city she arrived at about one o'clock, which city she arrived at about two o'clock, and which city she arrived at your city at three o'clock. The time T is different, and so are the spatial coordinates (X, Y, Z) of Xiao Hong.

And Red, who sits on the train with speed V, also has a map of her own space-time coordinates (X1, Y1, Z1, T1).

Of course, it is possible for you to read what she says by converting T.

Just this conversion appears to be a bit complicated, this is called the Lorentz transformation, belonging to the content of special relativity now.

Why does the conversion between different coordinate systems become so complicated after adding time T?

This is because time T, and the three coordinates of space (X, Y, Z) are somewhat different.

It was said earlier that a point A (X, Y, Z) its distance to the origin is

And for points located in four-dimensional space-time coordinates (X, Y, Z, T)?

According to special relativity, its "distance" to the origin can be considered as the following relationship

Yes, it is such a strange formula.

The transformation between four-dimensional space-time coordinates (X, Y, Z, T) is so complicated because four-dimensional space-time is a special shape, a shape that belongs to non-Euclidean geometry.

When the three-dimensional space (X, Y, Z) and the one-dimensional time T are put into a coordinate system, it enters the realm of non-Euclidean geometry.

In Euclidean geometry, the three sides of a right triangle are related as follows

But in non-Euclidean geometry, two parallel lines can intersect, the sum of the interior angles of a triangle can be greater than 180 degrees, and pi can be equal to any number.

And the three sides of a right triangle can also have the following relationship.

This is why special relativity is so difficult to understand, because it describes the shape of space-time itself, which is not what we can see in reality and what the brain can imagine.

In summary, we can conclude that the four-dimensional space-time coordinates (X, Y, Z, T) can be used to describe our world in an approximate way, which is not completely accurate.

But as we cannot say that Newtonian mechanics is wrong, but only that it is incomplete.

The relativistic description of four-dimensional space-time (X, Y, Z, T) is much more precise.

But relativity is not perfect.

There is not really a complete theory that can really describe the world.