IX. Initial remarks on space-time
The concept of space-time has already been adopted in classical mechanics as a Cartesian product of the Euclidean space and time. Time constituted here an additional dimension, but measured in other units and independent of space.
It was Hermann Minkowski who realised the fact that time and space can constitute one object in which time and space somehow can be mixed and exchanged. He discovered that via a four-dimensional space, the specific theory of relativity can be presented in a simple way.
One of the problems that needed to be resolved was to determine how distances should be measured in space-time. In space distances can be measured in meters and time in seconds. In order to combine them it is necessary to convert the distances into time or time into distances. A good solution appears to be the multiplication of time t by speed of light c, and instead of time we will abtain the distance. When to the three-dimensional space we add another time dimension multiplied by the speed of light we will receive a four-dimensional space in which all dimensions are in the same units. However, another problem occurred. Time slightly differs from space. When in space we can freely move backwards and forwards, going back in time leads to various contradictions. Minkowski solved the issue in the following manner, apart from the speed of light he multiplied the time dimension by the imaginary unit i. Then, the formula of distance in space-time received the following shape;
\(d = \sqrt {x^2+y^2+z^2+i^2*c^2*t^2}\),
due to the fact that \(i^2 = -1\)
it gives
\(d = \sqrt {x^2+y^2+z^2-c^2*t^2}\),
It is so-called the space-time interval that is employed to determine the distance in space-time. Thus, the mathematical model in space-time is not contraditory when it comes to causation and it enables a formal record of the specific theory of relativity of Einstein.
When it was formalised and formulated in equations, the obtained fromulas could be modified further. The imagnary unit is not applied any more, only the dimension of time takes a different sign than in the dimension of space. How it can be justified? Why that way not the other? Simply the identical sign leads to the contradition and the reverse sign allows to avoid it and no other possibilities were employed. Mathematical models can be freely created, however, their results should be interpreted more carefully.
The fact that the space-time interval is something that it should not be adopted as it is, I realised when I understood that what we observe is not a three-dimensional space, but it is only an excerpt of space-time. Every observed object is at a distance from us not only in space but also in time. When we observe an eruption in the Sun what is the distance between the eruption and our observation? In space there are about 150 million kilometers, in time about 8 minutes. What is the distance then between the two events in space-time? The Space-time Interval is determined as follows; from the distance in space, the time multiplied by the speed of light is subtracted. In our case it equals zero.
When we think about it we will understand that the space-time interval in a present form is not the distance between two events in space-time, it will be only the distance of the light signal between one event and the other.
Everything we now see is the space-time interval which equals zero. We see it more clearly when for the distance in space the spherical coordinates are used. The distance in space is established by specifying how much time the light needs to reach us from an object, that is, the speed of light is multiplied by time. Subsequently, for the distance in space-time we receive the speed of light multiplied by time less the speed of light multiplied by time, that is, zero. How then we can determine the distance in space-time? If we want to find an answer to that question, first of all, we have to refer to the initial remarks on time and space-time and then try to find a solution once again.