How Lorentz transformation improve the knowledge on space-time concept
Thanks to Lorentz transformation (name given by Henrì Poincarè) we have a theory that aim to give a scientific description of the change of viewpoint from one inertial frame to a second moving one. This specific change of viewpoint is called a (Lorentz) boost.
Why Lorentz transformations are so important for human knowledge?
His formulae for this boost are central to the theories of relativity, both special and general. So starting from the knowledge of a square root, you will have the possibility to study special relativity in all its features.
Lorentz transformations allow understanding that the concepts of length and time can depend from the observer. Indeed they are ‘relative’.
Scientists have explored alternative formulae for Lorentz boosts, especially where relative acceleration and relative velocity occurred. But the final point for this reasoning process and hypothetical method must match with the final experiment.
Lorentz transformation give us an important message: for a basic entity analysed, time and space can be seen as different (or mixed) elements.
This concept can be expressed stating that the concept of time is shown as the fourth dimension. The term fourth dimension is generally referred to a further extension of the objects with respect to the length, the width and the depth, which implies the need for a coordinated further addition to space, to uniquely identify the position of the points.
The fourth dimension admits, as any other dimension, an abstract description topology, where spaces with more than three dimensions naturally descend from the generalization of basic geometric concepts such as line, surface and volume.
In physics, and in particular in the theory of relativity, the fourth dimension is time-dependent, i.e the component that unified the four-dimensional space-time, where all events take place in our universe.
By the way all of us are using the statement of ‘space-time’ as the set of all events described using the four coordinate mentioned above.
If we think on the concept of space time as absolute, or observer-invariant its specific feature remains unchanged. But, if it is the case, we split it into its two concepts of space and time, then what we will have is a frame depending on personal viewpoint.
The space-time is also called the space-time of Hermann Minkowski. He was the teacher of Albert Einstein. Minkowsky was the first scientist who in 1904 was able to define the concept of space-time, thus capturing its universal utility. He later discovered that when gravitation occurred the space-time is curved. This point, known as ‘Reinmann space-time’ will be crucial to point ut the lows of general relativity.
We live in a space-time dimension, which is independent from the rest of the things that happen, or that we can observe in our daily lives. It is a container, a background for everything that happens.
And although systems of space-time coordinates can differ from the position and the observation made by the individual, we can say that there is one entity of space-time. Although, if dealt separately, both concept of space and time do not have this privilege. The foregoing also applies in the case of general relativity, consider the gravitation law.
The Minkowski space-time is still different from the developed centuries ago by Galileo. Both of their scientific theories assert that the set of points that concern the continuous space-time will behave in a similar manner. Both have a three-dimensional set, and a conformation perforated sphere, which is therefore free from a warp. The analysis predicts that space is therefore measured with a light beam, while the time is read from a clock. But in both cases the background, or the concept of space-time is maintained as an absolute, remaining the container of each and / or event. There is only one difference that Minkowski decides to operate compared to what was said by Galileo: he wants to do a mix of time-space concepts. And it is this idea of the mingling of space and time to make both mutually dependent on the observer’s point of view, and his position.
Mathematically, the time is a fourth dimension; It expands from space to the concept of space-time. And if it is called as ‘time’, the fourth dimension is just a statement of how the relativity calculates and has no deeper meaning.
The maximum speed present in nature, it then forced to describe the motion with this concept of space-time.
This is interesting, because in space-time, reducing everything to a minimum, movement cannot exist. The concept of movement have to exist only within a space, because in the dimension of space-time nothing moves.
In other words, instead of wondering why there is movement, we can ask what is the reason why space-time is crossed by some ‘world-lines’.
But at this point in history and the scientific progress we are still far from giving an answer to this important question. We can continue to do though, and follow the research and studies in the field of physics of what is the nature of this movement.
And how it happens.