Space-time - History, philosophy and methodology of natural sciences


The special theory of relativity revealed a close relationship of spatial and temporal features. In an effort to understand it, the mathematician and physicist Herman Minkowski invented the concept of space-time, to which he himself attached a radical significance: "From this hour, space in itself and time itself turn into shadows, and only their kind of union maintains independence" . Minkowski was clearly too categorical. The connection of any two existing does not mean their disappearance. It was necessary to reassess the nature of space and time in a new way.

Historical excursion

Researchers, who paid considerable attention to the adequate representation of the conceptual apparatus of classical mechanics, often came up with the idea of ​​combining space and time. Indicative in this sense is the position of d'Alembert and Lagrange. D'Alembert in 1754 stated that the idea of ​​time as the fourth dimension is the most sacred in his knowledge. Lagrange in 1797 noted that "it is permissible to regard mechanics as a four-dimensional geometry, and mechanical analysis as an extension of geometric analysis".

In fact, Lagrange clearly intended to realize the idea of ​​geometrization of mechanics. Such radical ideas are visited by mathematicians much more often than physicists. Be that as it may, the creation of a special theory of relativity clearly activated the program of geometrization of physics. Now back directly to the physical side of the case.

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It consists in the actualization of the concept of invariance. First, the Lorentz transformations turn out to be a turn in the four-dimensional Minkowski continuum, which is just called space-time. Secondly, it turns out that, in spite of classical mechanics, the invariance is not the extent (Δ r ) and the duration (Δ t ), but the interval (Δs):


It is the invariance of the interval that made a deep impression on physicists. As the invariants of length and duration, they really went into the shadows, and in their place came the interval. But as changing quantities, the value of which depends on the choice of the inertial reference frame, the length and duration have fully retained their significance.

The length and duration did not disappear, they were and still are actual signs of physical objects. And they have retained their uniqueness. This is evidenced by the formula (3.9). First, the lengths enter into this formula with a different sign than the length. Secondly, they have different units of measurement. Thirdly, only lengths enter into the same expression with the speed parameter of light.

Of course, it is also true that a three-dimensional space plus one-dimensional time does not form a four-dimensional manifold in the physical sense. This is clear in so far as the units of measure for space and time are different. From the physical point of view, time can be considered the fourth dimension of space only if it is measured in the same units as the extent. But this is not.

We should not leave out criticism and the term space-time & quot ;. There is time and space that are connected with each other. But as a result of this connection, there is no third reality, namely, space-time. Introduction of the term space-time is associated with the obligation to call his name some object. Hence the temptation to believe that the unity of time and space forms something that does not reduce to them. But you should always keep in mind that the term "space-time" is not an object name.

It seems that space-time can be considered a purely mathematical concept, not associated with the name of a physical object. But the author is just talking about physical concepts. It turns out that the concept of space-time is unsatisfactory because of its linguistic form. There is a situation of inadequacy of the available at the disposal of physicists of linguistic means. To emphasize the connection of time to space, there seems to be no better term than "space-time". But its use is extremely rare without overlap. The essence of the situation was perfectly expressed by NV Mickiewicz: "If the integration of space and time was facilitated by the introduction of 4-dimensional coordinates, then the disconnection is comprehended by means of formalisms of the frame of reference, and this new stage is much more meaningful than one could think in the days of Minkowski. Already such a dialectic itself carries great satisfaction for the researcher who is present at his birth. "

The introduction of the space-time concept shows that physicists should keep a certain degree of vigilance in interpreting theories. In our case, physical, mathematical and linguistic concepts were closely intertwined. They should in no way be identified with each other.

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1. Space-time is a mathematical, not a physical, concept.

2. It is legitimate to use in physical and mathematical modeling to identify the links that exist between durations and lengths.

3. The concept of the interval refines our understanding of the properties of space and time.

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