Cause and effect loop

A causal loop, sometimes called a causal loop ( Eng. Causal loop ) ^[1] , is a sequence of events that are a mutual cause of each other ^[2] . As an example, we can consider a billiard ball rolling along a certain trajectory, moved to the past by a time machine in such a way that it striking on itself, and creates a rolling trajectory before moving in time ^[3] .

One example of a cause-and-effect loop is a self-fulfilling prophecy. They call a prediction that directly or indirectly affects reality so that this prediction inevitably turns out to be true. The term was coined by Robert Merton in The Self-Fulfilling Prophecy, published in Antioch Review in the summer of 1948. An example of such a prophecy is the hypothetical situation in a fictional bank. Initially, financial affairs there are going well. But once, for some unknown reason, a large group of depositors simultaneously comes to the bank. They, seeing that there are many of them, begin to worry. There is an unfounded rumor that the bank has financial troubles, it is insolvent and will soon be declared bankrupt . As a result, the number of people who want to pick up money increases sharply. There is a panic. The Bank does not have the physical ability to fulfill deposit obligations and, as a result, is truly declared insolvent and declared bankrupt ^[4] .

The principle of self-consistency Novikov argues that the existence of causal loops may not violate the principle of causality , that is, hypothetically possible. In a simplified form, he postulates that when moving into the past, the probability of an action that changes an event that has already happened to a traveler tends to zero. For the first time in the scientific literature this idea was announced in 1975 by Ya. B. Zeldovich and I. D. Novikov ^[5] . It is argued that the existence of closed timelike lines does not necessarily violate the causality principle. Events on such a line can influence each other in a closed cycle, that is, be "self-consistent." A similar consideration is found in a later book by Novikov ^[6] , but a strict formulation of the principle appeared only in 1990 ^[7] :

We formulate this point of view in the form of the principle of self-consistency, which postulates that of all possible models allowed by the known laws of physics, only those that are globally self-consistent can exist locally in our Universe. This principle allows researchers to construct solutions of physical equations only under the condition that the local solution can be extended to a part (not necessarily unique) of the global solution, which is defined for all parts of space-time with the exception of singularities.

Original Text (Eng.)

We shall embody this viewpoint in a principle of self-consistency, which states that the only solutions to the laws of physics that can occur locally in the real Universe are those which are globally self-consistent. This principle allows one to build a local solution to the equations of physics only if that local solution can be extended to a part of a (not necessarily unique) global solution, which is well defined throughout the nonsingular regions of the spacetime.

• Time loop
• Closed time-like curve