Abstract
Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in neither of these theories considered a law or a principle. Its existence in physics has even been challenged by prominent opponents in part due to the time symmetric nature of the physical laws. With the use of the reduced action and the least action principle of Maupertuis along with a discrete dynamical time physics yielding an arrow of time, causality is defined as the partial spatial derivative of the reduced action and as such is position- and momentum-dependent and requests the presence of space. With this definition the system evolves from one step to the next without the need of time, while (discrete) time can be reconstructed.
Highlights
Derived from Maupertuis ReducedAccepted: 10 September 2021Causality is the relationship between a cause and its effect [1]
In the present approach a definition of causality within mechanics and special relativity is provided which relies on the least action principle of the reduced action, called the Maupertuis principle
It is demonstrated that mechanical causality can be defined as the partial derivative of the reduced action along the space coordinate with the request on the smallest possible momentum change along the trajectory
Summary
Causality is the relationship between a cause and its effect [1]. Causality describes the process and consequences from an action. While omnipresent in classical physics [2] as well as special and general theories of relativity [3,4], it is not considered a law or a principle, nor described by a formula. Dominant cause challenge: Causal notions can, if at all, only be legitimately employed in contexts in which we can isolate a small set of factors of interest as those responsible for the occurrence of an event—the dominant cause or causes—by drawing a distinction between causes and background conditions Such a distinction, it is argued, cannot be drawn in physics. The Maupertuis reduced action [12,13,14,15] is introduced in Section 2.1 in detail, followed by a discrete time physics theory in Section 2.2 expanded to special relativity in Section 2.3 and discussed in paragraph three
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