Causality (physics)

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Causality describes the relationship between causes and effects, and is fundamental to all natural science, especially physics. It is also studied from the perspectives of philosophy, computer science, and statistics.

In classical physics, it was assumed that all events are caused by earlier ones according to the known laws of nature, culminating in Pierre-Simon Laplace's claim that if the current state of the world were known with precision, it could be computed for any time in the future or the past. This is known as determinism.

According to classical physics, the cause simply had to precede its effect. In modern physics, the notion of causality had to be clarified.

The insights of the theory of special relativity confirmed the assumption of causality, but they made the meaning of the word "precede" observer-dependent. Consequently, the relativistic principle of causality says that the cause must precede its effect according to all inertial observers. This is equivalent to the statement that the cause and its effect are separated by a timelike interval, and the effect belongs to the future light cone of its cause. Equivalently, special relativity has shown that it is not only impossible to influence the past; it is also impossible to influence distant objects by signals that travel faster than the speed of light.

In the theory of general relativity, the concept of causality is generalized in the most straightforward way: the effect must belong to the future light cone of its cause, even if the spacetime is curved. New subtleties must be taken into account when we investigate causality in quantum mechanics and relativistic quantum field theory in particular. In quantum field theory, causality is closely related to the principle of locality. A careful analysis of the phenomena is needed, and the outcome slightly depends on the chosen interpretation of quantum mechanics: this is especially the case of the experiments involving quantum entanglement that require Bell's Theorem for their implications to be fully understood.

Despite these subtleties, causality remains an important and valid concept in physical theories. For example, the notion that events can be ordered into causes and effects is necessary to prevent causality paradoxes such as the grandfather paradox, which asks what happens if a time-traveller kills his own grandfather before he ever meets the time-traveller's grandmother. See also Chronology protection conjecture.

Causal contact

In physics, two entities are said to be in causal contact if there may be an event that has affected both in a causal way. Every object of mass in space, for instance, exerts a field force on all other objects of mass, according to Newton's law of universal gravitation. Because this force exerted by one object affects the motion of the other, it can be said that these two objects are in causal contact.

The only objects that are not in causal contact (according to accepted physics) are those for which there is no event in the history of the universe that could have sent a beam of light to both. For example, if the universe were not expanding and had existed for 13 billion years, anything more than 26 billion light-years away from the earth would not be in causal contact with it. Anything less than 26 billion light-years away would because an event occurring 13 billion years in the past that was 13 billion light-years away from both the earth and the object under question could have affected both (the gravity in question).

Image:World line.png

A worldline through a light cone in 2D space plus a time dimension.

A good illustration of this principle is the Light cone:

The light cone is constructed as follows. Taking as event <math>p</math> a flash of light (light pulse) at time <math>t_0</math>, all events that can be reached by this pulse from <math>p</math> form the future light cone of <math>p</math>, whilst those events that can send a light pulse to <math>p</math> form the past light cone of <math>p</math>.

Given an event <math>E</math>, the light cone classifies all events in spacetime into 5 distinct categories:

Events on the future light cone of <math>E</math>.

Events on the past light cone of <math>E</math>.

Events inside the future light cone of <math>E</math> are those which are affected by the beam of light emitted at <math>E</math>.

Events inside the past light cone of <math>E</math> are those which can emit a beam of light and affect what is happening at <math>E</math>.

All other events are in the (absolute) elsewhere of <math>E</math> and are those that will never affect and can never be affected by <math>E</math>.