# Spacetime interval

Two contrasting viewpoints on time divide prominent philosophers.

One view is that time is part of the fundamental structure of the universe – a dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is sometimes referred to as Newtonian time.

The opposing view is that time does not refer to any kind of “container” that events and objects “move through”, nor to any entity that “flows”, but that it is instead part of a fundamental intellectual structure (together with space and number) within which humans sequence and compare events.

This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, and thus is not itself measurable nor can it be travelled.

— Wikipedia on Time

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Special relativity declares a similar law for all motion: the combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light.

— The Fabric of the Cosmos: Space, Time, and the Texture of Reality

— Brian Greene

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Space is relative, in the sense that the space interval, $\Delta d$, (aka distance) between two events can have different values for different observers.

\displaystyle{ \begin{aligned} \Delta {d} &= \sqrt{{\left(\Delta {x}\right)}^{2}+{\left(\Delta {y}\right)}^{2}+{\left(\Delta {z}\right)}^{2}} \\ \end{aligned} }

Time is relative, in the sense that the time interval, $\Delta t$, (aka duration) between two events can have different values for different observers.

Spacetime is absolute, in the sense that the spacetime interval, $(\Delta s)^2$, between two events cannot have different values for different observers.

\displaystyle{ \begin{aligned} (\Delta s)^{2} &= (\Delta ct)^{2}-(\Delta x)^{2}-(\Delta y)^{2}-(\Delta z)^{2} \\ &= (\Delta ct)^{2}-(\Delta d)^{2} \\ \end{aligned} }

— paraphrasing The Fabric of the Cosmos

— Me@2020-01-26 12:46:41 AM

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