Question

Why is the c^2*t^2 factor negative in the spacetime interval formula? Also where did c even come from?

Answer 1

The spacetime interval formula is a fundamental concept in special relativity, and it relates the spacetime separation between two events in a four-dimensional spacetime. The formula is given by:

$\Delta s^2=c^2\Delta t^2-\Delta x^2-\Delta y^2-\Delta z^2$

where:

• $\Delta s$ is the spacetime interval between two events.
• $\Delta t$ is the time interval between the two events as measured by an observer in a reference frame.
• $\Delta x$, $\Delta y$, and $\Delta z$ are the spatial intervals in the three spatial dimensions between the two events.
• $c$ is the speed of light in a vacuum.

Now, let's address the questions:

1. Why is the $c^2\Delta t^2$ factor negative in the spacetime interval formula?

The reason for the negative sign in front of $c^2\Delta t^2$ is a consequence of the signature of spacetime. In special relativity, spacetime is described by a four-dimensional Minkowski spacetime, which has a non-traditional metric signature. Instead of the usual positive-definite Euclidean metric (++++), Minkowski spacetime has a metric signature (-+++). This means that the time component in the spacetime interval has an opposite sign compared to the spatial components. This is why the c2Δt2c^2 Delta t^2c2<span class="mo