In Minkowski spacetime, the speed of light is considered a fundamental constant and is denoted by the symbol "c." The concept of Minkowski spacetime arises from the theory of special relativity, which combines space and time into a unified four-dimensional framework.
In this framework, the interval between two events in spacetime is defined as:
Δs² = c²Δt² - Δx² - Δy² - Δz²
where Δs is the spacetime interval, Δt is the time interval, and Δx, Δy, and Δz are the spatial intervals in the x, y, and z directions, respectively.
For a light signal, the interval Δs is always zero since light travels along a null geodesic (a path with zero interval). Therefore, we can set Δs = 0 in the equation above:
0 = c²Δt² - Δx² - Δy² - Δz²
Assuming the light signal travels in a single direction along the x-axis (Δy = Δz = 0), we have:
0 = c²Δt² - Δx²
Rearranging the equation, we get:
Δx² = c²Δt²
Now, we can divide both sides by (Δt)²:
(Δx/Δt)² = c²
Taking the square root of both sides, we find:
Δx/Δt = c
This equation represents the speed of light in Minkowski spacetime. It states that the ratio of the spatial interval (Δx) to the time interval (Δt) for a light signal is always equal to the speed of light (c).