Learning special relativity and working with Minkowski diagrams for a while now i am still trying to get my head around some oddity.
From my understanding time can often be seen as the dependent variable in those diagrams, so why put it to the vertical axis? What confuses me even more is the apparent convention to denote a point in space time $(t,x)$ even though $x$ is on the horizontal and $t$ is on the vertical axis, so the usual notation would be to refer to that vector as $(x, t)$.
Are there mostly historical reasons or why is it beneficial to use this notation and to violate usual conventions?
Answer
In special relativity, one deals instead with 4-vectors rather than the 3-vectors to which you're probably accustomed. In 4-vector notation, you have $x^n = [x^0, x^1, x^2, x^3]$, where the superscripts are not exponents, but rather indices of a rank 1 tensor (if you read about this, note that a rank 1 tensor with a raised index is a vector, whereas a similar tensor with a lowered index is a covector, or dual vector).
Expressed in normal Cartesian coordinates, the 4-vector is $\hat x= [ct, x, y, z]$.
In practice, the axes on a Minkowski diagram may be interchanged without any problems - the important property is the asymptote $ct = x$, which denotes the worldline of massless particles.
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