4 ms·
Yeah normal time units still exist in relativity, clocks gotta clock. But ratber it's that there exists an operation which is almost entirely like rotation, bu
by crdrost 2y ago
Yeah normal time units still exist in relativity, clocks gotta clock.
But ratber it's that there exists an operation which is almost entirely like rotation, but it rotates x, y, or z into w=ct, where w is measured in meters just like x,y,z are, but t is measured in time units, and c is the speed of light converting between them. Instead of a rotation's formula with sines and cosines like
x' = x cos θ + y sin θ
y' = y cos θ – x sin θ
(x')² + (y')² = x² + y²
relativity has a slightly different set of functions sinh and cosh that are very closely related to sin and cos. (Sine and cosine have Taylor series where the polynomials alternate, sin(x) = x – x³/6 + x^5/120 – ..., and sinh and cosh have the exact same Taylor series with all + signs rather than alternating + – + –.) The analogous expressions are then,
w' = w cosh φ — x sinh φ
x' = x cosh φ — w sinh φ
(w')² – (x')² = w² – x².
This transformation, in relativity, is just built into how any acceleration works. So whenever you accelerate, even in pre-relativistic physics, you expect to see the emergence of some Doppler shifts. In relativity these shifts are not quite as strong as expected from the classical theory, and as a result when you subtract off the Doppler shifts and try to say "what has happened" you get an answer that "the meaning of the present moment, which historically defined a 3D universe frozen at a point in time, identifies a different 3D slice of the 4D spacetime." And this is what "rotates", it's the rotation of the plane that you think is the "present moment".
The fact that you are discretely "you" about ten times per second, I am taking as a fact of biology. But if you try to convert that biology into physics, that's where you convert t into w to get that t=0.1s converts to w = 30,000 km.