See pdf here.
Space with Time |
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Measure of motion | Time velocity: v_{t} = ds/dt ∼ ℓ^{−1} |
Space velocity: v_{s} ⇐ ℓ^{−1} = (dt/ds)^{−1} |
Mean velocity | Time mean velocity (Σ v_{i}/n) | Space mean velocity (Σ ℓ_{i}/n)^{−1} |
Normalized velocity | β = v/c ∼ (ℓ/k)^{−1} | β ⇐ (ℓ/k)^{−1} ∼ (v/c) |
Conversion & Lorentz factors | Time-length matrix |
ct = x; γ = 1/√(1 ‒ β²) |
See pdf |
Galilean transformations | See pdf | See pdf |
Normalized GTs | See pdf | See pdf |
Standard GTs | See pdf | See pdf |
Lorentz transformation | See pdf | |
Normalized LT | See pdf | |
Symmetric LT | See pdf |
Time with Space |
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Measure of motion |
Space lentcity ℓ_{s} = dt/ds ∼ v^{−1} |
Time lenticity ℓ_{t} ⇐ v^{−1} = (ds/dt)^{−1} |
Mean lenticity |
Space mean lenticity (Σ ℓ_{i}/n) |
Time mean lenticity (Σ v_{i}/n)^{−1} |
Normalized lenticity | 1/β = ℓ/k = 1/(v/c) | 1/β = 1/(v/c) ∼ ℓ/k |
Conversion & Lorentz factors | Length-time matrix | kx = t; −βγ = 1/√(1 ‒ 1/β²) | See pdf |
Galilean transformations | See pdf | See pdf |
Normalized GTs | See pdf | See pdf |
Standard GTs | See pdf | See pdf |
Lorentz transformation | See pdf | |
Standard LT | See pdf | |
Normalized LT | See pdf | |
Symmetric LT | See pdf |