lorentz-package: The Lorentz Transform in Relativistic Physics

In lorentz: The Lorentz Transform in Relativistic Physics

Description

The Lorentz transform in special relativity; also the gyrogroup structure of three-velocities. Includes active and passive transforms and the ability to use units in which the speed of light is not one. For general relativity, see the 'schwarzschild' package.

Details

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Author(s)

Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Maintainer: Robin K. S. Hankin <[e-mail]>

References

• Ungar 2006. “Thomas precession: a kinematic effect...”. European Journal of Physics, 27:L17-L20.

• https://www.youtube.com/watch?v=9Y9CxiukURw&index=68&list=PL9_n3Tqzq9iWtgD8POJFdnVUCZ_zw6OiB

Examples

u <- as.3vel(c(0.3,0.6,-0.1))  # u is a three-velocity
gam(u)                         # relativistic gamma term for u
U <- as.4vel(u)                # U is a four-velocity
B1 <- boost(u)                 # B1 is the Lorentz transform matrix for u
B1 %*% c(1,0,0,0)              # Lorentz transform of zero 4-velocity (=-u)

B2 <- boost(as.3vel(c(-0.1,0.8,0.3)))  
B3 <- boost(as.3vel(c(-0.1,0.1,0.9)))  # more boosts

Bi <- B1 %*% B2  # Bi is the boost for successive Lorentz transforms


pureboost(Bi)      # Decompose Bi into a pure boost...
orthog(Bi)         # and an orthogonal matrix

Bj <- B2 %*% B1    # B1 and B2 do not commute...

(B1 %*% B2) %*% B3 
B1 %*% (B2 %*% B3)    # ...but composition *is* associative



## Three velocities and the gyrogroup

## Create some random three-velocities:

u <- r3vel(10)
v <- r3vel(10)
w <- r3vel(10)

u+v
v+u        # Three-velocity addition is not commutative...

u+(v+w)   # ... nor associative
(u+v)+w 

lorentz documentation built on Oct. 23, 2020, 5:50 p.m.