- #1
the_emi_guy
- 766
- 79
If space only had one dimension would Einstein's speed of light postulate still lead to Lorentz transformation for motion along that one dimension?
Relativity of simultaneity can obviously be demonstrated in one dimension (lightning bolts hitting opposite ends of stationary and moving train). But all derivations of the Lorentz transformation seem to require at least a second space dimension (i.e. the familiar light clock and Einsteins original 1905 paper) in order to obtain the Lorentz factor. Also, description of light cone:
c2dt2=dx2+dy2+dz2 reduces to
cdt=dx so space-time intervals would no longer have the square roots of squares involved.
Relativity of simultaneity can obviously be demonstrated in one dimension (lightning bolts hitting opposite ends of stationary and moving train). But all derivations of the Lorentz transformation seem to require at least a second space dimension (i.e. the familiar light clock and Einsteins original 1905 paper) in order to obtain the Lorentz factor. Also, description of light cone:
c2dt2=dx2+dy2+dz2 reduces to
cdt=dx so space-time intervals would no longer have the square roots of squares involved.