The homogeneity of the ball inR
3 and special relativity |
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Authors: | Yaakov Friedman Ari Naimark |
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Institution: | (1) Department of Applied Mathematics, Jerusalem College of Technology, P.O.B. 16031, Jerusalem, Israel |
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Abstract: | Einstein's velocity addition formula ofspecial relativity (SR) defines a transformation
v of the ballB
c of radiusc inR
3, representing all possible velocities in an inertial systemK, onto identical ballB
c
, which represents the velocities in another systemK, moving with velocity v relative toK. Since
v maps the zero velocity ofB
c into arbitrary vector v ofB
c
,B
c is homogeneous under all possible
v.A similar homogeneity of the unit ballB inL(G, H) under a set of maps
a, a B, arises also in theLine Transmission Theory (TLT) for a lossless line. HereL(G, H) is the space of all linear operators between Hilbert spacesG,H, representing the signals on the line in the two directions. The explicit form of
a is obtained naturally in TLT. |
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Keywords: | special relativity homogeneous domains line transmission |
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