For this reason it is called the Lorentz matrix for the velocity v. (hint: Substitute 2 – 32 = 1 and solve for a.) . Compute L, for v = 4/5, i.e., 80% of the speed of light. What is the range of possible values for v in the formula for L.? What physical f
For this reason it is called the Lorentz matrix for the velocity v. (hint: Substitute 2 – 32 = 1 and solve for a.) . Compute L, for v = 4/5, i.e., 80% of the speed of light. What is the range of possible values for v in the formula for L.? What physical f
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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please send handwritten solution for Q8

Transcribed Image Text:7. For the Lorentz matrix
P =
use a? – 32 = 1 and v = B/a to verify that a = 1/vi – v² and 3 = v//1– v². Conclude that
1
P = Ly =
1
V1- v2
For this reason it is called the Lorentz matrix for the velocity v. (hint: Substitute 3 = va in
a² – 32 = 1 and solve for a.)
%3D
8. Compute L, for v = 4/5, i.e., 80% of the speed of light.
9. What is the range of possible values for v in the formula for L„? What physical fact does this
correspond to?
-[: : -
а в
10. If L, = %
and Le, =
are Lorentz matrices, show that the product Lu, Lva is a
Lorentz matrix Lvz where
vi + v2
V3 =
1+ vị v2
(hint: Why does this product have determinant 1? Use
að + Be ae + Bồ
ae + B8 að + ße
Lv, Lvz
XE + B8
að + ße
to compute v3. Dividing the top and bottom of
by að will help.)
The presence of this denominator1+ v1v2 # 1 indicates that in Special Relativity, velocities are
not additive!
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