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
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
Related questions
Question
please send handwritten solution for Q8
![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!](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe936eeeb-6b1b-47fb-af71-66789a476964%2Ff68d31b6-c5a1-4bdf-9ba1-71cc76a1d286%2F0ky1sxq_processed.png&w=3840&q=75)
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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