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14
Physics Formulary by ir. J.C.A. Wevers
W
2
=
m
2
0
c
4
+
p
2
c
2
.
p
=
m
r
v
=
γ
m
0
v
=
Wv/c
2
, and
pc
=
W
β
where
β
=
v/c
. The
force
is
deFned
by
±
F
=
d
±
p/dt
.
4vectors have the property that their modulus is independent of the observer: their components
can
change
after a coordinate transformation but not their modulus. The difference of two 4vectors transforms also as
a 4vector. The 4vector for the velocity is given by
U
α
=
dx
α
d
τ
. The relation with the “common” velocity
u
i
:=
dx
i
/dt
is:
U
α
=(
γ
u
i
,ic
γ
)
. For particles with nonzero restmass holds:
U
α
U
α
=

c
2
, for particles
with zero restmass (so with
v
=
c
) holds:
U
α
U
α
=0
. The 4vector for energy and momentum is given by:
p
α
=
m
0
U
α
=(
γ
p
i
,iW/c
)
. So:
p
α
p
α
=

m
2
0
c
2
=
p
2

W
2
/c
2
.
3.1.2
Red and blue shift
There are three causes of red and blue shifts:
1. Motion: with
±
e
v
·
±
e
r
=cos(
ϕ
)
follows:
f
±
f
=
γ
±
1

v
cos(
ϕ
)
c
²
.
This can give both red and blueshift, also
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This note was uploaded on 11/16/2010 for the course ENGR 201 taught by Professor Elder during the Spring '10 term at Blinn College.
 Spring '10
 elder

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