Velocity transformations
)(
)(
x
zz
yy
xx
ddxcdtdxvx //
dxdctdxdvx //
cV /
2/1)(
)(
cvV
Vv
xdd
dxdcv
x
xx
)/1()( 2cvV
v
xdd
zdcv
x
zz
)/1()( 2cvV
v
xdd
ydcv
x
y
y
!!!cvcv xx
!!!0 VvvV
Four vectors, …
1 0 0 0
0 1 0 0
0 0 γ -γβ
0 0 -γβ γ xy
z
xy
z
=
XX ´
XXgs 2
-1 0 0 0
0 -1 0 0
0 0 -1 0
0 0 0 1 = g
E=mc2
It followed from the special theory of relativity that mass and
energy are both but different manifestations of the same thing -- a
somewhat unfamiliar conception for the average mind. Furthermore,
the equation E is equal to m c-squared, in which energy is put equal
to mass, multiplied by the square of the velocity of light, showed
that very small amounts of mass may be converted into a very large
amount of energy and vice versa. The mass and energy were in fact
equivalent, according to the formula mentioned before. This was
demonstrated by Cockcroft and Walton in 1932, experimentally.
momentum
p must be conserved in all
the references frames !!! B rest
frame
CM
frame
Relativistic
mechanics
Classical
mechanics
v of a body under
a constant force
22 /1 cv
vm
vmp
m - particle rest mass
Energy
Kinetic energy
Low β
2
2
22
2
2
1
)1...2
1(
)1(
vm
c
vcm
cmEk
c
Ek
Rest energy
Total energy 2cmE
2cmE
Rest mass is just a
form of energy!
Fission and fusion
Binding energy
Fission – the splitting of an heavy atom
Fusion – the fusing of light atoms into heavy atom
mass Kinetic Energy
Particle Physics
Collides high energy
particles and observes
what comes out !
An example: the LEP @CERN
Kinetic Energy mass
DELPHI- the first WW event