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