anglais relativité diapo .pdf



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Special relativity
Special relativity was
originally proposed in
1905 by Albert Einstein
in the paper "On the
Electrodynamics of
Moving Bodies".

Two postulates




The laws of physics are invariant (i.e. identical) in
all inertial systems (non-accelerating frames of
reference).
The speed of light in a vacuum is the same for all
observers, regardless of the motion of the light
source.

Galilean transformation

x' = x-vt
y' = y
z' = z

vx'=v-v.t
vy'=v
vz'=vz
t'=t

Galilean composition of speed
Speed of the man in the train is
10 km/h
Speed of the train is 50 km/h
Speed of the man is 60 km/h
in the reférentiel frame of the
station
We sum the speed !!!!

Limit of the classic composition






A man run in a train with a speed of 60% of the
speed of light
The speed of the train is also 60% of the speed
of light
With the transformation of Galilee, the speed of
the man in the reference frame of the station is
120% of the speed of light !
It is not possible !!!

Lorentz transformation

The Lorentz transformation leads to
surprising relativistic effects :
A new composition of speeds
Contraction of lengths
The dilation of time

Relativistic speed composition

u' = Speed of the man in the train
v = Speed of the train
u = Speed of the man in the station

We found 1.2c with the
transformation of Galilee

Contraction of lenghts

Contraction of a pencil

Dilatation of time

In relativity time is not
absolute

Different values of Gamma and Beta

The gamma values as a function of
the velocity

Muon 




« The muon is a lepton which decays to form an
electron or positron »
« The lifetime of the muon is 2.20
microseconds. The muon is produced in the
upper atmosphere by the decay of pions
produced by cosmic rays »

The classic approach

Thanks you

http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html#c3
Wikipedia
Perez, Relativité et
invariance, dunod


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