The Light of Einstein

1
The Light of Einstein

• 1905
• David Atkinson

2
The nature of light

• Newton a light beam consists of particles in
  motion
• Huygens a light beam consists of waves in the
  luminiferous ether

3
Relative speed

• Speed of sound in air is c
• Speed of the observer relative to air is v
• Relative speed is c - v

4
Relative speed

• Speed of light measured by Bob
• is c 300 000 km / sec
• not c - v

5
Relative speed

• Michelson-Morley Experiment
• The measured
• return-speed
• of light is independent of
• the speed of the observer

6
Motion along ether wind
x' a (x vt) y' y z' z t' t a 1 / (1
v2 )
Newtons absolute time!
7
Motion across ether wind
x' a (x vt) y' ß y z' ß z t' t a 1 /
(1 v2 ) ß 1 / v (1 v2 )
Newtons absolute time!
8
Asymmetrical motion
x' ß2 (x vt) y' ß y z' ß z t' t ß 1
/ v (1 v2 )
Newtons absolute time!
9
Scaling of Time and Space
ß 1 / v (1 v2 ) x' ? ß2(x vt) y'
? ß y z' ? ß z
t' ? t
Space and time are scaled similarly, so speeds
are unchanged. Time is not absolute! Simultaneity
is still absolute.
?
10
Relativity of Time
ß 1 / v (1 v2 ) x' ? ß2(x vt) y'
? ß y z' ? ß z t' ?
t e (x vt)
An arbitrary multiple of x vt can be
added to t' without changing the return speed of
light . Simultaneity is now not absolute.
?
11
Transport Synchronization
ß 1 / v (1 v2 ) x' ? ß2(x vt) y'
? ß y z' ? ß z t' ?
t ?' (x vt)
Clocks in an inertial frame S are synchronized by
bringing them together, resetting, and then
separating them infinitesimally slowly. The same
procedure is followed in S', and agreement
between coincident clocks in S and S' is
required.
?
12
Equivalence of All Inertial Systems
Rotation invariance of space implies ? (v) ?
(-v) Equivalence of S and S' implies
y' ? ß y and y ? ß y' and hence
y ?2 ß2 y , whence ? ß 1 i.e. ?
1 / ß v (1 v2 ) so ?' v ß x' ß (x
vt) y' y z' z t' t /
ß v ß (x vt) ß ( t v x) .
?
13
Relative speed Lorentz transformation

• Assumptions
• (Empty) space is uniform
• (Empty) space is isotropic
• The speed of light is constant
• Consequences
• A moving body seems to be contracted
• A moving clock seems to go slowly

14
The moving train seems shorter than the
stationary train.

• The moving clock goes more slowly than the
  stationary clocks

15
Twin paradox

• 26 signals
• 1 received at t- ceti
• 25 on return journey

16
Twin paradox

• 5 years
• outbound
• 5 years
• inbound
• 26 years on
• earth

17
Twin paradox

• m particles are made in the upper atmosphere
  by collisions of protons from the solar wind
  and molecules of air.

• m particles decay in a microsecond, but
  they reach the surface of the earth, thanks to
  time dilation what is less than one microsecond
  for the particle is a minute for us.

18
Twin paradox

• The time dilation effect is taken into account 
  every day to help keep the atomic clocks on the
  24 Global Positioning System (GPS) satellites
  that encircle the Earth in sync with Earth-based
  atomic clocks

19
Non-Euclidean geometry
C number of matches on the circumference D
number of matches on a diameter C/D 18/6 3
Snapshot C/D 32/6 5.333...

• C/D 3.14159265358979323846264338327950

20
Energie en materie

• It followed from the special theory of relativity
  that mass and energy are both of a different
  manifestation of the same thing, a somewhat
  unfamiliar conception for the average man.
  Furthermore, the equation
• E mc²
• in which energy is put equal to mass multiplied
  with the square of the velocity of light, showed
  that (a) very small amount 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
  above. This was demonstrated by Cockcroft and
  Walton in 1932 experimentally.