Lorentz transformation

1
Lorentz transformation
2
Inverse Lorentz transformation
3
(No Transcript)
4
(No Transcript)
5
Properties and Consequences of the Lorentz
transformation
6
In order to maintain Newtons second Law
7
Rest Mass
m?m0
8
Remarks
9
(No Transcript)
10

• Following Einstein we interpret
• Emc2
• as the total energy of the particle

11
(No Transcript)
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15

• A consequence of the relativistic energy
  momentum relation is the possibility of a
• massless particle which possess
• momentum and energy but no rest mass
• Epc

16
Concept of a Photon

• Assumption The energy of a light wave can only
  be transmitted to matter in discrete amounts or
  quanta of value h? where h is Planks constant
  and ? is the frequency of the light.

17

• From our discussion above this means we can view
  light of being made up of zero rest mass
  particles each of energy
• h? and momenta of magnitude ph?/c

18
The Photoelectric Effect

• In this effect light is shone on a metal, and
  electrons are released, these electrons can be
  attracted towards a positively charged plate a
  certain distance below, thereby establishing a
  photoelectric current.   

19

• Millikan(1916) measured the photocurrent on a
  plate near the metal and applying an electric
  potential between the plate and the photosurface
  just adequate to stop the current. If the
  potential V0 then the energy lost by the
  electrons as they travel to the plate is
  (-e)(-V0)eV0
• At cut-off we have V0 Vc and consequently the
  photon hypothesis yields
• eVch?-W

20

• Millikan observed the cut-off voltage for several
  alkali metals.
• He found Vc was a linear function of ?
• With slope h/e and that it was independent of
  the intensity of the light!

?c
Frquency ?
21

• If the energy of the light were absorbed by the
  electrons according to the classical picture then
  the electrons would have had a wide energy
  distribution depending on the intensity of the
  light in sharp disagreement with Millikans
  experiment!

22

• The photon is a completely relativistic particle
  and as such Newtonian Physics provides gives us
  little insight into its properties. Unlike
  classical particles photons can be created and
  destroyed
• (absorbed and radiated)

23

• However they do obey the laws of conservation of
  energy and momentum as we have developed them
  within the relativistic theory.

24
Compton effect

• Compton scattered X-rays off electrons and
  measured the wavelength of the scattered waves.

25
Assume electron is at rest, with mass m0
26
Photon, energy E0collides with electron
27
The scattered photon is detected
28
(No Transcript)
29
(No Transcript)
30
Convervation of Energy and Momentum
31
(No Transcript)
32
(No Transcript)
33
Original figure from Compton (1923) experiments.
The original references are A. H. Compton, Phys.
Rev. 21, 483 (1923a) 22, 409 (1923b).
34

• The measurements agree with the derived formula
• The derivation depends on photon ideas
• A) Relativity
• B) Eh?

35
Pair Production

• The rest energy of an electron is

No!
Can a photon of this energy create an electron?
This would violate conservation of charge
36

• It might be possible to create an electron
  positron pair.

37
In Free Space
38

• These equations can not hold simultaneously since

39
(No Transcript)
40

• Substituting this last equation in the energy
  expression yields

41

• The threshold for pair production is thus
• 2m0c21.02 MeV.
• The nucleus plays an essentially passive role
  but by providing for momentum conservation it
  allows for an otherwise forbidden process to
  occur

42
The Doppler Effect

• The Doppler Shift in Sound

43
(No Transcript)
44
(No Transcript)
45
(No Transcript)
46
(No Transcript)
47
(No Transcript)
48
(No Transcript)
49
(No Transcript)