Inertial frames

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Inertial frames

• Physical laws are stated relative to some
  reference frame.
• A frame where Newtons Laws hold we will call an
  inertial frame
• Newton himself assumed there was a single
  inertial frame which was absolute. Defined by the
  fixed stars
• His laws would hold in any frame moving with
  constant velocity w. r.to the fixed stars
• Thus there are an infinity of inertial frames

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The Principles of Relativity

• All inertial frames are totally equivalent for
  the performance of all physical experiments
• Consequently
• The speed of light is a constant in all inertial
  frames

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Lorentz transformation
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Inverse Lorentz transformation
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Velocity transformations
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Recall
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Note 1
Note ?
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Note 1
Note ?
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These equations can also be interpreted as giving
the resultant U(u1,, u2, u3)of the two
velocities v(v,0,0) and u(u1, u2, u3) In
this role they are referred to as the
relativistic velocity addition formulae
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Newtons Second Law

• Law of conservation of momentum

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Assume that in frame S the following perfectly
elastic collision is observed two particles
with velocities,u and u move along the x-axis
and collide at the origin
y
x
After the collision the particles move along the
y-axis with equal and opposite velocities
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Cant have that !
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With this new definition momentum is conserved
for all collisions not just our special case
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Energy
Line integral of the change in momentum over path
Change in Kinetic Energy
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Let us apply this to our relativistic momenta
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Take the point b as arbitary and assume the
particle is at rest at a
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then
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then
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then
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Rest Mass
m?m0
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Remarks
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• Following Einstein we interpret
• Emc2
• as the total energy of the particle

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• Given this interpretation
• Energy conservation in mechanical situations
  holds in all inertial frames
• Further if an energy of ?E is added to a body,its
  mass will change by?m?E/c2
• ?E could represent mechanical work, heat energy,
  absorption of light or any other form of energy

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

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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.

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• 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

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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.   

?c
frequency
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• It is convenient not to measure this current
  itself but to measure the stopping potential V0
  required to reduce this current to zero. The
  stopping potential is related to the (maximum)
  kinetic energy of the ejected electrons by
• eV0 KE max .
• (4) There were several failings of the wave
  picture of light when applied to this phenomenon,
  but the most notable was the following No
  photoelectric electrons are emitted if the
  frequency of the light falls below some cutoff
  frequency, ?c .

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• Einstein suggested that the photons have an
  energy E h?. When these photons hit the
  metal, they could give up some or all of their
  energy to an electron. A certain amount of energy
  would be required to release the electrons from
  their bonds to the metal - this energy is called
  the work function, W , of the metal. The
  remaining energy would appear as kinetic energy
  of the released electron. Thus, the maximum
  kinetic energy the electrons could have is
•  

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• 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 V then the energy lost by the
  electrons as they travel to the plate is
  (-e)(-V)eV
• At cut-off we have VVc and consequently the
  photon hypothesis yields
• eVch?-W

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• 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!

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• 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!

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Radiation Pressure

• A consequence of Maxwells electromagnetic theory
  is that a light wave carries momentum which it
  will transfer to a surface when it is reflected
  or absorbed. The result is a pressure on the
  surface. The calculation of radiation pressure is
  complicated using the wave theory of light but in
  the photon picture. It is simple

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• 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)