Download Physics Oration - Part 2

Maps of space
Space:
N & E or M & H
Electromagnetism:
E & B or E & B
The Light Cone: Maps of space-time
time axis
Future
Elsewhere
Elsewhere
space axis
uni
Supernova!
PAST
home
• Events that
happen
“elsewhere” can
have no effect on
here and now
How fast are we going anyway?
Sun’s Orbit
around
galaxy:
250 km/s
Milky Way
Galaxy
trajectory
towards
Great
Attractor:
7000 km/s
Earth’s Orbit
around Sun:
30 km/s
E=mc² did not appear in the original 1905 paper,
but later that year
• How did it arise out of theories of relative motion?
– Consequence of the conservation of momentum and the Lorentz
transforms
• Energy becomes relative too - how can that be?
– We are used to this concept already! What is my kinetic energy
now? Relative to Earth? Sun? Galaxy?
• Where does all the energy go when the spaceship is not
actually getting (much) faster?
– Into mass!
The Lorentz transforms
  1/ 1  v2 / c2
Space-Time
Energy Momentum
x   ( x  vt)
y  y
px   ( p x  vE / c 2 )
py  p y
z  z
t    (t  vx / c 2 )
pz  pz
E    ( E  vpx )
Mass
The Victorian Synchrotron
“Synchronise” the ring magnets
for the effects of relativity
person
  1 / 1  v 2 / c 2  6000
Data:
• 30 GeV electrons
• 99.9999% speed
of light
• Mass 6000 times
ordinary
electrons!
The Lorentz Transformations
y
Catch
( x, y )
y
x   ( x  vt)
Catch
y  y
( x, y )
z  z
t    (t  vx / c 2 )
v
x
x
  1/ 1  v2 / c2
The Lorentz Transformations: Special Case
1
t 2 Time
interval
y
y
t1
t   t
t   t2  t1
Time Dilation
formula. Only if
y
x  0
t  0
x  0
v
v
x
x
  1/ 1  v2 / c2
x
The Lorentz Transformations: Special Case
2
y
Measure
Length
t1 : x1 x2
v
x
  1/ 1  v2 / c2
The Lorentz Transformations: Special Case
2
t1 Space
x  x / 
interval
y
y
t1 x1
x  x2  x1
t   0
y
x  0
t  0
Lorentz
contraction
formula. Only if
v
v
x
x
  1/ 1  v2 / c2
x
The Lorentz Energy Momentum Transformations
y
Energy
&
Momentum

px   ( p x  vE / c 2 )
py  p y
(p, E )
Energy
&
Momentum

(p, E )
pz  pz
E    ( E  vpx )
y
v
x
x
  1/ 1  v2 / c2
The Lorentz Velocity Transformations

u  (u x , u y , u z )
y
  1/ 1  v2 / c2
Velocity

u
y
Velocity

u
v
x
x
ux  v
uz
uy


ux 
uz 
uy 
2
2
2

(
1

vu
/
c
)
(1  vux / c )
 (1  vux / c )
x


ux  ux  v

uy  uy

uz  uz
Galilean
How are energy and mass related?
• Does mass have energy, does energy have mass?
– Yes – loosely speaking
• Why did Einstein say we will never get energy from mass?
– In 1905 nuclear reactions had not been discovered
– Chemistry is very feeble
– 1908 Rutherford Nobel prize (for Chemistry)
• Did he realise that was what was powering the Sun?
– Nobody understood the Sun until Hans Bethe
formulated the basic reactions of thermonuclear fusion in 1939!
(Nobel Prize 1967)
How are energy and mass related?
• Does mass have energy, does energy have mass?
– Yes – loosely speaking
• Why did Einstein say we will never get energy from mass?
– In 1905 nuclear reactions had not been discovered
– Chemistry is very feeble
– 1908 Rutherford Nobel prize (for Chemistry)
• Did he realise that was what was powering the Sun?
– Nobody understood the Sun until Hans Bethe
formulated the basic reactions of thermonuclear fusion in 1939!
(Nobel Prize 1967)
Were others on the verge of special relativity?
Poincare, Lorentz? Was it just waiting to happen?
• Galileo 1634
• Maxwell 1873
The laws of Physics do
not depend on absolute
motion
Does
include
• this
Heaviside
1897
electromagnetism?


• Newton 1687
–
–
An object once set in motion
remains in motion until acted
upon by an external force
The universe is governed by a
majestic clockwork where all
clocks everywhere at all times
tick in perfect synchronisation.





The great treatise of
electromagnetism
Electromagnetic fields
and waves propagate
through the Aether

 
FM  qv  B
1889:
Maxwell equations
Field
of a moving
• Poincare
1898
charge
–
–
–
Relativity of simultaneity:
telegraph
Concept of “local time”
Stuck on the Aether
• Lorentz 1904

Maxwell equations invariant under L.
transformations
The transition from Special to General
Relativity
• What are the differences?
– Special Relativity = all reference frames are equivalent
– … and speed of light the same in each
– General Relativity = everything falls at the same rate
– …and can cancel gravity by falling!
• Why is it said that although someone else would have soon
come up with special, general was much more of an
intellectual triumph?
– Equivalence of gravity and acceleration a great mystery to
Newton
– Everyone before Einstein thought this was an amazing
coincidence!
– Why is gravity so different to the other forces of nature?
– Idea of curved space arises from Special Relativity and the
equivalence principle
Curved space
When we say that an accelerated field is
equivalent to a gravitational field …
• What does that really mean?
– Everything falls at the same rate
– Can cancel gravity by falling
• The experiments inside an enclosed rocket either sitting on
Earth or out in space accelerating may look equivalent, but if
one looks out the window the scene is very different!
– True, but so does looking at the stars from Earth!
– Until Copernicus, humanity thought it was living on a stationary
Earth and the Stars orbited the Earth
Equivalence Principle
Gravitating
Accelerating
N
N
W
W
What’s the difference?
Equivalence Principle
Falling
Floating
What’s the difference?