I. Bernard Cohen
“For nonscientists and scientists,
relativity symbolizes revolution in
science in our century. But for
th...
Kelvin 1900
“There is nothing new to be discovered
in physics now.All that remains is more
and more precise measurement.”
Classical Physics
Newtonian mechanics as foundation (and standard)
for over 200 years
Problems
• Radioactivity - where doe...
What about the Atom?
Ernst Mach,Willhelm
Ostwald and others
Atoms were
mathematical rather
than physical entities.
Atoms w...
Einstein 1905
Albert Einstein
1879 - 1955
Special Relativity (1905)
General Relativity (1915)
Nobel Prize (1921)
Moved to US (1933)
Lett...
The Investigation of the State of
Aether in Magnetic Fields
Wunderjahr 1905
“A New Determination of Molecular Dimensions” (Ph.D thesis,
April)
“On a Heuristic Point ofView about the ...
Photoelectric Effect
Photoelectric Effect
“Energy, during the propagation of a ray of light, is not
continuously distributed over steadily incr...
Black-Body Radiation
Brownian Motion
Brownian Motion
Used kinetic theory of fluids to explain
Brownian Motion
Supported use of statistical mechanics
Provided ev...
Special Relativity
A Thought Experiment
Suppose there are two identical rooms. Both rooms
are completely sealed off from the outside world. N...
Inertial Reference Frame
Classical Physics
The laws of physics are
the same in all inertial
reference frames
There is no experiment
you can do to p...
Relativity Principle
Newton
However, we need an
absolute frame of
reference if we are to
be able to say to which
body a force has been
applied ...
Newton
"Absolute, true and mathematical time, of itself and
from its own nature, flows equably without relation
to anything...
Newton
Space is a three dimensional
grid with a central reference
point
Time is a constant clockwork
mechanism
Space and t...
Maxwell’s synthesis
James Clerk Maxwell
(1865)
Four laws of
electromagnetism
Predicted light to be an
electromagnetic wave...
Speed of Light
Date Author Result (km/
sec)
Error
1676 Olaus Roemer 214,000
1726 James Bradley 301,000
1849 Armand Fizeau ...
Definition of a Meter
The length of a pendulum with a half-period of one second (1790)
The distance between two lines on a ...
Maxwell’s problems
Waves need a medium
(the luminiferous aether)
However, the equations
did not obey the
relativity princi...
Were was the aether?
Attempts to directly detect it failed
Properties: immobile,denser than steel but objects
were still a...
Michelson Morley
Experiment
Detect interference
(change in velocity) in
a split light beam
Could not detect as
expected
Einstein
“On the
electrodynamics of
moving bodies” (1905)
A theory to make
physics invariant and
independent of
observer m...
Two Postulates
The laws of physics have the
same form in all inertial
reference systems (The
Principle of Relativity)
Ligh...
“[T]he same laws of electrodynamics and optics will be valid for all
frames of reference for which the equations of mechan...
RelativeVelocities are Additive
Most of the Time!
Invariance Theory
The laws of physics (and
the constants) do not
change for different
observers, i.e. are invariant,
but m...
Special Relativity
“Every general law of nature must be so
constituted that it is transformed into a law of
exactly the sa...
Hendrik Lorentz
Relativity
“The unsuccessful attempts to
discover any motion of the
earth relatively to the ‘light
medium,’ suggest that t...
Relativity
There is no privileged frame
of reference for space &
time
There is no (Newtonian)
absolute space and time
Hermann Minkowski
Geometrical
reformulation of
Einstein’s ideas.
“Space by itself, and time
by itself, are doomed to
fade ...
Spacetime
Four dimensional and (originally) Euclidian
All observers agree on the total
spacetime distance between two even...
No Absolute Simultaneity
Other Consequences
Time dilation - time passes more slowly when traveling
fast when compared to a “stationary” observer
Le...
Mass-Energy Equivalency
Based on work of Maxwell and Hertz
and special relativity
“The results of the previous
investigati...
Leó Szilárd
Theory & Experiment
It is required that the theory not be refuted by any
undisputed experiment within the theory’s domain ...
Tests of S.R.
Pre-1905 experiments
Light-speed isotropy (same value in any/every direction)
Measurement of speed of light ...
Inconsistent Experiments
Outside of domain of applicability of SR
Lacking error analysis, examination of systematic effect...
Einstein laughs at your puny claims !!
Relativity
Outside ordinary human
experience
Deals with the very fast
(special) and the very large
(general)
Newtonian phy...
General Relativity
Tension between Newtonian ideas
of gravitation and the new concept
of spacetime.
Special relativity app...
General Relativity and
the Geometry of Spacetime
First Solvay Conference, Brussels, 1911
General Relativity
Special relativity applies to constant velocity
(“inertial motion”), however we live in a
universe perm...
1907
“Then came to me the best idea of
my life ... [T]he gravitational field only
has a relative existence. Because for
an ...
Principal of Equivalence
"On the relativity principle and the conclusions drawn from
it" (1907)
Newtonian inertial (resist...
The 1907 Paper
Contains much of the General
Theory
But would require a new
mathematics (tensor calculus) and
a new non-Euc...
Euclidian Geometry
Henri Poincaré
What if the universe itself
was non-Euclidian?
The math for non-
Euclidian geometry is not
as simple, hence...
Gravity is Part of the
Fabric of Spacetime
Thought experiment of two observers
measuring the ratio of a rotating disk’s
ra...
Carl-Friedrich Gauss
1777 - 1855
Developed a theory of
curved surfaces
Conversion from co-
ordinate distance (map) to
real...
Bernhard Riemann
1826 - 1866
Generalized Gauss’
ideas to spaces of higher
dimensions
The required metric
tensor for 4D spa...
Field Equation (1915)
Ricci Tensor
Energy/
momentum
Tensor
Metric
Tensor
Einstein Tensor
A little simpler
Curvature of
Spacetime
Matter
ThirdVersion (1917)
A Theory of Gravitation
The observed gravitational
attraction between masses
results from the warping of
space and time by...
Classical Tests of General
Relativity (1916)
Gravitational redshift of light
Perihelion precession of
Mercury’s orbit
Defle...
Gravitational Redshift
Measured by Walter Sydney Adams in 1925
while looking at spectrum of Sirius B
Terrestrial experimen...
Newton predicts precession of 5555.62 arcsec/
century
Observed precession of 5600.73 arcsec/century
Difference of 43.11 ± ...
Bending of Light
Predicted - based on
Newtonian
mechanics - by Henry
Cavendish (1784)
Value of 0.83”
calculated by Johann
...
Einstein (1911)
• Specific prediction - based on GR - for the deflection
of light by a gravitational mass such as the Sun
• ...
London Times
17 Nov 1919
“Revolution in Science – New Theory of the
Universe – Newtonian Ideas Overthrown.”
Arthur Eddington Frank Dyson
Hyades Cluster
Possible Outcomes
No deflection
Half deflection (Newton)
Full deflection (Einstein)
Not so fast ...
Early accuracy relatively poor
However, experiment repeated
and confirmed in 1922
Most recent hi-precision
...
5th Solvay 1927
Max Planck Nils Bohr
Travel Time Delay
A time delay should occur
as a photon passes close to
the Sun (“Shapiro delay”)
Agreement at 5% when
tes...
Gravitational
Lensing
Light travels along “straight” lines in
a curved spacetime
extreme curvature of spacetime
Cygnus X-1
“Golden Age”
of General Relativity
1960 to 1975
Work by the likes of Richard Feynman, Stephen
Hawking & Roger Penrose
Theo...
Einstein
Einstein
Einstein
Einstein
Einstein
Einstein
Einstein
Einstein
Einstein
Einstein
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Einstein

  1. 1. I. Bernard Cohen “For nonscientists and scientists, relativity symbolizes revolution in science in our century. But for those in the know, quantum theory (especially in its revised form as quantum mechanics) may have been an even greater revolution. We may find a measure of Albert Einstein’s greatness as a scientist in his fundamental contributions to both revolutions.”
  2. 2. Kelvin 1900 “There is nothing new to be discovered in physics now.All that remains is more and more precise measurement.”
  3. 3. Classical Physics Newtonian mechanics as foundation (and standard) for over 200 years Problems • Radioactivity - where does the energy come from? • Blackbody radiation - how do you account for the energy spectrum? • Aether - where was it?
  4. 4. What about the Atom? Ernst Mach,Willhelm Ostwald and others Atoms were mathematical rather than physical entities. Atoms were a “useful fiction”
  5. 5. Einstein 1905
  6. 6. Albert Einstein 1879 - 1955 Special Relativity (1905) General Relativity (1915) Nobel Prize (1921) Moved to US (1933) Letter to F.D. Roosevelt (1939)
  7. 7. The Investigation of the State of Aether in Magnetic Fields
  8. 8. Wunderjahr 1905 “A New Determination of Molecular Dimensions” (Ph.D thesis, April) “On a Heuristic Point ofView about the Creation and Conversion of Light” (Photoelectric effect, March) “On the Motion of Small Particles Suspended in a Stationary Liquid, as Required by the Molecular Kinetic Theory of Heat” (Brownian Motion, May) “On the Electrodynamics of Moving Bodies” (Special Relativity, June) “Does the Inertia of a Body Depend Upon Its Energy Content?” (Mass-Energy Equivalency, September)
  9. 9. Photoelectric Effect
  10. 10. Photoelectric Effect “Energy, during the propagation of a ray of light, is not continuously distributed over steadily increasing spaces, but it consists of a finite number of energy quanta localised at points in space, moving without dividing and capable of being absorbed or generated only as entities.” Explained the photoelectric effect and black-body radiation Contradicts the wave theory of light
  11. 11. Black-Body Radiation
  12. 12. Brownian Motion
  13. 13. Brownian Motion Used kinetic theory of fluids to explain Brownian Motion Supported use of statistical mechanics Provided evidence for atoms and convinced many (including Ostwald) of their reality
  14. 14. Special Relativity
  15. 15. A Thought Experiment Suppose there are two identical rooms. Both rooms are completely sealed off from the outside world. No light, radio waves or any other information can get into the rooms from outside. Room A is sitting in the parking lot outside. Room B is sitting on the back of a truck driving down a perfectly smooth, perfectly straight road at a perfectly constant 100 mph. Question: You find yourself in one of the two rooms, but do not know which. What experiment could you do to tell whether you are in room A or room B?
  16. 16. Inertial Reference Frame
  17. 17. Classical Physics The laws of physics are the same in all inertial reference frames There is no experiment you can do to prove which frame is at rest or moving with constant velocity
  18. 18. Relativity Principle
  19. 19. Newton However, we need an absolute frame of reference if we are to be able to say to which body a force has been applied (i.e. which body is moving and which is not).
  20. 20. Newton "Absolute, true and mathematical time, of itself and from its own nature, flows equably without relation to anything external” “Absolute space, in its own nature, without relation to anything external, remains always similar and immoveable." Motion with respect to a privileged frame of reference (absolute rest)
  21. 21. Newton Space is a three dimensional grid with a central reference point Time is a constant clockwork mechanism Space and time exist independent of the distribution of matter in the universe
  22. 22. Maxwell’s synthesis James Clerk Maxwell (1865) Four laws of electromagnetism Predicted light to be an electromagnetic wave with the observed speed
  23. 23. Speed of Light Date Author Result (km/ sec) Error 1676 Olaus Roemer 214,000 1726 James Bradley 301,000 1849 Armand Fizeau 315,000 1862 Leon Foucault 298,000 500 1879 Albert Michelson 299,910 50 1907 Rosa & Dorsay 299,788 30 1926 Michelson 299,796 4 1947 Essen & Smith 299,792 3 1958 K.D. Froome 299,792.5 0.1 1973 Evanson et al. 299,792.4574 0.001 1983 AdoptedValue 299.792.458
  24. 24. Definition of a Meter The length of a pendulum with a half-period of one second (1790) The distance between two lines on a standard bar of an alloy of platinum with ten percent iridium measured at the melting point of ice (1889) The distance, at 0°C, between the axes of the two central lines marked on the prototype bar of platinum-iridium, this bar being subject to one standard atmosphere of pressure and supported on two cylinders of at least one centimeter diameter, symmetrically placed in the same horizontal plane at a distance of 571 millimeters from each other. (1927) The distance travelled by light in a vacuum during a time interval of 1 ⁄ 299,792,458 of a second (1983)
  25. 25. Maxwell’s problems Waves need a medium (the luminiferous aether) However, the equations did not obey the relativity principle and were not the same for all reference frames
  26. 26. Were was the aether? Attempts to directly detect it failed Properties: immobile,denser than steel but objects were still able to pass through it, imperceptible (“subtle”) Since the aether was assumed to be immobile, one could determine the earth’s absolute motion in space. Michelson & Morley (1887) attempted to determine how fast the Earth was moving through the aether
  27. 27. Michelson Morley Experiment Detect interference (change in velocity) in a split light beam Could not detect as expected
  28. 28. Einstein “On the electrodynamics of moving bodies” (1905) A theory to make physics invariant and independent of observer motion, not to make it “relative”
  29. 29. Two Postulates The laws of physics have the same form in all inertial reference systems (The Principle of Relativity) Light propagates through empty space with a speed independent of the speed of the emitting body(The Light Postulate)
  30. 30. “[T]he same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the ‘Principle of Relativity’) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.These two postulates suffice for the attainment of a simple and consistent theory of the electrodynamics of moving bodies based on Maxwell's theory for stationary bodies.The introduction of a ‘luminiferous ether’ will prove to be superfluous in as much as the view here to be developed will not require an ‘absolutely stationary space’ provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place.”
  31. 31. RelativeVelocities are Additive
  32. 32. Most of the Time!
  33. 33. Invariance Theory The laws of physics (and the constants) do not change for different observers, i.e. are invariant, but measurements of time and space are relative to the observer
  34. 34. Special Relativity “Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of space- time variables x, y, z, t of the original coordinate system K, we introduce new space time variables x’, y’,z’,t’ of a coordinate system K’… Or in brief: General laws of nature are co- variant with respect to Lorentz transformations.”
  35. 35. Hendrik Lorentz
  36. 36. Relativity “The unsuccessful attempts to discover any motion of the earth relatively to the ‘light medium,’ suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest.”
  37. 37. Relativity There is no privileged frame of reference for space & time There is no (Newtonian) absolute space and time
  38. 38. Hermann Minkowski Geometrical reformulation of Einstein’s ideas. “Space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.” (1908)
  39. 39. Spacetime Four dimensional and (originally) Euclidian All observers agree on the total spacetime distance between two events Observers disagree on how to split up the “space” and “time” components
  40. 40. No Absolute Simultaneity
  41. 41. Other Consequences Time dilation - time passes more slowly when traveling fast when compared to a “stationary” observer Length contraction - objects appear to be compressed along their direction of motion A moving light cone becomes focussed and thus brighter A moving light source seems to “beam” its light forward Nothing can move faster than the speed of light Twin paradox
  42. 42. Mass-Energy Equivalency Based on work of Maxwell and Hertz and special relativity “The results of the previous investigation lead to a very interesting conclusion, which is here to be deduced.” A mass at rest has “rest energy” distinct from classical kinetic and potential energies.
  43. 43. Leó Szilárd
  44. 44. Theory & Experiment It is required that the theory not be refuted by any undisputed experiment within the theory’s domain of applicability (i.e. the set of physical situations in which the theory is valid). It is expected that the theory be confirmed by a number of experiments that: - cover a significant fraction of the theory’s domain of applicability - examine a significant fraction of the theory’s predictions
  45. 45. Tests of S.R. Pre-1905 experiments Light-speed isotropy (same value in any/every direction) Measurement of speed of light (and c as limit) Test of Lorentz Invariance Time dilation Atomic clocks in flight Length contraction (indirect)
  46. 46. Inconsistent Experiments Outside of domain of applicability of SR Lacking error analysis, examination of systematic effects or statistical analysis “Amateurs look for patterns, professionals look at error bars” Unrepeatable Large uncertainties or unknowns At present there is no reproducible or generally accepted experiment that is inconsistent with Special Relativity
  47. 47. Einstein laughs at your puny claims !!
  48. 48. Relativity Outside ordinary human experience Deals with the very fast (special) and the very large (general) Newtonian physics still holds of the “everyday” experience
  49. 49. General Relativity Tension between Newtonian ideas of gravitation and the new concept of spacetime. Special relativity applies to constant velocity (“inertial motion”), however we live in a universe permeated by gravity which causes acceleration.What happens if the observer is accelerating?
  50. 50. General Relativity and the Geometry of Spacetime
  51. 51. First Solvay Conference, Brussels, 1911
  52. 52. General Relativity Special relativity applies to constant velocity (“inertial motion”), however we live in a universe permeated by gravity which causes acceleration.What happens if the observer is accelerating? How do you unify Newtonian gravitation with special relativity?
  53. 53. 1907 “Then came to me the best idea of my life ... [T]he gravitational field only has a relative existence. Because for an observer freely falling from the roof of a house, no gravitational field exists while he is falling. The experimental fact that the acceleration due to gravity does not depend on the material is thus a powerful argument for extending the relativity postulate to systems in non-uniform relative motion.” (1919)
  54. 54. Principal of Equivalence "On the relativity principle and the conclusions drawn from it" (1907) Newtonian inertial (resistance to acceleration) mass and gravitational (measure of susceptibility to gravitation) mass are the same thing “we [...] assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system.” There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating.
  55. 55. The 1907 Paper Contains much of the General Theory But would require a new mathematics (tensor calculus) and a new non-Euclidian geometry (Riemanian) before it could provide a quantification of the gravitational field and thus make specific numerical predictions.
  56. 56. Euclidian Geometry
  57. 57. Henri Poincaré What if the universe itself was non-Euclidian? The math for non- Euclidian geometry is not as simple, hence rejection would occur.
  58. 58. Gravity is Part of the Fabric of Spacetime Thought experiment of two observers measuring the ratio of a rotating disk’s radius to circumference (2π) Realized that Minkowski’s space time was non-Euclidean By the Principle of Equivalence this meant that the geometry of a gravitational field would also be non- Euclidean
  59. 59. Carl-Friedrich Gauss 1777 - 1855 Developed a theory of curved surfaces Conversion from co- ordinate distance (map) to real distance requires a metric tensor These will differ by location so will require a metric field.
  60. 60. Bernhard Riemann 1826 - 1866 Generalized Gauss’ ideas to spaces of higher dimensions The required metric tensor for 4D space (a “manifold”) had ten components.
  61. 61. Field Equation (1915) Ricci Tensor Energy/ momentum Tensor Metric Tensor Einstein Tensor
  62. 62. A little simpler Curvature of Spacetime Matter
  63. 63. ThirdVersion (1917)
  64. 64. A Theory of Gravitation The observed gravitational attraction between masses results from the warping of space and time by those masses Spacetime tells matter how to move, matter tells spacetime how to curve.
  65. 65. Classical Tests of General Relativity (1916) Gravitational redshift of light Perihelion precession of Mercury’s orbit Deflection of light by the Sun
  66. 66. Gravitational Redshift Measured by Walter Sydney Adams in 1925 while looking at spectrum of Sirius B Terrestrial experiments by Robert Pound & G.A. Rebka met predication by within 10% in 1959 Subsequently, Pound and J.L. Snider met prediction to within 1% in 1964 By 1980 the effect has been measured to 0.0001%
  67. 67. Newton predicts precession of 5555.62 arcsec/ century Observed precession of 5600.73 arcsec/century Difference of 43.11 ± 0.45
  68. 68. Bending of Light Predicted - based on Newtonian mechanics - by Henry Cavendish (1784) Value of 0.83” calculated by Johann Georg von Soldner (1804)
  69. 69. Einstein (1911) • Specific prediction - based on GR - for the deflection of light by a gravitational mass such as the Sun • Einstein realized he was wrong in 1915 and the value should be twice that originally calculated
  70. 70. London Times 17 Nov 1919 “Revolution in Science – New Theory of the Universe – Newtonian Ideas Overthrown.”
  71. 71. Arthur Eddington Frank Dyson
  72. 72. Hyades Cluster
  73. 73. Possible Outcomes No deflection Half deflection (Newton) Full deflection (Einstein)
  74. 74. Not so fast ... Early accuracy relatively poor However, experiment repeated and confirmed in 1922 Most recent hi-precision confirmation in 1967, 1973 & 2004 There remain false accusations of data manipulation
  75. 75. 5th Solvay 1927
  76. 76. Max Planck Nils Bohr
  77. 77. Travel Time Delay A time delay should occur as a photon passes close to the Sun (“Shapiro delay”) Agreement at 5% when testing radar reflections from Mercury &Venus (1971) Agreement at 0.002% using the Cassini probe (2002)
  78. 78. Gravitational Lensing
  79. 79. Light travels along “straight” lines in a curved spacetime
  80. 80. extreme curvature of spacetime
  81. 81. Cygnus X-1
  82. 82. “Golden Age” of General Relativity 1960 to 1975 Work by the likes of Richard Feynman, Stephen Hawking & Roger Penrose Theoretical exploration of Black Holes Discovery of quasars, pulsars, and candidate black holes Acceptance of Big Bang and discovery of the cosmic background radiation Acceptance of legitimacy of cosmology within physics

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