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.”

Kelvin 1900

“There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.”

Classical PhysicsNewtonian 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?

What about the Atom?

Ernst Mach, Willhelm Ostwald and others

Atoms were mathematical rather than physical entities.

Atoms were a “useful fiction”

Einstein 1905

Albert Einstein1879 - 1955

Special Relativity (1905)

General Relativity (1915)

Nobel Prize (1921)

Moved to US (1933)

Letter to F.D. Roosevelt (1939)

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 of View 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)

Photoelectric Effect

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

Black-Body Radiation

Brownian Motion

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

Special Relativity

A Thought ExperimentSuppose 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?

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 prove which frame is at rest or moving with constant velocity

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 (i.e. which body is moving and which is not).

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)

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

Maxwell’s synthesis

James Clerk Maxwell (1865)

Four laws of electromagnetism

Predicted light to be an electromagnetic wave with the observed speed

Speed of LightDate Author Result (km/

sec)Error

1676 Olaus Roemer 214,0001726 James Bradley 301,0001849 Armand Fizeau 315,0001862 Leon Foucault 298,000 5001879 Albert Michelson 299,910 501907 Rosa & Dorsay 299,788 301926 Michelson 299,796 41947 Essen & Smith 299,792 31958 K.D. Froome 299,792.5 0.11973 Evanson et al. 299,792.4574 0.0011983 Adopted Value 299.792.458

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)

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

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

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 motion, not to make it “relative”

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)

“[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.”

Relative Velocities 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 measurements of time and space are relative to the observer

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.”

Hendrik Lorentz

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.”

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 away into mere shadows, and only a kind of union of the two will preserve an independent reality.” (1908)

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

No Absolute Simultaneity

Other ConsequencesTime 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

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.

Leó Szilárd

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

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)

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

Einstein laughs at your puny claims !!

Relativity

Outside ordinary human experience

Deals with the very fast (special) and the very large (general)

Newtonian physics still holds of the “everyday” experience

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?

General Relativity andthe Geometry of Spacetime

First Solvay Conference, Brussels, 1911

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?

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)

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.

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.

Euclidian Geometry

Henri Poincaré

What if the universe itself was non-Euclidian?

The math for non-Euclidian geometry is not as simple, hence rejection would occur.

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

Carl-Friedrich Gauss1777 - 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.

Bernhard Riemann1826 - 1866

Generalized Gauss’ ideas to spaces of higher dimensions

The required metric tensor for 4D space (a “manifold”) had ten components.

Field Equation (1915)

Ricci TensorEnergy/

momentumTensor

Metric Tensor

Einstein Tensor

A little simpler

Curvature ofSpacetime

Matter

Third Version (1917)

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.

Classical Tests of General Relativity (1916)

Gravitational redshift of light

Perihelion precession of Mercury’s orbit

Deflection of light by the Sun

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%

Newton predicts precession of 5555.62 arcsec/century

Observed precession of 5600.73 arcsec/century

Difference of 43.11 ± 0.45

Bending of Light

Predicted - based on Newtonian mechanics - by Henry Cavendish (1784)

Value of 0.83” calculated by Johann Georg von Soldner (1804)

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

London Times17 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 confirmation in 1967, 1973 & 2004

There remain false accusations of data manipulation

5th Solvay 1927

Max Planck Nils Bohr

Travel Time DelayA 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)

GravitationalLensing

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

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