Would it be possible to detect this ‘fall’ (of about 10 -13 m across 30 m)?

Does light actually accelerate downwards at 9.8 m/s2 as it goes through Earth’s gravity despite its zero

mass?

• Would it be possible to detect this ‘fall’ (of about 10-13 m across 30 m)?

– Yes! But the fall is twice what is expected from Newton due to curvature of space due to gravity

• As a photon has momentum, does it have mass?

– No. A photon has no rest mass

A clock slows down when travelling at high speed

• It also slows down in a strong gravitational field.

• Is there some sort of equivalence between the two situations?

– Yes! Consider a rotating disk…

Fast moving clock = slow

by time dilation

Apply Equivalence Principle

• Gravitational red shift for clocks at different heights

t

tt

v

Resting clock

2

2

1

1

cv

Apply Equivalence Principle

Centripetal acceleration

t

tt

Apply Equivalence Principle

Centripetal acceleration

t

tt

• Gravitational red shift for clocks at different heights

Low slow clock

High fast clock

Does the light which "lenses" around a distant galaxy follow a "geodesic" - a natural pathway in curved

space-time?

• A laser beam fired horizontally on the moon will curve gently as it emerges into space.

• A bullet fired from the same spot might actually go into orbit, metres above the moon's surface

• Are both the laser beam and the bullet following the same curve in space-time?

– No. The bullet follows a parabolic projectile trajectory

– The light is following a geodesic

• Why does Mercury's orbit precess, which is supposed to be a proof of general relativity?

– It precesses because of the extra volume of space near the Sun created by the Sun’s gravity!

Constructing geodesicsParallel lines converge on

a curved surface

Curved space: Gravity of Sun

• Radio signals from distant space craft are delayed when Sun is near the path

• There is more space in between!

EarthSun

Venus

Earth

near Sun path

clear

pat

h

Curved Space: Radar echo from Venus

• Radar echo from Venus takes longer when Sun is nearby

Tim

e d

ela

y

Date

Curved Space: Advance in Perihelion of Mercury

• Perihelion (closest approach to Sun) advances owing to gravitational influence from rest of solar system by 531” every 100 years

• However this is insufficient to account for the observed advance of 574” every 100 years

• Residual 574 – 531 = 43” is due to General Relativity

Mercury

Einstein was a ‘social activist’• He held strong views about nationalism, about war, about materialism

• Were these views in any way related to his science?

• Did his ability to question basic assumptions about space and time flow over into a desire to question social assumptions and norms?

• Is there a message in here for us somewhere in this current climate of all sorts of untested assumptions?

– In Physics – Yes!

How do we know that time readings at two such distant places are properly correlated? Ultimately this boils down to the question: how do we decide when events at two different places in the same frame of reference occur at the same time, i.e., simultaneously? Isn't

universal simultaneity an intuitively obvious property of time? Here, I believe, Einstein was really helped by his philosophical readings. He undoubtedly got some help from his readings of Mach and Poincaré, but we know that he was engaged in a careful reading of Hume at about this time; and his later reminiscences attribute great significance to his reading of Hume's

Treatise on Human Nature. What could he have gotten from Hume? I think it was a relational-as opposed to an absolute-concept of time and space. This is the view that time and space are

not to be regarded as self-subsistent entities; rather one should speak of the temporal and spatial aspects of physical processes; "The doctrine," as Hume puts it, "that time is nothing but

the manner, in which some real object exists." I believe the adoption of such a relational concept of time was a crucial step in freeing Einstein's outlook, enabling him to consider

critically the tacit assumptions about time going into the usual arguments for the "obvious" velocity addition law. This was the second great moment of liberation of his thought.

This is the text of "'What Song the Syrens Sang': How Did Einstein Discover Special Relativity?" as printed in John Stachel, Einstein from "B" to "Z" (Boston : Birkhäuser, 2002), pp. 157-169.

Relativity and the GPS

1. GPS satellites clocks run slow by 6 millionths of a second per day (SR - time dilation)

2. Cannot synchronise by exchange of signals3. GPS satellite clocks run fast by 45 millionths of a

second per day (GR - gravitational blue shift)• Net effect: Run fast by 39 millionths of a second

per day (=error of 12 kilometres)!• SOLUTION: Make the clocks run slow to

compensate!

Mysterious Magnetism

N

S

+

–

Further Reading: Relativity

• Subtle is the Lord - The Science and life of Albert Einstein, Abraham Pais, Clarendon Press, Oxford, 1982.

• Spacetime Physics - Introduction to Special Relativity, Edwin Taylor and John A. Wheeler, Freeman, New York, 1992.

• Relativity - The Special and the General Theory, Albert Einstein, Crown, New York, 1971.

• The Principle of Relativity - A collection of original papers on the special and general theories, Einstein et. al, Dover 1952.

• APS Einstein Web site– http://www.aip.org/history/einstein/