A recap of the main points so far…
Observers moving uniformly with respect to each other
• do not agree on time intervals or distance intervals
• do not agree about the simultaneity or otherwise of events
A moving clock appears to run slow – time dilation
A moving ruler appears short – length contraction
•A moving object has an increased relativistic mass
•Mass can be converted into energy (and vice-versa)
E = m c2
The Twins Paradox
Symmetry
As far as the observer on the spaceship is concerned, a clock left on Earth is running slow and lengths are contracted in the direction of motion.
As far as the observer on Earth is concerned, a clock on the spaceship is running slow and lengths are contracted in the direction of motion.
The frames of reference are equivalent?
Underlying principles of General Underlying principles of General RelativityRelativity
The Equivalence Principle
No difference between a steady acceleration and a gravitational field
Gravity and Acceleration cannot be distinguished
h
V = a h/c
h Gravitational field
Equivalence principle – this situation should be the same
Consequences I. Gravitational Redshift
Size of effect (doppler shift equivalent speed)
Earth 0.2 m/s
Sun 0.6 km/s
White Dwarf 70 km/s
Neutron Star 100,000 km/s
Black-hole infinite
Gravitational redshift of Sirius B
Equivalent velocity 80 km/s
Corrections to GPS
Orbital radius 26,000 km
gh/c2 = 0.0000000026
Clocks “on the ground” would lose about 0.2 ms per day (actually a bit less).
Clocks on the GPS satellites run intentionally slowly!
Lensing of distant galaxies by a foreground cluster
QSO 2237+0305
The Einstein cross
Abell 1689
Plus derived
Mass Map
Galaxies at 3, 6 and 11 billion light years away
Einstein Rings
