A recap of the main points so far… Observers moving uniformly with respect to each other
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Transcript of A recap of the main points so far… Observers moving uniformly with respect to each other
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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
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The Twins Paradox
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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?
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Underlying principles of General Underlying principles of General RelativityRelativity
The Equivalence Principle
No difference between a steady acceleration and a gravitational field
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Gravity and Acceleration cannot be distinguished
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h
V = a h/c
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h Gravitational field
Equivalence principle – this situation should be the same
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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
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Gravitational redshift of Sirius B
Equivalent velocity 80 km/s
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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!
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Lensing of distant galaxies by a foreground cluster
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QSO 2237+0305
The Einstein cross
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Abell 1689
Plus derived
Mass Map
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Galaxies at 3, 6 and 11 billion light years away
Einstein Rings
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