Relativistic Laws Electromagnetism (Maxwell) is Lorentz-invariant Nuclear interactions have...
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Relativistic Laws Electromagnetism (Maxwell) is Lorentz-invariant Nuclear interactions have Lorentz-invariant form Quantum relativistic version (Quantum
Text of Relativistic Laws Electromagnetism (Maxwell) is Lorentz-invariant Nuclear interactions have...
Slide 1
Relativistic Laws Electromagnetism (Maxwell) is
Lorentz-invariant Nuclear interactions have Lorentz-invariant form
Quantum relativistic version (Quantum Field Theory 1940/1972.
Gravity???? 1
Slide 2
Relativistic Gravity is no good. Whose ? When? Maxwell gives a
relativistic version of in terms of electromagnetic fields We need
a field theory for gravity but Maxwells idea will not work mass is
not conserved. Energy-Momentum is conserved but not invariant What
is a gravitational force anyway?? 2
Slide 3
The Principle of Equivalence Observer in free fall only gravity
acts - there is no gravitational force. Stars and galaxies are in
free-fall! Conversely, accelerating frames exhibit gravitational
force in the absence of gravity Gravitation at one event can be
completely cancelled by choosing a suitably accelerating frame
letting go Gravity is acceleration? Tidal Forces - the change in in
space and time are truly gravitational 3
Slide 4
Gravity is Acceleration 4
Slide 5
Gravitational Redshift 5
Slide 6
Equivalence Principle: lower clock runs slow Pound Rebka 1959
measure the effect over height of tower in Jefferson Lab: complete
agreement GPS system needs to account for redshift 6
Slide 7
Gravity Small regions of spacetime, if observed by inertial
(freely falling) observers, appear free of gravity Inertial
determines acceleration. At any event are inertial observers with
all velocities and their experiences are related by Lorentz
transformations Tidal effects mean that inertial here and inertial
there do not share same acceleration Given a velocity there is a
unique inertial worldline starting with that velocity 7
Slide 8
Geometry Small regions of a curved space appear like flat space
and can be described with usual coordinates Through any point we
can draw straight lines going off in all directions and they are
related by rotations Curvature means straight lines here and there
are not related by rotation Given a point and an initial direction,
there is a unique geodesic (straight line) starting at that point
in that direction Shape of a space is encoded in distances between
points as coordinate-invariant information - curvature 8
Slide 9
A Simple and Familiar Example Earths surface is a
two-dimensional curved space To a good approximation, it is
spherical. Every point is like any other Start at pole (might as
well) in any direction and head due South along meridian Initially
paths behave like straight lines on plane Farther out notice they
are too near each other Earth is curved and eventually all meet at
opposite pole Great circles are geodesics of a sphere Positive
curvature means geodesics diverge less than in flat space 9
General Relativity Mass (Energy) is a source of spacetime
curvature Inertial (free-fall) motion is along geodesics At small
curvature and slow speeds reproduce Newton Complication:
Gravitational energy is a source. Equations are nonlinear 12
Slide 13
First Results Bound (negative energy) Newtonian orbits are
closed. After a period motion repeats Perturbations modify this.
Mercury orbit precesses 1.5 /century Planetary contributions
explain all but 43 Einstein uses effective potential to find
relativistic deviation 43 GR essential in close binaries! 13
Slide 14
Gravity Probe B Precision Measured deviation from Newtonian
predictions due to curved geometry and Earth rotation 14
Slide 15
Light Deflection Does Gravity act on light? Equivalence
principle or mass-energy equivalence: yes Full GR calculation:
Eddington 1919 eclipse measures deflection by Sun 15
Slide 16
16 Gravitational Lensing Massive objects in line of sight act
as lenses Use this to see dimmest objects Use lensing to learn
about the lens: Exoplanet detection Dark Matter detection
Slide 17
Binary Pulsar PSR1913+16 In Aquila at Millisecond pulsar with
period Periodic pulse delay with period Binary of two neutron stars
of mass and System is very eccentric (perturbed by SN?) with
periastron Perfect lab to study GR Pulse delay exhibits Doppler
effect as well as gravitational redshift Precession of perihelion
measured agrees with GR 17
Slide 18
Gravitational Waves As neutron stars orbit GR predicts they
will lose energy to gravitational waves Rate of period decrease
consistent with GR In merge 18
Slide 19
Can We See Them? Gravitational wave detectors like LIGO expect
to find evidence of violent neutron star mergers by detecting
change in length of 3km laser by fm 19
Slide 20
Gravitational Redshift Near Earth we found Away from Earth
expect something like In fact, observing from a great distance the
correct expression is 20
Slide 21
Horizons Black Holes What happens if you can get near ? Can
you? Neutron stars are close As you approach horizon redshift
Collapse past neutron degeneracy continues past horizon creating
black hole Looking from afar you never get there Slow and dim as
you near horizon as seen from afar No light comes out! Distant
light blueshifted as seen near horizon 21
Slide 22
Coming Closer If you can get to within a few relativistic
effects become marked Stable orbits exist for so nothing orbits
nearer At light in unstable circular orbit 22 Tidal forces can
become extreme at small However less so for large mass
Slide 23
Coordinate Issues At horizon time stands still as seen from
afar Use a better clock free falling in Horizon is in fact
lightlike Once inside even lightspeed will not get you out 23
Slide 24
Inside the Horizon What happens to the stellar core that
collapsed? Once inside horizon, within finite proper time (measured
by your clock) reach singularity At singularity tidal acceleration
diverges so matter ripped apart Divergence signals breakdown of
equations. We dont know. 24
Slide 25
Is This Real? Can We See Them? Technically, no. No light.. But
in our time core stuck at forever We see the effects of dense
massive objects With mass transfer have accretion disk to heated to
- X-rays Cygnus X-1 is an X-ray source in close binary with type O
supergiant Doppler produces mass for unseen X- ray source companion
Flickers in ms: 25
Slide 26
Images 26
Slide 27
Black Hole in M31 27
Slide 28
Big Holes Stellar motions near center of Milky Way show compact
object of mass Energetic jets and X-rays from SgR A* Most galaxies
seem to have massive black holes in their centers Intermediate-mass
black holes are new and under study 28
Slide 29
Black Hole Facts No Hair: Collapse loses all properties of
star. Black hole characterized completely by mass, angular
momentum, and electric charge Singularity is real (Hawking,
Penrose). General Relativity is incomplete Cosmic censorship
conjecture: singularities hidden inside horizons. Physics outside
well- defined 29
Slide 30
Wormholes Look again at description of region near horizon.
Describes two separate spacetimes touching for an instant Nothing
can get through Try to modify solution to get big wormholes not yet
Whats on the other side? 30
Slide 31
Quantum Black Holes Hawking: Quantum effects near horizon leads
to radiation with energy loss Hawking radiation is blackbody at
Negative specific heat: hotter as loses energy Evaporate in for
Microscopic black holes go faster if created? 31