Download Lecture on LIGO & Gravitational Waves

The sound of the Universe:
The search for Gravitational Waves
Giovanni Santostasi, Ph. D.
Baton Rouge Community College,
Baton Rouge, LA
Newton
and Einstein:
theories of Space and Time
Special Relativity = Space-Time
constant velocity
General Relativity = GeometrySpace-Time
acceleration
Space and Time Unified
Time and Space are not separated quantities but different aspects
of a same reality (Space-Time continuum)
Relativity of the reference system
“Absoluteness” of the laws of Physics
Light unifies Space and Time
Velocity of Light c=300,000 Km/s
=3x10^8 m/s=6.7 x 10^8 miles/hour
Equivalence Principle:
the fundamental principle that unifies inertial and
gravitational mass
M_inertial=M_gravitational
This simple experimental fact is the
essential basis for Einstein’s theory of
Gravity: General Relativity
Acceleration
It is not possible to distinguish between gravity
and an uniformly accelerated system
Gravity can be
simulated by an
accelerated system
The absence of gravity is
equivalent to free fall
The presence of gravity can be
neutralized in a
Reference system in free fall
The observer in free fall with the
elevator doesn’t see any change
in the vertical position of the
sphere
In the meanwhile the observer on
the ground sees an horizontal and
vertical change in position and
interprets the motion as a
“curved” path
Also light can be bent
The other way around If the
acceleration is produced by
gravity
As observed by the
observer inside the
elevator
Gravity = curvature in the
Fabric of Space-Time
if acceleration
is produced by rocket
this is what it will be observed
As
observed
by
external
observer
The essential effects of gravity
are of tideal nature
The difference is
that gravity has
GLOBAL
Geometric
properties
(locally just
undistinguishable
from accelerated
frame)
Curvature of Space Time caused by the
sun
This is a quasi-static
situation for what
concerns space-time
Matter tells space-time how
to curve; the curvature
“tells” to matter how to
move
Einstein ‘s Equation
G= 8pG/c^4 T
http://www.pbs.org/wgbh/nova/einstein/relativity/ani
mations.html
Acceleration of Mass
creates Gravitational
Waves
The waves travel at the velocity of light
(3x10^8m/s) and the waves’ amplitude
goes downs with distance
Gravitational radiation has 2 polarizations and the energy is
emitted mostly in the quadrupole (“football shape distribution
of matter required”)
Polarization
(cross) x
The wave arrives in
the direction
perpendicular to the
circle
Polarization
(plus) +
Sources of gravitational
waves
• Supenovae
• Neutron Stars that rotate (or wobble in space)
• Coalescent Binary Systems of Black Holes and/or
Stars
• Cosmic Background
caused by the Big Bang
Neutron
Detectors of Gravitational Waves
• Resonant Bars (LSU)
• Sphere (Rome ?)
• Interferometers
(LIGO)
Resonant Bars
Cylindrical Bars, typically made of alluminum
(about 1 ton. ). They work on the principle of
resonance, they are tuned at about 1000 Hz, the
resonant frequency of neutron stars . The wave
interacts with the bar and the motion is
transmitted to a sophisticated “microphone”
that transform the mechanical motion into an
electrical impulse: this is our signal.
The noise Problem
Noise
is bigger
than signalHow
in thetocurrent
Sources
of noise:
control
detectors (we don’t see anything than
• Seismic
(suspension system)
noise !). Noise at h=10^-20
maybe at h=10^-21
or less
• Signal
Thermal
(low
temperature)
• Eletronic tools to extract
(SQUID)
Mathemathical
signal: Filtering. For continuous
signals: Integration with long
observation times.
Interferometers
Mirror
• LIGO (USA, Louisiana & Washington)
Vacuum Pipes
4 km
• VIRGO (ITALY, Pisa)
Mirror
•TAMA (JAPAN)
• GEO 600 (GERMANy, Postdam)
Semi-transparent Mirror
Laser 10 Watts
Range of sensitivity on
• LISA
(NASA-ESA,
In
space,
2016)
earth 10-1000 Hz
In space 10^-4-1 Hz
Photodetector
Neutron stars
Continuous sources. They rotate up to frequencies
of 1000 Hz. To emit GW they have to be tri-axial
(football shaped).
They can also wobble:
The strain (h=deformation/length measured ) if axis of rotation
doesn’t coincide with
for a star with 3 axis is:
symmetry axis. In this
G
case star doesn’t need
2
h  2 4  I sin( 2t )
to be a football to emit
c R
Gravitational Waves.
Burst sources:
Supernovae and Coalescent
Systems
•Explosion of Supernovae have to be asymmetric
to radiate gravitationally. The neutron star that is
left over after the explosion vibrate violently
(~1000 Hz)
•Coalescent Systems: compact objects as black holes
and neutrons stars. Binary Systems are very “football
shape” like. They emit Gravity Waves so they loose
energy. The system is inspiraling until it collides (in
time scales of millions of years). Indirect evidence of
GW: pulsar 1913+16 (Taylor and Hulse: 1993 Nobel
Prize winners).
Cosmic Background
• The most ancient evidence of the birth of the Universe.
Electromagnetic Background300,000 years after the Big Bang
(a young baby, 0.7 day old).
• Gravitational Background is a “polaroid” of the birth of the
Universe (as it was born !) Gravity doesn’t interact a lot with
matter.
• We don’t know what to expect but we have some vague ideas
from other cosmological observations.
Conclusion: What can we learn
from Gravitational Waves?
• Another, fundamental confirmation of General
Relativity (Viva Einstein !)
•New window on the Universe.
•Radiation very different from EM and particles.
•Bulk Motion of mass.
• GW do not interact well with matter. We can probe
very high density region of the universe as neutron
stars and the core of black holes.
• Birth Cry of the Universe.