CVSP 204 K.M. Bitar 1
Nature of Space –Time
Curvature As Gravity
***
The Quantum Nature of Physical
Laws
CVSP 204 K.M. Bitar 2
Abstract
• Understanding the “nature” of Time and Space.
• Gravity as a property of space-time “curvature”
• An overview of the 'standard model' for interactions of radiation and matter: Quantization
• An understanding of the “origin of the universe from a physical point of view”.
Historical Milestones
• Aristotelian Universe
• Ptolemy
• Copernicus
• Kepler
• Newton Gravity – Mechanics-Calculus
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E&M
• Coulomb Electrostatics
• Ampere Currents and Magnetic fields
• Faraday Time changing fields create
electric fields
• Maxwell Time changing electric fields
create magnetic fields.
Hence Electromagnetic waves : Light &
Unification of electric and magnetic forces ! CVSP 204 K.M. Bitar 4
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1900: Classical Physics covered by
two laws:
• Newton‟s laws of “gravitation”
• Maxwell‟s equations
q
q1
Q
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Inverse Square Laws
Newton‟s law of gravitation:
F ~ G M m / R2
Coulomb‟s law of Electrostatics F ~ Q q / R2
Both require Instantaneous “action at a distance”
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“Classical” Space & Time
• Space is three dimensional ( Up –Right-
forward …and opposite directions)
• Time is absolute
• All phenomena are taking place on this
„stage‟ as time „flows‟.
Velocity is relative:
• Two observers ( 1 &2) moving at constant
velocity V relative to each other measure
two different velocities for the same object
they observe:
• V2 = V1 + V
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However
• Maxwell’s equations for E&M waves
(light !) indicate a Constant velocity for
ALL such waves including light.
• The Michelson Morley Experiment
confirms this:
“The speed of light is found to be
independent of the speed of the source or
the observer”
in contrast to every thing else…….
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20th Century Milestones
• 1900 Quantization of the energy of light
Plank : E= h X Frequency
Photons Introduced
• 1905 Special Relativity
Einstein : Time and space are not absolute
Mass is Energy
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Milestones “Cont‟d”
• 1916 Gravity reformulated
Einstein: Gravity is “curved space time”
• 1925 Quantum Mechanics
Schrodinger/ Heisenberg/Dirac:
Structure of Atoms and “Anti Matter” Must
exist
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Basic Concepts
• Space and Time Intervals are “relative” to
the observer and NOT absolute.
• Energy is extended to include “Mass”
• Gravitation is a reflection of the “Geometry
of Space/Time”
• “Quantum Behavior” is fundamental for
understanding natural phenomena.
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1905
Proposal by Einstein that the
“Speed” of light is constant for all inertial
observers as it travels in “vacuum”
( explicit in Maxwell‟s equations!)
i.e. the same for all observers moving with
relative CONSTANT velocities to each
other
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Space -Time
He further proposed to treat Space Time as a four dimensional coordinate system
(3 space + 1 time)
and that the
laws of Physics are invariant in FORM
under transformations between inertial reference frames (i.e. Observers moving at constant
velocities relative to each other)
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Space-Time: Cont‟d
Time and Space intervals may then
transform (i.e. as seen by different
observers) into each other and so would
many „Physical‟ observable quantities!
Examples:
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Lorentz Transformations
t„ = γ ( t β x )
x„ = γ (x – β t )
Where β = v/c
which is less than ONE
and γ = ( 1- β2 )-½
which is always then greater than ONE.
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Time dilatation
two „events‟ at the same place as seen by
one observer at times t1 and then t2 are
separated by a time interval of :
T=t2 –t1
Would appear for another observer at times
T‟=t2‟-t1‟= γ (t2 –t1)
T‟ = γ T > T
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Space Contraction
If we consider two events at the same time
but at x1 and x2 the „space‟ separation for
one observer which is
L = x2 – x1
Will appear for the moving observer as
L‟ = x2‟ – x1‟ = L / γ < L
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Time and Space
Time and Space „intervals‟ separating two
„events‟ then acquire a new meaning and
are dependent on the relative speeds of
observers of these events.
and
There is no absolute space time !
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Momentum and Energy are also
components of the same four dimensional
„vector‟ and do transform into each other!
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Energy Momentum four vector
(Pc , E)
length preserved
P2c2 - E2 = P‟2c2 - E‟2
For P=0
„rest‟ energy is :
E = m c2
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Cosequence
Mass is a measure of rest Energy
↓
Mass and Energy may be interchanged!
↓↓
This leads later to the Understanding of radioactivity
and later fission
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Pair Production and Annihilation
Photons (light) may change to massive
objects (particles)!
γ → e+ + e-
Electron positron pairs (particles) may Annihilate and
produce
two photons (light)
e+ + e- → γ + γ
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1916: General Relativity
Principle of Equivalence
Gravitational field indistinguishable from
being in an „accelerated‟ frame of
reference !
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Curved Space Time
Accelerated frames may be represented
mathematically by
„curved space times‟
and hence so would the effect of a
gravitational field!
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Geometry and the Gravitational
Force are ONE!
Gravitational forces are an effect seen as
motion along geodesics of a curved
space time
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Other large scale consequences
Einstein equations imply that space and
time and their Geometry are dynamical
variables!
↓↓
UNIVERSE is not STATIC!
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Effects
Bending of light in a gravitational field (yes)
Extreme case : Black holes! (yes)
„Ripples‟ in the Curved Geometry leads to Gravitational waves! (not yet)
(counterpart to EM waves!)
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Expansion ? Contraction?
Observations show that the Universe is
EXPANDING !
Distances between its constituents is
increasing as measure by the
RED shift
of the spectrum of light received for distant
objects!
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Origin?
An expanding Universe must have started
from a smaller universe ……
A BIG BANG!?
Estimated „age‟ can be determined by the
distance of the farthest objects ……
Current estimate
13 Billion years
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Physics at short distances then is as important to study the
ORIGIN of the UNIVERSE
as it is to study the structure of
ATOMS and NUCLEI !
↓↓
Quantum Mechanics
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On another front when studying radiation by
“hot” bodies
It is found that Classical E&M theory …..
Cannot explain the spectrum of such radiation …
To understand this spectrum required another
|drastic new assumption
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The Quantum of light
Proposal in 1900 by
Max Planck
That energy in light (E&M waves) is carried in packages each with amount:
E= h x frequency of light
With h= universal constant!
The package named „Photon‟ Is introduced
Classical E&M waves are streams of such photons
Interactions
• E&M interactions are then between
charges and these “Photons”.
• These interactions are transmitted at “light
speed” ….not instantaneous …..
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Atomic Spectra
• Light emitted by atoms and molecules
comes in specific frequencies
“characteristic of those atoms and
molecules” …..Atomic signature …..
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Short distance Physics
1924: Quantum Mechanics 1. Physical systems exist in well defined states identified by
some measurable quantities such as energy, angular momentum etc….
2.Systems transform themselves between these states with predictable „probabilities‟.
3.One can „fix‟ the state of a system only „after‟ a measurement.
4. „Likelihood‟ of the system to exist in other states after that can be calculated using „quantum mechanical‟ equations of „motion‟ of such states.
5. „Classical‟ quantities need not be all precisely known in a particular state: uncertainty relations exist!
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1926: Relativistic QM
Dirac equation combines QM with Special
Relativity
↓↓
Prediction of ANTI MATTER
↓↓
Discovery of Positron (e+) , anti-proton (p-)
Anti-neutron (n0), etc…..
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Further developments of
Relativistic Quantum Mechanics
The study of general interactions of EM radiation (photons) with Matter (electrons , protons etc…) necessitated the invention
of methods to generalize the Dirac equation to many (infinite!) „particle‟
systems.
↓↓
Quantum Field Theories of particle interactions
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Point Interactions
Photon emission by e
Photon emission by e+
Photon absorption by e
Photon absorption by e+
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Scattering
e- e+ Scattering: lowest
order
• Pair Production
• Pair Annihilation
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General Interactions
Higher order e – e+ Scattering
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Characteristics
• All interactions are point like !
• Interactions involve multitude of processes
• The net effect is obtained as a result of the
collective effect of all such interactions.
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Even Shorter Distances
Nuclear Forces
These are responsible for binding the Nucleus
Weak Forces
Responsible for decay of neutrons to protons (among other things!)
C14 → N14 + e + ν
Change of the nature of matter ….
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The nature of such interactions Is
just the same as Electron Photon
Interactions but more
Complicated
and
Involve a large number of
particles
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The Standard Model
The fundamental particles come in two
general categories:
1. Matter particles which carry mass
2. Radiation which has mass = 0
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Massive particles
• These come in two classes:
• Quarks that are constituents of „hadrons‟
(protons, neutrons ,etc…)
• Leptons
(electrons, muons )
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Quarks
Quarks come in
six
flavors and
three
colors!
• u d s u d s u d s
• c t b c t b c t b
• AND carry fractional Electric Charge ± 1/3, ± 2/3 e
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Leptons
Leptons carry a characteristic known as
lepton number and come in also
six
families
but
These particles carry integral charges ± e
Each family has associated with it a
(massive ?) Neutrino
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Mass less particles
Gluons
(g)
These are 8 photon like objects that carry a „color‟ and an „anti-color‟ each and couple only to „color‟
Weak Bosons
( W+, W- , Z0 )
These are three that couple to leptons and quarks
They acquire heavy masses due symmetry breaking by
“Higgs Boson”
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Interactions
Gluons
Interaction is point like and takes the following forms
leads to a stronger force as the distance increases !
This „strong‟ force is „confining‟…..NO escape for Quarks or Gluons !
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Detection of gluons and Quarks
Gluons → 3 jets
Quark events → 2 Jets
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Hadron (proton , Neutron etc…)
Structure
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Structure of Atoms
Atoms….
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Mesons
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Forces
Mediators :
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Particle Chart
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• History of the Universe
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Strings?
The current pictures is experimentally
verified ..but TOO complicated !!
Is there a simpler set of fundamental
constituents?
Strings ( two dimensional objects) may
provide the answer …..
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Indicators ….
Strings seem to point the way to a
UNIFICATION of Gravity with the
Standard Model ……
The good news …
A lot left for you to Pursue ….