Transcript Option J: Particle physics

Option J: Particle physics
J6 Cosmology and strings
J.6.1 State the order of magnitude of the
temperature change of the universe since the
Big Bang.
J.6.2 Solve problems involving particle
interactions in the early universe.
J.6.3 State that the early universe contained
almost equal numbers of particles and
antiparticles.
J.6.4 Suggest a mechanism by which the
predominance of matter over antimatter has
occurred.
J.6.5 Describe qualitatively the theory of
strings.
Option J: Particle physics
J6 Cosmology and strings
State the order of magnitude of the temperature
change of the universe since the Big Bang.
●In his astronomical studies in 1929,
Edwin Hubble observed that the red shift
of galaxies increased in proportion to
their distance away from us.
●An expanding universe would explain such
a red shift.
●As an analogy, consider a balloon covered with
ink dots. As you blow up the balloon, each dot
recedes from every other dot.
●Not only that, note that the farther away the
dots are, the faster they recede.
Option J: Particle physics
J6 Cosmology and strings
State the order of magnitude of the temperature
change of the universe since the Big Bang.
●Calculating backward, we find that the universe
began expanding about 15 billion years ago.
●We can imagine that whatever energy was in it at
the beginning, is still in it at the present.
●Since the volume is increasing, the energydensity is decreasing, so that the temperature of
the universe is always decreasing.
●The universe had a very early
temperature of more than 1032 K.
It has a current temperature of
2.7 K, as determined by Penzias
and Wilson in 1960.
FYI
We call the beginning of the
universe the “Big Bang.”
Option J: Particle physics
J6 Cosmology and strings
State the order of magnitude of the temperature
change of the universe since the Big Bang.
●The physics you have studied up to this time is
based on the fundamental measurements of length
and time.
●At the beginning of the Big Bang, which is when
the universe came into existence, there was no
length or time — the most basic quantities of
physics as we know it.
●Thus we know next to nothing about the physics
of the first 10-43 s after the Big Bang.
●But from 10-43 s to about 10-35 s, we can estimate
that the temperature of the universe must have
been about 1032 K.
FYI
This is equivalent to a particle energy of about
1019 GeV. Our colliders cannot attain this value.
Option J: Particle physics
J6 Cosmology and strings
State the order of magnitude of the temperature
change of the universe since the Big Bang.
Grand
Unification
Era
u
u


d

d
t = 0 - 10-35 s
T   - 1032 K
t = 10-35–10-12 s
T = 1032 - 1015 K
e+ e
-
●In the Grand Unification Era, photons became
particle-antiparticle pairs and particleantiparticle pairs annihilated back into photons.
●This free exchange between matter and energy
(its unification) continued until about 10-12 s.
Option J: Particle physics
J6 Cosmology and strings
State the order of magnitude of the temperature
change of the universe since the Big Bang.
●At 10-12 s the universe had expanded to a size
that “spread out” the energy to the extent that

the temperature was
Particle

15
about 10 K (100 GeV). Era
●At this temperature,
the quarks can now
d
dnu
combine to form protons,

neutrons, and the other
u
mesons and baryons that
pu
d
we see today.
●This is termed the
Particle Era.
FYI
t = 10-12 – 10 s
T = 1015 – 1010 K
These energies can be
attained by particle accelerators.
e+ e
-
Option J: Particle physics
J6 Cosmology and strings
State the order of magnitude of the temperature
change of the universe since the Big Bang.
●At 3 minutes the universe had cooled to a
temperature of about 109 K (0.1 MeV).
●At this temperature, Nuclear

the nucleons can now Formation

Era
combine to form
p
simple nuclei of
p
p
H+ and He+2.
●This is termed the

p
p
Nuclear Formation
p
Era.
n p
p n
●At the end of this
p
era the universe
p
consists of roughly
e e
90% hydrogen and 10%
3
t = 10 – 10 s
helium ions.
T = 1010 - 104 K
+
-
p
Option J: Particle physics
J6 Cosmology and strings
State the order of magnitude of the temperature
change of the universe since the Big Bang.
●At 105 years the
universe had cooled Recombination
e
Era
to a temperature of
p


e
4000 K (0.4 eV).
p
●At this temperature, the electrons
can now combine
e
e

with the nuclei to
p
p
e
e
form neutral atoms.
p
n p
●This is termed the
p n
Recombination Era.
e
●It is still too
p
hot for gravity to
e
pull atoms
p
t = 103 - 1013 s
together.
T = 104 - 3000 K
-
-
e-
p
-
-
-
-
-
-
p
Option J: Particle physics
J6 Cosmology and strings
State the order of magnitude
change of the universe since
●At 109 years the
Galaxy
universe had cooled
Era
to the point that
gravity could start
making matter accrete
into stars.
●And stars can now
begin to gather into
galaxies.
●This is termed the
Galaxy Era.
●We are in this era now.
●The higher elements are
produced in the stars from
hydrogen and helium.
of the temperature
the Big Bang.
t > 1013 s
T = 3000 – 2.7 K
Option J: Particle physics
J6 Cosmology and strings
Solve problems involving particle interactions in
the early universe.
●Because of the high temperatures of the early
universe, all of the particle interactions we
have studied can occur. These we can do!
●There is a new formula that we should know – one
which relates the temperature of the universe to
the average kinetic energy of particles:
EK = (3/2)kT
Boltzmann’s
equation
Where k = 1.3810-23 J K-1.
EXAMPLE: At what temperature will e-/e+ pairs stop
being created out of the ambient energy of space?
SOLUTION: Use EK = (3/2)kT  T = 2EK/(3k).
●EK = 2(0.511 MeV)(1.610-19 J/eV) = 1.63510-13 J.
T = 2EK/(3k)
= 2(1.63510-13)/[3(1.3810-23)] = 7.9109 K.
Option J: Particle physics
J6 Cosmology and strings
State that the early universe contained almost
equal numbers of particles and antiparticles.
●As alluded to in the beginning of this slide
show, the early universe was extremely hot right
after the Big Bang.
●High-energy photons, the leptons and quarks and
their antiparticles made up the cosmic soup in
the early universe.
●It is believed that at this point there was for
each particle a corresponding antiparticle, and
that pair production and annihilation were
occurring in an equilibrium state.




e-+
e

d
d
Option J: Particle physics
J6 Cosmology and strings
Suggest a mechanism by which the predominance of
matter over antimatter has occurred.
●Back in previous lectures you learned about
spin, which is a rather abstract concept if you
consider the wave/particle duality of matter —
after all, how does a WAVE spin.
●What SPIN really represents is a form of
SYMMETRY in the context of answering the question
“how much of a complete circle must we rotate an
object in order to bring it back into its
original configuration.”
FYI
As an aside, an electron has a spin number of
1/2, which means, using this model, that it must
be rotated through TWO COMPLETE REVOLUTIONS to
regain its original configuration.
●Obviously this is difficult to picture!
Option J: Particle physics
J6 Cosmology and strings
Suggest a mechanism by which the predominance of
matter over antimatter has occurred.
●Consider the three objects below:
1/4 rotation to
regain original
configuration
1/2 rotation to
regain original
configuration
1/1 rotation to
regain original
configuration
SPIN NUMBER:
SPIN NUMBER:
SPIN NUMBER:
1/1 OR 1
2/1 OR 2
4/1 OR 4
●First, find the rotation needed to bring each
object back to its original configuration:
●To find the spin number, take the reciprocal of
the partial rotation needed to regain the
original configuration:
Option J: Particle physics
J6 Cosmology and strings
Suggest a mechanism by which the predominance of
matter over antimatter has occurred.
●Recall that particles which carry force (gluons,
photons, W+, W-, Z0) have whole-integral spins,
whereas leptons and baryons (electrons, protons,
neutrons, etc.) have half-integral spins and that
all particles have spins in the range
{-2, -3/2, -1, -1/2, 0, 1/2, 1, 3/2, 2}.
●Recall furthermore that particles with halfintegral spin numbers obey the Pauli exclusion
principle, and particles with whole integral
spins do NOT.
●The particles having half-integral spins are the
matter particles, and the particles having the
whole-integral spins are the force particles.
Option J: Particle physics
J6 Cosmology and strings
Suggest a mechanism by which the predominance of
matter over antimatter has occurred.
●Now that we have a slight handle on the
importance of symmetry and the Pauli exclusion
principle, we would like to introduce you to
three different types of symmetry: The so-called
Charge, Parity and Time-reversal symmetries.
●A rough feel for these three symmetries is
needed in order to understand how the universe,
which was created with equal numbers of particles
and antiparticles, ended up as it is todaypredominantly more matter than antimatter
(instead of totally annihilated!).
Option J: Particle physics
J6 Cosmology and strings
Suggest a mechanism by which the predominance of
matter over antimatter has occurred.
●Symmetry C(harge): “The laws of physics are the
same for matter and antimatter.”
EXAMPLE: Symmetry C: The Coulomb force has
exactly the same effect on a positron as it does
on an electron, because it only acts on charge.
●Symmetry P(arity): “The laws of physics are the
same for any situation and its mirror image.”
EXAMPLE: Symmetry P : The Coulomb force has
exactly the same effect on an electron whose spin
is clockwise as the same electron whose spin is
counterclockwise. Charge doesn’t depend on spin.
FYI
These two symmetries seem reasonable and
understandable.
Option J: Particle physics
J6 Cosmology and strings
Suggest a mechanism by which the predominance of
matter over antimatter has occurred.
●Symmetry T(ime reversal): “The laws of physics
are the same in the forward and backward
direction of time.”
EXAMPLE: Symmetry T: If you reverse the
directions of all particles and antiparticles in
a particle interaction, the system should go back
to its original configuration.
●Up until 1956 it was believed that the laws of
physics obeyed each symmetry (C, P, and T).
●In 1956, however, it was suggested, and soon
verified, that the weak force
interaction did NOT obey symmetry
P. In other words, the weak force
would make our universe develop
in a different way from a mirror
image of our universe!
Option J: Particle physics
J6 Cosmology and strings
Suggest a mechanism by which the predominance of
matter over antimatter has occurred.
●As an interesting side note, the weak force WAS
believed to obey a combined CP symmetry, wherein
a mirror image antiparticle universe would
develop exactly the same as ours!
●This CP symmetry was later found to NOT be
obeyed by the decay of K-mesons, thus
establishing a fundamental asymmetry between
matter and antimatter.
FYI
This symmetry P (spin) violation of the weak
force causes matter to predominate in our present
universe. Live with it.
●I have a headache! IBO just says “once the
universe cooled enough, photons no longer
materialized into particle-antiparticle pairs.”
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●The history of physics (and all of the sciences)
is built up of partial theories – theories that
describe a limited range of happenings, and
perhaps neglect other effects, or approximate
them without understanding them.
EXAMPLE: Chemical reactions in chemistry can be
predicted without any knowledge of the internal
structure of the nucleus of the atoms. Thus, we
have a partial theory on how atoms chemically
combine (valence electrons, etc.) and we have a
partial theory on nuclear physics (to predict
such things as fusion and fission) and each
theory is valid in its own realm, but not in its
counterpart’s realm.
●The two partial theories of physics are quantum
mechanics and relativity.
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●Quantum mechanics very precisely describes the
world of the very small, and general relativity
precisely describes the world of the very large.
●One of the overarching goals of physics
is to somehow develop a theory that
explains both quantum mechanics and
relativity in a single unified theory.
●The strong, weak and electromagnetic
forces have all succumbed to a quantummechanical theory, whereas gravity has
remained a classical (non-quantum
mechanical) theory.
●Since quantum mechanics has as its root
Heisenberg’s uncertainty principle, the
key, then, is to somehow insert the HUP
into the gravitational partial theory.
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●To date, such an approach has not been
successful. In fact Einstein failed at such an
approach. Indeed, he may have tried halfheartedly, since he really did not like the
uncertainty principle philosophically: “God does
not play dice!”
●Ironically, Einstein’s photoelectric effect was
instrumental in bringing about the quantum
mechanical revolution!
●In 1972, a theory called supergravity attempted
to incorporate the HUP into relativity. In this
theory, a graviton (spin 2) was combined
(theoretically) with other new particles (with
spins of 3/2, 1, 1/2, and 0) in such a way that
all the particles could be considered as
manifestations of a single superparticle.
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●Thus, the force particles (spin 0, 1, and 2)
were unified with the matter particles (spins 1/2
and 3/2).
●Unfortunately, the theoretical calculations
needed to prove the viability of this theory were
so difficult that no one took them on.
●Even using the best computers of the time would
have taken calculations lasting four years, at
the end of which time even the smallest error
would have caused incorrect results.
●In 1960, a “string” theory was invented to try
to describe the strong force (before much was
known about it).
FYI
The idea was that particles could be regarded as
waves on a string.
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●The strong forces between the particles were
pieces of string that connected them (kind of
like a spider web).
●These strong force strings were visualized as
rubber-band-like, having only the length
dimension, and capable of a tension of the order
of ten tons.
●This early theory never caught on because quarks
were soon discovered and a theory based on quarks
and gluons yielded positive results with less
effort.
●In 1974, Scherk and Schwarz published a paper
that showed that string theory could be applied
to the gravitational force, provided that the
tension in the strings were of the order of 1039
tons!
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●Scherk and Schwarz showed in their paper that
their theory predicted the exact results of the
general theory of relativity on the normal range
of scales, but that they would predict new and
unusual results on the very small scale.
●In effect, this theory coupled with the string
theory for the strong force, showed a promising
link between quantum mechanics and relativity.
●For the same reason the strong-field string
theory was neglected (the quark theory and the
standard model) and
because Scherk
tragically died, the
gravitational string
theory was not
aggressively pursued.
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●Another “problem” was that string theories seem
to lead to the requirement for more than three
spatial dimensions (space-time must have anywhere
from 10 to 26 dimensions!) which didn’t set well
with many scientists (yourself included, if you
look deep down inside!).
EXAMPLE: Why do we “see” only 3 spatial and one
time dimension if there are so many spatial
dimensions?
SOLUTION: Because the “unseen” dimensions are
curved up into a very tiny space that is
something like 10-30 inches in size! So spacetime
is “smooth” at large-scale, and very “bumpy” at
small-scale dimensions, where the remaining
spatial dimensions become manifest.
●This is how the quantum effect can be introduced
into the spacetime of relativity.
●Spacetime is grainy at the quantum level.
●The “extra” spatial dimensions required by string
theory are “curled” in upon themselves and only visible
at very small dimensions.
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
FYI
Remember how it was discussed that high energy
accelerators were needed to produce particles of
large mass, and see dimensions of small scale? So
far we have not observed any of these curled-up
dimensions, but perhaps CERN may be able to
produce enough energy to see them.
●Do some research online, or calculations, or
both, to see if this is so.
 = hc/E
wavelength – energy relationship
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●In 1984 interest in strings revived for two
reasons:
(1) People were not making much progress
toward showing that supergravity could explain
the kinds of particles that we observe.
(2) The publication of a paper by Schwarz and
Green that showed that string theory might be
able to predict a property called lefthandedness exhibited by some particles
same string
and unexplained by other theories.
●String theories assume that particles
and forces are not points, but rather,
are strings.
●And different particles can be
manifestations of a single string under3 particles!
going different resonant oscillations:
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●The previous strings are examples of “open”
strings. Each end of an open string is free.
●There are also closed strings (loops) where
the ends are connected to each other.
●Besides the fact that no experiment
to date has revealed any sign of
even one additional spatial
dimension, there are a few
additional problems with string
theory.
(1) We do not yet know if all the
singularities (infinities) of the
theory cancel out.
(2) We do not yet know exactly how to
relate the waves on a string to the
particular types of particle that we observe.
Option J: Particle physics
J6 Cosmology and strings
Describe qualitatively the theory of strings.
●Finally, Feynman diagrams can be used for
strings as well as traditional particles:
x
x
t
t
Two
particles
coalescing
Two closed
strings
coalescing
Option J: Particle physics
J6 Cosmology and strings
Solve problems involving particle interactions in
the early universe.
●This is the remnants of the radiation of the
Big Bang.
●Since the universe is expanding, it is
cooling.
●It is currently at about 2.7 K, as observed
by Penzias and Wilson in 1960.
Option J: Particle physics
J6 Cosmology and strings
Solve problems involving particle interactions in
the early universe.
●All points will be
below present graph.
●Peak will be to
the right of
present graph.
●Temperature will be lower.
Option J: Particle physics
J6 Cosmology and strings
Solve problems involving particle interactions in
the early universe.
N
●The Nuclear Formation Era was at
t = 10 to 103 s and 1010 - 104 K.
●The Galaxy Era was
at t > 1013 s and T
= 3000 to 2.7 K.
G
Option J: Particle physics
J6 Cosmology and strings
Solve problems involving particle interactions in
the early universe.
●Since light travels at a finite speed, the
farther away a galaxy is, the farther back in
time we are observing.
●Thus at a previous time the temperature of
the universe was about 7 K, and now it is
about 3 K.
●Thus the universe is cooling.