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 physicsJ6 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.


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 energy-density 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.


FYIWe call the beginning of the universe the “Big Bang.”

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.


FYIThis is equivalent to a particle energy of about 1019 GeV. Our colliders cannot attain this value.

State the order of magnitude of the temperature change of the universe since the Big Bang.

●In the Grand Unification Era, photons became particle-antiparticle pairs and particle-antiparticle pairs annihilated back into photons.●This free exchange between matter and energy (its unification) continued until about 10-12 s.


T - 1032 Kt = 0 - 10-35 s t = 10-35–10-12 s

T = 1032 - 1015 K

e-e+

u

dd

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Grand UnificationEra

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 about 1015 K (100 GeV).●At this temperature, the quarks can now combine to form protons, neutrons, and the other mesons and baryons that we see today.●This is termed the Particle Era.


FYIThese energies can be attained by particle accelerators.

t = 10-12 – 10 sT = 1015 – 1010 K

e-e+

ud

ParticleEra

d

u udp

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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, the nucleons can now combine to form simple nuclei of H+ and He+2.●This is termed the Nuclear Formation Era.●At the end of this era the universe consists of roughly 90% hydrogen and 10% helium ions.


t = 10 – 103 sT = 1010 - 104 K

e-e+

NuclearFormationEra

pn pn

p

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pp p

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State the order of magnitude of the temperature change of the universe since the Big Bang.●At 105 years the universe had cooled to a temperature of 4000 K (0.4 eV).●At this temperature, the electrons can now combine with the nuclei to form neutral atoms.●This is termed the Recombination Era.●It is still too hot for gravity to pull atoms together.


t = 103 - 1013 sT = 104 - 3000 K

e-

RecombinationEra

pn pn

p

p

p

p p

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pe-

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e- e-

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State the order of magnitude of the temperature change of the universe since the Big Bang.●At 109 years the universe had cooled 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.


t > 1013 sT = 3000 – 2.7 K

GalaxyEra

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:


Boltzmann’s equation

EK = (3/2)kTWhere k = 1.3810-23 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)(1.610-19 J/eV) = 1.63510-13 J. T = 2EK/(3k) = 2(1.63510-13)/[3(1.3810-23)] = 7.9109 K.

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

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.”


FYIAs 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!

Suggest a mechanism by which the predominance of matter over antimatter has occurred.●Consider the three objects below:

●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:


1/4 rotation to regain original configuration



SPIN NUMBER: 4/1 OR 4



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 half-integral 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.


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 today-predominantly more matter than antimatter (instead of totally annihilated!).


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.”

●Symmetry P(arity): “The laws of physics are the same for any situation and its mirror image.”


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.

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.FYIThese two symmetries seem reasonable and understandable.

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.”

●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!


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.

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.


FYIThis 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.”

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.

●The two partial theories of physics are quantum mechanics and relativity.


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.

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 quantum- mechanical 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.


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 half-heartedly, 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.


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).


FYIThe idea was that particles could be regarded as waves on a string.

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!


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.


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.

Describe qualitatively the theory of strings.


FYIRemember 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.

wavelength – energy relationship = hc/E

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 left- handedness exhibited by some particles 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 under- going different resonant oscillations:


same string

3 particles!

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.


Describe qualitatively the theory of strings. ●Finally, Feynman diagrams can be used for strings as well as traditional particles:


Two particles coalescing

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Two closed strings coalescing

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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.



●Temperature will be lower.

●All points will be below present graph.●Peak will be to the right of present graph.



●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.

N

G



●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.

Option J: Particle physics J6 Cosmology and strings

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