PHY Final
The Demarcation Problem
*Karl Popper (1902-1994)* Key idea: empirical falsifiability falsification is the demarcation between science and non-science Nothing can ever be proven true. A scientific idea can be only be proven false
running coupling constant
• A coupling constant is a number that determines the strength of the force exerted in an interaction • For example, the electric charge of a particle is a coupling constant (so would it's mass for a theory of gravity) • A coupling constant plays an important role in dynamics. • We set up hierarchies of approximation based on the importance of various coupling constants. In the motion of a piece of magnetized iron, the magnetic forces are more important than the gravitational forces because of the relative magnitudes of the coupling constants • One of the most profound features of QFT is the prediction that the coupling constants "run", or change, with energy. There is no classical analogue of this effect. • The forces act differently at different energy levels. • The strong and weak force become "weaker" at high energies • The electromagnetic force becomes "stronger" at high energies • The three forces almost meet at one point. Almost...
Weak force
• A force which is responsible for radioactive decay (except alpha decay) and nuclear fusion • the range if the weak force is 0.001 fm • Beta decay = n -> p + β- + anti-neutrino • How do you know? • if a reaction is weak It involves leptons Overall change in quark flavour Strangeness not conserved
what is a group
• A group is a set of elements together with an operation that combines any two of its elements to form a third element satisfying four conditions called the group axioms • Closure, Associativity, Identity, Invertibility • For instance: the integers with addition • Groups share a fundamental kinship with the notion of symmetry. • A symmetry group encodes symmetry features of a geometrical object: the group consists of the set of transformations that leave the object unchanged and the operation of combining two such transformations by performing one after the other
spin networks
• A spin network is a type of diagram which can be used to represent states and interactions between particles and fields in quantum mechanics • This is the LQG equivalent of a Feynman diagram in particle physics • The diagrammatic notation often simplifies calculation because simple diagrams may be used to represent complicated functions • Three line segments join at each vertex (note the funny terms) • Each line segment is labeled with an integer called a spin number • A unit with spin number n is called an n-unit and has angular momentum nħ • For bosons, such as photons and gluons, n is an even number. For fermions, such as electrons and quarks, n is odd • A vertex may be interpreted as an event in which either a single unit splits into two or two units collide and join into a single unit • Diagrams whose line segments are all joined at vertices are called closed spin networks • Given any closed spin network, a non -negative integer can be calculated which is called the *norm* of the spin network. • Norms can be used to calculate the *probabilities* of various spin values. A network whose norm is zero has zero probability of occurrence (just like a path integral)
symmetries
• A symmetry of a physical system is a physical or mathematical feature of the system (observed or intrinsic) that is preserved or remains unchanged under some transformation • Spacetime symmetries are features of spacetime that can be described as exhibiting some form of symmetry • *Time translation:* A physical system may have the same features over a certain interval of time • *Spatial translation:* The system does not change with a continuous change in location • *Spatial rotation:* The system does not change with a rotation • *Poincaré transformations, Projective symetries, Inversion transformations* • The symmetry properties of a physical system are intimately related to the conservation laws characterizing that system • Noether's theorem gives a precise description of this relation • For example, spacial symmetry gives rise to the conservation of (linear) momentum, and time symmetry gives rise to conservation of energy • Note: these are the same variables related in Heisenberg's uncertainty principle • Some of these symmetry groups are more abstract. • These abstract symmetries are best described by groups.
interpretations of quantum mechanics
• An interpretation of quantum mechanics is a set of statements which attempt to explain how quantum mechanics informs our understanding of nature • Although quantum mechanics has held up to rigorous and thorough experimental testing, many of these experiments are open to different interpretations • It is important to understand that no matter the interpretation, the predictions of the theory are always the same. • All interpretations of quantum mechanics share two qualities • They interpret a formalism—a set of equations and principles to generate predictions via input of initial conditions • They interpret a phenomenology—a set of observations, including those obtained by empirical research and those obtained informally, such as humans' experience of an unequivocal world • Many of the greatest minds in physics had trouble with the probabilistic nature of quantum mechanics. This lead to the idea of hidden variables. • The simplest interpretation is called, "shut up and calculate"
confinement
• As any two electrically charged particles separate, the electric fields between them diminish quickly, allowing electrons to become unbound from atomic nuclei (ionization) • However, as a quark-antiquark pair separates, the gluon field forms a narrow tube (or string) of color field between them • Because of this behavior of the gluonic field, a strong force between the quark pair acts constantly—regardless of their distance • When two quarks become separated, as happens in particle accelerator collisions, at some point it is more energetically favorable for a new quark-antiquark pair to spontaneously appear • As a result of this, when quarks are produced in particle accelerators, instead of seeing the individual quarks in detectors, scientists see "jets" of many color-neutral particles (mesons and baryons), clustered together • This process is called hadronization, fragmentation, or string breaking, and is one of the least understood processes in particle physics
Bell's inequalities
• Bell's theorem is a no-go theorem that draws an important distinction between quantum mechanics (QM) and the world as described by classical mechanics • "No physical theory of local hidden variables can ever reproduce all of the predictions of quantum mechanics" • Bell showed that if a local hidden variable theory would hold, then these correlations would have to satisfy certain constraints, called Bell inequalities • The violations of Bell's inequalities, due to quantum entanglement, just provide the definite demonstration of something that was already strongly suspected, that quantum physics cannot be represented by any version of the classical picture of physics
CP violation
• CP violation (CP standing for Charge Parity) is a violation of the postulated CP-symmetry (or Charge conjugation Parity symmetry): the combination of C-symmetry (charge conjugation symmetry) and P-symmetry (parity symmetry) • CP-symmetry states that the laws of physics should be the same if a particle is interchanged with its antiparticle (C symmetry), and then its spatial coordinates are inverted ("mirror" or P symmetry) • The discovery of CP violation in 1964 in the decays of neutral Kaons resulted in the Nobel Prize in Physics in 1980 for its discoverers James Cronin and Val Fitch
quantum chromodynamics
• Color confinement, often simply called confinement, is the phenomenon that color charged particles (such as quarks) cannot be isolated singularly, and therefore cannot be directly observed • Quarks, by default, clump together to form groups, or hadrons • 2 quark objects are called mesons • 3 quark objects are called baryons • The constituent quarks in a group cannot be separated from their parent hadron, and this is why quarks currently cannot be studied or observed in any more direct way than at a hadron level • The reasons for quark confinement are somewhat complicated; no analytic proof exists that quantum chromodynamics should be confining
M-theory
• Using these dualities, we can see that all the different string theories are really all different versions of one "mother theory" that has been dubbed M -Theory • According to Witten, the M in M - theory can stand for "magic", "mystery", "membrane" or "matrix" according to taste
dark matter
• Dark matter is a kind of matter hypothesized in astronomy and cosmology to account for gravitational effects that appear to be the result of invisible mass • Dark matter cannot be seen directly with telescopes; evidently it neither emits nor absorbs light or other electromagnetic radiation at any significant level. • It is otherwise hypothesized to simply be matter that is not reactant to light • We don't know if it's small like a particle, or big, like a gas cloud. All we know is that it's not made of the same stuff we are made of (baryons). • Short answer: we don't know. Most correct response describes what it isn't rather than what it is. (It isn't "star stuff") • Cold dark matter is the simplest explanation for most cosmological observations. "Cold" dark matter is dark matter composed of constituents with a free-streaming length much smaller than the ancestor of a galaxyscale perturbation • ...the only really plausible dark-matter candidates are new particles. • When we talk about supersymmetry, we might find a possible DM candidate • It could also be a weird type of neutrino... • Also, warm and hot dark matter
Philosophy of Science
• Distinguishing between science and non-science is referred to as the demarcation problem. • For example, should psychoanalysis be considered science? • An area of study or speculation that masquerades as science is referred to as pseudoscience, fringe science, voodoo science, or junk science. • This is really important in a course like this. • Karl Popper • Thomas Kuhn
four-Fermi interaction
• Fermi's four-fermion theory describes the weak interaction remarkably well • Unfortunately, the calculated cross-section grows as the square of the energy 𝜎 ≈ 𝐺𝐹2𝐸2 making it unlikely that the theory is valid at energies much higher than about 100 GeV • The solution is to replace the four-fermion contact interaction by a more complete theory (UV completion)—an exchange of a W or Z boson as explained in the electroweak theory
hidden variables
• Hidden Variables: QM is incomplete, and the uncertainty in its predictions are the result of deterministic things we haven't figured out yet • Consistent histories, relational quantum mechanics, transactional interpretation, stochastic interpretation, objective collapse theory, ...
bulks and branes
• If we imagine more than one "extra" dimension, we can think of it as an extra "membrane" which is often called a brane in physics. • Imagine 10 dimensional brane, that is made of our four dimensions and the other six are called the "bulk" • Many higher dimensional theories have the SM forces confined to our four dimensions and let gravity travel off our brane and into the bulk • This happens naturally in string theory • This explains why gravity is the weakest force • This allows for dark matter to be matter confined to the bulk, off our brane
running coupling constant
• In SUSY, the near miss of the coupling is a hit • Now, note that this changes their properties long before unification (see the kink) • This meeting is very difficult in detail but it is a generic feature of SUSY • In many SUSY Standard Models there is a heavy stable particle (such as neutralino) which could serve as a weakly interacting massive particle (WIMP) dark matter candidate. • The existence of a supersymmetric dark matter candidate is closely tied to R-parity. • This is everything but gravity! Is that progress?
Kepler's laws
• In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun. Kepler's laws are now traditionally enumerated in this way • The orbit of a planet is an ellipse with the Sun at one of the two foci. • A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time • The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.
Inflation
• In physical cosmology, inflation is the exponential expansion of space in the early universe. • The inflationary epoch lasted from 10−36 seconds after the Big Bang to sometime between 10−33 and 10−32 seconds. • Following the inflationary period, the universe continues to expand, but at a less accelerated rate. • Why?! • Horizon problem • Flatness problem • Magnetic monopoles?
dualities
• In theoretical physics, T-duality is an equivalence of two physical theories, which may be either quantum field theories or string theories • In the simplest example of this relationship, one of the theories describes strings propagating in an imaginary spacetime shaped like a circle of some radius R, while the other theory describes strings propagating on a spacetime shaped like a circle of radius 1/R • The two theories are equivalent in the sense that all observable quantities in one description are identified with quantities in the dual description • For example, momentum in one description takes discrete values and is equal to the number of times the string winds around the circle in the dual description • In general, T-duality relates two theories with different spacetime geometries. • In this way, T-duality suggests a possible scenario in which the classical notions of geometry break down in a theory of Planck scale physics. • The geometric relationships suggested by T-duality are also important in pure mathematics • S-duality is useful for doing calculations in theoretical physics because it relates a theory in which calculations are difficult to a theory in which they are easier • S-duality generalizes a well known fact from classical electrodynamics, namely the invariance of Maxwell's equations under the interchange of electric and magnetic fields. • One of the earliest known examples of S-duality in quantum field theory is Montonen-Olive duality which relates two versions of a quantum field theory called N = 4 supersymmetric Yang-Mills theory • Another realization of S-duality in quantum field theory is Seiberg duality, which relates two versions of a theory called N=1 supersymmetric Yang- Mills theory
electro-weak force
• Successfully combines two forces into one theory • According to the electroweak theory, at very high energies, the universe has four massless gauge boson fields similar to the photon and a complex scalar Higgs field doublet • However, at low energies, gauge symmetry is spontaneously broken down to the symmetry of electromagnetism • These three fields become the W+ , W− and Z bosons of the weak interaction, while the fourth gauge field, which remains massless, is the photon of electromagnetism • This theory has made a number of predictions, including a prediction of the masses of the Z and W bosons before their discovery
wave particle duality
• Wave-particle duality is a theory that proposes that *every* elementary particle exhibits the properties of not only particles, but also waves 𝜆 =ℎ/𝑝 • Planck's constant is very, very small and momentum is large, so the wavelike nature of fundamental particle is quite small, but measureable.
Kaluza-Klein theory
• Kaluza-Klein theory (KK theory) is a unified field theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the usual 4 of space and time • The five-dimensional theory was developed in three steps • The 5-dimensional metric has 15 components. • 10 components are identified with the 4 -dimensional spacetime metric • 4 components with the electromagnetic vector potential • One component with an unidentified scalar field sometimes called the "radion" or the "dilaton" • The 5-dimensional Einstein equations yield the 4- dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field • The Higgs boson is a scalar field! • Kaluza also introduced the hypothesis known as the "cylinder condition", that no component of the 5- dimensional metric depends on the fifth dimension (this simplifies the equations greatly) and makes that 5th dimension very, very small • Up to now, no experimental or observational signs of extra dimensions have been officially reported. • Another effect of KK dimensions are particle resonances • An analysis of results from the LHC in December 2010 severely constrains theories with large extra dimensions • Lightest KK particle would have to be heavier than about 2.5 TeV
loop quantum gravity
• Loop quantum gravity (LQG) is a theory that attempts to describe the quantum properties of the universe and gravity • It is also a theory of quantum space and quantum time, because, according to general relativity, the geometry of spacetime is a manifestation of gravity • The main output of the theory is a physical picture of space where space is *granular* • This is just like photons in quantum theory, but space itself is discrete • More precisely, space can be viewed as an extremely fine fabric or network "woven" of finite loops • These networks of loops are called "spin networks". The evolution of a spin network over time is called a "spin foam" • The predicted size of this structure is the Planck length, which is approximately 10^−35 meters. According to the theory, there is no meaning to distance at scales smaller than the Planck scale • Therefore, LQG predicts that not just matter, but also space itself has an atomic structure • The most well-developed is the application of LQG to cosmology, called loop quantum cosmology (LQC)
Newtonian gravity
• Newton explains Kepler's laws •Newton was very displeased that he could only describe how gravity worked, but did not know "what it was" or why it existed. • "Action at a distance" • 𝐹 = 𝐺 𝑀1𝑚2/𝑟2 • 𝐺 = 6.674 × 10−11N m2/kg2
problems with Newtonian gravity
• Newton's universal law of gravity was the gold standard for centuries and was adequate for many purposes • 𝐹 = 𝐺 m1𝑚2/𝑟2 • However there were fundamental contradictions • Did not accurately explain deflection of light under gravity • Did not explain precession of the perihelion of Mercury • Observation of stat movements at extremely far distances from galactic center did not square with Newtonian gravity, they were moving too fast *More EX* • Precession of the Perihelion • Extra-fast stars (dark matter) • Flyby anomaly (as large as 13 mm/s) • Accelerating expansion (dark energy) • Anomalous increase of the astronomical unit • Extra energetic photons • Extra massive hydrogen clouds
Frame dragging
• Non-static, stationary mass-energy distributions affect space time in a peculiar way giving rise to a phenomenon usually known as frame dragging • They predicted that the rotation of a massive object would distort the space time metric, making the orbit of a nearby test particle precess • This does not happen in Newtonian mechanics for which the gravitational field of a body depends only on its mass, not on its rotation • Gravity Probe B satellite observed these effects
differences between bad science and non-science
• Pathological science, wherein genuine scientists deceive themselves • homeopathy, Martian canals, N-rays, polywater, water memory, perpetual motion, and cold fusion • Junk science, speculative theorizing which bamboozles rather than enlightens • global warming was due to solar variation, FUD (Fear, Uncertainty, and Doubt) • Pseudoscience proper, work falsely claiming to have a scientific basis, which may be dependent on supernatural explanations • astrology, alchemy, medical quackery, and occult beliefs combined with scientific concepts • Fraudulent science, exploiting bad science for the purposes of fraud • BlackLight Power
what two theories of the universe do we currently use
• Quantum Field Theory •General Relativity
quantum entanglement
• Quantum entanglement is a physical phenomenon that occurs when pairs or groups of particles are generated or interact in ways such that the quantum state of each particle cannot be described independently • Measurements of physical properties such as position, momentum, spin, polarization, etc. performed on entangled particles are found to be appropriately correlated
Randall- Sundrum model
• Randall-Sundrum models (also called 5-dimensional warped geometry theory) imagines that the real world is a higher-dimensional universe described by warped geometry. • The first, called RS1, has a finite size for the extra dimension with two branes, one at each end • The second, RS2, is similar to the first, but one brane has been placed infinitely far away, so that there is only one brane left in the model
string (open and closed)
• String theory includes both open strings, which have two distinct endpoints, and closed strings, which form a complete loop • The two types of string behave in slightly different ways, yielding different particle types • For example, all string theories have closed string graviton modes, but only open strings can correspond to the particles known as photons. • Because the two ends of an open string can always meet and connect, forming a closed string, all string theories contain closed strings
background independence
• String theory is usually formulated with perturbation theory around a fixed background. While it is possible that the theory defined this way is background-invariant, if so it is not manifest • One attempt to formulate string theory in a manifestly backgroundindependent fashion is string field theory, but little progress has been made in understanding it • Another approach is the AdS/CFT duality, which is believed to provide a full, non-perturbative definition of string theory in spacetimes with antide Sitter asymptotics. If so, this could describe a kind of superselection sector of the putative full, background-independent theory. A full nonperturbative definition of the theory in arbitrary space-time backgrounds is still lacking.
what are the four forces
• Strong Interaction(Force) • Electromagnetic Force • Weak Interaction(Force) • Gravitational Force
supergravity
• Supergravity (SUGRA for short) is a field theory that combines the principles of supersymmetry and general relativity. • Together, these imply that, in supergravity, that supersymmetry is a local symmetry • This is not like the MSSM where SUSY is a global symmetry • Since the generators of supersymmetry (SUSY) are convoluted with the Poincaré group to form a super-Poincaré algebra, it can be seen that supergravity follows naturally from supersymmetry • One of these supergravities, the 11-dimensional theory, generated considerable excitement as the first potential candidate for the theory of everything. This excitement was built on four pillars, two of which have now been largely discredited
supersymmetry
• Supersymmetry (SUSY) is a proposed extension of spacetime symmetry that relates two basic classes of elementary particles: bosons, which have an integer-valued spin, and fermions, which have a half-integer spin • Each particle from one group is associated with a particle from the other, called its superpartner, whose spin differs by a half-integer • In a theory with perfectly unbroken supersymmetry, each pair of superpartners shares the same mass and internal quantum numbers besides spin • For example, a "selectron" (superpartner electron) would be a bosonic version of the electron
The Big Bang
• The Big Bang theory is the prevailing cosmological model for the early development of the universe • The key idea is that the universe is expanding. Consequently, the universe was denser and hotter in the past. Moreover, the Big Bang model suggests that at some moment all matter in the universe was contained in a single point, which is considered the beginning of the universe. • After the initial expansion, the universe cooled sufficiently to allow the formation of subatomic particles, including protons, neutrons, and electrons. Though simple atomic nuclei formed within the first three minutes after the Big Bang, thousands of years passed before the first electrically neutral atoms formed. • The Big Bang theory offers a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background, large scale structure, and Hubble's Law. • Georges Lemaître proposed what became the Big Bang theory in 1927. • He called his hypothesis "the primeval atom" or the "Cosmic Egg" • The framework for the Big Bang model relies on Albert Einstein's theory of general relativity and on simplifying assumptions such as homogeneity and isotropy of space. • As of 2015, this expansion is estimated to have begun 13.799 ± 0.021 billion years ago. • Given the size of the universe, does anyone have a problem with this number?
CKM matrix
• The Cabibbo-Kobayashi-Maskawa matrix (CKM matrix) is a unitary matrix which contains information on the strength of flavor-changing weak decays
EPR paradox
• The EPR paradox yields a dichotomy that physical reality as described by quantum mechanics is incomplete • EPR tried to set up a paradox to question the range of true application of Quantum Mechanics • We have a source that emits electron-positron pairs, with the electron sent to destination A, where there is an observer named Alice, and the positron sent to destination B, where there is an observer named Bob • It is one thing to say that physical measurement of the first particle's momentum affects uncertainty in its own position, but to say that measuring the first particle's momentum affects the uncertainty in the position of the other is another thing altogether
color charge
• The color charge of quarks and gluons is completely unrelated to visual perception of color • Particles have corresponding antiparticles • A particle with red, green, or blue charge has a corresponding antiparticle in which the color charge must be the anticolor of red, green, and blue, respectively, for the color charge to be conserved in particle-antiparticle creation and annihilation • All three colors mixed together, or any one of these colors and its complement (or negative), is "colorless" or "white" and has a net color charge of zero
Cosmic Microwave Background
• The cosmic microwave background (CMB) is the thermal radiation left over from the Big Bang. • The cosmic microwave background radiation is an emission of uniform, black body thermal energy coming from all parts of the sky. • The radiation is isotropic to roughly one part in 100,000: the root mean square variations are only 18 µK • The cosmic microwave background was first predicted in 1948 by Ralph Alpher, and Robert Herman.
Signs of Bad Science
• The discoverer pitches the claim directly to the media • The discoverer says that a powerful establishment is trying to suppress his or her work • The scientific effect involved is always at the very limit of detection • Evidence for a discovery is anecdotal • The discoverer says a belief is credible because it has endured for centuries • The discoverer has worked in isolation • The discoverer must propose new laws of nature to explain an observation • Perpetual Motion (or Free Energy) • Cold fusion • Gravitational shielding • Human spaceflight (in terms of scientific return)
loop quantum cosmology
• The distinguishing feature of LQC is the prominent role played by the quantum geometry effects of loop quantum gravity • In particular, quantum geometry creates a brand new repulsive force which is totally negligible at low space-time curvature but rises very rapidly in the Planck regime, overwhelming the classical gravitational attraction and thereby resolving singularities of general relativity (black holes without singularities) • In LQC the big bang is replaced by a "quantum bounce"
Electromagnetism
• The electromagnetic force is the one responsible for practically all the phenomena one encounters in daily life above the nuclear scale, with the exception of gravity • Roughly speaking, all the forces involved in interactions between atoms can be explained by the electromagnetic force acting on the electrically charged atomic nuclei and electrons inside and around the atoms, together with how these particles carry momentum by their movement • This includes the forces we experience in "pushing" or "pulling" ordinary material objects, which come from the intermolecular forces between the individual molecules in our bodies and those in the objects • It also includes all forms of chemical phenomena
Heisenberg uncertainty
• Uncertainty Principle • Nobel Prize in 1932 • Atomic and nuclear models • Forms of molecular hydrogen • In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the precision with which certain pairs of physical properties of a particle known as complementary variables, such as position 𝑥 and momentum 𝑝, can be known simultaneously 𝜎𝑥𝜎𝑝 ≥ ℏ/2 𝜎𝐸𝜎𝑡 ≥ ℏ/2
holographic principle
• The holographic principle is a property of string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a boundary to the region • In a larger sense, the theory suggests that the entire universe can be seen as a two -dimensional information structure "painted" on the cosmological, such that the three dimensions we observe are an effective description only at macroscopic scales and at low energies • The holographic principle was inspired by black hole thermodynamics, which conjectures that the maximal entropy in any region scales with the radius squared, and not cubed as might be expected • In the case of a black hole, the insight was that the informational content of all the objects that have fallen into the hole might be entirely contained in surface fluctuations of the event horizon • The holographic principle resolves the black hole information paradox within the framework of string theory
Photoelectric effect
• The photoelectric effect is the observation that many metals emit electrons when light shines upon them. Electrons emitted in this manner may be called photoelectrons • According to classical electromagnetic theory, this effect can be attributed to the transfer of energy from the light to an electron in the metal. • From this perspective, an alteration in either the amplitude or wavelength of light would induce changes in the rate of emission of electrons from the metal. • Furthermore, according to this theory, a sufficiently dim light would be expected to show a lag time between the initial shining of its light and the subsequent emission of an electron. However, the experimental results did not correlate with either of the two predictions made by this theory
string landscape
• The string theory landscape or anthropic landscape refers to the large number of possible false vacua in string theory • The "landscape" includes so many possible configurations that some physicists think that the known laws of physics, the standard model and general relativity with a positive cosmological constant, occur in at least one of them (?!) • The anthropic landscape refers to the collection of those portions of the landscape that are suitable for supporting human life, an application of the anthropic principle that selects a subset of the theoretically possible configurations. • In string theory the number of false vacua is thought to be somewhere between 10^10 to 10^500 • The large number of possibilities arises from different choices of Calabi- Yau manifolds (and something even more technical)
ultraviolet catastrophe
• The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe, was a prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation with infinite power • According to classical physics, the power emitted from a blackbody is proportional to the inverse of the wavelength to the fourth power 𝐸~𝜆−4 • A solution to this problem was found by Max Planck at the cost of "quantizing" the particles of light, which he called photons. Einstein was the first to suggest that this was not just mathematical, but a real particle
Strong force
• The word strong is used since the strong interaction is the "strongest" of the four fundamental forces • Its strength is around 102 times that of the electromagnetic force, some 106 times as great as that of the weak force, and about 1039 times that of gravitation, at a distance of a femtometer (10-15 m) or less • The contemporary understanding of strong force is described by quantum chromodynamics (QCD), a part of the standard model of particle physics • In many, many ways QCD is simply a more complicated version of QED • Quarks and gluons are the only fundamental particles that carry nonvanishing color charge, and hence participate in strong interactions •At 1 fm (~size of nuclueus), strong force is ●10^2 times stronger than EM ●10^6 times stronger than weak force ●10^39 times stronger than gravity • How do protons and neutrons bind? • We can think of the pions as force carriers, but its just like Fermi's interaction, its an approximation to a more complicated process.
Higgs Boson
• There is this other particle called a "Higgs Boson" • It does not carry a force (not a gauge boson) • It interacts with any particle that has mass (everything but photons) • Its interactions with particles "gives" those particle their mass • Prime Minister analogy
AdS/CFT correspondence
• This is a conjectured relationship between two kinds of physical theories • On one side of the correspondence are conformal field theories (CFT) which are quantum field theories, including theories similar to the Yang- Mills theories that describe elementary particles. • On the other side are anti-de Sitter spaces (AdS) which are used in theories of quantum gravity, formulated in terms of string theory or Mtheory. • It provides a non-perturbative formulation of string theory with certain boundary conditions and because it is the most successful realization of the holographic principle
Mininal supersymmetry
• This is the least amount of SUSY you can introduce • Each SM particle has one Superpartner (there could be up to 8) • This is meant to stabilize the mass of the Higgs boson • It also allows for a dark matter candidate
the standard model
• This is what you get when you combine QM and SR • "The Theory of Almost Everything" • Governed by Quantum Field Theory (QFT) • Was discovered empirically and theoretically over the past fifty years • Very high level of experimental and theoretical verification • We will talk about each of the forces and why we believe in them separately, along with gravity
Calabi-Yau manifold
• Two ways have been proposed to resolve apparent contradiction of where the extra dimension go. The first is to compactify the extra dimensions. • To retain a high degree of supersymmetry, these compactification spaces must be very special • One of these is called a Calabi -Yau manifold
types of string theory
• Type I string theories have one supersymmetry in the ten-dimensional sense (16 supercharges). This theory is special because it is based on unoriented open and closed strings, while the rest are based on oriented closed strings • Type II string theories have two supersymmetries in the ten-dimensional sense (32 supercharges). There are actually two kinds of type II strings called type IIA and type IIB. They differ mainly in the fact that the IIA theory is non-chiral (parity conserving) while the IIB theory is chiral (parity violating) • The heterotic string theories are based on a peculiar hybrid of a type I superstring and a bosonic string. There are two kinds of heterotic strings differing in their ten-dimensional gauge groups: the heterotic E8×E8 string and the heterotic SO(32) string
dark energy
• We know very little about dark matter • We know less about dark energy • Dark energy is a hypothetical form of energy which permeates all of space and tends to accelerate the expansion of the universe • On a mass-energy equivalence basis, the density of dark energy is very low. In the solar system, it is estimated only 6 tons of dark energy would be found within the radius of Pluto's orbit. • However, it comes to dominate the mass-energy of the universe because it is uniform across space (as space expands, it doesn't dilute like everything else) • Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously and scalar fields such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space • Distance measurements and their relation to redshift, which suggest the universe has expanded more in the last half of its life • The theoretical need for a type of additional energy that is not matter or dark matter to form the observationally flat universe (absence of any detectable global curvature) • Dark energy is thought to be very homogeneous, not very dense and is not known to interact through any of the fundamental forces other than gravity
what unanswered questions are in the standard model
• What gives rise to the Standard Model? • Why do we have the gauge groups we have? • Why are there three generations of quarks and leptons? • Why are there no fractionally charged/colored objects? • Why do they have the masses that they have? • What is the origin of CP violation? • Why is there more matter than anti-matter? • What is dark matter, dark energy?
Black holes
• When mass is concentrated into a sufficiently compact region of space, general relativity predicts the formation of a black hole - a region of space with a gravitational effect so strong that not even light can escape • There are several properties that make black holes most promising sources of gravitational waves • One reason is that black holes are the most compact objects that can orbit each other as part of a binary system; as a result, the gravitational waves emitted by such a system are especially strong • These are a huge and fascinating subject
