What Do We Know?

Particles

Mass units: E = mc2 1 eV (electron-Volt) is a unit of Energy so, m = E/c2, and so we can measure mass in eV/c2 MeV = million eV (106 = 1,000,000) GeV = giga eV (109 = 1,000,000,000)

Feynman Diagrams

This is what beta decay looks like, this is a very important process. - - 𝑛 → 𝑝 𝑒 𝜈𝑒 Beta decay can turn a bound proton or neutron into each other inside a nucleus. This can also happen to a free neutron, but not to a free proton as far as we can tell. Why? Mass constraints.

Richard Feynman

• 11 May 1918 - 15 February 1988 • Contributions include • Work on the Manhattan Project • Invention of diagrams to represent particle interactions • Theory of weak interactions • Reformation of quantum mechanics • Superfluid helium • Challenger investigation • Shared Nobel Prize in 1965

Murray Gell-Mann

• 15 September 1929 - • Worked on theoretical studies of subatomic particles • Coined the name for "quarks" • George Zweig called them "aces" • Nobel Prize in 1969 • Developed what is called "The Eightfold Way"

Luminiferous Ether

• 19th Century physicists compared electromagnetic waves to mechanical waves. • Mechanical waves need a medium to support the disturbance. • The luminiferous ether was proposed as the medium required (and present) for light waves to propagate. • Present everywhere, even in empty space • Massless, but rigid medium • Could have no effect on the motion of planets or other objects • This would mean that the speed of light should vary with relative motion

Paul Adrien Maurice Dirac

• 8 August 1902 - 20 October 1984 • Instrumental in understanding antimatter • Aided in the unification of quantum mechanics and relativity • Contributions to quantum physics and cosmology • Dirac was regarded by his friends and colleagues as unusual in character. • Nobel Prize in 1933

Feynman Diagrams

• A graphical representation of the interaction between two (sometimes three) particles • The photon is the field particle that mediates the interaction. • The photon transfers energy and momentum from one electron to the other. • The photon is called a virtual photon. • It can never be detected directly because it is absorbed by the second electron very shortly after being emitted by the first electron

An Eightfold Way for Baryons

• A hexagonal pattern for the eight spin ½ baryons • Strangeness vs. charge is plotted on a sloping coordinate system. • Six of the baryons form a hexagon with the other two particles at its center. • Particles with spin 1/2 and 3/2 are called fermions.

Conservation Laws

• A number of conservation laws are important in the study of elementary particles. • The new ones are • Conservation of Baryon Number • Conservation of Lepton Number • Conservation of Strangeness

Galilean Relativity - Example

• A passenger in a moving truck throws a ball straight up. • It appears to move in a vertical path. • This is the same motion as when the ball is thrown while at rest on the Earth. • The law of gravity and equations of motion under uniform acceleration are obeyed

Proton Stability

• Absolute conservation of baryon number indicates the proton must be absolutely stable • Otherwise, it could decay into a positron and a neutral pion • Never been observed • Currently can say the proton has a half-life of at least 10^33 years • Some theories indicate the proton can decay. • If so, baryon number would not be absolutely conserved • Theory doesn't really say either way!

Let's Not Get Ahead of Ourselves

• All Particle Physics fits in a diagram: but it is incomplete! • 95% of the universe is missing: dark matter and dark energy

Special Relativity

• All the laws of physics are the same in all inertial frames. • The speed of light in a vacuum has the same value in all inertial reference frames, regardless of the velocity of the observer or the velocity of the source emitting the light. • This is a sweeping generalization of the principle of Galilean relativity, which refers only to the laws of mechanics. • The results of any kind of experiment performed in a laboratory at rest must be the same as when performed in a laboratory moving at a constant speed past the first one. • No preferred inertial reference frame exists. • It is impossible to detect absolute motion.

Conservation of Lepton Number

• Assigning electron-lepton numbers • 𝐿𝑒 = 1 for the electron and the electron neutrino • 𝐿𝑒 = −1 for the positron and the electron antineutrino • 𝐿𝑒 = 0 for all other particles • Similarly, when a process involves muons, muon-lepton number must be conserved and when a process involves tau particles, taulepton numbers must be conserved. • Muon- and tau-lepton numbers are assigned similarly to electron-lepton numbers.

Verifying the Luminiferous Ether

• Associated with an ether was an absolute frame where the laws of E&M take on their simplest form. • Since the earth moves through the ether, there should be an "ether wind" blowing. • If 𝑣 is the speed of the ether relative to the earth, the speed of light should have maximum (a) or minimum (b) value depending on its orientation to the "wind".

Particles (in your experience)

• Chemistry is about atoms (atomic/chemical interactions) • Atoms are made of protons, neutrons, and electrons • Protons and neutrons are made of quarks (Proton is uud and Neutron is ddu) • Quarks are of two varieties (up-type and down-type) • Quarks are fractionally charged (+2/3 and -1/3 that of an electron) • Quarks come in three colors (red, green, and blue) • Quarks are held together by gluons • Quarks come in three generations (u/d, c/s, t/b) • So do electrons (e, mu, tau) • Electrons have a spooky, almost massless partner called a neutrino • Virtually your whole life will be interactions with just protons, neutrons, and electrons (also, photons)

Galilean Relativity

• Choose a frame of reference. • Necessary to describe a physical event • According to Galilean Relativity, the laws of mechanics are the same in all inertial frames of reference. • An inertial frame of reference is one in which Newton's Laws are valid. • Objects subjected to no forces will move in straight lines.

What Do We Know? Why Unification?

• Current theories • Quantum Field Theory • General Relativity • These theories describe the same universe to exquisite detail • They do not play well together. In fact, they contradict each other involving several key issues • To bring these two theories together, we will need a new framework • This is our current thinking, not a hard and fast rule

Michelson-Morley Experiment

• First performed in 1881 by Michelson • Repeated under various conditions by Michelson and Morley between April and July, 1887 at what is now Case Western Reserve University in Cleveland, and published in November of the same year. • Designed to detect small changes in the speed of light • By determining the velocity of the earth relative to the ether

Antiparticles

• For every particle, there is an antiparticle. • From Dirac's version of quantum mechanics that incorporated special relativity • An antiparticle has the same mass as the particle, but the opposite charge. • The positron (electron's antiparticle) was discovered by Anderson in 1932. • Since then, it has been observed in numerous experiments. • Practically every known elementary particle has a distinct antiparticle. • Exceptions - the photon and the neutral pi particles are their own antiparticles

It Gets Worse...

• Galilean Relativity does not apply to experiments in electricity, magnetism, optics, and other areas. • Results do not agree with experiments. • The observer should measure the speed of the pulse as 𝑣 + 𝑐 • Actually measures the speed as 𝑐 • There is something special about light

Things You Should Know

• How many forces of nature are there? • 4 • What does the Higgs Boson do? • Gives mass to particles • When was this talk given? • 2018 • How many particles of matter are there? • 12

Special Relativity

• In Special Relativity, Einstein abandoned the assumption of simultaneity. • Two events that are simultaneous in one reference frame are in general not simultaneous in a second reference frame moving relative to the first. • That is, simultaneity is not an absolute concept, but rather one that depends on the state of motion of the observer. • In a thought experiment, both observers are correct, because there is no preferred inertial reference frame.

Hadrons

• Interact through the strong force • Two subclasses • Mesons • Decay finally into electrons, positrons, neutrinos and photons • Integer spins • Baryons • Masses equal to or greater than a proton • Non-integer spin values • Decay into end products that include a proton (except for the proton) • Composed of quarks

Special Relativity

• Length contracts with velocity • The measured distance between two points depends on the frame of reference of the observer. • The proper length of an object is the length of the object measured by someone at rest relative to the object. • Time dilates with velocity • All physical processes slow down relative to a clock when those processes occur in a frame moving with respect to the clock. • These processes can be chemical and biological as well as physical. • This is sometimes known at the "Twin Paradox" • What about accelerating reference frames?

The Eightfold Way

• Many classification schemes have been proposed to group particles into families. • These schemes are based on spin, baryon number, strangeness, etc. • The eightfold way is a symmetric pattern proposed by Gell-Mann and Ne'eman. • There are many symmetrical patterns that can be developed. • The patterns of the eightfold way have much in common with the periodic table. • Including predicting missing particles

Michelson-Morley Experiment

• Measurements *failed to show any change* in the fringe pattern. • No fringe shift of the magnitude required was ever observed. • (Modern versions of this experiment have shown that the velocity of the ether would have to be smaller than 10−17 𝑐 ≈ 3 nm/s • Light is now understood to be an electromagnetic wave, which requires no medium for its propagation. • The idea of an ether was discarded

Where Did Physics Go Wrong?

• Newtonian Mechanics is very successful in describing the motion of objects moving at much less than the speed of light. • It fails when applied to particles having speeds approaching the speed of light. • The speed of every particle in the universe *always* remains less than the speed of light. • This universal speed limit has many consequences. • The usual concepts of force, momentum and energy no longer apply. • Observers moving at different speeds will measure different time intervals and displacements between the same two events.

Where Did Physics Go Wrong?

• One of the great questions of physics (science in general) is how to identify when a theory (paradigm) is not working, and what to replace it with, and when to replace it. • The physics of Isaac Newton (built on a few conservation laws and calculus) withstood the test of time because it is based on everyday experiences. • We begin to see shortcomings when objects become very small (smaller than a spec of dust) and/or very fast (moving faster than about half the speed of light).

Leptons

• Participate in the weak interaction • All have spin of ½ • Leptons appear truly elementary • No substructure (to the limit of current experiments) • Point-like particles • Scientists currently believe only six leptons exist, along with their antiparticles. • Electron and electron neutrino • Muon and its neutrino • Tau and its neutrino

Does NOT Play Well With Others

• QFT is a "quantum theory" and gravity in the framework of GR can not be quantized! In particular, it cannot be renormalized • This means at high energies, the theory loses it ability to make predictions in any meaningful way • GR is a theory of curvature of space-time, curved space-time causes particles to appear out of no where in QFT • GR predicts black holes, the singularity of a black hole cannot be handled within QFT • QFT has Heisenberg uncertainty principle built in, this makes a gravitational field of a single particle impossible to determine • Finally, "time" has a different meaning in QFT and GR

Special Relativity

• Relative motion is unimportant when measuring the speed of light. • We must alter our common-sense notions of space and time. • Restricting the discussion to concepts of length, time, and simultaneity • In relativistic mechanics • There is *no such thing as* absolute length. • There is *no such thing as* absolute time. • Events at different locations that are observed to occur *simultaneously* in one frame are not observed to be simultaneous in another frame moving uniformly past the first.

Strange Particles

• Some particles discovered in the 1950's were found to exhibit unusual properties in their production and decay and were given the name strange particles. • Peculiar features include • Always produced in pairs • Although produced by the strong interaction, they do not decay into particles that interact via the strong interaction, but instead into particles that interact via weak interactions • They decay much more slowly than particles decaying via strong interactions.

The Virtual Photon

• The existence of the virtual photon would be expected to violate the law of conservation of energy. • But, due to the uncertainty principle and its very short lifetime, the photon's excess energy is less than the uncertainty in its energy. • The virtual photon can exist for short time intervals, such that Δ𝐸Δ𝑡 ≈ ℏ • That is an "uncertainty" relationship, we will talk about this when we talk about QM

An Eightfold Way for Mesons

• The mesons with spins of 0 can be plotted. • Strangeness vs. charge on a sloping coordinate system is plotted. • A hexagonal pattern emerges. • The particles and their antiparticles are on opposite sides on the perimeter of the hexagon. • The remaining three mesons are at the center. • Particles with spin 0 or 1 are called bosons.

Eightfold Way Patterns

• The patterns of the eightfold way have much in common with the periodic table. • Whenever a vacancy occurs in the pattern, experimentalists have a guide for their investigations. • Example: Ω− was predicted to have a spin 3/2, a charge −1, a strangeness −3, and a mass of about 1680 MeV/c2 • A short time later, experimenters at Brookhaven found the particle and confirmed all its properties.

Forces

• The three forces of the Standard Model are carried by particles called gauge bosons. • Photon - carries the electromagnetic force. This particle will only interact with charged particles, will not interact with itself because it is neutral. • W/Z bosons - carries the weak force. These particles will interact with each other, they also carry a charge. • Gluons - carry the strong force. There are eight of these and will only interact with "colored" particles, like quarks.

Galilean Relativity - Conclusion

• The two observers disagree on the shape of the ball's path. • Both agree that the motion obeys the law of gravity and Newton's laws of motion. • Both agree on how long the ball was in the air. • Conclusion: There is no preferred frame of reference for describing the laws of mechanics.

Verifying the Luminiferous Ether

• The wind could have an intermediate value. • The velocity of the ether should equal the orbital velocity of the Earth. • A change in speed should be detected in the upwind or downwind directions.

Conservation of Lepton Number

• There are three conservation laws, one for each variety of lepton. •*Law of Conservation of Electron-Lepton Number* states that the sum of electron-lepton numbers before a reaction or a decay must equal the sum of the electron-lepton number after the process.

Galilean Relativity - Example

• There is a stationary observer on the ground. • Views the path of the ball thrown to be a parabola • The ball has a velocity to the right equal to the velocity of the truck.

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

General Relativity

• This is our current theory of gravity • Proposed by Albert Einstein in 1916 • GR is an extension of Special Relativity involving acceleration • Newtonian gravity involves forces • GR is about the shortest path in a curved space, this is called a geodesic • GR says that the source of the curvature of space is matter • There are many, many very subtle effects of GR, and they are in fantastic agreement with experiments • Precession of the perihelion, orbital decay, frame dragging, gravitational lensing, existence and properties of black holes, all modern Cosmology

Quantum Field Theory

• This is the theoretical framework of the Standard Model • It includes quantum mechanics and unstable particles • It is known as a "gauge theory" • It is based on "symmetry groups" • There are some other very nice mathematical properties that interest physicists, in particular, renormalization and unitarity. • It can be expanded, it is self-consistent.

Standard Model of Particles

• 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

Strangeness

• To explain these unusual properties, a new law, conservation of strangeness, was introduced. • Also needed a new quantum number, S • 𝑆 = ±1 for strange particles, 𝑆 = 0 for non-strange particles • The *Law of Conservation of Strangeness* states that the sum of strangeness numbers before a reaction or a decay must equal the sum of the strangeness numbers after the process. • Strong and electromagnetic interactions obey the law of conservation of strangeness, but the weak interactions do not.

Classification of Particles

• Two broad categories • Excluding those that transmit forces • Classified by interactions • Hadrons • Interact through strong force • Composed of quarks • Leptons • Interact through weak force • Thought to be truly elementary • Some suggestions they may have some internal structure

Conservation of Baryon Number

• Whenever a baryon is created in a reaction or a decay, an antibaryon is also created. • B is the Baryon Number • 𝐵 = +1 for baryons • 𝐵 = −1 for antibaryons • 𝐵 = 0 for all other particles • *The Law of Conservation of Baryon Number* states the sum of the baryon numbers before a reaction or a decay must equal the sum of baryon numbers after the process.