Hot Topics in Physics - hep.fsu.edu
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1 OLLI lectures Fall 2016 Horst D Wahl ([email protected]) lecture 1, 11 Oct 2016 Hot Topics in Physics
Transcript of Hot Topics in Physics - hep.fsu.edu
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OLLI lectures Fall 2016Horst D Wahl
lecture 1, 11 Oct 2016
Hot Topics in Physics
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Outline of 1st class Organizational
Outline of course
Present paradigm
Space and time
The stuff of nature: energy
Fields
Gravity and Space
Quanta
Particles
Cosmos
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Organizational Class: 6 lectures:
Tue, 11, 18, 25, Oct., and 1, 8, 15 Nov
Resources for further reading
Website: http://hep.fsu.edu/~wahl/olli16physics/ = “olli16physics”
“The Fabric of the Cosmos” by Brian Greene, Vintage Books (2005),posted in olli16physics
Particle Data Group (http://www-pdg.lbl.gov/ )
Contemporary Physics Education Project (http://www.cpepphysics.org/ )
“Conceptual Physics” by Benjamin Crowell(http://www.lightandmatter.com/cp.pdf)
“Light and Matter” by Benjamin Crowell (http://www.lightandmatter.com/lm/also available as “Lectures on Physics”(http://www.vias.org/physics/index.html)
Other documents as needed and convenient
About the course:
flow of course rather “free running” – may redefine as we go along
aim is to have lots of interaction and discussion
will post lecture notes and other documents on website
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Outline of Course
1. Present paradigm (setting the stage)
2. Neutrinos
3. Matter and Antimatter
4. Dark Matter
5. Dark Energy
6. Origin of elements
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The present paradigm
1. Space
2. The stuff of nature: energy
3. Fields
4. Gravity and Space
5. Quanta
6. Particles
7. Cosmos
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1. Space
What is space? the boundless three-dimensional extent in which objects and events
have relative position and direction. (Encyc. Britannica)
Questions about space: is it itself an entity ?
a relationship between entities ?
or part of a conceptual framework?
physicists’ consensus until beg. of 20th century: space = great empty container, large box containing the universe
Bodies move through space, motion influenced by forces
Isaac Newton: space and time exist independently of matter,absolute, motion with respect to absolute space
Ernst Mach: all motion relative to massive bodies in the universe
Geometry of space is Euclidean
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Space (2)Today’s paradigm
about space:
We live in 3-dim.Space
3 space and onetime dimensioncombined in 4-dim.spacetime
Geometry ofspacetimedetermined bydistribution ofmass/energy
But some theories requireadditional spatial dimensions
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Minkowski’s spacetime
In Galilean space (3-dim. Euclidean) the distance between twoadjacent points is
(Pythagoras – Euclidean geometry)
The Galilei Transformation follows when we declare this distanceinvariant under coordinate transformations and take the time asindependent of space
In the Minkowski spacetime the distance between two adjacent eventsis
The Lorentz transformation (and thus special theory of relativity) follows ifwe declare this distance invariant under coordinate transformation.Lorentz transformation is the transformation under which this distance isinvariant
2 2 2 2ds dx dy dz
2 2 2 2 2( ) ( )ds cdt dx dy dz
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Spacetime Diagrams
Events can be represented as points in aspacetime diagram
Tim
e
Space
A B
Those that have thesame time values (in a givenframe of reference) such asevents A and B, are said tobe simultaneous
Space + time = spacetime
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Earth’s Time Axis
3016 CE
2016 CE
2516 CE
yx
now
Event: A place at a given timeSpacetime: The set of all events
(t,x,y,z)A
B
CD
O
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Geometry of spaceIs space Euclidean or not?
Until 19th century, this question not even asked
Implicit assumption: Euclidean (nothing elseconceivable)
During 19th century:
Mathematicians and physicists start thinkingabout non-Euclidean geometry
Gauss
Bolyai
Lobachewski
Riemann
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Euclidean Space
“Elements” of Eucleides ca 300 BCE.
Axioms, from which theorems (propositions) can be derived
Axiom 1: A straight line segment can be drawn between any two points. .
Axiom 2: Any straight line segment can be extended indefinitely in a straight line.
Axiom 3:Given any straight line segment, a circle can be drawn having thesegment as radius and one endpoint as center.
Axiom 4: All right angles are congruent.
Axiom 5 If two lines are drawn which a third intersects in such a way that the sumof the interior angles on one side is smaller than two right angles, then those linesintersect each other on that side (parallel axiom).Is equivalent to the statement: for any given line and point not on the line, there isone parallel line through the point not intersecting the line.
5th axiom cannot be proven as a theorem (many tried); first 28 theorems of Euclid areproved without it
Theorem 32 The sum of the interior angles of a triangle equals 2 right angles
One of the consequences: The ratio of the radius and the circumference of a circle isconstant (=2 in modern parlance)
http://aleph0.clarku.edu/~djoyce/elements/elements.html
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Geometry of space (2) non-Euclidean geometries:
All studies started out from attempts at provingEuclid’s 5th axiom
o for any given line and point not on the line, there isone parallel line through the point not intersecting theline.
Carl Friedrich Gauss (1820s)
Nikolai Iwanowich Lobachewski (1826)hyperbolic geometry
János Bolyai (1832) hyperbolic geometry
Johann Bernhard Riemann (1854) more general
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Geometry of space (3)
C.F. Gauss (1777-1855), mathematician,astronomer, geodesist, physicist,…
“disquisitiones generales circasuperficies curvas” (1827)
Studied Euclid’s 5th axion (parallelaxiom), non-Euclidean geometry
Did geodetic survey of Kingdom ofHannover (1821-1825); measuredangles in triangle of 3 mountains:
o Brocken, Hoher Hagen, Inselsberg
o Triangle of sides 69 km (Hoher Hagen –Brocken), 84 km (Hoher Hagen –Inselsberg) and 106 km (Brocken –Inselsberg)
o Sum of angles =180º ± 0.2”
Gaussian curvaturehttps://www.wikiwand.com/de/Gaußsche_Landesaufnahme
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Geometry of space (4) – hyperbolic geometry
Nikolai Ivanovich Lobachevsky(Никола́й Ива́нович Лобаче́вский)(1792-1856), mathematician andgeometer Teacher at university: Johann Christian
Martin Bartels, friend of C.F. Gauss
Developed geometry without 5th axiom –“hyperbolic geometry” (paper rejected byPetersburg Acad. of Sciences)
Johann (János) Bolyai (1802-1860),engineer, military officer, mathematician Non-Euclidean geometry (hyperbolic
geometry), published 1832 as appendix togeometry book by his father FarkasWolfgang Bolyai
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Geometry of space (5)
Georg Friedrich Bernhard Riemann(1826-1866) Student of Gauss, studied foundations
of geometry on suggestion by Gauss
"Über die Hypothesen, welche derGeometrie zu Grunde liegen" ("On thehypotheses which underlie geometry")(1854) (seehttp://www.emis.de/classics/Riemann/ )
Presents generalization to n dimensionsof Gauss differential geometry ofsurfaces
Now considered one of the mostimportant works in geometry
Riemann curvature tensor
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Types of geometries
Geometry
curvature
Sum of angles intriangle
Ratio
Circumference /radius of circle
Elliptical, spherical
>0
>180º
< 2π
Flat, euclidean
=0
=180º
= 2π
Hyperbolic
>0
<180º
> 2π
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Geometry of space (6)
Albert Einstein (1879-1955)
Geometry of spacetime (curvature tensor) isdetermined by matter/energy distribution in theuniverse
Objects move in geodesics in curved space
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2. Stuff of the universe: energy
Present view of physics: every physical entity is amanifestation of energy
What is energy? ??
Conservation of energy: a law in naturegoverning all phenomena that we know – noexceptions
o There is a certain quantity (“energy”) that does notchange in any change that nature undergoes
We do not really know what energy is
Energy comes in many different forms – have toaccount for all of them
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Conservation of EnergyEnergy conservation:
the total energy of all participants in any process isunchanged throughout that process. Energy can betransformed (changed from one energy form to another),and transferred (moved from one place to another), butcannot be created or destroyed. In an isolated system thetotal amount of energy is conserved.
Conservation laws in physics “conserved quantities”: = quantities that do not change - “are
conserved”
Conservation laws are related to “symmetry” property of system-also called “invariance” property.
Every invariance property is associated with a conservedquantity.
Energy conservation is related to “invariance under translationin time” (i.e. laws of physics do not change as time passes).
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Types of energy
Many different kinds of energy; can be transformed backand forth into each other:
kinetic energy = energy of motion = work that system cando because of its motion; (translational or rotational)
potential energy = energy of position or state;(gravitational, elastic, electric, chemical, nuclear)
gravitational energy = work system can do due toobjects having been raised against gravitational force;depends on “reference level” i.e. on how far object canfall down;
elastic energy due to ability of deformed (stretched,squeezed,..) system to snatch back (e.g. rubber band,spring..)
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Types of energy, cont’d thermal energy = kinetic energy of random motion of
molecules; brought into system by “heating”; different fromother forms of energy - not all of it can be converted back.
electromagnetic energy (electric energy) = energy due toelectromagnetic forces;
radiant energy = energy carried by electromagneticradiation;
chemical energy = energy stored in molecular structure ofchemical compounds; can be “liberated” by chemicalreactions converting compound into other compounds withless stored chemical energy.
nuclear energy = energy due to nuclear structure, i.e. howprotons and neutrons are bound to each other to form
nuclei.
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Development of energy concept
What is energy?
Gk ἐνέργεια energeia "activity, operation“
G.W. Leibniz (1676)
o “vis viva” (loving force), a measure of quantity ofmotion, = mass x speed2
o is conserved; loss of vis viva due to friction (heating up) thermal energy = random motion ofconstituents
Thomas Young (1807) calls it energy
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Energy, cont’d
Emilie de Châtelet (1706-1749) speculates on conservationof total energy
equivalence of of mechanical energy and heat
Experiments by Count Rumford (Benjamin Thompson)(heat generated in boring cannons)
elaborated on and reformulated by Karl Friedrich Mohr(1837) (“on the nature of heat”)
Principle of mechanical equivalence principle (JuliusRobert Mayer, 1842)
Measurement of mechanical equivalent of heat (JamesPrescott Joule, 1843)
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Energy, contConservation of energy:
Hermann von Helmholtz “Über die Erhaltungder Kraft” (1847)
William Rankine “law of conservation of energy”(1850)
Thermodynamics (2nd half of 19th century)
Developed by James Thomson (Lord Kelvin),Rudolf Clausius, Walther Nernst, Willard Gibbs..
“1st law of thermodynamics” = conservation ofenergy
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Principal laws of thermodynamics
Mayer, Joule: first lawHeat is a form of energy, and energy is conserved.
There is no perpetual motion machine of the first kind. But... many processes that are permitted according to thefirst law of thermodynamics do not occur
A cooled cup of coffee does not heat up(spontaneously), a fallen stone will notcome back up (spontaneously).A broken egg does not reassemble itself.You will only get older, not younger.
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(Clausius) Heat can not spontaneously pass from amaterial at a lower temperature to a material at a highertemperature.
Second law
(Thomson - Lord Kelvin) It is not possible for heat to becompletely converted to work. No heat engine has 100%efficiency.
(Clausius, Boltzmann, Planck et al.) Only thoseprocesses are possible in which the total entropy of theuniverse does not decrease.
Certain processes are irreversible.There is no perpetual motion machine of the second kind.
T1 < T2
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Energy today
Matter particles (e.g. atoms), light, gravity are allforms of energy
All of them related to or contained in “fields”
Fields diffused through space
Fields carry energy
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3. Fields
up to mid 19th century:
universe = space containing objects (matterparticles)
Objects can carry energy, exert forces on eachother
Michael Faraday (1791 – 1867) and James ClerkMaxwell (1831 – 1879)
Electric and magnetic → electromagnetic field fills space, exerts force, carries energy
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Electromagnetism: field
The length of the arrow indicates the (relative)strength of the field site, the direction indicates thedirection of the field.Meaning: power on a (test) charge q: F = qE
E
Faraday: the concept of field:Electric and magnetic charges bring the space intoa condition which is characterized by electric andmagnetic vector fields...
Note: there is a fieldline through every point
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The field can be represented by field lines: in every point E is thedirection of the tangent to the field line through that point. The density ofthe field lines gives the (relative) intensity of E. Field lines begin at +charges (or infinity), and end at - charges (or, in the infinite)
example: field lines of a dipole
through everypoint goes afield line.
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Electric Field
“field of force”: exists in a region of space when an appropriate object (called the “testobject” or “probe”) placed at any point in the region experiences a force.
force depends on a property of the test object (e.g. charge,..), the “test charge”;
“field strength” = (force experienced by test object) divided by (test charge), = “forceper unit test charge”;
for electrostatic force, this field strength is called “electrostatic field” or “electric field”;
field can be visualized by “lines of force” or “field lines”, which give the direction of thefield at every point, i.e. the force experienced by a test-charge at any point in spaceis in the direction tangent to the line of force at that point;
the density (concentration) of field lines corresponds to the magnitude of the fieldstrength: the denser the concentration of lines, the stronger the field; the farther apartthe lines, the weaker the field;
electrostatic field lines begin on positive and end on negative charges;
field lines do not cross;
originally, field lines were invented (by Faraday) as means of visualization, buteventually were regarded as standing for an invisible physical reality - the electricfield;
In modern view, all forces (“interactions”) are due to fields, described by “gauge fieldtheories”.
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Maxwell’s equations
(1) The electric field leaving a volumeis proportional to the charge inside.
(2) There are no magneticmonopoles; the total magnetic fluxpiercing a closed surface is zero.
(3) The voltage accumulated around aclosed circuit is proportional to thetime rate of change of the magneticflux it encloses.
(4) Electric currents and changes inelectric fields are proportional to themagnetic field circulating about thearea they pierce.
0
0 0
(1)
(2) 0
(3)
(4)
E
B
BE
t
EB J
t
James Clerk Maxwell (1831 – 1879):”A Dynamical Theory of theElectromagnetic Field” (1865)
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Particles vs fields Particle
has a position (occupies a point in space), mass, energy,momentum
Particle’s energy and momentum localized at position of particle
If particle moves freely →its energy and momentum is conserved and moves with it
All fundamental fields of nature Exist throughout space and time, field’s energy and momentum
spread all over space
“strength” of field at a point in spacetime = measure of the field’senergy and momentum at that point
Time evolution of field → e. + m. of field redistributed from one point to another; conserves e. + m.
Field can interact with particles, exchange energy and momentumwith field, total (field + particle) e. + m. conserved
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4. Gravity
Newton’s “universal law of gravity”:
Massive bodies exert gravitational force oneach other
Requires “action at a distance” puzzle
19th century:
Gravitational field in analogy to electric field
Force exerted by gravitational field
1 22
m mF G
R
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Gravity (2)Albert Einstein:
Newton’s gravity law violates special relativity
o Requires simultaneous measurement of position of 2bodies (possibly) far apart, and “simultaneous” onlydefined wrt given reference frame
o What if bodies move? Instantaneous change of force?
After many tribulations: “General Theory of Relativity”:
o Gravitational field does not fill space, it IS space
o Distribution of matter and energy determines geometry ofspace
o matter tells spacetime how to curve, and curved spacetells matter how to move (J.A. Wheeler)
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Path to GRT
Principle of special relativity:
All inertial frames are equivalent observed phenomena areindependent of the state of motion of the observer, as long asobserver a rest in an inertial frame.
Can we extend this to non-inertial systems? For example, to abraking train or a carousel?
Can one formulate a “principle of general relativity”?
Commonality of gravitation and electromagnetism:
both understood as field: mass changes the space just like chargedoes
change propagates with the speed of light.
No "immediate effect at a distance."
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Test of General Relativity 1919 6 November 1919:
joint meeting of the Royal Societyand the Royal Astronomical Society:
measured light deflection 1.98’’ 0.30’’ in Sobral and 1.61’’ 0.30’’ inSão Thomé e Príncipe
chairman J.J. Thomson:
o “The deflection of light by matter,suggested by Newton in the first ofhis Queries, would itself be a resultof first-rate scientific importance; it isof still greater importance when itsmagnitude supports the law ofgravity put forward by Einstein”
https://www.mpg.de/9244824/solar-eclipse-1919http://astrogeo.oxfordjournals.org/content/50/4/4.12.fullhttp://www.esa.int/Our_Activities/Space_Science/Relativity_and_the_1919_eclipsehttp://w.astro.berkeley.edu/~kalas/labs/documents/kennefick_phystoday_09.pdfhttp://news.bbc.co.uk/2/hi/science/nature/8061449.stm
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7 November 1919London Times
p 12 col 6:
New York Times of 10November 1919
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Straight line – always the shortest distance?
Term “geodesics” is a generalization of the notion of “straight line”,when applied to a curved space.
shortest distance between two points = straight line – always???
Sometimes it is, sometime it isn’t!
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Path of airplanes path of airliners:
the shortest path between airports = geodesic on the surface of the Earth
which at first sight doesn’t seem like the shortest!
name “geodesics”: from geodesy – the science of measuring the size andshape of Earth.
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GENERAL THEORY OF RELATIVITY
Special theory of relativity: Laws of physics are same for allobservers in inertial reference frames (i.e. unacceleratedobservers);What about accelerated observers?
Albert Einstein (1915):“Die Grundlage der allgemeinen Relativitätstheorie‘” (Thefoundation of the general theory of relativity)
Principle of general relativity:The laws of nature are to be expressed by equations whichhold in all frames of reference (systems of coordinates) , i.e.are “covariant” with respect to any substitutions(i.e. there are appropriate coordinate transformations torelate description in one frame of reference to another);every accelerated observer experiences the same laws of
nature;
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“Die Grundlage der allgemeinen Relativitätstheorie”
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Field Equations of GR
GR field equations = set of 10 coupled non-linear partialdifferential equations for the components of the metric tensor
“solution” of the field equation = the metric tensor (all of itscomponents)
solution mathematically very difficult, solutions have been foundonly for some special cases
E.g. Schwarzschild, de Sitter, Friedmann, Robertson,Walker,..
Einstein’s Field Equation: (just for fun…)
G = Einstein Tensor describinghow spacetime is curved;R = Ricci curvature tensor,gmn = metric tensor,R = Ricci curvature number
Stress-Energy Tensor describingdistribution of mass and energy
= Cosmological Constant(added 1917)
Einstein’s “Biggest Blunder”(resurrected as dark energy)
4
1 8
2G R Rg T g
c
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Geometry of space The geometry of space is determined by the distribution of
gravitational matter and energy
Consequences of these principles:
“space is warped‘”(“non-Euclidean”)“geodesic lines” (= shortest connections between two points) arenot necessarily straight lines;
light passing near a massive object is bent; (i.e. light hasgravitational mass!)
gravitational mass = inertial mass
gravitational radiation
gravitational redshift
clocks go slower near mass
yardsticks shorter near mass
perihelion precession of Mercury
black holes
expansion (or contraction) of the Universe
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GR: a Genuine Scientific Revolution
The General Relativity view
Relegated “gravity” to the interaction between massand spacetime
Abolished the notion that the geometry of spacetime iseverywhere flat
Mixed the concepts of space and time
GR does not mean “everything is relative”!
The basic concept is that the equations/laws thatdescribe physical systems should not depend on yourreference frame.
“Coordinate Invariance” would be a better term...
Einstein wanted to call it “The Theory of Invariants”
GR = theory of gravitation applicable to the universe(cosmology).
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Summary of GR
• Gravitation of General Relativity is not a force; it is theproperty of spacetime, its curvature.
• Mass curves spacetime, while curved spacetimedetermines the motion of mass.
• Mathematical form of General Relativity = Einstein’s FieldEquation that bind together the metric (curvature) ofspacetime and the stress-energy (mass/energy distribution).
• General solution of Einstein’s Field Equation is difficult;some important special-case solutions are known
• GR is basis of our understanding of cosmology.
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5. Quanta “Classical Physics”:
developed in 15th to 20th century;
provides very successful description of “every day,ordinary objects”
o motion of trains, cars, bullets,….
o orbit of moon, planets
o how an engine works,..
subfields: mechanics, thermodynamics,electrodynamics,
Quantum Physics:o developed early 20th century, in response to shortcomings of
classical physics in describing certain phenomena(blackbody radiation, photoelectric effect, emission andabsorption spectra…)
o describes “small” objects (e.g. atoms and their constituents)
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“Classical” vs “modern” physics
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Quantum Physics QP is “weird and counterintuitive”
o “Those who are not shocked when they first comeacross quantum theory cannot possibly haveunderstood it” (Niels Bohr)
o “Nobody feels perfectly comfortable with it “ (MurrayGell-Mann)
o “I can safely say that nobody understands quantummechanics” (Richard Feynman)
But:
o QM is the most successful theory ever developed byhumanity
o underlies our understanding of atoms, molecules,condensed matter, nuclei, elementary particles
o Crucial ingredient in understanding of stars, …
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Path to Quantum Theory
Puzzles around 1900:
Atomic spectra
Black body radiation
Photoelectric effect
Attempts to solve puzzle:
Max Planck: energy of electromagnetic field inhot box distributed in “quanta” (= packets ofenergy) – explains black body radiation
Albert Einstein: light = electromagnetic radiationcomes in packets – “photons” – explainsphotoelectric effect
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Explanation of photoelectric effect
1905: Albert Einstein (1879-1955) (Bern)
Gives explanation of observation relating tophotoelectric effect:
o Assume that incoming radiation consists of “light quanta” ofenergy h (h = Planck’s constant, =frequency)
o electrons will leave surface of metal with energy
E = h – WW = “work function” = energy necessary toget electron out of the metal
o there is a minimum light frequency for a given metal (that forwhich quantum of energy is equal to work function), belowwhich no electron emission happens
o When cranking up retarding voltage until current stops, thehighest energy electrons must have had energy eVstop onleaving the cathode
o Therefore eVstop = h – W
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Verification of Einstein’s explanation
1906 – 1916: Robert Millikan (1868-1963)(Chicago)
Did not accept Einstein’s explanation
Tried to disprove it by precise measurements
Result: confirmation of Einstein’s theory,
measurement of h with 0.5% precision
1923: Arthur Compton (1892-1962)(St.Louis):
Observes scattering of X-rays on electrons
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Classical Point of View – Newtonian Mechanics
Motion of particles: particle trajectories. Particle:
indivisible mass point object with well-defined properties(observables) that can be measured,
Observables (e.g. position and momentum) specify the state ofthe particle
All properties of a particle can be known to infinite precision. System:
= collection of particles which interact among themselves viainternal forces, and/or with the outside world via external forces.
State of a system = collection of the states of the particles thatcomprise the system.
Conclusions: trajectory state descriptor of Newtonian physics, Evolution of the state Use Newton's second law Causality: Two identical systems with the same initial conditions,
subject to the same measurement will yield the same result.
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Quantum Point of View
Quantum particles can act as both particles and wavesWave – particle duality
Quantum state:
conglomeration of several possible outcomes ofmeasurement of physical properties
Quantum mechanics uses the language ofprobability theory (random chance)
Observer is part of the system which is studied:
observer cannot observe a microscopic system withoutaltering some of its properties.
Quantization:
Many observables are "quantized", i.e. spectrum ofpossible values is not continuous:
o Energy, angular momentum, …
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Heisenberg Uncertainty Principle
For a microscopic particle, one cannot preciselyspecify the values of a particle's position and itsmomentum, i.e.
“Uncertainties” of our knowledge of position andmomentum cannot be arbitrarily small
Position and momentum are “incompatiblevariables”.
Heisenberg uncertainty principle strikes at thevery heart of classical physics, the particletrajectory.
1
2 2 2x
hx p
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Uncertainty principle (Werner Heisenberg, 1925)
it is impossible to simultaneously know a particle's exactposition and momentum p x ħ/2
h = 6.63 x 10-34 Js = 4.14 x 10-15 eV·sħ = h/(2) = 1.055 x 10-34Js = 6.582 x 10-16 eV·s(p (x) means “uncertainty” in our knowledge of p (x))
“Uncertainties” of our knowledge of position and momentumcannot be arbitrarily small
Heisenberg uncertainty principle strikes at the very heart of theclassical physics, the particle trajectory.
corresponding relation for energy and time:E t ħ/2 (precision of energy is limited due
to lifetime of state or observation time )
note that there are many such uncertainty relations in quantummechanics, for any pair of “incompatible” (non-commuting)observables (represented by “operators”)
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Features of QP Quantum physics is basically the recognition
that there is less difference between waves andparticles than was thought before
key insights:o “wave-particle duality”
light can behave like a particle particles can behave like waves (or wave packets)
o “quantization of energy” waves gain or lose energy only in "quantized amounts“
o particles (e.g. electrons) are indistinguishableo detection (measurement) of a particle
wave will change suddenly into a new waveo quantum mechanical interference – amplitudes
addo QP is intrinsically probabilistico what you can measure is what you can know
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Some facts from quantum theory Energies of electrons in atoms are “quantized” -- only certain values
allowed
“states” with well-defined energy levels, angular momentum,…
Transition between states needs energy in form of photons– absorbed or emitted
Angular momentum of charged particles is accompanied by “magneticmoment”, i.e. charged particles with angular momentum and/or spinare microscopic magnets generate magnetic field and areinfluenced by external magnetic field
Electrons have “spin” accompanied by spin magnetic moment
Nuclei also can have spin; interaction between electron’s dipolemoment and magnetic field from nuclear spin leads to “hyperfinesplitting” of energy levels
Magnetism arises from orbital angular momentum and spin ofelectrons, with a very small contribution from nuclear spin
External magnetic fields lead to splitting of energy levels – differentorientations of angular momentum with respect to magnetic fielddirection give different energy levels
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Quantum physics – open questions Quantum theory does not describe what happens to the physical
system, but only how a physical system affects another physicalsystem
there is no objective reality independent of whoever interactswith whatever
equations of quantum mechanics and the consequences areused daily in widely varying fields --- by physicists, engineers,chemists, biologists
extremely useful in all contemporary technology (e.g. notransistors without quantum mechanics)
but some amount of questioning among physicists, that there isstill some deep puzzle that we have not yet understood
Is it a blunder that works by coincidence?
is it a clue to something profound regarding the structure of theworld that we have not yet properly digested?
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6. Particles
Richard Feynman: “If, in some cataclysm, all of scientific
knowledge where to be destroyed, and onlyone sentence passed on to the nextgenerations of creatures, what statementwould contain the most information in thefewest words? I believe it is the atomichypothesis -- that all things are made ofatoms – little particles that move around inperpetual motion, attracting each other whenthey are a little distance apart, but repellingupon being squeezed into one another. Inthat one sentence, you will see, there is anenormous amount of information about theworld, if just a little imagination and thinkingare applied.”
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Sizes and
distance scales
virus 10-7
Molecule 10-9m
Atom 10-10m
nucleus 10-14 m
nucleon 10-15m
Quark <10-19m
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The Building Blocks of a Dew Drop A dew drop is made up of 1021
molecules of water.
Each water molecule = oneoxygen atom and two hydrogenatoms (H2O).
Each atom consists of a nucleussurrounded by electrons.
Electrons are leptons that arebound to the nucleus by photons,which are bosons.
nucleus of a hydrogen atom = asingle proton.
Protons consist of three quarks. Inthe proton, gluons hold the quarkstogether just as photons hold theelectron to the nucleus in theatom
Quarks may consist of smallerconstituents -- ????
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Particles of the Standard Model
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ContemporaryPhysics
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“every-day” matter
Proton
d u
d
ne
Neutron
e
u d
u
Electron Electron Neutrino
g
Photon
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Forces (interactions)
Strong interaction 1
Binds quarks to form hadrons (protons,…)
Binds protons and neutrons to form nuclei
Electromagnetic interaction 10-2
Binds electrons and nuclei to form atoms
Binds atoms to form molecules etc.
Weak interaction 10-10
Causes radioactivity
Gravitational interaction 10-40
Binds matter on large scales
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What holds the world together?
interaction
participants
relative strength
field quantum
(boson)
strong
quarks
1
g
gluon
electro-magnetic
chargedparticles
10-2
photon
weak
all particles
10-10
W± Z0
gravity
all particles
10-40
G
graviton
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Beta decay
d u
d
Neutron
Proton
u d
u
e
Electronne
Anti-electron Neutrino
W -
Mean lifetime of a freeneutron ~ 10.3 minutes
Mean lifetime of a freeproton > 1032 years!Question: Why doesn’tthe neutron in thedeuteron decay? Hint:deuteron mass = 1875.6MeV/c2
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Quantum Field Theory
Energy and matter are equivalent (E = mc2)
“Virtual particles” A particle-antiparticle pair can pop out of empty space (“the vacuum”) And then vanish back into it
Consequence: structure of the universe depends on particles that don’t exist in the
usual sense (but did when the Universe was very young and hot)
One of the aims of particle physics: understand those particles,even though they do not appear visibly in our everyday experience We do not see these particles in everyday life We must recreate the state of the early hot universe to make them
t
t
Vacuum FluctuationInvolving top quarks
. .
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field or particle?
All fields have small packets of energy associated withthem --- “field quanta”
Quantum of electromagnetic field = photon ()
Quanta are ”excitations” of field -- can become “real” iffield kicked hard enough
Field quanta are particles that carry forces
Elementary particles interact by exchangeof field quanta
e-
e-
g
e-
e-
Interaction of 2 electrons bythe exchange of a photon.The photon is the quantum ofthe electromagnetic field
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The world around us
Most of what’s around us is made of very fewparticles: electrons, protons, neutrons (e, u, d)
this is because our world lives at very low energy
all other particles were created at high energiesduring very early stages of our universe
can recreate some of them (albeit for very shorttime) in our laboratories (high energy acceleratorsand colliders)
this allows us to study their nature, test thestandard model, and discover direct or indirectsignals for new physics
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Study of high energy interactions -- going back in time
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pp physics at the LHC correspondsto conditions around here
HI physics at the LHC correspondsto conditions around here
76LHC Physics Highlights
Pbar p physics at the Tevatron correspondsto conditions around here
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“Standard Model” of Particle Physics
Quantum field theory
Particles are excitations of the fields (electron field,quark field,…)
Interactions are mediated by quanta of “gauge fields”
Gauge fields and form of interactions are determined by“symmetry” of the “Lagrangian” of the theory, wheresymmetry means invariance under certaintransformations (“gauge transformations”)
invariance under gauge transformations leads totheories with massless particles
Higgs field provides mechanism to break symmetry soas to allow particles to have mass while still preservingnice features of the theory
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“Gauge Transformations”
Hermann Weyl (1920):
noted scale invariance of electromagnetism
tried to unify general relativity andelectromagnetism
conjectured that “Eichinvarianz” (scaleinvariance) may be also a local gauge theory ofgeneral relativity – did not work out
later realized that requiring the Schrödingerequation to be invariant under a local gauge(phase) transformation leads naturally toelectromagnetic field and gives the form of theinteraction of a charged quantum particle
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Global and local gauge transformations
global transformation: same transformation carried out at all space-time points
(“everywhere simultaneously”) local transformation:
different transformations at different space-time points globally invariant theories in general not invariant under
local transformations in quantum field theory, can restore invariance under local
gauge (phase) transformation by introducing new forcefields that interact with the original particles of the theory ina way specified by the invariance requirement
i.e. in this sense the dynamics of the theory is governedby the symmetry properties
can view these force fields as existing in order to permitcertain local invariances to be true
electroweak interaction theory as well as QCD followfrom gauge invariance which is a generalization of thegauge invariance of Maxwell’s equations
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7. Architecture of the Cosmos
GRT, together with particle physics, nuclearphysics,.. used as basis for development ofquantitative cosmological model
Today’s generally accepted “standard Big-BangModel, the “Lambda-CDM model” explains broadrange of phenomena, including the abundance oflight elements, the cosmic microwave background,large scale structure and Hubble's Law.
Earliest times (<10-43 sec) not yet understood
Some other problems and unsolved questions(e.g. size of cosmological constant, matter vsantimatter, heavy element synthesis,…)
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Cosmology In 1919:
The known universe only contains the galaxy.
Many open questions:o Are there stars / star systems beyond our galaxy?
o Is the universe static?
o How big is the universe?
o Does the universe have a beginning?
o What is the material and energy content of the universe?
1920 “The great debate”:
Shapley: The galaxy is vast and includes globular systems andcloud systems of stars. The sun is located at the edge.
Curtis: The galaxy is small and the sun is close to the center.Outside there are other galaxies
1920-1924 Hubble:
Andromeda “Nebula” is outside the galaxy, and is itself a kind ofgalaxy.
1929 Hubble: the universe expands.
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GRT vs cosmology
1916: Schwarzschild presents the first solution of the
field equations. (describes the sphericallysymmetric gravitational field outside a spherical,uniform and non-rotating mass distribution M)
Contains two distances where the solution "doesnot exist" (singularities):
o (1) r=0 (the origin). Here space and time cease toexist.
o (2) rs=2GM/c2 (the Schwarzschild radius)
Meaning of rs: if all mass M is compressed withinrs then the light can not escape black hole.
Example: the rs of the Earth is …9mm
Black holes exist -- some very massive (many solarmasses);
the center of our galaxy contains a massive blackhole.
Artist’s impression ofa Black Hole
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Big Bang
Einstein 1917
Thinks that there are no mass-free solutions (Mach's principle).
With the strengthening action of the masses, the universecollapses; introduces an additional term: the cosmologicalconstant Λ, so as to make the universe static.
De Sitter shows immediately that there exist mass free solutions.("That man does not understand his own theory.")
Friedman 1922
shows that the original field equations allow expanding solutions.
Weyl and Eddington 1923
show that in the de Sitter universe test particles are moving awayfrom each other. Einstein gives the cosmological constant up ("Mybiggest blunder").
Hubble 1929
shows that the universe expands: beginning of the big bangtheory.
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Beginning of Time: Big Bang
Big Bang theory with inflation
Most widely accepted cosmological theory
Starts with “Big Bang”, i.e. abrupt appearance ofexpanding space time (13.7980.037)Gy ago
inflationary epoch: t 10-36 to 10-32, space expands byhuge factor 1027 to size of a grapefruit
After cosmic inflation, expansion continues atdecreasing rate
Expansion cooling formation of particles, nuclei
“recombination”: at t 380ky formation of atoms (H) Cosmic background radiation (CMB)
Accelerated expansion: from t 7 Gy to now
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Timeline of the metric expansion of space; space (including hypothetical non-observableportions of the universe) is represented at each time by the circular sections. On the left thedramatic expansion occurs in the inflationary epoch, and at the center the expansionaccelerates (artist's concept; not to scale). (https://www.wikiwand.com/en/Big_Bang )
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Other cosmological theories
Cyclic theory (Big Bang – Big Crunch):
Every Ty (1012 years), expansion changes tocontraction universe shrinks, becomesinfinitesimally small, then a new Big Bang
Cycles of Big Bang and Big Crunch continueforever
Eternal inflation:
Spacetime infinite in space and in past andfuture time
Our Big Bang and universe is just one of many
…..
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Hubble deep field view
http://hubblesite.org/newscenter/archive/releases/2014/27/image/a/format/xlarge_web/
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Planck -- CMB
The anisotropies of the Cosmic microwave background (CMB) as observed by Planck. The CMB is a snapshot ofthe oldest light in our Universe, imprinted on the sky when the Universe was just 380 000 years old. It shows tinytemperature fluctuations that correspond to regions of slightly different densities, representing the seeds of all futurestructure: the stars and galaxies of today. (blue – hot – less dense, red – cold – denser)
http://www.esa.int/spaceinimages/Images/2013/03/Planck_CMB
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The "angular power spectrum" of the fluctuations in the Planck full-sky map. This shows therelative brightness of the "spots" in the map vs. the size of the spots. Green line = fit with “standardmodel”, red dots = Planck measurements
http://sci.esa.int/science-e-media/img/63/Planck_power_spectrum_orig.jpg
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Content of the Universe WMAP data reveals that its contents include
4.6% atoms, the building blocks of stars andplanets. Dark matter comprises 23% of theuniverse. This matter, different from atoms,does not emit or absorb light. It has only beendetected indirectly by its gravity. 72% of theuniverse, is composed of "dark energy", thatacts as a sort of an anti-gravity. This energy,distinct from dark matter, is responsible for thepresent-day acceleration of the universalexpansion. WMAP data is accurate to twodigits, so the total of these numbers is not100%. This reflects the current limits ofWMAP's ability to define Dark Matter and DarkEnergy.
Credit: NASA / WMAP Science Team
http://map.gsfc.nasa.gov/media/080998/index.html
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Contents of the universe
Planck's high-precision cosmic microwave background map has allowed scientists to extract the most refined valuesyet of the Universe's ingredients. Normal matter that makes up stars and galaxies contributes just 4.9% of theUniverse's mass/energy inventory. Dark matter, which is detected indirectly by its gravitational influence on nearbymatter, occupies 26.8%, while dark energy, a mysterious force thought to be responsible for accelerating the expansionof the Universe, accounts for 68.3%. (http://sci.esa.int/planck/51557-planck-new-cosmic-recipe/ )The 'before Planck' figure is based on the WMAP 9-year data release presented by Hinshaw et al., (2012).
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CosmicHistory
WMAP observes the first light of the universe- the afterglow of the Big Bang. This light emerged 380,000 years after the BigBang. Patterns imprinted on this light encode the events that happened only a tiny fraction of a second after the Big Bang. Inturn, the patterns are the seeds of the development of the structures of galaxies we now see billions of years after the BigBang.
Credit: NASA / WMAP Science Team
http://map.gsfc.nasa.gov/media/020622/index.html
