L23/24, part 1: let s end up with the story of relativity

Transcription

1 L23/24, part 1: let s end up with the story of relativity Special relativity showed that space and time are not absolute Instead they are inextricably linked in a fourdimensional combination called spacetime In spacetime, inertial frames are equivalent Maybe we can have also equivalence between accelerated frames? 1

2 The Equivalence Principle Einstein postulated that all motion is relative by pointing out that the effects of acceleration are exactly equivalent to those of gravity 2

3 Key Ideas of General Relativity Gravity arises from distortions of spacetime Time runs slowly in gravitational fields The universe may have no boundaries and no center but may still have finite volume Changes in the velocity of masses can cause gravitational waves 3

4 Rubber Sheet Analogy Matter distorts spacetime in a manner analogous to how heavy weights distort a rubber sheet 4

5 Rules of Geometry in Flat Space Straight line is shortest distance between two points Parallel lines stay same distance apart Angles of a triangle sum to 180 Circumference of circle is 2πr 5

6 Gravity, Newton, and Einstein Newton viewed gravity as a mysterious action at a distance Einstein removed the mystery by showing that what we perceive as gravity arises from curvature of spacetime 6

7 Geometry on a Curved Surface Straight lines are shortest paths between two points in flat space Great circles are the shortest paths between two points on a sphere 7

8 Rules of Spherical Geometry Great circle is shortest distance between two points Parallel lines eventually converge Angles of a triangle sum to > 180 Circumference of circle is < 2πr 8

9 Rules of Saddle-Shaped Geometry Piece of hyperbola is shortest distance between two points Parallel lines diverge Angles of a triangle sum to < 180 Circumference of circle is > 2πr 9

10 Gravitational Lensing Curved spacetime alters the paths of light rays, shifting the apparent positions of objects in an effect called gravitational lensing Observed shifts precisely agree with general relativity 10

11 Time in a Gravitational Field Effects of gravity are exactly equivalent to those of acceleration Time must run more quickly at higher altitudes in a gravitational field than at lower altitudes Passage of time has been measured at different altitudes has been precisely measured Time indeed passes more slowly at lower altitudes in precise agreement with general relativity Gravitational redshift 11

12 Paths in curved Spacetime 12

13 Gravitational Waves General relativity predicts that movements of a massive object can produce gravitational waves just as movements of a charged particle produce light waves Gravitational waves have not yet been directly detected 13

14 Light waves take extra time to climb out of a deep hole in spacetime leading to a gravitational redshift 14

15 Esempio: velocita di fuga; buco nero

16 Se la Terra e il Sole fossero buchi neri Terra: m ~ kg, R T ~ 6400 km Sole: m ~ kg, R ~ 100 R T 16

17 Gravity under extreme conditions M= 3.6 x 10 6 Solar Masses Terra Radiazione dal Centro Galattico Prime osservazioni di raggi gamma: 2004/05 17

18 Black Holes and Accretion Disks Although light from a black hole cannot escape, light from events taking place near the black hole is visible If a binary star system has a black hole and a normal star, the material from the normal star can be pulled into the black hole This material forms an accretion disk around the black hole Friction among the particles in the disk transforms mechanical energy into internal energy MAGIC

19 A black hole s mass strongly warps space and time in vicinity of event horizon Spacetime is so curved near a black hole that nothing can escape The point of no return is called the event horizon Event horizon is a three-dimensional surface Event horizon 19

20 Black Hole Verification Need to measure mass Use orbital properties of companion Measure velocity and distance of orbiting gas It s a black hole if it s not a star and its mass exceeds the neutron star limit (~3 M Sun ) It emits huge amounts of energy in gamma rays!!! 20

21 One famous X-ray binary with a likely black hole is in the constellation Cygnus 21

22 Part 2: Fundamental Particles What are the basic building blocks of matter? What are the forces that hold matter together? How did the universe begin? Will the universe end, and if so, how and when? (maybe, in the next few hours?) How to be happy? 22

23 The Building Blocks of Matter We have thought of electrons, neutrons, and protons as elementary particles, because we believe they are basic building blocks of matter. In this lecture the term elementary particle is used loosely to refer to hundreds of particles, most of which are unstable and not fundamental. 23

24 Accelerators Dawn of particle physics: cosmic rays (1910-) Particle physics was not able to develop fully until particle accelerators were constructed with high enough energies to create particles with a mass of about 1 GeV/c 2 or greater (1940 onwards) There are two main types of accelerators used presently in particle physics experiments: linear accelerators, and colliders. Colliders are the most effective Presently E ~ 10 TeV 24

25 Early Discoveries In 1930 the known elementary particles were the proton, the electron, and the photon. Thomson identified the electron in 1897, and Einstein s work on the photoelectric effect can be said to have defined the photon (originally called a quantum) in The proton is the nucleus of the hydrogen atom. Despite the rapid progress of physics in the first couple of decades of the twentieth century, no more elementary particles were discovered until 1932, when Chadwick proved the existence of the neutron, and Carl Anderson identified the positron in cosmic rays. 25

26 The Positron; antiparticles Dirac in 1928 introduced the relativistic theory of the electron when he combined quantum mechanics with relativity. Various attempts Final success between 1930 and 1935 The smallest space is C 4 Dirac s wave equation had negative, as well as positive, energy solutions. Spin and antisymmetry of fermion wavefunction come for free! Dirac s theory, along with refinements made by others, opened the possibility of antiparticles which: Have the same mass and lifetime as their associated particles Have the same magnitude but are opposite in sign for such physical quantities as electric charge and various quantum numbers The positron was identified as the antiparticle of the electron 26

27 The Fundamental Interactions We have learned that the fundamental forces act through the exchange or mediation of particles. The exchanged particle in the electromagnetic interaction is the photon. The Glashow-Weinberg-Salam theory (1960), called the electroweak theory, unified the electromagnetic and weak interactions as Maxwell had unified electricity and magnetism into the electromagnetic theory a hundred years earlier. The theory was confirmed experimentally by Rubbia (1983). M ~ 90 GeV 27

28 The Standard Model The most widely accepted theory of elementary particle physics at present is the Standard Model. It is a simple, comprehensive theory that explains hundreds of particles and complex interactions with six quarks, six leptons, and three force-mediating particles See later It is a combination of the electroweak theory and quantum chromodynamics (QCD), but does not include gravity See later 28

29 Classification of Elementary Particles We discussed that particles with half-integral spin are fermions and those with integral spin are bosons. This is a particularly useful way to classify elementary particles because all stable matter in the universe appears to be composed, at some level, of constituent fermions. Mediators of forces appear on the contrary to be bosons at the fundamental level: Photons, gluons, W ±, and the Z are the gauge bosons responsible for the strong and electroweak interactions. Fermions exert attractive or repulsive forces on each other by exchanging gauge bosons, which are the force carriers. 29

30 The Higgs Boson One other boson that has been predicted, but not yet detected, is necessary the theory to explain why the W ± and Z have such large masses, yet the photon has no mass. The search for the Higgs boson is of the highest priority in elementary particle physics. At reach in the next 3 years 115 GeV < m < 166 GeV (95% C.L.) 30

31 Leptons (don t feel the strong force) The leptons are perhaps the simplest of the elementary particles. They appear to be pointlike, that is, with no apparent internal structure, and seem to be truly elementary. Thus far there has been no plausible suggestion they are formed from some more fundamental particles. There are only six leptons plus their six antiparticles. 31

32 The electron and the muon Each of the charged leptons (τ, μ, e) has an associated neutrino, named after its charged partner (for example, muon neutrino). The muon decays into an electron, and the tau can decay into an electron, a muon, or even hadrons (which is most probable). The muon decay (by the weak interaction) is: 32

33 Neutrinos Neutrinos have zero charge. Their masses are known to be very small. The precise mass of neutrinos may have a bearing on current cosmological theories of the universe because of the gravitational attraction of mass. All leptons have spin 1/2, and all three neutrinos have been identified experimentally. Neutrinos are particularly difficult to detect because they have no charge and little mass, and they interact very weakly. 33

34 Hadrons These are particles that act through the strong force. Two classes of hadrons: mesons and baryons. Mesons are particles with integral spin having masses greater than that of the muon (106 MeV/c 2 ). All baryons have masses at least as large as the proton and have half-integral spins. 34

35 Mesons Mesons are bosons because of their integral spin. The meson family is rather large and consists of many variations, distinguished according to their composition of quarks. The pion (π-meson) is a meson that can either have charge or be neutral. In addition to the pion there is also a K meson, which exists in both charged (K ± ) and neutral forms (K 0 ). The K meson is the antiparticle of the K +, and their common decay mode is into muons or pions. All mesons are unstable and not abundant in nature. 35

36 Baryons The neutron and proton are the best-known baryons. The proton is the only stable baryon, but some theories predict that it might be also unstable with a lifetime greater than years. All baryons except the proton eventually decay into protons. 36

37 Particles and Lifetimes The lifetimes of particles are also indications of their force interactions. Particles that decay through the strong interaction are usually the shortest-lived, normally decaying in less than s. The decays caused by the electromagnetic interaction generally have lifetimes on the order of s, and The weak interaction decays are even slower, longer than s. 37

38 Quarks From 1930 to 1960, particles were studied at accelerators and with cosmic rays Hundreds of elementary particles were discovered and it became likely that they were composite. In 1963 Gell-Mann, Zweig and Ne eman proposed that hadrons were formed from fractionally charged particles called quarks. The quark theory described properties of the particles like reactions and decay. Three quarks were proposed, named the up (u), down (d), and strange (s), with the charges +2e/3, e/3, and e/3, respectively. All the known hadrons could be specified by some combination of such quarks and antiquarks. Quarks are, at the present level of investigation, pointlike, just like leptons. Then new particles were discovered, and three more quarks were needed: charm c (+2e/3), bottom b (-e/3), top t (2/3 e). 38

39 Quark Properties We can now present the given quark properties and see how they are used to make up the hadrons. The spin of all quarks (and antiquarks) is 1/2.

40 Quark Description of Particles A meson consists of a quark-antiquark pair, which gives the required baryon number of 0. Baryons consist of three quarks. The structure is quite simple. For example, a π consists of, which gives a charge of ( 2e/3) + ( e/3) = e, and the two spins couple to give 0 ( 1/2 + 1/2 = 0). A proton is uud, which gives a charge of (2e/3) + (2e/3) + ( e/3) = +e; its baryon number is 1/3 + 1/3 + 1/3 = 1; and two of the quarks spins couple to zero, leaving a spin 1/2 for the proton (1/2 + 1/2 1/2 = 1/2).

41 Quantum Chromodynamics (QCD) Because quarks have spin 1/2, they are all fermions and according to the Pauli exclusion principle, no two fermions can exist in the same state. Yet we have three strange quarks in the Ω. This is not possible unless some other quantum number distinguishes each of these quarks in one particle. A new quantum number called color circumvents this problem and its properties establish quantum chromodynamics (QCD). Color is the charge of the strong nuclear force, analogous to electric charge for electromagnetism. There are 3 colors conventionally R, G, B. 41

42 Confinement Physicists now believe that free quarks cannot be observed; they can only exist within hadrons. This is called confinement. When a high-energy gamma ray is scattered from a neutron, a free quark cannot escape because of confinement. For high enough energies, an antiquark-quark pair is created (for example, ), and a pion and proton are the final particles. 42

43 The Families of Matter - I We now have a brief review of the particle classifications and have learned how the hadrons are made from the quarks. In summary: We presently believe that the two varieties of fermions, called leptons and quarks, are fundamental particles. These fundamental particles can be divided into three simple families or generations. Each generation consists of two leptons and two quarks. The two leptons are a charged lepton and its associated neutrino. The quarks are combined by two or three to make up the hadrons. 43

44 The Families of Matter - II Leptons are pointlike (no internal structure). There are three leptons with mass and three others with little mass (the neutrinos). Quarks and antiquarks make up the hadrons (mesons and baryons). Quarks may also be pointlike (< m) and are confined together, never being in a free state. There are six flavors of quarks (up, down, strange, charmed, bottom, and top) and there are three colors (green, red, and blue) for each flavor. Rules for combining the colored quarks allow us to represent all known hadrons. Bosons mediate the four fundamental forces of nature: gluons are responsible for the strong interaction, photons for the electromagnetic interaction, W ± and Z for the weak interaction, and the as yet unobserved graviton for gravitation 44

45 The Families of Matter - III Most of the mass in the universe is made from the components in the first generation (electrons and u and d quarks). The second generation consists of the muon, its neutrino, and the charmed and strange quarks. The members of this generation are found in certain astrophysical objects of high energy and in cosmic rays, and are produced in high-energy accelerators. The third generation consists of the tau and its neutrino and two more quarks, the bottom (or beauty) and top (or truth). The members of this third generation existed in the early moments of the creation of the universe and can be created with very high energy accelerators. 45

46 Beyond the Standard Model Although the Standard Model has been successful in particle physics, it doesn t answer all the questions. For example, it is not by itself able to predict the particle masses. Why are there only three generations or families of fundamental particles? Do quarks and/or leptons actually consist of more fundamental particles? Why there is more matter than antimatter? 46

47 Grand Unifying Theories There have been several attempts toward a grand unified theory (GUT) to combine the weak, electromagnetic, and strong interactions. Many of such theories involve symmetries between fermions and bosons (supersymmetry), and/or extra dimensions Predictions 1) The proton is unstable with a lifetime of to years. Current experimental measurements have shown the lifetime to be greater than years. 2) Neutrinos may have a small, but finite, mass. This has been confirmed. 3) Massive magnetic monopoles may exist. There is presently no confirmed experimental evidence for magnetic monopoles. 4) The proton and electron electric charges should have the same magnitude. 47

48 Part 3: Cosmology and particle astrophysics Now we describe one of the most fascinating theories in all of science the Big Bang theory of the creation of the Universe and the experimental evidence that supports it. This theory of cosmology states that the Universe had a beginning and erupted from an extremely dense, pointlike singularity about 14 billion years ago.such an extreme of energy occurred in the first few instants after the Big Bang that it is believed that all four interactions of physics were unified and that all matter melted down into an undifferentiated quark-gluon primordial soup. 48

49 Astronomy Scales Nearest Stars Nearest Galaxies Nearest Galaxy Clusters 4.5 pc 450 kpc 150 Mpc 1 pc ~ 3.3 ly 49

50 Our Galaxy: The Milky Way Magnetic field few μg 50

51 What do we know about our Universe? Many things, including the facts that Particles are coming on Earth at energies 10 8 times larger than we are able to produce The Universe expands (Hubble ~1920): galaxies are getting far with a simple relationship between distance & recession speed

52 Redshift 52

53 Hubble s law Today: H 0 = 73 ± 3 (km/s) / Mpc Slope = H 0 (Hubble costant) 53

54 Once upon a time... our Universe was smaller Primordial singularity!!! => BIG BANG 54

55 How far in time? Extrapolating backwards the present expansion speed towards the big bang T ~ 1/H 0 ~ 14 billion years (note that the present best estimate, with a lot of complicated physics inside, is T = 13.7 ± 0.2 Gyr) Consistent with the age of the oldest stars 55

56 What is our future? Depending on the interplay between gravity and kinetic energy, the Universe will continue to expand or recollapse eventually 56

57 Critical density

58 Time & temperature (=energy) Once upon a time, our Universe was hotter Expansion requires work (and this is the most adiabatic expansion one can imagine, so the work comes from internal energy) T 15 ~ 10 t 9 K 58

59 Decoupling γ particles+antiparticles γ proton-antiproton γ electron-positron ( ) then matter became stable Time Two epochs 59

60 Cosmology and particle astrophysics

61 Accelerators Large Hadron Collider E BR R 10 km, B 10 T E 10 TeV Tycho SuperNova Remnant R km, B T E 1000 TeV ( NB. E Z Pb/Fe higher energy)

62 Particle Physics Particle Astrophysics Terrestrial Accelerators Cosmic Accelerators Active Galactic Nuclei Diameter of collider LHC CERN, Geneva, 2007 SuperNova Remnant Binary Systems Cyclotron Berkeley 1937 Energy of accelerated particles 62

63 Ultra High Energy from Cosmic Rays From laboratory accelerators From cosmic accelerators cross-section (mb) Particle cross-sections measured in accelerator experiments Fixed target beamlines particle flux /m 2 /st/sec/gev Flux of cosmic ray particles arriving on Earth Colliders FNAL LHC Colliders FNAL LHC Energy GeV Energy GeV Ultra High Energy Particles arrive from space for free: make use of them 63

64 The Universe at very high energies (gamma-rays) 64

65 Detection of cosmic rays Via satellites or large detectors at ground

66 The problem of rotation curves

67 67

68 Flat rotation curves => ~80-90% of the matter is dark Ω m ~ 0.03 Ω dark ~ 0.23 This leads to another copernican revolution: We are not the center of the Universe AND, likely, We are not made of what most of the Universe is made of. 68