4/22/10 Lecture 22: The Big Bang (Continued) & The Fate of the Earth and Universe Review: The Wave Nature of Matter A2020 Prof. Tom Megeath Louis de Brogilie in 1928 proposed (in his PhD thesis) that matter had a wave-like nature Wavelength given by λ = h/p = h/mv where h = Planck’s constant (remember E = hν for photons) Objects are moving fasting have smaller wavelenghts Less massive objects have a larger wavelength De Brogilie won the Nobel Prize for this work in 1929 The Bohr Hydrogen Atom see: http://www.7stones.com/Homepage/Publisher/ n λ = 2 π r The Wave Nature of Matter Bohr.html n = integer (1, 2, 3, ..) r = radius of orbit 2πr = circumference of orbit λ = h/mv (de Broglie) n h/mv = 2πr r = n h/(2πmv) E = k e2/r (e charge of electron or What does the amplitude of an electron wave mean? proton, k = Coulomb constant) Balance centrifugal and coulomb force between electron and proton Sound wave: amplitude is loudness mv2/r = ke2/r2 Light wave: amplitude is strength of electric field/intensity 1/2 m (nh/2πm)2 r)3 = ke2/r2 2 (nh/2πm)2/ke2 = r Electron wave: amplitude is probability that electron will be E = 2π2k2e4m2/n2h2 found there. Introduced by Niels Bohr in 1913 1 4/22/10 Uncertainty Principle Fundamental Particles Location and Momentum Uncertainty Uncertainty Planck’s > in position X in momentum Constant (h) Energy and Time Uncertainty Uncertainty Planck’s > (Baryons are particles in energy X in time Constant (h) made of 3 quarks) Fundamental Particles Quarks • Protons and neutrons are made of quarks • Up quark (u) has charge +2/3 • Down quark (d) has charge -1/3 (Baryons are particles made of 3 quarks) 2 4/22/10 Four Forces Matter and Antimatter • Strong Force (holds nuclei together) – Exchange particle: gluons • Electromagnetic Force (holds electrons in atoms) – Exchange particle: photons • Weak force (mediates nuclear reactions) – Exchange particle: weak bosons • Gravity (holds large-scale structures together) • Each particle has an antimatter counterpart – Exchange particle: gravitons • When a particle collides with its antimatter counterpart, they annihilate and become pure energy in accord with E = mc2 Matter and Antimatter Virtual Particles • Uncertainty principle (in energy & time) allows production of matter-antimatter particle pairs • But particles must annihilate in an • Energy of two photons can combine to create a undetectably short particle and its antimatter counterpart (pair production) period of time 3 4/22/10 What is the history of the The different Eras of the universe according to the Big Universe Bang theory? Around 300,000 after the big band, the universe cooled to the points that atoms formed from a hot gas of electrons and protons (we’ll look at this in more detail in the next lecture) Planck Era The early universe must Before Planck have been time (~10-43 extremely hot sec) and dense No theory of quantum gravity 4 4/22/10 Do forces unify at high temperatures? GUT Era Four known forces Lasts from in universe: Planck time (~10-43 sec) to Strong Force end of GUT force (~10-38 Electromagnetism sec) Weak Force Gravity Yes! Maybe Who knows? (Electroweak) (GUT) (String Theory) Electroweak Particle Era Era Amounts of Lasts from end matter and of GUT force antimatter (~10-38 sec) to nearly equal end of electroweak (Roughly 1 force (~10-10 extra proton sec) for every 109 proton- antiproton pairs!) 5 4/22/10 Era of Nucleo- Photons converted into synthesis particle-antiparticle pairs and vice-versa Begins when matter annihilates 2 E = mc remaining antimatter at ~ 0.001 sec Early universe was full of particles and radiation Nuclei begin to because of its high fuse temperature Era of Nuclei Era of Atoms Helium nuclei Atoms form at form at age age ~ 380,000 ~ 3 minutes years Universe has Background become too radiation cool to blast released helium apart 6 4/22/10 Era of What have we learned? Galaxies • What were conditions like in the early Galaxies form universe? at age ~ 1 – The early universe was so hot and so dense billion years that radiation was constantly producing particle-antiparticle pairs and vice versa • What is the history of the universe according to the Big Bang theory? – As the universe cooled, particle production stopped, leaving matter instead of antimatter – Fusion turned remaining neutrons into helium – Radiation traveled freely after formation of atoms How do the abundances of elements support the Big Bang theory? Protons and neutrons combined to make long-lasting helium nuclei when universe was ~ 3 minutes old 7 4/22/10 Abundances of other light elements agree with Big Bang model having 4.4% normal matter – more evidence for WIMPS! Big Bang theory prediction: 75% H, 25% He (by mass) Matches observations of nearly primordial gases Thought Question Thought Question Which of these abundance patterns is an unrealistic Which of these abundance patterns is an unrealistic chemical composition for a star? chemical composition for a star? A. 70% H, 28% He, 2% other A. 70% H, 28% He, 2% other B. 95% H, 5% He, less than 0.02% other B. 95% H, 5% He, less than 0.02% other C. 75% H, 25% He, less than 0.02% other C. 75% H, 25% He, less than 0.02% other D. 72% H, 27% He, 1% other D. 72% H, 27% He, 1% other 8 4/22/10 How do we probe the physics of The Large Hadron Collider When protons arrive in the LHC they are the big bang? travelling at 0.999997828 times the To probe the physics of the Particle, Electroweak and GUT era, we need to speed of light. simulate the incredible temperatures of that era. Each proton goes around the 27km ring over 11,000 times a second. We cannot heat a gas to this temperature, but we can collide individual A nominal proton beam in the LHC will particles like protons or electrons accelerated to speeds near the speed of have an energy equivalent to a person in light. a Subaru driving at 1700 kph. Equivalent to temperatures of 1017 K Evidence for the Big Bang Now the future of the Universe • Why are the Galaxies expanding away from us and follow Hubble’s law? – The observed expansion can be simply explained by the expansion of space. If we follow back that expansion, the density of matter increases dramatically. • Why is the darkness of the night sky evidence for the Big Bang? – If the universe were eternal, unchanging, and everywhere the same, the entire night sky would be covered with stars – The night sky is dark because: • we can see back to a time when there were no stars • Cosmic expansion • How do we observe the radiation left over from the Big Bang? – Radiation left over from the Big Bang is now in the form of microwaves—the cosmic microwave background—which we can observe with a radio telescope on the ground or from satellite. – Radiation gives us information on the curvature of the universe and the origin of structure (i.e. of clusters of galaxies and galaxies) • How do the abundances of elements support the Big Bang theory? Not enough – Observations of helium and other light elements agree with the predictions for dark matter fusion in the Big Bang theory 9 4/22/10 The Arrow of Time Entropy If I showed you a movie, you could tell me if I was playing that movie forward or in Entropy is a measure of disorder in a system. reverse. Time has a distinct direction. 2nd law of Thermodynamics: Entropy always increases. Newton’s laws, Relativity and Quantum Mechanics don’t have an intrinsic arrow of time. If I showed you a movie of the planets going around the solar system, you would Processes in which entropy increases are called irreversible. have a hard time deciding if I was showing forward or in reverse. Examples: Consider two situations: As the ice cube melts, the entropy increases. A ball falls to the ground. It bounces, but on each bounce, some of its kinetic energy is converted into heat energy, until it sits on the ground (conservation of energy). When ball hits ground and heats up and entropy increases. Can the heat energy get absorbed by the ball and the ball fly into the air? Question: how does life form? You put an ice cube in your water. The heat from the water is absorbed by the ice cube, Answer: we can lower the entropy in one particular place by dumping entropy and it melts the ice cube until you have a glass of water at one temperature. somewhere else. Entropy decreases locally, but total entropy increases in the universe. Can an ice cube reform spontaneously by the heat energy leaving from a “cube” of water? Example: your refrigerator can reduce entropy locally and produce ice cubes, but it increases entropy in the universe (by heating up your house). What is the Future of the Entropy Universe? If we think of that quantity which with reference to a single body I have called entropy, as formed in a consistent way, with consideration of all the circumstances, for the whole Can we predict this using the laws of physics universe, and if we use in connection with it the other and our understanding of cosmic evolution? simpler concept of energy, we can express the fundamental laws of the mechanical theory of heat in the following simple form: Following lecture based on the paper: A 1. The Energy of the Universe is Constant Dying Universe: The Long Term Fate and Evolution of Astrophysical Objects by 2.