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Michael Luke University of Toronto Particle Physicists Web More » (And Others) Particle Physics and the Theory of Nothing Michael Luke University of Toronto Particle Physicists Web more » (and others) like to talk about 1 10 171,000 "Theory of Everything" 0.20 finding a “theory of Theory Of Everything everything” ... ... ... ... theory of everything ... Theory of Everything ... THEORY OF EVERYTHING ... Theory of Everything Theory of Everything ... ... Theory of Everything Particle Physicists (and others) like to talk about finding a “theory of everything” ... ... but what we could really use is a theory of Nothing. Nothing (an experimental definition): - seal the box and pump out all the air - shield with 103 light-years of lead to keep out the neutrinos We do not understand what is in the box. But I can tell you some of the things it does: screens charges (~dielectric) superconducts makes electrons (and other elementary particles) massive determines the nature of beta decay confines quarks into hadrons “melts” when heated to 1012 K is the same stuff as ~70% of the energy in the Universe Understanding what is in an empty box is the central goal of particle physics! back to 1905 .... “On a Heuristic Point of View about the Creation Ann. Phys. (Leipzig) 14, Supplement, 164 –181 (2005) and Conversion of Light” (Annalen der Physik. 17: 132, 1905) Ann. Phys. (Leipzig) 14, Supplement (2005) / www.ann-phys.org 165 c 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim c 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim “On the Electrodynamics of Moving Bodies” Ann. Phys. (Leipzig) 14, Supplement, 164 –181 (2005) (Annalen der Physik. 17:891, 1905) Ann. Phys. (Leipzig) 14, Supplement, 194-224 (2005) A. Einstein, Annalen der Physik, Band 17, 1905 c 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim c 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim “Does the Inertia of a Moving Body Depend Upon Ann. Phys. (Leipzig) 14, Supplement, 225–228 (2005) its Energy-Content?” (Annalen der Physik. 18: 639, 1905) 226 A. Einstein, Annalen der Physik, Band 18, 1905 c 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim c 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Two revolutions of 20th century physics: special relativity and quantum mechanics E = mc2 mass and energy are equivalent E = hν = hc/λ electromagnetic energy comes in individual “lumps” (photons) - an electromagnetic field (classical wave) is composed of particles (quantized modes of vibration) What happens when we put relativity + QM together? “Particle in a Box” Quantum Relativity (Heisenberg) (Einstein) ∆x∆p ∼ h¯ ∆v ! c L ∆p ∼ h¯/L (no problem!) ⇒∆v ∼ h¯/(mL) h¯ L ! mc What happens when we put relativity + QM together? “Particle in a Box” Quantum Relativity (Heisenberg) (Einstein) ∆x∆p ∼ h¯ ∆v ! c ?? ∆p ∼ h¯/L use relativistic L kinematics! ⇒∆v ∼ h¯/(mL) E=(p2c2+m2c4)1/2 h¯ L ! 2 mc ∆E ! mc What happens when we put relativity + QM together? “Particle in a Box” Quantum Relativity (Heisenberg) (Einstein) ∆x∆p > h¯ ∆v ! c ?? ∆p ∼ h¯/L use relativistic L kinematics! ∆v ∼ h¯/(mL) E=(p2c2+m2c4)1/2 h¯ L ! 2 mc ∆E ! mc number of particles in the box is uncertain! “virtual particles” - relativity when you are not moving fast! - even an “empty” box is complicated ... “vacuum bubbles”: virtual particle creation/ annihilation allowed by the Uncertainty Principle - nature of the Vacuum depends on all of the details of all of the interactions! ... and it changes depending on the distance scale you look at The exchange of virtual particles also provides the microphysical origin of forces: incoming scattered electron e electron virtual photon exchanged - carries energy and momentum e energy of system is raised when the “clouds” of virtual photons around the electrons overlap -> repulsive force MORAL: The Vacuum is NOT empty. Vacuum = State of Lowest Energy (INCLUDES mass energy, potential energy, ... - complicated trade-off to get the ground state) The Vacuum is a MEDIUM. The Vacuum as a Dielectric: - like a dielectric, the Vacuum screens charge - virtual electron-positron pairs are effectively dipoles, which screen the charge of the electron at long distances e2 α ≡ experiment: h¯c - - (“fine structure constant”) + + 1 - α(r → ∞) = . + - 137 03599911(46) - - + + + measured in + - Quantum Hall Effect + e0 + - −18 1 - α(r = 2 × 10 m) = . + + 127 918(18) - + - + - measured in high - + energy collisions - at shorter distances, e(r = 2 × 10−18 m) $ 1.035 effective charge on e(r → ∞) electron increases! (less screening) “Condensates” The nature of the Vacuum can be very complicated... Energy of a field comes from mass energy and potential energy. If potential energy wins, a field (i.e. particles) can “condense” in the ground state! Whether or not a condensate forms is a detailed dynamical question. V (ϕ) costs energy to condense out field - no condensate in ground state ϕ “Condensates” The nature of the Vacuum can be very complicated... Energy of a field comes from mass energy and potential energy. If potential energy wins, a field (i.e. particles) can “condense” in the ground state! Whether or not a condensate forms is a detailed dynamical question. V (ϕ) potential energy gained exceeds mass energy required ... condensate forms ϕ The known elementary particles, and their properties: Forces: strong, weak, electromagnetic ... are all just variations on a theme (“gauge theories”*) *Only freedom is overall charge of particles. The rest is dictated by symmetry (gauge invariance) (1) Electromagnetism (“QED”) - e fundamental process: photon emission/ absorption proportional to electric charge γ - couples to electric charge (Feynman, Schwinger, Tomonaga - Nobel Prize, 1965) Forces: strong, weak, electromagnetic ... are all just variations on a theme (“gauge theories”) (2) Weak Force e- νe (responsible for beta decay, - - neutrino interactions, ...) e e Z0 Z0 W- W- W+ 3 force carriers - + quarks + ... W W- + W Z0 + “weak gauge bosons” - have W SELF-interactions - couples to “flavour” charge (Glashow, Salam, Weinberg - Nobel Prize, 1979) Forces: strong, weak, electromagnetic ... are all just “variations on a theme” (3) Strong Force (“QCD”) (binds quarks and gluons into composite “hadrons” i.e. proton, neutron, pions, ...) g qj g g g qi g gij g g “colour” of quark/gluon (just a label) - couples to “colour” charge (Gross, Politzer, Wilczek - Nobel Prize, 2004) but they don’t look ANYTHING alike! 10-18 m=1/1000 radius of proton but they don’t look ANYTHING alike! at distances of 10-18 m, the weak and electromagnetic forces are essentially the same strength but they don’t look ANYTHING alike! but at a distance 30 × greater, the weak force is 4 orders of magnitude weaker! but they don’t look ANYTHING alike! at distances of 10-18 m, the strong force is 25 × stronger than electromagnetism but they don’t look ANYTHING alike! but at a distance 30 × greater, the strong force is 60 × stronger! but they don’t look ANYTHING alike! SOLUTION: the differences arise from the properties of the Vacuum! (This is why you get a Nobel Prize for showing they are variations on a theme ...) e- - - The Weak Force e e Z0 Z0 W- Gauge Invariance makes several unambiguous predictionsν:e mZ0 = mW ± = 0 mquarks = mleptons = 0 Experiment: quarks: from 5 MeV to 150 GeV m = 80.4 GeV mZ0 = 91.2 GeV W ± leptons: from ~0 to 1.5 GeV (1 GeV=103 MeV⋲mass of proton) the Weak force is weak because virtual W’s and Z’s can only propagate ~ -h/mc ~ 10-18 m (by the uncertainty principle) LOOPHOLE: This only holds if the Vacuum is EMPTY this sort of thing is seen all the time in condensed matter physics ... “Spontaneous Symmetry Breaking” - the ground state of a material can be less symmetric than the corresponding laws of physics ex: ferromagnet T > Tc - spins aligned randomly; no net magnetization - ground state is rotationally invariant “Spontaneous Symmetry Breaking” - the ground state of a material can be less symmetric than the corresponding laws of physics → ex: ferromagnet M T < Tc - spins aligned along a single (arbitrary) direction - net magnetization - ground state is NOT rotationally invariant ... and a physicist living in the ferromagnet would have no idea that the laws of Nature were rotationally invariant. rotational invariance is said to be “spontaneously broken” in a ferromagnet Superconductor (a theorists’ definition): a material in which electromagnetic gauge invariance is spontaneously broken iθ x ψ → e ( )ψ electromagnetic gauge Aµ → Aµ − ie∂µθ(x) invariance⇔massless photon B! electromagnetic gauge invariance spontaneously broken .. photon mass ≠ 0 inside, magnetic fields can’t penetrate magnetic fields cannot penetrate the Meissner Effect superconductor! Claim: the weak force is weak because the Vacuum is in a 16 superconducting phase! (with Tc~10 K) Why is the Universe a giant superconductor? condensate of Cooper pairs in a superconductor breaks BCS Theory: EM gauge invariance, gives photon a mass (complicated, dynamical) Weak we have no clue what the condensate is made of ... presumably the mechanism is something equally interactions: complicated and dynamical. BUT ... (1) low energy (<100 GeV) physics is almost independent of the details (universality) - so it’s hard to find! (2) quantized excitations of the condensate MUST show up at the few × 100 GeV scale (“unitarity”) - this is the energy scale we are currently probing at accelerators! Why is the Universe a giant superconductor? Standard Model “Higgs Field” condenses in Vacuum (simplest possible mechanism - like Landau-Ginsberg theory) ... put in (Weinberg, Salam): by hand normal phase superconducting phase Quantized excitations about the ≡ minimum “Higgs boVso(ϕn) ” - new particle with mass in the 100 GeV range, signature of symmetry Pϕeter Higgs breaking The masses of the quarks and leptons are also determined by the strength of their interactions with the Vacuum: e e interactions with Vacuum e slow electron down; give it an e −18 effective mass. Stronger Higgs? 10 m coupling=heavier particle.
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