Quantum Field Theory and the Limits of Knowledge. Sean Carroll, Caltech

Transcription

1 Quantum Field Theory and the Limits of Knowledge Sean Carroll, Caltech

2 Two claims: 1. The laws of physics underlying everyday life are completely known. 2. The structure of quantum field theory provides a warrant for claim 1.

3 Laws of physics underlying everyday life = The Core Theory Quantum field theory in a 4-dimensional spacetime. Matter (fermions): quarks,leptons. Strong, weak, electromagnetic forces. Gravitation = general relativity. Higgs field.

4 Long history of embarrassingly premature triumphalism [We are] probably nearing the limit of all we can know about astronomy. Simon Newcomb, 1888 The more important fundamental laws and facts of physical science have all been discovered. Albert Michelson, 1894 Physics as we know it will be over in six months. Max Born, 1928 There is a 50% chance that we would find a complete unified theory of everything by the end of the century. Stephen Hawking, 1980

5 Perfectly obvious but necessary caveats We re nowhere close to understanding the fundamental theory of everything. We don t understand the non-everyday: dark matter, quantum gravity, the Big Bang We don t fully understand macroscopic aggregations: condensed matter, chemistry, biology, economics Quantum mechanics or quantum field theory could always be wrong.

6 Higher-level macro-phenomena of everyday life Astrophysics, cosmology Known particles/forces, general relativity (Core theory) Dark matter/energy, new particles/forces, hidden sectors Underlying reality (theory of everything)

7 The Core Theory in more detail: Quantum Mechanics Think of configurations, e.g. the location x of a particle. Assign a complex number to every possible configuration. Y(x) x x That describes a quantum state: a wave function Y(x) that lives in a very-high-dimensional Hilbert space. Schrödinger evolution equation:

8 Measurements in Quantum Mechanics But we don t see the wave function. Measurements return some specific value of the configuration (or other observable). Probability of measurement outcome = wave function 2. After measurement, wave function collapses (becomes suddenly concentrated on observed outcome). Seems absurd. But good enough to successfully predict the outcome of every experiment ever done.

9 (Some) Observables are Quantized Standard example: Simple Harmonic Oscillator. Particle moving in a potential, where x is the position and w is the frequency. Energy is quantized into discrete levels:

10 Quantum Field Theory QFT is not a successor/alternative to QM; it s just a particular QM model, with a particular Hamiltonian. Namely: configurations are values of (relativistic) fields throughout space. E.g. f(x). The quantum state (wave function) is a complex amplitude for each possible field configuration, Y[f(x)]. Examples: electromagnetic field, electron field, top quark field, gravitational field (metric), etc.

11 Particles from fields Decompose oscillating field into a sum of modes of different wavelengths (Fourier transform): = Each mode acts like a simple harmonic oscillator! Energy levels = number of particles. Wavelength = 1/momentum. Indeed, relativity+qm+particles QFT.

12 Interactions Particle interactions are encoded in Feynman diagrams. = + + +

13 Adding up virtual particles Every particle has a momentum, and total is conserved at each vertex. When there are loops, momentum flowing through the loop (q) is arbitrary, and gets summed over. Result is often infinite.

14 Ken Wilson: organize QFT by energy/length scale Remember: energy & momentum ~ 1/(wavelength). long wavelengths/ low energies IR short wavelengths/ high energies don t need to worry about what happens here UV L ( cutoff energy scale)

15 Effective Field Theory Think of your theory as only describing energies below the ultraviolet cutoff scale L. I.e., only include wavelengths longer than 1/L. Result is an effective field theory below L.

16 There are an infinite number of terms in EFT equations of motion All diagrams with N legs contribute to an interaction term (in Lagrangian) between N particles. f 4 f 6 f 8

17 but only a finite number of terms matter Both the field f and the cutoff L have units of energy, and the Lagrangian governing interactions is (energy) 4. So schematically we have: relevant marginal irrelevant Higher-order terms are negligible at low energy (<< L). Only a finite number of relevant/marginal interactions.

18 Effective field theories tell us their regime of applicability: below the ultraviolet cutoff L. At energies below L, an EFT can be a complete theory. Above L, new phenomena can kick in. E.g. Fermi theory of weak interactions Standard Model. Fermi coupling

19 Quantum Gravity? We haven t quantized gravity, but I m treating gravity like a perfectly ordinary effective field theory. Because it is as long as gravity is weak (far from black holes, Big Bang, etc.). In terms of curvature parameter R, interactions look like Here on Earth, 1 st term is times bigger than 2 nd.

20 Multiple realizability A given effective field theory with cutoff L could have many ultraviolet completions at higher energies. That s why it s hard to do experiments relevant to quantum gravity: we expect L ~ E planck ~ E LHC. loop quantum gravity string theory dynamical triangulations

21 Underlying physics only influences us via Core Theory. Higher-level emergent phenomena of everyday life Astrophysics, cosmology Known particles/forces, general relativity (Core theory) Dark matter/energy, new particles/forces, hidden sectors Underlying reality (theory of everything)

22 What about new particles/forces? strongly interacting accessible known knowns inaccessible known unknowns weakly interacting heavy/ short range/ high energy light/ long range/ low energy Unknown unknowns = violations of QFT itself.

23 QFT puts very tight constraints on new phenomena. If a new particle can interact with ordinary particles: new particle new interaction Then that particle can be created in high-energy collisions. time Crossing symmetry.

24 Constraints on new particles As-yet-undiscovered particles must be either: 1. very weakly interacting, 2. too heavy to create, or 3. too short-lived to detect. In any of those cases, the new particle would be irrelevant to our everyday lives.

25 To be relevant to everyday physics, any new forces must interact with protons, neutrons, electrons, and/or photons. Two ways to hide: Constraints on new forces 1. weak interactions, or 2. very short ranges. Experiments are ongoing (torsion balances) to search for new, weak, long-range forces.

26 Strength (relative to gravity) Experimental limits on new forces Ruled Out Allowed new gravitationalstrength force (10-36 E&M) Range [Long et al. 2003; Antoniadis 2003]

27 New particles/forces are too heavy/weak to influence us. Higher-level emergent phenomena of everyday life Astrophysics, cosmology Known particles/forces, general relativity (Core theory) Dark matter/energy, new particles/forces, hidden sectors Underlying reality (theory of everything)

28 Punchline: the laws of physics underlying everyday experience. quantum mechanics spacetime gravity other forces matter Higgs Other phenomena are too massive or weakly-coupled to have any impact on the particles of which we are made.

29 Implications of the Core Theory Astrology is not correct. You can t bend spoons with your mind. The soul does not survive the body.

30 Loopholes? 1. New forces with environment-dependent couplings. 2. Breakdown of QFT itself. E.g. non-local constraints/ interactions from quantum gravity (holography). 3. Accessible deviations from textbook QM. (Hidden variables, spontaneous/induced collapse.) 4. Divine intervention.

31 Higher-level emergent phenomena of everyday life Astrophysics, cosmology Known particles/forces, general relativity (Core theory) Dark matter/energy, new particles/forces, hidden sectors Underlying reality (theory of everything)