Presocratic Quantum Gravity. John Lindner Department of Physics The College of Wooster

Transcription

1 Presocratic Quantum Gravity John Lindner Department of Physics The College of Wooster

2 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

3 Presocratic Timeline Thales Anaximander Anaximenes Pythagoras Leucippus Socrates Democritus Plato Parmenides Aristotle Heraclitus Zeno of Elea Anaxagoras Empedocles Epicurus Zeno the Stoic Cleanthes Chrysippus

4 Two World Views Heraclitus All is flux Everything changes Parmenides Change is an illusion Nothing changes

5 Zeno Defends Parmenides Zeno paradoxes transcend the historical Zeno Relevant to modern views of space & time

6 Zeno s Paradoxes Motion Unexists The Dichotomy L? ( ) The Achilles The Arrow The Stadium ( 1 T = 2T? ) 2 Plurality Unexists ( 0 =?)

7 Zeno s Zigzag Finite path: S = L fi 2S = L = 2 + S fi S = 2 But no logical exit direction, as no last mirror

8 Zeno s Maze Finite total path But no final direction Ray can t continue Ray can t escape

9 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

10 Nothing exists but atoms and empty space; everything else is opinion. Democritus

11 Chasing Democritus size in atoms atom size in meters Molecules Atoms Nuclei & Electrons 1 10, 000 nucleus Nucleons Quarks 1 100, , 000, 000 neutron & proton quarks & electron < 10-18

12 Particle/Forces g (photon) bosons (forces) W (weakon) g (gluon) fermions (matter) leptons quarks n (neutrino) e (electron) u (up) d (down)

13 Fundamental Interactions e - n d R d B weak W - strong g RB e - e - electric g gravity t

14 But particles and void are not so simple!

15 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

16 Special Relativity SR Fundamental scale, invariant speed of light c ~ 10 8 m s Relative lengths & durations, invariant spacetime ds 2 = ( dx) 2 + ( dy) 2 + ( dz) 2 - ( cdt) 2 Energy, momentum, mass -( mc 2 ) 2 = ( p x c) 2 + ( p y c) 2 + ( p z c) 2 - E 2

17 Special Relativity SR Worldlines in spacetime Being, not becoming No moving now s 14 March 1879 Ulm, Württemberg, Germany 18 April 1955 Princeton, New Jersey, USA t

18 The distinction between past, present, and future is only an illusion, even if a stubborn one. Albert Einstein

19 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

20 General Relativity GR Fundamental scale G ~ N m 2 kg 2 Newton s gravity constant F = G Mm d 2 Gravity is spacetime curvature R mn g mn R = 8pG c 4 T mn Spacetime is a dynamical variable

21 Spacetime Curvature Slows time Warps space z j r

22 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

23 Quantum Mechanics QM Fundamental scale h ~ J s Non commuting operators qp - pq = ih Uncertainty Indeterminacy Relation DqDp h

24 Quantum Mechanics QM Wave particle duality Fields & quanta

25 Quantum Many Worlds Atoms don t behave classically Described by a wave function or vector rotating deterministically in an infinite dim Hilbert space Wave functions can describe counterintuitive nonclassical states like superpositions of live and dead cats In 1920s, physicists explained away this weirdness by postulating that observations randomly collapse wave functions into classical states

26 Quantum Many Worlds Einstein objected, God does not play dice In 1957, Everett showed that quantum mechanics is consistent without the random collapse postulate Rather, classical reality continually splits into superpositions of many different realities Observers experience splitting as randomness

27 The Nature of Time Either way, all possible states exist at any moment Now you are in Universe A looking at this slide...

28 The Nature of Time Either way, all possible states exist at any moment Now you are in Universe A looking at this slide... And now you are in Universe B looking at this slide & with memories of looking at the last slide All universes are static & change is illusory Time is simply a way to sequence the universes in the multiverse

29 Implications for Determinism Suppose you have perfect knowledge of the multiverse, including the life histories of all copies of you There is no way for you tell which copy is you they all feel like you There is no way for you to predict your future without living it

30 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

31 Quantum Field Theory QFT QFT = SR + QM Antimatter Mirror image particles Annihilate to pure energy: e + + e - Æ g + g Quantum Vacuum Seething with virtual activity Nothing s something

32 Quantum Vacuum s t Anything allowed by UP, DtDE h Vacuum polarization & charge renormalization Clear tension a.k.a dark energy Casimir forces

33 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

34 Compton Length QM => determining position of mass m to within its Compton wavelength l C ~ h mc requires enough energy to create another particle m.

35 Schwarzschild Length GR => compressing mass m to within its Schwarzschild radius creates a black hole. l S ~ Gm c 2

36 l C ~ h mc versus l S ~ Gm c 2 l C << l S Æ GR l C >> l S Æ QFT Both GR and QM needed when l C ~ l S Æ m = m P ~ hc G Æ l P ~ l C ~ l S ~ hg c 3 and t P ~ l P c ~ hg c 5

37 Planck Scale l P ~ meters t P ~ seconds

38 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

39 2 Fundamental Theories GR Includes gravity but excludes QM Spacetime curved but no UP QFT = SR + QM Includes QM but excludes gravity Includes UP but pretends spacetime flat

40 2 Roles for Time GR space time is dynamical t Depends on mass and motion QM No preferred foliation t Time is a global parameter

41 Synthesis? Profound Difficulties Technical / Mathematical Conceptual / Philosophical 3 Approaches Canonical quantization Loop quantum gravity Theory formerly know as superstrings

42 Loop Quantum Gravity Gravity is curved spacetime as in GR Not a GUT Spacetime 3+1 dimensions Discrete & quantized ~ l P Foamy network of interacting loops Spin networks represent quantum states of spacetime geometry

43 Outline Presocratics Particles & Fields Physics Foundations Special Relativity General Relativity Quantum Mechanics Quantum Field Theory Quantum Gravity Planck Scale Loop Quantum Gravity String/M Theory

44 Super String Theory Replace 0 dim particles by 1 dim strings of energy Gravity mediated by gravitons as in QFT GUT unifies 4 forces Fundamental particles are different string vibration modes

45 Particles are Pythagorean notes played on strings with fixed tension!

46 1+1 Dim Spacetime Strings In particle physics, interactions occur at points of zero volume leading to infinities String theory spreads out interactions over nonzero volumes yielding finite predictions t

47 Super String Theory Spacetime 9+1 dimensions 6 compacted or we are fixed to a 3 brane Continuous T Duality => there is a smallest size ~ l P Requires supersymmetry

48 M Theory Subsumes 5 different string theories + supergravity GUT unifies 4 forces Spacetime 10+1 Dim? Coherent vibrations of superstrings in graviton mode creates spacetime out of timeless, spaceless realm Space, time, matter all made of super strings!