Quantum Gravity: Physics?

Transcription

1 academics.hamilton.edu/physics/smajor/ Quantum Gravity: Physics? Seth Major Hamilton College UMass Dartmouth 14 March 007

2 Quantum Gravity and Physics What is Quantum Gravity? - Why? Approaches to QG Loop Quantum Gravity - Discrete Spatial Geometry Quantum Gravity Phenomenology - Mod. Special Relativity & Particle Thresholds 1

3 We don't k now. Must have two th eories as limits: 1915 General Relativity G; c No Background: Space and time are dynamical quantities Geometry is continuous Geometry determines Motion of Matter determines Geometry determines Quantum Theory h Built on xed background spacetime Discrete quantities e.g. H ato m E n = 13:6=n Fundamental uncertainty to physical quantities e.g. x; p Sup erp osition, measurement pro cess, determining physical states.... ev What is Quantum Gravity?

4 1915 General Relativity G; c No Background: Space and time are dynamical quantities Geometry is continuous Geometry determines Motion of Matter determines Geometry determines Quantum Theory h Built on xed background spacetime Discrete quantities e.g. H ato m E n = 13:6=n Fundamental uncertainty to physical quantities e.g. x; p Sup erp osition, measurement pro cess, determining physical states.... ev What is Quantum Gravity? We don t know. Must have two th eories as limits: -a

5 No Background: Space and time are dynamical quantities Geometry is continuous Geometry determines Motion of Matter determines Geometry determines... Built on xed background spacetime Discrete quantities e.g. H ato m E n = 13:6=n Fundamental uncertainty to physical quantities e.g. x; p Sup erp osition, measurement pro cess, determining physical states.... ev What is Quantum Gravity? We don t know. Must have two theories as limits: 1915 General Relativity G, c 195 Quantum Theory h -b

6 Geometry is continuous Geometry determines Motion of Matter determines Geometry determines... Discrete quantities e.g. H ato m E n = 13:6=n Fundamental uncertainty to physical quantities e.g. x; p Sup erp osition, measurement pro cess, determining physical states.... ev What is Quantum Gravity? We don t know. Must have two theories as limits: 1915 General Relativity G, c No Background: Space and time are dynamical quantities 195 Quantum Theory h Built on fixed background spacetime -c

7 Geometry determines Motion of Matter determines Geometry determines... Fundamental uncertainty to physical quantities e.g. x; p Sup erp osition, measurement pro cess, determining physical states... What is Quantum Gravity? We don t know. Must have two theories as limits: 1915 General Relativity G, c No Background: Space and time are dynamical quantities Geometry is continuous 195 Quantum Theory h Built on fixed background spacetime Discrete quantities e.g. H atom E n = 13.6/n ev -d

8 What is Quantum Gravity? We don t know. Must have two theories as limits: 1915 General Relativity G, c No Background: Space and time are dynamical quantities Geometry is continuous Geometry determines Motion of Matter determines Geometry determines Quantum Theory h Built on fixed background spacetime Discrete quantities e.g. H atom E n = 13.6/n ev Fundamental uncertainty to physical quantities e.g. x, p Superposition, measurement process, determining physical states... -e

9 What is Quantum Gravity? How about the QG scale? Planck length Planck energy Planck time E P = l P = t P = hc 5 G hg c 3 hg c 5 = m = 108 ev = 10 9 J = s Figure of merit E LHC /E P Doing quark-physics by watching a soccer game!! 3

10 Why? General relativity needs QG Singularities in General Relativity - Big Bang and Gib Gnab - Black Holes, Hawking Radiation, and Evaporation More speculative reasons: 4

11 Pioneer 10 and 11? Quantum mechanics? \Low energy" relics - cosmic rays? \There's a lot we don't know ab out nothing." - John Baez Why? Several results may be QG effects Cosmology: WMAP, Supernovae, Galaxy Rotation Curves map.gsfc.nasa.gov 5

12 Why? Several results may be QG effects Cosmology: WMAP, Supernovae, Galaxy Rotation Curves nobleprize.org 006 Nobel Prize in Physics John Mather and George Smoot for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation 6

13 Pioneer 10 and 11? Quantum mechanics? \Low energy" relics - cosmic rays? Why? Several results may be QG effects Cosmology: WMAP, Supernovae, Galaxy Rotation Curves There s a lot we don t know about nothing. - John Baez 6-a

14 Why? Several results may be QG effects Cosmology: WMAP, Supernovae, Galaxy Rotation Curves There s a lot we don t know about nothing. - John Baez Pioneer 10 and 11? Quantum mechanics? Low energy relics - cosmic rays? 6-b

15 Approaches to Quantum Gravity String Theory: The whole kit and caboodle Causal Sets: Causal order is fundamental Dynamical Triangulations : Discrete and Causal Loop Quantum Gravity: GR plus matter, quantize 7

16 Loop Quantum Gravity A Hamiltonian approach: SPACE + TIME (Dirac, Bergmann, ADM, Ashtekar, Jacobson, Rovelli, Sen, Smolin,...) 8

17 Loop Quantum Gravity A Hamiltonian approach: SPACE + TIME (Dirac, Bergmann, ADM, Ashtekar, Jacobson, Rovelli, Sen, Smolin,...) 8-a

18 Loop Quantum Gravity A Hamiltonian approach: SPACE + TIME (Dirac, Bergmann, ADM, Ashtekar, Jacobson, Rovelli, Sen, Smolin,...) 8-b

19 Loop Quantum Gravity Quantize SPACE then TIME. How? Use electromagnetic field variables and electric field lines 9

20 Loop Quantum Gravity Geometric field lines. Three differences with familiar E field (1.) Use closed loops (Loop QG) (.) Lines are labeled with spin j = 1, 1, 3,,... (3.) Lines intersect at vertices Labeled graphs or spin networks (Penrose) 10

21 Loop Quantum Gravity A quantization of general relativity using electromagnetic variables yields a - Discrete structure to spatial geometry: quantum states of geometry are represented by spin networks 11

22 Discrete Spatial Geometry Familiar geometric quantities arise through measurement on the spin network states Area: spin network lines are flux lines of area (Baez) Volume arises only at vertices Angle is defined at vertices 1

23 Discrete Spatial Geometry What geometry does it have? C. Rovelli, Physics World Nov

24 Discrete spectra for Geometry Area : Â S s = a s a = l P N n=1 jn (j n + 1) Angle : ˆθ s = θ s ( ) j r (j r + 1) j 1 (j 1 + 1) j (j + 1) θ = arccos [j 1 (j 1 + 1) j (j + 1)] 1/ Rovelli,Smolin Nuc. Phys. B 4 (1995) 593; Asktekar,Lewandowski Class. Quant. Grav. 14 (1997) A43 SM Class. Quant. Grav. 16 (1999)

25 Discrete spectra for Geometry Area: Â S s = a s Suppose a single edge, with j = 3/, passes through the surface A measurement of area would yield a = l P j(j + 1) = l 15 P 15

26 Discrete Spatial Geometry What if the Planck length were l P = m? Suppose you observed a growing whale... 16

27 Discrete Spatial Geometry What if the Planck length were l P = m? Suppose you obseved a growing whale... with surface area (all edges with j = 1/) A W = l P m 17

28 Discrete Spatial Geometry What if the Planck length were l P = m? Suppose you observed a growing whale... who grew the minimum amount to A W = l P m 18

29 Discrete Spatial Geometry Even if the Planck length was not so large... black holes satisfy M = c4 16πG A For the minimum change in area, δa = l P 3/, δm = c4 1 3πG M δa From E = Mc = hν the frequency of the emitted quanta would be 3 c 3 ν = 18π GM.8 10M SUN M Radio waves! A Mercury-mass black hole could be heard on your cell phone!! BUT... 19

30 Loop Quantum Gravity DISCRETE SPACE. What about TIME? The spin network state evolves via moves in the network: But there a number of unresolved problems... 0

31 Loop Quantum Gravity DISCRETE SPACE. What about TIME? O time, thou must untangle this, not I It is too hard a knot for t untie -Shakespeare Twelfth Night 1

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33 Alfaro, Morales-Tecotl, Urru tia suggested that certain states in Lo op Quantum Gravity mo di fy the classical equations of motion (PRD 65 (00) ; 66 (00) 14006) - Quantum geometry aects the propagation of elds Mo died Disp ersion Relations (MDR) For massive particles (units with c = 1) E E = p = p + m + m + p E 3 P Physics of Quantum Gravity? A history of an idea (T. Konopka,SAM New J. Phys. 4 (00) 57) 3

34 Mo died Disp ersion Relations (MDR) For massive particles (units with c = 1) E E = p = p + m + m + p E 3 P Physics of Quantum Gravity? A history of an idea (T. Konopka,SAM New J. Phys. 4 (00) 57) Alfaro, Morales-Tecotl, Urrutia suggested that certain states in Loop Quantum Gravity modify the classical equations of motion (PRD 65 (00) ; 66 (00) 14006) - Quantum geometry affects the propagation of fields 3-a

35 Mo died Dispersion E = p + m For + p E 3 P Physics of Quantum Gravity? A history of an idea (T. Konopka,SAM New J. Phys. 4 (00) 57) Alfaro, Morales-Tecotl, Urrutia suggested that certain states in Loop Quantum Gravity modify the classical equations of motion (PRD 65 (00) ; 66 (00) 14006) - Quantum geometry affects the propagation of fields Relations massive particles (MDR) (units with c = 1) E = p + m 3-b

36 Physics of Quantum Gravity? A history of an idea (T. Konopka,SAM New J. Phys. 4 (00) 57) Alfaro, Morales-Tecotl, Urrutia suggested that certain states in Loop Quantum Gravity modify the classical equations of motion (PRD 65 (00) ; 66 (00) 14006) - Quantum geometry affects the propagation of fields Modified Dispersion Relations (MDR) For massive particles (units with c = 1) E = p + m E = p + m + κ p3 E P 3-c

37 Modified Dispersion Relations (MDR) E = p + m 4

38 Modified Dispersion Relations (MDR) E = p + m E = p + m + κp 3 /E P 4-a

39 Modified Dispersion Relations (MDR) κ order unity κ is positive or negative There is a preferred frame! Special Relativity is modified! Effects are important when E crit (m E p ) 1/ and ev for electrons and protons Model limited by p << E P MDR take the leading order form in which m << p << E P E p + m p + κ p E P 5

40 Example: Photon Stability 6! e SR forbids. MDRs allow photon decay Energy conservation E = E + + E + + e Call photon! and electron!. 4-momentum conservation and MDR give p E P = m p e + + p E + P + m p e + p E P Model with MDR Assume exact energy-momentum conservation Assume MDR cubic corrections Seperate parameters for photons, fermions, and hadrons 6

41 Call photon! and electron!. Using E p + and momentum conservation p + p E P = p + + m p e + + p E + P + p + m p e + p E m p P + p E P Model with MDR Assume exact energy-momentum conservation Assume MDR cubic corrections Seperate parameters for photons, fermions, and hadrons Example: Photon Stability γ e + + e SR forbids. MDRs allow photon decay Energy conservation E γ = E + + E 6-a

42 and momentum conservation Model with MDR Assume exact energy-momentum conservation Assume MDR cubic corrections Seperate parameters for photons, fermions, and hadrons Example: Photon Stability γ e + + e SR forbids. MDRs allow photon decay Energy conservation E γ = E + + E Call photon κ η and electron κ ξ. Using E p + m p + κ p E P p γ + ξ p γ E P = p + + m e p + + η p + E P + p + m e p + η p E P 6-b

43 Model with MDR Assume exact energy-momentum conservation Assume MDR cubic corrections Seperate parameters for photons, fermions, and hadrons Example: Photon Stability γ e + + e SR forbids. MDRs allow photon decay Energy conservation E γ = E + + E Call photon κ η and electron κ ξ. Using E p + m p + κ p and momentum conservation E P ξ p γ E P = m e p + + η p + E P + m e p + η p E P 6-c

44 Photon Stablity Key question: How is the momentum partitioned? Jacobson, Liberatti, Mattingly arxiv:hep-ph/ From T. Konopka thesis Hamilton 0 7

45 Photon Stablity It is energetically favorable to asymmetrically partition the momenta. With the outgoing p = p o and p + = p o + (p o = p γ /) we have = p o 1 m e ηl p p 3 o Asymmetric momenta partitioning is a new phenomenon in these models. 8

46 Photon Stablity Particle process thresholds are highly sensitive to this kind of modification!! Thresholds become p γ = and [ ] 8m 1/3 e E P for η 0 (η ξ) p γ = [ 8ξm e E P (η ξ) ] 1/3 for ξ < η < 0 Observations of high energy photons produce constraints on ξ and η. e.g. 50 TeV photons from Crab Nebula 9

47 A model with MDR Red region is ruled out by photon stability constraint Planck scale limits! 30

48 Model with MDR Many other processes limit the extent of MDR: - dispersion - birefringence - vaccum Cerenkov radiation - photon absoprtion - pion stability - synchotron radiation - ultra-high energy cosmic rays... 31

49 A Ultra-High Energy Cosmic Ray Paradox? Greisen, Zatsepin and Kuzmin (GZK) observed in 1966 that high energy particles (protons) would interact with CMB photons p + γ p + π At large distances 1 Mpc this reaction yields a cutoff in the energy spectrum of protons at ev MDRs can move this threshold. Is the GZK threshold seen?? 3

50 Is the GZK cutoff observed? De Marco et. al. see no cutoff at a.5 σ level! AGASA HiRes Data and astro-ph/

51 Pierre Auger Observatory Auger is the largest cosmicray air shower array in the world (> 70 sq.mi.) 34

52 Pierre Auger Observatory One of 1600 Cerenkov detectors in Argentina For GZK, need more statis- A Quantum Gravity detector??? tics... 35

53 Pierre Auger Observatory After one year of data (still under construction) 36

54 Status of MDR 007 Myers & Pospelov: Effective field theory framework 3 parameters for QED - helicities independent [PRL 90 (003) 11601] Jacobson, Liberati, Mattingly, Stecker: New constraints from synchotron radiation in SN remnants and polarization dependent dispersion from gamma ray burst GRB0106 Recent review: JLM, Annals Phys. 31 (006) Collins, Perez, Sudarsky: A fine tuning problem theoretical framework is questioned. [PRL 93 (004) ] Amelino-Camelia: Should be be using field theory at all for phenomenology? [NJP 6 (004) 188] 37

55 Status of MDR 007 arxiv:astroph/

56 Summary: Quantum Gravity and Physics - Physics from QG? Not yet But there are - Preliminary results: Discrete geometry - New Middle Ground Quantum Gravity Phenomenology - MDR and Threshold effects yield Planck scale constraints 39