Physics without fundamental time

Transcription

1 Physics without fundamental time Carlo Rovelli I. Time, who? II. Physics without fundamental time III. A real world example

2 What are we talking about when we talk about time?

3 Aristotle : (Changing) Substance Descartes: Res extensa Newton: Time Space Particles Faraday-Maxwell: Fields Particles Einstein 05: Spacetime Einstein 15: Covariant fields Quantum: Quantum Fields Quantum gravity?: Covariant Quantum Fields

4 Change is the actuality of that which potentially is, qua such (Aristotle Physics 201a9-11) Time is a number of change (Aristotle Physics 219b1)

5 Conceptual framework (Space, time, reality, causality, observation, objectivity, language, ) Scientist evolve as well! data theories improve evolve Non foundationalism: - There is no final scientific theory of the world. We learn. - There is no definitive metaphysics.

6 On the basis of general relativity, space, as opposed to what fills space, has no separate existence. If we imagine the gravitational field to be removed, there does not remain a space [...], but absolutely nothing. A Einstein, Relativity, the special and general theory, 1917 General relativity takes away from space and time the last remnant of physical objectivity A Einstein, The foundations of general relativity, 1916

7 Time = Z d r g µ ( ( )) d µ d d d gravitational field

8 Τ2 Τ1 ΔΤ = Τ2 - Τ1

9 Times in physics: Thermodynamical (and common sense): oriented, metric, universal Special initial conditions or special observer Classical and quantum mechanical: metric, universal Low relative velocities Special relativistic, quantum field theoretical: metric, frame dependent Low curvature Dynamics on curved spacetime: metric, path dependent Negligible backreaction Dynamics of gravitational field: relational Negligible quantum gravity effects Quantum gravity: none

10 Can we do physics, without time? Of course yes! Lagrange,, Dirac, Souriau, Arnold, DeWitt, Quantum gravity Carlo Rovelli CUP 2004 Introduction to Canonical Loop Quantum Gravity Francesca Vidotto, Carlo Rovelli CUP 2014

11 x t Position (dependent variable): Time (independent variable): Equations of motion: General solution (motions): x 2 C t 2 R d 2 x(t) dt 2 =! 2 x(t) x(t) =A sin(!t + )

12 x Variables (dependent and independent not distinguished): (x, t) 2 E = C R t partial observables Cfr: Sean Cfr: Brian Equations of motion: dx pdt= 0; dp +! 2 xdt=0 General solution (motions): f(x, t) =x A sin(!t + )=0 Time and configuration variables can be treated on equal footings.

13 Hamitonian physics in terms of partial observables Extended configuration space: Extended phase space: q =(x, t) 2 E = T E Hamiltonian constraint: C :! R Equations of motion:!(x) C =0 =0 Cfr: Oliver = Sean There is no need to ever use the notion of time in order to have a predictive and complete theory of dynamics

14 q t This is not the space of the instantaneous states! It is the space of the histories!

15 Hamitonian physics in terms of partial observables Extended configuration space: Extended phase space: q =(x, t) 2 E = T E Hamiltonian constraint: C :! R Equations of motion: Quantum theory Wheeler dewitt equation:!(x) C =0 =0 Cfr: Oliver (q) = (x, t) C =0 = Sean = Sean Amplitudes: W (x, t; x 0 t 0 )=hx, t P x 0 t 0 i, P (C) = hx e ih(t t0) x 0 i There is no need to ever use the notion of time in order to have a predictive and complete theory of dynamics

16 q q This is not the space of the instantaneous states! It is the space of the histories!

17 Classical and quantum physics without time (x, t)! q set of all partial observables Extended configuration space: Extended phase space: q =(x, q t) 2 E = T E Hamiltonian constraint: C :! R Equations of motion:!(x) C =0 =0 q1 q 1 q2 q 2 Quantum theory Wheeler dewitt equation: Amplitudes: (q) q = (x, t) C =0 q3 q 3 q4 q 4 W (x, q t; ; xq 00 t 0 )=hx, q t P xq 0 t 00 i, P (C) = hx e ih(t t0) x 0 i There is no need to ever use the notion of time in order to have a predictive and complete theory of dynamics

18 What needs to be diff invariant are the transition amplitudes between partial observables s eigenstates, not the observables themselves!

19 Dynamics describes evolution of dynamical variables in time. Dynamics describe relations between partial observables This is possible for any dynamical system. It is necessary for a system including gravity.

20 Please do not confuse: Evolving constants of motion: Quantum evolving constants Carlo Rovelli Physical Review D44, 1339 (1991) x T = x T (x, p, t, p t ) ˆx T = x T (ˆx, ˆp, ˆt, ˆp t ) x T (x, p, t, p t )= 1 2 (x2 + p 2 ) sin!(t t) + arctan!x p ˆx T = 1 2 (ˆx2 +ˆp 2 ) sin!(t ˆt) + arctan!ˆxˆp Partial observables: Quantum Gravity Carlo Rovelli (CUP 2004) f(x, p, t, p t ; x 0,p 0,t 0,p 0 t)=0 W (x, t; x 0 t 0 )=hx, t P x 0 t 0 i Covariant Loop Quantum Gravity Carlo Rovelli, Francesca Vidotto (CUP 2014) W (x, t, x 0,t 0 )= m! h sin(!(t t 0 ) apple i (x 2 +x 02 )cos(!(t t 0 )) 2xx 0 1 ~ 2 e sin 2 (!(t t 0 ))

21 Dirac observable: Can be predicted Partial observable: Can be measured

22 What is observable in GR is not controversial because all experimenters agree when they make general relativistic observations

23 General relativity: Spacetime is the physical trajectory the gravitational field. Quantum theory: Physical trajectories do not exist. Processes are transitions. There is no spacetime in quantum gravity, and in particular there is no time

24 A process, and its amplitude Boundary state = in out Boundary Amplitude of the process A = W ( ) Spacetime region Cfr: Bianca For example, Loop Quantum Gravity gives a precise mathematical definition of the state of space, the boundary observables, and the amplitude functional. (Processes, not a frozen spacetime...)

25 General relativistic dynamics cfr Donald q 2 E Extended configuration space: space of 3-geometries and other fields on a boundary Extended phase space: = T E Hamiltonian constraint: C :! V Equations of motion:!(x) C =0 =0 Quantum theory: Boundary states: Transition amplitudes: 2 H, = in out A = W ( )=h out P out i All these quantities are well defined in Loop Quantum Gravity

26 Covariant loop quantum gravity. Full definition. h l n 0 l n Kinematics Boundary State space Operators: H = L 2 [SU(2) L /SU(2) N ] where 3 (h l ) H = lim!1 H spin network (nodes, links) v e f C spinfoam (vertices, edges, faces) Dynamics Bulk Transition amplitudes Vertex amplitude W C (h l )=N C Z A(h vf )= Z Y dh vf SU(2) f Y X dge 0 SL(2,C) f j (h f ) Y v A(h vf ) (2j + 1) D j mn(h vf )D (j+1) j jmjn (g e g 1 e 0 ) W = lim C!1 W C h f = Y v h vf 8 ~G =1

27 - The notion of Time is not needed to describe change. - The notion of Time is not of use, and in fact misleading, in relativistic quantum gravitational physics.

28 ' Boundary functional W [', ] = Z =' D e is[ ] Σ But in a generally covariant theory: W [', ] =W ['] Spacetime region Distance and time measurements Particle detector In a general relativistic theory, distance and time measurements are field measurements like the other ones: they are determined by the boundary data of the problem. 28

29 A concrete application

30 A technical result in classical GR: I The following metric is an exact vacuum solution, plus an ingoing and outgoing shell, of the Einstein equations outside a finite spacetime region (grey). III II ds 2 = F (u, v)dudv + r 2 (u, v)(d 2 + sin 2 d 2 ) I Region I Region II Matching: Region III F (u I,v I )=1, r I (u I,v I )= v I u I. 2 v I < 0. F (u, v) = 32m3 r r I (u I,v I )=r(u, v) e r 2m F (u q,v q )= 32m3 r q 1 r e r 2m 2m = uv. u(u I )= 1 1+ u I e u I 4m. v o 4m e rq 2m, rq = v q u q. Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling Hal M. Haggard, Carlo Rovelli arxiv: The metric is determined by three constants: m,,

31 Minkowski region I Outgoing (null) shell Quantum region III II Past trapped horizon White hole Schwarzschild region I Conventional black hole Future trapped horizon Incoming (null) shell Minkowski region

32 I I The Fingers Crossed

33 Time dilation T R = r 1 2m R (2(R 2m) 4m log v o) T: bounce time (very large) internal m 1ms external m years v o A black hole is a short cut to the future

34 Time dilation T R = r 1 2m R (2(R 2m) 4m log v o) T: bounce time (very large) internal m 1ms external m years v o A black hole is a short cut to the future

35 The external metric is determined by two constants: - m is the mass of the collapsing shell. v o - determines the time between the collapse and the explosion T R = r 1 2m R (2(R 2m) 4m log v o) T = 4m log v o What determines T (m)? v o

36 Covariant loop quantum gravity. Calculation of T(m). j,k n v n A(j, k) = Z SL(2C) dg Z SU2 dh Z X dh + SU2 j + j e (j + j) 2 e (j + j) 2 j,-k Tr j+ [e k 3 Y gy ]Tr j [e k 3 Y gy ] A(j, k) 2 1 relation j-k relation m-time T (m)

37 Black to white hole tunnelling and Planck stars Planck stars Carlo Rovelli, Francesca Vidotto Int.J.Mod.Phys. D23 (2014) 12, n j,k v n Planck star phenomenology Aurelien Barrau, CR. Phys.Lett. B739 (2014) 405 j,-k For T~m 3 primordial black hole give signals in the cosmic ray spectrum l For T~m 2 primordial black hole give signals in the radio: Fast Radio Bursts? Signature: Frequency distance dependence z

38 Detectable? Already detected? Figure 2. Characteristic plots of FRB In each pa datafast wereradio smoothed in time frequency by a factor of 30 a For T~m2 primordial black hole give signals Bursts andand White Hole Signals respectively. The Carlo top panel a dynamic spectrum of the Aurélien Barrau, Rovelli,isFrancesca Vidotto. in the radio: Fast Radio Bursts? Phys.Rev. D90showing (2014) 12,the ery observation 0.7 s during which FRB across the frequency band. The signal is seen to become cantly dimmer towards the lower part of the band, and som facts due to RFI are also visible. The two white curves show pected sweep for a ν 2 dispersed signal at a DM = pc The lower left panel shows the dedispersed pulse profile av across the bandpass. The lower right panel compares the on spectrum (black) with an off-pulse spectrum (light gray), a reference a curve showing the fitted spectral index (α = 10) overplotted (medium gray). The on-pulse spectrum was calc by extracting the frequency channels in the dedispersed da Duration: ~ millisecondsresponding to the peak in the pulse profile. The off-pulse spe is the extracted frequency channels for a time bin manually Frequency: 1.3 GHz to be far from the pulse. Fast Radio Bursts Observed at: Parkes, Arecibo time, Origin: Likely extragalactic and pulsar broadening were all fitted. The sian pulse width (FWHM) is 3.0 ± 0.5 ms, and we Estimated emitted power: 1038 erg an upper limit of τd < 1.5 ms at 1.4 GHz. The re Physical source: unknown. DM smearing within a frequency channel is 0.5 m 0.9 ms at the top and bottom of the band, respect The best-fit value was α = 11 but could be as low = 7. The fit for α is highly covariant with the Gau

39 - In quantum gravity we need transition amplitudes between boundary states. - States may (or may not) depend on quantities that may happen to have an interpretation in terms of some clock time.

40 What about the temporal aspect of time? (time flows, special direction, memory..) These are all thermodynamical and statistical phenomena. They do not pertain to the fundamental equations. They pertain to the the domain of incomplete information, coarse graining, special observers. Statistical mechanics of gravity and the thermodynamical origin of time Carlo Rovelli Class.Quant.Grav. 10 (1993) Von Neumann algebra automorphisms and time thermodynamics relation in general covariant quantum theories A. Connes, Carlo Rovelli, Class.Quant.Grav. 11 (1994) General relativistic statistical mechanics Carlo Rovelli, Phys.Rev. D87 (2013) 8, Why do we remember the past and not the future? The 'time oriented coarse graining' hypothesis Carlo Rovelli, arxiv: Statistical mechanics of reparametrization invariant systems. Takes Three to Tango Thibaut Josset, Goffredo Chirco, Carlo Rovelli,arXiv:

41 Conclusion i. The notion of time is not needed for mechanics: rather than describing how physical variables ( partial observables ) change in time we can describe how they change with respect to one another. ii. This relational form of dynamics is necessary when dealing with the dynamics of the gravitational field, because Newtonian space and times are aspects of this field. iii. In Quantum Gravity, the fundamental equations do not involve time. The theory gives transition amplitudes for boundary states. This allows us doing standard physics. iv. The temporal and common sense aspects of the non relativistic time variable pertain to thermodynamics and statistical mechanics, not to the fundamental theory.

42 The mistake: There is change Therefore there is a preferred time variable

43 Change? CM: Relations between partial observables QM: Transition amplitudes! Time variable? Forget!

44 Forget time!