Critical Acceleration and Vacuum Structure Johann Rafelski Department of Physics, the University of Arizona Charles a Whitten Memorial Symposium Dec 15/16 2011

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Critical Acceleration and Vacuum Structure Johann Rafelski Department of Physics, The University of Arizona Charles A Whitten Memorial Symposium Dec 15/16 2011

I discuss foundational ultra-high acceleration physics challenges arising in the context of relativistic laser pulse interactions: pulse interaction with the quantum vacuum, the opportunity to improve understanding of inertia, quantum vacuum as modern day aether, and the materialization of pulse energy directly into high energy particles.

Supported by US DoE Grant: DE-FG02-04ER41318 Overview

1 Introduction 2 Critical acceleration 3 Fundametal Interaction 4 Mach and Inertia, Aether Quantum Vacuum 5 High energy particles

graphics credit to: S.A. Bulanov, G. Mourou, T. Tajima The 21st Century Foundational Physics Challenges How does the structured quantum vacuum control inertia, • and many other laws of physics Is there a deeper understanding of time? • Rôle of the Universe expansion in deﬁning time? What is the cosmological dark energy, • 4 3 5 2 3 λ = (2.4meV) ~− c− = 4.3keVc− /cm Is this excited state quantum Vacuum with non-zero point energy? If so how can we induce vacuum decay? What is the magnitude of causal velocity (‘velocity of light’) in the different vacuum states? What is the origin of grand scales as expressed by • 19 a) the Planck mass: MP = ~c/GN = 1.310 mproton and 13 b) Higgs VEV h = 254 GeVp 10 mneutrino. h i ≃ Space-time: dimensionality (3+1) (n + 1): n > 3? • → Fractal dimension n < 3? Lattice? (Mem)brane? Discovery is driven by new tools: acceleration 1899: Planck units

“These scales retain their natural meaning as long as the law of gravitation, the velocity of light in vacuum and the central equations of thermodynamics remain valid, and therefore they must always arise, among different intelligences employing different means of measuring.” M. Planck, “Über irreversible Strahlungsvorgänge.” Sitzungsberichte der Königlich Preußischen

Akademie der Wissenschaften zu Berlin 5, 440-480 (1899), (last page) Critical ‘Planck’ acceleration In presence of high acceleration↔ we probe connection between forces (interactions) and the structure of space-time. In that sense there is also a ‘limiting’ Planck acceleration, which to avoid misunderstanding we term ‘critical’ acceleration ac. Einstein’s gravity is built upon Equivalence Principle: a relation of gravity to inertia(=the resistance to acceleration). Note that when interactions are ‘geometrized’ like gravity in string theories, we are doing away with acceleration. Thus current super-theories really go in direction of removing force. It is quantum physics that allows us today to create devices that expose particles to acceleration. Critical Acceleration Critical acceleration acting on an electron: 3 mec 29 2 ac = 2.331 10 m/s ~ → × This critical acceleration can be imparted on an electron by the critical ‘Schwinger’ (Vacuum Instability) field strength of magnitude: 2 3 mec 18 Ec = = 1.323 10 V /m e~ × Truly dimensionless unit acceleration arises when we introduce specific acceleration a c = c = ℵ mc2 ~ Specific unit acceleration arises in Newton gravity at Planck 2 length distance: G/L = c/~ at Lp = ~G/c. In presence ℵG ≡ p of sufficiently strong electric field Ec by virtuep of the equivalence principle, we probe electrons subject to Planck scale force. Critical acceleration probably achieved at RHIC Two nuclei smashed into each other from two sides: components ‘partons’ can be stopped in CM frame within ∆τ 1 fm/c. Tracks show multitude of particles≃ produced, as observed at RHIC (BNL). The acceleration a achieved to stop some/any of the components of • ∆y the colliding nuclei in CM: a ∆ . Full stopping: ∆ySPS = 2.9, and ≃ Mi τ ∆yRHIC = 5.4. Considering constituent quark masses Mi MN /3 310 MeV we need ∆τSPS < 1.8 fm/c and ∆τRHIC < 3.4 ≃ ≃ fm/c to exceed ac. Observed unexplained soft electromagnetic radiation in hadron reactions• A. Belognni et al. [WA91 Collaboration], “Confirmation of a soft photon signal in excess of QED expectations in π–p interactions at 280-GeV/c,” Phys. Lett. B 408, 487 (1997) . Recent suggestions that thermal hadron radiation due to Unruh • type phenomena P. Castorina, D. Kharzeev and H. Satz, “Thermal Hadronization and Hawking-Unruh Radiation in QCD,” Eur. Phys. J. C 52, 187 (2007), also Biro, Gyulassy [arXiv:1111.4817] Other path towards super-critical (Planck) acceleration 3 29 2 a = 1(= mec /~ 2.331 10 m/s ) → × Directly accelerated electrons at rest in lab by ultra intense laser pulse: requires Schwinger scale field Present laser pulse intensity technology misses several orders of magnitude, further development needed. Shortcut: we can Lorentz-boost: to reach the critical acceleration scale today: we collide a counter-propagating electron with a laser pulse. Laser pulse in electron’s rest frame

Figure shows boost (from left to right) of the force applied by a Gaussian photon pulse to an electron, on left counter propagating with γ/ cos θ = 2000. Pulse narrowed by (γ cos θ)−1 in the longitudinal and (γ sin θ)−1 in the transverse direction. Corresponds to Doppler-shift: ′ ω ω = γ(ω + ~v nk) → · as applied to different frequencies making up the pulse. SLAC’95 experiment near to critical acceleration

duα p0 = 46.6 GeV; in 1996/7 a = 0.4, = .073[m ] (Peak) e 0 dτ e

Multi-photon processes observed: Nonlinear Compton scattering • Breit-Wheeler electron-positron pairs •

D. L. Burke et al., “Positron production in multiphoton light-by-light scattering,” Phys. •Rev. Lett. 79, 1626 (1997) C. Bamber et al., “Studies of nonlinear QED in collisions of 46.6 GeV electrons with • intense laser pulses” Phys. Rev. D 60, 092004 (1999). EM Probe of critical acceleration possible today IZEST, or SLAC, CEBAF: experiments CEBAF: There is a 12 GeV possible in principle (γ = 2400) electron beam There is a laser team There is appropriate high radiation shielded experimental hall Mach, Acceleration Inertia → To measure acceleration we need to refer to an inertial• frame of reference. Once we know one inertial observer, the class of inertial observers is deﬁned.

Before Einstein’s relativity, Mach posited, as an alternative to Newton’s• absolute space, a) that inertia (resistance to acceleration) could be due to the background mass in the Universe, and b) that the reference inertial frame must be inertial with respect to the Universe mass rest frame. The latter postulate Einstein called ‘Mach’s principle’. Any observer inertial wrt CMB frame qualiﬁes: “Mach’s ﬁxed stars". • GR and later Cosmology motivated by Machs ideas, yet Einstein nearly• eliminated acceleration: geometrization of gravity means that dust of GR point masses is in free fall. Inertia, the resistance to acceleration requires presence of non-geometric• forces and/or extended quantum matter leading to rigid extended material body. QFT provides the quantum vacuum, the Aether, as Mach’s frame. • Maxwell, Lorentz and Inertia: ad-hoc combination

The action comprises three elements: (F αβ ∂αAβ ∂βAα) I ≡ − 1 dx mc = d 4x F 2 + q dτ A + dτ(u2 1). I −4 Z Zpath dτ · 2 Zpath −

Path is fixed at the end points assuring gauge-invariance. The two first terms upon variation with respect to the field, produce •Maxwell equation including radiation emission in presence of accelerated charges. The second and third term, when varied with respect to the form of the• material particle world line, produce the Lorentz force equation: particle dynamics in presence of fields. Maxwell and Lorentz equations which arise NEED NOT BE CONSISTENT, the form of dictated by gauge- and relativistic-invariance. ManyI modifications are possible. There is no reference to Mach’s inertial frame allowing definition of acceleration. Gravity and other interactions not truly unified

1 4 = √ g + d x√ gR J I − 8πG Z − There are acceleration paradoxes arising combining gravity and electromagnetism: Charged electron in orbit around the Earth will not radiate if bound• by gravitational ﬁeld, but it will radiate had it been bend into orbit by magnets. A free falling electron near BH will not radiate but an electron resting• on a surface of a table should (emissions outside observer’s horizon. A micro-BH will evaporate, but a free falling observer may not see• this. Is the BH still there? One is tempted to conclude that we do not have a theory incorporating acceleration. New Physics Opportunity if we can create unit strength (critical) acceleration. Better foundational theory not around the corner

Old idea: geometrize EM theory: 5-d Kaluza-Klein. EM potential part of 5-metric. To lowest order in charge, Lorentz• force arises from 5-d geodetic. Hilbert-Einstein 5-d action reduces to 4-d Einstein-Maxwell action. Pro: Any geometric EM theory has ‘æther’ and is Machian just like GR; charge is a property of the ‘æther; the missing degrees of freedom appear in 5th dimension. Con: Lack of understandings of dynamics in 5-d extra dimension, solutions arbitrary. No experiment showing generalized equivalence principle justifying use of 5-d geodetic. Should the generalization of Maxwell-Lorentz be geometric, critical acceleration experiments will be capable to explore this uniﬁcation. Einstein’s Aether as an inertial frame of reference Albert Einstein at ﬁrst rejected æther as unobservable when formulating special relativity, but eventually changed his initial position, re-introducing what is referred to as the ‘relativistically invariant’ æther. In a letter to H.A. Lorentz of November 15, 1919, see page 2 in Einstein and the Æther, L. Kostro, Apeiron, Montreal (2000). he writes: It would have been more correct if I had limited myself, in my earlier publications, to emphasizing only the non-existence of an æther velocity, instead of arguing the total non-existence of the æther, for I can see that with the word æther we say nothing else than that space has to be viewed as a carrier of physical qualities. In a lecture published in May 1920 (given on 27 October 1920 at Reichs-Universität zu Leiden, addressing H. Lorentz), published in Berlin by Julius

Springer, 1920, also in Einstein collected works: In conclusion: . . . space is endowed with physical qualities; in this sense, therefore, there exists an æther. . . . But this æther may not be thought of as endowed with the quality characteristic of ponderable media, as (NOT) consisting of parts which may be tracked through time. The idea of motion may not be applied to it. Importance of quantum theory

Without quantum theory we would not have extended bodies, without extended material bodies we cannot create critical acceleration – acceleration due to interplay of quantum and EM theories.

Quantum vacuum state is providing naturally a Machian reference frame lost in classical limit. Critical acceleration in quantum theory (critical fields) leads to new particle production phenomena which have a good interpretation and no classical analog or obvious limit. Laws of Physics and Quantum Vacuum Development of quantum physics leads to the recognition that vacuum fluctuations define laws of physics (Weinberg’s effective theory picture). All this is nonperturbative property of the vacuum. The ‘quantum æther’ is polarizable: Coulomb law is modified; • E.A.Uehling, 1935 New interactions (anomalies) such as light-light scattering arise • considering the electron, positron vacuum zero-point energy; Euler, Kockel, Heisenberg (1930-36); Casimir notices that the photon vacuum zero point energy also induces • a new force, referred today as Casimir force 1949 Non-fundamental vacuum symmetry breaking particles possible: • Goldstone Bosons ’60-s ‘Fundamental electro-weak theory is effective - model of EW • interactions, ‘current’ masses as VEV Weinberg-Salam ’70-s Color confinement and high-T deconfinement • Quark-Gluon Plasma ’80-s Quantum Vacuum Structure

The best known and widely accepted vacuum property is that it is a dielectric medium: a charge is screened by particle-hole (pair) excitations.

In Feynman language the real photon is decomposed into a bare photon and a photon turning into a virtual pair. The result is a renormalized electron charge smaller than bare, and slightly stronger Coulomb interaction (0.4% effect).

At any ﬁeld strength the conversion of ﬁeld energy into pairs possible Acceleration and temperature

Unruh observes that an accelerated observers will • perceive temperature a T = U 2π relation to Hawking radiation: strong acceleration = ?? strong gravity Properties of quantum vacuum ‘accelerated’ in a constant • field can be cast into a form displaying heat capacity at temperature a T = , a = eE/m E π resolution of factor 2 and of the related issue of Fermi-Bose statistics choice remain a challenge Euler-Heisenberg Z. Physik 98, 714 (1936) evaluate Dirac zero-point energy with (constant on scale of ~/mc) EM- fields, transform to action ∂E E(D, H) →L(E, B)= E − ED, E ≡ ∂D ∞ 1 ds −m2s sE sB 1 2 2 2 L(E, B)= − 2 3 e − 1 + (E − B )s . 8π Ziǫ s »tan sE tanh sB 3 – E, B relativistic definition in terms of invariants 2 2 2α ~ 2 ~ 2 ~ ~ 2 L(E, B) → 4 E − B + 7(E · B) = light − light scattering 45m »“ ” – Schwinger 1951 studies in depth the imaginary part – see zeros in tan sE:

2 ∞ 2 −2Im L α −2 −nπm2/eE |h0+|0−i| = e , 2Im L = n e π2 Xn=1 is the vacuum persistence probability in adiabatic switching on/off the E-field. For E → 0 essential singularity. Note: vacuum unstable for any finite value of E and there is no analytic E → 0 limit!. The light–light perturbative term is first term of semi convergent expansion which fails in a subtle way. Temperature for vacuum fluctuations at a =Const. Using identity [B.Müller, W.Greiner and JR, PLB63A (1977) 181]: x cos x x 2 1 2x 4 = 1 + sin x − 3 k 2π2 x 2 k 2π2 Xk=1 − give after resummation a “statistical” form with T = eE/πm = a/π:

2 ∞ m T −ω/T 2 2 (E)= 2s 2 ρ(ω) ln(1 e )dω, ρ = ln(ω m + iǫ); L − 8π Z0 − − Same sign of pole residues source of Bose statistics. For scalar loop x x 2 ( 1)k 2x 4 particles we have = 1 + + − which yields sin x 6 k 2π2 x 2 k 2π2 Xk=1 − same expression up to: 1) statistics turns from Bose into Fermi: −ω/T −ω/T ln(1 e ) ln(1+e ) and 2) factor 2s 1. Note that the − − → → statistics is reversed compared to expectations and temperature is twice larger compared to Hawking-Unruh observer. Potential improvements needed in the nonperturbative approach to constrain symmetry of the vacuum state. Materialization into Particles at ULTRA High Energy Two high energy photons colliding head on can make particle in laboratory rest frame. Same is true for two coherent laser pulses. To produce particles at high rapidity we collide two (or more) laser pulses in a different geometry. For nearly parallel beams [L.Labun and J.R. Phys Rev D84,0330003 (2011)] pairs arise in a frame of reference that is moving with high Pointing Momentum:

µ µν 0 1 2 2 1 µ i i p := T uν, p = ε (E~ + B~ )+ T p = ε (E~ B~ ) = S~ 2 4 µ × The mass density is 1 µ2 := p2 = ε2( 2+ 2)+(T µ/4)2 = (B~ 2 E~ 2); = E~ B~ S P µ S 2 − P · Expressed in comoving rest frame 2 d 2 + b2 µ2 = ε2 + (T µ/4)2 2 µ Where the covariant ﬁeld deﬁnition is

d 2 = 2 + 2 E~ 2 b2 = 2 + 2 + B~ 2 pS P −S→| | pS P S → | | Integration over all volume yields mass available for materialization. Particles are produced with high CM frame rapidity with respect to lab frame of reference

2 2 ~ ~ 2 0 2 2 µ + ε (E B) (p ) cosh yS = × = µ2 µ2 and emerge depending on angle of collision and asymmetry of intensity r with rapidity

1 + r sin θ + r 2/2 cosh2 y = + (α2r 3) r 2(sin2 θ + r sin θ sin φ + r 2/4) O Summary

New opportunity to study foundational physics involving acceleration and search for generalization of laws of physics – motivated by need for better understanding of inertia, Mach’s principle, Einstein’s Aether, and the temperature of the accelerated quantum vacuum .

Critical acceleration possible in electron-laser pulse collisions. Exploration of physical laws in a new domain possible

Experiments should help resolve the old riddle of EM theory and radiation reaction Rich ﬁeld of applications follows

Application: Ultra high energy particle production without acceleration.