Quantum Structure of Spacetime and Its Entropy in a Cyclic Universe with Negative Curvature I: A Theoretical Framework

We construct a model of the Cyclic Universe from a joint theory of General relativity, Thermodynamics and Quantum information theory. Friedmann equations and the thermodynamical Gibbs-Duhem relation determine a general form of the Hubble function which predicts a dynamical Dark Energy (DE) and a dynamical Dark Matter (DM) described by new entropic terms and by the equations of state w_0=-1 and w_M=0, respectively, at all z. We posit that the spacetime has a quantum structure described by the Quantum information theory. We identify the space quanta \rho with two-qubit quantum states of of massless gravitons with helicity states |\pm 2>. All space quanta carry quantum information entropy S(\rho). All entangled quanta carry entanglement entropy S_E(\rho) and form DE. All non-entangled quanta form DM. In the absence of Baryonic matter DM and SE are described by probability distributions p(\vec{x},S) and q(\vec{x},\chi) where \chi=S_E(\rho)+S(\rho). Fisher information metric generates from these distributions the vacuum gravitational fields of DM and DE. Tn the presence of the Baryonic matter the distributions are displaced p->p' and q->q'. Fisher metric then defines the displaced fields. In Einstein's theory of General relativity Space is a gravitational field which we identify with the gravitational fields of DE and DM. The theory predicts the existence of a new "residual" matter term with equation of state w_r=-1/3 in the Hubble function, and a negative spatial curvature the consequence of which are constraints on cosmological parameters. We recover Robertson-Walker metric and the Friedmann equations from the gravitational fields of Dark Energy and Dark Matter at cosmological scales. The predictions of the theory are tested and confirmed in the Part II of this work.Comment: 44 pages including 2 appendices; equations (3.17) and (4.29) corrected, previous equations (3.35) and (3.36) deleted, equations (9.20) and (9.21) added; Subsection IV.D added; change in the addres

Violation of Generalized Bose-Einstein symmetry and quantum entanglement of pi(-)pi(+) isospin states in pion pair production piN->pi(-)pi(+)N

Generalized Bose-Einstein symmetry requires that J+I=even for two-pion angular states of spin J and total isospin I. We show that the symmetry predicts three linearly independent constraints on partial wave intensities with even spin for pi(-)p->pi(-)pi(+)n, pi(-)p->pi(0)pi(0)n and pi(+)p->pi(+)pi(+)n. Available data violate all three constraints for S, D^0, D^U and D^N partial waves. The violations of the symmetry imply a presence of the symmetry violating contributions to transversity amplitudes in pi(-)p->pi(-)pi(+)n and predict quantum entanglement of pi(-)pi(+) isospin states which is excluded by the symmetry. We derive approximate lower and upper bounds on entanglement amplitudes |a_S| and |a_A|. The bounds provide a clear evidence for entanglement of pi(-)pi(+) isospin states below 840 MeV and suggest the entanglement at higher dipion masses. The small values of |a_S| \sim 0.10-0.20 below 840 MeV explain the puzzling differences between the S-wave intensities in pi(-)p->pi(-)pi(+)n and pi(-)p->pi(0)pi(0)n and reveal a suppression of isospin I=0,2 contribution in the S-wave amplitudes in pi(-)p->pi(-)pi(+)n. The large isospin I=1 contribution of rho^0(770) to both S- and P-wave amplitudes is due to large entanglement amplitude |a_A| \sim 0.98-0.99. These findings confirm the predictions of a model of non-unitary dynamics of the pion creation processes arising from a CPT violating interaction of these processes with a quantum environment.Comment: 23 pages, 13 figure

Study of piN->pipiN processes on polarized targets II.: The prediction of rho^0(770)-f_0(980) spin mixing

In Part I. of this work we have presented evidence that the measured relative phases of transversity amplitudes in piN->pipiN processes differ from those predicted by the unitary evolution law. We ascribed this difference to a non-unitary interaction of the produced final state rho_f(S) with a universal quantum environment in the Universe. This new kind of interaction must be a pure dephasing interaction. If the quantum environment is to be an integral part of the Nature then its dephasing interactions must be fully consistent with the Standard Model. In this work we impose on the dephasing interaction the requirements of the conservation of the identities and four-momenta of the final state particles, Lorentz symmetry, P-parity and the conservation of total angular momentum and isospin. From this consistency alone we find that in piN->pipiN the dephasing interaction must be a dipion spin mixing interaction. The theory predicts rho^0(770)-f_0(980) mixing in the S- and P-wave amplitudes in pi(-)p->pi(-)pi(+)n. The predicted moduli and relative phases are in agreement with experimental results. The spin mixing of S-matrix amplitudes to form new observable amplitudes is a new phenomenon beyond the Standard Model. It is our conjecture that the pure dephasing interaction describes the non-standard interaction of baryonic matter with dark matter and dark energy which we identify with the quantum environment.Comment: 40 pages, 8 figures. Subsections III.C & V.C deleted. Subsections III.B, VII.D, Section VIII, Conclusions revised. New Sections IX,X,XI. Old ref.17,18,21,30,31,35,36 deleted, new ref.11,12,13,18,23,35-39 adde

Evidence for evolution from pure states to mixed states in pion creation process pi(-) p -> pi(-)pi(+) n on polarized target and its physical interpretation

In 1982 Hawking suggested that quantum fluctuations of space-time metric will induce a non-unitary evolution from pure initial states to mixed final states in particle interactions at any energy. This hypothesis can be tested using existing CERN data on pi(-) p -> pi(-)pi(+) n on polarized target at 17.2 GeV/c. The purity of the final state is controlled by the purity of recoil nucleon polarization. We develop a spin formalism to calculate expressions for recoil nucleon polarization for two specific pure initial states. Imposing conditions of purity on the recoil nuclon polarization we obtain conditions on the amplitudes which are violated by model independent amplitude analysis of CERN data at large t. We conclude that pure states can evolve into mixed states in pi(-) p -> pi(-)pi(+) n. In quantum theory such non-unitary evolution occurs in open quantum systems interacting with an environment. We present evidence to validate the view of the pion creation process as an open quantum system interacting with a quantum environment. The observed process is time-irreversible and violates CPT symmetry.Comment: 44 pages, 4 figures, 3 tables, references adde

Consistency of pipi phase shift analyses with rho^0(770)-f_0(980) spin mixing in pi(-)p->pi(-)pi(+)n

We have performed two analytical pipi phase shift analyses using a Standard amplitude analysis of the CERN data on pi(-)p->pi(-)pi(+)n on polarized target at 17.2 GeV/c and a more recent analysis of the same data using Spin Mixing Mechanism (SMM). There are two solutions for helicity amplitudes labeled (1,1) and (2,2) in the Standard analysis and SpinMixing and S-Matrix in the SMM analysis which are related to the pipi scattering amplitudes. Our first phase shift analysis is an elastic scattering analysis below KKbar threshold. Our second analysis is a joint pipi phase shift analysis of pi(-)pi(+) and pi(0)pi(0) data below 1080 MeV. Our elastic Solution (2,2)1 and elastic Solution SpinMixing 1 for delta^0_S are in a remarkable agreement with the 1997 Cracow Solution Down-flat using the same CERN data on polarized target. Our joint Solution (2,2) and joint Solution SpinMixing are also in a remarkable agreement with the 2002 joint Cracow Solution Down-flat. Solutions elastic (1,1) and joint (1,1) agree with the Cracow Solutions Up-flat and are rejected. Model independent amplitude analyses of measurements of pi(-)p->pi(-)pi(+)n at 17.2 and 1.78 GeV/c and pi(+)n->pi(+)pi(-)p at 5.98 and 11.85 GeV/c reveal evidence for rho^0(770)-f_0(980) spin mixing in the S-wave transversity amplitudes. These transversity amplitudes define single-flip helicity amplitudes which have been related to pipi scattering amplitudes. Our key observation is that the presented and the Cracow solutions are consistent with the evidence for rho^0(770)-f_0(980) spin mixing in the measured transversity amplitudes from which all these phase shifts ultimately arise.Comment: 29 pages, 20 figures, labels in Figure 2 correcte

Serial Acceleration-Deceleration Transitions in a Cyclic Universe with Negative Curvature

In this work we develop a general phenomenological model of the Cyclic Universe. We construct periodic scale factor a(t) from the requirements of the periodicity of a(t) with no singular behavior at the turning points t_\alpha and t_\omega and the requirement that a unique analytical form of the Hubble function H(z) can be derived from the Hubble function H(t) to fit the data on H(z). We obtain two versions of a(t) called Model A and Model C. Hubble data select Model A. With the analytical forms of the Hubble functions H(t) and H(z) known we calculate the deceleration parameters q(t) and q(z) to study the acceleration-deceleration transitions during the expansion phase. We find that the initial acceleration at t_\alpha=0 transits at t_{ad1}=3.313x10^{-38}s into deceleration period that transits at t_{da}=6.713 Gyr to the present period of acceleration. The present acceleration shall end in a transition to the final deceleration at t_{ad2}=38.140 Gyr. The expansion period lasts 60.586 Gyr. The complete cycle period is T=121.172 Gyr. We use the deceleration parameters q(z) and q(t) to solve the Friedmann equations for the energy densities of Dark Energy \Omega_0 and Dark Matter \Omega_M to describe their evolutions over a large range of z and t. We show that in the Model A the curvature density \Omega_c(z) evolves from a flat Universe in the early times to a curves anti de-Sitter spacetime today. There is no Standard Model Inflation in the Model A.Comment: 29 pages, 5 figures, 6 tables; typos corrected, change in the address. Note: The City of Westmount is within the City of Montrea

Study of piN->pipiN processes on polarized targets: Quantum environment and its dephasing interaction with particle scattering

Unitary evolution law describes isolated particle scattering processes in an empty Minkowski spacetime. We put forward a hypothesis that the physical Universe includes a quantum environment that interacts with particle scattering processes. While the scattering process is governed by the S-matrix the interaction evolves the produced state rho_f(S) to observed state rho_f(O). To be consistent with the Standard Model this new interaction must be a pure dephasing interaction governed by a non-unitary evolution law modifying the phases of the amplitudes. We present the first test of the unitary evolution law in particle scattering. The unitary evolution law evolves pure initial states into pure final states in exclusive processes. This fact leads to 9 independent constraints on 16 components of angular intensities in piN->pipiN processes. When expressed in terms of P-parity conserving transversity amplitudes all 9 constraints are identities provided a single constrain on the transversity amplitudes holds true. The constraint implies that the relative phases between transverity amplitudes of the same naturality and transversity must be 0 or +/- pi. All previous amplitude analyses of the piN->pipiN processes found non-unitary relative phases in an apparent violation of the unitary evolution law. The contrast between the predicted and the observed relative phases presents an unambigous evidence for the existence of the quantum environment and its pure dephasing interaction with particle scattering processes.Comment: 38 pages, 5 figures, 5 tables. Final version as it appears in Physical Review D. Typos correcte

Evidence for rho^0(770)-f_0(980) mixing in pi(-)p->pi(-)pi(+)n from CERN measurements on polarized target

We present model independent high resolution amplitude analyses of CERN data on pi(-)p->pi(-)pi(+)n at 17.2 GeV/c for dipion masses 580-1080 MeV at small momentum transfers on polarized target (Analysis I) and unpolarized target (Analysis II). The results for S- and P-wave transversity amplitudes from the Analysis I are used in a model independent determination of helicity amplitudes. All three analyses provide similar evidence for rho^0(770)-f_0(980) mixing in S- and P-wave amplitudes. In Analyses I and II the S-wave amplitudes |S_d|^2 peak at rho^0(770) mass while the P-wave amplitudes |L_d|^2 dip at f_0(980) mass. In both analyses the S-wave amplitudes S_tau are nearly in phase with amplitudes L_tau for both transversitities tau=u(spin up) and d(spin down), indicating resonant phases of rho^0(770) also in the S-wave. The S-wave single flip amplitudes |S_1|^2 and the relative phases Phi(S_1)-Phi(L_1) show the same pattern. While the non-flip amplitudes |L_0|^2 are small below 960 MeV, there is a sudden rise above this mass that may reflect the presence of f_0(980) resonance. We show that the apparent dependence of rho^0(770) width on helicity in amplitudes |U_tau|^2 and |N_tau|^2 results from the interference of amplitudes with helicities lambda=+/-1 and not from the violation of rotational/Lorentz symmetry. This suggests that the production mechanism and the mechanism responsible for rho^0(770)-f_0(980) mixing have independent dynamical origins.Comment: 34 pages, 15 figures. Errors added in Figures 8,9,10. New Figure 15 added. Subsection VI.E omitted, new Section VIII added. References 26,27 omitted, new references 15,16,27,31-35,37,38 added. Some modification of the text in Abstract, Subsection VI.D and Conclusions. arXiv admin note: substantial text overlap with arXiv:0709.0688, arXiv:0709.221

Determination of S- and P-wave helicity amplitudes and non-unitary evolution of pion creation process pi(-)p -> pi(-)pi(+)n on polarized target

We present the first model independent determination of S- and P-wave helicity amplitudes from CERN measurements of pi(-)p -> pi(-)pi(+)n on polarized target at small t and dipion masses 580-1080 MeV. The purely analytical determination of the helicity amplitudes is made possible by our finding analytical solution for relative phase omega_ij between S-wave amplitudes S_d and S_u of opposite transversity for each set of solutions for transversity amplitudes A_u(i), A_d(j),i,j=1,2. Of the six possible solutions for omega_ij only the solution with omega_ij=pi yields physical helicity amplitudes. Assigning rho^0(770) phase to the dominant P-wave helicity flip amplitude L_1(ij) necessitates a phase of the S-wave helicity flip amplitude S_1(ij) that is near to the rho^0(770) phase.These two amplitudes are consistent with rho^0(770)-f_0(980) mixing. The relative phases omega_ij=pi satisfy certain selfconsistency relation that must be satisfied in order for the four sets of solutions A_u(i),A_d(j),i,j=1,2 to be all physical solutions that can be identified with coevolution amplitudes describing the interaction of the pion creation process with a quantum environment. This test on phases omega_ij provides a new test of Kraus representation of the mixed final state density matrix. We show that the probabilities p_ij determining the final state rho_f in terms of solution states rho_f(ij) can be determined in measurements of recoil hyperon polarization in pi(-)p->pi(-)K(+)Lambda0 on polarized target.Comment: 41 pages, 20 figures, 4 table

Evidence for a narrow sigma(770) resonance and its suppression in pipi scattering from measurements of pi(-)p->pi(-)pi(+)n on polarized target at 17.2 GeV/c

We present a new model independent amplitude analysis of reaction pi(-)p->pi(-) pi(+)n measured at CERN at 17.2 GeV/c on polarized target using a Monte Carlo method for dipion mass 580-1080 MeV. The two solutions for measured moduli |Sbar|^2 and |S|^2 of the two S-wave transversity amplitudes Sbar and S show res onant behaviour below 800 MeV corresponding to a scalar resonance sigma(770). Simultaneous fits to |Sbar|^2 and |S|^2 include f_0(980). The CERN data on polar ized target supplemented by the assumption of analyticity of production amplitud es in dipion mass allow to determine the helicity amplitudes S_0 (a_1 exchange) and S_1 (pi exchange) from fitted transversity amplitudes. The sign ambiguity in sigma(770) contribution leads to 2 solutions. In the "down" solution sigma(770) is suppressed in the helicity flip amplitude S_1 and thus also in pi(-)pi(+)-> pi(-)pi(+) scattering. Most contribution of sigma(770) to pion production is in the nonflip amplitude S_0, or in pi(-)a_1(+)->pi(-)pi(+) scattering. In the "up" solution the situation is reversed. The "up" solution is excluded by unitarity in pipi scattering. The "down" solution, and thus the evidence for sigma(770), is in agreement with unitarity in both pi(-)pi(+)->pi(-)pi(+) and pi(-)a_1(+)-> pi(-)pi(+) scattering. There are 4 "down" solutions (1, 1bar), (2, 1bar), (1, 2bar) and (2, 2bar). The sigma(770) resonance manifests itself as a broad resonant structure at ~ 720 MeV in the flip amplitude |S_1|^2 in solutions (1, 1bar) and (2, 1bar). The contribution of sigma(770) to |S_1|^2 is small in solutions (1, 2bar) and (2, 2bar). The metamorphosis of a narrow sigma(770) in the nonflip amplitude S_0 into a broad resonant structure in the flip amplitude S_1 is a new phenomenon related to breaking of scale and chiral symmetry in QCD.Comment: 29 pages (RevTex), 13 figure