Presentation on theme: "1 I L Zhogin (Novosibirsk -- Saint Petersburg) QFTG-2012, Tomsk Suppression of gravitational short waves in a 4-th order gravity."— Presentation transcript:
1 I L Zhogin (Novosibirsk -- Saint Petersburg) QFTG-2012, Tomsk Suppression of gravitational short waves in a 4-th order gravity
2 Social laws vary in space and time -- Hammurapis code, Rome law, Jackson-Vanik amendment, et cetera (sometimes they would be ignored). OTOH, the physical laws are seemingly invariable and supposedly should be united as a single Fundamental law (or theory; the FT). Einstein supposed: (~) Our world is simple – otherwise is not interesting. One just needs to understand a small piece of the universe – others are similar. (How can this tiny & simple piece hold information on all those fundamental constants?) Does it means that the FT should have no free parameters? Otherwise its a set of similar theories, not a single one. If a parameters 20 th digit costs a few trillion of money (+ a 100-year experiment -- tiny time), it wont be measured. Never. Parameters might emerge as slowly varying features of solutions, not of the theory itself. If the FT is simple, one should not be a Solomon that to understand it. 1 Arranging the scene The human doesnt know the Fundamental theory now [despite the self-naming homo sapiens (sapiens)]; this opens the door for numerous speculative models and theories [emergent gravities, inflation models, dark matter and dark energy (a dark disguise ?), baby universes, LQG, extra Ds, …] – most to be of no concern.
3 The main(stream) speculation – string theory (still doesnt deserve the) – has (next to) no chances to be falsified (qualitative positive predictions, e.g. SUSY, are not falsifiable), and is not free from free parameters (Its not a real FT candidate). There are seemingly no prospects that a QFT (or some string/brane branch) can contrive to easily answer those simple particles questions. The Fundamental theory should be responsible for the entire Universe, easily answering the simple questions about the particles (what is the meaning of lepton flavors? why do just these particles exist and not others? etc.), and give rise to a set of robust and sighted phenomenological models. It seems desirable to be beyond the QFT-scope, but whereabouts? 2 Searching for the Fundamental theory Ill talk of a complete, ready theory (a reasonable candidate; no free factors, D=5): an exceptional e-qn of frame field, h a m, which prevents the field square matrix from degeneration (when rank h a m < 5 or rank h q h a m < 5); solutions are free from singu- larities and can carry digital information – topological (quasi) charges; T-charges
4 These new, derivative letters help to explain the striking variety of polarizations, degrees of freedom, their dramatically different behavior (as they relate to different parts of L -tensor) The symmetry of AP eq-ns is great, symmetries of SR & GR are embraced: 3 Features of the frame field theory (absolute parallelism, AP) Metric is included (as a quadratic form): Simple 1 st order covariant and its irreducible parts: Most polarizations do not carry D-momentum – i.e. a bit intangible Identities should be considered: Tensor f (it turns out, only this tensor carries D-momentum): Riemann curvature tensor:
5 4 An example of compatible eq-n (nonlinear system) of AP; co-singularities A typical compatible AP eq-nhas D(D-2) polarizations (the linearized eq-n looks as a D-set of Maxwells eq-ns), and is plagued with singularities of solutions The compatibility test can be extended to the 1-degenerate co-frame D=4 - forbidden 2-minor The determinant and minors are multi-linear in co-frame elements || 1-minor (co-rank 1) There are two special cases (when two parts should be taken separately) Exceptional eq-n, EE, antipode of GR GRT: 1-minor appears in the other part Symmetrical part Skew-symmetrical part (or Riemann tensor)
6 5 Contra-singularities and unique D One should use a contra-variant frame density of some weight, where D * depends on the choice of equation (D * = 2 for GR): Note, the inverse transform is singular for D=D * The exceptional equation, where D * =4 (forbidden dimension) takes on the next tri-linear form: the best choice for D: D=5 ! ! If D=5, 1-minor of «working» matrix coincides with co- frame; that is, the contra-singularities simultaneously imply co-singularities (of very low rank); but thats impossible for the exceptional equation h a m = H p H a m, p = 1/(4-D); p = -1 if D = 5 h a m = H -1 H a m Nature, if she abhors singularities, should choose just this equation, EE, and D=5
7 6 Linear instability of the trivial solution EEs (skew- and just) symmetric parts: The extended eq-n looks as Maxwells one; the current is trivial The dual form, *S, is exact; one can introduce a pseudo-vector P: * The linearized equations and extended identity lead to the next evolution eq-n with a source: 3 unstable, resonant growing polarizations, ~ t ; one can introduce a new, shadow EM-ish field: The main set: tensor + GI vector + NGI vector (LP) + pseudo-scalar = 8 degrees These fields embrace all polarizations: (no overlaps; GI marks gradient invariance) GI No GI Main set, 4D degrees, 8: Extra set, weak degrees, 7: (P 4 ) 1(LP) ShadowEM GWaves PseudoEM Long.P. SuperEM
8 7 Energy-momentum tensor and meta-Lagrangian Symmetrical equation does not lead to energy-momentum (no positive energy): Only f-field (three super-degrees in D=5) carries 5-momentum and angular momentum (tangible waves); other 12 polarizations are intangible (its very unusual – how to quantize?); f-waves feel only metric and S-field which has effect only on polarization of f: S does not enter eikonal equation, and f-waves move along usual Riemannian geodesics Hopefully, the following further phenomenology of T-quanta will inherit these features (Lagrangian, Riemann geodesics, etc.) This eq-n follows also from the next meta-Lagrangian (quadratic in the field eq-s): New gravity as a bonus ! ! No ad hoc activity ! Extended equation,, can be given a form of 4 th -order gravity: tensor `B has symmetries of Riemann tensor and gives no contribution to D- and angular momentum Interestingly, the energy-momentum pseudo-tensor is trivial here
9 8 Further points (just a few) The job of inflation is done -- as a kind of relativistic effect My main point here is: the emerging phenomenology of topological quanta in such a stochastic background can look as a 4D QFT, a T-superstructure over a classical basement. Hopefully, such an opportunity should be interesting for specialists in QFTs. Shadow-waves make non-linear effects inevitable; this opens the door to new actors – topological quanta, localized non-linear configurations which carry digital information – T-charges and T-quasi-charges R~T= Γt (radius=extra-D; ΔRΓ = L) The math of a QFT is not a patented property, nor a holy cow – just a math based on a few principles; their list is short: Lorentz covariance (+ if quanta are rare) Least action principle and positive energy (+ will be shown) Causality (+ legacy of well-posedness) Gauge invariance (+ not bad chances) Superposition principle (? a bit strange) One just should find arguments that all these principles are to be valid in the emerging phenomenology of T-quanta Possible scenario: an ovoid T-charge in a center issues at times longitudinal waves, which become expanding, more or less spherical, S 3 -shells. A shell, a hump of shifted metric can serve as a shallow wave-guide for super-waves. Here, with time, shadow-waves become large and form a stochastic background, with some scaling parameters, full of T-(quasi)charge fluctuations.
10 9 Topological charges and quasi-charges Group of topological charge: The left T-charge never converts to the right one; to explain masses, we need a kind of pseudo- vector condensate of quanta, relating to O 2 -generated symmetries (with inversion I=P 3, where both quaternion spheres are involved). Symmetries and quasi-charge groups Symmetries of cosmological background: cylindrical+ discrete P(4) relates to the charge conjugation The set of quasi-charges depends on background symmetries; hadron bags can be of higher temperature and higher symmetry, with other set of T-QCs and T-quanta. SO 4 is represented by a pair of unit quaternion
11 10 Superposition principle This meadow looks some desolate, but in fact, an invisible person is walking there But if there is raining (or snowing), she becomes quite well visible Lets start with an illuminating illustration L The harder precipitation, the better visible she is T-quanta are confined in the wave-guide; they acquire geometrical energy E g by scattering f-waves, it should depend on the amplitude, h f, and can differ from phenomenological energy, E ph, by a factor. The superposition principle emerges due to (a) huge size L of T- quanta along the extra-D and (b) the fact that f-waves are almost tangential in the shell -- scattering amplitudes of quantum pieces with the same projection (i.e. co-phased) should be summed up. A photon of frequency ω has E ph = ω, and disturbs metric as λ Pl ω; but a T-quantum with ω-grating should have E g ~ h f ω, & disturbance L 2 E g. 2 2 One may conclude: the Planck length is not a fundamental scale, but a composite value, λ Pl = h f L !
12 Take a mass distribution along the extra dimension (L=1) as to make initial correction zero, δF(0)=0; ie the Rindler term vanishes For a point mass the `new gravity' gives: 11 Newtons law revisited Force between two point masses r<Lr>L One can find the potential energy (and the force) of two masses extended along the extra-dimension (there is the only typical scale L; it is difficult to observe, no difference; frozen D)
13 12 Generation of gravitational waves (GWs) Gravitational waves are generated by the Ricci tensor (this follows from Bianchi identities): GR strongly overestimates the intensity of short GWs -- by factor (L/λ) 4, where λ is the GW wavelength and L is the thickness of the cosmological waveguide along the extra-D (in co-moving system; perhaps, from data on wide binaries, L~10 3 AU) The difference between these two gravities, with respect to GW generation, can be tested: the method to observe very long (nHz) GWs using pulsar timing is actively discussing nowadays Excluding space derivatives (they dont matter in the wave zone), one obtain (using the 4-th order gravity): While in GR we have something different: For short enough GWs (λ<
14 The inflationary expansion promotes the growth of fluctuations on all scales, and angular correlations at all angles (the dashed curve – for the standard cosmological model). However, the observed angular correlation function almost vanishes at angles larger than 60°. If we trust to this observation, perhaps we can change the choice of the absolute rest system (back to Aristotle): instead of condition that the dipole component is zero (the dipole component is not something special as compared with the quadruple one, etc) its worth choosing the following requirement: C(-1)=0 μK2μK2 13 CMB and the angular correlation function The two-point angular correlation function reads C(cosθ)= nm Correlation function: ΛCDM (with inflation) vs WMAP data
15 Thank you for your attention ! 14 A few concluding remarks (and apologies) A simple and beautiful theory (of great symmetry) does exist: AP grants a unique, remarkable eq-n, no singularities -- no free parameters (D =5 is a must); topological quanta whose 4D-phenomenology can look like a QFT (on a classical background with modified gravity and some other fields) Can this `mathematical reality coincide with our Universe? – Maybe. Some qualitative predictions are in order: a new 4 th order gravity -- the GRT is not valid for large scales; short-wave GWs are suppressed; no inflation – anti-Milne cosmology, d L =(1+z) ln(1+z); some insights on lepton flavors (three or four, no more); neutrinos are true neutral (a kind of Majorana); no room for SUSY and DM; no spin zero elementary quanta -- only 1 and ½ (no higher spins -- sorry, guys); New unexpected experimental opportunities (pseudo-scalar field of rotating Earth, stationary and non-stationary Brown effect (shadow fields), interference of single photons or neutrons (indivisibility of T-quanta); Quantum cosmology is an oxymoron here (and QG as well; sorry)...
16 15 Interference of single photons (to feel the extra-dimension) New question (to Nature): whether a wave-function of a particle (e.g., photon or neutron) is separable or not? Impenetrable partition Source of single photons, ~50kHz Delay line 1000 m Fiber beam splitter, 50/50 Fringe pattern should lose its visibility 1D detector Fast chopper A ~ 1/r r Topological quasi-charge should choose a part; the other disapears
17 SNe Ia data from Hicken, et al. arXiv: The same as FRW-model with a~t, k=+1 (Milne model has k=-1) Good fitting of SNe Ia data Anti-Milne model arXiv: Interesting cosmology Milne model (or empty model) - as the reference point here Green balls – anti-Milne and gamma ray bursts (GRB)
18 17 Observation of Brown effect; V.P.Delyamure (Dnepropetrovsk) NaCl solution 20 kV supply Cu wire, Ø90μm pointer corbel plate lower clamp electrode sensing element vessel upper clamp electrode 160 The installation uses a torsion meter; its sensing element (foil-coated glass fiber laminate, 2.5 mm) rotates on 25° when 20 kV voltage is applied (F~10 -5 N) 90 Cu wire, Ø90μm
19 18 An attempt to register the dipole pseudo-scalar field of the rotating Earth Systematic errors were some bigger than the expected effect ρ ~ P,j H j -- pseudo-charge (about 0.1 pC/liter for magnetic field H~1 T) Ferrite magnets (from a pump Nord-100)
20 19 LHC and Higgs (two questions about two-photon events) E, GeV Atlas CMS 1000 <200 ratio 1.7 >2.5 - varies?! Bi-photon events What does it means? Perhaps, some parameters (detecting efficiency, collinearity criteria) vary with energy some differently for the two. Are these variations smooth or fluctuate? There is little info about systematic errors despite the presence of many deeps (inverse bumps). Madam, where will we make the waist- line? Just a joke It would be interesting to look at the energy distributions of three-photon events Atlas CMS ! Congratulations !