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Abstract the Paper Is an Introduction Into General Ether Theory (GET View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Abstract The paper is an introduction into General Ether Theory (GET). We start with few assumptions about an universal “ether” in a New- tonian space-time which fulfils i @tρ + @i(ρv )=0 j i j ij @t(ρv )+@i(ρv v + p )=0 For an “effective metric” gµν we derive a Lagrangian where the Einstein equivalence principle is fulfilled: −1 00 11 22 33 √ L = LGR − (8πG) (Υg − Ξ(g + g + g )) −g We consider predictions (stable frozen stars instead of black holes, big bounce instead of big bang singularity, a dark matter term), quan- tization (regularization by an atomic ether, superposition of gravita- tional fields), related methodological questions (covariance, EPR cri- terion, Bohmian mechanics). 1 General Ether Theory Ilja Schmelzer∗ February 5, 2000 Contents 1 Introduction 2 2 General Ether Theory 5 2.1Thematerialpropertiesoftheether............... 5 2.2Conservationlaws......................... 6 2.3Lagrangeformalism........................ 7 3 Simple properties 9 3.1Energy-momentumtensor.................... 9 3.2Constraints............................ 10 4 Derivation of the Einstein equivalence principle 11 4.1 Higher order approximations in a Lagrange formalism . 13 4.2 Weakening the assumptions about the Lagrange formalism . 14 4.3Explanatorypowerofthederivation............... 15 5 Does usual matter fit into the GET scheme? 15 5.1TheroleoftheEinsteinLagrangian............... 16 5.2TheroleofLorentzsymmetry.................. 16 5.3Existingresearchaboutthesimilarity.............. 17 6 Comparison with RTG 18 ∗WIAS Berlin 2 7 Comparison with GR with four dark matter fields 19 8 Comparison with General Relativity 20 8.1Darkmatterandenergyconditions............... 20 8.2Homogeneousuniverse:nobigbangsingularity........ 21 8.3Isthereindependentevidenceforinflationtheory?....... 22 8.4Anewdarkmatterterm..................... 24 8.5Stablefrozenstarsinsteadofblackholes............ 24 9 General-relativistic quantization problems 25 9.1Causality............................. 26 9.2Informationlossproblem..................... 27 10 Atomic ether theory 28 11 Canonical atomic ether quantization 30 11.1Regularizationusingamovinggrid............... 31 11.2 Constraints and conservation laws in a moving grid . 33 11.3Universality............................ 34 12 Comparison with canonical quantization of general relativity 35 12.1ADMformalism.......................... 35 12.2Tetradandtriadformalism.................... 36 12.3Ashtekarvariables......................... 36 12.4Discretemodelsofgeometry................... 37 12.5Summary............................. 37 13 Quantum field theory 38 13.1Semi-classicalquantizationofascalarfield........... 39 13.2Particleoperatorsandvacuumstate............... 40 13.3Differentrepresentations..................... 42 13.4Gaugefieldquantization..................... 43 13.5Non-abeliangaugefieldquantization.............. 45 13.6Hawkingradiation........................ 45 14 Methodology 46 14.1TheinsightsofBohmianmechanics............... 47 14.2Relativityasatheoryaboutobservables............ 48 3 15 The violation of Bell’s inequality 49 15.1 Bell’s inequality for schoolboys .................. 50 15.2 The difference between special relativity and Lorentz ether . 51 15.3Aspect’sdevice.......................... 52 15.4Shouldwequestioneverything?................. 53 15.5Noapplicationfortheviolation................. 54 15.6 Objections against a preferred frame .............. 55 15.7Nocontradictionwithquantummechanics........... 55 15.8ObjectionsinconflictwithEinsteincausality.......... 56 15.9Discussion............................. 58 16 Conclusions 58 A Covariant description for theories with preferred coordinates 60 A.1MakingtheLagrangiancovariant................ 61 A.2Conservationlawsinthecovariantformalism.......... 62 B Relationalism 63 B.1Whatisthetrue“insight”ofgeneralrelativity?........ 65 B.2 What are insights which are “forever”? ............. 66 C The problem of time 67 C.1clocktimevs.truetime..................... 68 C.2 About positivistic arguments against true time ......... 69 C.3Relativityasaninsightabouttruetime............. 70 C.4Technicalaspectsoftheproblemoftime............ 71 D Quantum gravity requires a common background 72 D.1Anon-relativisticquantumgravityobservable......... 73 D.2 The problem: generalization to relativistic quasi-classical gravity 76 D.3Thesolution:afixedspace-timebackground.......... 77 D.4 Comparison of Regge calculus and dynamical triangulation . 79 E Realism as a methodological concept 80 E.1Principlesofdifferentimportance................ 80 E.2 A definition of reality and causal influence ........... 81 E.3 Bell’s inequality as a fundamental property ........... 82 E.4Themethodologicalcharacterofthisdefinition......... 83 4 E.5Causalityrequiresapreferredframe............... 84 E.6 Relation between our definition and the EPR criterion . 85 E.7 Methodological principles as the most fundamental part of sci- ence................................ 86 E.8ThemethodologicalroleofLorentzsymmetry......... 87 E.9Discussion............................. 88 F Bohmian mechanics 89 F.1SimplicityofBohmianmechanics................ 89 F.2Clarityoftheinterpretation................... 90 F.3Relativisticgeneralization.................... 91 F.4Discussion............................. 92 1 Introduction The purpose of the present work is to present an alternative metric theory of gravity. The Lagrangian of the theory −1 00 11 22 33 √ L = LGR − (8πG) (Υg − Ξ(g + g + g )) −g is very close to the GR Lagrangian, and in the limit Ξ, Υ → 0weobtain the classical Einstein equations. The key point is that this Lagrangian may be derived starting with a few assumptions about the “ether” – a classical medium in a classical Newtonian background with Euclidean space and absolute time R3 ⊗ R.We need only a few general principles: a Lagrange formalism and its relation with standard conservation laws. The gravitational field gµν is defined by the “general” steps of freedom of the ether – density ρ,velocityvi, pressure pij.1 The matter fields describe its material properties. What explains the Einstein equivalence principle is that the ether is universal: all fields describe properties of the ether, there is no external matter. Therefore, observers are also only excitations of the ether, unable to observe some of the ether properties. This explains that we are unable to observe all steps of freedom of the ether. We need no artificial conspiracy or highly sophisticated model to obtain relativistic symmetry in an ether theory. 1 As usual, we use latin indices for three-dimensional indices√ and greek indices for four- dimensional indices. We also use the notationg ˆµν = gµν −g. 5 The only difference to GR are two additional terms which depend on the preferred coordinates Xi,T. In “weak” covariant formulation (with the preferred coordinates handled as “fields” Xi(x),T(x)) we obtain: √ − −1 µν − µν i j − L = LGR (8πG) (Υg T,µT,ν Ξg δijX,µX,ν) g Instead of no equation for the preferred coordinates, we obtain a well- defined general equation for these coordinates: the classical conservation laws, which appear to be the harmonic coordinate condition. But this changes a lot. It is, essentially, a paradigm shift as described by Kuhn [44]. We revive the metaphysics of Lorentz ether theory in its full beauty. This requires the reconsideration of the whole progress made in fundamental physics in this century. Therefore, after derivation of the theory and their comparison with existing theories of gravity we reconsider different domains of science from point of view of the new paradigm. Of course, this may be only a raw overview, a program for future research instead of a summary of results. But this raw overview does not suggest serious problems for the new paradigm, while essential problems of the relativistic paradigm disappear. The preferred background leads to well-defined local energy and momen- tum conservation laws. Moreover, the additional terms seem to be useful to solve cosmological problems. The Ξ-term defines a nice homogeneous dark matter candidate. The Υ-term is even more interesting: it avoids the big bang singularity and leads instead to a bounce. Such a bounce makes the cosmological horizon much larger and therefore solves the cosmological hori- zon problem without inflation. This term stops also the gravitational collapse immediately before horizon formation. Because of the underlying Euclidean symmetry, the flat universe is the only homogeneous universe. Therefore, GET is not only in agreement with observation, but allows to solve some serious cosmological problems solved today by inflation theory. A very strong argument in favour of GET is the violation of Bell’s inequal- ity. In our opinion, it is a very simple and decisive proof of the existence of a preferred foliation – as simple and decisive as possible in fundamental physics. Only if we try to avoid this simple conclusion, the issue becomes complicate – we have to reject simple fundamental principles like the EPR criterion of reality or causality. In our opinion, there is a lot of confusion in this question. For example, it is often assumed that the EPR criterion is in contradiction 6 with quantum theory. But the existence of Bohmian mechanics proves that there is no such contradiction. In quantum field theory the reintroduction of a preferred frame does not lead to problems. Instead, it allows to generalize Bohmian mechanics into the relativistic domain and clarifies the choice of
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