Astronomical Tests Possible Violations of . . . Possible Violations - PowerPoint PPT Presentation

Relativistic Celestial . . . Towards Extended . . . Possible Violations of . . . Astronomical Tests Possible Violations of . . . Possible Violations of . . . of Relativity: Possible Cosmological . . . Possible Effects of Torsion beyond Parameterized Finsler (Non- . . . Post-Newtonian Title Page Formalism (PPN), ◭◭ ◮◮ ◭ ◮ to Testing Page 1 of 12 Fundamental Principles Go Back Full Screen Vladik Kreinovich University of Texas at El Paso Close vladik@utep.edu Quit http://www.cs.utep.edu/vladik

Relativistic Celestial . . . 1. Relativistic Celestial Mechanics: Current Status Towards Extended . . . and Related Interesting Opportunity Possible Violations of . . . • Starting 1919: experimentally compare general relativ- Possible Violations of . . . ity (GRT) with Newton’s mechanics. Possible Violations of . . . Possible Cosmological . . . • 1960s: compare different relativistic gravitational the- Possible Effects of Torsion ories, e.g., the Brans-Dicke Theory. Finsler (Non- . . . • 1970s: Parameterized Post-Newtonian Formalism (PPN). Title Page • Current status: all the observations have confirmed ◭◭ ◮◮ General Relativity (GRT). ◭ ◮ • Challenges. GRT needs to be reconciled with: Page 2 of 12 – quantum physics (into quantum gravity); Go Back – numerous surprising cosmological observations. Full Screen • Idea: prepare extended PPN, to test possible quantum- Close and cosmology-related modifications of GRT. Quit

Relativistic Celestial . . . 2. Towards Extended Post-Newtonian Formalism (EPN) Towards Extended . . . • Idea: prepare extended PPN, to test possible quantum- Possible Violations of . . . and cosmology-related modifications of GRT. Possible Violations of . . . Possible Violations of . . . • Details: include the possibility of violating fundamen- Possible Cosmological . . . tal principles Possible Effects of Torsion – that underlie the PPN formalism but Finsler (Non- . . . – that may be violated in quantum physics. Title Page • These fundamental principles include: ◭◭ ◮◮ – T-invariance, ◭ ◮ – P-invariance, Page 3 of 12 – scale-invariance, Go Back – energy conservation, – spatial isotropy, etc. Full Screen • Plan: we present the first attempt to design the corre- Close sponding extended PPN formalism. Quit

Relativistic Celestial . . . 3. Possible Violations of T-Invariance Towards Extended . . . • Possible non-T-invariant terms PN terms in metric: Possible Violations of . . . � m a · ( � � m a · e a,j e a · � v a ) Possible Violations of . . . δg 00 = δ 1 · , δg 0 j = δ 2 · . r a r a Possible Violations of . . . • Fact: light is determined by c − 2 terms in g αβ . Possible Cosmological . . . Possible Effects of Torsion • Corollary: no effect on light. Finsler (Non- . . . 0 = x 0 + α · � m a · ln( r a ). • Additional coord. transf.: x ′ Title Page • Change in metric: δ ′ 1 = δ 1 + 2 α , δ ′ 2 = δ 2 + α . ◭◭ ◮◮ • Corollary: T-invariant ⇔ δ 1 = 2 δ 2 . ◭ ◮ • Lagrange function exists ⇔ T-invariant. Page 4 of 12 • Motion Lorentz-invariant ⇔ T-invariant. Go Back • Conclusion: ether-dependent. Full Screen • Perihelion shift per rotation doesn’t depend on m a , r a . Close • Restricted 3-body problem: no effects modulo m 2 . Quit

Relativistic Celestial . . . 4. T-Non-Invariance w/o Scale Invariance Towards Extended . . . a = � • General formula: � f ( m a ,� r,� r a ,� v,� v a ). Possible Violations of . . . Possible Violations of . . . • Requirements: rotation-invariant; � f = 0 when m a = 0. Possible Violations of . . . • Additional requirement: energy conservation (impossi- Possible Cosmological . . . ble to have a closed cycle and gain some work). Possible Effects of Torsion • 1st conclusion: radial motion in a central field is T- Finsler (Non- . . . invariant. Title Page • Second conclusion: under P-invariance, circular motion ◭◭ ◮◮ in a central field is T-invariant. ◭ ◮ • Fact: for planets, orbits are almost circular. Page 5 of 12 • Conclusion: P-invariance ⇒ T-invariance (mod. e ). Go Back • Additional assumption: � f analytical w.r.t. m a , � v , and Full Screen � v a , and Lorentz-covariant. Close • Conclusion: the effect of non-T-invariant terms is c − 5 , Quit negligible in post-Newton approximation.

Relativistic Celestial . . . 5. Possible Violations of P-Invariance Towards Extended . . . • Most general term: δg 0 j = ε · � m a · ( � v a × � r a ) j . Possible Violations of . . . r 2 a Possible Violations of . . . • Observation: all P-asymmetric terms are T-invariant. Possible Violations of . . . • Conclusion: PT-invariance implies P- and T-invariance. Possible Cosmological . . . Possible Effects of Torsion • Fact: no new coordinate transformations. Finsler (Non- . . . • Lagrange function exists ⇔ P-invariant. Title Page • Motion Lorentz-invariant ⇔ P-invariant. ◭◭ ◮◮ • Perihelion effects with | � w | ≈ 700 km/s lead to ◭ ◮ | δ 1 − 2 δ 2 | < 3 · 10 − 7 and | ε | ≤ 0 . 01 . Page 6 of 12 • Comment: discrete asymmetry is compatible with gen- Go Back eral covariance. Full Screen • Example: L = L 1 + L 2 , where L 1 is a scalar and L 2 is Close a pseudo-scalar. Quit

Relativistic Celestial . . . 6. Possible Violations of P-Invariance (cont-d) Towards Extended . . . • Secular effects in the 2-body problem: Possible Violations of . . . Possible Violations of . . . da dt = de dt = d M dt = 0; Possible Violations of . . . Possible Cosmological . . . di m a 2 √ dt = ε · 1 − e 2 · ( w x · cos(Ω) + w y · sin Ω); Possible Effects of Torsion Finsler (Non- . . . d Ω m a 2 √ dt = − ε · 1 − e 2 · (cot( i )( w x · sin(Ω) − w y · cos(Ω)) − w z ); Title Page ◭◭ ◮◮ dω m a 2 √ dt = ε · 1 − e 2 · (cot( i ) · cos( i ) · ( w x sin Ω − w y cos Ω) − w z · cos( i )) . ◭ ◮ • The effects are of the usual form m Page 7 of 12 a 2 . Go Back • Conclusion: ε ≤ accuracy of measuring perihelion shift, Full Screen i.e., | ε | ≤ 0 . 01 . Close Quit

Relativistic Celestial . . . 7. Possible Violations of Equivalence Principle and Towards Extended . . . Their Relation to Non-Conservation of Energy Possible Violations of . . . a 1 = − G · m P 1 · m A Possible Violations of . . . • General idea: � 2 F 1 = m I 1 · � · � r 12 . r 3 Possible Violations of . . . 12 • Question: what if energy is preserved? Possible Cosmological . . . Possible Effects of Torsion • Experiment: connect 2 bodies by a rod; the system moves with force � F = � F 1 + � Finsler (Non- . . . F 2 ∼ ( m P 1 · m A 2 − m P 2 · m A 1 ) . Title Page • If � F � = 0, we can get energy out of nothing. ◭◭ ◮◮ a 1 = − G · m A 1 · m A F = 0 ⇒ m A ∝ m P ⇒ m I • � 2 1 · � · � r 12 . r 3 ◭ ◮ 12 • Annihilation: a + � a ↔ 2 γ . Page 8 of 12 • C-symmetry: m a = m � a . Go Back • Experiments: we let a + � a move, then annihilate them, Full Screen and let photons move back. Close • Conclusion: if m I �∝ m A , energy is not preserved. Quit

Relativistic Celestial . . . 8. Possible Cosmological Effects Towards Extended . . . • Traditional PPN: flat background metric g αβ = η αβ . Possible Violations of . . . • Cosmological terms: g αβ = η αβ + h ij + a αβγ x γ + . . . Possible Violations of . . . Possible Violations of . . . • Order of magnitude: a αβγ x γ ≈ r/R , where r is Solar Possible Cosmological . . . system, R is of cosmological order. Possible Effects of Torsion • Conclusion: safely ignore quadratic terms. Finsler (Non- . . . • Combining with PPN: Title Page g αβ = g PPN + h αβ + a αβγ x γ . ◭◭ ◮◮ αβ • Effect on restricted 2-body problem: ◭ ◮ � L = ds dx α dx β Page 9 of 12 dt = g αβ dt . dt Go Back • Analysis: main term is ∆ L = 2 a 0 ij x i v j . Full Screen • Conclusion: modulo full time deriv. ∆ L ∼ � b · ( � v × � x ). Close • Resulting force: magnetic-like � F = 2 � b × � v . Quit

Relativistic Celestial . . . 9. Possible Effects of Torsion Towards Extended . . . • General idea: Possible Violations of . . . Possible Violations of . . . T αβ | γ = T αβ ; γ + T αδ S δ δβ + T δβ S α δβ = 0 . Possible Violations of . . . Possible Cosmological . . . def • Due to asymmetry: T αβ ; γ + T αδ S β = 0, where S β = S δ δβ . Possible Effects of Torsion • General PPN-type dependence: Finsler (Non- . . . � m a · ( � � m a · e ai e a · � v a ) Title Page S 0 = β T · ; S i = β T · . r 2 r 2 ◭◭ ◮◮ a a • Additional T-non-invariant and P-non-invariant terms ◭ ◮ are also possible. Page 10 of 12 • Interesting conclusion: we have a class of theories in- Go Back cluding Newton’s gravity and intermediate theories. Full Screen • Corollary: we can simplify computations, since one Close term is Netwonian. Quit