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Parameterized Newtonian TheoryPowerPoint Presentation

Parameterized Newtonian Theory

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Outline

- Introduction
- Why is it useful?/How is it used?
- Theory
- General formulation of PPN formalism
- Application to GR and Brans-Dicke theory
- Experimental tests
- Time delay/Light deflection

What is PPN formalism?

- Parameterized Post-Newtonian formalism express Einstein's’ equation in terms of deviation from Newtonian theory.
- Well describes weak field. Bring us further comprehension on Solar-system.
- Theoretical foundation for experimental tests for alternative (metric) gravitational theory.

Alternative Gravitational Theories

- Metric theories
- Have symmetric metric
- Test bodies follow geodesics of the metric
- In local Lorentz frames, non-gravitational laws are those of SR.

Historical Background

- A. S. Eddington (1922) – Analysis of vacuum gravitational field outside the Sun.
- K. Nordtvedt (1968) developed the first full PPN formalism.
- C. M. Will introduced hydrodynamical description.

PPN Formalism by Will

- γ - How much space curvature gij is produced by unit rest mass ?
- β - How much nonlinearity is there in the superposition law for gravity g00 ?
- β1 - How much gravity is produced by unit kinetic energy ?
- β2 - How much gravity is produced by unit gravitational potential energy ρ0 / U ?
- β3 - How much gravity is produced by unit internal energy ρ0Π ?
- β4 - How much gravity is produced by unit pressure p ?
- ζ - Difference between radial and transverse kinetic energy on gravity
- η - Difference between radial and transverse stress on gravity
- Δ1 - How much dragging of inertial frames g0j is produced by unit momentum ρ0v ?
- Δ2 - Difference between radial and transverse momentum on dragging of inertial frames

Solution in PPN approximation

Brans-Dicke

Application of PPN formalism to GR & Brans-Dicke theoryDeflection/Time Delay of Light

- One of the PPN parameter (γ) is related to the deflection of light.
- It also describes the time delay of light.

Experimental Results

- VLBI light deflection 0.02 % from unity (1995).
- Cassini spacecraft agrees with GR to 10-3 %. γ-1 = (2.1±2.3)×10-5 (2003)

Summary

- PPN formalism, with sophistication of experimental technique, enabled to test the validity of metric theories.
- GR has survived through all the experimental testing so far, while myriads of alternative gravitational theories disappeared.

Thank you!

- Reference
- Misner, Thorne, Wheeler, (1973) Gravitation
- Nordvedt (1976) Phys. Rev. 169, 1017-1025
- Will. Living Rev. Relativity 9 (2006), 3
- Chandrasekhar, Phys. Rev. Lett. vol 14, 1965
- Nutku, Astro. Journal, vol 155, March 1969
- Blanchet, Living Rev. Relativity 9 (2006), 4

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