Where will Einstein fail?
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The document discusses where and why Einstein's theory of general relativity may fail. It notes that while relativity has been extremely precise in experiments and observations to date, there are still major unresolved problems like the cosmological constant problem that suggest modifications to gravity may be needed. The author discusses several proposals for modifying gravity, such as introducing screening mechanisms or violating Lorentz symmetry, in ways that could address problems like dark energy. Throughout, the author emphasizes the importance of empirical tests in physics and proposes several observational tests like using neutron stars or black hole mergers that could reveal deviations from general relativity.
![AETHER AND BLACK HOLES
We can solve for the black hole spacetime in this theory
p0 is the aether pressure at infinity
f(r) is an analytic function of r that diverges at r≈2m & r→∞
➥UV-IR coupling thru aether pressure, p0
➥Finite redshi% at r=2m
➥ No Horizon(similar to Fuzzba( models)
ds2
= 1
2m
r
[1 + 4 p0f(r)]
2
dt2
1
2m
r
1
dr2
r2
d 2
28
28Thursday, 4 July, 13](https://image.slidesharecdn.com/eisnteinfailsuperjedijuly2013-130801073634-phpapp01/85/Where-will-Einstein-fail-41-320.jpg)
Where will Einstein fail?
- 1. WHERE WILL EINSTEIN FAIL? AND WHY ASTRONOMERS SHOULD CARE Niayesh Afshordi Super Jedi 2013, Mauritius 4 July 2013 1 1Thursday, 4 July, 13
- 2. Super Jedi 2013, Mauritius, 4 July, 2013 OUTLINE Why will Einstein fail? Solving the Cosmological Constant Problem Astrophysical Tests Where will Einstein Fail? 2Thursday, 4 July, 13
- 3. Super Jedi 2013, Mauritius, 4 July, 2013 EINSTEIN’S LEGACY Lorentz symmetry: geometry of flat spacetime Equivalence Principle: gravity is spacetime geometry special and general relativity Most precise theories, period! 3Thursday, 4 July, 13
- 4. Super Jedi 2013, Mauritius, 4 July, 2013 LORENTZ WAS RIGHT! Liberati 2012 4Thursday, 4 July, 13
- 5. Super Jedi 2013, Mauritius, 4 July, 2013 SO WAS EINSTEIN! Tests of equivalence principle Tests of strong gravity (Parametrized Post Newtonian) 5Thursday, 4 July, 13
- 6. Super Jedi 2013, Mauritius, 4 July, 2013 SO WAS EINSTEIN! Tests of equivalence principle Tests of strong gravity (Parametrized Post Newtonian) 5Thursday, 4 July, 13
- 7. Super Jedi 2013, Mauritius, 4 July, 2013 SO WAS EINSTEIN! Tests of equivalence principle Tests of strong gravity (Parametrized Post Newtonian) 5Thursday, 4 July, 13
- 8. Super Jedi 2013, Mauritius, 4 July, 2013 Well, for the most part! 6Thursday, 4 July, 13
- 9. IUCAA, Oct. 15, 2011 (ASTROPHYSICIST’S) QUANTUM GRAVITY PROBLEMS Finiteness/Renormalizability Big Bang Singularity/Initial Conditions Old Cosmological Constant Problem (Pauli 1920’s) |ρvac| ≳ 1033 kg/m3 (Standard Model of Particle Physics) New Cosmological Constant Problem: Dark Energy ρvac = (7.1 ± 0.9) ⨉ 10-27 kg/m3 Coincidence Problem ρvac ≈ 2.7 ρm,0 7 7Thursday, 4 July, 13
- 10. Super Jedi 2013, Mauritius, 4 July, 2013 COSMOLOGICAL CONSTANT PROBLEM Einstein Equation: (Planck Mass)2 × Einstein Curvature = Energy-Momentum spacetime curvature (10 3 eV)4 standard model (100 GeV)4 + excitations Anthropic Solution: We live in a rare but habitable part of Cosmos* 8 8Thursday, 4 July, 13
- 11. Super Jedi 2013, Mauritius, 4 July, 2013 9Thursday, 4 July, 13
- 12. Super Jedi 2013, Mauritius, 4 July, 2013 Astronomer: But what’s wrong with a small constant? 9Thursday, 4 July, 13
- 13. Super Jedi 2013, Mauritius, 4 July, 2013 Astronomer: But what’s wrong with a small constant? Particle Physicist: No symmetry protects its smallness; would be the first time in the history of Physics! 9Thursday, 4 July, 13
- 14. Super Jedi 2013, Mauritius, 4 July, 2013 Astronomer: But what’s wrong with a small constant? Particle Physicist: No symmetry protects its smallness; would be the first time in the history of Physics! 9Thursday, 4 July, 13
- 15. Super Jedi 2013, Mauritius, 4 July, 2013 Astronomer: But what’s wrong with a small constant? Particle Physicist: No symmetry protects its smallness; would be the first time in the history of Physics! Alternative: Landscape/Multiverse Conundrum 9Thursday, 4 July, 13
- 16. Super Jedi 2013, Mauritius, 4 July, 2013 WHICH PRINCIPLES TO KEEP? • Lorentz symmetry • Locality • Action principle • Unitarity • Falsifiability • Predictivity 710 10Thursday, 4 July, 13
- 17. Super Jedi 2013, Mauritius, 4 July, 2013 “A GLORIOUS HISTORICAL ACCIDENT!” Barbour: Mach suggested that Physics only depends on the change in observables. Relativity (and Lorentz Invariance) emerges as a consistency condition Horava: A transition to Lifshitz symmetry: E ∝p3, makes gravity power- counting renormalizable 11Thursday, 4 July, 13
- 18. A LESSON FROM PERIHELION PRECESSION OF MERCURY 12 12Thursday, 4 July, 13
- 19. A LESSON FROM PERIHELION PRECESSION OF MERCURY Newtonian Gravity has a symmetry between angular and radial coord’s: r ↔ θ, Ωr = Ωθ 12 12Thursday, 4 July, 13
- 20. A LESSON FROM PERIHELION PRECESSION OF MERCURY Newtonian Gravity has a symmetry between angular and radial coord’s: r ↔ θ, Ωr = Ωθ Is this fundamental? 12 12Thursday, 4 July, 13
- 21. A LESSON FROM PERIHELION PRECESSION OF MERCURY Newtonian Gravity has a symmetry between angular and radial coord’s: r ↔ θ, Ωr = Ωθ Is this fundamental? No. It only emerges at low energies, but is broken at high energies → perihelion precession of Mercury 12 12Thursday, 4 July, 13
- 22. A LESSON FROM PERIHELION PRECESSION OF MERCURY Newtonian Gravity has a symmetry between angular and radial coord’s: r ↔ θ, Ωr = Ωθ Is this fundamental? No. It only emerges at low energies, but is broken at high energies → perihelion precession of Mercury Same could happen to Lorentz symmetry 12 12Thursday, 4 July, 13
- 23. A LESSON FROM PERIHELION PRECESSION OF MERCURY Newtonian Gravity has a symmetry between angular and radial coord’s: r ↔ θ, Ωr = Ωθ Is this fundamental? No. It only emerges at low energies, but is broken at high energies → perihelion precession of Mercury Same could happen to Lorentz symmetry Cosmologist:Universe has already done this! 12 12Thursday, 4 July, 13
- 24. Super Jedi 2013, Mauritius, 4 July, 2013 COSMOLOGICAL CONSTANT PROBLEM Einstein Equation: (Planck Mass)2 × Einstein Curvature = Energy-Momentum spacetime curvature (10 3 eV)4 standard model (100 GeV)4 + excitations MODIFY GRAVITY!! 13 13Thursday, 4 July, 13
- 25. MODIFIED GRAVITY: PHENOMENOLOGICAL APPROACH Idea: We didn’t see Dark Energy coming. Maybe gravity is also different. Why we don’t see it in the solar system? Screening Mechanisms: Chameleon (Khoury & Weltman), Symmetron (Khoury & Hinterbichler), Vainshtein Let’s parametrize it in cosmology: Hu & Sawicki; Pogosian,Hojjati & Zhao; Narimani & Scott ... Equivalence principle violation for stars, dwarf galaxies: Hui, Jain, Sakstein, Nicolis ... 14 14Thursday, 4 July, 13
- 26. DANGER! Searches for modified gravity are bound to find them! It’s important to know what you’re looking for! 15 JCAP 0908:030,2009 15Thursday, 4 July, 13
- 27. DE-GRAVITATION Idea: Modifications of gravity should address the cosmological constant problem, i.e. de-gravitate the Quantum Vacuum Cascading gravity (Khoury, Dvali, Tolley, de Rham, Pujolas, ...) (Partially) Massive Gravity (Hoffman, Hinterbichler, Tolley, de Rham, Rosen, ...) Supersymmetric Large Extra dimensions (C.P. Burgess, ...) Problem: Why radiation era happened? 16 16Thursday, 4 July, 13
- 28. Super Jedi 2013, Mauritius, 4 July, 2013 WHAT IF NEWTON KNEW QUANTUM FIELD THEORY (AND SPECIAL RELATIVITY)?! 2 = 4 G( + p/c2 )) 17 17Thursday, 4 July, 13
- 29. Super Jedi 2013, Mauritius, 4 July, 2013 WHAT IF NEWTON KNEW QUANTUM FIELD THEORY (AND SPECIAL RELATIVITY)?! 2 = 4 G( + p/c2 ) 18 18Thursday, 4 July, 13
- 30. Super Jedi 2013, Mauritius, 4 July, 2013 WHAT IF NEWTON KNEW QUANTUM FIELD THEORY (AND SPECIAL RELATIVITY)?! 2 = 4 G( + p/c2 ) 18 •Quantum vacuum degravitates 18Thursday, 4 July, 13
- 31. Super Jedi 2013, Mauritius, 4 July, 2013 WHAT IF NEWTON KNEW QUANTUM FIELD THEORY (AND SPECIAL RELATIVITY)?! 2 = 4 G( + p/c2 ) 18 •Quantum vacuum degravitates •This can be made covariant (NA 2008), a.k.a GravitationalAether 18Thursday, 4 July, 13
- 32. Super Jedi 2013, Mauritius, 4 July, 2013 Deviations from GR sourced by Pressure or Vorticity Neutron Star Structure Cosmology Intrinsic Gravitomagnetic Effect (LAGEOS, GPB) (Kamiab & NA, 2011) (Aslanbeigi, Robbers, Foster, Kohri, NA, 2011) 19 19Thursday, 4 July, 13
- 33. Super Jedi 2013, Mauritius, 4 July, 2013 COINCIDENCE PROBLEM: WHAT SETS THE OBSERVED SCALE OF DARK ENERGY? Neutrino mass ∼ meV? (see Valeria) Large extra dimensions ∼ 0.1 mm Stellar Black Hole scale ∼ 10 M☉ Radiation-Matter Transition (k-essence) 20Thursday, 4 July, 13
- 34. Super Jedi 2013, Mauritius, 4 July, 2013 WHERE WILL EINSTEIN FAIL? Usual Suspects: Early Universe, Inside Black Holes Unusual Suspects: Cosmological Constant Problem → Cosmic Microwave Background, Matter-Radiation transition Neutron star structure, Mergers: Gravitational Wave astronomy Gravitomagnetic effect; Tests of Equivalence Principle Black Holes⇔Dark Energy: cosmic evolution and structure formation, astronomical probes of BH horizon Neutrino Physics 21 21Thursday, 4 July, 13
- 35. ON SCIENTIFIC METHOD In spite of all our prejudices, Physics is an Empirical Science Credibility of a theory is only judged by its concrete predictions against Nature, NOT its popularity, elegance, parsimony, etc. Do you hold your favourite theories to this standard?! 22 22Thursday, 4 July, 13
- 36. POSSIBLE PROJECTS: Aether v.s. Planck Inflation with Gravitational Aether Stable Dark Energy/Neutrino Coupling Phenomenology of Black Holes/ Dark Energy Coupling 23 23Thursday, 4 July, 13
- 37. Super Jedi 2013, Mauritius, 4 July, 2013 BLACK HOLES: ENTROPY AND DARK ENERGY 2012: Unitary evolution leads to firewalls @ BH horizons: Almheiri, Marolf, Polchinski & Sully Empty Black Holes, Firewalls, Fuzzballs: Israel Junction condition ⇒An incompressible fluid sits at the horizon ➨ Thermal entropy per unit area = 1/4 (Saravani, NA, Mann 2012) Resolving the singularity at horizon ties Dark Energy scale to Black Hole mass ➨ Dark Energy as a Quantum hair of astrophysical Black Holes (Prescod-Weinstein, NA, Balogh 2009) 24Thursday, 4 July, 13
- 38. Super Jedi 2013, Mauritius, 4 July, 2013 NEUTRON STARS AND AETHER Deviations from Einstein gravity are sourced by relativistic pressure or vorticity Neutron Stars are perfect laboratories to test Aether! Aether decreases the maximum mass (effectively so%ens EOS), so discovery of very massive Neutron Stars can rule it out Uncertainty in nuclear equation of states ! Can test with Gravitational Wave detection from NS-NS mergers ☺ Aether General Relativity Kamiab & NA 2011 25 25Thursday, 4 July, 13
- 39. Super Jedi 2013, Mauritius, 4 July, 2013 COSMOLOGY (GN/GR = 0.75 OR 1?) 0.0210 0.0215 0.0220 0.0225 0.0230 0.0235 0.0240 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 b h2 GN /GR General Relativity Gravitational Aether X X Big Bang Nucleosynthesis (Aslanbeigi, Robbers, Foster, Kohri, NA, 2011) 26 Cosmic Microwave Background 26Thursday, 4 July, 13
- 40. Super Jedi 2013, Mauritius, 4 July, 2013 COSMOLOGY (GN/GR = 0.75 OR 1?) 27 27Thursday, 4 July, 13
- 41. AETHER AND BLACK HOLES We can solve for the black hole spacetime in this theory p0 is the aether pressure at infinity f(r) is an analytic function of r that diverges at r≈2m & r→∞ ➥UV-IR coupling thru aether pressure, p0 ➥Finite redshi% at r=2m ➥ No Horizon(similar to Fuzzba( models) ds2 = 1 2m r [1 + 4 p0f(r)] 2 dt2 1 2m r 1 dr2 r2 d 2 28 28Thursday, 4 July, 13
- 42. ... AND DARK ENERGY! Let us propose that maximum redshift at “horizon” is set to Planck Temperature/ Hawking Temperature by quantum gravity effects: Aether pressure has the same sign and magnitude as Dark Energy for stellar mass black holes! ➥Conjecture: Formation of stellar black holes causes cosmic acceleration ➥Conjecture: Evolution of Astrophysical black holes leads to dynamical Dark Energy p0 = 1 256 2m3 m 74 M 3 pDE,obs!! 29 29Thursday, 4 July, 13
- 43. ... AND DARK ENERGY! Let us propose that maximum redshift at “horizon” is set to Planck Temperature/ Hawking Temperature by quantum gravity effects: Aether pressure has the same sign and magnitude as Dark Energy for stellar mass black holes! ➥Conjecture: Formation of stellar black holes causes cosmic acceleration ➥Conjecture: Evolution of Astrophysical black holes leads to dynamical Dark Energy p0 = 1 256 2m3 m 74 M 3 pDE,obs!! Prescod-Weinstein, NA, Balogh 2009 DarkEnergyequationofstate MeanBlackHoleMass(M⨀) 29 29Thursday, 4 July, 13
- 44. JOINT DARK ENERGY MISSIONS: (WFIRST, LSST, EUCLID) Probe Dark Energy history with incredible precision over the next decade →confirm/rule out aether predictions 30 30Thursday, 4 July, 13
- 45. THERMODYNAMIC ARGUMENT NA 2010 31 31Thursday, 4 July, 13
- 46. What if gravitational aether has a thermal pressure? Let’s consider QG corrections to BH thermal properties: Entropy: Energy/Mass: Volume: Pressure becomes: THERMODYNAMIC ARGUMENT ! NA 2010 31 31Thursday, 4 July, 13
- 47. What if gravitational aether has a thermal pressure? Let’s consider QG corrections to BH thermal properties: Entropy: Energy/Mass: Volume: Pressure becomes: THERMODYNAMIC ARGUMENT ! NA 2010 31 31Thursday, 4 July, 13
- 48. INCOMPRESSIBLE AETHER IN HISTORY! “Similar to Newton, but mathematically in greater detail, Bernhard Riemann assumed in 1853 that the gravitational aether is an incompressible fluid and normal matter represents sinks in this aether ...” http://en.wikipedia.org/wiki/Mechanical_explanations_of_gravitation Riemann, B. (1876), "Neue mathematische Prinzipien der Naturphilosophie", Bernhard Riemanns Werke und gesammelter Nachlass (Leipzig): 528–538 32 32Thursday, 4 July, 13
- 49. Super Jedi 2013, Mauritius, 4 July, 2013 AETHER & MISSING BARYONS! NA, Lin, Nagai & Sanderson 2007 WMAP WMAP+ACT+SPT WMAP+ACT+SPT+SNe+BAO+H0 33 33Thursday, 4 July, 13
- 50. Super Jedi 2013, Mauritius, 4 July, 2013 A SIDE ON LITHIUM! Observations of Lithium in old stars is 3-5 times lower than predictions of standard Big Bang Nucleosynthesis Aether diminishes the discrepancy, but doesn’t remove it Lithium remains ionized throughout the cosmic history, and so diffuses out of first dark matter haloes (Pospelov & NA 2012) redshift =20 Monaco, et al. 2010 34Thursday, 4 July, 13
- 51. Super Jedi 2013, Mauritius, 4 July, 2013 MEET PROF. LORENTZ! Hendrik Antoon Lorentz (1853-1928) Nobel prize (w/ Zeeman) in 1902, for explaining Zeeman effect In 1892 and 1895, he discovered a group of transformations of space and “local time” that left Maxwell equations of electromagnetism unchanged. 35Thursday, 4 July, 13
- 52. Super Jedi 2013, Mauritius, 4 July, 2013 Let us propose (NA 2008): The metric is now blind to vacuum energy In order to satisfy Bianchi identity: Further assume an incompressible fluid (or gravitational aether) **Disclaimer: The field equations do not follow from an Action principle HOW TO DO IT COVARIANTLY? Tµ = vacgµ + excitations (8 G ) 1 Gµ⇥ = Tµ⇥ 1 4 T gµ⇥ + ... (8 G ) 1 Gµ⇥ = Tµ⇥ 1 4 T gµ⇥ + Tµ⇥, T µ ⇥;µ = 1 4 T ,⇥ Tµ = p (uµu gµ ) 36 36Thursday, 4 July, 13