Outline: Reasons, and a method, for modifying inertia (MiHsC)

1. From the Pioneer-flyby anomalies to an alternative cosmology. Mike McCulloch. (Honorary Fellow, University of Exeter, UK. M.E.McCulloch@exeter.ac.uk) . Talk for Cosmo-08, 26th August 2008 Outline: Reasons, and a method, for modifying inertia (MiHsC) MiHsC predicts a minimum acceleration: c2/R (dark energy?) MiHsC predicts the Pioneer anomaly (when unbound)… and the flyby anomalies (using mutual accelerations) First attempts at a cosmology. Conclusions

2. The Pioneer anomaly: most easily explained using modified inertia Pioneer 10 & 11 after gravity-assist flybys show an unexplained extra acceleration of 8.7x10-10 m/s2 towards the Sun (Anderson et al., 1998) No mundane explanation so far (Anderson et al., 2002) Earth, 1973 Jupiter Pioneer Saturn The Pioneer have anomalous accelerations, but not the planets. This is easier to explain with a modification of inertia.

3. How to reduce inertia for very small accelerations: Milgrom’s break Accelerations (a) too, cause event horizons that radiate at temperature T (Unruh, 1976) Hawking (1974) showed black hole event horizons radiate at a temperature T Acc Milgrom (1999): for low acc Unruh waves are longer than the Hubble- scale so inertia collapses (MOND). Haisch et al. (1994) derived inertia from part of the Unruh radiation. Magnetic Lorentz force: looks like inertia. Universe’s edge Milgrom (1999) can’t explain the Pioneer anomaly: the accelrtn’ is too high.

4. A Hubble-scale Casimir effect (McCulloch, 2007) The wavelength λof the Unruh radiation varies as A rocket accelerates within the observable universe It sees Unruh waves (red lines) At low accelerat’ns the Unruh waves are longer, and fewer fit into the Hubble-scale. (see the dashed red line) This can be modelled as a Hubble-scale Casimir effect. The inertial mass varies as: Modified inertia by a Hubble- scale Casimir effect (MiHsC). Observable Universe Doesn’t fit Fits

5. Consequences of MiHsC Eq. Prin F=ma MOND Has MOND-ish behaviour: 1 MiHsC Mi / mg Putting this into Newton’s laws we get an equation of motion: Acceleration a0 g Even when M=0, acceleratn ~ cH ~ c2/Θ (cosmic acceleration, dark energy?)

6. MIHSC agrees with the Pioneer anomaly Observed values are shown as error bars. Average a=8.7x10-10 ms-2. Predicted: Outside 12 AU, the Pioneer Anomaly is predicted without adjustable parameters (some dependence on choice of Θ) Inside 10 AU it doesn’t agree. Here the Pioneer were bound? Published in: McCulloch, 2007. MNRAS, 376, 338-342 (arXiv:astro-ph/0612599)

7. The flyby anomalies, Anderson et al. (2008) Unexpected speed-up of Earth flyby craft by a few mm/s (dv) seen by: Antreasian & Guinn (1998) Anderson et al. (2008). Not: relativistic frame dragging computer error, engine firing, tides, Solar wind, geoid error. Lammerzahl et al. (2006).. dv dv Anderson et al. (2008) found the following empirical formula: And said the cause may be ‘something to do with rotation’…

8. What if we consider rotational accelerations in MiHsC? A spacecraft on an equatorial approach has slightly larger mutual accelerations. So its inertial mass is slightly larger Acceleration of a point mass Earth’s rotation On a polar exit trajectory We have smaller mutual accelerations So inertia reduces By cons of mtum, speed increases Reminiscent of Mach? Does it work?..

9. MiHsC (using mutual accelerations) gives the right answer. Conservation of momentum for craft & Earth before (1) and after (2) flyby Assumed infinite x Derived Observed

10. The Observed and predicted (MiHsC) flyby anomalies (mm/s) The MiHsC theory agrees in 3 out of 6 cases. Not as accurate as the empirical formula of Anderson et al. (2008), but MiHsC has no adjustable parameters. A good test: flybys of different planets because their Rs and ves are different. Published in: McCulloch (2008) MNRAS-letters, 389 (1), L57-60(arXiv/0806.4159)

11. The maximum mass for a black hole in MiHsC (McCulloch, 2007) A black hole’s Hawking temperature is: T Using Wien’s law λ=βhc/kT gives M Assume Hawking waves larger than the observable universe can’t exist (λ=Θ): The mass of the observable universe is observed to be. So can we model the observable universe as a black hole?

12. Assuming M is the universe’s mass => steady state theory + CMB Is similar to Hoyle’s (1948) steady state formula The universe’s mass derived from MiHsC: Steady state theory was rejected because it didn’t predict a hot early universe (& the CMB), but MiHsC does predict a hot early universe: An example: when T=3000K, Hubble-diameter Θ=2mm. The acceleration Attributed to dark energy can also be derived from the above.. McCulloch 2009?, submitted to MNRAS-Letters…

13. Conclusions • The model: MiHsC, without adjustable parameters, agrees with the following: • Cosmic acceleration: c2/R • The Pioneer anomaly (when unbound) arXiv: astro-ph/0612599 • The flyby anomalies (using mutual accelerations) arXiv:0806.4159 • The mass of the observable universe • A Steady State theory, with a hot early universe. • MiHsC does not agree with: • Planetary orbits, Earth-bound equivalence principle tests (boundedness?) • To do: • Why does boundedness matter? Or does it? • Model galaxies/clusters with MiHsC and mutual accelerations • Set up a more direct test in the lab! (eg, see: arXiv:0712.3022) • Many thanks to the Royal Astronomical Society • & the Institute of Physics’s C.R.Barber trust fund for travel grants.