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Modelling the Pioneer Anomaly as Modified Inertia. Mike McCulloch,

Modelling the Pioneer Anomaly as Modified Inertia. Mike McCulloch, Ocean modelling, Met Office, UK. Edinburgh, 20 th April 2006. Why modify inertia? Look at a possible cause of inertia Show how this cause could fail at low accelerations Derive the implied expression for inertial mass

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Modelling the Pioneer Anomaly as Modified Inertia. Mike McCulloch,

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  1. Modelling the Pioneer Anomaly as Modified Inertia. Mike McCulloch, Ocean modelling, Met Office, UK. Edinburgh, 20th April 2006 Why modify inertia? Look at a possible cause of inertia Show how this cause could fail at low accelerations Derive the implied expression for inertial mass Show it forecasts the Pioneer anomaly when r > 15 AU Discuss problems with orbital motion

  2. Is the Pioneer Anomaly a gravity or inertia problem? 1972/3 a’ Anderson et al (1998) a’=8.7*10-10 ms-2 http://www.nineplanets.org/overview.html • If the a’ is new physics it could mean that: • G is stronger than expected at long distances or low accelerations • The inertial mass is lower at long distances or low accelerations.

  3. What should a modification of inertia look like? To fit galaxy curves Milgrom (1983) derived empirical correction for Newton’s 2nd law (MOND): when accelerations are familiar then μ=1 when accelerations ~ 1.2*10-10 ms-2 then μα a/1.2*10-10 Aim: find a theory that produces a function like μ..

  4. A possible model for inertia: Hawking & Unruh radiation Hawking (1973) Unruh (1974). Alokik Kanwal

  5. A break in the response of the vacuum. Haisch, Rueda & Puthoff (1994): Unruh radiation could cause inertial drag. Milgrom (1999): At very low accelerations, these wavelengths might be too large to fit into the Hubble distance. There should then be a break in the response of the vacuum.

  6. Can Milgrom’s break account for the Pioneer Anomaly? High acceleration Disallowed mi α the total energy in the spectrum Low acceleration Tiny acceleration λ (m) a0=1.2*10-10 m/s2 =1.4*10-10 m/s2 At this acceleration the Unruh spectrum And inertial mass might disappear. Feedback…minimum acceleration Acceleration of Pioneer is still larger than the cut-off. So Pioneer should be unaffected… H=2.3*10-18

  7. A more gradual break in the response of the vacuum (new). Only wavelengths of Unruh radiation that fit exactly into 2c/H are allowed. mi α the total energy in the spectrum High acceleration Lower acceleration Tiny acceleration λ (m) Pioneer Since E’ = E when λ > Hubble distance E’ is zero when λ approaches zero.

  8. Modelling Pioneer with & without Modified Inertia: Results Simulated Pioneer’s trajectory with & without the new term, v0=20,000 m/s. *10-10 OK Not OK Outside ~15 AU, the Pioneer Anomaly is predicted without any adjustable parameters (although depends on choice of Λ)

  9. A prediction: maximum black hole mass. Hawking (1973)’s expression for a black hole’s temperature Using Wien’s law again: As before, assume Hawking radiation above a limiting λ is not allowed: M < 1053 kg The theory predicts a maximum black hole mass of 1023 solar masses. Also implies there is a minimum allowed acceleration for all bodies.

  10. Conclusions Assuming that inertia is caused by Unruh radiation, and is quantised, it is possible to predict the Pioneer Anomaly (for radii > 15 AU) without any adjustable parameters. These ideas could provide a physical reason for MOND? Theory also predicts a maximum mass of 1023 solar masses for black holes. Theory predicts all bodies have a minimum possible acceleration. However: The anomalous acceleration close the sun, and in galaxies, is overestimated by a factor of about five. A possible reason is that Unruh’s equation is only valid for linear acceleration. An Unruh equation valid for circular motion would be very helpful.

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