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Laboratory Test of Newton ’ s Second Law for Small Accelerations

Laboratory Test of Newton ’ s Second Law for Small Accelerations. Ki-Young Choi Sogang University Stephan Schlamminger, Chris Spitzer, Jens Gundlach, University of Washington, Seattle Brian Woodahl, Jennifer Coy, Ephraim Fischbach Purdue University. PRINCIPIA: Law II.

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Laboratory Test of Newton ’ s Second Law for Small Accelerations

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  1. Laboratory Test of Newton’s Second Law for Small Accelerations Ki-Young Choi Sogang University Stephan Schlamminger, Chris Spitzer, Jens Gundlach, University of Washington, Seattle Brian Woodahl, Jennifer Coy, Ephraim Fischbach Purdue University

  2. PRINCIPIA: Law II The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

  3. PRINCIPIA: Law II The change of motion is proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

  4. Reasons to Doubt Flatness of the galactic rotation curves imply more acceleration for very small forces, than Newton’s 2nd law (NSL). Rotation velocity (km/s) Distance from center (kpc)

  5. Reasons to Doubt Flatness of the galactic rotation curves imply more acceleration for very small forces, than Newton’s 2nd law (NSL). Rotation velocity (km/s) Milgrom in 1983 suggested this modification of NSL: Astrophys. J. 270, 371 (1987) Distance from center (kpc) For a>>a0μ=1 => recover NSL For a<<a0μ=a/a0 Slope=1 Slope=2 a0=1.2 x 10-10 m/s2 a0 MOdified Newtonian Dynamics

  6. Reasons to Doubt Flatness of the galactic rotation curves imply more acceleration for very small forces, than Newton’s 2nd law (NSL). Rotation velocity (km/s) Milgrom in 1983 suggested this modification of NSL: Astrophys. J. 270, 371 (1987) Distance from center (kpc) For a>>a0μ=1 => recover NSL For a<<a0μ=a/a0 Slope=1 Slope=2 a0=1.2 x 10-10 m/s2 a0 MOdified Newtonian Dynamics

  7. A Torsion Balance to Measure F=ma Simulated trace for a0=10-11 m/s2 Assume: Hooke’s law is valid Measured trace

  8. The Experimental Setup Allows to damp the pendulum to without storing energy in the fiber. Measures the excursion of the pendulum. Dynamic range: ±1.3 mrad Noise: 10-8 rad/√Hz

  9. The Torsion Pendulum 20 m diameter tungsten fiber (length: 108 cm) =2.39 nNm 8test masses (4 Be & 4 Ti ) 4.84 g each (within 0.1 mg) (can be removed) 4 mirrors tuning screws for adjusting tiny asymmetries torsional frequency: 1.266 mHz quality factor: ~ 4000 decay time: ~ 12 days machining tolerance: 5 m total mass : 70 g 5 cm

  10. Power Spectral Amplitude Thermal Noise Data

  11. Amplitude Gain Probability, that the measured amplitude < x after 1600 s (2 torsional periods) In order to measure low amplitudes we have to repeatedly damp the pendulum and measure. 326 traces

  12. Data Analysis

  13. Data Analysis

  14. Data Analysis

  15. Data Analysis

  16. Results PRL 98, 150801 (2007)

  17. Conclusion & Outlook • Good agreement with Newton’s 2nd law at accelerations as small as 5x10-14 m/s2. • Our result does not constrain MOND, since for MOND |a|=0. • In the future we want to test Fg=ma, where Fg is a gravitational force.

  18. THE END

  19. More Simulations

  20. More reasons to be doubtful a0=(8.7 ± 1.3) x 10-10 m/s2

  21. More reasons to be doubtful a0=(8.7 ± 1.3) x 10-10 m/s2 Coincidentally: c H0=3 x 108 m/s x 71 km/s /Mpc =7 x 10-10 m/s2

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