Laboratory test of newton s second law for small accelerations
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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

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
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.


Principia law ii1
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.


Laboratory test of newton s second law for small accelerations

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)


Laboratory test of newton s second law for small accelerations

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


Reasons to doubt
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


A torsion balance to measure f ma
A Torsion Balance to Measure F=ma

Simulated trace for a0=10-11 m/s2

Assume:

Hooke’s law is valid

Measured trace


Laboratory test of newton s second law for small accelerations

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


Laboratory test of newton s second law for small accelerations

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


Power spectral amplitude
Power Spectral Amplitude

Thermal Noise

Data


Amplitude gain
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






Results
Results

PRL 98, 150801 (2007)


Conclusion outlook
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.




More reasons to be doubtful
More reasons to be doubtful

a0=(8.7 ± 1.3) x 10-10 m/s2


More reasons to be doubtful1
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