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Testing for violations of Newton's 2nd law

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There've been a few threads here about a topic that I think is among the most interesting in cosmology: the missing mass problem. Often this problem is addressed by postulating that some sort of matter that doesn't interact with light is more abundant than the regular matter we see. But there is a much less popular idea that explains why galaxies move differently than we'd expect them to: maybe the equations aren't quite right. There was a hubbub over the summer when the best evidence yet for dark matter was unveiled but I wouldn't count out the alternative model just yet. If you want a little background (in a slightly different context) on these modifications to gravity (or inertia) look in this thread.

The interesting thing is that someone is now suggesting an experimental test for these alternative models.

Experiment sets the ultimate test for Newton's laws

16 March 2007

A physicist in Australia has come up with an experiment that could potentially reveal a flaw in Newton's law of gravitation. If the flaw exists, it would be the first evidence in support of theories that explain the movement of galaxies without having to introduce "dark matter" (Phys. Rev. Lett. 98 101101).

For the past 70 years or so, physicists have been bothered by a nagging question: why do the centres of galaxies rotate too fast for the amount of mass we can see through telescopes? The most popular answer is that most of the mass is hidden in large bands of "dark matter", a substance that is invisible because it doesn't interact strongly with light. If it exists, dark matter could account for 95% of the mass in galaxies, and would explain many other aspects of the universe.

However, a lack of evidence for dark matter has led a small camp of physicists to promote an alternative answer: the gravitational force that holds galaxies together decays more gently with distance than presently estimated, meaning that Newton's law of gravitation is not quite as simple as an inverse-square relationship. The theory, which is known as modified Newtonian dynamics (MOND), proposes adding extra factors to Newton's 300-year-old equations so that the gravitational behaviour only alters at very low accelerations. Unfortunately the turmoil of gravitational forces produced in the galaxy means that such accelerations are hard to come by, leaving proponents of MOND with no easy way to test their theory.

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However, Alex Ignatiev from the Theoretical Physics Research Institute in Melbourne claims to have predicted instances on the Earth where most of these forces will cancel out. Ignatiev first considered how an object at rest in the centre-of-mass of our galaxy would appear to be accelerating when viewed from a laboratory on Earth. This involved listing all the major accelerations such as the Earth's rotation around the Sun and the Sun's orbit in our galaxy. He then looked for solutions where all of the accelerations add up to zero.

The solutions indicated that, on either of the two annual equinoxes, there will be two places on the Earth's surface where the force cancellation occurs. For example, on the equinox of 22 September 2008, one will be in the far north of Greenland and the other will be on the opposite side of the world in Antarctica (see figure: "X marks the spot"). Ignatiev says that if a gravitational wave detector is set-up to monitor a static test object at one of these times and places, it might just be able to glimpse a tiny, 0.2 × 10-16 m deflection over a period of 0.5 ms – what he calls "SHLEM" (static high-latitude equinox modified inertia). If SHLEM is observed, it would be the first evidence in support of MOND.

"Even if the result were negative it would be a very significant step forward, because an interesting theory would be ruled out," Ignatiev told Physics Web. "But if the predicted SHLEM effect were observed – well, we'd have to rewrite our most basic theories."


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There's an article that I think is slightly better in the current Nature that I'll throw in:

On 21 March — the spring equinox — something very strange may have happened. In two particular places on Earth, objects might have started to move without any force acting on them.

Such motion would violate Newton’s second law, a fundamental principle of mechanics, which states that objects accelerate by an amount proportional to the force acting on them. But it needn’t involve anything paranormal. According to Alexander Ignatiev of the University of Melbourne in Australia, this weird phenomenon would be proof of a new kind of mechanics called modified newtonian dynamics (MOND).

First suggested in 1983 by Israeli physicist Moti Milgrom, MOND aims to provide an alternative to dark matter, the invisible and so far unidentified stuff invoked by physicists to explain why rotating galaxies don’t fall apart.

MOND is very speculative, but interest in it has been boosted in recent years by the observation that the Pioneer 10 and 11 spacecraft, launched in the early 1970s to study the planets, seem to be veering from their expected paths as they leave the Solar System. No one knows whether the anomaly is real or just the result of faulty observations of the spacecraft’s motion.

Finding evidence for MOND would be hugely important: “The foundations of physics would have to be revised,” says Ignatiev. But measuring the predicted deviations from Newton’s theory is extremely difficult. MOND diverges from newtonian dynamics only at very small accelerations, around a hundred trillionths of a metre per second per second. At this rate, an object that began to move when Newton published his second law in 1687 would now be travelling at one metre per second.

To check out the theory, Ignatiev says, you need a test object moving with an acceleration small enough (relative to the rest of the Galaxy) for MOND effects to be apparent. Even if an object sits motionless on a lab bench, it is generally accelerating with respect to the Galaxy because of Earth’s rotation and orbit around the Sun, and the Sun’s motion in space.

But Ignatiev’s calculations have shown that at a particular moment each year, at two points on Earth, these accelerations cancel out for about half a millisecond. This, he calculates, coincides with either the spring or autumn equinox (A. Yu. Ignatiev Phys. Rev. Lett. 98, 101101; 2007). The points of cancellation are always at latitudes 79 50ʹ above and below the Equator, whereas the longitude varies each year. This spring they will be at 178 E, high above Siberia in the Arctic Sea and on the Ross Ice Shelf of Antarctica. The autumn equinox of 2008 will be a little more amenable to experimenters, when the northern point is in Greenland.

Ignatiev cautions, however, that these are approximate locations, and ignore the subtle effects of the Moon and planets. Before you make the journey, he says, you had better do the full calculation, as the effect acts over an area just a few centimetres across.

So what might you hope to see? As external acceleration effects cancel out, says Ignatiev, the object’s acceleration would fall below the MOND threshold — and if the theory is correct, it will spontaneously jump over a small distance.

The predicted jump is tiny: about 0.2×10^–16 metres, or one fiftieth of the diameter of a proton. But Ignatiev reckons it could be measured by interferometry, which detects minute differences in the path lengths of light beams. The technique is being developed in huge instruments for detecting gravitational waves, which are predicted to alter the dimensions of space very slightly as they pass. Gravitational-wave detectors typically involve light corridors several kilometres long. But there are now other types of detector that are more portable, and which it might be possible to carry to Antarctica or Greenland. The MiniGRAIL detector being developed at Leiden University in the Netherlands, for example, is a metal ball 68 centimetres in diameter.

Others in the field are sceptical about Ignatiev’s chances. Orfeu Bertolami, a physicist at the Instituto Superior Técnico in Lisbon, says that although the proposal is “a brave attempt” to suggest how MOND could be tested, he is not convinced it would work. He points out that Ignatiev used newtonian mechanics to calculate the points of zero acceleration, and that these rules wouldn’t necessarily apply in the MOND world he wants to test.

Even if the theory works, Bertolami doubts it would be possible to observe exact cancellation of acceleration. A medium-sized iceberg passing 10 kilometres away in the Antarctic or Arctic Ocean, he says, would induce a gravitational acceleration comparable to the MOND threshold.

And the MOND hypothesis itself is looking decidedly shaky, because there is now rather good evidence that dark matter, which MOND attempts to eliminate, does exist. Last year, a galaxy cluster was found to have an asymmetrical distribution of visible matter that could only easily be explained if it was balanced by dark matter (see Nature doi:10.1038/news060821-6; 2006). After this, says Bertolami, “any attempt to force MOND on us is difficult to swallow”.

But Ignatiev argues that the debate is far from settled. “Experimental searches for dark matter are conducted in many laboratories across the world,” he says. “MOND should be given thesame chance.” ■

Philip Ball

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Well, it seems someone else did a different test of Newton's second law. Looks like we might be able to rule out modified inertia versions of MOND:

New lower limit set for Newton’s law

25 April 2007

Everyday experience tells us that force equals mass times acceleration, but does Newton's second law still hold for very small accelerations? By observing a torsion pendulum oscillating with a very long period, physicists in the US have now found that the law is valid down to accelerations of about 5 x 10-14 m/s2 -- a thousand times smaller than the previous lower limit. The researchers say that the results could give further credence to the existence of dark matter (Phys. Rev. Lett. 98 150801).

While Newton’s second law has been proven over and over again here on Earth, astronomical evidence has led some physicists to suggest that it may not hold for all values of acceleration. Stars at the outer edges of galaxies, for example, rotate faster than predicted by the second law. This rotation can be explained by either accepting that Newton’s law breaks down at very small accelerations or by the introduction of dark matter, which has yet to be observed directly. In our own solar system, the Pioneer 10 and 11 spacecraft appear to be affected by an acceleration as yet unexplained by Newton’s law as they travel away from the sun.

It turns out that both of these gravitational anomalies could be explained by introducing a characteristic acceleration below which Newton’s law breaks down. For rotating galaxies this acceleration is about 1 x 10-10 m/s2 and for Pioneer 10 and 11 it is about 9 x 10-10 m/s2.

In 1986, physicists verified the second law to about 10-11 m/s2, which suggested that researchers should look elsewhere for explanations. Now, Jens Gundlach and colleagues at the University of Washington along with co-workers in Indiana have used a torsion pendulum to confirm Newton’s law for accelerations down to 5 x 10-14 m/s2 -- providing even stronger evidence that a breakdown of Newton’s law is not responsible for these anomalies.

The pendulum weighed 70 g and was suspended from a metre-long tungsten wire that was 20 µm in diameter. When twisted, the wire exerted a restorative force on the weight, causing it to oscillate with a period of about 13 minutes. The weight was made to oscillate over a range of extremely small amplitudes (13 nrad to 19 µrad), which meant that weight experienced extremely small accelerations for relatively long periods of time. Any breakdown in Newton’s law during these periods of small acceleration should have caused the oscillation frequency of the pendulum to deviate from that predicted by Newton’s law.

The researchers measured pairs of amplitudes and frequencies over a wide range of amplitudes. The amplitude was then used to calculate the maximum force on the weight and the oscillation and amplitude were used to calculate the maximum acceleration. The physicists found that force did indeed equal mass times acceleration down to an acceleration of 5 x 10 -14 m/s2.

While this shows that Newton’s law holds at very low accelerations, the measurements were made using a mechanical restoring force and not gravity. Gundlach and colleagues are now devising an experiment that will test Newton’s law at very small accelerations in which the force is gravitational.


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