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					Testing Galileo and Einstein
Chapters 1, 2, 8, 9, 12 Posted on Capt: 7 May 2004 Four hundred years ago Galileo Galilei realised that (in the absence of air drag) if you dropped things off the Leaning Tower of Pisa like canon balls, musket balls, gold, silver and wood, they would all hit the ground at the same time. Gravity accelerates all objects at the same rate, regardless of their mass or composition. This is now known as the "Equivalence Principle". Einstein devised his theory of gravity, i.e., the general theory of relativity, assuming the Equivalence Principle is true. Some modern theories suggest that the acceleration of gravity does depend on the material composition of the object in a very subtle way. If so, the theory of relativity would need re-writing and there would be a revolution in physics. A group of NASA-supported researchers are going to test the Equivalence Principle by shooting laser beams at the Moon. Their experiment is possible because, more than 30 years ago, Apollo astronauts put mirrors on the Moon -- small arrays of retroreflectors that can intercept laser beams from Earth and bounce them straight back. Using lasers and mirrors, researchers can "ping" the Moon and precisely monitor its motion around Earth. In effect it is a modern version of the Leaning Tower of Pisa thought experiment. Instead of balls dropping to the ground, the experiment will monitor the Earth and Moon dropping towards the Sun. Like musket balls and cannon balls, the Earth and Moon are made of a different mix of elements, and they have different masses. Are they accelerated toward the Sun at the same rate? If yes, the Equivalence Principle holds. If not, a violation of the Equivalence Principle would reveal itself as a skewing of the Moon's orbit, either toward or away from the Sun. Using masses as large as the Earth and Moon, may be able to show this subtle effect, if it exists. Scientists have in fact been pinging the Moon since the Apollo days. So far, Einstein's theory of gravity -- and the Equivalence Principle -- has held up to a precision of a few parts in 1013. But that's not good enough to test all the theories vying to overthrow Einstein. Current lunar laser ranging can measure the distance to the Moon – roughly 385,000 km -- with an error of about 1.7 cm. The new facility will boost this accuracy 10-fold to better than 2 mm. This improvement in accuracy will mean that scientists can detect deviations from Einstein's theory 10 times smaller than currently possible. This may be sensitive enough to find the first evidence of flaws. To achieve that accuracy the "Apache Point Observatory Lunar Laser-ranging Operation" (APOLLO), must time the laser pulses' roundtrip flight to the Moon within a few picoseconds (10-12 secs). The speed of light is known, so the time of flight for the laser pulse is directly proportional to the distance between the APOLLO telescope and the mirror sitting on the surface of the Moon. This overall 10-fold improvement is achieved in several ways. Using a larger telescope 3.5 meters vs. 0.72 meters catches more of the photons of light returning from the Moon. The existing smaller telescope only catches, on average, one returning photon for every 100 out-going laser pulses (each pulse contains more than 1017 photons); the APOLLO telescope will catch about 5 photons from each pulse, which greatly improves the statistical strength of the results. Several potential disturbances have to be reckoned with. (i) The Earth's atmosphere can distort the path of the pulse of laser light due to changes in its refractive index (this is also the reason why starlight twinkles). (ii) Tiny tectonic motions of the ground beneath the APOLLO observatory, typically a few centimeters per year, could affect the long-term results. So the telescope is

situated on a mountaintop in New Mexico that has a particularly calm overhead atmosphere and ground that is relatively stable. A superconducting gravimeter and precision GPS sensor alongside the observatory will detect the slow ground movements, and an array of precision barometers will map the state of the atmosphere. ref:

Running up vertical surfaces
Chapter 8 (vector diagrams?) Posted on Capt: 23 April 2004 Some partridges have been observed to run up vertical walls flapping their wings to achieve a similar effect as a 'spoiler' on a formula one racing car. The increased load on their legs provides enough traction to climb. In fact, so called "wing-assisted incline running" (WAIR) works beyond the vertical (90 degrees) to overhanging slopes of 105 degrees. No wing assist was needed until the slope exceeded 60 degrees. For steeper slopes both the wings and legs share the propulsion, while the wings also provide the thrust towards the wall so that the legs can grip. For slopes > 60 degrees the legs provide about 65% of the vertical work, the wings the remaining 35%. For vertical slopes the percentages are reversed. But even then the legs are pushing against the wall with a force of more than 2.5 times the body weight. It is the vertical component of the reaction to this thrust that raises the bird. Ref: Nature 18/25 December 2003 pp777-778 Humans (film stars anyway) can do something similar. In the film "Singing in the Rain", Donald O'Connor runs at, then part way up, a wall, does a back flip to land back on his feet again. Harold Lloyd in an earlier film, does something similar in which he runs up and over an arched entrance. More recently Jackie Chan's trademark move in many of his films is to run at a corner or two opposing walls and bounces 2-3 times up and off them to reach the top of an otherwise impossibly high jump. (Thanks to film buff Ken Zetie for the information in the last paragraph).

What time is it?
Chapters 3, 8, 11 Posted on Capt: 19 June 2003 The fundamental time scale we use today is based upon atomic clocks (International Atomic Time), but it is very inconvenient for general use. There are still very good reasons for relating timescales in general use to the rotation of the Earth. Coordinated Universal Time (effectively Greenwich Mean Time) was first synchronized with Atomic Time in 1972. However, under the influence of the Moon's gravitational field the period of the Earth's rotation is slowing down, and so GMT has to corrected if it is not to differ from Atomic Time. Leap Seconds are added to achieve this. [This is similar to adding Leap years to compensate for the fact the

period of the Earth's motion round the sun (the year) is not an exact multiple of its period of rotation on its axis (the day)]. Since 1972 a total of 32 leap seconds have been added to GMT. However an additional complication arose in 1980 with the advent of the Global Positioning System. This uses GMT, but has not been adjusted by the 13 leap seconds since then, because the very precisely synchronized satellite network cannot cope with such changes. So now the different "users" of time cannot agree whether to continue with the practice of leap seconds. Air Traffic controllers and computer network managers are at loggerheads with astronomers. Ref: Nature 12 June 2003 p671]

Even more accurate clocks
Chapters 3, 8, 17 Date posted on Capt: 24 January 2003 A new generation of clocks so stable that they should only be out by 1 second in 100 billion years is being developed. (Recall that Universe itself is perhaps 6 times younger than this time scale!). This performance is a thousand times better than existing atomic clocks. Why bother? Well GPS precision will improve to be able to pinpoint locations to + a few cms, and the finesse available to determine the fundamental constants of physics will allow crucial tests of quantum physics etc. All clocks have two basic components: an oscillator to provide events that repeat with a regular period, and a counter. The sundial repeats its cycle roughly every 24 hours (~ 1.16 10 E-5 Hz): a pendulum repeats perhaps each second (1 Hz): particular microwave radiation from caesium atoms oscillates at 9,192,631,770 Hz. The new clocks using optical radiation from e.g. mercury ions will improve precision from 15 to 18 decimal places (the ratio of microwave to optical frequencies). So how will they know if the most accurate clock is OK? (eg a household clock that loses exactly a second a day would be stable but inaccurate). You need another clock to compare it with. If they stay synchronized then both maybe OK, but what if they differ? A third identical clock is needed to arbitrate: one result is an observation, two identical results could be a coincidence, but three consistent results has the makings of a measurement. You are never far from basic lab procedures! Ref: Nature, January 16th, pages 207-208 (2003)

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