Wednesday, 21 August 2013

Gravitational Waves- Einstein's Final Straw

Like ripples through a rubber sheet, they squeeze and stretch spacetime and move outwards at the speed of light. Gravitational waves are still up for grabs. An exotic prediction of general relativity yet to be observed yet having profound implications for cosmology and astrophysics. If we picture a star in a relativistic orbit around a supermassive black hole, it may continue so for thousands of years but never forever. Neglecting even drag due to gas, the orbit would lose energy gradually until the star spiralled into the hole; the reason for this plunge is the emission of gravitational radiation. We know that if the shape or size of an object is altered, so is the gravity surrounding it; Newton realised the sphere was an exception since the gravitational field outside it is invariant (remains the same) if it merely expands or contracts. Changes in the gravitational field can't spread out instantly because this would imply a conveyance of information about the shape and size of an object at superluminal speeds (which is forbidden by relativity). If the sun were to somehow alter its shape and the gravitational field around it, 8 minutes would elapse for the effect to be 'felt' on the earth and at very large distances, this is evident as radiation (a wave of changing gravity) moving away from its source. This is analogous to the manner in which fluctuations in an electric field produces electromagnetic waves (a rotating bar with a charged ends produces an electric field unlike which is different from when the bar is end-on or sideways-on). But there are two main distinctions to be made between gravitational and electromagnetic waves. Firstly, gravitational waves are especially weak (except if very large masses are involved). Diatomic molecules are great emitters of electromagnetic radiation but terrible at transmitting gravitational waves. Because there is no such thing as negative mass (negative gravitational charge) to neutralise (or cancel out) positive ones (like in electricity), on large scales, gravity competes with electromagnetism. This lack of negative gravitational charge gives gravity an advantage over electromagnetism but it implies a deep paradox: it weakens the strength of an object to make gravitational radiation. Which brings us to the second difference between gravitational and electromagnetic waves:

The most productive (i.e. efficient) way of making electromagnetic radiation is for the 'centre of electric charge' to stagger or wobble  in relation to the centre of mass. Dipole radiation is an example of this, where the ends of a spinning bar are positively charged on one end while negative on the other. But the Equivalence Principle (which dictates that gravitation is indistinguishable from acceleration, much like how a rising elevator makes you feel heavier while a descending one makes you feel lighter) also mentions that everything exerts a gravitational force equal to its inertial mass, hence at all points in spacetime, all bodies experience the same gravitational acceleration. Translating into english: this implies that the 'centre of gravitational charge' is really just the centre of mass and since the former can't wobble relative to the latter, dipole gravitational radiation can't exist. We compare gravitational radiation to the spinning bar by envisaging it possesses positive charges  at both ends so that 'the centre of charge' remains set (fixed) at the centre and thus, low amounts of radiation are produced owing the existence of a quadrupole moment (it's only quantity that changes: it describes the distribution of shape and charge). Due to gravitational radiation, binary systems loses energy and their orbital period shrinks progressively, causing the component stars to coalesce; when two black holes meet, their even horizons combine into a larger one and in accordance with the 'no hair theorems', returns to a state described by the Kerr Metric (hole has mass and spin). 

But the detection of such gravitational radiation (or waves) is causing a stir, it is Einstein's final straw. Any object in the way of a gravitational wave would experience a tidal gravitational force that acts transverse (perpendicular) to the direction in which the wave moved outward. If you interrupt a gravitational wave some sort of circular hoop head-on, it will eventually be contorted into an ellipse. In Louisiana, the LIGO detector uses laser interferometry, where a laser beam is divided and reflected off mirrors which are connected to two masses (kilometers away) in a perpendicular fashion (an L shape). If a gravitational wave were to arrive, it would cause two lengths, X and Y to change. To be continued...

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