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Why Gravitational Waves Are Memoryless

When gravitational waves are emitted from merging black holes, it is tacitly assumed that the gravitational waves, assumed to propagated as the same speed of light, will remain constant with respect to the center of gravity of the cataclysmic final merger of of such binaries as GW150914 until they reach LIGO's 4-km arm, which they subsequently change by a thousandth of the width of a proton.


However, there are intermediary gravitational fields through which the gravitational waves must pass before they reach the lenses and mirrors of the LIGO interferometer. And just like light, the propagation of gravitational waves through any medium, no matter how rare, involves the continual absorption and re-radiation of gravity waves as secondary radiation. This has the effect of erasing any memory that gravitational waves have of the original black hole merger. The effect is known as extinction which gravitational waves are subject to. The emerging gravitational waves that emerge from such a dispersive medium will possess the characteristics of the medium they have just passed through and not their original source. This occurs after a single extinction length.


In other words, the gravitational wave signal has become corrupted as it passes through other gravitational fields so that it does not remember the characteristics of the source that created it. The information concerning inspiralling, merger, and ringdown would all be washed out. How masses of the initial black holes that would be between 36 and 29 solar masses could transform into a resulting black hole of 62 solar masses would be entirely lost in space and time that it took for the gravitational waves to reach earth, or some 1.3 billion years.


Yet, surprises are constantly in store when dealing with LIGO's discovery. In a paper entitled "Persistent Gravitational Wave Observables: General Framework, published in Phys Rev D on the 26 of April, the claim is made that gravitational waves do leave a lasting imprint on particles that were initially in flat space-time and return to flat space-time after experiencing a gravitational wave. The idea is to compare two accelerating observers and their geodesic curve deviation as compared to two accelerating observers in flat space time. Note the necessity on "accelerating" observers and not stationary mirrors as in LIGO's set-up. Other comparisons concerning their angular momenta and spin.


Yet, general relativity cannot solve the two body problem so it is not clear how comparisons of two accelerating observers can be carried out in such a framework. Moreover, electromagnetic waves, that travel at the same speed as gravitational waves, should also leave imprints of memory on the particles they interact with. And if gravitational waves do leave imprints on the particles they interact with, then they must look energy in the process. Such would also be the case when gravitational waves interact with particles in galactic dust. Hence, the authors of the article admit to the fact that gravitational waves do loose memory. But who says gravitational waves carry energy to begin with? Certainly not general relativity which treats gravitational energy in terms of a pseudo-tensor which can be nullified by means of a mere coordinate transformation.

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