## Friday, February 12, 2016

### Detection Of Gravitational Waves From Colliding Black Holes Vindicates Existence For Both

Depiction of the gravitational disturbance from two colliding black holes dispersing gravitational waves

In 1915, in a remarkable achievement of theoretical physics, Albert Einstein used an abstruse form of math known as tensor calculus to show how gravity arises when mass and energy warp space time. The ground breaking Einstein field equations can be summarized in the tensor form:

G mn   =  - ½ g mn  G=  - 8 p T mn

Where the  T mn    denotes the associated  “stress-energy” tensor which incorporates internal stresses, the density of matter and its component velocities (u, v, w or in some texts: u1, u2 and u3).   From this one can see that if no matter is present, one would have:  G mn   =  0

If matter is present there must then be internal stresses and velocities so that:  G mn   =  K mn  where  (as seen from the field equations):  K mn   = - 8 p T mn

We have then for the  T mn  : analogous to the g’s in standard form

T 11      T 12      T 13        T 14
T 22     T 23         T
24

T 33         T 34
T 44

=

p 11  + r u2, p 12 + uv,    p 13    +r uw,  - ru

p 22  +
r v2,   p  23  +r vw,    - rv

p 33 +
r w2 ,      - rw

r

Which again is still vastly oversimplified. A year later, based on these equations Einstein predicted that massive objects undergoing the right kind of oscillating disturbance should actually emit ripples in space time: gravitational waves that propagate at light speed. Of course, this prediction remained controversial for decades because the mathematics of general relativity  - a tiny bit of which is presented above - is so complicated. Besides, many theoretical physicists noted that even if the waves did exist, detecting them would test the very limits of our technological capability. This is given that most predictions included estimates for their wavelength as low as  10 -14 m. To fix ideas this is about the diameter of an atomic nucleus and is only an order of magnitude larger than the fermi (fm). (The LIGO design is such that it is capable of detecting a gravitational wave with a wavelength 1000 times less than the diameter of a proton.)

One of the earliest pioneers in gravitational wave detection was Joseph Weber of the University of Maryland. In 1969 Weber even claimed to have discovered them. He used a detector consisting of two massive aluminum cylinders 1.5 m long and 0.6 m wide, one of which was in Illinois, the other in College Park, Maryland.   Weber's contention was that a gravitational wave would stretch a bar and cause it to vibrate like a tuning fork and electrical sensors could then detect the stretching.

Weber's problem was that other physicists were unable to reproduce his published results, leading some - like IBM physicist Richard Garwin-  to argue that the universe would have had to have converted all its energy to gravitational radiation in 50 million years for Weber's claim to be valid.

While Weber's efforts were stillborn, he is still regarded as the father of gravitational wave detection and his research triggered the development of the LIGO (Laser Interferometer Gravitational Wave Observatory). Now, we have learned that an international team using LIGO has detected a slight stretching and squeezing of space-time from one of the most violent events in astrophysics: two colliding black holes.

LIGO’s discovery, accepted for publication in Physical Review Letters,  see abstract e.g.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.061102

not only provides the first direct evidence for gravitational waves but also opens the door to using them to study the powerful cosmic events that create them.

Unlike Weber's aluminum drum detectors, LIGO features 2 L-shaped detectors (one in Hanford, WA, the other in Livingston, LA)  made up of two perpendicular arms totaling 2.5 miles long. Then a laser beam is split and travels along both arms, bouncing off respective mirrors to return to the L-intersection. Normally, the beams are aligned so they balance each other out and hence there's nothing to detect. But if a gravitational wave is intercepted it creates a tiny mismatch which is what LIGO detects. (One of the authors of the paper has referred to it as a "chirp".  The effect of this chirp or ripple changes the arms' lengths by a tiny amount, and that change can be detected by lasers.

Based on the paper cited in the above link, the two black holes are each roughly 30 times the mass of the Sun. They evidently merged some 1.3 billion light years from Earth. The  gravitational waves themselves were generated in the final moments before the black holes merged. The signal was brief but definitive and we on Earth have now received it.

The measurements are dramatic proof that gravitational waves do exist. The signal in the detector matches well with what's predicted by Einstein's original theory, according to Saul Teukolsky, of Cornell University, who was briefed on the results. It matches predictions of the ripples produced by two large black holes, in the final moments before they merge, swirling together at an enormous speed.

Another gratifying aspect is that this find puts the question of black holes existence to rest once and for all. It is in fact the most direct observation of black holes ever made. We acknowledge that black holes can't be seen with ordinary telescopes, so their existence has been inferred by the x-rays detected from binary systems.  Mathematically, the very brief periods of less than a millisecond betray an extremely compact volume. The x-rays indicate accretion to a large mass. Together, these can be matched to predictions given in the Einstein general relativity equations and Voila! the black hole emerges as an object consistent with the observations.

Unlike the x-rays signals from binary systems (stellar envelope mass accreting onto the hole's event horizon to generate them) the newly detected  gravitational signal comes directly from the holes, and it is virtually incontrovertible proof that the holes are out there.

As Teukolsky avers:

"If black holes didn't really exist, you couldn't explain these waves,"

We will now await other confirmations of this find, but certainly from the Physical Review Letters paper it looked very much like 'case closed'.