Gravitational Waves, or Not??

On February 11, 2016 LIGO reported that on September 14, 2015, they had verified the existence of gravitational waves, the “ripples in spacetime” predicted by General Relativity. In 2017, LIGO/Virgo laboratories announced the detection of a gravitational wave signal from merging neutron stars, which was verified by optical telescopes, and which led to the award of the Nobel Prize to three physicists. This was science in action and while I suspect most people had no real idea what this means, the items were big news. The detectors were then shut down for an upgrade to make them more sensitive and when they started up again it was apparently predicted that dozens of events would be observed by 2020, and with automated detection, information could be immediately relayed to optical telescopes. Lots of scientific papers were expected. So, with the program having been running for three months, or essentially half the time of the prediction, what have we found?

Er, despite a number of alerts, nothing has been confirmed by optical telescopes. This has led to some questions as to whether any gravitational waves have actually been detected and led to a group at the Neils Bohr Institute at Copenhagen to review the data so far. The detectors at LIGO correspond to two “arms” at right angles to each other running four kilometers from a central building. Lasers are beamed down each arm and reflected from a mirror and the use of wave interference effects lets the laboratory measure these distances to within (according to the LIGO website) 1/10,000 the width of a proton! Gravitational waves will change these lengths on this scale. So, of course, will local vibrations, so there are two laboratories 3,002 km apart, such that if both detect the same event, it should not be local. The first sign that something might be wrong was that besides the desired signals, a lot of additional vibrations are present, which we shall call noise. That is expected, but what was suspicious was that there seemed to be inexplicable correlations in the noise signals. Two labs that far apart should not have the “same” noise.

Then came a bit of embarrassment: it turned out that the figure published in Physical Review Letters that claimed the detection (and led to Nobel prize awards) was not actually the original data, but rather the figure was prepared for “illustrative purposes”, details added “by eye”.  Another piece of “trickery” claimed by that institute is that the data are analysed by comparison with a large database of theoretically expected signals, called templates. If so, for me there is a problem. If there is a large number of such templates, then the chances of fitting any data to one of them is starting to get uncomfortably large. I recall the comment attributed to the mathematician John von Neumann: “Give me four constants and I shall map your data to an elephant. Give me five and I shall make it wave its trunk.” When they start adjusting their best fitting template to fit the data better, I have real problems.

So apparently those at the Neils Bohr Institute made a statistical analysis of data allegedly seen by the two laboratories, and found no signal was verified by both, except the first. However, even the LIGO researchers were reported to be unhappy about that one. The problem: their signal was too perfect. In this context, when the system was set up, there was a procedure to deliver artificially produced dummy signals, just to check that the procedure following signal detection at both sites was working properly. In principle, this perfect signal could have been the accidental delivery of such an artifical signal, or even the deliberate insertion by someone. Now I am not saying that did happen, but it is uncomfortable that we have only one signal, and it is in “perfect” agreement with theory.

A further problem lies in the fact that the collision of two neutron stars as required by that one discovery and as a source of the gamma ray signals detected along with the gravitational waves is apparently unlikely in an old galaxy where star formation has long since ceased. One group of researchers claim the gamma ray signal is more consistent with the merging of white dwarfs and these should not produce gravitational waves of the right strength.

Suppose by the end of the year, no further gravitational waves are observed. Now what? There are three possibilities: there are no gravitational waves; there are such waves, but the detectors cannot detect them for some reason; there are such waves, but they are much less common than models predict. Apparently there have been attempts to find gravitational waves for the last sixty years, and with every failure it has been argued that they are weaker than predicted. The question then is, when do we stop spending increasingly large amounts of money on seeking something that may not be there? One issue that must be addressed, not only in this matter but in any scientific exercise, is how to get rid of the confirmation bias, that is, when looking for something we shall call A, and a signal is received that more or less fits the target, it is only so easy to say you have found it. In this case, when a very weak signal is received amidst a lot of noise and there is a very large number of templates to fit the data to, it is only too easy to assume that what is actually just unusually reinforced noise is the signal you seek. Modern science seems to have descended into a situation where exceptional evidence is required to persuade anyone that a standard theory might be wrong, but only quite a low standard of evidence to support an existing theory.

Marsquakes

One of the more interesting aspects of the latest NASA landing on Mars is that the rover has dug into the surface, inserted a seismometer, and is looking for marsquakes. On Earth, earthquakes are fairly common, especially where I live, and they are generated through the fact that our continents are gigantic lumps of rock moving around over the mantle. They can slide past each other or pull themselves down under another plate, to disappear deep into the mantle, while at other places, new rock emerges to take their place, such as at the mid-Atlantic ridge. Apparently the edges of these plates move about 5 – 10 cm each year. You probably do not notice this because the topsoil, by and large, does not move with the underlying crust. However, every now and again these plates lock and stop moving there. The problem is, the rest of the rock is moving, so considerable strain energy is built up, the lock gives way, very large amounts of energy are released, and the rock moves, sometimes be several meters. The energy is given out as waves, similar in many ways as sound waves, through the rock. If you see waves in the sea, you will note that while the water itself stays more or less in the same place on average, in detail something on the surface, like a surfer, goes up and down, and in fact describes what is essentially a circle if far enough out. Earthquake waves do the same thing. The rock moves, and the shaking can be quite violent. Of course, the rock moves where the actual event occurred, and sometimes the waves trigger a further shift somewhere else.

Such waves travel out in all directions through the rock. Now another feature of all waves is that when they strike a medium through which they will travel with a different velocity, they undergo partial reflection and refraction. There is an angle of incidence when only reflection occurs, and of course, on a curved surface, the reflected waves start spreading as the angles of incidence vary. A second point is that the bigger the difference in wave speed between the two media, the more reflection there is. On Earth, this has permitted us to gather information on what is going on inside the Earth. Of course Earth has some big advantages. We can record seismic events from a number of different places, and even then the results are difficult to interpret.

The problem for Mars is there will be one seismometer that will measure wave frequency, amplitude, and the timing. The timing will give a good picture of the route taken by various waves. Thus the wave that is reflected off the core will come back much sooner than the wave that travels light through and is reflected off the other side, but it will have the same frequency pattern on arrival, so from such patterns and timing you can sort out, at least in principle, what route they took and from the reflection/refraction intensities, what different materials they passed through. It is like a CT scan of the planet. There are further complications because wave interference can spoil patterns, but waves are interesting that they only create that effect at the site where they interfere. Otherwise, they pass right through other waves and are unchanged when they emerge, apart from intensity changes if energy was absorbed by the medium. There is an obvious problem in that with only one seismometer it is much harder to work out where the source was but the scientists believe over the lifetime of the rover they will detect at least a couple of dozen quakes.

Which gets to the question, why do we expect quakes? Mars does not have plate tectonics, possibly because its high level of iron oxide means eclogite cannot form, and it is thought that the unusually high density of eclogite leads to pull subduction. Accordingly the absence of plate tectonics means we expect marsquakes to be of rather low amplitude. However, minor amplitude quakes are expected. One reason is that as the planet cools, there is contraction in volume. Accordingly, the crust becomes less well supported and tends to slip. A second cause could be magma moving below the surface. We know that Mars has a hot interior, thanks to nuclear decay going on inside, and while Mars will be cooler than Earth, the centre is thought to be only about 200 Centigrade degrees cooler than Earth’s centre. While Earth generates more heat, it also loses more through geothermal emissions. Finally, when meteors strike, they also generate shockwaves. Of course the amplitude of these waves is tiny compared with that of even modest earthquakes.

It is hard to know what we shall learn. The reliance on only one seismometer means the loss of directional analysis, and the origin of the quake will be unknown, unless it is possible to time reflections from various places. Thus if you get one isolated event, every wave that comes must have originated from that source, so from the various delays, paths can be assigned. The problem with this is that low energy events might not generate enough reflections of sufficient amplitude to be detected. The ideal method, of course, is to set off some very large explosions at known sites, but it is rather difficult to do that from here.

What do we expect? This is a bit of guesswork, but for me we believe the crust is fairly thick, so we would expect about 60 km of solid basalt. If we get significantly different amounts, this would mean we would have to adjust our thoughts on the Martian thermonuclear reactions. I expect a rather tiny (for a planet) iron core, the clue here being the overall density of Mars is 3.8, its surface is made of basalt, and basalt has a density of 3.1 – 3.8. There just is not room for a lot of iron in the form of the metal. It is what is in between that is of interest. Comments from some of the scientists say they think they will get clues on planetary formation, which could come from deep structures. Thus if planets really formed from the combination of planetesimals, which are objects of asteroid, size, then maybe we shall see the remains in the form of large objects of different sonic impedance. On the other hand, the major shocks to the system by events such as the Hellas impactor may mean that asymmetries were introduced by such shock waves melting parts. My guess is the observations will not be unambiguous in terms of their meaning, and it will be interesting to see how many different scenarios are considered.

The Roman “Invisibility” Cloak – A Triumph for Roman Engineering

I guess the title of this post is designed to be a little misleading, because you might be thinking of Klingons and invisible space ships, but let us stop and consider what an “invisibility” cloak actually means. In the case of Klingons, light does not come from somewhere else and be reflected off their ship back to your eyes. One way to do that is to construct metamaterials, which involve creating structures in them to divert waves. The key involves matching wavelengths to structural variation, and it is easier to do this with longer wavelengths, which is why a certain amount of fuss has been made when microwaves have been diverted around objects to get the “invisibility” cloak. As you might gather, there is a general problem with overall invisibility because electromagnetic radiation has a huge range of wavelengths.

Sound is also a wave, and here it is easier to generate “invisibility” because we only generate sound over a reasonably narrow range of wavelengths from most sources. So, time for an experiment. In 2012 Stéphane Brûlé et al. demonstrated the potential by drilling a two-dimensional array of boreholes into topsoil, each 5 m deep. They then placed an accoustic source nearby, and found that much of the waves’ energy was reflected back towards the source by the first two rows of holes. What happens is that, depending on the spacing of the holes, when waves within a certain range of wavelengths pass through the lattice, there are multiple reflections. (Note this is of no value to Klingons, because you have just amplified the return radar signal.)

The reason is that when waves strike a different medium, some are reflected and some are refracted, and reflection tends to be more likely as the angle of incidence increases, and of course, the angle of incidence equals the angle of reflection. A round hole provides quite chaotic reflections, especially recalling that during refraction there is also a change of angle, and of course a change of medium occurs when the wave strikes the hole, and when it tries to leave the hole. If the holes are spaced properly with respect to the wavelength, there is considerable destructive wave interference. The net result of that is that in Brûlé’s experiment much of the wave energy was reflected back towards the source by the first two rows of holes. It is not necessary to have holes; it is merely necessary to have objects that have different wave impedance, i.e.the waves travel at different speeds through the different media, and the bigger the differences in such speeds, the better the effect. Brûlé apparently played around with holes, etc, and found the best positioning to get maximum reflection.

So, what has this got to do with Roman engineering? Apparently Brûlé went on holiday to Autun in central France, and while being touristy he saw a photograph of the foundations of a Gallo-Roman theatre, and while the image provided barely discernible foundation features, he had a spark of inspiration and postulated that the semi-circular structure bore an uncanny resemblance to half of an invisibility cloak. So he got a copy of the photo and superimposed it on one of his photos and found there was indeed a very close match.

The same thing apparently applied to the Coliseum in Rome, and a number of other amphitheatres. He found that the radii of neighbouring concentric circles (or more generally, ellipses) followed the required pattern very closely.

The relevance? Well, obviously we are not trying to defend against stray noise, but earthquakes are also wave motion. The hypothesis is that the Romans may have arrived at this structure by watching which structures survived in earthquakes and which did not, and then came up with the design most likely to withstand such earthquakes. The ancients did have surprising experience with earthquake design. The great temple at Karnak was built on materials that when sodden, which happened with the annual floods and was sufficient to hold the effect for a year, absorbed/reflected such shaking and acted as “shock absorbers”. The thrilling part of this study is that just maybe we could take advantage of this to design our cities such that they too reflect seismic energy away. And if you think earthquake wave reflection is silly, you should study the damage done in the Christchurch earthquakes. The quake centres were largely to the west, but the waves were reflected off Banks Peninsula, and there was significant wave interference. In places where the interference was constructive the damage was huge, but nearby, where interference was destructive, there was little or no damage. Just maybe we can still learn something from Roman civil engineering.