Ross 128b a Habitable Planet?

Recently the news has been full of excitement that there may be a habitable planet around the red dwarf Ross 128. What we know about the star is that it has a mass of about 0.168 that of the sun, it has a surface temperature of about 3200 degrees K, it is about 9.4 billion years old (about twice as old as the sun) and consequently it is very short of heavy elements, because there had not been enough supernovae that long ago. The planet is about 1.38 the mass of Earth, and it is about 0.05 times as far from its star as Earth is. It also orbits its star every 9.9 days, so Christmas and birthdays would be a continual problem. Because it is so close to the star it gets almost 40% more irradiation than Earth does, so it is classified as being in the inner part of the so-called habitable zone. However, the “light” is mainly at the red end of the spectrum, and in the infrared. Even more bizarrely, in May this year the radio telescope at Arecibo appeared to pick up a radio signal from the star. Aliens? Er, not so fast. Everybody now seems to believe that the signal came from a geostationary satellite. Apparently here is yet another source of electromagnetic pollution. So could it have life?

The first question is, what sort of a planet is it? A lot of commentators have said that since it is about the size of Earth it will be a rocky planet. I don’t think so. In my ebook “Planetary Formation and Biogenesis” I argued that the composition of a planet depends on the temperature at which the object formed, because various things only stick together in a narrow temperature range, but there are many such zones, each giving planets of different composition. I gave a formula that very roughly argues at what distance from the star a given type of body starts forming, and if that is applied here, the planet would be a Saturn core. However, the formula was very approximate and made a number of assumptions, such as the gas all started at a uniform low temperature, and the loss of temperature as it migrated inwards was the same for every star. That is known to be wrong, but equally, we don’t know what causes the known variations, and once the star is formed, there is no way of knowing what happened so that was something that had to be ignored. What I did was to take the average of observed temperature distributions.

Another problem was that I modelled the centre of the accretion as a point. The size of the star is probably not that important for a G type star like the sun, but it will be very important for a red dwarf where everything happens so close to it. The forming star gives off radiation well before the thermonuclear reactions start through the heat of matter falling into it, and that radiation may move the snow point out. I discounted that largely because at the key time there would be a lot of dust between the planet and the star that would screen out most of the central heat, hence any effect from the star would be small. That is more questionable for a red dwarf. On the other hand, in the recently discovered TRAPPIST system, we have an estimate of the masses of the bodies, and a measurement of their size, and they have to have either a good water/ice content or they are very porous. So the planet could be a Jupiter core.

However, I think it is most unlikely to be a rocky planet because even apart from my mechanism, the rocky planets need silicates and iron to form (and other heavier elements) and Ross 128 is a very heavy metal deficient star, and it formed from a small gas cloud. It is hard to see how there would be enough material to form such a large planet from rocks. However, carbon, oxygen and nitrogen are the easiest elements to form, and are by far the most common elements other than hydrogen and helium. So in my theory, the most likely nature of Ross 128b is a very much larger and warmer version of Titan. It would be a water world because the ice would have melted. However, the planet is probably tidally locked, which means one side would be a large ocean and the other an ice world. What then should happen is that the water should evaporate, form clouds, go around the other side and snow out. That should lead to the planet eventually becoming metastable, and there might be climate crises there as the planet flips around.

So, could there be life? If it were a planet with a Saturn core composition, it should have many of the necessary chemicals from which life could start, although because of the water/ice live would be limited to aquatic life. Also, because of the age of the planet, it may well have been and gone. However, leaving that aside, the question is, could life form there? There is one restriction (Ranjan, Wordsworth and Sasselov, 2017. arXiv:1705.02350v2) and that is if life requires photochemistry to get started, then the intensity of the high energy photons required to get many photochemical processes started can be two to four orders of magnitude less than what occurred on Earth. At that point, it depends on how fast everything that follows happens, and how fast the reactions that degrade them happen. The authors of that paper suggest that the UV intensity is just too low to get life started. Since we do not know exactly how life started yet, that assessment might be premature, nevertheless it is a cautionary point.

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Asteroids

If you have been to more than the occasional science fiction movie, you will know that a staple is to have the trusty hero being pursued, but escaping by weaving in and out of an asteroid field. Looks like good cinema, they make it exciting, but it is not very realistic. If asteroids were that common, according to computer simulations their mutual gravity would bring them together to form a planet, and very quickly. In most cases, if you were standing on an asteroid, you would be hard pressed to see another one, other than maybe as a point like the other stars. One of the first things about the asteroid belt is it is mainly empty. If we combined all the mass of the asteroids we would get roughly 4% of the mass of the Moon. Why is that? The standard theory of planetary formation cannot really answer that, so they say there were a lot there, but Jupiter’s gravity drove them out, at the same time overlooking the fact their own theory says they should form a planet through their self-gravity if there were that amny of them. If that were true, why did it leave some? It is not as if Jupiter has disappeared. In my “Planetary formation and Biogenesis”, my answer is that while the major rocky planets formed by “stone” dust being cemented together by one other agent, the asteroid belt, being colder, could only manage dust being cemented together with two other agents, and getting all three components in the same place at the same time was more difficult.

There is a further reason why I do not believe Jupiter removed most of the asteroids. The distribution currently has gaps, called the Kirkwood gaps, where there are very few asteroids, and these occur at orbital resonances with Jupiter. Such a resonance is when the target body would orbit at some specific ratio to Jupiter’s orbital period, so frequently the perturbations are the same because in a given frame of reference, they occur in the same place. Thus the first such gap occurs at 2.06 A.U. from the sun, where any asteroid would go around the sun exactly four times while Jupiter went around once. That is called a 4:1 resonance, and the main gaps occur at 3:1, 5:2, 7:3 and 2:1 resonances. Now the fact that Jupiter can clear out these narrow zones but leave all the rest more or less unchanged strongly suggests to me there were never a huge population of asteroids and we are seeing a small residue.

The next odd thing about asteroids is that while there are not very many of them, they change their characteristics as they get further from the star (with some exceptions to be mentioned soon.) The asteroids closest to the sun are basically made of silicates, that is, they are essentially giant rocks. There appear to be small compositional variations as they get further from the star, then there is a significant difference. How can we tell? Well, we can observe their brightness, and in some cases we can correlate what we see with meteorites, which we can analyse. So, further out, they get significantly duller, and fragments that we call carbonaceous chondrites land on Earth. These contain a small amount of water, and organic compounds that include a variety of amino acids, purines and pyrimidines. This has led some to speculate that our life depended on these landing on Earth in large amounts when Earth was very young. In my ebook “Planetary Formation and Biogenesis”, I disagree. The reasons are that to get enough, a huge number of such asteroids would have to impact the Earth because they are still basically rock, BUT at the same time, hardly any of the silicate based asteroids would have to arrive, because if they did, the isotopes of certain elements on Earth would have to be different. Such isotope evidence also rules these out as a source of water, as does certain ratios such as carbon to chlorine. What these asteroid fragments do show, however, is that amino acids and other similar building blocks of life are reasonably easily formed. If they can form on a lump of rock in a vacuum, why cannot they form on Earth?

The asteroid belt also has the odd weird asteroid. The first is Ceres, the largest. What is weird about it is that it is half water. The rest are essentially dry or only very slightly wet. How did that happen, and more to the point, why did it not happen more frequently? The second is Vesta, the second largest. Vesta is rocky, although it almost certainly had water at some stage because there is evidence of quartz. It has also differentiated, and while the outer parts have olivine, deeper down we get members of the pyroxene class of rocks, and deeper down still there appears to be a nickel/iron core. Now there is evidence that there may be another one or two similar asteroids, but by and large it is totally different from anything else in the asteroid belt. So how did that get there?

I rather suspect that they started somewhere else and were moved there. What would move them is if they formed and came close to a planet, and instead of colliding with it, they were flung into a highly elliptical orbit, and then would circularise themselves where they ended up. Why would they do that? In the case of Vesta, at some stage it suffered a major collision because there is a crater near the south pole that is 25 km deep, and it is from this we know about the layered nature of the asteroid. Such a collision may have resulted in it remaining in orbit roughly near its present position, and the orbit would be circularised due to the gravity of Jupiter. Under this scenario, Vesta would have formed somewhere near Earth to get the iron core. Ceres, on the other hand, probably formed closer to Jupiter.

In my previous post, I wrote that I believed the planets and other bodies grew by Monarchic growth, but that does not mean there were no other bodies growing in a region. Monarchic growth means the major object grows by accreting things at least a hundred times smaller, but of course significant growth can occur for other objects. The most obvious place to grow would be at a Lagrange point of the biggest object and the sun. That is a position where the planet’s gravitational field and the sun’s cancel, and the body is in stable or metastable orbit there. Once it gets to a certain size, however, it is dislodged, and that is what I think was the source of the Moon, its generating body probably starting at L4, the position at the same distance from the sun as Earth, but sixty degrees in front of it. There are other metastable positions, and these may have also formed around Venus or Mercury, and these would also be unstable due to different rocky planets. The reason I think this is that for Vesta to have an iron core, it had to pick up bodies with a lot of iron, and such bodies would form in the hotter part of the disk while the star was accreting. This is also the reason why Earth has an iron core and Mars has a negligible one. However, as I understand it, the isotopes from rocks on Vesta are not equivalent to those of Earth, so it may well have started life nearer to Venus or Mercury. So far we have no samples to analyse that we know came from either of these two planets, and I am not expecting any such samples anytime soon.

A Giant Planet Around a Dwarf Star

The news here, at least, has made much of the discovery of NGTS-1b, described as a giant planet orbiting a dwarf star. It is supposed to be the biggest planet ever found around such a small star, and it is supposed to be inexplicable how such a big planet could form. One key point that presumably everyone will agree with is, a small star forms because there is less gas and dust in the cloud that will form the star than in the cloud that forms a big star. Accordingly there is less total material to form a planet. Missing from that statement is the fact that in all systems the amount of mass in the planets is trivial compared to the mass of the star. Accordingly, there is nothing at all obscure about an unexpectedly big planet if the planet was just a bit more efficient at taking material that would otherwise go into the star.

So, a quick reality check: the star is supposed to be about 60% the size of the sun, and the planet is about 80% the mass of Jupiter, but has a somewhat larger radius. Planets up to twenty times the size of Jupiter are known around stars that are not more than about three times the size of our sun, so perhaps there is more being made of this “big planet” than is reasonable.

Now, why is it inexplicable how such a large planet could form around a small star, at least in standard theory? The mechanism of formation of planets in the standard theory is that first gas pours in, forms the star, and leaves a residual disk (the planetary accretion disk), in which gas is essentially no longer moving towards the star. That is not true; the star continues to accrete, but several orders or magnitude more slowly. The argument then is that this planetary accretion disk has to contain all the material needed to form the planets, and they have to form fast enough to get as big as they end up before the star ejects all dust and gas, which can take somewhere up to 10 million years (10 My), with a mean of about 3 My. There is some evidence that some disks last at least 30 My. Now the dust collides, sticks (although why or how is always left out in the standard theory) and forms planetesimals, which are bodies of asteroid size. These collide and form bigger bodies, and so on. This is called oligarchic growth. The problem is, as the bodies get larger, the distance between them increases and collision probability falls away, not helped by the fact that the smaller the star, the slower the orbiting bodies move, the less turbulent it will be, so the rate of collisions slows dramatically. For perspective purposes, collisions in the asteroid belt are very rare, and when they occur, they usually lead to the bodies getting smaller, not bigger. There are a modest number of such families of detritus asteroids.

The further out the lower the concentration of matter, simply because there is a lot more space. A Jupiter-sized body has to grow fast because it has to get big enough for its gravity to hold hydrogen, and then actually hold it, before the disk gases disappear. Even accreting gas is not as simple as it might sound, because as the gas falls down the planetary gravitational field, it gets hot, and that leads to some gas boiling off back to space. To get going quickly, it needs more material, and hence a Jupiter type body is argued (correctly, in my opinion) to form above the snow line of water ice. (For the purposes of discussion, I shall call material higher up the gravitational potential “above”, in which case “below” is closer to the star.) It is also held that the snow line is not particularly dependent on stellar mass, in which case various planetary systems should scale similarly. With less material around the red dwarf, and as much space to put it in, everything will go a lot slower and the gas will be eliminated before a planet is big enough to handle it. Accordingly, it seems that according to standard theory, this planet should not form, let alone be 0.036 A.U. from the star.

The distance from the star is simply explained in any theory: it started somewhere else and moved there. The temperature at that distance is about 520 degrees C, and with solar wind it would be impossible for a small core to accrete that much gas. (The planet has a density of less than 1, so like Saturn it would float if put in a big enough tub of water.) How would it move? The simplest way would be if we imagined a Jupiter and a Saturn formed close enough together, when they could play gravitational billiards, whereby one moves close to the star and the other is ejected from the system. There are other plausible ways.

That leaves the question of how the planet forms in the first place. To get so big, it has to form fast, and there is evidence to support such rapid growth. The planet LkCa 15b is around a star that is slightly smaller than the sun, it is three times further out than Jupiter, and it is five times bigger than Jupiter. I believe this makes our sun special – the accretion disk must have been ejected maybe as quickly as 1 My. Simulations indicate that oligarchic growth should not have led to any such oligarchic growth that far out. My explanation (given in my ebook “Planetary Formation and Biogenesis”) is that the growth was actually monarchic. This is a mechanism once postulated by Weidenschilling, in 2004 (Weidenschilling, S., 2004. Formation of the cores of the outer planets. Space Science Rev. 116: 53-56.) In this mechanism, provided other bodies do not grow at a sufficient rate to modify significantly the feed density, a single body will grow proportionately to its cross-sectional area by taking all dust that is in its feed zone, which is augmented by gravitation. The second key way to get a bigger planet is to have the planetary accretion disk last longer. The third is, in my theory, the initial accretion is chemical, and the Jupiter core forms like a snowball, by water ice compression fusing. Further, I argue it will start even while the star is accreting. That only occurs tolerably close to the melting point, so it is temperature dependent. The temperatures are reached very much closer to the star for a dwarf. Finally, the planet forming around a dwarf has one final growth advantage: because the star has a lower gravity, the gas will be drifting towards the star more slowly, so the growing planet, while having a less dense feed, also receives a higher fraction of the feed.

So, in my opinion, apart from the fact the planet is so lose to the star, so far there is nothing surprising about it at all, and the mechanisms for getting it close to the star are there, and there are plenty of other “star-burning” planets that have been found.

Why has the monarchic growth concept not taken hold? In my opinion, this is a question of fashion. The oligarchic growth mechanism has several advantages for the preparation of scientific papers. You can postulate all sorts of initial conditions and run computer simulations, then report those that make any sense as well as those that don’t (so others don’t waste time.) Monarchic growth leaves no real room for scientific papers.

Gravitational Waves and Gold

One of the more interesting things to be announced recently was the detection of gravitational waves that were generated by the collision of two neutron stars. What was really interesting to me was that the event was also seen by telescopes, so we know what actually caused the gravitational waves. Originally it was thought that gravitational waves would be generated by colliding black holes, but I found that to be disturbing because I thought the frequency of detection should be rather low. The reason is that I thought black holes themselves would be rather rare. As far as we can tell most galaxies contain one in their centre, but the evidence for more is rather sparse. True, they are not easy to see, but if they come into contact with gas, which is present within galaxies, the gas falling into them will give out distinct Xray signals and further, they would perturb the paths of close stars, which means, while we cannot see the black hole, if they were common, there should be some signs.

There are some signs. The star Cygnus X-1 is apparently shedding material into some unseen companion, and giving off X-rays as well as light. A similar situation occurs for the star M33-X-7, which is in the galaxy Messier 33, which in turn is 2.7 million light years away. Now obviously there will be more that we cannot see because they are not tearing stars apart, but they are still rare. Obviously, collisions would be rarer still. With all the stars in the Universe, how often do we see a collision between stars? I am unaware of any in my life. Nevertheless, there have been estimates that there are about a billion moderately sized black holes (i.e. about 15- 20 times the size of our sun) in our galaxy. However, when we probe to see how they came up with this figure, it turned out that it arose because it was obvious that you needed them to be this common to get the frequency of the detection of gravitational waves. That reasoning is somewhat circular.

How would they collide? Like other stars within the galaxy, they would travel in orbit around a galactic centre, in which case the chances of meeting are rather low. And even if they did approach, why would they collide? The problem involves the conservation of angular momentum (the same sort of thing that the skater uses to slow down the spin by sticking her arms out). When one body approaches another, assuming they are not going to directly collide (in which case there is no angular momentum in their joint system) then they follow a hyperbolic orbit around each other and end up going away from each other in the reverse of however they approached. For one to capture the other, either the systems have to spin up to conserve angular momentum, or they have to throw something out and whichever they do, orbital decay requires a mechanism to get rid of a lot of energy. Further, they cannot spin up, which is an exchange of angular momentum, without tidal interactions forcing it. Now tidal interactions work by part of one body “flowing” in response the gravity of the other. The material does not have to move a lot, but it has to be able to move, and the black hole is so dense I don’t see it is very likely, although admittedly we know nothing about what goes on inside a black hole. We do know that nothing can escape from a black hole, so the mechanism of losing energy and angular momentum by ejecting something is out.

Now that such an event has been properly assigned to the collision of two neutron stars it makes me, at least, feel that everything is far more likely to be correct. Neutron stars are what is left over from a supernova, and it is easier to see neutron stars capture each other. First, neutron stars are made from very large stars, and while these are rarer than most other types of star, sometimes they come as double stars. That would make neutron stars close to each other, which is a start. Further, neutron stars are more likely to be deformable, and most certainly are more able to eject material into space. Neutron stars are really only held together by their intense gravity, and as they approach each other, the gravity tends to cancel, as the approaching object pulls against the pre-existing force. If the force needed to hold the neutrons becomes insufficient, the ejection of a significant amount of material is possible. After all, nuclei with a significant number more neutrons than protons are quite unstable, and each decaying neutron gives off over 1 MeV of energy. The neutron star is effectively a huge nucleus, but is held together by intense gravity rather than the strong force.

Apparently in this collision, a huge amount of material was ejected into space, and it is argued that this sort of event is what caused the formation of the metals heavier than iron, including gold and platinum. Such atoms then get mixed with the ejecta from supernovae and the hydrogen and helium from the start of the Universe, and here we are. It is a good story. However, I wonder if it is true that that is where all the gold etc. comes from? What bothers me about that explanation is that it is argued that atoms up to iron are made in stars and supernovae, but heavier ones are not because in the clouds of the ejecta, there isn’t time for the processes we know about. In my opinion, the intense pressures of the supernova that forms the neutron star would also form heavier elements. They don’t have to be made by adding protons and neutrons, after all, the synthetic elements we make, such as element number 118, are made by colliding big nuclei together. In this context, if you see a graph of the relative occurrence of the various elements, the curve is more or less smooth. Yes, there is a bit of a peak for elements around iron, but it then decays smoothly, and I would have expected that if some were made by a totally different procedure, then their relative concentrations would lie on different curves. I guess I shall never know. I can’t see anyone taking samples from the core of a supernova any time soon.

The Face of Mars

Image

In 1976, the Viking 1 mission began taking photographs of the surface of Mars, in part to find landing sites for future missions, and also to get a better idea of what Mars was like, to determine the ages of various parts of Mars (done by counting craters, which assumes that once the great bombardment was over, the impacts were more or less regular over time if we think in terms of geological timing.) On the Cydonia Mensae, an image came back that, when refined, looks surprisingly like a face carved into a large rock. Two points are worth mentioning. The first is, if it were such a head, the angle of the light only allows you to see the right side of the head; the rest is in deep shadow. The second is all we received of this object was 64 pixels. The “face” is clearly a butte standing up from the surface (and there are lot of these in the region) and it is about 2.5 km long, about 1.5 km wide, and something like up to 800 m above the average flat ground at its highest point. As you might imagine, with only 64 pixels, the detail is not great, but there is a crater where the right eye should be, a rise that makes the nose, and some sort of “crack” or depression that hints at a mouth, but most of the “mouth” would be in the shade, and hence would be invisible. The image was also liberally splattered with black spots; these were “failed pixels” i.e. a transmission problem. What you see below is that primary image.

640x472 pixels-FC

So, what was it? The most obvious answer was a rock that accidentally looked like a face. To the objection, what is the probability that you could end up with that, the answer is, not as bad as you might think. There are a lot of mesas and rock formations on Mars, so sooner or later one of them might look like something else. There are a number of hills etc on Earth where you can see a head, or a frog, or something if you want to. If you think about it, an oval mesa is not that improbable, and there are a lot of them. There are a very large number of impact craters on Mars, so the chances of one being roughly where an eye would be is quite high (because there is quite a bit of flexibility here) and there are really only two features – the eye and the “mouth”. The rise for the nose only requires the centre to be the highest part, and that is not improbable. As it happens, when you see the whole thing, the left side of the head has sort of collapsed, and it is a fracture offshoot from that collapse that gives the mouth.

However, the image caught the imagination of many, and some got a little carried away. Richard Hoagland wrote a book The Monuments of Mars: A City on the Edge of Forever. If nothing else, this was a really good selling book, at one stage apparently selling up ot 2000 copies a month. Yep, the likes of me are at least envious of the sales. So, what did this say? Basically, Hoagland saw several “pyramids” near the Face, and a jumble of rocks that he interpreted as a walled city. Mars had an ancient civilisation! Left unsaid was why, if there were such “Martians” did they waste effort building pyramids and carving this Face while their planet was dying? For me, another question is why does something this fanciful become a best seller, while the truth languishes?

So what caused this? I don’t know, and neither does anyone else. It is reasonably obviously caused by erosion, but what the eroding agent was remains unknown. If you believe Mars once had an ocean, the Cydonian region is roughly where one of the proposed shorelines was. It could also be caused by glaciation, or even wind erosion, aided by moisture in the rock. The freezing/thawing of water generates very powerful forces. What we need is a geologist to visit the site to answer the question, although there would be far more important things to do on Mars than worry about that rock.

Suppose it was carved by a civilization? I included that possiblity in my novel Red Gold. In this, one character tried pulling the leg of another by announcing that it was “obviously carved” by aliens with the purpose of encouraging humans to go into space. “It is worth it,” the aliens would be saying. So why is it so rough? Because the aliens were plagued by accountants, who decided that the effort to do it properly was not worth the benefit; if humans cannot take the hint from the roughly hewn rock, so be it.

It also figures in another of my novels: A Face on Cydonia. Again, it is intended as a joke in the book, but on whom? Why did I do that? Well, I started writing when I heard that Global Surveyor was going to settle this issue, so I thought I should try to have something ready for an agent. However, Global Surveyor, which took very narrow strip images, and could have taken two years to cover this area, took only a few weeks. Out of luck again! Fortunately, the story was never really about the rock, but rather the effect it had on people.

A quick commercial: if anyone is interested, the ebook is at 99 cents on Amazon (or 99p) for the first week of September. The book is the first of a trilogy, but more about people being taken to levels higher than their abilities, and also about what causes some to descend to evil. It also has just a toiuch of science; while you can ignore this and just consider it a powerful explosive, it has the first mention of a chemical tetranitrotetrahedrane. That would be a really powerful explosive, if it could be made, but the more interesting point is why is that there?

The Fermi Paradox and Are We Alone in the Universe?

The Fermi paradox is something like this. The Universe is enormous, and there are an astronomical number of planets. Accordingly, the potential for intelligent life somewhere should be enormous, but we find no evidence of anything. The Seti program has been searching for decades and has found nothing. So where are these aliens?

What is fascinating about this is an argument from Daniel Whitmire, who teaches mathematics at the University of Arkansas and has published a paper in the International Journal of Astrobiology (doi:10.1017/S1473550417000271 ). In it, he concludes that technological societies rapidly exterminate themselves. So, how does he come to this conclusion. The argument is fascinating relating to the power of mathematics, and particularly statistics, to show or mislead.

He first resorts to a statistical concept called the Principle of Mediocrity, which states that, in the absence of any evidence to the contrary, any observation should be regarded as typical. If so, we observe our own presence. If we assume we are typical, and we have been technological for 100 years (he defines being technological as using electricity, but you can change this) then it follows that our being average means that after a further 200 years we are no longer technological. We can extend this to about 500 years on the basis that in terms of age a Bell curve is skewed (you cannot have negative age). To be non-technological we have to exterminate ourselves, therefore he concludes that technological societies exterminate themselves rather quickly. We may scoff at that, but then again, watching the antics over North Korea can we be sure?

He makes a further conclusion: since we are the first on our planet, other civilizations should also be the first. I really don’t follow this because he has also calculated that there could be up to 23 opportunities for further species to develop technologies once we are gone, so surely that follows elsewhere. It seems to me to be a rather mediocre use of this principle of mediocrity.

Now, at this point, I shall diverge and consider the German tank problem, because this shows what you can do with statistics. The allies wanted to know the production rate of German tanks, and they got this from a simple formula, and from taking down the serial numbers of captured or destroyed tanks. The formula is

N = m + m/n – 1

Where N is the number you are seeking, m is the highest sampled serial number and n is the sample size (the number of tanks). Apparently this was highly successful, and their estimations were far superior to intelligence gathering, which always seriously overestimated.

That leaves the question of whether that success means anything for the current problem. The first thing we note is the Germans conveniently numbered their tanks, and in sequence, the sample size was a tolerable fraction of the required answer (it was about 5%), and finally it was known that the Germans were making tanks and sending them to the front as regularly as they could manage. There were no causative aspects that would modify the results. With Whitmire’s analysis, there is a very bad aspect of the reasoning: this question of whether we are alone is raised as soon as we have some capability to answer it. Thus we ask it within fifty years of having reasonable electronics; for all we know they may still be asking it a million years in the future, so the age of technological society, which is used to base the lifetime reasoning, is put into the equation as soon as it is asked. That means it is not a random sample, but causative sample. Then on top of that, we have a sample of one, which is not exactly a good statistical sample. Of course if there were more samples than one, the question would answer itself and there would be no need for statistics. In this case, statistics are only used when they should not be used.

So what do I make of that? For me, there is a lack of logic. By definition, to publish original work, you have to be the first to do it. So, any statistical conclusion from asking the question is ridiculous because by definition it is not a random sample; it is the first. It is like trying to estimate German tank production from a sample of 1 and when that tank had the serial number 1. So, is there anything we can take from this?

In my opinion, the first thing we could argue from this Principle of Mediocrity is that the odds of finding aliens are strongest on earth-sized planets around G type stars about this far from the star, simply because we know it is at least possible. Further, we can argue the star should be at least about 4.5 billion years old, to give evolution time to generate such technological life. We are reasonably sure it could not have happened much earlier on Earth. One of my science fiction novels is based on the concept that Cretaceous raptors could have managed it, given time, but that still only buys a few tens of millions of years, and we don’t know how long they would have taken, had they been able. They had to evolve considerably larger brains, and who knows how long that would take? Possibly almost as long as mammals took.

Since there are older stars out there, why haven’t we found evidence? That question should be rephrased into, how would we? The Seti program assumes that aliens would try to send us messages, but why would they? Unless they were directed, to send meaningful signals over such huge distances would require immense energy expenditures. And why would they direct signals here? They could have tried 2,000 years ago, persisted for a few hundred years, and given us up. Alternatively, it is cheaper to listen. As I noted in a different novel, the concept falls down on economic grounds because everyone is listening and nobody is sending. And, of course, for strategic reasons, why tell more powerful aliens where you live? For me, the so-called Fermi paradox is no paradox at all; if there are aliens out there, they will be following their own logical best interests, and they don’t include us. Another thing it tells me is this is evidence you can indeed “prove” anything with statistics, if nobody is thinking.

What is nothing?

Shakespeare had it right – there has been much ado about nothing, at least in the scientific world. In some of my previous posts I have advocated the use of the scientific method on more general topics, such as politics. That method involves the rigorous evaluation of evidence, of making propositions in accord with that evidence, and most importantly, rejecting those that are clearly false. It may appear that for ordinary people, that might be too hard, but at least that method would be followed by scientists, right? Er, not necessarily. In 1962 Thomas Kuhn published a work, “The structure of scientific revolutions” and in it he argued that science itself has a very high level of conservatism. It is extremely difficult to change a current paradigm. If evidence is found that would do so, it is more likely to be secreted away in the bottom drawer, included in a scientific paper in a place where it is most likely to be ignored, or, if it is published, ignored anyway, and put in the bottom drawer of the mind. The problem seems to be, there is a roadblock towards thinking that something not in accord with expectations might be significant. With that in mind, what is nothing?

An obvious answer to the title question is that a vacuum is nothing. It is what is left when all the “somethings” are removed. But is there “nothing” anywhere? The ancient Greek philosophers argued about the void, and the issue was “settled” by Aristotle, who argued in his Physica that there could not be a void, because if there were, anything that moved in it would suffer no resistance, and hence would continue moving indefinitely. With such excellent thinking, he then, for some reason, refused to accept that the planets were moving essentially indefinitely, so they could be moving through a void, and if they were moving, they had to be moving around the sun. Success was at hand, especially if he realized that feathers did not fall as fast as stones because of wind resistance, but for some reason, having made such a spectacular start, he fell by the wayside, sticking to his long held prejudices. That raises the question, are such prejudices still around?

The usual concept of “nothing” is a vacuum, but what is a vacuum? Some figures from Wikipedia may help. A standard cubic centimetre of atmosphere has 2.5 x 10^19 molecules in it. That’s plenty. For those not used to “big figures”, 10^19 means the number where you write down 10 and follow it with 19 zeros, or you multiply 10 by itself nineteen times. Our vacuum cleaner gets the concentration of molecules down to 10^19, that is, the air pressure is two and a half times less in the cleaner. The Moon “atmosphere” has 4 x 10^5 molecules per cubic centimetre, so the Moon is not exactly in vacuum. Interplanetary space has 11 molecules per cubic centimetre, interstellar space has 1 molecule per cubic centimetre, and the best vacuum, intergalactic space, needs a million cubic centimetres to find one molecule.

The top of the Earth’s atmosphere, the thermosphere goes from 10^14 to 10^7. That is a little suspect at the top because you would expect it to gradually go down to that of interplanetary space. The reason there is a boundary is not because there is a sharp boundary, but rather it is the point where gas pressure is more or less matched by solar radiation pressure and that from solar winds, so it is difficult to make firm statements about further distances. Nevertheless, we know there is atmosphere out to a few hundred kilometres because there is a small drag on satellites.

So, intergalactic space is most certainly almost devoid of matter, but not quite. However, even without that, we are still not quite there with “nothing”. If nothing else, we know there are streams of photons going through it, probably a lot of cosmic rays (which are very rapidly moving atomic nuclei, usually stripped of some of their electrons, and accelerated by some extreme cosmic event) and possibly dark matter and dark energy. No doubt you have heard of dark matter and dark energy, but you have no idea what it is. Well, join the club. Nobody knows what either of them are, and it is just possible neither actually exist. This is not the place to go into that, so I just note that our nothing is not only difficult to find, but there may be mysterious stuff spoiling even what little there is.

However, to totally spoil our concept of nothing, we need to see quantum field theory. This is something of a mathematical nightmare, nevertheless conceptually it postulates that the Universe is full of fields, and particles are excitations of these fields. Now, a field at its most basic level is merely something to which you can attach a value at various coordinates. Thus a gravitational field is an expression such that if you know where you are and if you know what else is around you, you also know the force you will feel from it. However, in quantum field theory, there are a number of additional fields, thus there is a field for electrons, and actual electrons are excitations of such fields. While at this point the concept may seem harmless, if overly complicated, there is a problem. To explain how force fields behave, there needs to be force carriers. If we take the electric field as an example, the force carriers are sometimes called virtual photons, and these “carry” the force so that the required action occurs. If you have such force carriers, the Uncertainty Principle requires the vacuum to have an associated zero point energy. Thus a quantum system cannot be at rest, but must always be in motion and that includes any possible discrete units within the field. Again, according to Wikipedia, Richard Feynman and John Wheeler calculated there was enough zero point energy inside a light bulb to boil off all the water in the oceans. Of course, such energy cannot be used; to use energy you have to transfer it from a higher level to a lower level, when you get access to the difference. Zero point energy is at the lowest possible level.

But there is a catch. Recall Einstein’s E/c^2 = m? That means according to Einstein, all this zero point energy has the equivalent of inertial mass in terms of its effects on gravity. If so, then the gravity from all the zero point energy in vacuum can be calculated, and we can predict whether the Universe is expanding or contracting. The answer is, if quantum field theory is correct, the Universe should have collapsed long ago. The difference between prediction and observation is merely about 10^120, that is, ten multiplied by itself 120 times, and is the worst discrepancy between prediction and observation known to science. Even worse, some have argued the prediction was not right, and if it had been done “properly” they justified manipulating the error down to 10^40. That is still a terrible error, but to me, what is worse, what is supposed to be the most accurate theory ever is suddenly capable of turning up answers that differ by 10^80, which is roughly the same as the number of atoms in the known Universe.

Some might say, surely this indicates there is something wrong with the theory, and start looking elsewhere. Seemingly not. Quantum field theory is still regarded as the supreme theory, and such a disagreement is simply placed in the bottom shelf of the minds. After all, the mathematics are so elegant, or difficult, depending on your point of view. Can’t let observed facts get in the road of elegant mathematics!