Book Discounts

From December 25 through to January 1, my books on Smashwords will be significantly discounted, and one free. To view the books go to https://www.smashwords.com/profile/view/IanMiller

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Leaders failing.

Leadership is an interesting concept, and I have tried to make it the centrepiece of some of my novels, without being too obvious. The leader may appear to be obvious, but recall just because someone is in front and there are a lot behind does not mean the one in front is leading. The others could be queuing up for a backstab! And the bigger the problem, the easier it is for a leader to fail. Brexit is a clear failure of leadership. In the first place, Britain was comfortable in Europe. There were the inevitable politicians who wanted out, but there was no pressing issue requiring an immediate vote. The politicians who called it really wanted to stay in, so first, why did they call it, and second, if they felt they had to call the vote, why did they not wait until they had mounted a campaign that made it much more likely they would succeed? Having called it, they then should have campaigned hard to maximise their chances of winning. Instead, they went through the motions, and seemed like stunned mullets when they lost. They then accused the other side’s campaign of being full of lies. That might make them feel better, but if it were true, why did they not point out the lies during the campaign? Did it not occur to them that when the voters voted the way they did, just maybe what the politicians and their rich friends wanted was not representing what the voters wanted?

As for how to go about it, there are at least two pieces of advice from Sun Tzu that should have gone to the top of the list: first, know thyself, and second, know the adversary. The second one is a little more difficult but the first should be mandatory. Accordingly, the first step must be to decide whether to leave, i.e.whether to honour the referendum, and whatever you decide must be final. At first sight it might look like they did that, but nevertheless a lot of the politicians have been hoping some reason will arise whereby they can flag the whole thing away and stay. What I think Theresa May should have done was to individually make each member of her own party pledge to honour the referendum, and to work for the betterment of Britain, or resign. If they refused to do either, then she needed to call an election, and ensure those who refused to go by the decision of the party were prevented from standing for the party. That could effectively be a second referendum, but it is pointless to continue when about a third of your team are busily trying to undermine you. In any case, she called an election without anything to do with Brexit, and that was not a fortunate result for her. Had she got her party to commit, when she went to Europe she could say Brexit is going to happen, no matter what. What we are now discussing is what our relations will be then.

That leaves the question of negotiation. I have done a little of this with a multinational company that lead to two joint ventures, so I have some knowledge of what is required. The very first step is to meet with your own team and get agreement on what the bottom lines are going to be. These are the things that if you do not get them, you walk away from the negotiations. It is important that these are extremely important, and there must not be many of them. These are NOT to be used to gain an advantage over the opposition, and they are not to try to force the other side to give something up. They are simply the things that make walking inevitable. For the Brexit negotiations, one of those required bottom lines might be the question of Ireland; whatever the outcome, Northern Ireland must continue to be treated the same way as the rest of the UK. That they never recognised this until apparently now meant that they have got themselves into a position where it is difficult to see how they can progress the way they wish to progress. If you tell the opposition that something is a bottom line, and it is a reasonable one, then they will accept it and try to work around it if they want to negotiate.

Which gets to the next point: each side has to see an advantage in the end position. To some extent, Europe cannot help but see Brexit as a negative, so the emphasis has to be to determine what advantages there are for Europe for what the UK wants. That means there have to be concessions, and here the UK have made many. However, there also has to be a clear point at which if the opposition wants too much, you have to be able to say no and walk. And one of the most important points is that when you represent your team, the other side must believe that all the team will stand behind you. Of course there are also times when you must say, “I must consult my team,” over something. The leader must never wing it, other than for minor issues.

The EU leaders have also failed. They have done their best to get everything they could, which is all very well, but if they demand so much that the whole becomes unpalatable, they too end up with nothing. What they have failed to recognise is the person fronting for Britain was not really leading. So far Britain has made quite a lot of future concessions regarding payments of this and that. No deal means all those billions of pounds are lost to the EU. The EU can also lose, and the tragedy is, the various failures of the leaders have most likely ended with a lose-lose scenario.

To change the subject entirely, Christmas is near, so I wish you all a very Merry Christmas, and all the best for 2019. This will be my last post for the year, and I shall resume mid January.

Book Discount

From December 13 – 20, Miranda’s Demonswill be discounted to 99c on Amazon in the US and UK. In 2285, the 34 exhausts of a badly mauled alien battle fleet are seen travelling at relativistic velocities to end on Miranda, the innermost moon of Uranus. Representatives of a Terran Corporation accidentally meet two aliens on Mars and do a deal: give us Mars and we shall give you the slave labour and metals you need to repair your ships. Natasha Kotchetkova, the Commissioner for Defence is faced with an alien race that totally outclasses any Earth military technology.  War is coming, but even if Terran forces can win, who wins the following peace? Meanwhile, Scaevola has followed the aliens, and arrives on Earth to meet his prophesied “second woman in his life: the ugliest woman in the world”.

A hard science fiction epic with 18 major characters, four alien races, several romances, not all of which end well, treachery, and is set variously in 3 continents, the Earth-Moon L-4 space station, Mars, Iapetus, the asteroid belt and Miranda. Book IV of a series, but originally written as a stand-alone.

http://www.amazon.com/dp/B00ZH851G8

International Tension

There have been two situations on the international scene lately that have the potential to bring the close of 2018 into the likelihood of a serious deterioration in international peace and prosperity, although the first is probably going to be put to one side after more arm-waving and pontificating. This one involves three Ukrainian naval vessels trying to get from the Black Sea to the Sea of Azov, and in particular to their port of Mariupol, the port for south east Ukraine. These vessels were stopped, some by ramming, and arrested by the Russian coastguard, possibly the navy, and FSB officers. The incident occurred at a place that would be within the territorial waters of Russia, although Ukraine does not recognize Crimea as being part of Russia, which would alter the argument. Ukraine states that it started just outside such territorial waters, but has not provided accurate and detailed coordinates and in any case the Ukrainian ships proceeded into clear territorial waters. There is apparently a 2003 agreement that the Kerch Strait is a shared waterway, which allows free passage.

This has created the usual heat and not much light. Time magazine had an opinion by retired US Admiral Stavridis that makes a number of interesting statements. The first is that Putin more or less engineered this because the Mueller investigation is “coming to a head” (really?) and there was a need for the US to persuade its allies to take a firmer stand with Russia. (How does the second follow from the first?) Also the US should bolster Ukrainian defence, presumably to make Putin regret engineering this. Leave aside the bluster, notice anything? The Ukrainian ships had to enter the waters around the Kerch strait, so Ukraine controlled the timing. That makes it difficult for Putin to have engineered it. A further statement was that Russia needed to secure communications and control this Strait “to truly consolidate Crimea”. Needless to say, what is missing from this article is the fact that Russia has secured communication by building a bridge across the Strait. Access to the Sea of Azov requires passing under the bridge, which involves a relatively narrow piece of waterway. As an Admiral, he should know something about ship handling. Do you want two ships coming head-on into a very narrow choke-point? The Russians argue that anyone can pass through, but they must register the intention so that traffic control can be maintained. That seems reasonable to me. The Ukrainian sailors apparently have said they did not register, and they were ordered to ignore Russian controls. Form your own opinion, but it seems to me that Ukraine was deliberately trying to prod Russia. Why? Well, one theory is that Ukrainian elections are due in a few months, Poroshenko currently would be lucky to get 25% of the vote, so why not generate a foreign crisis? The significant point about this, for me, is the US position as stated by this Admiral: what is stated is at best half-truths, and the really important information is left out.

The second incident was that Meng Wanzhou, the Chief Financial Officer of Huawei, has been arrested at Vancouver airport in order that she be extradited to the US to face unspecified crimes, but ones that probably relate to the fact that Huawei is selling telecommunications equipment to Iran. That is about all we know for sure, but apparently John Bolton knew this could occur in advance and presumably approved of it.

Going back a bit, a number of countries signed a deal with Iran that they would trade with it if Iran agreed not to proceed with the development of nuclear weapons. The US then pulled out of the deal, seemingly on the basis  that Trump believes that if when a deal has been struck, if he then pulls out at some future random time he can add more concessions to make a new deal more favourable to himself. Iran has refused Trump’s rhetoric, which is basically to side with Saudi Arabia against Iran. So the US imposed sanctions against Iran, and has stated it will sanction anyone else who deals with Iran. A number of other signatories did not impose sanctions when Iran has seemingly complied with the deal. The EU has stated that the EU will continue to trade with Iran as long as it maintains its part of the nuclear weapons deal. Thus the usual explanation for Meng’s arrest is that Huawei is breaking US sanctions by supplying to Iran. If this is so, does this not introduce a rather ugly precedent?

Thus we have the situation where if another country continues with a deal that the US joined, but then arbitrarily pulled out of, then the US requires the other countries to follow the US dictates, and if they do not, the US will arrest their citizens. That makes the president of the US almost able to dictate to the rest of the world.

Huawei is having a bad time, thanks to the US. A number of countries have been told by the US they should not implement Huawei 5G technology for undefined security reasons. As far as security goes, why does the US feel its technology is so secure? If it is secure, why are various politicians making continual assertions of election hacking? As it happens Huawei 5G technology appears to be more advanced than any US technology in telecommunications, and this has the ugly theme of if you can’t compete fairly, you will bully the opposition. This to me is the misuse of power. However, China is not really a country that will bow down to bullying. Apparently China had made concessions to Trump to buy more US exports before they knew about this arrest. What is the bet this won’t go ahead? But worse than that, by what right do you arrest a citizen of another country who is following the law of the country they live in just because (a) that country is in a spat with the US, and (b) the person was apparently in a transit lounge. A person cannot follow two contradictory laws, so why does the US think its Presidential edicts prevail everywhere?

Phlogiston – Early Science at Work

One of the earlier scientific concepts was phlogiston, and it is of interest to follow why this concept went wrong, if it did. One of the major problems for early theory was that nobody knew very much. Materials had properties, and these were referred to as principles, which tended to be viewed either as abstractions, or as physical but weightless entities. We would not have such difficulties, would we? Um, spacetime?? Anyway, they then observed that metals did something when heated in air:

M   + air +  heat        ÞM(calx) ±  ???  (A calx was what we call an oxide.)

They deduced there had to be a metallic principle that gives the metallic properties, such as ductility, lustre, malleability, etc., but they then noticed that gold refuses to make a calx, which suggested there was something else besides the metallic principle in metals. They also found that the calx was not a mixture, thus rust did not lead to iron being attached to a lodestone. This may seem obvious to us now, but conceptually this was significant. For example, if you mix blue and yellow paint, you get green and they cannot readily be unmixed, nevertheless it is a mixture. Chemical compounds are not mixtures, even though you might make them by mixing two materials. Even more important was the work by Paracelsus, the significance of which is generally overlooked. He noted there were a variety of metals, calces and salts, and he generalized that acid plus metal or acid plus metal calx gave salts, and each salt was specifically different, and depended only on the acid and metal used. He also recognized that what we call chemical compounds were individual entities, that could be, and should be, purified.

It was then that Georg Ernst Stahl introduced into chemistry the concept of phlogiston. It was well established that certain calces reacted with charcoal to produce metals (but some did not) and the calx was usually heavier than the metal. The theory was, the metal took something from the air, which made the calx heavier. This is where things became slightly misleading because burning zinc gave a calx that was lighter than the metal. For consistency, they asserted it should have gained but as evidence poured in that it had not, they put that evidence in a drawer and did not refer to it. Their belief that it should have was correct, and indeed it did, but this avoiding the “data you don’t like” leads to many problems, not the least of which include “inventing” reasons why observations do not fit the theory without taking the trouble to abandon the theory. This time they were right, but that only encourages the act. As to why there was the problem, zinc oxide is relatively volatile and would fume off, so they lost some of the material. Problems with experimental technique and equipment really led to a lot of difficulties, but who amongst us would do better, given what they had?

Stahl knew that various things combusted, so he proposed that flammable substances must contain a common principle, which he called phlogiston. Stahl then argued that metals forming calces was in principle the same as materials like carbon burning, which is correct. He then proposed that phlogiston was usually bound or trapped within solids such as metals and carbon, but in certain cases, could be removed. If so, it was taken up by a suitable air, but because the phlogiston wanted to get back to where it came from, it got as close as it could and took the air with it. It was the phlogiston trying to get back from where it came that held the new compound together. This offered a logical explanation for why the compound actually existed, and was a genuine strength of this theory. He then went wrong by arguing the more phlogiston, the more flammable the body, which is odd, because if he said some but not all such materials could release phlogiston, he might have thought that some might release it more easily than others. He also argued that carbon was particularly rich in phlogiston, which was why carbon turned calces into metals with heat. He also realized that respiration was essentially the same process, and fire or breathing releases phlogiston, to make phlogisticated air, and he also realized that plants absorbed such phlogiston, to make dephlogisticated air.

For those that know, this is all reasonable, but happens to be a strange mix of good and bad conclusions. The big problem for Stahl was he did not know that “air” was a mixture of gases. A lesson here is that very seldom does anyone single-handedly get everything right, and when they do, it is usually because everything covered can be reduced to a very few relationships for which numerical values can be attached, and at least some of these are known in advance. Stahl’s theory was interesting because it got chemistry going in a systemic way, but because we don’t believe in phlogiston, Stahl is essentially forgotten.

People have blind spots. Priestley also carried out Lavoisier’s experiment:  2HgO  + heat   ⇌   2Hg  + O2and found that mercury was lighter than the calx, so argued phlogiston was lighter than air. He knew there was a gas there, but the fact it must also have weight eluded him. Lavoisier’s explanation was that hot mercuric oxide decomposed to form metal and oxygen. This is clearly a simpler explanation. One of the most important points made by Lavoisier was that in combustion, the weight increase of the products exactly matched the loss of weight by the air, although there is some cause to wonder about the accuracy of his equipment to get “exactly”. Measuring the weight of a gas with a balance is not that easy. However, Lavoisier established the fact that matter is conserved, and that in chemical reactions, various species react according to equivalent weights. Actually, the conservation of mass was discovered much earlier by Mikhail Lomonosov, but because he was in Russia, nobody took any notice. The second assertion caused a lot of trouble because it is not true without a major correction to allow for valence. Lavoisier also disposed of the weightless substance phlogiston simply by ignoring the problem of what held compounds together. In some ways, particularly in the use of the analytical balance, Lavoisier advanced chemistry, but in disposing of phlogiston he significantly retarded chemistry.

So, looking back, did phlogiston have merit as a concept? Most certainly! The metal gives off a weightless substance that sticks to a particular gas can be replaced with the metal gives off an electron to form a cation, and the oxygen accepts the electron to form an anion. Opposite charges attract and try to bind together. This is, for the time, a fair description of the ionic bond. As for weightless, nobody at the time could determine the weight difference between a metal and a metal less one electron, if they could work out how to make it. Of course the next step is to say that the phlogiston is a discrete particle, and now valence falls into place and modern chemistry is around the corner. Part of the problem there was that nobody believed in atoms. Again, Lomonosov apparently did, but as I noted above, nobody took any notice of him. Of course, is it is far easier to see these things in retrospect. My guess is very few modern scientists, if stripped of their modern knowledge and put back in time would do any better. If you think you could, recall that Isaac Newton spent a lot of time trying to unravel chemistry and got nowhere. There are very few ever that are comparable to Newton.

Is Science in as Good a Place as it Might Be?

Most people probably think that science progresses through all scientists diligently seeking the truth but that illusion was was shattered when Thomas Kuhn published “The Structure of Scientific Revolutions.” Two quotes:

(a) “Under normal conditions the research scientist is not an innovator but a solver of puzzles, and the puzzles upon which he concentrates are just those which he believes can be both stated and solved within the existing scientific tradition.”

(b) “Almost always the men who achieve these fundamental inventions of a new paradigm have been either very young or very new to the field whose paradigm they change. And perhaps that point need not have been made explicit, for obviously these are the men who, being little committed by prior practice to the traditional rules of normal science, are particularly likely to see that those rules no longer define a playable game and to conceive another set that can replace them.”

Is that true, and if so, why? I think it follows from the way science is learned and then funded. In general, scientists gain their expertise by learning from a mentor, and if you do a PhD, you work for several years in a very narrow field, and most of the time the student follows the instructions of the supervisor. He will, of course, discuss issues with the supervisor, but basically the young scientist will have acquired a range of techniques when finished. He will then go on a series of post-doctoral fellowships, generally in the same area because he has to persuade the new team leaders he is sufficiently skilled to be worth hiring. So he gains more skill in the same area, but invariably he also becomes more deeply submerged in the standard paradigm. At this stage of his life, it is extremely unusual for the young scientist to question whether the foundations of what he is doing is right, and since most continue in this field, they have the various mentors’ paradigm well ingrained. To continue, either they find a company or other organization to get an income, or they stay in a research organization, where they need funding. When they apply for it they keep well within the paradigm; first, it is the easiest way for success, and also boat rockers generally get sunk right then. To get funding, you have to show you have been successful; success is measured mainly by the number of scientific papers and the number of citations. Accordingly, you choose projects that you know will work and shuld not upset any apple-carts. You cite those close to you, and they will cite you; accuse them of being wrong and you will be ignored, and with no funding, tough. What all this means is that the system seems to have been designed to generate papers that confirm what you already suspect. There will be exceptions, such as “discovering dark matter” but all that has done so far is to design a parking place for what we do not understand. Because we do  not understand, all we can do is make guesses as to what it is, and the guesses are guided by our current paradigm, and so far our guesses are wrong.

One small example follows to show what I mean. By itself, it may not seem important, and perhaps it isn’t. There is an emerging area of chemistry called molecular dynamics. What this tries to do is to work out is how energy is distributed in molecules as this distribution alters chemical reaction rates, and this can be important for some biological processes. One such feature is to try to relate how molecules, especially polymers, can bend in solution. I once went to hear a conference presentation where this was discussed, and the form of the bending vibrations was assumed to be simple harmonic because for that the maths are simple, and anyhting wrong gets buried in various “constants”. All question time was taken up by patsy questions from friends, but I got hold of the speaker later, and pointed out that I had published paper a long time previously that showed the vibrations were not simple harmonic, although that was a good approximation for small vibrations. The problem is that small vibrations are irrelevant if you want to see significant chemical effects; they come from large vibrations. Now the “errors” can be fixed with a sequence of anharmonicity terms, each with their own constant, and each constant is worked around until the desired answer is obtained. In short you get the asnswer you need by adjusting the constants.

The net result is, it is claimed that good agreement with observation is found once the “constants” are found for the given situation. The “constants” appear to be only constant for a given situation, so arguably they are not constant, and worse, it can be near impossible to find out what they are from the average paper. Now, there is nothing wrong with using empirical relationships since if they work, they make it a lot easier to carry out calculations. The problem starts when, if you do not know whyit works, you may use it under circumstances when it no longer works.

Now, before you say that surely scientists want to understand, consider the problem for the scientist: maybe there is a better relationship, but to change to use it would involve re-writing a huge amount of computer code. That may take a year or so, in which time no publications are generated, and when the time for applications for further funding comes up, besides having to explain the inactivity, you have to explain why you were wrong before. Who is going to do that? Better to keep cranking the handle because nobody is going to know the difference. Does this matter? In most cases, no, because most science involves making something or measuring something, and most of the time it makes no difference, and also most of the time the underpinning theory is actually well established. The NASA rockets that go to Mars very successfully go exactly where planned using nothing but good old Newtonian dynamics, some established chemistry, some established structural and material properties, and established electromagnetism. Your pharmaceuticals work because they have been empirically tested and found to work (at least most of the time).

The point I am making is that nobody has time to go back and check whether anything is wrong at the fundamental level. Over history, science has been marked by a number of debates, and a number of treasured ideas overthrown. As far as I can make out, since 1970, far more scientific output has been made than in all previous history, yet there have been no fundamental ideas generated during this period that have been accepted, nor have any older ones been overturned. Either we have reached a stage of perfection, or we have ceased looking for flaws. Guess which!

What is Dark Matter?

First, I don’t know what dark matter is, or even if it is, and while they might have ideas, neither does anyone else know. However, the popular press tells us that there is at least five times more of this mysterious stuff in the Universe than ordinary matter and we cannot see it. As an aside, it is not “dark”; rather it is transparent, like perfect glass. The reason is light does not interact with it, nevertheless we also know that there are good reasons for thinking that something is there because assuming our physics are correct, certain things should happen, and they do not happen as calculated. The following is a very oversimplified attempt at explaining the problem.

All mass exerts a force on other mass called gravity. Newton produced laws on how objects move according to forces, and he outlined an equation for how gravity operates. If we think about energy, follow Aristotle as he considered throwing a stone into the air. First we give the stone kinetic energy (that is the energy of motion) but as it goes up, it slows down, stops, and then falls back down. So what happened to the original energy? Aristotle simply said it passed away, but we now say it got converted to potential energy. That permits us to say that the energy always stayed the same. Note we can never see potential energy; we say it is there because in makes the conservation of energy work. The potential energy for a mass munder the gravitational effect of a mass Mis given by V = GmM/r. Gis the gravitational constant and ris the distance between them.

When we have three bodies, we cannot solve the equations of motion, so we have a problem. However, the French mathematician Lagrange showed that any such system has a function that we call a Lagrangian, in his honour, and this states that the difference between the total kinetic and potential energies equals this term. Further, provided we know the basic function for the potential energy, we can derive the virial theorem from this Lagrangian, and for gravitational interactions, the average kinetic energy has to be half the magnitude of the potential energy.

So, to the problem. As the potential energy drops off with distance from the centre of mass, so must the kinetic energy, which means that velocity of a body orbiting a central mass must slow down as the distance from the centre increases. In our solar system Jupiter travels much more slowly than Earth, and Neptune is far slower still. However, when measurements of the velocity of stars moving in galaxies were made, there was a huge surprise: the stars moving around the galaxy have an unexpected velocity distribution, being slowest near the centre of the galaxy, then speeding up and becoming constant in the outer regions. Sometimes the outer parts are not quite constant, and a plot of speed vs distance from the centre rises, then instead of flattening, has wiggles. Thus they have far too much velocity in the outer regions of the galactic disk. Then it was found that galaxies in clusters had too much kinetic energy for any reasonable account of the gravitational potential energy. There are other reasons why things could be considered to have gone wrong, for example, gravitational lensing with which we can discover new planets, and there is a problem with the cosmic microwave background, but I shall stick mainly with galactic motion.

The obvious answer to this problem is that the equation for the potential is wrong, but where? There are three possibilities. First, we add a term Xto the right hand side, then try to work out what Xis. Xwill include the next two alternatives, plus anything else, but since it is essentially empirical at this stage, I shall ignore it in its own right. The second is to say that the inverse dependency on ris wrong, which is effectively saying we need to modify our law of gravity. The problem for this is that Newton’s gravity works very well right out to the outer extensions of the solar system. The third possibility is there is more mass there than we expect, and it is distributed as a halo around the galactic centre. None of these are very attractive, but the third option does save the problem of why gravity does not vary from Newtonian law in our solar system (apart from Mercury). We call this additional mass dark matter.

If we consider modified Newtonian gravity (MOND), this starts with the proposition that with a certain acceleration, the force takes the form where the radial dependency on the potential contained a further term that was proportional to the distance rthen it reached a maximum. MOND has the advantage that it predicts naturally the form to the velocity distribution and its seeming constancy between galaxies. It also provides a relationship for the observed mass and the rate of rotation of a galaxy, and this appears to hold. Further, MOND predicts that for a star, when its acceleration reaches a certain level, the dynamics revert to Newtonian, and this has been observed. Dark matter has a problem with this. On the other hand, something like MOND has real trouble trying to explain the wiggly structure of velocity distributions in certain galaxies, it does not explain the dynamics of galaxy clusters, it has been claimed it offers a poor fit for velocities in globular clusters, the predicted rotations of galaxies are good, but they require different values of what should be constant, and it does not apply well to colliding galaxies. Of course we can modify gravity in other ways, but however we do it, it is difficult to fit it with General Relativity without a number of ad hocadditions, and there is no real theoretical reason for the extra terms required to make it work. General Relativity is based on ten equations, and to modify it, you need ten new terms to be self-consistent; the advantage of dark matter is you only need 1.

The theory that the changes are due to dark matter has to assume that each galaxy has to incorporate dark matter roughly proportional to its mass, and possibly has to do that by chance. That is probably it biggest weakness, but it has the benefit that it assumes all our physics are more or less right, and what has gone wrong is there is a whole lot of matter we cannot see. It predicts the way the stars rotate around the galaxy, but that is circular reasoning because it was designed to do that. It naturally predicts that not all galaxies rotate the same way, and it permits the “squiggles” in the orbital speed distribution, again because in each case you assume the right amount of dark matter is in the right place. However, for a given galaxy, you can use the same dark matter distribution to determine motion of galaxy clusters, the gas temperature and densities within clusters, and gravitational lensing, and these are all in accord with the assumed amount of dark matter. The very small anisotropy of the cosmic microwave background also fits in very well with the dark matter hypothesis, and not with modified gravity.

Dark matter has some properties that limit what it could be. We cannot see it, so it cannot interact with electromagnetic radiation, at least to any significant extent. Since it does not radiate energy, it cannot “cool” itself, therefore it does not collapse to the centre of a galaxy. We can also put constraints on the mass of the dark matter particle (assuming it exists) from other parts of physics, by how it has to behave. There is some danger in this because we are assuming the dark matter actually follows those relationships, and we cannot know that. However, with that kept in mind, the usual conclusions are that it must not collide frequently, and it should have a mass larger than about 1 keV. That is not a huge constraint, as the electron has a mass of a little over 0.5 MeV, but it says the dark matter cannot simply be neutrinos. There is a similar upper limit in that because the way gravitational lensing works, it cannot really be a collection of brown dwarfs. As can be seen, so far there are no real constraints on the mass of the dark matter constituent particles.

So what is the explanation? I don’t know. Both propositions have troubles, and strong points. The simplest means of going forward would be to detect and characterize dark matter, but unfortunately our inability to do this does not mean that there is no dark matter; merely that we did not detect it with that technique. The problem in detecting it is that it does not do anything, other than interact gravitationally. In principle we might detect it when it collides with something, as we would see an effect on the something. That is how we detect neutrinos, and in principle you might think dark matter would be easier because it has a considerably higher mass. Unfortunately, that is wrong, because the neutrino usually travels at near light speed; if dark matter were much larger, but much slower, it would be equally difficult to detect, if not more so. So, for now nobody knows.

Just to finish, a long shot guess. In the late 20th century, a German physicist B Heim came up with a theory of elementary particles. This is largely ignored in favour of the standard model, but Heim’s theory produces a number of equations that are surprisingly good at calculating the masses and lifetimes of elementary particles, both of which are seemingly outside the scope of the standard model. One oddity of his results is he predicts a “neutral electron” with a mass slightly greater than the electron and with an infinite lifetime. If matter and antimatter originally annihilated and left a slight preponderance of matter, and if this neutral electron is its own antiparticle, then it would survive, and although it is very light, there would be enough of it to explain why its total mass now is so much greater than matter. In short Heim predicted a particle that is exactly like dark matter. Was he right? Who knows? Maybe this problem will be solved very soon, but for now it is a mystery.