Maxwell's demon

It often happens that scientists need to use metaphors for explaining their point to other scientists and the general public. This is how many mysterious fantastic creatures are born. Many of these creatures were fabricated during the debates on the Second Law of Thermodynamics. Undoubtedly,  the most popular of all those creatures was Maxwell demon – a product of a thought experiment created by the physicist James Clerk Maxwell, the author of the famous Maxwell's equations that accurately describe the electromagnetic field.

Since 1871, Maxwell's demon had occupied the great minds of science. Scientists still look for processes which would allow heat to pass from less hot bodies to hotter bodies. Of course, all of us (or at least those of us who still remember our physics classes) know that heat can be passed from hot to cold bodies. The paradigm called the Second Law of Thermodynamics seemed irrefutable until it was challenged by the existence of Maxwell’s demon.

The idea of Maxwell’s demon is very simple: imagine a sealed container, divided into two gas-tight parts with by the wall with door that would allow just one gas atom to pass through it. At the beginning of the experiment, the upper part of the vessel contains gas, and at the bottom part is filled with vacuum. The door in the middle of the wall dividing both parts is guarded by an imaginary microscopic janitor who is vigilantly watching over molecules. The janitor would allow fast molecules to go through the door to the bottom of the container, while the slow molecules are left in the top half. Clearly, if such a watchman is on duty at the door for a long time, the gas will be divided into two parts: in the upper part of the container there would be cold gas contained of slow molecules, and in the bottom part of the container there would be hot gas consisting of fast molecules. This mythical janitor opening and closing the door was nicknamed “Maxwell's demon”.

Maxwell's demon has such special powers that he can monitor every single molecule in its movements and recognize its speed. He opens the door only to fast or slow molecules, forcing them to move to different parts of the container. Thus, in one part of the container the temperature and pressure are getting higher than in the other which yields the unlimited supply of energy at no costs. In case Maxwell's demon remains on duty forever (or several Maxwell’s demons do shifts), the container can be turned into full-functioning “perpetuum mobile”.

Many prominent scientists argue that Maxwell's demon was merely a joke of the great physicist. Indeed, Maxwell's demon is not effective in a container with two molecules. In that case, all molecules might end up in just one part of the container to begin with. However, if the number of molecules is high, the probability of such a case is extremely small.

Maxwell’s demon keeps occupying many scientists’ minds. Not long ago, there was an article published on that issue in one scientific journal that explains the existence of Maxwell's demon in a form of a quantum oscillator, a laser which separates the molecules with high energy from the low-energy molecules.

Recently, the debate on the existence or non-existence of Maxwell's demon was enforced by the quantum entanglement theory that aims at developing supercomputers, instant Internet and even teleporting devices. In their recent paper Japanese physicists showed that quantum effects make information translation into energy to be more efficient than previously thought. Although their paper was not yet accepted for publication, its pre-print is available at Cornell University’s archive and can be downloaded here: http://arxiv.org/abs/1207.6872.

The Japanese scientists’ major innovation is the introduction of quantum entanglement into Maxwell’s experiment. In their extension of Maxwell’s experiment, there were two vessels with quantum entangled particles. By measuring the rate of only one of these particles, one can obtain information about the other. If all the particles in the experiment are entangled in pairs, this means that the demon will need only half of the time to recognize the nature of the particle than in the case of classical particles. The authors performed statistical calculations that take this into account and showed quantum entanglement would effectively increase the performance of Maxwell’s demon.

So far, no one has proved whether Maxwell’s demon exists or whether it is just a myth. But one thing is certain - Maxwell's demon might help scientists to heat up the interest in further research in natural sciences!

Happy Halloween everyone!

EL and WS

Something wicked this way comes...

Is everyone looking forward to the forthcoming Halloween? The 'All Hallows Evening' is at our doorstep and everyone is preparing for trick-or-treating, brushing off their scary costumes, renting horror movies, carving pumpkins and generally intending to have fun.

We were told that the apple harvest this year was enormous. Apart from making plenty of traditional apple pies and cider (ah, we all love that, don't we?), one can do the traditional Halloween thing - the apple bobbing. Apple bobbing is a very old tradition that dates back to the Roman conquest of Britain, when the old Celtic customs of worshiping the pentagram (yeah, this is right: many nations worshiped the five-pointed star, with the Soviets being the latest addition to that tribe) was fused with the new Roman tradition of fruit goddess Pomona (it is rumored that the Romans were actually the ones who introduced the apple tries to Britain after all). You see, when the apple is cut, a pentagram-shaped form is revealed. Thence, apples gained respect and popularity among the Celts and have been consumed in a pie or as a cider ever since. This is quite interesting, since the Romans preferred their wine and never learned to fiddle with their apples so much. 
Anyways, apple bobbing is a game when the large tub is filled with water and several apples are left floating on the surface. The players try to catch the apples with their teeth (which makes this game not very hygienic and thence not very attractive to some people), while they also try not to fall into the tub (unfortunately, this happens sometimes, as for example in Agatha Christie's 'Hallowe'en Party', in which poor Joyce Reynolds drowned in the tub). 

Well, as the Halloween approaches, we are glad to announce that we also have a Halloween gift for you. Hereby, we are glad to present the recent fruit of our supernatural economics activities: in November a journal called 'Modern Economy' will publish our article (co-authored by Dr. Welkins). The article that is a study investigating the possibility of peaceful co-habitation of humans and vampires, can be downloaded here. Read and enjoy! There is more to come, of course, and we will be posting some other interesting and scary things right before Halloween! Stay tuned, stay away from the tubs and follow 'Supernatural Economics'!

WS and EL

Karl Marx: Vampire Hunter?

Karl Marx: Vampire Hunter?

Did you know that the works of Karl Marx and his followers are full of mentioning of vampires? It has been calculated that Marx used the vampire metaphor at least three times in Capital. For example, in one of the cases Marx describes British industry as “vampire-like” which “could but live by sucking blood, and children’s blood too”. Here is another quote: "“Capital is dead labour which, vampire-like, lives only by sucking living labour, and lives the more, the more labour it sucks".

Marx’s colleague and long-time sponsor Frederick Engels also used the vampire metaphor in his works and public addresses. In one of his works entitled The Condition of the Working Class in England, Engels identifies and blames the “vampire property-holding class” as the source of "all the social troubles".

Marx’s and Engel’s perception of vampires corresponds very much to the recent Hollywood film Abraham Lincoln: Vampire Hunter directed by Timur Bekmambetov. In the film, based on the eponymous book by Seth Grahame-Smith, the 16^th president of the United States leads a secret life of a vampire hunter searching and destroying vampires. Vampires in the film supported slave trade and intended to start the Civil War to conquer the North and enslave all American population. In his secret diary, Abraham Lincoln writes that those vampires are “virtually everywhere” - layers, bankers, shop owners, in short the bourgeoisie accused by Marx and Engels of blood thirst.

Marx described vampires’ habits, their greediness and their lounging for blood in such a detail that in many cases it crossed the boundaries of the mere metaphor. Although many researchers perceive Marx’s vampires as metaphoric abstract bourgeois bloodsuckers feeding on working people, his knowledge of vampires is very peculiar. In one particular case, when describing Wallachian peasants performing forced labour for their boyars, Marx refers to one specific “boyar” who was “drunk with victory” and who might have been no one but Wallachian prince Vlad (called “The Impaler”) – or Count Dracula himself!

All this is very interesting because the best-known novel of vampiric genre, Bram Stoker’s Dracula, did not see the daylight until 1897, the whole 14 years after Marx’s death. Surely, one can place the Marx’s metaphor in the wider context of nineteenth-century gothic and horror stories which were abundant these days, and of which Marx was a huge fan. On the other hand, one might assume that some of the vampire legends were true and Marx and his contemporaries were aware of that.

A time travel paradox

Who of us has never dreamed of time travel? Seeing your own grandfather as a child, correcting mistakes of the past or ameliorating the future – all these ideas can be found in sci-fi literature in a great abundance.

However, there are not just writers who endorse these ideas. Scientists also indulge themselves with plans of building some elaborate time travel device. From time to time the world of science is shaken by the new hypotheses that allegedly prove the possibility of time travel (either to the past or to the future) without contradicting the laws of nature.
One of these hypotheses was presented to the public in 1934 in a story “Branches of Time” by David Daniels. In his book “Time travel and other mathematical bewilderments” Martin Gardner puts this in like that: “The basic idea is as simple as it is fantastic. Persons can travel to any point in the future of their universe, with no complications, but the moment they enter the past, the universe splits into two parallel worlds, each with its own time track. Along one track rolls the world as if no looping had occurred. Along the other track spins the newly created universe, its history permanently altered. When I say "newly created," I speak, of course, from the standpoint of the time traveller’s consciousness. For an observer in, say, a fifth dimension the traveller’s world line simply switches from one space-time continuum to another on a graph that depicts all the universes branching like a tree in a meta-universe”.

It might seem to you that the idea is totally bizarre. However, many scientists, including many respectful physicists, are still obsessed with it. For instance, Hugh Everett III's Ph.D. thesis "'Relative State' Formulation of Quantum Mechanics" (Reviews of Modern Physics 29, July 1957, pp. 454-462) outlined a meta-theory in which the universe at every micro-microinstant branched into countless parallel worlds, each a possible combination of micro-events that could occur as a result of micro-level uncertainty. The dissertation was commented by John A. Wheeler's who provided a rather favourable assessment in which he pointed out that “classical physicists were almost as uncomfortable at first with the radical notions of general relativity”.

Another extravagant hypothesis that concerned time travel was forged in the depth of theoretical physics. The hypothesis that introduced the concept of so-called “time loops” still encourages many time travel fans. The “time loops” (or “closed timelike curves” (CTC)) concept was most introduced by Kurt Gödel in 1949. The scientist constructed a rotating cosmological model in which one can, in theory, travel to any point in the world’s past as well as future, although travel to the past is ruled out as physically impossible. In such a universe, the distance between particles of matter is unchangeable. Therefore, one can start travelling from any given point in the universe, circle it and come back to the initial point. In another words, the traveller is circling the universe not only in space but in time and his path looks like a spiral span around a cylinder. And because single loops of the spiral might be located close to each other, the hypothesis allows “skipping the spirals” and thence “time hopping”.
Each of these hypotheses is interesting in its own way and yet each of them is full of huge discrepancies and contradictions. From the points of view of orthodox scientists, none of these hypotheses might sustain any serious critics. For many people it might seem that the time travel problem is just another amusing paradox invented by sci-fi writers but the thing is not that simple.

A brilliant Russian astrophysicist from the University of Copenhagen, Igor D. Novikov, who wrote “River of Time”, a book about paradoxes of time travel, explains the possibility of time travel on the basis of the relativist effect when time slows down for the object that moves with relatively high speed. An astronaut who would come back to Earth after a thirty-year travel in a spaceship might find himself more than one and a half century into the future, right in time to meet his grand-grand-grandchildren. Thence, the possibility of time travel into the future was more or less explained by the science. However, the problem with the time travel into the past still remained unexplained.

Thinking of how the possible time machine might look like, physicists draw a model of two black holes with entrances and exits marked by the letters A and B. However, the question that still troubled them was: what would happen if one connects both entrances with a tunnel? Suppose that you can stabilize the walls of this tunnel using some supernatural substance and place the entrance B to some distant star. Therefore, the entrances A and B of both black holes would be located at a unimaginable distance from each other, while the exits would be connected by a relatively short tunnel.

Igor D. Novikov describes that both the diameters of entrances and the “tunnel” might, in theory, be modelled in such a way that the gravitational influence on living beings in the tunnel would be sustainable. The resulting construction would represent a true space machine! If a traveller covers the distance from A to B in the “normal” space and then would come back trough the tunnel, nothing much would happen: some time – say, 10 years, will be spent in route. However, if the entrance A remains still but the entrance B starts spinning around A with an enormous speed, we would end up with a time machine!
In a structure like this, a watch placed in entrance B would lag behind from the watch placed in entrance A. Therefore, the time would flow slower and that would be clearly registered by the observers in entrances A and B.
Imagine a traveller moving from A to the orbit of B. The traveller would find a precise time when the entrance B is in front of him and would plunge into it. After that, the traveller would travel back to B through the “tunnel”. Suppose that the traveller spent 10 years to get to B (in A’s time). However, according to the B time, only 5 years had passed. In B’s time, the start happened at 10th year and by the time the traveller was in B, the watch showed 15 years. However, by that time the watch in A had already counted 30 years. Now the traveller jumps into the whole B; if he could see the watch in A, he would register that the same watch shows the same time as in B, i.e. 15 years after the spin. The traveller quickly passes the short “tunnel” and emerges from the whole A in the same time he started his journey.
However, he started his journey when the watch in A showed 20 years but he came back when it showed 15 years! Thence, the traveller came back before he started in journey – he made a time travel!

As you can see, the physicists like to play tricks. The idea of “time loops” might seem unbelievable to some of you, however time (and science) will show whether this idea might be implemented to build something many people are lounging for – a genuine time machine!

Recommending you a new book on vampires: Emily Welkins' "Till the last drop!"

Dear Followers,

We are glad to announce that a fellow researcher, Dr Emily Welkins, published her book entitled "Till the last drop!" on what she describes as "modelling peaceful co-existence of vampires and humans.

The book is a real guide to vampiric lore (all you need to know about vampires and were afraid to ask, so to speak :)) It is a mixture of a research paper and popular science literatere and it will make you an expert on vampires (and not just the one who knows how to use silver bullets and garlic, but that kind who would be able to juggle (and fiddle) with numbers, quote respectful sources and amuse (and startle) your friends with a deep knowledge on vampyrism.

Read what one of the the readers wrote in her review of the book:

"If vampires were real and were planning their debut or coming-out party,this would probably be the book that they would cite to get everyone thinking about a peaceful co-existence. Maybe they are planning to show up spontaneously. Science and progress these days are far beyond imagination. Artificial blood may be invented soon (then there would be no reason for vampires to hide any more!).

I thoroughly enjoyed reading "Till the last drop!", especially because I am a fan of watching vampire films and TV series (I knew all the
book's popular cultural references!). The tone of the book is interesting: sometimes comedic and sometimes dry ... but this balances out well and keeps interest levels high.

I highly recommend this book! Congratulations on a job well done, Emily Welkins!"

We greatly recommend this book to you too!

Best regards,

WS and EL

Lunar phases and crimes: do werewolves exist?

For quite some time now, scientists have been wondering whether there has been any connection between phases of the moon and crime rates. Moon, by some accounts, is massive object in the sky that affects, for example, the cycle of tidal waves or the growth of plants. Some mentally unstable individuals claim to be attracted by the full moon, others experience sleep disorders and anxiety. Artists are fascinated by the full moon and its depiction might be found on many famous works of art (for instance, Van Gough's). There have been many recorded cases of sleepwalking caused by what doctors believe to be the change in moon cycles. For many people the causality is straightforward: the moon attracts the Earth's waters and governs its seas' and oceans' tides and because human body consists of 80% of liquids, why should not the moon attract these liquids too?

There are lots of studies dealing with what is called “the lunar effect”. For instance, Templer, Veleber, and Brooner (1982) claimed in their study that an unusual number of traffic accidents occurred during the evenings right around the full and new moons (although later the same researchers came up with an explanation that during the time period covered in their study a disproportionate number of full and new moons felt on weekends and traffic accidents are always higher on weekends). A study of homicides in Dade County, Florida (Lieber and Sherin, 1972) found an upsurge in killings in the 24 hours before and after the full moon. Other researchers, however, argued that the Dade County researchers employed dubious statistical methods (when the numbers were reevaluated, the pattern disappeared altogether).

Rotton and Kelly (1985) conducted a meta-analysis of 37 studies of the moon's effect on things like psychiatric admissions, suicides and crime (they called it BILE (Belief in Lunar Effects)). The researchers found that the moon accounted for no more than 0.03 of 1 percent of the monthly variation. The results of the BILE study indicated that there was a greater belief in lunar effects in the older participants than in the younger ones. The researchers also determined that belief in lunar effects appears to be based on age and not on social class or education. Another study (Jorgenson, 1981) concluded that persons with an external locus of control were more likely to believe in lunar effects on human behavior than would persons who possess an internal locus of control. Rotton, Kelly, and Elortegui did a follow-up study in 1986 to determine if belief in lunar effect on human behavior was more predominant in police officers and people working in psychiatric areas than among other people. It turned out that police officers exhibited a high belief in lunar effect as opposed to a lower belief by regular people. However, psychiatric care workers did not seem to give any credit to lunar effect. The explanation might be that they were influenced by articles in recent scientific journals regarding research being done in this area.

Most recently, Leflet (2009) examined a correlation between lunar phases, criminal activity and crisis calls. He conducted a study of individuals arrested by law officials and emergency calls made within the St. Joseph, Missouri area for a two-month period beginning July 17, 1999, and ending September 12, 1999. On the basis of the study, he concluded that common folklore concerning the effect of the changes in lunar phase and human behavior is unsubstantiated. However, the study had one limitation: namely that the observation period was conducted for two months, which is a relatively short period of time.

In spite of all that, there definitely should be some connection (and it probably is), however our story twists here to examine a quite more bizarre causality. We would like to look at the available data of crime rates for various countries and by comparing and matching the crime statistics (especially murder statistics) with phases of full moon try to answer the question: Would the existence of werewolves be possible in the world we live in?

Unlike vampires, werewolves are far more primitive creatures by all accounts. They ravish in the depth of the forests, kill animals and people and their bite might turn a human into a werewolf. In addition, unlike vampires who are in that state permanently, werewolves do not differ from humans most of the time. Turning into a wolf (or a beer or a jaguar) is triggered by the full moon and usually happens once a month. According to the most of the accounts described in popular literature, comic books and films, many werewolves do not actually know they are werewolves because their memory is gone every time they transform themselves from their human to their animal form and back (see Jack Nicolson's "The Wolf").

It is not completely clear how they multiply, although the werewolf gene might be transferred by bloodlines (see Stephanie Meyer’s “Twilight Saga” for instance). Therefore, for the purpose of this research we can assume that the only way werewolves might strengthen their numbers, is by biting humans and turning them into werewolves. In most of the cases, however, werewolves kill their victims.

Therefore, a sudden surge in crime rate during full moon phases in various countries, controlled by the place of occurrence (forested areas might be the best candidate for werewolves’ appearance), might provide us with a good lead in our attempt to answer the question about the existence of such creatures as werewolves.

We are going to give it a thought (and conduct our research using all available data we will be able to get our hands on) and inform all our blog readers about our results soon.

Keep reading our blog and see you later, alligators (or werewolves)?

The Joss Whedon model and beating the disease

Looks like the disease has passed and we are back to work! Being ill actually made us think about the hypothetical situation in which vampires were real and humans would have decided to develop effective measures to fight this (vampiric) disease. What would have happened?

Well, one possible outcome was portrayed very well in a film called “Daybreakers”, a 2009 science-fiction horror directed by Spierig brothers. In the film some strange disease (a plague) has turned most of the Earth’s population into vampires. Humans lost their war on vampiric disease and became outlaws and human blood (since no substitute was found – ah, where are you, True blood? :)) became scarce (which made it a very desirable commodity – remember the paradox of value (diamonds-water paradox) from your Microeconomics class?). Vampires began to hunt humans and harvested them for blood but almost depleted the resources (we, humans, always do – whether we are turned into vampires or not, it seems). Luckily, the salvation came with one former ragged vampire who calls himself Elvis and who was able to turn himself back into human form after the car crash (we see the Hand of God here, do you?).

Have you ever wondered what would happen if humans turned against vampires as they often do against diseases and succeeded? The concept is not new. The creator of “Buffy the Vampire Slayer” (TV series), Joss Whedon (and its spin-off “Angel”), presents the most simplistic, yet the most dreadful “doomsday” scenario of vampire-human interaction (similar to Zombie infection outbreak in other fiction movies, such as “28 days later” or “Resident Evil”). The vampire bites its victim who (in a very short period of time) rises as another undead vampire and, in turn, bites another human victim, and so on. Luckily enough for humans, the world is populated by an unknown (but considerably large) number of vampire slayers (with a girl named Buffy Summers being their most remarkable representative).
Killing a vampire according to the Whedon model is relatively easy: using a wooden stake, a crucifix or a variety of other methods are pretty efficient. The model reveals how unstable the equilibrium between humans and vampires might be.
The initial conditions of the Whedon model are the following: five million vampires, 6 159 million people, there are organized groups of zealot vampire slayers (who kill vampires not just for profit but out of persuasion and in an altruistic attempt to destroy the Evil and save mankind). The model can be presented in a form of a diagram

where H denotes humans, V denotes vampires and VS denotes vampire slayers. H0 is the initial state of human population, kH denotes the exponential growth of human population, v0 is the initial state of vampire population, aHV and baHV both describe interactions between a human and a vampire (with a as the coefficient of a lethal outcome for vampire-human interaction for humans (which is higher this time) and b as the coefficient describing the rate with which humans are turned into vampires) and cV denotes the death rate for vampires (with a much more higher c).

Although the model allows for the stationary solution, the initial conditions of the problem lead to the disbalance in the system. The Whedon model is too unstable to be realistic. Vampires and humans cannot co-exist for a long period of time because human vampire slayers (e.g. famous Miss Summers) exterminate all vampires entirely. The human population recovers from the damage caused to it by vampires and continues to grow steadily.
Even though, the Whedon model’s structure theoretically allows for co-existence of humans and vampires, the laborious vampire slayers contribute to putting the system out of balance by killing all vampires. This outcome is predetermined by the initial parameters of the Whedon model (vampires constantly need to feed, cannot effectively control their blood thirst and attack humans whenever possible). A very important feature of the Whedon model is for the vampire slayers to exterminate all vampires before they do an irreversible damage to the human population and it will fail to return to its initial state and continue to grow peacefully.