Wednesday, March 16, 2011

The Geocentric Universe - Part 4

The Church and Cosmology

The Christian church held sway over Europe throughout the middle ages. To the church the Earth was full of sinfulness which directly opposed the holiness of the heavenly realm. The invasion by the Crusades of Jerusalem and rediscovery of many of the former Greek teachings especially that of Aristotle helped strengthen the geocentric model. This viewpoint took much from Theory of Forms by Plato. The church adopted a lot of Plato’s and Aristotle’s ideas but they could not accept the finite universe proposed by Aristotle. Instead the church proposed that the universe was unlimited so it would match their view point of God as an unlimited being not bound to any one place. This view of the universe made it virtually impossible for the church to accept any heliocentric model.
  
Cosmology Reborn

 The geocentric model would dominate within cosmology until the arrival of several of sciences true giants. It would take the publication of De Revolutionibus Orbium Coelestium in 1543 by Nicolaus Copernicus (1473 – 1543). This book was not well received. For many years it was overlooked and had not made much impact on the beliefs within Europe. Since this model proposed by Copernicus of a heliocentric system opposed the Church’s view it would be assumed that they would have greatly condemned such a publication. But it would take more than 60 years for the Church to respond to this book in any true authoritative way.

This response came about due to the work of Galileo (1564 – 1642). He had made many great discoveries with the aid of the telescope (the design of which he improved). He discovered the moons around Jupiter and the phases of Venus. Galileo displayed remarkable abilities for his scientific method, for him observation and mathematical explanation was central to science.  His writings proved to be controversial in which he made the pope at the time out to be a fool. The Church decided to silence Galileo and warn him that he could not defend or speak in favour of the Copernican system.

Galileo called before the pope and forced to recant his beliefs.
It is said he responded before he left  "Eppur si muove" (still it moves).

Another nail in the coffin of the geocentric model was hammered in by Johannes Kepler (1571 – 1630). Kepler was a gifted mathematician who worked briefly with Tycho Brahe prior to his death. Kepler inherited Brahe’s extensive observational data from which he formulated his theory on the elliptical orbits of the planets. Here for the first time a model was put forward which proved to be more accurate than that of Ptolemy.




This era in Europe would help usher in a new revolution in science. Again the natural world and mathematics were united. This would end the domination of Aristotle and geocentric model of Ptolemy.

Tuesday, March 15, 2011

The Geocentric Universe - Part 3

Late Greek Cosmology

I have deliberately omitted Aristotle and Plato up to this point.  The series of posts presented here are for the most part in chronological order. The reason for the omission is that of the philosophers and great thinkers of the Greek time, many had tried to separate heavenly influence from the science but this did not continue in most part due to Aristotle (384 – 322 B.C). At the time Aristotle was considered by many as the greatest thinker of his age much the same as we now see Newton or Einstein. With a person held in such reverence very few would dare put forward theories that would challenge or contradict Aristotle.

Raphael's School of Athens.
Note the two central figures of Plato and Aristotle
Aristotle believed in a hierarchical view of the cosmos. To him there was a major distinction between what he saw as an imperfect world of change and the eternal and immutable heavens. To him the heavens were perfect such that all bodies revolved about the Earth in perfect circles. Due to his influence this view was held in the highest regard and most other theories fell by the way side. Many had argued for the divorce of mysticism from science but the view put forward by Aristotle again united them.

This view was upheld by Plato (424 – 448 B.C) who dismissed natural science in favour of believing in the perfect heavens with the imperfect and changing Earth at the centre. Plato at this time established his academy (which would continue to teach for almost 900 years); through this academy these teachings would gain prominence and would dominate cosmology for centuries to come.

People now would question why did this view point persist even when faced with some major errors? This model could not explain why the planets moved with retrograde motion or following on from that when the brightness of the planets varied. To us now it almost seems foolish but it has to be remembered that this was Aristotle and other renowned philosophers’ viewpoint and as such it was accepted. Also as stated earlier humans like to see themselves at the centre and it fitted the views of many people and their religion.

The geocentric model championed by Aristotle persisted even with its flaws. With the quality of the measurements that could be made of the night sky at the time of the Greeks it was obvious that it was incorrect, this however was about to change. The rise to fame of Ptolemy (83 – 161 AD) would cement the geocentric model in cosmology. Many had tried to come up with explanations to support the geocentric model of perfect circular orbits but none could find a satisfactory answer. Ptolemy however tackled and solved this problem with the use of complex geometric patterns.

In Ptolemy’s theory (published in his treatise Almagest) the Earth remains stationary at the centre which each planet orbiting in a perfect circle known as a deferent. Within this deferent the planet moved with a circular motion known as an epicycle. Each planet had multiple epicycles. To add to this complexity planets also orbited in what was known as an equat. The equat was an offset for each orbit which placed the Earth not at the centre but slightly off. This eccentric model solves some the problems with the orbits. This model was highly complex but it did allow for good navigation and was able to provide somewhat accurate celestial predictions. With the apparent victory for this model and with the president set by Aristotle and Plato before, the geocentric model would prevail for centuries to come.

Ptolemy's Geocentric Model
The Dark Ages

The term Dark Ages refers to a time in Europe which spans from the late 5th century to the start of the 11th century. This is a list of discoveries in chronological order note the lack of advancement between the 5th and 11th centuries within Europe. This era was started with the fall of the Roman Empire and the collapse of the Greek states. Many of the great works of the Greek philosophers had been lost. With the religious turmoil and denigration this all added to the problems of the everyday person at this time. With such upheaval, stable government, schools and many forms of academia were now a distance memory. The only stabilizing force within this time was organised religion. The Catholic Church at this time was a powerful force and with such troubling times in Europe many turned to god for comfort.


While Europe seemed to have fallen from grace, the Muslim and Islamic civilizations flourished. They embraced many of the mathematical ideas from the Greeks along with their astronomical observations. Science developed within these cultures greatly during this time period. Trade with the east from India introduced many other concepts which they embraced. This upsurge in science would bring Europe out of the “darkness” it had endured for centuries. The Spanish had retaken many of the towns and cities conquered by the Muslims in which they found vast libraries of scientific teachings dating back to the time of the Greeks. These discoveries would help lay the foundations of learning within Europe and herald a new beginning in science.

Monday, March 14, 2011

The Geocentric Universe - Part 2

Early Greek Cosmology

Early Greek cosmology is dominated by several great thinkers. The foundations of philosophy and many mathematical principals would find their birth in this time. About the time 640 B.C, a movement known as the Ionic physical philosophy began. Thales of Miletos (620 – 547 B.C) is considered to be the founder of this school of thought. He sought to explain the world around us without resorting to any supernatural cause but instead to develop an explanation by naturalistic means.

Thales of Miletos

This break from old ideas of deities or other supernatural beings having control over terrestrial events would herald a new beginning in science. For the first time people began to try and solve problems in a mathematical or mechanical sense rather than resort to any supernatural explanation. From this school of thought many other philosophers arose, Anaximander was an early example.

Anaximander (610 – 546 B.C) considered the Earth to be one of many bodies in space and it was able to move free about space. According to Anaximander the Earth did not move as it had no reason to move, as it simply floated motionless in space. Many ideas at the time theorized that the Earth was held in place by some godly means. This again is a sign of the Greek thinking of moving away from any supernatural explanation and trying to solve it using mechanics and maths. Anaximander also theorized that all matter in the universe came from the one substance which he called apeiron (unlimited). This substance was transformed into all the different types of matter and eventually into what we know as Earth. From this idea arose his belief that the universe extending infinitely in time and space.

A student of Anaximander, Anaximenes (585 – 525 B.C) believed the Sun and the other heavenly bodies were globes of fire. He placed the Sun and the stars on a giant crystal sphere which rotated about the Earth. Anaximense also believed that the Universe was made of one substance, in his eyes he believed that air made up all of the matter. Anaximenes theorized that when air was compressed it got cold and so here on Earth it was compressed enough to become solid and cold just like rock or metal. In space it was allowed to expand and become hot at which point it became fire, this gave rise to the idea that the Sun and all the other points of light were spheres of fire. Another philosopher of this school of thought Anaxagoras (500 – 428 B.C), put forward the idea that the solar system formed from a spinning disc where all the most dense matter stayed near the centre and coalesced to form the planets and the Sun. He strongly augured that the Sun was a fiery ball and not deity, for this he was imprisoned. He also gave an explanation for solar ellipses, saying that the moon passed between the Earth and the Sun. This was the first time that a non supernatural explanation was put forward to explain this event.

The work started by the Ionian philosophers was continued and expanded upon. The separation of any godly explanation to terrestrial or celestial events was carried on by Pythagoras (c580 – 500 B.C). His belief was that all events and truth could be found within mathematics. To Pythagoras all events had an underlying explanation in number sequences or series. Pythagoras considered the Earth to be a sphere not a cylinder as Anaximander believed. Pythagoras like many before him believed the Earth was at the centre around which the other bodies revolved. This geocentric model made sense to the people at the time. Even though they separated science and the supernatural the egocentric tendency of humanity prevailed and they continued to place the Earth at the centre of the universe. It was not challenged until the theories of Aristarchus came forward.

Aristarchus (310 – 230 B.C) put forward the idea that the Earth rotates about the Sun and in doing so spins on its own axis. This he said explains the day/night cycle. For the first time the heliocentric model was given a voice. However this idea did not receive any support. Even though Greeks had begun to move away from the supernatural explanations there was still the idea that we were the centre. To move away from this would lessen the importance of man in the universe and this did not sit well with the Greek establishment. To put it simply Aristarchus was shouted down by the other philosophers at the time. Without any backing, his theory was lost to history. This set-back in cosmological theory cannot be under-stated. It would take almost 2000 years before this theory was challenged again.

Aristarchus's Heliocentric Model
The arguments against this theory to modern day observers seem almost ridiculous but without the idea of gravity and the vacuum of space these ideas would appear to make sense. The arguments said that if the Earth was indeed spinning on its own axis, then why were we not simply thrown off the surface as if we were on a merry-go round. Another pro-geocentric argument was that if we are orbiting the Sun why do we not feel a wind blowing against us as we move through space. At the time it was believed that space contained matter, be it a gas or liquid that the Earth floated in and as we passed through it we should feel its presence blowing against us. Looking at these arguments without the knowledge we have now it does appear to make some sense. Another point to note is that there was no hard evidence to prove Aristarchus’s theory and as such it was lost.

Aristarchus was also able to make estimates about the relative distances of the moon and the sun. He based a lot of this work on prior studies and theories of Eratosthenes. He too like Aristarchus was able to calculate relative distances. But too his credit he deduced the diameter of the Earth to a high degree of accuracy.

Eratosthenes's method for measuring the
diameter of the Earth, accurate to within 2% of the true value

At this time (c250 BC) the Ionian school of thought was in decline as was the Pythagorean brotherhood, this left the way open for a new school of thought which was lead by such philosophers like Plato and Aristotle. This movement and with the model developed by Ptolemy would hamper cosmology for centuries to come.

This would end the age of the true first scientific revolution. For the first time people began to seek answers to the bigger questions by looking to science rather than the heavens. Many great mathematicians and scholars of this age are still known to this day. Euclid and Archimedes are known to this day for their discoveries. As will be seen later in this essay the knowledge of the Greeks would remain static up to the second scientific revolution in Europe in the 1400’s. 

Sunday, March 13, 2011

The Geocentric Universe - Part 1

Introduction


"We may become the markers of our fate when
we have ceased to pose as its prophets"
- Karl Popper

Mankind has always put itself at the centre of reality. This egocentric view on existence extends throughout history. None more so than than the idea that the Earth was centre of the universe, which found its birth in early cosmology. This idea persisted for almost 2000 years until it was finally toppled in what was the rebirth of cosmology. The theory published in 1543, De Revolutionibus Orbium Coelestium by Mikolaj Kopernik (better known as Copernicus) lay the foundations for what would be a true revolution in cosmology. This theory would help trigger new theories and ideas which would lead to the acceptance of the heliocentric model.

De Revolutionibus Orbium Coelestium

In this series of posts I will present the ideas of early cosmology and the evolution of these theories, from the observations of the Babylonians to the Greek geocentric model and how knowledge and freedom of thought was lost to the Dark Ages in Europe. In these posts I will only be dealing with the advancement of cosmology in the western world. Cosmology also developed throughout the rest of the world at this time but here I am only concerned with how the geocentric model developed by the Greeks evolved and persisted for so many years.


Pre-Greek Cosmology

Cosmology can trace its history back to the earliest recorded human history (c3500 B.C.). The Babylonians are considered the first astronomers, they made detailed observations of the sky. With the aid of these observations they developed calenders and were ab;e to predict eclipses. The Babylonians used 30 stars as reference points to help in their predictions.

Babylonian Star Calender


In 625 BC the Babylonian empire was invaded by the Chaldean empire even though they ransacked many of the cites, they took care not to destroy the data and the observations made by the Babylonian astronomers. They even went to the extent of embracing the data and expanding on it. They expanded on the set of 30 stars to help make up the first constellations and further developed the calender.

As with many civilizations at this time celestial events were linked with those on Earth. This area of interest is known as astrology. The belief was that events in the celestial could influence or predict events here on Earth. Astrology and cosmology remained linked and developed together until the scientific revolution in the 15th century. Even today astrology remain popular even in the light of overwhelming evidence to the contrary. 

Friday, March 11, 2011

Who Ordered That? - Part 6

The Higgs Boson


The Higgs boson was theorized by a group in the mid 1960’s led by Peter Higgs. In this theory there is a Higgs field which permeates all space. Particles which interact with this field appear to us as having mass, particles which don’t, appear massless. This field explains why forces act the way they do.



The Higgs boson is an important element of the standard model theory. It is the only remaining particle predicted by the standard model that has not been observed. This was one of the main driving forces in the construction of the Large Hadron Collider in CERN and the Tevatron at Fermilab. In these accelerators it is hoped that we will get our first glimpse of this elusive particle.  The discovery of this particle would go a long way to helping physicists explain why particles have the mass they do and why forces work the way they do.
They is of course the question does the Higgs particle even exist? A positive or negative result would yield a change in understanding. If Higgs isn’t found it means we must find a new theory and if it is found we can build upon it to try and integrate gravity in to an all inclusive theory. So what lies beyond the standard model and the Higgs boson?

Beyond the Standard Model

The standard for all its power has limits to its knowledge which it cannot answer.
  • Can we unify all the fundamental forces?
  • Why only three generations of leptons and quarks?
  • Is there something more fundamental than the quark and lepton families?
  • What are Dark Matter and Dark Energy?
  • Why is there more matter than anti-matter?
  • What is the explanation of neutrino mass?
  • Why are the fundamental forces so vastly different in terms of strength?
  • Where does the cosmological constant originate from?

These are just some of the questions the standard model is not able to answer. To try to answer these questions there are several theories.

String theory is one of the major developments of the last 40 years. It attempts to find some common ground between quantum physics and general relativity. In this theory, it proposes that quark and leptons are one dimensional strings. The vibrations of these strings give rise to their apparent properties. This theory, it is hoped, will reconcile gravity with quantum theories and could possibly lead to a theory of everything. String theory isn’t without its flaws; it is by its nature untestable. It has also failed to make any concrete predictions. It is viewed by many as a mathematical framework rather than an actual physical theory.

Another candidate is the supersymmetric standard model. In this model each particle has a partner which is at a much higher energy level. This symmetry would help explain several key questions which the standard model fails to do. In this model it predicts that the fundamental forces are somehow bound at higher energies. This theory indicates that at some time proceeding the big bang there was a singular force called the super force. From this super force we got the four fundamental forces. As the universe cooled after the initial explosion these fundamental forces arose, gravity first followed by the strong, weak and finally EM force. Another prediction from this theory is a candidate for dark matter. We may get an answer for this theory very soon. In this theory the first of these super partners should be a particle called the neutralino. If predictions are correct it may be possible that it could be observed at CERN.

So here we are, with the LHC and Tevatron operational we are possibly on the verge of a major paradigm shift in physics. Just as at the beginning of the 20th century, when the first hints of atomic theory and quantum theory excited and fired the imaginations of physicists, here we await the first glimpses of new ground in the search for a theory of everything. 

Thursday, March 10, 2011

Who Ordered That? - Part 5

The Electro-Weak Interaction


Each of the four fundamental forces in nature were well established by the 1960’s. How were they linked or how they functioned was a matter of great debate and theory. It was assumed that some form of messenger particle was responsible for passing information to and from interacting particles. The electromagnetic force was described by a theory called quantum electrodynamics (QED). This theory stated that the interaction between charged particle was mediated by the photon. This allowed the electron and proton to sense each other's presence. In a similar vein, a theory for the weak force was developed, which had at its heart the massive W and Z gauge bosons. These particles mediated the weak force between all particles. Due to these particles' relatively large mass, this force was extremely short ranged.



The success of the weak force theory led physicists to the conclusion that the EM force and the Weak force were somehow linked at a more fundamental level. These two forces were two sides of the same coin and so developed the electroweak theory. This theory parallels the work of Maxwell and his unification of electricity and magnetism years earlier. From this new theory, predictions for the mass and charge of the W and Z particles were made. Conformation of these predictions came in the early 1980’s at CERN.

The Theory of Quantum Chromodynamics


The theory of the strong force had been theorized to account for the interactions between nucleons. This force allowed for the nucleus to remain stable even though it should fly apart as the protons repelled one other. With the discovery of the quark, was there now an interaction between them which bound them internally within the hadron. Was this the same force which bound the nucleus? From this theory a messenger particle dubbed the gluon was predicted. From this prediction the gluon was much like the photon, it was massless and carried the information from one particle to another. For interactions with quarks the gluon had to have certain properties which it must carry. One such property which was newly developed was the idea of colour.

This is not colour in the sense of what we see in everyday life, i.e. the manifestation of certain wavelengths of EM radiation. This colour property comes in three flavours: red, yellow and blue. This theory formed the basis of what we now call quantum chromodynamics (QCD). According to this theory quarks can only combine in combinations that are colour neutral. There are several possible ways this can occur:
  •  Combination of red-yellow-blue is white so therefore is colour neutral
  • Combination of anti-red, anti-yellow and anti-blue is colour neutral
  • Combination of any colour and its anti-partner is also colour neutral
To achieve balance with this system we must have what is called gauge symmetry. This symmetry is central to understanding QCD. A gluon carries with it a colour and an anti-colour (not necessarily of corresponding pairs). When a quark changes colour it emits a gluon, this gluon in turn interacts with another quark which immediately changes colour in the right manner so as to maintain colour neutrality within the hadron. This allows the quark to change colour continually which does not affect the colour neutrality of hadrons.

This new theory could account for the force that binds not only protons and neutrons together but also the force that binds quarks together to form hadrons. This is an oversimplified view of QCD, the theory is one of the great achievements of 20th century physics but at its core is a very mathematical model which it difficult to adequately describe in a few paragraphs.


The Birth of the Standard Model and its Limits


It you were to ask any scientist what are the greatest accomplishments of science, the most likely response would include the like of Darwin’s Theory of Evolution, the discovery of DNA, penicillin, the internet and the Standard Model. The standard model is the crown jewels of modern physics. If offers a common ground between the leptons, quarks, QCD and QED.  Within this model all members of the particle zoo could be accounted for. The interaction between these particles could be predicted with accuracy. This theory helped to link the two major fields in physics: QED and QCD. Within the confines of the standard model we have a common framework for three of the fundamental forces.



The standard model predicted many of the masses and properties of the myriad of sub atomic particles. These were subsequently discovered at facilities such as CERN throughout the 1980’s and 1990’s.

The standard model helps answer the question as to why, if these fundamental forces are so intrinsically linked, they are they so different? Why does the photon have no mass yet the W and Z boson are massive? To answer these questions the development of a theory dating back to the mid 1960’s is required. Peter Higgs (b.1929) proposed that there was an all-encompassing field that permeates all space which gave particles their apparent mass. Since the photon does not interact with this field it has no mass. So what we perceive as mass is the interaction between particles and this Higgs field.

The standard model has helped us predict that there are only three generations of quark and leptons. Have we reached the end of the rainbow and found our pot or gold? The very simple answer is no. The standard model offers us a very accurate model for the majority of what we see but it has limits in application.

The standard model does not include gravity nor can it explain the phenomena of dark matter or dark energy. We also cannot use the standard model to return back to the initial starting point of the universe. The standard model breaks down as we approach time zero. From observation, neutrinos would appear to have mass, the standard model has no explanation as to why this is so. 

Who Ordered That? - Part 4

The Discovery of Quarks and Leptons


By the mid 1960’s the hadron family had grown to over a hundred members. These hadrons all fitted within the framework of this new quark model. So the experimentalists were tasked with finding these newly predicted quarks. As noted earlier these quarks had a fractional charge, so identifying these new particles should be easy. The early searches for the elusive quark failed. It was suggested that it may not be possible to find them as no accelerator currently operating was powerful enough to generate collision energies needed to observe quarks. It was also possible that there was no such thing as quarks but these were just abstract mathematical tools to help give a pattern to the particles we observed.

In 1968 at the Stanford Linear Accelerator, SLAC, direct evidence was observed for their existence. This was again observed at CERN in early 1970. This discovery owed a lot to the Rutherford experiment back in 1911 which used the idea of scattering to probe the inner structure of the atom.

Standford Linear Accelerator


The scale of the atom is generally 10-10m and the nucleus about 10-15m. The electron is far smaller again at 10-18m, why is the proton almost a thousand times bigger? It was assumed prior to the quark model that the proton was this apparent size due to the force carrying particle the pion.



Now with the advent of the quark model, the size that the proton had could be attributed to the way the quarks moved about, similar to how the electron orbiting the nucleus gives an atom its ‘size’. Due to its size and the energies the electron was the perfect particle to probe the inner structure of the neutron and the proton. With quarks having fractional charge it could be predicted how electrons would scatter as they passed by these quarks. If the proton had charge evenly spread throughout its structure the electrons would show a diffuse pattern from which no evidence could be gleaned. On the other hand, if the proton was indeed made up of three point like particles, there should be a very discernable pattern emerging from the electron scattering.



It was observed that indeed the proton and neutron were made up of three quarks as predicted. It also showed another particle was present within the innards of the proton and neutron. This particle it seemed might be the mediator of the force which binds quarks together and was called the gluon. From the initial results it seemed that the quarks were free to move about within the confines of the proton and that they were weakly bound together. So why then could we not observe a free unbound quark? No matter how energetic the collisions no unbound quark was forthcoming.

By the early 1970’s the quark model was refined and a more complete picture emerged. From this new model a fourth quark was theorized, called charm. At this time no hadrons were known of that required this quark. Work continued to produce ever more hadrons and finally in 1974 two teams of experimenters produced a new particle. One team was led by Samuel Ting (Brookhaven) and the other by Burton Richter (SLAC). Both groups have given this particle a different name so the particle was known by its joint name J/Ψ. This new particle required the new charm quark to explain its properties. Both Ting and Richter received the Nobel prize for this ground breaking work.

By now we had four quarks (up, down, strange and charm) and four leptons (electron, muon, neutrino and muon neutrino), were these two distinct groups linked in some manner? In 1975 a fifth lepton was discovered called the tau. Due to the similar nature of these two groups it was suggested that there may be a fifth quark. Since all the previous lepton had a paired neutrino was there also a sixth quark? In 1977 a group at Fermi Lab led by Leon Lederman discovered a massive meson which could only be made by a new quark which they dubbed the bottom quark. The discovery of the sixth lepton and quark would take nearly twenty more years of work. These two new particles, the top quark and tau neutrino, were so massive no accelerators were available until the late 1990’s that could provide collision energies high enough to produce these particles.


Wednesday, March 9, 2011

Who Ordered That? - Part 3

The Eight Fold Way and the Quark Model


Theoretical physicists were now playing catch up as the experiments of the 1950's had expanded the range of sub atomic particles to ever increasing heights. The first task was to identify shared properties which might hint to some underlying pattern.

This problem is something very similar to what chemists faced in the late 1800's. At this time there was a wide array of elements which at first glance did not appear to share any common ground. Many attempts were made to group and classify these elements into some pattern. It wasn't until Russian chemist Dmitri Mendeleev (1834-1907) grouped them by similar chemical properties and increasing atomic mass, designing the now familiar table we know as the Periodic Table. Could there be a similar table for the particle zoo?

Dmitri Mendeleev
To get any hint of this we must first try to understand what properties you can attribute to sub atomic particles. It would appear that there were only six leptons (the electron and muon are members of this family) and six corresponding anti particles, which behaved like point particles, while the hadrons (the proton and neutron are members of this family) had a far greater number of family members and a definite extension in space. Leptons obey a conservation of lepton number while in the hadron family, only the baryons obeyed a conservation law. There was another new property which was attributed to the newly discovered kaons called strangeness. This new property was due to these new particles only forming in pairs and so their associated strange value must be zero. With so many new properties and conservation laws it was easy for scientists to think that there was no way to make sense to this particle zoo. It would take one of the most talented physicists of the 20th century to solve this disturbing problem.





All these tables taken from an excellent CPEP poster.

In 1961 Murray Gell-Mann (b.1929) discovered there was an underlying pattern to the hadrons. Using a branch of mathematics called group theory, he was able to group the hadrons into families of particles. The proton and neutron became part of a family called the baryon octet while the pion became a member of a different octet called the meson octet. Gell-Mann dubbed this new view the eightfold way in homage to a Buddhist teaching belief. This model was very successful and in 1962 it enabled Gell-Mann to predict a new particle (much in the same vein as Mendeleev did years earlier) with certain properties and mass. This new particle, omega minus (Ω-), was found by a team of researchers at Brookhaven in 1963. Now armed with this powerful new theory could they now unravel what the underlying relationship between this menagerie of particles.

The question now was why did this eightfold way work? The hadrons could be grouped in patterns of 1,8,10 and 27, so was there some common ground they shared which gives rise to this pattern? Gell-Mann and George Zweig (b. 1937) would solve this puzzle. Both of them developed a theory independently that there must be some new fundamental particle. These new particles, which they believed there were three of, made up all the observed hadrons. Combining these three new particles in triplets could give rise to all the hadrons. This new particle was named the quark. These new quarks were named up, down and strange. These new particles were similar to the leptons with spin ½ and acted like point particles. The baryon family of the hadrons must be made up of a triplet of quarks similar to the proton and neutron. The meson family on the other hand are made up of just two quarks, a quark and anti-quark pair. The reason for this grouping is due to the rules of conservation developed in mathematical symmetry by Gell-Mann earlier which we refer to as SU(3). These new quarks were required to have a fractional charge for this new system to function. Now armed with this theory the experimentalists set out to find these new particles.


Tuesday, March 8, 2011

Its All Fun And Games Until Someone Loses a Vote

"It is enough that the people know there was an election. The people who cast the votes decide nothing. The people who count the votes decide everything." - Joesph Stalin


Watching the recent elections here in Ireland was fascinating. The coverage by our national broadcaster was excellent as it provided hours of drama as old political careers were destroyed and new ones started all in the glare of live television. Here in Ireland we use proportional representation with a single transferable vote. It is considered a fair system but as often is the case it makes it very difficult to avoid coalition governments. Watching how it all played out as the votes were tallied I couldn't help think about a book I read last year "Prediction" by Bruce Bueno De Mesquita. In his book Bruce describes with the aid of game theory how we can forecast and even engineer events.



In this book he gives various examples from his work about how he used game theory to predict foreign political events for the U.S. Government. However the story that sticks out for me is a very simple one. He was hired to help a retiring CEO. The CEO did not have a favourite in mind to replace him but he did know who he didn't want. However this person was the favourite among the board. Bruce was hired in secret to engineer a result in the up coming vote of the board to choose a successor. He couldn't for obivious reasons rig the vote as it had to appear to the board to be a fair vote. So how do you change the system to enigneer the outcome but on the surface appear fair?



The board consisted of 15 members which could all vote. Of the 15 members 5 canidates were put forward, Anthony, Barry, Claire, David and Ellie. Anthony is the popular choice among the board members but the CEO doesn't want him. Instead he wants David to win. The key to solving this is information. First we must gauge how each member of the board ranks each canidate. Luckily in this case the CEO knew his board members well so could provide a good estimate of how each member ranked the canidates. Armed with this knowledge Bruce could divide the board in certain voting blocks.

There were five distinct blocks, each containing three members. There prefrences from most to least as follows
  • Anthony, Claire, Barry, David, Ellie
  • Anthony, Ellie, David, Barry, Claire
  • Ellie, Anthony, David, Barry, Claire
  • Claire, Ellie, David, Barry, Anthony
  • Barry, Claire, David, Ellie, Anthony
In a straight forward one person one votes scienero Anthony would get 6 votes, Ellie, Barry and Claire 3 votes and David  0 votes. This exactly what the CEO wanted to avoid. So maybe a different system might help. One system would be the Borda count system. In this system each voter ranks their preferences in order. The number one preference in the case above gets 4 votes, the second 3 votes, the third two votes, the fourth one vote and the last vote 0 votes. Using the above preferences for each voting block the canidates now rank as follows;


  • Anthony      33 votes
  • Ellie             33 votes
  • Claire          30 votes
  • Barry          27 votes
  • David          27 votes
With a tie for first there would be a run off in which going by preferences Ellie would win. Poor old David doesn't stand a chance in this system. Also if the CEO were to change the voting system to such a degree it would raise suspicions that something wasn't quite right. To solve this problem a slightly different approach is needed. 

If we inspect the preferences we can see that in fact there is a solution in which we can get David elected in what would appear to be a fair system. The system used will be a head-to-head elimination system. To the board the two main candidates were Anthony and Ellie. So it would seem fair to ask the board to choose either Anthony or Ellie in a straight vote. The winner of this vote would than be placed against one of the remaining candidates until there was only one person remaining. Seems fair right?

In the first vote Ellie would beat Anthony 9 votes to 6. This is due to the above preferences in block 1 and 2 Anthony is favoured while in blocks 3,4 and 5 Ellie is favoured. Now the the next step is very important, who do you put up against Ellie? The CEO was very happy at this stage as Anthony would not be the new CEO but he still wanted to see David take over. Next Ellie and Claire would face off against each other. In this contest Claire would win 9 votes to 6. Now at this stage both favourites had been eliminated the CEO was very happy. 

In the third contest Claire would face Barry. Again returning to the preferences we see that Barry would win by 9 votes to 6 as he had the support in blocks 2,3 and 5 over Claire. This leaves us with the finally contest Barry against David. Using the above preferences we see that David has the support of blocks 2,3 and 4 making him the winner over Barry by 9 votes to 6. David was elected as the new CEO to the delight of the retiring CEO. To the board members it seemed a fair and open contest, no secret ballots, all they were asked to do was to pick between two people until all were eliminated bar one. This system was anything but fair.

  • Anthony versus Ellie: Ellie Wins
  • Ellie versus Claire: Claire Wins
  • Claire versus Barry: Barry Wins
  • Barry versus David: David Wins!
This was only possible for two very important reasons. One, the retiring CEO could provide enough information to properly understand all the possible outcomes of this scenario. Two, analysis of the preferences indicted that the voting was circular in nature, it could be setup in such a way to make any of the candidates the winner. Lesson to be learned here just because it looks fair doesn't mean it is.

Monday, March 7, 2011

Who Ordered That? - Part 2

The Particle Zoo



By the 1930's we had developed a model of what was believed to be the fundamental building blocks of matter; electron, proton, and neutron. This belief was turned on its head by several ground breaking theories.

In 1928 a young British physicist, Paul Dirac (1902-1984), published a paper which predicted the possibility of there being an anti-electron. This theory had several holes which he could not explain. A revised paper 1929 tried to tackle the confusing negative energy result but to avail. However, Dirac persisted and in 1931 he published a paper which gave rise to a particle known as the positron (e+), a particle which would be discovered a year later by Carl David Anderson (1905-1991). This was just the beginning for the discovery of many strange new particles.

At this time the formulation of theories for both the strong and weak nuclear forces had thrown up the possibility of new particles. Fermi had shown with the weak nuclear force that a neutron could decay into a proton and an electron. There was a snag, the energies of the reaction did not add up nor did the spin. Did he just discover some physical effect which didn't obey the conservation of energy and conservation of angular momentum? Wolfgang Pauli (1900-1958) suggested that there might be some new particle responsible for the missing energy and spin. Based on this Fermi came up with the neutrino (n). This seemly mass-less and charge-less particle could have a range of energies so would be responsible for the various energies of beta decay that we see. We know now that what he actually discovered was the antineutrino.

Yukawa, with the strong nuclear force theory, had postulated that this force was mediated by the exchanging of a particle between the neutrons and protons. He named this new particle the pion. The pion would come in several different forms; position pion (W+), negative pion (W-) and neutral pion (Z0). This bewildering array of new particles gave rise to the term particle zoo.

Summary of elementary particles

Armed with all of these new theories, physicists raced to find these elusive particles. A new age of experimentation had begun. There were two distinct paths to the discovery of these new particles; particle accelerators and cosmic rays.

It was known at this time that the upper atmosphere of the earth was bombarded by high energy stream of particles (referred to as cosmic rays). These cosmic rays would collide with particles and shower the Earth in a large assortment of exotic particles.  Using balloons and working on mountain tops provided the best means from observing these strange particles. With the aid of cloud chambers, the tracks made by these new particles were analysed and from this their properties deduced. It was then in 1936 when research teams were looking for Yukawa's new particle that another particle was observed which did not match any theory. This was a great surprise to the field of particle physics, was there even more strange particles lying in wait? What they had discovered was the muon. This would later been seen to be a new elementary particle.

This image is a pion (right track) which decays into a muon (the upper left track anti clockwise rotation) which then decays into an electron (top track that spirals towards the top).
Yukawa's pion would eventually be found by a mountaintop observatory in 1948 in the French Pyrenees. In 1950 there was a shock in store for experimenters when a strange track was observed in a cloud chamber. It was a v shaped track which appeared to come from nowhere. By 1955 they had identified 3 similar particles which they named kaons. The particle zoo was growing beyond expectations, adding to the confusion that was spreading throughout particle physics.

As the field of particle physics became more prevalent, the search for more powerful particle accelerators expanded. For the first true accelerators we must first return to the early 1930s at Cambridge University. In 1932 John Cockcroft (1897-1967) and Ernest Walton (1903-1995) developed the linear accelerator. It was used to study the transmutation of atomic nuclei. From this early success more advanced models were pioneered and by the 1960's several different types of accelerators in institutes around the world were beginning to replicate results seen from cosmic ray observations.

Walton in the observation hut of the linear accelerator at Cambridge

By the 1960's the particle zoo had grown to almost nightmarish proportions. What had begun as an exploration as to the force than binds the nucleus had lead down a path of what seemed like a never ending discovery of new particles. The beautiful simplicity of the early atomic physics was now gone and replaced by this unwieldy monster. To solve this we now shift focus from the experimental to theoretical. 

Sunday, March 6, 2011

Faster, Higher, Stronger .... Smarter?

The Olympic motto Citius, Altius, Fortius encapsulates the human will to achieve more but is there a limit? In a recent book 'The Perfection Point' author John Brenkens discusses the physical limitations of humans in various endeavours. In 1911 the men's 100 metre record stood at 10.5 seconds, today that record stands at 9.58 seconds by the ever entertaining Usain Bolt. Several different scientists put the theoretical limit for a human at anywhere between 9.45 and 9.35 seconds. Of course this does not account for some freak athlete which through some genetic abnormality can exceed this predefined limits. There is of course a limit but that limit is constantly shifting as we gain a better understand of the human body and how is maximize its potential. 

Bolt out on his own

The question arises is there a mental limit? I had this discussion at length a few weeks ago with a friend of mine. A lot of the discussion centered around the how we both defined evolution and progress. My argument is that we will quickly reach our limit as our progress will quickly catch up with evolution and we will find ourselves hindered by our intellect. My friend argued that evolution is moving at a greater pace than I though and that we are a long way off reaching our mental limit. I may be a little bias here but the areas of physics and mathematics are at the furthest reaches of human intellect. Research in physics has pushed the boundaries of our knowledge further than any other field of research. A glance at any of the leading journals in theoretical physics just show how far we have come. The question is as we explore the frontier of our knowledge will we reach a point where our brains do not have the required complexity to understand a problem or find its solution?



A good place to start with this problem is how complex is the human brain. Current estimates put the number of connections in the human brain at about 1 quadrillion (1015) connections. With an estimated peak performance of 100 million million instructions per second. For a comparison the latest Intel processor Core i7 has a performance rating of 160 thousand million instructions per second. Unlike the human brain they can not rearrange their physical connections so any real comparison isn't entirely fair but suffice to say the human brain far exceeds anything we can currently make. The human brain as complex as it is, is still finite in its capacity. 

Given the complexity of the human brain and the complexity of the problems we face in science will we be able to solve them before we reach our mental capacity? We could possible develop a quantum computer which could exceed our owns limits but then again the question arises can we program them with enough complexity to solve the problem? One solution may lie in genetic manipulation.

Evolution is generally a slow process where steps are measured in hundreds of lifetimes. Genetics may offer us a shortcut. We could potentially increase our mental capacity to overcome any shortcomings. However genetic manipulation opens up many more questions and problems. 

This of course could all be totally wrong as one day we may find the ultimate truth and be able to sum up all existence in one equation and then this renders my argument void. If that were to happen what else would there be left to do? Now that is a scary proposition.


Who Ordered That? - Part 1

"Three quarks for Muster Mark!
    Sure he has not got much of a bark
                  And sure any he has it's all beside the mark."
        - James Joyce, Finnegans Wake 


Prologue


By the start of the 1930's, physicists believed that all the constituents of the atom's inner structure had been discovered and all that remained was the task for formulating a theoretical framework to explain their behaviour. If we consider the constituents of matter; electron, proton and neutron, to be the building blocks of matter, then the forces of nature is the cement which binds them. We will see that there are four distinct fundamental forces in nature which govern all the interactions of matter, from the galactic, to the sub atomic scale.

This belief in these three elementary particles was rocked by several new theories. A slew of new, exotic particles were discovered, even some which weren't predicted. As particle accelerators grew in size, more and more particles began to emerge. This exciting, albeit confusing time in physics is best summed up by Isidor Isaac Rabi (1898-1988), who upon the observation of the muon, a hitherto unknown particle, exclaimed "Who ordered that?".

The Forces of Nature


The ebb and flow of the tide, a bright summers day, the myriad array of elements and the colour of this ink are all governed by four fundamental forces. The interaction and properties of these forces - gravity, electromagnetism, strong and weak nuclear force - is the most important idea in understanding the universe.
Gravity was the first force to be formulised into a theory. In 1687 Sir Isaac Newton (1643 -1727) published his Philosohhiæ Naturalis Principia Mathematica, within which he theorized his Universal Law of Gravitation. This theory helped explain a vast array of events, from the falling of an apple to the orbit of the planets. The force of gravity is what is known as an inverse square force, the strength of attraction between two interacting bodies is proportional to the inverse of the distance between them. 



The force of gravity acts over an infinite range and as far as we know is only attractive. In comparison to the other forces, gravity is very weak so its effects at the atomic level are negligible. However as it is only an attractive force its effects add up and this is particularly noticeable in acting over cosmological scales.

The electromagnetic force (EM force) is the next most obvious force as we can readily see it effects in everyday life. This force is both attractive and repulsive. It is magnitudes of strength more powerful than gravity and acts over an infinite range, so why doesn't it prevail over the galactic scale? It is its very nature of both attraction and repulsion which tends to cancel out its influence. It is the force which is responsible for binding atoms to form molecules and the magnetic shield which protects the Earth from the harmful effects of the solar wind. Prior to the 1800's the effect of electric and magnetic fields were observed but their mutual relationship seemed independent. In 1820, Danish physicist, Hans Christian Ørsted (1771-1851), observed that a changing electric field caused a change in motion of a magnetic compass needle. It would take several more years of intense research from many great scientists until in 1864 a brilliant Scottish physicist, James Clerk Maxwell (1831-1879), unified electricity and magnetism to what we now call electromagnetism. Maxwell's equations predicted many new phenomena and formed the basis for a major development in physics in the 20th century.

James Clerk Maxwell


The two remaining forces of nature are the strong and weak nuclear forces. Both of these forces act within the confines of the sub atomic world. The stability of the nucleus of the atom was a major snag of early atomic theory, how could positively charged protons be in such close proximity in the nucleus? With the discovery of the neutron many believe that this particle held the key to solving this dilemma. In 1935 Hideki Yukawa(1907-1981) theorized that some unseen force was present which only acts over extremely short ranges between protons and neutrons. This force was dubbed the strong nuclear force as it prevailed over the electromagnetic force at these short ranges. This strong force (and the addition of the EM force) is what drives the emission of alpha particles and gamma rays in radioactivity.

The beta decay of atoms raised many questions. For example: what governed the change of a neutron to a proton, electron and antineutrino? This decay could not be explained by the strong nuclear force or the EM force, so there had to be another unseen force which drove this reaction. This force would again be limited to extremely short ranges like the strong nuclear force, but must also be much weaker than the strong force. In 1934 Italian physicist Enrico Fermi (1901-1954) theorized a new force which explains the decay structure responsible for beta decay. At the time this theory was deemed "too remote from reality" for it to be published in the world renowned Nature journal (this was overturned in 1939). This new force was named the weak nuclear force.

These four fundamental forces were the foundations upon which the whole universe is based. As will be shown in later sections, all of these forces have an associated messenger particle. Now that we knew of these four distinct forces, was there some underlying relationship between them? This question would fuel an ever increasing ambition within the physics community to combine these fundamental forces under a unified law. 


Summary of the four fundamental forces