Analysing Particle Physics And Its Models Philosophy Essay

Particle physics is the science of what everything we know is made of. Particle Physicists study the fundamental particles which make up all of matter, and how these particles interact with each other. Everything around us is made up of these building blocks of nature. So, what are they?

In the early 1900's it was thought that atoms were the fundamental blocks; they were thought to be the smallest piece of nature and were not composed of anything smaller.

Soon many experiments were done to see if this was truly the case. It was later discovered that atoms were not fundamental, but were made up of 2 parts: a positively charged nucleus surrounded by negative electrons.

Thereafter the nucleus was probed, but it too was found to be made up of something smaller; positive protons and neutral neutrons bound together with the mass of electrons surrounding it.

After these protons and neutrons were found, it was time to see if they were fundamental or not. It was discovered that they too were made up of smaller particles called "quarks", which are now believed to be truly fundamental, along with electrons. Furthermore, electrons belong to a family of fundamental particles, which are called leptons. Quarks and leptons, along with the other forces that allow them to interact, are arranged in a neat theory named The Standard Model.[2]

1.2 Standard Model

The Standard Model is a picture that shows how all the different elementary particles are organized and how they interact with each other along with the known different forces. The elementary particles are split up into 2 branches, namely the quarks and the leptons. Both of these families consist of 6 particles, split into 3 generations, with the first generation being the lightest, and the third the heaviest. Furthermore, there are 4 different force carrying particles which lead to the interactions between these particles. [2]

1.3 AntiMatter

An interesting fact that has been found about matter particles is that each has a corresponding anti-particle. The term anti may be a bit deceiving, as it is still real matter. The difference between a particle and its anti-particle is that an anti-particle has an opposite electrical charge to that of the particle.

Think of them as mirror images. In our experience right and left are the only things to reverse when looking at the mirror. Similarly, in the particle world, charge is what reverses when looking at the "mirror". Its spin, mass and most (quarks have something else called colour charge which is also changed in the mirror) other properties remain the same.

In general, an anti-particle is the particles name with "anti" as a prefix. For example, the anti-particle of hydrogen is the anti-hydrogen. An exception to this rule is the electron, whose anti-particle is known as positron. [2]

1.4 Quarks

To start with, there are 6 types of quarks (plus their 6 anti-quarks), which are coupled into 3 pairs. They are the top-bottom (sometimes known as truth-beauty), the charm-strange, and the up-down. Another interesting thing about quarks is that you can never find one alone, as they are always with some other quarks arranged to form composite particles. The terminology for these composite particles is hadrons. Quarks, like protons and electrons, have an electric charge. However, their electric charges are fractions not integers, either 2/3 or -1/3 (-2/3 and 1/3 for anti-quarks), and they always arrange to form particles with have an integer charge (-1, 0, 1, 2..). [2]

Flavour

Mass

(GeV/c2)

Electric Charge

(e)

u

up

0.004

+2/3

d

down

0.08

-1/3

c

charm

1.5

+2/3

s

strange

0.15

-1/3

T

top

176

+2/3

B

bottom

4.7

-1/3

Because quarks combine with each other to form particles with an integer charge, not every kind of combination of quarks is possible in nature. There are 2 fundamental types of hadrons. They are baryons, which are composed of 3 quarks, and mesons which are made up of a single quark and a single anti-quark. 2 examples of a baryons are the neutrons and protons.

The proton is made of 2 up quarks and 1 down quark. When the charges from the individual quarks are summed up, you arrive at the charge of +1 for the proton.

The neutron is made up of 2 down quarks and 1 up quark. Again, summing up the charges from the quarks, we arrive at zero.

An example of a meson is a pion. It is composed of 1 up quark and 1 down anti-quark. Because mesons are a combination of a particle and an anti-particle, they tend to be very unstable and decay very rapidly.

1.5 Leptons

Similar to quarks, there are 6 types of leptons, and again, in 3 pairs. Electron-neutrino, muon- neutrino, and tau-neutrino (these 3 neutrinos are different). The electron, muon, and tau each carry a -ve charge, whereas the 3 neutrinos carry no charge. Leptons, unlike quarks, can exist by themselves, and, like all other particles, have a corresponding anti-particle. [2]

Flavour

Mass

(GeV/c2)

Electric Charge

(e)

electron neutrino

<7 x 10-9

0

electron

0.000511

-1

muon neutrino

<0.0003

0

muon

(mu-minus)

0.106

-1

tau neutrino

<0.03

0

tau

(tau-minus)

1.7771

-1

As the chart indicates, the muon and tau are much heavier than the electron. Furthermore, they are not found in normal matter. This is because they decay very rapidly, usually into lighter leptons. There are a few of rules that govern the decay of leptons.

Rule 1: One decay product of the heavy lepton will be its corresponding neutrino. The other products could be either a quark and its anti-quark, or a lighter lepton and its anti-neutrino.

Rule 2: The total number of members before and after must be conserved (realizing that an anti-particle is considered a negative member). For example, if a tau particle decays into a lighter lepton, the tau's corresponding neutrino will be the product of the decay, keeping a total of 1 family member before and after the decay. The other products could be the lighter lepton and its corresponding anti-neutrino, keeping a total of 0 members before and after for that family of leptons. Because of the fact that:

1 + (-1) = 0

Chapter 2

Baryons

2.1 Introduction

A baryon is a composite particle which is made of 3 quarks. Baryons are opposed to mesons which are made of 1 quark and 1 antiquark. Both baryons and mesons belong to the hadron family, which are the particles that are made of quarks.

As baryons are composed of quarks, they participate in strong interaction. Leptons are not made of quarks and as such do not take part in strong interactions that baryons do. The most well-known baryons to us are the protons and neutrons which make up most of the mass in the observable matter in the universe, where-as electrons (the other major part of atoms) are leptons. Each baryon has a corresponding antiHYPERLINK "http://en.wikipedia.org/wiki/Antiparticle"-particle (anti-baryon) where quarks are replaced by their corresponding anti-quarks. For example, a proton is made of 2 up quarks and 1 down quark; and its corresponding anti-particle, the antiHYPERLINK "http://en.wikipedia.org/wiki/Antiproton"-proton, is made of 2 up anti-quarks and 1 down anti-quark.

Baryons are strongly interacting fermions; they undergo strong nuclear force and are described by Fermi-Dirac statistic, which apply to all particles that obey the Pauli’s Exclusion Principle. This is in contrast to bosons, which do not obey the principle.

Baryons, along with mesons, are hadrons, they are particles composed of quarks. Quarks have baryon numbers of B = 1⁄3 and anti-quarks have baryon numbers of B = −1⁄3. The term ‘baryon’ usually refers to tri-quarks—baryons made of 3 quarks (B =1⁄3+1⁄3+1⁄3 = 1). [6]

2.2 Baryonic Matter

Baryonic matter is the matter composed mainly of baryons (by mass), which includes atoms of all sorts (and therefore includes all matter that we encounter or experience in everyday life, including in our bodies). Non-baryonic matter, as implied by its name, is that sort of matter which is not mainly composed of baryons. This might include such normal matter as the neutrinos or free electrons; however, it may also include exotic types of non-baryonic dark matter, such as super-HYPERLINK "http://en.wikipedia.org/wiki/Supersymmetry"symmetric particles, black holes or axions.

The difference between baryonic and nonbaryonic matter is vital in the field of cosmology, because the Big Bang nucleosynthesis models set strict constraints on the amount of baryonic matter that was present in the early universe. [6]

The very existence of baryons is also an important issue in cosmology today as we assumed that the Big Bang produced a universe with equal amounts of baryons and anti-baryons. The process by which baryons outnumbered their anti-particles is called baryogenesis [5]

2.3 Properties

2.3.1 Isospin and charge

The concept of isospin as known today was first given by W Heisenberg in 1932 to show the similarity between protons and neutrons under the strong interaction. Although these particles had different charges, their mass was so similar that scientists believed they were one and the same. Their different electric charges were shown as being caused due to an unknown excitation like spin. This unknown excitation was later called isospin by E Wigner in 1937.

This belief lasted till M Gell-Mann explained the quark model in 1964(originally containing only the s, d and u quarks).The success of the isospin theory is shown to be the result of similar mass of the d and u quarks. Since the d and u quarks have similar mass, particles which are made of the same number of them also have similar masses. The exact d and u quark number determines the charge of the particle; u quarks carry charge +2⁄3 and d quarks carry −1⁄3. For example the 4 Deltas all have different charges (Δ++ (uuu), Δ+ (uud), Δ0 (udd), Δ− (ddd)), but similar masses (~1,23 MeV/c2) and as each of them is made of a total 3 d and u quarks. In the isospin model, they were thought to be one particle in different charged states.

The science of isospin was modeled after that used in spin. Isospin projections varied in increments of +1 just like in spin, and to each projection was associated with a charged state. Since the Delta particle had 4 charged states, it was said to be of an isospin I = 3⁄2. Its charged state Δ++, Δ+, Δ0, and Δ−, corresponded to the isospin projections I3 = +3⁄2, I3 = +1⁄2, I3 = −1⁄2, and I3 = −3⁄2 respectively. One more example is the nucleon particle; as there are 2 nucleon charged states, it was said to be of isospin 1⁄2. The +ve nucleon N+ (proton) was identified as I3 = +1⁄2 and the neutral nucleon N0 (neutron) as I3 = −1⁄2.

In the isospin picture, the 4 Deltas and the 2 nucleons were thought to be different states of 2 particles. Although in the quark model, the deltas are different states of nucleons (the N- or N++ are forbidden by the Pauli's exclusion principle). Isospin, although conveying an incorrect picture of things, is still used to classify baryons today, leading to an unnatural and often confusing nomenclature. [5]

2.3.2 Flavour quantum number

The strangeness flavour quantum number abbreviated as S (not related to spin) was noticed to go up and down along with the particle mass. The higher the mass was, the lower the strangeness becomes (the more s quarks). Particles could then be described with isospin projections (related to charge) and their strangeness (mass). As more and more quarks were discovered, new quantum numbers had similar description to that of udc and udb octets and decuplets. As only the u and d mass are similar, this description of particle mass and charge in terms of isospin and flavour quantum numbers works for octet and decuplet made of 1 u, 1 d and one other quark and breaks down for the all other octets and decuplets (for example ucb octet and decuplet). If all the quarks had the same mass, their behaviour would be called as symmetric, as they would all behave in the same way with respect to strong interaction. Since quarks don’t have the same mass, they don’t interact in the same way (just like an electron placed in an electric field would accelerate more than a proton placed in the field because of its lighter mass), and the symmetry is said to be broken. [6]

2.3.3 Spin, orbital angular momentum, and the total angular momentum

Spin (quantum number S) is a vector quantity that represents the "intrinsic" angular momentum of a particle and it comes in increments of 1⁄2 ħ (h-bar). The ħ is often dropped because it is the fundamental unit of spin, and hence it is implied that "spin 1" means "spin 1 ħ". In some systems of natural units, ħ is chosen to be equal to 1. Therefore it does not appear anywhere.

Quarks are fermionic particles of spin equal to1⁄2 (S = 1⁄2). As spin projections vary in increments of 1 (that is 1 ħ), a single quark has a spin vector of length 1⁄2, and has 2 spin projections (Sz = +1⁄2 and Sz = −1⁄2). 2 quarks can have their spins aligned, in which case the 2 spin vectors add to make a vector of length S = 1 and 3 spin projections (Sz = +1, Sz = 0, and Sz = −1). If 2 quarks have unaligned spins, the spin vectors would add up to make a vector of length S = 0 and this has only 1 spin projection (Sz = 0), etc. Since baryons are made of exactly 3 quarks, their spin vectors can add to make a vector of length S = 3⁄2 which has 4 spin projections (Sz = +3⁄2, Sz = +1⁄2, Sz = −1⁄2, and Sz = −3⁄2), or give a vector of length S = 1⁄2 with 2 spin projections (Sz = +1⁄2, and Sz = −1⁄2).

There is also another quantity of angular momentum, called the orbital angular momentum (L) which comes in increments of 1 ħ, it represents the angular moment due to quarks orbiting around each other. The total angular momentum of a particle (quantum number J) is therefore the combination of the intrinsic angular momentum (called spin) and orbital angular momentum. It can take a value from J = |L − S| to J = |L + S|, in increments of 1.

Particle physicists are very interested in baryons which have no orbital angular momentum (L = 0), as they correspond to ground states—states of least energy. Therefore the groups of baryons most studied are the S = 1⁄2; L = 0 and S = 3⁄2; L = 0, which correspond to J = 1⁄2+ and J = 3⁄2+ respectively, and they are not the only ones. It is also possible to obtain J = 3⁄2+ particle from S = 1⁄2 and L = 2, as well as S = 3⁄2 and L = 2. This phenomenon of having many particles in the same total angular momentum configuration is called as degeneracy. [5]

2.3.4 Parity

If the entire universe was reflected in a mirror, most of the laws of physics would be left identical—things would behave the same way regardless of what we call right and what we call left. The concept of mirror reflection is the intrinsic parity or parity (abbreviated as P). The electromagnetic force, gravity, and the strong interaction all behave in a similar way regardless of whether or not the universe is reflected, and therefore are said to conserve parity (P symmetry). However, the weak interaction does distinguish left from right, a phenomenon known as parity violation (P-violation).

Based on this, we might think that if the wave-function for each particle (more precisely, the quantum-field for each particle) were simultaneously mirror reversed, the new set of wave functions would perfectly satisfy the laws of physics (apart from that of the weak interaction). As it turns out, that this is not the case: In order for the equations to work, the wave functions of certain types of particles have to be multiplied by −1, in addition to being mirror reversed. Such particle types are said to have odd or negative parity (P = −1, or alternatively P = –), while all the other particles are said to have even or positive parity (P = +1, or alternatively P = +). [5]

2.3.5 Nomenclature

Baryons are divided into groups according to their isospin (I) values and quark (q) content. There are 6 groups of baryons—nucleon (N), Delta (Δ), Lambda (Λ), Sigma (Σ), Xi (Ξ), and Omega (Ω). The rules for classification are defined by the Particle Data Group. These rules consider the up (u), down (d) and strange (s) quarks to be light and the charm (c), bottom quark (b), and top (t) to be heavy. The rules cover all the particles that can be made from 3 of each of the 6 quarks, even though baryons made of t quarks are not expected to exist because of the t quark's short lifetime. The rules do not cover pentaquarks.[13]

Baryons with 3 u and/or d quarks are the N's (I = 1⁄2) or the Δ's (I = 3⁄2).

Baryons with 2 u and/or d quarks are the Λ's (I = 0) or the Σ's (I = 1). If the third quark is heavy, its identity is given by a subscript.

Baryons with 1 u or d quark are the Ξ's (I = 1⁄2). 1 or 2 subscripts are used if one or both of the remaining quarks are heavy.

Baryons with no u or d quarks are the Ω's (I = 0), and subscripts indicate any heavy quark content.

Baryons that decay strongly have their masses as part of their names. For example, Σ0 does not decay strongly, but Δ++(1232) does.

It is also a widespread practice to follow some additional rules when differentiating between some states which would otherwise have the same symbol.[8]

Baryons in total angular momentum J = 3⁄2 configuration which have the same symbols as their J = 1⁄2 counterparts are denoted by an asterisk (*).

Two baryons can be made of 3 different quarks in J = 1⁄2 configuration. In this case, a prime (′) is used to differentiate between them.

Exception: When 2 of the 3 quarks are 1 up and 1 down quark, 1 baryon is dubbed Λ while the other is dubbed Σ.

Quarks carry a charge, so knowing the charge of a particle indirectly gives us the quark content. For example, the rules above say that a Ξ+c contain a c quark and some combination of 2 u and/or d quarks. The c quark as a charge of (Q = +2⁄3), therefore the other 2 must be a u quark (Q = +2⁄3), and a d quark (Q = −1⁄3) to have the correct total charge (Q = +1). [5]

Chapter 3

The Big Bang

3.1 introduction

One of the most frequently asked question in today’s world is: How was the universe made? Many people believed that the universe has no beginning or an end and is actually infinite. After the introduction of the Big Bang theory, however, we could no longer consider the universe to be infinite and our view of the universe was forced to take on the properties of a finite phenomenon, one which possessed a beginning and a history. 

Around 13.7 billion years ago a tremendous "bang" started the expansion of the universe. This explosion is aptly named as the Big Bang. At the point of this event, all of the matter and energy of space was contained at a single point called the singularity. What may have existed prior to this event is totally unknown and is a matter of speculation. This occurrence was not any conventional explosion but rather an event that filled all of space with all of the particles of the embryonic universe expanding away from each other. The Big Bang consisted of an explosion of space within itself unlike a normal explosion of a bomb were fragments are tossed outward. The galaxies were not clumped together, but rather the Big Bang caused the foundations for the universe to emerge. 

The origin of the Big Bang theory can be credited to Edwin Hubble. Hubble made an observation that the universe is continuously expanding. He discovered that a galaxy’s velocity relative to us is proportional to its distance from us. Galaxies that are thrice as far from us move thrice as fast. Another fact is that the universe is expanding in every possible direction. This observation means that it has taken each and every galaxy in the universe the same time to move from a common starting point to its current location. While the Big Bang provided us with the foundation of the universe, Hubble’s observations provided us the foundation of the Big Bang theory. 

Since the beginning of the Big Bang, the universe has been expanding and, there has been more and more displacement between clusters of galaxies. This phenomenon of galaxies moving farther and farther away from each other is known as the red shift. As light from distant galaxies approaches the earth there is an increase of space between earth and the galaxy, which leads to wavelengths of light being stretched, causing it to move into the red spectrum. 

In addition to the understanding the velocity of galaxies emanating from a single location, there is further evidence for the Big Bang. In the year 1964, two astronomers, Arno Penzias and Robert Wilson, in an attempt to try to detect microwaves from outer space, discovered a noise of extra-terrestrial origin. This noise did not seem to emanate from any one location but instead, it came from all directions at the same time. It became quite obvious that what they heard was the radiation from the farthest reaches of the universe which was left over after the Big Bang. This discovery of the radioactive aftermath of the initial explosion supported the Big Bang theory. 

Even more recently, NASA’s COBE satellite was detected cosmic microwaves emanating from the furthest reaches of the universe. These microwaves were remarkably uniform which showed the homogeneity of the early stages of the universe (just after the big bang). However, the satellite also found that as the universe started to cool and was still expanding, and small fluctuations began to crop up due to temperature differences. These fluctuations helped verify prior calculations done on the possible cooling and development of the universe just moments after its creation. These fluctuations in the universe helped provide a more detailed description of what happened in first moments after the Big Bang.

The Big Bang theory provides a useable solution to one of the most important questions of all time. It is prudent to understand, however, that the theory itself is continuously being revised. As more observations and calculations are made and more research is conducted, the Big Bang theory becomes more and more complete and our knowledge about the origins of the universe becomes more substantial. [4]

3.2 The First Atoms

Now that we are familiar with the theory of the Big Bang, the next logical question that comes into our mind would be what happened afterward? In the infinitesimally small fractions of the first second after creation what was once a complete "emptiness" began to change into what we know now as the universe. In the beginning there was nothing except for a soup of superhot plasma. What is known of these brief moments in time, at the start of our study of cosmology, is largely conjecture. However, science has devised a sketch of what probably happened then, based on what is known about today’s universe. 

Just after the Big Bang, as one might imagine, the universe was extremely hot as a result of particles of both anti-matter and matter rushing away in all directions. As it cooled, at about 10^-43 seconds after creation, there existed an almost equal although asymmetrical amount of anti-matter and matter. As these two materials are created together, they collide and annihilate one another resulting in pure energy. Fortunately for us, there was a slight asymmetry in favour of matter. As a direct result of an excess of just about one part per billion, the universe was able to mature in a way favourable for matter to persist. As the universe began to expand, this discrepancy grew bigger. The particles of matter began to dominate. They were created and they decayed without the accompaniment of an equal creation or decay of an anti-particle.