A matter dominated universe

We live in a world of matter – and its existence is vital to the evolution of a universe that has allowed galaxies, stars, planets and eventually human life to develop.  However, this scenario is not as obvious as we would assume, and the conditions that allowed a matter inhabited universe to come into being are believed to be the result of unusual and obscure processes.  This report will examine how matter has come to dominate the current universe, by focusing on its other half, anti-matter.  It will ask the key question of how matter managed to survive, whilst anti-matter did not.

Anti-matter is an arbitrary term applied to a family of particles that complement the particles that make up our universe (as well as those that are believed to have existed in the past).  The term is arbitrary, because there is nothing intrinsic about anti-matter that makes it different, other than being essentially non-existent in our observations.  For this reasons it is presented as the opposite of what we know the world to be.  In this report, when a particle or scenario is referred to as normal, this normality is in terms of familiarity only. Anti-matter is also referred to as anti-particles.  An anti-particle is the specific opposite particle of a normal particle, normally designated with the prefix anti (e.g. anti-neutrino, anti-proton, anti-quark).  One exception to this rule is the opposite particle of an electron, which for historical reasons is known as a positron, having a positive charge.  The positron was the first anti-particle discovered, and retains this name.  The abundance of anti-particles that were later discovered made coming up with new names very taxing on scientists (particularly as many of these anti-particles were discovered at the same time as the partner particles, which needed new names of their own).  However, the term anti-electron is just as accurate. Anti-matter is the collection of all anti-particles, and may be used to describe any anti-particle.  On a larger scale, anti-matter can imply physical structures of atomic size and upwards, that are matter opposites of those we know, such as anti-atoms of anti-hydrogen.  The study of how large scale structures would operate if made of anti-matter (e.g. anti-stars) and how they would differ from their matter counterparts is one of the interesting areas of study in this field.

What is anti-matter?

If we start by taking a look at the familiar world around us, and probe to the atomic level, we find that matter is made up overwhelmingly of three key particles – protons, electrons and neutrons.  All matter we are familiar with is made of these particles, and limiting yourself to these, you could build an acceptable description of matter.  These particles can be defined by a number of attributes, such as their mass and energy (which are related via special relativity), and their electrical charge.  It is well known that electrons have a negative electrical charge, whilst protons have a positive charge, and neutrons have no electrical charge (keeping in mind that these designations of positive and negative are once again arbitrary human distinctions).  In terms of mass, neutrons and protons are roughly the same size (the neutron being slightly larger), being about 2000 times as large as an electron[i]. Simply stated, anti-particles are the equivalent of normal particles, with their electrical charge reversed.  Thus an anti-electron (herein called a positron) has the same mass and energy as an electron, but has a positive electrical charge.  Likewise the anti-proton is the negatively charged equivalent of the proton.  (The anti-neutron is a slightly more tricky proposition that will be discussed later.) E=mc² is a well know equation, although its true significance is often obscured.  The equation shows a relationship between rest mass and energy, with mass being a store of large amounts of energy.  In appropriate conditions, mass and energy are interchangeable.  Although atomics weapons and power plants utilise this relationship to derive their power, only a small amount of matter is actually converted to energy in these processes (about 2%).  By comparison, one of the defining properties of an anti-particle is that it when it collides with its matching particle, 100% of the mass of both particles is converted to energy, causing complete annihilation of both particles.  Because C² (the speed of light squared) is such a large number, large amounts of energy are released. Whilst the ability to convert matter to energy is generally well known, the reverse process is just as feasible.  However, just as large amounts of energy are released from matter, large amounts of energy are required to produce matter – the energy required being proportional to the mass of the particle.  These energy levels do not exist in the current world, and so the reverse process of matter being created out of energy is not a familiar natural process.  Particle accelerators on earth do manage to achieve these energy levels for brief periods (on atomic scales), and much of the understanding we have of these processes is derived from these experiments. In the early universe, however, pressure and temperatures were of such high levels that matter was routinely created from energy.  Just as a particle/anti-particle pair annihilate to release radiation, radiation at sufficiently high energy levels will produce a particle/anti-particle pair.  Because electrons have lower mass, electron/positron pairs are produce at lower energy levels than proton/anti-proton pairs.  But providing sufficient energy is available, any particle/anti-particle pair may be produced.  Whilst this process sounds straightforward, the energy levels are very large, and only in the first 10^-4 seconds of the universe were sufficient energy levels available[ii].  Thus all the base constituents of matter (protons, neutrons, electrons) in the universe were ‘created’ in the first 10^-4 of a second. Whilst the special relativity equation E=mc² is well known, it is actually a special case solution (when the particle is at rest) to the generic relativity equation E² = m²c⁴+p²c²,which defines the relationship between momentum (p) and energy[iii].  Paul Dirac was a leader in the early field of linking relativity with quantum mechanics, and the Dirac equation, describing particle wave functions, yielded four solutions that satisfied the energy-momentum relation.  Two of the solutions involved negative energy levels (all quadratic equations yield a positive and negative root), which Dirac correctly deduced referred to two separate particles – antiparticles[iv]. Positrons were predicted by Paul Dirac in a paper published in Nature in 1930, although he was not himself sure whether they actually existed.  However, in 1932 Carl Anderson, performing experiments with cloud chambers, was able to determine that cosmic rays contained particles that had the same weight as electrons, but an opposite electrical charge (shown by their response to a magnetic field)[v].  These experimental results confirmed the existence of anti-particles, and introduced anti-matter as a valid physical phenomenon.

Where is the anti-matter?

Because matter and anti-matter are created in equal proportions, we can ask ‘where is all the anti-matter’.  This is an interesting question.  Cosmic rays (which are ionised atomic nuclei – the high energy levels separating the electrons) coming from space overwhelmingly contain matter, with anti-matter particles being produced during their high energy collisions with earth’s atmosphere(these were the positrons detected by Anderson)[vi].  If there are regions of space with matter and anti-matter that are interacting, then large quantities of gamma rays would be emitted at the regions of interaction (and annihilation).  To data no regions of gamma ray emission have been associated with anti-matter.  Because annihilations take place at the edges of interacting regions, they should be visible (at gamma ray frequencies) as boundary regions.  Most gamma ray sources are more centrally focused. Potentially there are regions of anti-matter that are significantly separated from regions of matter, allowing them to survive and form into galactic structures.  Anti-matter exhibits the same physical properties as normal matter (with some rare exceptions discussed later), so a star made of anti-matter would shine identically to a normal star, and anti-hydrogen would produce the same spectrum as regular hydrogen. Despite these difficulties, NASA developed the Alpha Magnetic Spectrometer (see figure 1), an anti-matter particle detector that is scheduled to be attached to the space station in 2003.  This instrument will analyse cosmic rays for anti-particles, specifically anti-helium.  Because helium formed after the universe had cooled below the threshold for proton/anti-proton pair creation, the existence of anti-helium nuclei would go a long way towards confirming the existence of anti-matter in the universe (producing anti-helium outside an anti-star or the early universe would be virtually impossible)[vii]. Figure 1 As well as anti-particle cosmic rays, there is another difference between stars that are made of anti-matter and those made of matter.  In the cores of regular stars, where energy is created by the fusion of protons into helium nuclei, a small electrically neutral particle called a neutrino is created during this reaction.  In a theoretical anti-matter star, however, anti-neutrinos would be produced via the fusion reactions of anti-protons.  A star emitting large streams of anti-neutrinos would be a candidate for an anti-matter star. Unfortunately, neutrinos and anti-neutrinos react very weakly with normal matter, and apart from solar neutrinos (and very high-energy phenomenon such as super-novas), detecting neutrinos from definable interstellar objects is beyond current experimental  capabilities, and such a ‘neutrino telescope’[viii] may prove impossible to construct.  Adding to this difficulty, the milky way galaxy is safely assumed to be devoid of significant amounts of anti-matter, so any anti-stars would come from distant intergalactic sources, making detection even more difficult.

How did we get here?

Whilst “where is the anti-matter?” seems a logical question to ask, a more appropriate question is “why is there matter?”. The special relativity equation that links matter and energy shows no preference for matter over anti-matter.  Therefore, the mass created from energy will consist of equal amounts of matter and anti-matter.  However, as we have identified, the creation of matter from energy requires very high energy levels (temperatures), and once the temperature of the universe dropped below these levels, these matter creation processes ceased.  Accordingly,  this should leave an equal number of particles and anti-particles, with no more able to be created.  However, as particle/anti-particle pairs annihilate, these equal quantities should have annihilated one and other, leaving no matter, only a sea of radiation.  As matter is the building block of all structure in the universe, the balancing of these processes is inconsistent with the world around us. There are two broad explanations for this matter/anti-matter asymmetry (as it is generally referred to).  Firstly, we can postulate that this imbalance was built into the universe at conception.  Because the known laws of physics breakdown at the singularity that represent the start of the big bang (time = 0), no knowledge of these conditions can be derived.  Whether this point is analysed from a theological or scientific perspective, it is impossible to prove or disprove the makeup of this initial state, and allows us to explain observed phenomenon quite readily. However, this approach does not assist in the scientific process, and its arbitrariness means that it does not need to be consistent with other physical phenomenon, and places it outside the realms of scientific investigation. The other possibility is that at some stage during its evolution,  the universe moved from a state of matter/anti-matter symmetry into its present matter dominated state.  The possibility of this occurring, and the evidence for processes that contributed to this asymmetry will be the basis for the remainder of this report.

Conservation laws

In studying the elementary nature of physics, scientists have established a number of laws that they believe rule processes within the universe.  A group of these laws are referred to as conservation laws, and cover the maintenance of the balance of specific quantities during physical processes.  The conservation of electrical charge and conservation of mass-energy are two such laws that appear to be rock solid[ix].  These theories have been tested many times, and their frameworks are key to describing key physical processes, particularly in light of relativity and quantum mechanics. Another law is referred to as the conservation of baryon number.  Baryons are a collective term for protons and neutrons.  Protons and neutrons are assigned a baryon number of 1, whilst anti-protons and anti-neutrons are assigned a baryon number of –1.  All other particles have a baryon number of 0.  The law of baryon conservation says that the baryon number of the universe must never change, and that physical processes must conserve baryon number.  There are several examples of physical reactions that involve changes to baryons:

• the creation of a baryon/anti-baryon particle pair from a high energy state
• the decay of a free neutron into an electron and a proton (and an anti-neutrino)
• the merging of proton and an electron in a neutron star to form a neutron.

In each of these cases, either the changes to baryon number cancel each other our (baryon(+1)/anti-baryon(-1) creation/annihilation – net change 0), or another baryon replaces the original baryons (neutron (1) decaying into a proton(1) – net change 0). If the law of baryon conservation is unbreakable, then it would appear that assuming that the universe started in a start of equilibrium, there was no possibility of matter/anti-matter asymmetry to come into being.  Any increases in baryons over anti-baryons would have violated this law. However, there is not the significant basis for the conservation of baryon number (the concept of baryon number is just an accounting device, unlike electrical charge, which drives a crucial physical mechanism).  Accordingly, scientists have started to search for reactions that breach this law.  As the neutron follows an established path of decay outside the nucleus which does not breach baryon conservation, researchers are focusing on the proton, which is the smallest stable baryon.  Evidence of proton decay would show that baryon conservation is not absolute. Once the possibility of proton decay was identified, a number of experiment were established attempting to detect such decay.  Based on general approximations, the minimum life span of a proton is 10¹⁸ years[x], but initial theories predicted a life of 10²⁹ years[xi].  Although this is a very  long time (the universe if 10¹⁰ years old), predicted life spans are probability factors.  If protons have a lifetime of 10²⁹ years, then in a mass containing 10²⁹ protons, one should decay each year.  However, experiments using even larger quantities of protons have failed to detect proton decay, raising the lower limit on life span, and causing scientists to consider alternate paths for matter/anti-matter asymmetry. Although proton decay does not appear to be the direct cause of matter/anti-matter asymmetry (if discovered, then it is just as likely there is a process of anti-proton decay), it would demonstrate a breach of the law of baryon conservation.  It is also predicted by several theories that endeavour to solve the matter/anti-matter asymmetry problem.

Symmetries in nature

Nature exhibits many symmetries, and it is these symmetries that appear to prevent matter and anti-matter being produced at different rates.  Symmetries refer to the notion that physical reactions will occur in an identical fashion even is the symmetrical properties are reversed.  A key symmetry is referred to as CPT symmetry, and has three elements:

1. Charge conjugation – a process will operate identically if the particles are replaced with their anti-particles.  Thus, the decay of a neutron into a proton, electron and anti-neutrino will be identical to the decay of an anti-neutron into an anti-proton, a positron and a neutrino.
2. Parity – particles have been shown to rotate around their own axis.  This property is referred to as ‘spin’.  In particles, spin can take on only two forms.  It can either be parallel to the direction of motion, or the opposite direction, which are arbitrarily called left and right handedness.  Parity symmetry implies that nature has no preference for left or right handedness.
3. Time – a reaction will be identical regardless in which direction of time it occurs.  Thus the decay of a particle will be identical to the formation of a particle if the process is reversed.

Whilst each individual element of CPT symmetry was held to apply to physical reactions, breaches have been found for each one.  CPT symmetry proposes that change to one element must be offset be changes to another, preserving the symmetry of the overall system, even though individual elements are compromised.

Conditions for matter/anti-matter asymmetry

Soviet scientist Andre Sakharov was a pioneer in the field of cosmology research, and focused on the issue of matter/anti-matter asymmetry.  He determined three conditions that must exists for this to occur.

1. There must be processes that produce baryons out of non-baryons.
2. These baryon creation reactions must breach C and CP symmetry, or the production of baryons will be matched by the production of anti-baryons, leaving baryonic equilibrium.  For such a breach to occur, and for CPT symmetry to be maintained, a time reversal invariance must exist.  This is often referred to as ‘time having an arrow’[xii].
3. The universe must move from a state of thermal equilibrium to one of disequilibrium.  If a system is in thermal equilibrium, any reaction changing the number of baryons and anti baryons (which have the same mass) will still cause them to exist in equal abundance[xiii].

Although his paper was published in 1967, it was not influential in western research for another decade.  Nonetheless, in the intervening years, research revealed conditions that met each of these three requirements.

Breaches of symmetry

Up until about 1954 (when contradictory experimental evidence began to emerge[xiv]),  the individual elements of CPT symmetry were believed to hold firm.  Since then, a number of reactions that breach these symmetries have been discovered.  Neutron decays at low temperatures were shown to give off electrons which showed a preference for a particular parity (Wu; Lee and Yang)[xv].  However, this is offset by the notion that the same reaction with anti-neutrons would give off particles with a reversed parity, thus maintaining CP symmetry.  Likewise experiments examining the decay of muons into electrons, electron neutrinos and muon neutrinos (Garwin, Lederman, Weinrich) shows a preference for left-handedness[xvi].

An arrow of time

Whilst appearing obvious at a macroscopic level (broken glasses do not unbreak), on a microscopic level, most physical reactions are believed to be capable of time reversal.  This concept is linked to antimatter, and if true would mean that “every process that can occur involving particles can also occur at precisely the same rates if all particles are replaced by their antiparticles…”[xvii]  Thus, if a neutron decays into a proton, electron and anti-neutrino, then an anti neutron will decay into an anti-proton, a positron and a neutrino at the same rate. However, if matter/anti-matter asymmetry was introduced into a symmetrical universe, then the previously described particle decays would occur at different rates, indicating that reactions do indeed favour one direction of time.  If a reaction could be identified that supported a single direction of time, then the case for matter/anti-matter asymmetry would be improved. Our discussions to date have treated proton and neutrons as basic particles, but they are in fact made up of simpler particles known as quarks.  Each baryon contains three quarks of two different types (referred to as up and down quarks).  Likewise, anti-baryons are made of three anti-quarks of two different types (this is how an anti-neutron, which has no charge, is distinguished from a neutron). Four other types are postulated to exist, but these do not make up regular matter, and instead form the basis of exotic particles that can only exist in high energy scenarios (and which decay very rapidly after creation).  One of these quarks is termed a strange quark, and is a component of an exotic particle called a k-meson, or a kaon. Studies of kaon decay (Christenson, Cronin, Fitch, and Turlay[xviii]) have revealed that the neutral kaon (which is its own anti-particle) decays in a way that breaches CP symmetry, and that in a time reversal of this process, the rate of particle creation for neutral kaons would be different, giving evidence of time asymmetry.  Kaon decay is the only observed process that meets the requirement for time reversal invariance to be violated.

A solution to matter/anti-matter asymmetry

One of the difficulties facing physicists is that the conditions in the early universe are far more intense with regards to temperature and density than can be replicated through particle accelerators on earth.  As scientists probe matter to a new level they learn many things.  However, many processes that may contribute to matter/anti-matter asymmetry took place in conditions that are many orders of magnitude beyond those scientists can utilise.  This divergence of scale is a double edged sword.  Because so little is truly known about these conditions, there is great scope for developing solutions to many problems.  However, gaining experimental evidence, the corner-stone of scientific inquiry, is heavily restricted, and the most plausible of theories remain speculation, without concrete results obtainable. The weak force that causes particle decay, converting one particle into another, is the only force that is shown to violate CP symmetry. As discussed earlier, when dealing with early conditions of the universe, bold extrapolations can be made, but they must be viewed as such.  One set of such extrapolations are the so-called Grand Unified Theories (GUTs), which endeavour to link the three non-gravitational forces (electromagnetism, strong and weak forces). Over very small scales (15 orders of magnitude beyond those observable today), these forces are believed to be the same, with the small scale allowing the quantum fluctuations to have minimal impact on the forces[xix].  In the gauge theory of forces, force carrier particles are postulated for each of the forces (photons for electromagnetism, gluons for strong force and bosons for weak force)[xx].  These different particles interact differently with the quantum background, and therefore have different strengths and manifestations[xxi].  The weak force that allows time invariance violation will at higher temperature under GUT allow a broader range of particle conversions, converting quarks into other particles, such as electron and neutrinos. GUTs makes several predictions about the nature of matter in the early universe.  Chief amongst these is the existence of a massive particle called an X boson (W and Z bosons are the particles that are believed to govern the weak decay in the present universe[xxii]).  The X boson is a massive (10¹⁵ GeV – compared with a protons mass of just under 1 GeV[xxiii]) unstable particle.  Because of its instability, it does not exist in the current universe.  Moreover, because of it large mass, it can only be created under extremely energetic conditions – when the temperature of the universe was greater than 10¹⁵ GeV.  The universe is believed to have cooled below this level after about 10^-35 seconds, but prior to this, the X boson would have been “the dominant constituent of matter”[xxiv] GUTs predict several reactions involving the X boson.  If an up quark emits an X Boson, it changes into an anti-up quark.  The emitted X boson would decay into an anti-down quark and a positron.  This reaction meets the first or Sakharov’s criteria, creating quarks (which form baryons) where none existed previously.  However, for every X boson, there would be an anti-X boson, decaying in a similar manner, but producing anti-particles of the X-boson decay particles. As the universe cooled, these particles would have stopped being created, and annihilated with each other.  However, prior to annihilating, some may have decayed in the manner described above, creating quarks and leptons.  As well as decaying into an anti-down quark and a positron, an X boson can decay into two quarks[xxv].  However, like the kaon, but affecting quarks and leptons, the X boson and anti-X boson decays do not operate at the same rate, and breaches C and CP symmetry occur.  These breaches produce an excess of quarks over anti-quarks, and are believed to be the cause of the matter dominance that is seen in the universe today. Finally, because the big bang theory predicts an expanding and cooling universe, Sakharov’s third requirement of thermal disequilibrium is provided.  GUT combined with big bang cosmology provide a possible explanation for who the universe developed matter/anti-matter asymmetry.

So, here we are!

The reaction appears to leave a very slight excess of matter over anti-matter.  Is this enough to build the universe we see in a consistent manner?  We are helped in this question by an observation that is central to all discussions of cosmology – the cosmic background radiation.  CBR is a sea of low energy radiation that appears to inhabit the entire universe, and is believed to be the residue of photons left over from the big bang.  Studies of the CBR have shown a ratio of photons to baryons of about a billion to one.  This implies that as the temperature of the universe dropped below levels allowing matter/energy equilibrium (at levels sufficient for baryon/anti-baryon particle pair creation), to produce current ratios there must have been 1 extra matter particle for each billion anti-matter particles.  So the process that created matter/anti-matter asymmetry was fairly subtle, perhaps explaining the difficulties faced today in identifying the exact processes involved. Whilst this may seem a neat solution, it must be remembered, that part of the reason that the symmetry laws provide such an obstacle to seeking a cause for asymmetry is their overwhleming dominance of processes in the present universe.  The shift from symmetry to asymmetry was brief, and once it occurred, the present matter component of the universe appears to have been fixed.  Once the level of matter over anti-matter was established, it was fixed for the rest of time (proton decay not with standing!). Whilst we have shown a logical path for matter/anti-matter asymmetry, we have no proof that such a process talk place, and are unlikely to be able to reproduce these circumstances to test our hypothesis in any useful time frame.  However, we can look for other components of GUT that may cause reactions that can be observed now or in the future.  One of the predictions of GUT is the decay of protons, which we discussed earlier.  X particles are predicted to be produced and exchanged during the collision of quarks.  Whilst a quark collision is a very rare event, it is not an impossible event, and so expectations of quark collisions leading to proton decay exist, triggering a number of proton detection experiments. Although many extrapolations are required, and many questions still remain, the combination of GUT and observed physical reactions provide a mechanism introducing matter/anti-matter asymmetry into the early universe, and causing the dominance of matter over anti-matter that we see in the universe today.  Consistency with other physical theories and support for other observed phenomenon allow scientists to use these theories as the basis for further research and prediction into other areas of physics and cosmology.  As our understanding of particle physics and the early universe increase, and more powerful particle accelerators provide greater amounts of data, further advances upon these theories are likely, ideally giving as greater insight into the how the universe (and ourselves) came into being. Bibliography Adams, F. and Laughlin, G. “Five ages of the Universe”, Touchstone, 1999 Fraser, G. “Anti-matter:  The Ultimate Mirror”, Cambridge University Press, 2000 Feynman, R. “The Feynman Lectures in Physics – Volume 1”, Addison Wesley, 1977 Greene, B. “The Elegant Universe”, Vintage, 2000 Gribbin, J. “In Search of the Big Bang”, Penguin Books, 1998 Krauss, L. “Atom”, Little, Brown and Company, 2001 Sartori, L. “Understanding Relativity”, University of California Press, 1996 ‘t Hooft, G. “Gauge Theories of the Forces between Elementary Particles”, contained in “Particle Physics in the Cosmos”, W. H. Freeman and Co, 1989 Wilczek, F. “The Cosmic Asymmetry Between Matter and Anti-matter”, contained in “Particle Physics in the Cosmos”, W. H. Freeman and Co, 1989