1. Symmetry in Atomic and Quantum Physics

2. Symmetry in Atomic and Quantum Physics 1
1 Symmetry in Quantum and Atomic Physics
From the interpretive symmetries found in the creativity and subjectivity of human nature, to the sheer
factual objectivity found all around us, we can now shift our focus of symmetry to the largest and most
amazing canvas of them all, the universe.
1.1 A Perfectly Symmetrical Universe
It is widely accepted that 13.7 billion years ago the universe began with an event known as the Big
Bang, whilst the name holds a tone of ironic simplicity; details of the events at the birth of the universe
still prove elusive to us now. It is within these first milliseconds of the universe that our journey into
symmetry begins.
A number of decades ago a type of theory called Supersymmetric Grand Unified Theories began to
emerge from the scientific community [Ode87], these theories suggested that in these first few moments
the universe may have been in a state of perfect symmetry, broken only by time. The consequence of
this would mean that an unlimited number of transformations, reflections and rotations would result in
no change in the universe. It was even suggested by Vilenkin [Vil83] that the universe was created out
of ”nothingness”, he proposes that through quantum tunnelling the universe reaches ”de Sitter” space.
Quantum tunnelling is the concept that dictates the probability that particle can penetrate a barrier
which it does not have the energy to do so [Col01] . De Sitter space is a theoretical concept that was
first created in order to satisfy Einstein’s theory of general relativity, its important characteristics to
us are that it has no matter [Jor06a, Jor06b]. Whilst the fundamentals of his theory are important,
this report requires focus more on the symmetry interlaced into these events. With regards to the state
that Vilenkin refers to as ”nothingness”, would there be an infinite symmetry or no symmetry? Heinz
Pagels describes the geometry of this period as ”The nothingness ’before’ the creation of the universe is
the most complete void we can imagine. No space, time or matter existed. It is a world without place,
without duration or eternity...” [Ode87]. Can our laws of symmetry exist outside of our space-time (as it
is in our dimension, it is primarily governed by this. Further, is there any possibility for CPT: ’Charge,
Parity and Time’ to exist if there is no ”classical” time?)? Conversely, could this be considered, in
fact, as a flawless state of symmetry? I believe it would be highly informative to investigate whether
time can be considered to be infinite during the period of ”no time”. This would at least allow for an
application of at least one aspect of CPT, and to consider the parameter of time as an influential factor;
although whether or not it would reflect symmetry would be cause for another investigation. In terms
of symmetry within our given concept and realm of ’time’, exactly what part ’time’ actually plays on
the symmetry of the universe will be discussed later on in Subsection 1.6 .
As we know, the entropy of the universe can only increase in the long run (according to the second
law of thermodynamics [Woo99]), hence chaos is created from order, therefore if at a point when time
was initialised it can be assumed that the entropy of the universe was at its lowest and hence it had the
potential for perfect symmetry. If there was any matter added to this state of ”nothingness”, then it
would result in the breaking of the perfect symmetry as the distribution of matter would not be equal.
It is our belief that this does reflect perfect symmetry, as where there is a ”nothingness”, there can be
nothing to break symmetry, however we do not, by any means, deem this to be a conclusive statement,
as the mathematics involved is beyond the limits of a report such as this.
1.2 Part of a Bigger Jigsaw
Since the Big Bang, the universe has continued to expand and many moons, planets, stars and galaxies
have been formed among a host of other celestial bodies. This has comprehensively broken the ”perfect
symmetry” mentioned above as the distribution of matter became unequal. The scale to which the
symmetry has been decreased is daunting indeed, with the universe containing over one hundred billion

3. Symmetry in Atomic and Quantum Physics 2
galaxies, and each of these galaxies encompassing hundreds of billions of stars. Despite this, the universe
caries a property that we consider to be astoundingly beautiful, the cosmological principle [HL07] states
that if the universe is considered over a suitably large area and compared to any another area, the
distribution of matter will be approximately the same. This is quite remarkable considering the size and
expanse of the universe (which is approximately equal to the age of the universe, 13.7 billion, multiplied
by a light year, 9,500,000,000,000 [note that disregards any theory on inflation at the beginnings of the
universe as it is outside the realms of application of this report]) in relation to its potential to retain
symmetry. A wonderfully simple analogy of this would be to consider running ones finger over a plane
of glass; whilst it may feel smooth to touch, it is highly uneven at microscopic level [HL07]. It was
unanimously agreed within the group that this is an example of ”beautiful” symmetry, and further
helps demonstrates the ’natural’ art inherently found within our world.
1.3 How Long is this Piece of String?
It has been shown that the universe may have statistical transitional symmetry on a large scale. Likewise,
it is important to consider whether there will be the symmetry of time (note the use of future tense
as at present the universe is still expanding). On a small scale, it is impossible to reverse the arrow
of time; i.e there is no force that will reverse a parachute jumper’s descent. If there was, then why
would the Earth continue to rotate about the Sun when gravity was reversed? [Pit99] Therefore, the
aforementioned hypothesis can be proven to be true. However, how does this apply to the universe on
a larger scale? This question primarily concerns if the universe will begin to contract naturally, thus
will the influence of gravity eventually overcome the kinetic force driving the universe’s expansion. We
know that the universe is currently expanding, due to the redshift caused by the Doppler Effect [AC95],
however there is much debate as to whether it will continue to do so.
There are three possibilities: first, if the density of the universe is below what is known as a critical
level, the universe will continue to expand for an infinite period of time, eventually tearing apart all forms
of matter, even subatomic matter [Par11a], into a universe tending towards de Sitter space. Secondly,
the forces of gravity and expansion could reach a point of equilibrium, where there will be a state of no
expansion or contraction. Finally, the universe could eventually collapse under the force of gravity in
an event known as ”The Big Crunch”.
It is known that the universe continues to expand in accordance with the Hubble Constant [oTdfpa94]
, however whether it will continue to do so is still very debatable. A collaborative paper [Kal02] concludes
that it is possible for all three possibilities to occur, all be it in the extremely distant future. Evidently,
the fate of the universe whose outcome provides the best symmetry, in regards to time, is the one in
which the universe contracts back into the singularity from which all was born so many billions of years
ago, the Big Crunch. If this was the case, it would certainly provide an astonishing level of symmetry
over the universe. However, the extent to which the expansion would be reflected in the contraction is
very much undiscovered; leading to the question of ”Would the influence of gravity provide a perfect
inverse for the expansion?” It is not yet known whether the events which followed nanoseconds after the
Big Bang, such as the separation and creation of the electromagnetic and weak forces, would reverse
and, for example, collapse back into the primal ’electroweak’ force which preceded today’s current forces
[Sat96]. Furthermore, would the factor of time-scale be exactly symmetrical, given that reversing effects
did occur? For example, would the collapse of forces into the electroweak force exist for exactly the
10 picoseconds [Bak07] that it initially existed after the Big Bang, or would the current asymmetrical
nature of the universe affect how quickly or slowly the reverse would happen? It is apparent from the
current uncertainty that, over the coming years, this subject will be one of much debate and interest.

4. Symmetry in Atomic and Quantum Physics 3
1.4 Quantum Entanglement and Quantum Spin
The phenomenon known as Quantum Entanglement is one such area of physics that demonstrates
an innate presence of symmetry in its nature. First off, Quantum Entanglement is the theory that,
under certain circumstances, two particles can become ’entangled’, meaning their properties, such as
speed, momentum, energy, and notably spin, become linked [VV10]. What’s significant about this
process is that these properties remain linked regardless of spatial (and temporal) positioning, relative
to each other. For example, if a property of one entangled particle is measured, the same property of
the entangled pair, a theoretically infinite distance away, would instantaneously be defined; this can be
described as a ”faster-than-light communication” [WCY05] between two particles, known as non-locality.
This is where symmetry plays an interesting part. One property that can become entangled is
Quantum Spin, which has exactly two spin orientations (or Quantum States), known as ’Spin Up’ and
’Spin Down’ [ea04]. Due to the nature of an entangled pair, one particle must always have a Spin Up,
and the other a Spin Down, thus must always be opposites. However, their spin properties are not
simply the reverse of each other, but an exact reflectional symmetry of each other’s properties. It is
yet unknown exactly why entangled particles reflect their properties in this manner, but this occurrence
does demonstrate the power and practicality of symmetry; the natural application of symmetry allows
two particles to remain linked, transcending, essentially, space and time. The power of this ’time
travelling’ connection, thus, is demonstrated by it innately counteracting Albert Einstein’s theory of
general relativity; the statement that ’nothing can travel faster than light’. [Got02] This is demonstrated,
for example, by taking two unknown entangled particles, keeping one on Earth and sending the other
to Alpha Centauri, the closest star to Earth at approximately 4.27 light years. Both particles have
unmeasured properties, and therefore are undefined. If these particles were not entangled, then to know
the Spin of both, it would take 4.27 years (at the very least, given light transmission as the fastest means
of travel) to receive the data from Alpha Centauri, but by measuring the single entangled particle on
Earth, it instantaneously fixes and defines, by symmetry, the state of the entangled partner, that large
distance away [Par11c].
1.5 Symmetric Wave Functions
Another case of symmetry comes from light, itself; or more specifically, the particles which make up light,
called photons. Photons are part of a subatomic group called bosons, which have specific properties.
Essentially, bosons are particles with absolutely symmetrical wave functions, and therefore have more
consistent behaviours [MF01], implying far more predictable actions, in theory.
Because of this symmetry, more than one boson can occupy the exact same Quantum State at any
one period of time. Therefore, unlike other particles (known as fermions, which include protons and
electrons), whose behaviour is erratic and individual; bosons demonstrate unified or ’group’ behaviour,
where each particle acts in a far more coordinated manner [Par11a]. In the aforementioned case of
the photons, this group behaviour is demonstrated in an experiment known as the ”Quantum Double
Slits” experiment, initially created by Thomas Young and developed vastly later on, which harbours
interesting results connected to symmetry. In short, the Quantum Double Slits experiment initially
attempted to demonstrate whether photons act as waves or particles, and was tested by shining a beam
of light through two minuscule slits in front of a solid screen. This demonstrated light as a wave,
as the second screen had what is known as ’interference fringes’, or bands of dark and lighter shades
created by a variation in distance travelled to different areas of the screen, with light from each slit
interfering with each other [Bli04]. Given that the light is coherent and monochromatic (most notably
found in laser light), which essentially produces a pure light; the interference fringes will be an exact
reflectional symmetry with respect to the midpoint of the two slits. This demonstrates the regularity
and symmetrical properties of boson wave functions when grouped together (into one beam of light)
[RAS06]. However, what is even more startling is that manipulating this experiment slightly results in

5. Symmetry in Atomic and Quantum Physics 4
the demonstration of a photon as a particle, as well as a wave, as well as another case of symmetry.
Instead of shining a beam of light at the two slits, it was made so only one boson, one photon, was
shone at the slits any one time. As this was only one particle or wave, it had to traverse through
either one or the other slit, and as it had no other form of light to interfere with, logically in theory, it
didn’t have any means of interference; therefore interference fringes could not be generated. Conversely,
however, when a plethora of single photons of light were fired in practice, one by one, with the resultant
position marked after each attempt, eventually, the original interference pattern appeared, without any
interference present [Par11b]. This creates an identity symmetry with the previous example, but more
interestingly, demonstrates that the symmetric wave function of a photon is identical to its probability
distribution of where to most likely find the particle, the interference pattern; therefore demonstrating
that the interference pattern has a symmetrical probability distribution. This is theorised to be due to
the single photon interfering with itself through the midpoint of the two slits and, in practice, somehow
passing through both slits, thereby symmetrically splitting itself into two when traversing to the screen,
resulting in the two sides of the probability distribution.
1.6 Synoptic Symmetry Breaking
A final case of symmetry within the realms of Physics and the universe takes into account a few ideas
already discussed previously in Subsections 1.3 and 1.5 . As mentioned before, bosons are particles with
symmetric wave functions, but they are also particles associated with the fundamental forces, and in the
following case, the electromagnetic and the strong and weak forces. Because of this, bosons are typically
known as ”force carriers” [Wax10].
Under conditions we now consider as ’normal’, i.e. conditions reflective of the universe as it is
currently, three of the four fundamental forces have an abundance of symmetrical properties, notably
the reflective symmetry and charge exchange of the strong force. This allows these forces to act in
a predictable and coherent manner, akin to the symmetrical probability waves of photons. However,
one force lacks this array of properties: the weak force. This goes a partial way in explaining why the
weak force (with relative strength of 1025 ) is substantially weaker than the strength of its comparative
other, the strong force (of strength 1038 ); the lack of symmetrical properties implies that its inherent
behaviours do not possess the same focus that the strong force does. This is most evidential by the fact
the weak force can act mainly upon left-handed systems (thus an asymmetrical application), such as
quarks and leptons, and the large mass of its bosons inferring a substantially short affect field (ie. its
range). [Cro08] What is crucial about the fact that the W and Z bosons of the weak force are heavy is the
factor of energy levels. When compared to the electromagnetic force, the two are exceptionally different
at low energy levels. However, as the energy of the two systems rise beyond perceivable levels by the
standards of today’s universe, the two forces become more and more symmetrical, tending towards one
identical set of properties; properties of the primal electroweak force. [RAS05] These levels of energy
are parallel to those seen from the outset of the Big Bang, and thus go some way to explaining how
the single electroweak force gave way to two such different forces. In this sense, with the Big Bang as
the starting point of time, time is what creates the diminishing energy levels of the electroweak force,
therefore ’time’ can be considered as the ”symmetry breaker” of the electromagnetic and weak force
symmetry. [McC07] This, therefore, goes some small way in demonstrating how much less symmetrical
the great, big universe is now, compared to the infinite symmetry that it potentially had at the very
foundation of time, or, in fact, before time.

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8. Symmetry in Atomic and Quantum Physics 7
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