Unifying the fundamental forces
Jay Patel and Evan Snook
Preface:
Our goal for this project is to present the inner workings of the standard model and explain the
significance of the lack of a relationship between General Relativity and Quantum mechanics and thus
this document is meant to be read and understood as though we were presenting. Our entire
presentation is based on the most basic of theories in physics and so we are prepared to explain them in
such a way that the class can understand and engage in them. In our project we will start off with briefly
accounting for the parts of the standard model that the class will need to understand and then we will
delve deeper in to the fundamental forces that are: gravity, the weak interaction, the strong interaction,
and electro magnetism. Everybody already know that these forces exist, they have simply never cared
about what they are called or how they work and so once they are pointed out it should be easy to see.
Finally, we will unite all of this knowledge together using string theory (as it is currently the most
accepted theory of unification). This will include explaining all 11 dimensions that the theory requires,
how a particle can have no physical mass, and most importantly why it matters that we can unite
general relativity and quantum mechanics. This will probably take up the last third to half of the
presentation as it is more philosophy than physics since none of it is, or likely ever will be proven as fact.
This is the standard model. It encompasses our most basic
knowledge of the universe as it consists of the smallest known
particles in our window of existence. It is broken up into 2
categories which are bosons (seen in red) and fermions (seen in
blue and yellow). The fermions are further classified into quarks
(blue) and leptons (yellow). Each particle has a mass, charge, and a
spin that makes it unique. However, there are 2 key particles that
are missing from the model and those are the graviton and the
Higgs boson. The Higgs particle (often referred to as the god
particle) is predicted to be the key in understanding what gives
particles mass and thus broaden our understanding of science as
a whole. It may have been discovered earlier this year through
research at the large Hadron collider, but there not sure and so
further testing is being done. Gravitons on the other hand are strictly theoretical though they are just as
important as we need them to complete the standard model and complete a theory of everything which
will be discussed more later on.
This presentation will be mainly focusing on the boson as that’s what interested us the most as well as
gives an understanding of the world around us. This is because the bosons are responsible for the
fundamental forces. These forces are the weak interaction (W and Z bosons), the strong interaction
(gluons), Electro magnetism (photons), and General relativity (gravitons). The Higgs field would also be
included among these forces though once again that is not necessary to our presentation. (What makes
these forces special is how they all have no mass, they are a wave and no rest mass)
To start of simply is to start off with general relativity, or as you all know it, gravity.
It is called general relativity because it combines the theory of relativity with
Newton’s laws of gravitation into a single theory. Gravity is explained by general
relativity as an attractive force that pulls large objects together. But why? It is
because of something referred to as the fabric of space-time. Space-time consists
of our comprehendible reality that is the four dimensions we live in: length, width,
height, and time. This hypothetical blanket that covers the universe bends and
moulds to the shape of the objects that are placed on it and thus as seen in the
picture, it creates an alteration that dissipates over distance. How heavy the object
is will determine how greatly the fabric of space-time is altered as heavier objects
will distort the fabric over a greater distance. But what does this have to do with gravity? It works so
that when an object traveling at any given velocity crosses through the distortion made by a much larger
object, its path curves along with the distortion. Now depending on the speed of the object and its path
through the distortion, it can easily begin to orbit the object given that it doesn’t have a great enough
velocity to escape. We interact with gravity in a slightly different way in that we are so small and so
close to the earth, and the distortion around us is so great that it simply holds us down and to escape is
like climbing an invisible wall that is impossible to grasp.
General relativity is a standalone theory as it does not fit into the standard model in any way. The
remaining 3 theories are all a part of quantum mechanics as they are inter-related. The strange part
about quantum mechanics is how there are no calculate able outcomes about events. In fact the only
consistency about events seems to be how inconsistent they are. The plane of quantum mechanics looks
very different from that of space time as it is unpredictable and random as it waves and bounces in
different directions as opposed to the calm, flat plane of space-time. This makes forming theories and
equations very hard as only one of several outcomes ever occurs, however we can calculate the chances
of each outcome and from that there have been 3 forces derived that govern quantum mechanics.
Electro-magnetism is the first of these forces and is quite literally the unification of electricity and
magnetism into a single theory. Electro-magnetism is not an unfamiliar topic as everybody knows how
magnets work. There are positive charges and negative charges. Opposite charges attract and same
charges repel, the greater the charge, the greater the attraction or repulsion. These same laws work on
a quantum level as they hold everything we know together. Nature is constantly trying to balance out its
charges to be neutral because that is when a substance is strongest. Most things we know are neutrally
charged and thus don’t react with each other. This makes the world around us solid and gives justice to
the fact that we cannot pass a solid through a solid or why tables don’t fuse themselves to the floor
every time we set them down. Electromagnetism is a much stronger force than gravity as magnets can
pick stuff up, thus defying gravity. Perhaps a better example of this is how the ground is made of
electromagnetic bonds, as are we, and gravity is strong enough to hold us close together, but not strong
enough to pull us through. Electro-magnetivity is represented by photons because they interact with
electric and magnetic fields. They do this through electrons as they have the ability to transfer their
energy to an electron to free it of its current bond, the electron can then release the photon at any point
and give up its independence to bond again. This means that when a photon travels through an electric
or magnetic field it interacts with the particles and changes the properties of the field. This is called the
photo electric effect.
The next force we are looking at is the weak
interaction. Like electromagnetism, the weak
interactions purpose is to balance out the
charges in nature, though on a much smaller
scale. This is done in 2 ways as the force covers
both the W- and W+ particles as well as the Zboson. The first way is done through a process
called beta decay in which particles absorb the
necessary W-Boson and shed beta particles (electrons and positrons) in order to keep an optimal
charge. This is done through the intervention of W- and W+ bosons. The Z boson is much stranger as it
has no charge and so nothing happens when it is exchanged other than its momentum is gained (more
on Z-Bosons). The diagram above shows the most common beta decay for a neutron as it is turned into a
proton and 2 fermions. This is because the W-boson emitted was negative and thus giving the neutrino a
positive charge while releasing an electron and its neutrino from the W boson as soon as it decayed. The
reason that all of the charges on earth are not balanced yet is because every particle has a lifespan, and
when this lifespan is up it must break down into smaller particles. These particles can then attract
together again in the right conditions thus forming a seemingly infinite cycle. Beta Decay is most
prevalent in radioactive particles as they have a very short lifespan and so they decay rapidly and give
off radiation.
The last of the fundamental forces is the strong interaction. This is represented
with gluons and controls how they interact with fermions. Gluons glue quarks,
leptons, and other particles together regardless of their charge(why>?) the glue
elementary particles together to make larger particles that we know like protons
and neutrons, and they also hold protons and neutrons together in the nucleus of
the atom. As shown in the picture, the gluons are like waves as they are passed
between particles within an atom to keep it together. Every once and a while the
particles will pass the gluon to an adjacent atom and form a bond with it as they
begin to exchange gluons as well. It’s like playing catch in gym class where everybody has partners to
throw too but then there’s always somebody that has to whip the ball across the gym to a buddy that
wasn’t his partner or you have somebody who is really bad at throwing and completely misses there
partner and hits somebody else.
To reiterate we have gravity that keeps the planets in orbit and us on the ground, electromagnetism
that keeps us from going through the ground, the weak force that keeps everything neutrally charged,
and the strong force that holds the atoms together. The problem with these theories is that gravity
works really well for large things and quantum mechanics works really well for small things, but when
one is exchanged with the other, nonsensical answers are formed as they just don’t work together.
This is where string theory comes in.
What is string theory? It is the most basic fundamental things making everything that’s around us.
Everything is made of atoms. Atoms are made of electrons, protons and neutrons. The protons and
neutrons are made of quarks. The string theory goes farther than this. String theory says that the
elementary particles are each made up of a string. All the string vibrates in the different patterns that
can be calculated mathematically.
All of the strings vibrate in the difference frequency. The different frequencies produce the different
particles. The different particle makes the world around us. This is unification because here we get to
see that the matter and all the force particles are made of one fundamental idea the string. There is
some problem with the string theory first is that the string theory’s mathematics doesn’t work just in the
3D space and 1d time it works in the 10 D. Therefore the string theory requires ten dimensional space
and 1D of time. There could be two types of dimensions the large ones and the small ones. All the
dimensions could be around us but we just can’t feel it or we just can’t see it. These dimensions are
curled up to so tiny in the space and time curved. It is so tiny that the most powerful technology in the
world cannot see the dimensions. Let’s take a look at the dimensions. For example we see the cable for
the traffic light from our house window. We see that it is just the line one dimensional object. When
magnified, a second dimension- one that is in the shape of the circle and is
curled around –becomes visible. So now imagine that the ant is walking on the cable the ant can actually
have two independent directions in which it can walk: along the left-right dimension. The direction is
“clockwise-counterclockwise dimension”. The ant can walk horizontal extent; the other dimension is
circular, is short and curled up. So we show big dimension but there is some dimension that is so small
and curled up that is not possible to see but let’s take a look at the small curled up dimension.
The grid line resent the extend dimensions of common experience, whereas the
circle is the new, tiny, curled-up dimension. Like the circular loops of thread
making up the pile of the carpet, the circles exist at every point in the familiar
extended dimension. If we were small enough then we can walk in the circle
dimension which would be five dimensions, one more than the normal
dimensions which would be space and time. Kaluza thought that the dimensions are so small that is
would be smaller than the Planck’s length. There are other 5 dimensions curled up all to they create
Calabi-Yau shapes.
Therefore, there are 3 space+1 time+6 curled, small D+1=11
The string theory is not only about the dimensions but it is also about the
unification of all forces including the general relativity and quantum machines. The
Calabi-Yau Shape
string theory gives the basic understand how the universe is formed and made of but
the problem occurs is that there are 5 different kinds of string theories.
Type I, Type IIB, Type IIA, Heterotic-O, Heterotic-E. There isn’t a single
explanation for each theory because they are all explained in math. They
shared many common ideas-their vibrational patterns determine the
possible mass and force charges, they require a total of 10 space-time
dimensions, their curled-up dimensions must be in one of the Calabi-Yau
shape. All of this five string theory is combining to make the unified
theory the M-theory. The M theory has eleven dimensions(ten space and one time). They found one
additional one called spatial dimension allowed for an unexpected merger of general relativity and
electromagnetism. The other things that M theory states that they know that it contains vibrating string
but it is more then that. It also includes the vibrating two dimension membrane and the three-brane.
These is M theory.
Black holes:
-Tachyons- theoretical particles that are faster than light.
-Wormholes, black holes, big bang theory
Wormhole: A tube-like region of space connecting one region of the universe to another. The
-Examples to do-
-special relativity
Q.M theories are related by the uncertainty principle and wave- particle duality
How m-theory connects the forces