A master’s degree thesis

Nobody will argue that a master’s degree thesis is a daunting and long work, and it is an obligatory requirement if you want to get a diploma. However, do not hurry to panic. With some planning and organization skills, almost all students manage to complete their master’s degree theses successfully.

Do you want to know more about these techniques? Do you want to know the main secrets of a successful thesis that can bring you a master’s degree? We are glad to share them!

Successful master’s degree thesis: secret 1

Since you are going to deal with a really long work, start as early as possible. Procrastination is one the leading failure factors.

Successful master’s degree thesis: secret 2

Before getting down to work, make sure you know all the specific requirements of your institution. As a rule, almost all master’s degree theses are organized according to a similar pattern. However, many institutions have their own specific requirements that you definitely have to follow.

Successful master’s degree thesis: secret 3

Do not wait until your master’s degree thesis is finished to submit it for review. Better do it each time a new section of your project is done. First, it is easier for your advisor to check your thesis in chunks. Second, you will have less work if you correct mistakes just in one chapter, but not in the whole project.

Successful master’s degree thesis: secret 4

Pay special attention to the literature review section of your master thesis. Do you remember the main purpose of completing this huge project? You have to demonstrate an in-depth understanding of the chosen field of study. A perfect literature review is the most effective way to do it.

Successful master’s degree thesis: secret 5

Keep all materials (documents, photographs, statistics, etc.) that you use for writing your master’s degree thesis in one place. You will have to use some of them to make appendices.

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Space changing with time

Think of a very large ball. Even though you look at the ball in three space dimensions, the outer surface of the ball has the geometry of a sphere in two dimensions, because there are only two independent directions of motion along the surface. If you were very small and lived on the surface of the ball you might think you weren't on a ball at all, but on a big flat two-dimensional plane. But if you were to carefully measure distances on the sphere, you would discover that you were not living on a flat surface but on the curved surface of a large sphere.
The idea of the curvature of the surface of the ball can apply to the whole Universe at once. That was the great breakthrough in Einstein's theory of general relativity. Space and time are unified into a single geometric entity called spacetime, and the spacetime has a geometry, spacetime can be curved just like the surface of a large ball is curved.
When you look at or feel the surface of a large ball as a whole thing, you are experiencing the whole space of a sphere at once. The way mathematicians prefer to define the surface of that sphere is to describe the entire sphere, not just a part of it. One of the tricky aspects of describing a spacetime geometry is that we need to describe the whole of space and the whole of time. That means everywhere and forever at once. Spacetime geometry is the geometry of all space and all time together as one mathematical entity.

What determines spacetime geometry?

Physicists generally work by looking for the equations of motion whose solutions best describe the system they want to describe. The Einstein equation is the classical equation of motion for spacetime. It's a classical equation of motion because quantum behavior is never considered. The geometry of spacetime is treated as being classically certain, without any fuzzy quantum probabilities. For this reason, it is at best an approximation to the exact theory.
The Einstein equation says that the curvature in spacetime in a given direction is directly related to the energy and momentum of everything in the spacetime that isn't spacetime itself. In other words, the Einstein equation is what ties gravity to non-gravity, geometry to non-geometry. The curvature is the gravity, and all of the "other stuff" -- the electrons and quarks that make up the atoms that make up matter, the electromagnetic radiation, every particle that mediates every force that isn't gravity -- lives in the curved spacetime and at the same time determines its curvature through the Einstein equation.

What is the geometry of our spacetime?

As mentioned previously, the full description of a given spacetime includes not only all of space but also all of time. In other words, everything that ever happened and ever will happen in that spacetime.
Now, of course, if we took that too literally, we would be in trouble, because we can't keep track of every little thing that ever happened and ever will happen to change the distribution of energy and momentum in the Universe. Luckily, humans are gifted with the powers of abstraction and approximation, so we can make abstract models that approximate the real Universe fairly well at large distances, say at the scale of galactic clusters.
To solve the equations, simplifying assumptions also have to be made about the spacetime curvature. The first assumption we'll make is that spacetime can be neatly separated into space and time. This isn't always true in curved spacetime, in some cases such as around a spinning black hole, space and time get twisted together and can no longer be neatly separated. But there is no evidence that the Universe is spinning around in a way that would cause that to happen. So the assumption that all of spacetime can be described as space changing with time is well-justified.
The next important assumption, the one behind the Big Bang theory, is that at every time in the Universe, space looks the same in every direction at every point. Looking the same in every direction is called isotropic, and looking the same at every point is called homogeneous. So we're assuming that space is homogenous and isotropic. Cosmologists call this the assumption of maximal symmetry. At the large distance scales relevant to cosmology, it turns out that it's a reasonable approximation to make.
When cosmologists solve the Einstein equation for the spacetime geometry of our Universe, they consider three basic types of energy that could curve spacetime:
1. Vacuum energy
2. Radiation
3. Matter
The radiation and matter in the Universe are treated like a uniform gases with equations of state that relate pressure to density.
Once the assumptions of uniform energy sources and maximal symmetry of space have been made, the Einstein equation reduces to two ordinary differential equations that are easy to solve using basic calculus. The solutions tell us two things: the geometry of space, and how the size of space changes with time.

String Theory

hink of a guitar string that has been tuned by stretching the string under tension across the guitar. Depending on how the string is plucked and how much tension is in the string, different musical notes will be created by the string. These musical notes could be said to be excitation modes of that guitar string under tension.
. In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings.
. In string theory, as in guitar playing, the string must be stretched under tension in order to become excited. However, the strings in string theory are floating in spacetime, they aren't tied down to a guitar. Nonetheless, they have tension. The string tension in string theory is denoted by the quantity 1/(2 p a'), where a' is pronounced "alpha prime"and is equal to the square of the string length scale.
. If string theory is to be a theory of quantum gravity, then the average size of a string should be somewhere near the length scale of quantum gravity, called the Planck length, which is about 10-33 centimeters, or about a millionth of a billionth of a billionth of a billionth of a centimeter. Unfortunately, this means that strings are way too small to see by current or expected particle physics technology (or financing!!) and so string theorists must devise more clever methods to test the theory than just looking for little strings in particle experiments.
. String theories are classified according to whether or not the strings are required to be closed loops, and whether or not the particle spectrum includes fermions. In order to include fermions in string theory, there must be a special kind of symmetry called supersymmetry, which means for every boson (particle that transmits a force) there is a corresponding fermion (particle that makes up matter). So supersymmetry relates the particles that transmit forces to the particles that make up matter.
. Supersymmetric partners to to currently known particles have not been observed in particle experiments, but theorists believe this is because supersymmetric particles are too massive to be detected at current accelerators. Particle accelerators could be on the verge of finding evidence for high energy supersymmetry in the next decade. Evidence for supersymmetry at high energy would be compelling evidence that string theory was a good mathematical model for Nature at the smallest distance scales.

String theory

Think of a guitar string that has been tuned by stretching the string under tension across the guitar. Depending on how the string is plucked and how much tension is in the string, different musical notes will be created by the string. These musical notes could be said to be excitation modes of that guitar string under tension.
. In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings.
. In string theory, as in guitar playing, the string must be stretched under tension in order to become excited. However, the strings in string theory are floating in spacetime, they aren't tied down to a guitar. Nonetheless, they have tension. The string tension in string theory is denoted by the quantity 1/(2 p a'), where a' is pronounced "alpha prime"and is equal to the square of the string length scale.
. If string theory is to be a theory of quantum gravity, then the average size of a string should be somewhere near the length scale of quantum gravity, called the Planck length, which is about 10-33 centimeters, or about a millionth of a billionth of a billionth of a billionth of a centimeter. Unfortunately, this means that strings are way too small to see by current or expected particle physics technology (or financing!!) and so string theorists must devise more clever methods to test the theory than just looking for little strings in particle experiments.
. String theories are classified according to whether or not the strings are required to be closed loops, and whether or not the particle spectrum includes fermions. In order to include fermions in string theory, there must be a special kind of symmetry called supersymmetry, which means for every boson (particle that transmits a force) there is a corresponding fermion (particle that makes up matter). So supersymmetry relates the particles that transmit forces to the particles that make up matter.
. Supersymmetric partners to to currently known particles have not been observed in particle experiments, but theorists believe this is because supersymmetric particles are too massive to be detected at current accelerators. Particle accelerators could be on the verge of finding evidence for high energy supersymmetry in the next decade. Evidence for supersymmetry at high energy would be compelling evidence that string theory was a good mathematical model for Nature at the smallest distance scales.

Antimatter

Antimatter sounds like the stuff of science fiction, and it is। But it's also very real. Antimatter is created and annihilated in stars every day. Here on Earth it's harnessed for medical brain scans.

"Antimatter is around us each day, although there isn't very much of it," says Gerald Share of the Naval Research Laboratory. "It is not something that can be found by itself in a jar on a table."

So Share went looking for evidence of some in the Sun, a veritable antimatter factory, leading to new results that provide limited fresh insight into these still-mysterious particles.

Simply put, antimatter is a fundamental particle of regular matter with its electrical charge reversed. The common proton has an antimatter counterpart called the antiproton. It has the same mass but an opposite charge. The electron's counterpart is called a positron.

Antimatter particles are created in ultra high-speed collisions.

One example is when a high-energy proton in a solar flare collides with carbon, Share explained in an e-mail interview. "It can form a type of nitrogen that has too many protons relative to its number of neutrons." This makes its nucleus unstable, and a positron is emitted to stabilize the situation.

But positrons don't last long. When they hit an electron, they annihilate and produce energy.

"So the cycle is complete, and for this reason there is so little antimatter around at a given time," Share said.

The antimatter wars

To better understand the elusive nature of antimatter, we must back up to the beginning of time.

In the first seconds after the Big Bang, there was no matter, scientists suspect. Just energy. As the universe expanded and cooled, particles of regular matter and antimatter were formed in almost equal amounts.

But, theory holds, a slightly higher percentage of regular matter developed -- perhaps just one part in a million -- for unknown reasons. That was all the edge needed for regular matter to win the longest running war in the cosmos.

"When the matter and antimatter came into contact they annihilated, and only the residual amount of matter was left to form our current universe," Share says.

Antimatter was first theorized based on work done in 1928 by the physicist Paul Dirac. The positron was discovered in 1932. Science fiction writers latched onto the concept and wrote of antiworlds and antiuniverses.

Potential power

Antimatter has tremendous energy potential, if it could ever be harnessed. A solar flare in July 2002 created about a pound of antimatter, or half a kilo, according to new NASA-led research. That's enough to power the United States for two days.

Laboratory particle accelerators can produce high-energy antimatter particles, too, but only in tiny quantities. Something on the order of a billionth of a gram or less is produced every year.

Nonetheless, sci-fi writers long ago devised schemes using antimatter to power space travelers beyond light-speed. Antimatter didnt get a bad name, but it sunk into the collective consciousness as a purely fictional concept. Given some remarkable physics breakthrough, antimatter could in theory power a spacecraft. But NASA researchers say it's nothing that will happen in the foreseeable future.

Meanwhile, antimatter has proved vitally useful for medical purposes. The fleeting particles of antimatter are also created by the decay of radioactive material, which can be injected into a patient in order to perform Positron Emission Tomography, or PET scan of the brain. Here's what happens:

A positron that's produced by decay almost immediately finds an electron and annihilates into two gamma rays, Share explains. These gamma rays move in opposite directions, and by recording several of their origin points an image is produced.

Looking at the Sun

In the Sun, flares of matter accelerate already fast-moving particles, which collide with slower particles in the Sun's atmosphere, producing antimatter. Scientists had expected these collisions to happen in relatively dense regions of the solar atmosphere. If that were the case, the density would cause the antimatter to annihilate almost immediately.

Share's team examined gamma rays emitted by antimatter annihilation, as observed by NASA's RHESSI spacecraft in work led by Robert Lin of the University of California, Berkeley.

The research suggests the antimatter perhaps shuffles around, being created in one spot and destroyed in another, contrary to what scientists expect for the ephemeral particles. But the results are unclear. They could also mean antimatter is created in regions where extremely high temperatures make the particle density 1,000 times lower than what scientists expected was conducive to the process.

Details of the work will be published in Astrophysical Journal Letters on Oct. 1.

Unknowns remain

Though scientists like to see antimatter as a natural thing, much about it remains highly mysterious. Even some of the fictional portrayals of mirror-image objects have not been proven totally out of this world.

"We cannot rule out the possibility that some antimatter star or galaxy exists somewhere," Share says. "Generally it would look the same as a matter star or galaxy to most of our instruments."

Theory argues that antimatter would behave identical to regular matter gravitationally.

"However, there must be some boundary where antimatter atoms from the antimatter galaxies or stars will come into contact with normal atoms," Share notes. "When that happens a large amount of energy in the form of gamma rays would be produced. To date we have not detected these gamma rays even though there have been very sensitive instruments in space to observe them."

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