Hello and welcome to my presentation. I would like to show you what I have been working for, for the last couple of weeks. The topic of my BSc project is called ‘Grand Unification in Extra dimensions’, and during the next 12 minutes I will explain you the main idea of the concept of a so-called ‘Unification of the forces’ in particle physics, and its relation to the idea of having more than 4 spacetime dimensions. Before starting, I should point out, that my project is of a purely theoretical nature, so I neither spent any time in the lab, nor did I write any line of code. What I spent my time with was almost exclusively literature research to review an interesting theory in modern particle physics.

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I will start my presentation by showing you which ‘problem’ actually gave rise to the invention of a ‘Grand Unification Theory’, which is namely the effect that the well-known fundamental forces behave differently at very high energies.

I will then go on and show you the current explanation for this behaviour according the present ‘Standard Model’ of particle physics. This is the so-called ‘quantum fluctuation’, which arises from uncertainty principle. There are, however, some points this model cannot explain.

Finally I will demonstrate an idea to find such a grand unified theory, namely ‘extra dimensions’. At that point, however, I will be up to the point where I currently am with my work, and therefore I will not give you a final solution to the problem, but rather show you, what I am going to investigate the next weeks.

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So, as we all know, there are four fundamental forces in nature. These are gravity, which is the weakest force of all, then the electromagnetic force, which is quite a bit stronger,then the weak interaction, which is still a bit stronger, and the strong interaction, which is unsurprisingly the strongest of all forces.

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For this work we will set gravity apart and only consider the three remaining forces.

The electromagnetic force and the weak interaction have already successfully been incorporated into a single theory called ‘electroweak interaction’. A theory incorporating the weak interaction, electromagnetism, and the strong interaction is called ‘Grand Unified Theory’.

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So let’s think about what the ‘strength of a forces’ actually means. We measure the strength of a force by placing two particles a certain distance apart (which is actually a natural unit length). The ratio of the resulting potential energy to the particle’s rest mass is then a dimensionless number and a measure of the force’s strength. It turns out, that for low energies, this is actually a constant and is therefore called ‘coupling constant’ and it is usually denoted by alpha. In the case of electromagnetism this is actually also the fine-structure constant which is directly related to the unit charge by the relation alpha = e²/4πε0ħc, which is about 1/137. Similar calculations also work for the weak and the strong interaction.

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We can now compare the strengths of the forces. Here I have plotted the inverse of the coupling constants, that is 1/alpha over energy. This means, that, at low energies, the electromagnetic force is the weakest, then comes the weak interaction, and the strong interaction the strongest, just as we expected. However, at high energies, the strengths of the forces start to deviate, and somewhere at very high energies of the order of 10^14 GeV, all the three forces, are of almost the same strength! This effect is known as the ‘running of the coupling constants’.

So the first question that arises is obviously, why the coupling constants vary at high energies. This effect is well understood by the standard model of particle physics. The second question is then, why the couplings only ALMOST meet at certain energy and not exactly.

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We are looking for a theory in which all three forces unify in one single point at a single energy. This is then referred to as ‘unification of the forces’.

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When we measure the strength of a force, say, for example the electromagnetic one, we essentially shoot two particles, - in this case electrons - towards each other in a particle collider, and see, how strongly they repel. Nothing special so far.

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Now, by the uncertainty principle, an electron can spontaneously emit a photon. If the photon has enough energy, it can then decay into an electron-positron pair. Of course, since the electron and the positron attract each other, they will soon annihilate again into a photon, so they are rather short-lived.

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This leads to an electron effectively being surrounded by electrons and positrons, that are spontaneously created, survive for a while and are then annihilated again. Since the original electron attracts positive charges, the created positrons will on average be closer to the original electron, and the created electrons will be further away. This way, the vacuum has effectively become a polarisable medium, and is therefore screening the charge in the centre.

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In experiments at low energy, electrons that are shot towards another, don’t approach each other very closely. They are quickly repelled, and therefore feel only the screened charge due to the electron-positron cloud. At high energies however, the electrons can penetrate the electron-positron cloud and therefore don’t feel the screening. Therefore they repel more strongly, and the measured charge appears to be bigger. So this way we can explain and actually also calculate the running of the coupling constants we saw earlier. According to this calculation however, there is no unification of the forces in a single point!

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To also achieve unification of the forces, there are basically two ideas. One is super symmetry, which means that for every particle there exists an integer and a half-integer spin variant. The other one – the one I am dealing with – is extra dimensions. Current theories of extra dimensions assume 10 or 11 spacetime dimensions. All of the additional dimensions are thought to be ‘compactified’, which means, that they are ‘curled up’ into small circles and hence very small and not visible at large scales. This is the reason why they haven’t been experimentally observed yet. These extra dimensions, however, can contribute a correction to the running coupling constants.

And this is the part I still have to do for my project.

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So what I have done for my project so far is the following:

I have described the concept of compactified extra dimensions – for which I unfortunately didn’t have enough time here.I also have reviewed quantum fluctuation and the resulting charge screening and I also have derived the equations that describe the running of the coupling constants in the standard model.

What I still have to do is, to investigate the effect of extra dimensions on the running coupling constants. It will eventually turn out, that compact extra dimensions actually change the running of the coupling constants in a way, that all the 3 forces unify at one single point at a certain high energy.

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