# SRP i fysik på SDU

Som gymnasieelev er du altid velkommen til at kontakte en af vores forskere med spørgsmål om deres forskning, eller muligheden for at samarbejde med dem om fx. et studieretningsprojekt.

Vi tilbyder allerede en række SRP tilbud som du kan læse mere om her. Hvis du er interesseret i arbejde sammen med os som del af din SRP så kontakt os direkte eller via din underviser. Du vil få mulighed for at få hjælp på SDU over en række dage hvor vores undervisere og studerende vil hjælpe dig med inspiration, problemskitse og arbejde med dit forskningsproblem.

Nærmere oplysninger om programmet følger.

## Findes mørkt stof i Universet?

Kun 5% af stoffet (massen) i universet, galakser, stjerner, planeter gas, støv, fodvorter, etc, etc. kan beskrives af de kendte elementarpartikler. Fem gange så meget består af mørkt stof – og resten består af mørk energi.
Ingen ved i dag hvad mørkt stof består af – det er et af de største og vigtigste problemer i astrofysikken og partikelfysikken at finde ud af hvad det er.

Men i dette projekt vil vi forsøge at bevise mørkt stof eksisterer.
Vi vil studere data fra stjerner i galakser, de såkaldte rotationskurver, dvs. målinger af galaksens stjerners hastighed i deres cirkelbevægelse omkring galaksens centrum (ofte et supermassivt sort hul). Vores egen sol bevæger sig med ca. 220 km/s (!) rundt om mælkevejens centrum.
Og vi vil bygge en matematisk model, baseret på Newtons love, for hvordan stjernerne burde bevæge sig og gennem den vil vi søge at påvise at det der i virkeligheden styrer stjernernes bevægelse ikke kan observeres og i stedet må være det mystiske mørke stof.

Projektet vil benytte data-analyse, en lille smule differential og integral-regning og newtons lov for tyngdekraften. Det vil vi naturligvis hjælpe dig med og baseret på disse simple elementer vil vi kunne sige noget ekstremt dybt og overraskende om naturen: At langt det meste af Universet stadig idag er skjult for os!

## Quantum world: From certain to uncertain

Thomas Ryttov

Classical physics describes the behaviour of matter and energy at the macroscopic level including the behaviour of astronomical bodies. On the other hand, at the beginning of the 20th century scientists discovered phenomena in the tiny world of atoms that classical physics failed to explain.
In order to be able to theoretically accommodate for the new phenomena physicists realized that the Universe does not obey strict determinate laws. Instead the best we can ever hope for is to describe the world around us in a probabilistic way. The Universe is inherently uncertain. For instance we cannot simultaneously know the position and momentum of a particle at the same instant of time. This is encoded in the famous Heisenberg uncertainty relations.
During the project sessions we will discuss the seemingly paradoxical nature of the experiments with which physicists are faced and many of the fundamental elements of quantum mechanics that nevertheless are able to explain them. In order to do this we have to introduce several new mathematical tools and concepts.

We will introduce some of the physical and mathematical ideas of quantum mechanics. This includes the wave function and the Born interpretation, operators, observables, inner products, eigenfunctions, eigenvalues and the Schrödinger equation. As two examples we will look at the infinite square well and the harmonic oscillator.

“Those who are not shocked when they first come across quantum theory cannot possibly have understood it.”
–Niels Bohr

## Quantum world: wave or particle

Sebastian Hofferberth

In the beginning of the 20th century, the Quantum revolution changed our understanding of physics. In the tiny world of atoms, our classical understanding of mechanics and electromagnetism had to be replaced with a completely new theory, Quantum Mechanics.

For over 100 years, the predictions of quantum mechanics have been confirmed time and again by experiments on atoms, photons, other elementary particles, but also on larger and larger objects such as viruses or mechanical oscillators. Still, many of the fundamental rules of quantum mechanics and their consequences remain hard to understand on an intuitive level.

One of the most prominent sources of confusion is what Bohr named “wave-particle-duality:” The behaviour of quantum objects reminds us sometimes of particles and sometimes of waves – in the end, they are neither and we need new concepts to descripe the world on the quantum level.

In this project, you get the chance to build and perform an optical experiment, where you can study both the wave and the particle nature of light quanta – photons – yourself. With help from SDU physics students you will build a single-photon interferometer. You will count light photon by photon and see with your own eyes what confused the likes of Bohr and Einstein so profoundly – you can then make up your own mind if their opinions are still up-to-date.

This project offers you hands-on experience in building your own optics experiment from lab-grade components and to record and process data. Based on your preferences, it can be combined with the theory introduction to quantum mechanics (see above).

“It seems as though we must use sometimes the one theory and sometimes the other, while at times we may use either. We are faced with a new kind of difficulty. We have two contradictory pictures of reality; separately neither of them fully explains the phenomena of light, but together they do.”
–Albert Einstein

## The Logistic Map

Paolo Sibani

The logistic map was introduced by (sir) Bob May (1976) as a naive model for the yearly variations of an insect population. Let $$x_n$$ be the number of insects in the $$n$$’th year. Clearly, $$x_n$$ will be some function of $$x_{n−1}$$, the number of insects the previous year. Assuming simple proportionality $$x_n = rx_{n−1}$$, one easily finds (try!) the exponential law, $$x_n \propto r^n$$. An exponential growth $$(r > 1)$$ is reasonable for small values of $$n$$, but cannot be sustained indefinitely (why?). To mend the model we therefore assume that the growth from one year to the next becomes less pronounced if the number of insects is large. In fact, if the number of insect is too large the insect population will exhaust its food supply before being able to lay eggs, and it will therefore drop to zero the following year.

## The fundamental structure of space and time

Astrid Eichhorn

What are the fundamental building blocks of our universe? We already know that matter is made out of discrete building blocks, the atoms. But what is the fundamental structure of space and time? This is the question at the heart of the research area of quantum gravity. In this project, we will get to know causal set quantum gravity. In analogy to the atomic structure of matter, this theoretical model postulates that the fundamental structure of space and time is also atomic or “discrete”.

During the project session we will discuss how one can image that the fundamental fabric of our universe is a discrete network of “atoms of spacetime” on which information propagates. We will also learn how to construct such a network – which is called a causal set – on a computer, and build our own model for the fundamental structure of the spacetime around us.

This project gives you the opportunity to discuss some of the most fascinating questions of fundamental physics and gives you a glimpse at cutting-edge research in physics.