Physics Projects

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Reseach Paper on Non-Ideal Quantum Reference Frames
ETH Master Thesis on Quantum Reference Frames
ETH Master Semester Project on Black Hole Information & Analogue Gravity
Activities in Analytical Mechanics (german)
ETH Bachelor Semester Project on the Shadow of a Rotating Black Hole
cuRRay - CUDA Relativistic Raytracer

Research Paper: The Perspectives of Non-Ideal Quantum Reference Frames

title:
The Perspectives of Non-Ideal Quantum Reference Frames

collaborators:
Ladina Hausmann, institute of theoretical physics, ETH Zürich, Switzerland
Dr. Esteban Castro-Ruiz, institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Austria

abstract
We define the perspective of any quantum reference frame (QRF) and construct reversible transformations between different perspectives. Our construction is based on two principles motivated operationally by the change from relative to absolute coordinates and leads to an incoherent group averaging approach with general symmetry group. Thereby, it extends the framework of [arXiv:2110.13199] from ideal QRFs, which generally require infinite resources like energy or angular momentum, to non-ideal QRFs, with only finite resources. We find that the perspective of a non-ideal QRF deviates significantly from that of an ideal QRF: Firstly, systems described relative to a non-ideal QRF appear superselected. Secondly, the structure of the perspective of a non-ideal QRF attests that successive relational operations on a system lead to back-reaction on this QRF.

pre-print:
doi:10.48550/arXiv.2512.19343

PDF file (v2):
paper

relational quantum observables — To measure a quantum observable of the quantum system S relative to another quantum system A, one can imagine first measuring A, and, depending on the outcome, perform an accordingly compensated measurement on S. In this sense, A becomes a quantum reference frame (QRF) for observing S and quantities measured relative to the QRF in this way are called **relational observables**.

The **perspective of the QRF** is then derived as a representation of physics which is particularly suited to the relational observables. Roughly speaking, this diagram shows on the horizontal axis how much of the degrees of freedom of S can be resolved by the QRF as a function of so-called **total charge** on the vertical axis. Here, the ability to resolve these degrees of freedom decreases towards extreme values of the charge because the QRF is **non-ideal**: it only has limited charge itself. Charge can for example be energy; and since energy is fundamentally finite, investigating non-ideal QRF perspectives is physically relevant.

ETH Master Thesis on Quantum Reference Frames

All observations in physics require a reference relative to which the observation is done, a so-called reference frame. Reference frames are often described abstractly (e.g. as coordinate systems), although they have to be implemented by real, physical objects in real-world experiments. Since matter is generally described by quantum theory, it thus makes sense to consider the possibility of using quantum objects as reference frames. Such considerations are even necessary in certain regimes of physics. This leads us to the field of quantum reference frames. One distinguishes two types of (quantum) reference frames: perfect or ideal ones, and imperfect or non-ideal ones. Perfect reference frames are infinitely precise, contrary to imperfect ones. Imperfect reference frames are more realistic, but perfect reference frames are a very useful idealization and easier to work with.

This project is an attempt to explore such imperfect quantum reference frames by seeing imperfect frames as parts of larger, perfect frames. This approach yields non-invertible transformations into imperfect frames.

title:
Transformations Between Imperfect Quantum Reference Frames

supervision:
Dr. Esteban Castro-Ruiz, LMF, Université Paris-Saclay, CNRS, ENS Paris-Saclay, France
Ladina Hausmann, institute of theoretical physics, ETH Zürich, Switzerland
Prof. Dr. Renato Renner, institute of theoretical physics, ETH Zürich, Switzerland

abstract:
Starting from the point of view of an observer, we provide a new construction for unitary quantum reference frame transformations between observer perspectives, and under physical assumptions derive the existence of an observer-independent, external view. The non-trivial problem of reversibly transforming between physically relevant imperfect reference frames is solved by embedding such frames in perfect ones. Thanks to this embedding, our approach allows transforming into the perspective of an imperfect quantum reference frame, in a way which is consistent with the rich information theory of such frames. We explore the consequences of the embedding and explain the point of view of an observer whose frame is imperfect. The findings are applied to imperfect reference frames for one-dimensional Galilei transformations, in light of potential future applications in quantum gravity.

publication in ETH research collection:
doi:10.3929/ethz-b-000620796

PDF file:
master thesis

ETH Master Semester Project on Black Hole Information & Analogue Gravity

For my master in physics I wrote a semester project in theoretical physics on the black hole information loss paradox in the context of analogue gravity models. Roughly speaking, the information loss paradox is a contradiction between quantum field theory in curved spacetime and black hole thermodynamics: The former predicts that black holes lose mass through so-called Hawking radiation, and that the entropy of said radiation always increases. The latter says that the entropy of a black hole decreases as its mass decreases. For the two to be compatible, the entropy of the black hole must always be larger than that of the radiation. But the exact opposite happens.

Analogue gravity models are physical systems in which wave propagation mathematically resembles the propagation of a field (typically a massless scalar field) in curved spacetime. Thus, certain aspects of the system behave mathematically analogously to a field in curved spacetime. Interestingly, such analogue models can describe spacetimes of black holes, and one can even find Hawking radiation in those models. This leads to the question of whether the information loss paradox can also be described in analogue gravity models.

The goal of the semester project was to investigate this question: I argued that the analogy does not extend to the paradox, because black hole entropy has no useful analogy in the model. As a by-product, I developed a new approach to introducing a large class of analogue gravity models, including two of the most important ones.

title:
The Black Hole Information Loss Paradox in the Context of Analogue Gravity

supervision:
Giulia Mazzola, institute of theoretical physics, ETH Zürich, Switzerland
Prof. Dr. Renato Renner, institute of theoretical physics, ETH Zürich, Switzerland

abstract:
We investigate the possibility of approaching the black hole information loss paradox from the point of view of analogue gravity models. More generally, we ask whether analogue models can at all make inferences about gravity. To this end we give an intro-duction to black holes, the black hole information loss paradox, and analogue gravity models, before attempting to formulate the information loss paradox in the context of analogue gravity. We find that crucially, the notion of black hole entropy is missing, placing a discussion of the paradox in that context out of reach. Simultaneously, we argue based on the ubiquity and generality of analogue models that they are unlikely to possess deep connections with gravity.

PDF file:
semester project

Increase of Hawking radiation entropy (predicted by quantum field theory in curved spacetime), compared to the decreasing black hole entropy (predicted by black hole thermodynamics). To solve the paradox, the radiation entropy could for instance follow a so-called Page curve.

Blue lines indicate the flow of a fluid; its speed increases towards the left. The red cones indicated 'sound cones', i.e. the trajectories of sound waves sent out towards the left and right. H marks a so-called 'apparent horizon': it can be traversed by sound only from right to left. This fluid is a simple analogue model for a black hole in one spatial dimension, with sound propagation in the fluid being analogous to light propagation in spacetime.

Activities in Analytical Mechanics (german)

This is a loose collection of independent activities in classical mechanics, special relativity, as well as Lagrangian and Hamiltonian mechanics. Each activity is provided with solutions, further comments and fitting literature.

The activities were create as part of my exercise class for the lecture Allgemeine Mechanik held by Prof. Dr. Renato Renner (institute of Theoretical Physics, ETH Zurich, Switzerland) in the fall semester of 2021.

For more information, see the german version of this page.

ETH Bachelor Semester Project on the Shadow of a Rotating Black Hole

In the last semester (spring 2021) of my BSc physics at ETH Zürich, I wrote a semester project in theoretical physics on the shadow of rotating black holes. The shadow of a black hole is the completely black area in the sky an observer sees when looking at an unobstructed black hole; the shape and size depends on the properties of the black hole and can even be used to infer some of these properties. The project is a literature review of fundamental as well as recent research in the field. As such, it can serve as a structured introduction to the field of black hole shadows.

Title:
The Shadow of a Rotating Black Hole

Supervision:
Prof. Dr. Philippe Jetzer (main supervisor), Physik-Institut, University of Zürich, Switzerland
Prof. Dr. Renato Renner (internal ETH member), Institute of Theoretical Physics, ETH Zürich, Switzerland

Abstract:
The aim of this work is to provide an introduction to the field of shadows of rotating Kerr black holes. We review the mathematics of light propagation in Kerr spacetime and derive the equations describing the edge of a Kerr black hole shadow in the sky of a distant observer. We also discuss recent research concerning the possibility of determining the spin parameter a and the inclination angle θ_O of the observer from direct observations of the shadow. Finally, we showcase two applications of the theory of black hole shadows to the Event Horizon Telescope collaboration image of the supermassive black hole M87*.

PDF file:
semester project
The project can also be found on the webpage of Prof. Jetzer's research group: here.

Kerr shadows — The shadow edge of various rotating black holes (colours distinguish spin parameters, green is zero, red is maximal), seen from various inclination angles **θ_O**. This is fig. 3 of the semester project.

cuRRay - CUDA Relativistic Raytracer

cuRRay is an acronym for CUDA relativistic raytracer, a software I programmed. The software calculates the trajectories of light particles, that is, light rays, near black holes. This way, images of objects near these cosmological monsters can be created. According to Einstein's theory of general relativity, light rays are deflected by the extreme gravity of black holes. The curved light rays lead to highly distorted images of the objects. cuRRay uses NVIDIA CUDA to efficiently compute the paths of light using the graphics card.

cuRRay is the software I programmed for my Matura project at my former high school, Kantonsschule Wohlen. The project won two main prizes at the 2018 swiss national contest of Schweizer Jugend Forscht (SJF): Firstly, a participation at the Stockholm International Youth Science Seminar (SIYSS) 2018, a week-long programme in the context of the Nobel prizes in Stockholm, Sweden. Secondly, a participation at the 2018 European Union Contest for Young Scientists (EUCYS) in Dublin, Ireland. There the project won a special price offered by the European Southern Observatory (ESO) allowing me to travel to Chile and visit telescopes and research sites of ESO. As a hobby astrophotographer, I particularely enjoyed this amazing trip.

You can find more information on cuRRay here.

cuRRay at GitLab

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