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Routledge eBooks

Quantum Chaos

Paul Thomas

Published Oct 20, 2025• 0 citations
Publisher

Abstract

In my own artistic practice, I have sought to address the complexity of making the invisible visible. This statement is particularly true when it comes to my Quantum Chaos Series. Using a variety of mediums, from computer-based algorithms to traditional painting, I aim to visualise the liminal space dividing the “classical” and quantum worlds. We exist at an everyday level in a world made real by various cognitive systems and approaches to sensation. Yet at the submolecular level, the world of discrete and independent objects and the uncertain world of quantum flux are clearly distinct.

DOI
10.4324/9781003683285-10

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In my own artistic practice, I have sought to address the complexity of making the invisible visible. This statement is particularly true when it comes to my Quantum Chaos Series. Using a variety of mediums, from computer-based algorithms to traditional painting, I aim to visualise the liminal space dividing the “classical” and quantum worlds. We exist at an everyday level in a world made real by various cognitive systems and approaches to sensation. Yet at the submolecular level, the world of discrete and independent objects and the uncertain world of quantum flux are clearly distinct.
Art has the remarkable capacity to reveal things previously unrecognisable until they emerge visually, allowing us to accept new images and expand our ability to interpret the world. Such images become additions to the mental archive we use to recognise and understand our surroundings. Imagining something entirely new is, perhaps, altogether impossible insofar as our understanding is rooted in mental models we compare with external images. When it comes to quantum theory, for instance, we struggle to find any existing schema in our reliquary of mental images to draw from—with attempts to visualise quantum phenomena frequently creating only greater confusion as we try to make sense of its novel qualities within more traditional frameworks. An artwork expressing something unfamiliar about the world can challenge viewers to expand their canvas of consciousness, welcoming new possibilities. By attentively examining a work of art, we can sidestep preconceptions that might otherwise cast the unknown as alien. Art invites us to ask, “What sensations does this image offer me? What gift is it extending?”
Departament d’Astronomia i Astrofisica. Universitat de ValenciaBefore entering into any deeper philosophical discussions,our immediate intuition is that our world is comprised of ourown consciousness, with its contents and varying states,and an outer world that is independent of our conscious-ness. Take, for example, a table and the image and idea wehave of that table. Let’s say the table is brown. Yet, what isbrown? The table, you reply, which even had it been red orgreen would still be a table. This table is also, to a greater orlesser extent, hard to the touch. So, let’s try again. What isthis hard, brown object? The very table under discussion, atall times the table, which moreover occupies a given placeand has certain dimensions. The table, that if I close my eyesdisappears from sight, but returns if I open them. This tableis the object of somebody else’s comments, (oh, that memo-rable meal we had on it one day!) and my expectations(now, I leave, but when I come back tomorrow, I know I willfind it in the same corner of the room). Yet it seems that thistable, the real table, whatever be the significance of this ass-esment, is not the brown colour I perceive, nor the tactilesensation, nor its environment, nor its apparent size in myeyes, nor the comments I have heard about it, nor the mem-ory I keep of it, nor the expectations to which it gives rise.From the beginning, it is none of these, nor can it be ac-counted for by the most complete series of characteristicsthat we might predicate. At the level of our immediate intu-ition, the table is something which is previous to this andconcerning which we can predicate all the elements in thatcomplete series. What then is the nature of this enigmaticprevious object, if such a question has any meaning?Perhaps it is worth pointing out at this point that the set ofsensations, opinions, judgements, memories, expectations,etc. in relation to the table is endowed with a certain stand-ing, structural and global existence, which is separable fromthe complete set of sensations, opinions, etc.,that constitutethe entirety of our conscious life. For example, we can pre-dict that, if standing alongside the said table, we reach out ahand, we will experience a clearly defined tactile sensation-that of touching the table; if we drum our fingers on its sur-face we will receive an unmistakeable sound sensation; if wedraw close to the table the image we have of it will grow insize, and if we move away from it, the table becomes small-er, etc., etc. So, the set of experiences in relation to the tablehas a given structure: This structure, the stable set of specif-ic experiential interrelations, forms a part of the object«table». If we were unable to perceive these interrelations, ifthe only thing we perceived was an indifferentiated magmaof table-experiences, un-separated in our inner concious-ness from the rest of our mental experiences, we would bediagnosed as suffering a clinical madness: a chaos of sen-sations devoid of the richness of distinction and order thatcaracterises our subjective lives. But, this consideration apart, the claim I am making is that the «stable set of specificexperiential interrelations» forms a part of this object. I couldperhaps take this one step further and argue that the struc-tured series of table-experiences is the very object underdiscussion. Without it, the object no longer exists and afteranalysing the object and my perception of it, as we have justdone, nothing additional has appeared. Nevertheless, ifseeking to be coherent with the result of this analysis, one at-tempts to move forward and to dissolve the object (i.e., thething for which we predicated each of the elements in the se-ries «table») within its structured series, then, it raises in ourinner consciousness the basic intuition that the object existsindependently of ourselves, that behind the above structurelies something more, without entailing that this supposed re-ality adds anything new to our experience, nor calls intoquestion our experience. We might see it as a sort of uselessunattainable ontological patch, to which we cannot, howev-er, renounce and which perhaps give us a basic reliance onour inner life.
My research has three main foci, one which is of interest to the fields of quantum information and quantum optics is to characterize the effects of coupling between quantum systems. Advances in technology made since the conception of quantum mechanics spurred the development of quantum technologies like quantum optics and quantum computing. These applications require a good understanding of the quantum systems that compose them, and the clever ways in which the information in these systems is stored and manipulated. By understanding the ways which quantum systems interact with their environment, their usefulness can be further utilized. The second is to develop methods of calculation which simplify the calculational and computational side of quantum dynamics. Understanding how quantum systems evolve in time is very important, but traditional methods of solving for the dynamics of quantum systems struggle to deal with time dependent parameters. Using results from the theory of Lie algebras, I will show how quantum dynamics problems can be made less computationally intensive by avoiding the partial differential equations typically associated with such problems and reducing the problem to a system of coupled ordinary differential equations. The third focus is to develop methods of visualizing properties of quantum systems. I think this is important as an educational tool and as a way to develop intuition about how quantum systems evolve considering how few opportunities there are to visualize quantum effects on a macroscopic scale. This problem is particularly challenging because quantum mechanics is non-deterministic, meaning that the only nontrivial definitive statements that can be made regarding quantum systems deal with probabilities. This coupled with the fact that many of the systems of interest depend on upwards of six variables and also evolve in time make creating useful visual representations challenging. Despite the challenges, I feel that useful insights can be gained from the visualizations, and will illustrate a few examples.
In this chapter, I offer some personal reflections about the nature of reality, shaped by my work as a quantum physicist, my experimentation with psychedelic drugs during the 1960s, and my more recent studies of modern cognitive science. Traditionally, questions about the essential nature of reality are asked by philosophers. In the twentieth century, these questions were asked for the first time by scientists as well. During the first three decades of the century, the exploration of the atomic and subatomic world brought physicists in contact with a strange and unexpected reality that shattered the foundations of their worldview and forced them to think in entirely new ways. Quantum physics showed scientists “a new reality,” and from that time on, the nature of reality became a popular subject of discussion not only in philosophy but also in science. In recent decades, cognitive scientists took another radical step in the scientific conception of the nature of reality. They asserted that the features of our ordinary, everyday reality are not features of an independently existing world, but are created in the very process of perception. In a way this generalizes the influence of the act of perception on the perceived object, which was famously analyzed in quantum physics by Werner Heisenberg, to everyday perception. In other words, even our everyday reality is just one of many alternate realities.
Post-quantum cryptography (PQC) is a critical area of research aimed at addressing the threat quantum computing poses to traditional cryptographic systems. It focuses on evaluating the efficiency, security, and practical performance of PQC algorithms through experimental analysis. This research supports the development of optimized cryptographic solutions, contributes to standardization efforts, and ensures secure and efficient implementations for a wide range of applications. Despite progress in PQC, gaps still exist in practical performance evaluations, particularly in resource-constrained environments. There is a lack of standardized comparisons, hindering the selection of suitable algorithms for specific use cases like IoT and cloud systems. Furthermore, research on scalability, integration challenges, and the trade-offs between security and efficiency remains insufficient. The methodology involves creating a comprehensive framework to evaluate various PQC algorithms, including lattice-based (e.g., Kyber, Dilithium), code-based (e.g., McEliece), and hash-based (e.g., SPHINCS+). These algorithms will be tested in diverse environments, from resource-constrained devices to high-performance infrastructures such as cloud platforms. Key metrics such as encryption/decryption speed, key sizes, memory usage, and computational efficiency will be measured, focusing on the trade-offs between security, efficiency, and scalability. The results will be benchmarked against standardized metrics to provide a clear understanding of each algorithm's suitability for real-world deployment. The findings indicate that lattice-based algorithms like Kyber offer a strong balance between security and efficiency but require considerable computational resources. Code-based algorithms like McEliece are highly secure but come with large key sizes and slower speeds. Hash-based schemes like SPHINCS+ provide strong security but are computationally expensive, making them less suitable for resource-limited systems. The highlights the importance of optimizing PQC algorithms according to specific application requirements, where the choice of algorithm must balance security, efficiency, and resource constraints, with continuous optimization needed to address evolving real-world demands.