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arXiv:2501.08583 · The Physics Teacher

Explaining Quanta with Optical Illusions

Gianluca Li Causi

Published Dec 30, 2024• 3 citations
arXivHTMLPDF

Abstract

In this work, I propose a way to help high school students and the general population understand quantum concepts by adopting a new inherently dual representation. Major difficulties in explaining to people the basic concepts of quantum mechanics reside in the apparent impossibility of representing quantum superposition with examples taken from everyday life. In this context, I propose a new pictorial paradigm that illustrates a number of quantum concepts by means of optical illusions, potentially without raising misconceptions. The method is based on "bistable reversible figures", which induce in the viewer a multistable perception, conveying a direct understanding of superposition, random collapse, and observer effect via a sensorial experience. I present the advantages and discuss the limitations of this analogy, and show how it extends to the concepts of complementarity and quantum entanglement, also helping to avoiding misconceptions in quantum teleportation. Finally, I also address quantum spin and quantum measurement by using different types of optical illusions.

DOI
10.1119/5.0147178

Related papers

Art makes quantum intuitive

Grégoire Cattan, Karolina Duś, Sławomir Kuśmia +1 more

Not so long ago, humans were a group of primates living on the savannah. We are reasonably proficient at estimating the trajectory of medium-sized objects, such as falling rocks and arrows, moving at moderate speeds. However, one must acknowledge that our intuition falters when it comes to understanding the behaviour of micro objects moving at very high speeds.Consider, for instance, the famous double-slit experiment. If you throw a ball towards two slits, the ball will pass through one slit, according to a common-sense prediction. However, when small particles, such as photons or electrons, are projected through two closely spaced apertures, the result is as if the particles simultaneously pass through the two apertures. In quantum physics, this unintuitive observation is explained by the wave-particle duality. It means that, physical entities can possess wavelike as well as particle-like characteristics. The duality is analogous to the two sides of a coin; the same reality can be described from different perspectives. Unfortunately, this knowledge does not cause that quantum mechanisms are entirely understandable and intuitional. Therefore, the following question remains open, how can we define quantum art when we are unable to fully grasp quantum mechanics? On a similar note, art itself is challenging to understand, albeit for different reasons. It is widely accepted that art is, to a significant extent, a subjective experience. An artist creates a piece of art that evokes diverse emotions and interpretations when presented to different people. Consequently, how can we bridge the gap between quantum mechanics, which is primarily comprehended through mathematics, and art, which is intuitively understood without the need for conscious reasoning? In other words, how can quantum art make the enigmatic world of quantum more intuitive and accessible?To address these questions, we created a challenge for the HackYeah! hackathon, one of the most prominent stationary events in Europe. We invited people to find an artistic way to illustrate the principles of quantum mechanics, including quantum superposition, entanglement, and decoherence. Approximately 700 individuals attended the event. Multiple challenges were submitted by different companies, and the Quantum Art challenge was chosen by 15 teams that ranged in size from two to seven people. After a short description of the challenge in Section 2, we explore some of these contributions in Section 3. Lastly, Section 4 concludes the paper. In our opinion, the artwork presented, especially the visual ones, helped to makes quantum principles more understandable, intuitive.The purpose of the challenge was to find an artistic way to illustrate quantum mechanics, specifically quantum superposition, entanglement, and decoherence.Quantum superposition refers to a phenomenon where a single particle can exist in two states simultaneously. In contrast to a 'normal' bit, which can be either 0 or 1, a quantum bit is a superposition of both 0 and 1.The measurement operation is the process through which a quantum state is collapsed to either the state 0 or 1. Let us consider two quantum bits; the possible measurement outcomes can be one of the following four combinations: 00, 01, 10, or 11. When only two of these combinations are possible, such as 00 and 11 or 10 and 01, one can state that the quantum bits are entangled because the state of one qubit affects the state of the second qubit and vice-versa.Decoherence of the quantum state is an effect that results from microscopic interactions between the quantum bits and the environment. This environmental noise impacts the state of the quantum bits and can lead to errors in computation. In other words, multiple measurements of the same quantum computation may yield different results. Different quantum computer architectures exhibit varying levels of noise.Here, the following question arises: How can people represent the principles of quantum mechanics in a way that it is tangible, visible, or even audible?In this section, we present a selected panel of examples that were implemented during the HackYeah! hackathon.This project effectively demonstrates the concept of quantum decoherence. It showcases a mosaic in which the arrangement of image elements is determined by the outcomes of quantum measurements (Figure 1). Various mosaics are generated following these measurements and are subsequently combined into an animated GIF. Notably, the greater the instability of the quantum computer, the more pronounced the glitches become within the mosaic. As a testament to its excellence, this project emerged as the winner of the challenge. The project is available on GitHub at https://github.com/lukilesny/quantmosaic.This code is based on the previous quantum art of Wiktor Mazin, 1 which exploits the Julia fractal set for image generation. Julia fractals are fractals based on a recursive suite of a complex number.The code performs a straightforward computation that involves the measurement of two qubits. The probabilities of these qubits being in either state 0 or 1 are employed to initialise the real and imaginary part of the complex numbers in the Julia set. The resulting Julia fractal is presented as an image, which is then further customised through user input. This customised image is subsequently passed to the text-to-image artificial intelligence model Stable Diffusion to create both personalised and quantum artwork. This project also illustrates the concept of quantum decoherence. The project is available on GitHub at https://github.com/Havystar/QUANTIUM.This work is also inspired by the contributions of Wiktor Mazin; however, it diverges by focusing on the creation of music rather than images. It resonates with the European project on Quantum Music2 (e.g., (1)), with the distinction being that instead of encoding notes into quantum states, it employs fractals to generate eight distinct musical notes.The project is available on GitHub at https://github.com/kmazrolina/Quanterpoint.This project is also an application of quantum music. It breaks down musical compositions into 4/4 tempo measures. Each measure is encoded using a set of four qubit quantum circuits, with each quantum bit symbolising a distinct musical element, encompassing notes, rhythm, and pauses. Diverse variations of a melody are generated, each of which is closely tied to a specific quantum architecture. It is akin to experiencing music through a quantum lens that unveils the distinctive quantum voice of each architecture.The project is available on GitHub at https://github.com/git-stashic/quantum-art.This project serves as an in-depth exploration of variational quantum circuits (VQCs) applied to the classification of the IRIS dataset. The classification results are then presented through Seaborn graphs (a library for scientific visualisation). This project is classified as scientific visualisation rather than art, but the effort merits our attention. A similar approach with VQCs can be observed in the pyRiemann-qiskit library (2), as showcased in the library documentation. 3 In this example, the learning parameters of the VQC are ingeniously illustrated as a spiral, with each branch signifying the variation in weight of a specific parameter.Additionally, the project delves into Bubble Art, drawing inspiration from the work of Radha Pyari Sandhir. 4 The core concept involves encoding a string into qubits and subsequently measuring the outcomes of computations performed on them. The resulting measurements are then transformed into bubbles. The size and number of bubbles convey information, with smaller, numerous bubbles indicating more noise, while larger bubbles represent measurements that yield the same results.The project is available on GitHub at https://github.com/dr3du4/Quantium.Autoencoders are a class of neural networks that are commonly employed to extract an efficient representation of specific data, akin to dimension reduction techniques. In this particular scenario, the team proposed the use of a variational autoencoder, with its parameters initialised with the measurement of a quantum circuit. The autoencoder's purpose is to learn a concise representation of a cat by using the Kaggle CAT dataset. Dimensionality reduction essentially serves as a means of compressing the data, resulting in a deliberately artistic blurring or fuzziness effect on the original image.The project is available on GitHub at https://github.com/polish-mountain/quantum-vae.Here, the concept revolves around the initialisation of a quantum circuit with brain wave frequencies, such as alpha and beta waves. Quantum operations are run on these states, and the outputs are measured in classical bits. Then, the resulting measurements are translated into values of saturation and luminance, ultimately contributing to the customisation of a piece of artwork.Essentially, it can be described as an electroencephalography (EEG) state personalised through quantum randomness. What makes this idea particularly intriguing is its potential for expansion. By introducing different qubits that represent the mental states of other users, brain synchronisation could be further represented by entangled states. When two users are competing or cooperating to solve a task, the synchronization between their mental states only allow for certain measurement probabilities, which is akin to a form of entanglement. This notion also resonates with the concept of the quantum brain hypothesis (3), according to which the brain coexists in multiple states simultaneously, which subsequently collapse. In this idea, EEG measurements become a measurement of these quantum brain states, and the task executed by the user while recording the electroencephalogram could be further represented by specific quantum operations. Just to be clear, we do not pretend that this is actually the case, but this project could lead to interesting metaphors between brain states and quantum representation.The project is available on GitHub at https://github.com/kinga-marszalkowska/QuantumBrainArt.Various artistic viewpoints were submitted as part of the Quantum Art challenge at the HackYeah! hackathon, including images, animations, and music. By far, quantum decoherence -that is, quantum noise -was the most exploited quantum concept. While quantum superposition was used internally, it was not -in our opinion -sufficiently highlighted by the presented artworks. As for quantum entanglement, it was explored under the concept of quantum music. Apparently, it is not always intuitive for people to understand quantum entanglement simply by hearing music. Saying that, you need a certain level of knowledge to build appreciation. For example, children need to learn different tastes to appreciate food. Among the aforementioned works, we noticed the use of quantum principles for creating artistic visualisations of mental states through EEG, as well as the use of art to enhance the visualisation of machine learning techniques. Here, we see art's potential to enhance the comprehensibility and natural intuition of quantum phenomena. This is an interesting approach to make quantum more accessible, intuitive, especially for neophytes.The question that lingers is whether visualisation truly qualifies as art. The answer is nuanced and may rely on the intent itself. A good visualisation can be a piece of art if the machine learning model was created with the sole purpose of producing art rather than for merely explaining a machine learning algorithm.Another perspective is that of Japanese contemporary artist Matsuzawa Yutaka (1922-2006), although we admit that we have not had the opportunity to read the original Japanese text. Our understanding is based on the writings of Alan Longino from the Department of Art at the University of Chicago (4):"Trough Quantum Art, Matsuzawa invited future readers, viewers, and participants to conceive of a world where objects, bodies, images, and matter become less defined, more permeable, and bound together in limitless intimacy".In essence, the artist's manifesto is a call for renewal, a break from artistic conventions, similar to the role of quantum physics in the physical sciences.

Frontiers in Quantum Science and Technology•May 17, 2024•2 citations

Quantum Mechanics

Shabnam Siddiqui

Quantum mechanics is one of the most challenging subjects to learn. It is challenging because quantum phenomenon is counterintuitive, and the mathematics used to explain such a phenomenon is very abstract, and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas step- by- step in a structured way with a comparison between quantum and classical concepts. It provides a clear distinction between classical and quantum logic. Conceptual questions are provided after every important section so that the reader can test their understanding at every step. Such an approach aids in preventing misconceptions. Problem solving is not restricted to solving differential equations and integration. But it requires to systematically and creatively analyze a problem, to apply the new and powerful concepts for finding a solution and to understand the physical meaning of the solution. The tutorials on special topics are an effort to teach problem solving by actively engaging the reader in a thinking process, to apply the concepts and to understand the physical meaning of the solution. The simulations are provided for some of the topics. The simulations aid in the visualization of the quantum phenomenon, and for meaningful understanding of the mathematics. This approach may lead to development of "quantum mechanical intuition "as well as learning mathematical techniques for problem solving. Most importantly, the book is not flooded with numerous topics that makes the reader confused and distracted, rather the most important topics are discussed at a deeper level. The understanding of quantum mechanics is incomplete without understanding the early ideas and experiments that lead to the development of the quantum theory. Thus, the first two chapters of the book are dedicated to such topics. The key features of this book are: A simplified, structured, and step-by-step introduction to quantum mechanics. The simplification is attained through use of two-level system, step- by- step discussion of important topics in a simplified language at a deeper level, analogies, and visualization using illustrations and simulations A systematic arrangement of topics, and numerous worked- out examples. The presentation of the structure in the mathematical formalism of quantum mechanics provides clarity in understanding complicated and abstract mathematics. It also helps to understand the distinction between the quantum mechanical and classical approaches Conceptual questions at the end of every important section. The conceptual questions can be used in a classroom as a point of discussion between an instructor and students Tutorials on special topics. Simulations on special topics aid in the visualization of the physical phenomenon, and demonstration of the application of mathematics An in-depth discussion of the wave-particle duality, measurement problem, and their philosophical implications in Chapter 2 provides an understanding of the broader meaning of quantum mechanics

CRC Press eBooks•Oct 10, 2018•1 citation

Entanglement isn't just for spin

Daniel V. Schroeder

Quantum entanglement occurs not just in discrete systems such as spins, but also in the spatial wave functions of systems with more than one degree of freedom. It is easy to introduce students to entangled wave functions at an early stage, in any course that discusses wave functions. Doing so not only prepares students to learn about Bell's theorem and quantum information science, but can also provide a deeper understanding of the principles of quantum mechanics and help fight against some common misconceptions. Here I introduce several pictorial examples of entangled wave functions that depend on just two spatial variables. I also show how such wave functions can arise dynamically, and describe how to quantify their entanglement.

arXiv:1703.10620•American Journal of Physics•Oct 17, 2017•32 citations

Conceptual understanding of quantum mechanics : an investigation into physics students' depictions of the basic concepts of quantum mechanics

Mengesha Ayene Ejigu

Not only is Quantum Mechanics (QM) conceptually rich, it is also a theory that physics students have found abstract and technically formidable. Nevertheless, compared to other classical topics of physics, university students’ understanding of QM has received minimal attention in the physics education literature. The principal purpose of this study was to characterize the variation in the ways that undergraduate physics students depict the basic concepts of QM and to extrapolate the results to scaffold possible changes to instructional practices at the university that provided the context for the study. In so doing, an adaptation of a developmental phenomenographic perspective was chosen. Empirically, the study was approached through in-depth interviews with 35 physics students from two Ethiopian governmental universities after they had been exposed to the traditional QM course for one-third of a semester. Interview responses were analyzed using phenomenographic approach where a picture of students’ depictions was established for each quantum concept by expounding the given responses. For each basic quantum concept addressed, the structure of the description categories was separately constructed, and overall, it was found that naive, quasi-classical ontology and/or variants of classical ways of visualization are dominant in students’ responses. For example, it was found that students’ depictions of the photon concept could be described with three distinct categories of description, which are (a) classical intuitive description, (b) mixed model description and (c) quasi-quantum model description. Similarly, the findings revealed that it is possible to establish three qualitatively different categories of description to picture students’ depictions of matter waves, namely, (a) classical and trajectory-based description, (b) an intricate blend of classical and quantum description and (c) incipient quantum model description. Likewise, it was found that students’ depictions of uncertainty principle can be described as: (a) uncertainty as classical ignorance, (b) uncertainty as measurement disturbance and (c) uncertainty as a quasi-quantum principle. \nWith regard to learning QM, the categories of description made clear several issues: most students did not have enough knowledge to depict the basic concepts of QM properly; they were influenced by the perspective of classical physics and their perceptions in making explanations about QM; and they also applied mixed ideas, one based on their classical model and the other from newly introduced QM. These results are also supported by the findings of previous studies in similar domains. Findings from the study were used to guide the design of multiple representations-based instructions and interactive learning tutorials on the conceptual aspects of QM that has been shown to address specific difficulties identified in the study. Theoretical and practical implications of the study, as well as potential future considerations are drawn.

•Jul 1, 2014•1 citation

Quantum physics from waves: An analogy-based approach for high school

Marcelo Arlego, María de los Ángeles Fanaro, Lorenzo Galante

In this paper we present a proposal for teaching basic aspects of quantum mechanics in high school. Our proposal is based on a wave approach that makes use of the analogies between wave phenomena at macroscopic scales and phenomena at atomic or subatomic scales. Although the classical and the quantum model are completely different, there is a common underlying wave mathematical layer. This allows to address, via analogies, quantum aspects that are not accessible to direct experience. The quantization of energy levels, the quantum interference and the uncertainty relations are examples of quantum aspects having an analog concept in classical physics wave phenomena. In our approach we break the wave-particle “duality”, which is totally counterintuitive. Instead we enhance the underlying wave mathematical structure as a path to reach and explain emerging features of particles and quantum systems in general.

Revista Brasileira de Ensino de Física•Jan 1, 2021•1 citation

Quantum Weirdness

WJ Mullin

Quantum mechanics allows a remarkably accurate description of nature and powerful predictive capabilities. The analyses of quantum systems and their interpretation lead to many surprises, for example, the ability to detect the characteristics of an object without ever touching it in any way, via "interaction-free measurement," or the teleportation of an atomic state over large distances. The results can become downright bizarre. Quantum mechanics is a subtle subject that usually involves complicated mathematics -- calculus, partial differential equations, etc., for complete understanding. Most texts for general audiences avoid all mathematics. The result is that the reader misses almost all deep understanding of the subject, much of which can be probed with just high-school level algebra and trigonometry. Thus, readers with that level of mathematics can learn so much more about this fundamental science. The book starts with a discussion of the basic physics of waves (an appendix reviews some necessary classical physics concepts) and then introduces the fundamentals of quantum mechanics, including the wave function, superposition, entanglement, Bell's theorem, etc., and applications to Bose--Einstein condensation, quantum computing, and much more. The interpretation of the mathematics of quantum mechanics into a world view has been the subject of much controversy. The result is a variety of conflicting interpretations, from the famous Copenhagen view of Bohr to the multiple universes of Everett. We discuss these interpretations in the chapter "What is a wave function?" and include some very recent advances, for example, quantum Bayesianism, and measurements of the reality of the wave function.

Oxford University Press eBooks•Mar 16, 2017•7 citations
In this work, I propose a way to help high school students and the general population understand quantum concepts by adopting a new inherently dual representation. Major difficulties in explaining to people the basic concepts of quantum mechanics reside in the apparent impossibility of representing quantum superposition with examples taken from everyday life. In this context, I propose a new pictorial paradigm that illustrates a number of quantum concepts by means of optical illusions, potentially without raising misconceptions. The method is based on "bistable reversible figures", which induce in the viewer a multistable perception, conveying a direct understanding of superposition, random collapse, and observer effect via a sensorial experience. I present the advantages and discuss the limitations of this analogy, and show how it extends to the concepts of complementarity and quantum entanglement, also helping to avoiding misconceptions in quantum teleportation. Finally, I also address quantum spin and quantum measurement by using different types of optical illusions.
Not so long ago, humans were a group of primates living on the savannah. We are reasonably proficient at estimating the trajectory of medium-sized objects, such as falling rocks and arrows, moving at moderate speeds. However, one must acknowledge that our intuition falters when it comes to understanding the behaviour of micro objects moving at very high speeds.Consider, for instance, the famous double-slit experiment. If you throw a ball towards two slits, the ball will pass through one slit, according to a common-sense prediction. However, when small particles, such as photons or electrons, are projected through two closely spaced apertures, the result is as if the particles simultaneously pass through the two apertures. In quantum physics, this unintuitive observation is explained by the wave-particle duality. It means that, physical entities can possess wavelike as well as particle-like characteristics. The duality is analogous to the two sides of a coin; the same reality can be described from different perspectives. Unfortunately, this knowledge does not cause that quantum mechanisms are entirely understandable and intuitional. Therefore, the following question remains open, how can we define quantum art when we are unable to fully grasp quantum mechanics? On a similar note, art itself is challenging to understand, albeit for different reasons. It is widely accepted that art is, to a significant extent, a subjective experience. An artist creates a piece of art that evokes diverse emotions and interpretations when presented to different people. Consequently, how can we bridge the gap between quantum mechanics, which is primarily comprehended through mathematics, and art, which is intuitively understood without the need for conscious reasoning? In other words, how can quantum art make the enigmatic world of quantum more intuitive and accessible?To address these questions, we created a challenge for the HackYeah! hackathon, one of the most prominent stationary events in Europe. We invited people to find an artistic way to illustrate the principles of quantum mechanics, including quantum superposition, entanglement, and decoherence. Approximately 700 individuals attended the event. Multiple challenges were submitted by different companies, and the Quantum Art challenge was chosen by 15 teams that ranged in size from two to seven people. After a short description of the challenge in Section 2, we explore some of these contributions in Section 3. Lastly, Section 4 concludes the paper. In our opinion, the artwork presented, especially the visual ones, helped to makes quantum principles more understandable, intuitive.The purpose of the challenge was to find an artistic way to illustrate quantum mechanics, specifically quantum superposition, entanglement, and decoherence.Quantum superposition refers to a phenomenon where a single particle can exist in two states simultaneously. In contrast to a 'normal' bit, which can be either 0 or 1, a quantum bit is a superposition of both 0 and 1.The measurement operation is the process through which a quantum state is collapsed to either the state 0 or 1. Let us consider two quantum bits; the possible measurement outcomes can be one of the following four combinations: 00, 01, 10, or 11. When only two of these combinations are possible, such as 00 and 11 or 10 and 01, one can state that the quantum bits are entangled because the state of one qubit affects the state of the second qubit and vice-versa.Decoherence of the quantum state is an effect that results from microscopic interactions between the quantum bits and the environment. This environmental noise impacts the state of the quantum bits and can lead to errors in computation. In other words, multiple measurements of the same quantum computation may yield different results. Different quantum computer architectures exhibit varying levels of noise.Here, the following question arises: How can people represent the principles of quantum mechanics in a way that it is tangible, visible, or even audible?In this section, we present a selected panel of examples that were implemented during the HackYeah! hackathon.This project effectively demonstrates the concept of quantum decoherence. It showcases a mosaic in which the arrangement of image elements is determined by the outcomes of quantum measurements (Figure 1). Various mosaics are generated following these measurements and are subsequently combined into an animated GIF. Notably, the greater the instability of the quantum computer, the more pronounced the glitches become within the mosaic. As a testament to its excellence, this project emerged as the winner of the challenge. The project is available on GitHub at https://github.com/lukilesny/quantmosaic.This code is based on the previous quantum art of Wiktor Mazin, 1 which exploits the Julia fractal set for image generation. Julia fractals are fractals based on a recursive suite of a complex number.The code performs a straightforward computation that involves the measurement of two qubits. The probabilities of these qubits being in either state 0 or 1 are employed to initialise the real and imaginary part of the complex numbers in the Julia set. The resulting Julia fractal is presented as an image, which is then further customised through user input. This customised image is subsequently passed to the text-to-image artificial intelligence model Stable Diffusion to create both personalised and quantum artwork. This project also illustrates the concept of quantum decoherence. The project is available on GitHub at https://github.com/Havystar/QUANTIUM.This work is also inspired by the contributions of Wiktor Mazin; however, it diverges by focusing on the creation of music rather than images. It resonates with the European project on Quantum Music2 (e.g., (1)), with the distinction being that instead of encoding notes into quantum states, it employs fractals to generate eight distinct musical notes.The project is available on GitHub at https://github.com/kmazrolina/Quanterpoint.This project is also an application of quantum music. It breaks down musical compositions into 4/4 tempo measures. Each measure is encoded using a set of four qubit quantum circuits, with each quantum bit symbolising a distinct musical element, encompassing notes, rhythm, and pauses. Diverse variations of a melody are generated, each of which is closely tied to a specific quantum architecture. It is akin to experiencing music through a quantum lens that unveils the distinctive quantum voice of each architecture.The project is available on GitHub at https://github.com/git-stashic/quantum-art.This project serves as an in-depth exploration of variational quantum circuits (VQCs) applied to the classification of the IRIS dataset. The classification results are then presented through Seaborn graphs (a library for scientific visualisation). This project is classified as scientific visualisation rather than art, but the effort merits our attention. A similar approach with VQCs can be observed in the pyRiemann-qiskit library (2), as showcased in the library documentation. 3 In this example, the learning parameters of the VQC are ingeniously illustrated as a spiral, with each branch signifying the variation in weight of a specific parameter.Additionally, the project delves into Bubble Art, drawing inspiration from the work of Radha Pyari Sandhir. 4 The core concept involves encoding a string into qubits and subsequently measuring the outcomes of computations performed on them. The resulting measurements are then transformed into bubbles. The size and number of bubbles convey information, with smaller, numerous bubbles indicating more noise, while larger bubbles represent measurements that yield the same results.The project is available on GitHub at https://github.com/dr3du4/Quantium.Autoencoders are a class of neural networks that are commonly employed to extract an efficient representation of specific data, akin to dimension reduction techniques. In this particular scenario, the team proposed the use of a variational autoencoder, with its parameters initialised with the measurement of a quantum circuit. The autoencoder's purpose is to learn a concise representation of a cat by using the Kaggle CAT dataset. Dimensionality reduction essentially serves as a means of compressing the data, resulting in a deliberately artistic blurring or fuzziness effect on the original image.The project is available on GitHub at https://github.com/polish-mountain/quantum-vae.Here, the concept revolves around the initialisation of a quantum circuit with brain wave frequencies, such as alpha and beta waves. Quantum operations are run on these states, and the outputs are measured in classical bits. Then, the resulting measurements are translated into values of saturation and luminance, ultimately contributing to the customisation of a piece of artwork.Essentially, it can be described as an electroencephalography (EEG) state personalised through quantum randomness. What makes this idea particularly intriguing is its potential for expansion. By introducing different qubits that represent the mental states of other users, brain synchronisation could be further represented by entangled states. When two users are competing or cooperating to solve a task, the synchronization between their mental states only allow for certain measurement probabilities, which is akin to a form of entanglement. This notion also resonates with the concept of the quantum brain hypothesis (3), according to which the brain coexists in multiple states simultaneously, which subsequently collapse. In this idea, EEG measurements become a measurement of these quantum brain states, and the task executed by the user while recording the electroencephalogram could be further represented by specific quantum operations. Just to be clear, we do not pretend that this is actually the case, but this project could lead to interesting metaphors between brain states and quantum representation.The project is available on GitHub at https://github.com/kinga-marszalkowska/QuantumBrainArt.Various artistic viewpoints were submitted as part of the Quantum Art challenge at the HackYeah! hackathon, including images, animations, and music. By far, quantum decoherence -that is, quantum noise -was the most exploited quantum concept. While quantum superposition was used internally, it was not -in our opinion -sufficiently highlighted by the presented artworks. As for quantum entanglement, it was explored under the concept of quantum music. Apparently, it is not always intuitive for people to understand quantum entanglement simply by hearing music. Saying that, you need a certain level of knowledge to build appreciation. For example, children need to learn different tastes to appreciate food. Among the aforementioned works, we noticed the use of quantum principles for creating artistic visualisations of mental states through EEG, as well as the use of art to enhance the visualisation of machine learning techniques. Here, we see art's potential to enhance the comprehensibility and natural intuition of quantum phenomena. This is an interesting approach to make quantum more accessible, intuitive, especially for neophytes.The question that lingers is whether visualisation truly qualifies as art. The answer is nuanced and may rely on the intent itself. A good visualisation can be a piece of art if the machine learning model was created with the sole purpose of producing art rather than for merely explaining a machine learning algorithm.Another perspective is that of Japanese contemporary artist Matsuzawa Yutaka (1922-2006), although we admit that we have not had the opportunity to read the original Japanese text. Our understanding is based on the writings of Alan Longino from the Department of Art at the University of Chicago (4):"Trough Quantum Art, Matsuzawa invited future readers, viewers, and participants to conceive of a world where objects, bodies, images, and matter become less defined, more permeable, and bound together in limitless intimacy".In essence, the artist's manifesto is a call for renewal, a break from artistic conventions, similar to the role of quantum physics in the physical sciences.
Quantum mechanics is one of the most challenging subjects to learn. It is challenging because quantum phenomenon is counterintuitive, and the mathematics used to explain such a phenomenon is very abstract, and difficult to grasp. This textbook is an attempt to overcome these challenges. Every chapter presents quantum ideas step- by- step in a structured way with a comparison between quantum and classical concepts. It provides a clear distinction between classical and quantum logic. Conceptual questions are provided after every important section so that the reader can test their understanding at every step. Such an approach aids in preventing misconceptions. Problem solving is not restricted to solving differential equations and integration. But it requires to systematically and creatively analyze a problem, to apply the new and powerful concepts for finding a solution and to understand the physical meaning of the solution. The tutorials on special topics are an effort to teach problem solving by actively engaging the reader in a thinking process, to apply the concepts and to understand the physical meaning of the solution. The simulations are provided for some of the topics. The simulations aid in the visualization of the quantum phenomenon, and for meaningful understanding of the mathematics. This approach may lead to development of "quantum mechanical intuition "as well as learning mathematical techniques for problem solving. Most importantly, the book is not flooded with numerous topics that makes the reader confused and distracted, rather the most important topics are discussed at a deeper level. The understanding of quantum mechanics is incomplete without understanding the early ideas and experiments that lead to the development of the quantum theory. Thus, the first two chapters of the book are dedicated to such topics. The key features of this book are: A simplified, structured, and step-by-step introduction to quantum mechanics. The simplification is attained through use of two-level system, step- by- step discussion of important topics in a simplified language at a deeper level, analogies, and visualization using illustrations and simulations A systematic arrangement of topics, and numerous worked- out examples. The presentation of the structure in the mathematical formalism of quantum mechanics provides clarity in understanding complicated and abstract mathematics. It also helps to understand the distinction between the quantum mechanical and classical approaches Conceptual questions at the end of every important section. The conceptual questions can be used in a classroom as a point of discussion between an instructor and students Tutorials on special topics. Simulations on special topics aid in the visualization of the physical phenomenon, and demonstration of the application of mathematics An in-depth discussion of the wave-particle duality, measurement problem, and their philosophical implications in Chapter 2 provides an understanding of the broader meaning of quantum mechanics
Quantum entanglement occurs not just in discrete systems such as spins, but also in the spatial wave functions of systems with more than one degree of freedom. It is easy to introduce students to entangled wave functions at an early stage, in any course that discusses wave functions. Doing so not only prepares students to learn about Bell's theorem and quantum information science, but can also provide a deeper understanding of the principles of quantum mechanics and help fight against some common misconceptions. Here I introduce several pictorial examples of entangled wave functions that depend on just two spatial variables. I also show how such wave functions can arise dynamically, and describe how to quantify their entanglement.
Not only is Quantum Mechanics (QM) conceptually rich, it is also a theory that physics students have found abstract and technically formidable. Nevertheless, compared to other classical topics of physics, university students’ understanding of QM has received minimal attention in the physics education literature. The principal purpose of this study was to characterize the variation in the ways that undergraduate physics students depict the basic concepts of QM and to extrapolate the results to scaffold possible changes to instructional practices at the university that provided the context for the study. In so doing, an adaptation of a developmental phenomenographic perspective was chosen. Empirically, the study was approached through in-depth interviews with 35 physics students from two Ethiopian governmental universities after they had been exposed to the traditional QM course for one-third of a semester. Interview responses were analyzed using phenomenographic approach where a picture of students’ depictions was established for each quantum concept by expounding the given responses. For each basic quantum concept addressed, the structure of the description categories was separately constructed, and overall, it was found that naive, quasi-classical ontology and/or variants of classical ways of visualization are dominant in students’ responses. For example, it was found that students’ depictions of the photon concept could be described with three distinct categories of description, which are (a) classical intuitive description, (b) mixed model description and (c) quasi-quantum model description. Similarly, the findings revealed that it is possible to establish three qualitatively different categories of description to picture students’ depictions of matter waves, namely, (a) classical and trajectory-based description, (b) an intricate blend of classical and quantum description and (c) incipient quantum model description. Likewise, it was found that students’ depictions of uncertainty principle can be described as: (a) uncertainty as classical ignorance, (b) uncertainty as measurement disturbance and (c) uncertainty as a quasi-quantum principle. \nWith regard to learning QM, the categories of description made clear several issues: most students did not have enough knowledge to depict the basic concepts of QM properly; they were influenced by the perspective of classical physics and their perceptions in making explanations about QM; and they also applied mixed ideas, one based on their classical model and the other from newly introduced QM. These results are also supported by the findings of previous studies in similar domains. Findings from the study were used to guide the design of multiple representations-based instructions and interactive learning tutorials on the conceptual aspects of QM that has been shown to address specific difficulties identified in the study. Theoretical and practical implications of the study, as well as potential future considerations are drawn.
In this paper we present a proposal for teaching basic aspects of quantum mechanics in high school. Our proposal is based on a wave approach that makes use of the analogies between wave phenomena at macroscopic scales and phenomena at atomic or subatomic scales. Although the classical and the quantum model are completely different, there is a common underlying wave mathematical layer. This allows to address, via analogies, quantum aspects that are not accessible to direct experience. The quantization of energy levels, the quantum interference and the uncertainty relations are examples of quantum aspects having an analog concept in classical physics wave phenomena. In our approach we break the wave-particle “duality”, which is totally counterintuitive. Instead we enhance the underlying wave mathematical structure as a path to reach and explain emerging features of particles and quantum systems in general.
Quantum mechanics allows a remarkably accurate description of nature and powerful predictive capabilities. The analyses of quantum systems and their interpretation lead to many surprises, for example, the ability to detect the characteristics of an object without ever touching it in any way, via "interaction-free measurement," or the teleportation of an atomic state over large distances. The results can become downright bizarre. Quantum mechanics is a subtle subject that usually involves complicated mathematics -- calculus, partial differential equations, etc., for complete understanding. Most texts for general audiences avoid all mathematics. The result is that the reader misses almost all deep understanding of the subject, much of which can be probed with just high-school level algebra and trigonometry. Thus, readers with that level of mathematics can learn so much more about this fundamental science. The book starts with a discussion of the basic physics of waves (an appendix reviews some necessary classical physics concepts) and then introduces the fundamentals of quantum mechanics, including the wave function, superposition, entanglement, Bell's theorem, etc., and applications to Bose--Einstein condensation, quantum computing, and much more. The interpretation of the mathematics of quantum mechanics into a world view has been the subject of much controversy. The result is a variety of conflicting interpretations, from the famous Copenhagen view of Bohr to the multiple universes of Everett. We discuss these interpretations in the chapter "What is a wave function?" and include some very recent advances, for example, quantum Bayesianism, and measurements of the reality of the wave function.