Some truths exist independently of our beliefs about them. This article endeavors to unravel the intricate fabric of reality, particularly through the lens of Schrödinger’s famous thought experiment involving a cat that is simultaneously alive and dead until observed. This paradox, often dismissed as absurd, serves as a profound commentary on the nature of quantum mechanics.
Conceived by Erwin Schrödinger in 1935, this thought experiment critiques the Copenhagen interpretation of quantum mechanics, which posits that particles exist in a state of superposition—where their properties remain undefined until measured. The scenario involves a cat, a Geiger counter, and a radioactive atom, where the cat’s fate is intertwined with the unpredictable decay of the atom[56][57][59]. If the atom decays, the Geiger counter triggers a mechanism that kills the cat; if it does not decay, the cat remains alive. Schrödinger did not advocate for the concept of superposition as a genuine aspect of reality. Subsequent developments in quantum theory and numerous experiments have confirmed that superposition is indeed, however, a real phenomenon at the quantum level.
So is the cat both alive and dead if you set up this experiment?
In theory, yes. In practice, no. In reality, the thought experiment is absurd, because our experience of reality reflects the truth: macroscopic objects interact with their environment in ways that lead to decoherence. This means that any superposition of states quickly collapses into a definite state due to interactions with the surrounding environment. So you couldn’t actually design such an experiment. The trick was in realizing this and the fact that consciousness was not the trigger, it was whatever touched the particle in a state of superposition in order to measure it.
Well that’s the answer. If you want to learn a bunch of physics, read on.
What is Superposition?
Superposition also applies to wave phenomena, where overlapping waves can create interference patterns. In quantum mechanics, particles exhibit wave-like behavior, and their states can interfere, leading to observable phenomena.
Superposition is a fundamental principle in quantum mechanics, where a quantum system can exist in multiple states simultaneously until a measurement is made.
You have experience in daily life with various things which are superimposed or combined into one. Superposition is the observed fact of superimposed things. It extends beyond quantum physics into daily life, where superposition is ubiquitous.
- Sound you hear is a superposition of different wavelengths creating various tones. Your brain can pick one instrument or voice out among other sounds but all of the different sounds first hit and move a single eardrum (per ear), creating a single complex wave. An audio frequency spectrum analyzer in music production software can visually show an audio superposition.
- Similarly, sunlight is a superposition of different light wavelengths. This can be observed in the forming of a rainbow when sunlight get expanded by water droplets into bands of different colors of light.
- Geologists also use superposition to determine the relative ages of rock layers based on their superimposed positions.
Picking apart components of light, sound or large matter shows the truth of superposition on our scale. At the scale of electrons and photons, experiments have shown the truth of superposition as well.
Superposition allows quantum systems to be in multiple states until measured, as demonstrated by Thomas Young’s double-slit experiment with light waves, highlighting how particles can act like waves and create interference patterns[4]. Just as you can not see the colors in sunlight until they are split, superposition itself cannot be directly observed. Its effects, however, such as interference patterns, are readily observable. This has significant implications for future quantum computing where information will be processed as qubits in superposition states[4].
Quantum Superposition
In quantum superposition, “superposition” refers to the ability of a quantum system to exist in multiple states simultaneously until it is measured. This means that any two or more states can be combined to create a new state, where the system is in a combination of these original states. When a system is in superposition, it can be thought of as being in a linear combination of different quantum states, each with its own probability of being observed.
Linear Combination
In quantum mechanics, superposition can be mathematically represented as a linear combination of basis states. A linear combination refers to a sum of functions or vectors, where each component is multiplied by a constant coefficient. In the context of quantum mechanics, a linear combination of eigenfunctions or states is a fundamental concept. It involves combining different quantum states with specific coefficients to create a new state that represents a superposition of the original states. These coefficients are complex numbers, allowing for interference effects between the states. The resulting state reflects the probabilities of each individual state and can evolve over time according to the Schrödinger equation. In quantum mechanics, linear combinations play a crucial role in representing quantum states and describing the behavior of quantum systems[35][36][37].
Complex Numbers
A complex number is a number that can be expressed in the form , where a and b are real numbers, and i represents the imaginary unit defined as the square root of -1.
Imaginary numbers are used in real physics? What is an imaginary number and how can it be used in real physics?
The ability of complex numbers to encode both magnitude and phase information is crucial for describing the behavior of quantum systems. When quantum states are represented as linear combinations of eigenstates with complex coefficients, these coefficients introduce phase information that can interfere constructively or destructively. Constructive interference occurs when the phases of the complex coefficients align, leading to an amplification of certain outcomes, while destructive interference happens when the phases oppose each other, resulting in cancellation of probabilities. Interference effects that are essential for phenomena like wave-particle duality, entanglement, and quantum computing.
The resulting state is not a blend or average of the original states but a new valid quantum state that reflects the probabilities of each individual state. This principle is fundamental in quantum mechanics and plays a crucial role in phenomena like quantum computing and the behavior of particles such as electrons and photons.
In other words, the use of complex numbers in quantum mechanics allows for the representation of probabilities and their interference effects. The probabilities of finding the cat alive or dead upon measurement are derived from the square of the magnitude of the complex coefficients.
Superimposed Waves
Superposition, a fundamental concept in quantum mechanics, can be understood through everyday experiences where waves combine to form new patterns. Just like waves on a pond overlapping to create complex patterns, quantum objects like electrons exhibit superposition, existing in multiple states simultaneously with probabilities described by mathematical equations[1][3]. This phenomenon may challenge intuition. Remember, for most of human history it was not known or accepted that sunlight contains different colors (wavelengths of light) all superimposed. Superposition in fundamental particles that make up the universe is shown in experiments like the double-slit experiment, where individual electrons behave like waves and create interference patterns when passed through two slits[3].
What are Quantum Systems?
To fully understand Schrodinger’s Cat experiment, you must also know what a quantum really means, and what quantum systems are. Quantum means limited to certain values. Imagine a dial with a pointer to one of five numbers (1 to 5) where changing from one number to the next is instantaneous. There is absolutely no time at which the pointer is in between of two numbers. Ever. Quantum means something that has no in between states. This is very counterintuitive. We do not have day to day experience with macroscopic items with quantum states. Things in the macroscopic physical world to not jump instantly from one location to another, they pass between locations.
Quantum systems, such as electrons and photons, are characterized by quantized states. These systems can be manipulated and measured, leading to insights into their behavior.
Computer Data Bits are Quantized Data
In quantum computing, classical bits are replaced with quantum bits (qubits), which can exist in superpositions of states. This property allows quantum computers to perform calculations more efficiently than classical computers.
To further understand the term quantum, realize that computer data bits are an example of quantized data. Quantization, in the context of digital information like computer data, involves approximating or representing real-valued data using a finite set of discrete values or levels. In the case of bits, which are the smallest units of information in a computer storing either 0 or 1, they represent a basic form of quantized data where continuous analog information is discretized into distinct levels. This process is fundamental in digital signal processing and various applications like data compression, ensuring efficient storage and transmission of digital data while balancing fidelity and bit rate[24].
Why We Know Electron Shells are Quantized
Enter a famous Albert. Einstein played a crucial role in understanding how electron shells are quantized. In the context of the Bohr model of the atom, Einstein’s work on the photoelectric effect and his concept of quantized energy levels were foundational. Specifically, Einstein’s equation E = relates the energy of a photon to its frequency, where is Planck’s constant and is the frequency. This equation was instrumental in linking the energy absorbed or emitted by electrons in different orbits within an atom to specific differences in their energy levels. By applying this principle, it became evident that electrons in atoms can only exist with certain discrete energies, corresponding to specific states or orbitals, characterized by an integer quantum number n = 1, 2, 3, .... This understanding of quantized energy levels for electrons laid the groundwork for the development of the quantum mechanical model of the atom, which revolutionized our comprehension of atomic structure and electron behavior[25].
The quantization of electron shells in atoms is explained by Bohr’s theory, which posits that electrons occupy discrete energy levels. This quantization is a consequence of the wave-particle duality of electrons and leads to the stability of electron orbits. The arrangement of electrons in shells, the limited number of electrons per shell, and the distances between shells are determined by fundamental principles such as the Pauli exclusion principle, Schrödinger equation, and uncertainty principle. These principles govern how electrons behave within atoms and why they are distributed in specific patterns around the nucleus
Bohr’s Theory
Bohr’s model of the atom introduced the idea that electrons orbit the nucleus in fixed paths or shells, with energy levels corresponding to these orbits.
Electrons exist at quantized energy levels around atoms. Electrons around in atoms exist in specific energy levels called “shells,” as proposed by Bohr’s Theory. These shells are stable and have associated energies, with electrons moving in specific orbits around the nucleus. The observed quantization of electron energies has shown that electrons can only occupy certain allowed orbits characterized by discrete energies. When electrons transition between these orbits, they emit or absorb photons, leading to the quantization of energy levels within atoms.
Overall, the quantization of angular momentum in the Bohr model revolutionized our understanding of atomic structure, providing a framework that reconciled classical mechanics with emerging quantum principles and paving the way for modern quantum theory.
Conservation of Angular Momentum
The stability of electron orbits is governed by the conservation of angular momentum, which dictates that electrons can only occupy certain allowed energy states. The quantization of angular momentum in the Bohr model is significant for several reasons:
Stability of Electron Orbits
By quantizing the angular momentum of electrons in orbit around the nucleus, the Bohr model explains how electrons can exist in stable orbits without continuously radiating energy and collapsing into the nucleus. This quantization ensures that electrons can only occupy specific discrete energy levels, leading to stable atomic structures[27][28].
Explanation of Spectral Lines
The quantization of angular momentum in the Bohr model provides a basis for understanding the discrete spectral lines observed in the hydrogen atom’s spectrum. These lines correspond to transitions of electrons between quantized energy levels, with the emission or absorption of photons matching the energy differences between these levels[27]. When electrons transition between energy levels, they emit or absorb photons, resulting in spectral lines that provide insight into the electronic structure of atoms.
Foundation for Quantum Mechanics
The concept of quantized angular momentum in the Bohr model was a crucial step towards the development of quantum mechanics. It laid the groundwork for further advancements in understanding atomic structure and behavior beyond classical physics, leading to more accurate models like the Schrödinger equation[28]. Bohr’s model laid the groundwork for modern quantum mechanics, providing a framework for understanding atomic behavior.
Derivation from Fundamental Principles
The quantization of angular momentum in the Bohr model can be derived from fundamental principles such as energy conservation and Planck’s quantization, highlighting its deep connection to key concepts in quantum physics[26]. The principles of quantum mechanics are derived from fundamental theories, including wave-particle duality and uncertainty principles.
Wave-Particle Duality
Wave-particle duality is a fundamental concept in quantum mechanics that describes how particles, such as electrons and photons, exhibit both wave-like and particle-like properties. This duality challenges classical notions of physics, where entities are typically categorized strictly as either waves or particles. For instance, light can behave like a wave, demonstrating interference and diffraction patterns, while also exhibiting particle characteristics, such as being emitted in discrete packets called photons. The famous double-slit experiment exemplifies this duality; when light passes through two slits without observation, it creates an interference pattern characteristic of waves. However, if the path of the light is measured, it behaves like a particle, resulting in two distinct points on a screen. This interplay between wave and particle behavior is a cornerstone of quantum theory, illustrating the complex nature of reality at the microscopic level and leading to profound implications for our understanding of the universe.[40]
Uncertainty Principles
The uncertainty principle, formulated by Werner Heisenberg in 1927, is a cornerstone of quantum mechanics that asserts a fundamental limit to the precision with which certain pairs of complementary properties, such as position and momentum, can be simultaneously known. This principle highlights that the more accurately one property is measured, the less accurately the other can be determined. The uncertainty principle is not merely a reflection of measurement limitations; it arises from the intrinsic wave-like nature of quantum particles. For example, if one attempts to measure the exact position of a particle, its wave function becomes more localized, leading to greater uncertainty in its momentum. Conversely, if the momentum is precisely measured, the particle’s position becomes uncertain. This trade-off is akin to a seesaw, where focusing on one side inevitably affects the other, underscoring the inherent limitations of our understanding of quantum systems and the fundamental nature of reality itself.[41][42][43][44][45]
Pauli Exclusion Principle
The Pauli exclusion principle, formulated by Wolfgang Pauli in 1925, states that no two identical fermions can occupy the same quantum state simultaneously within a quantum system. This principle is crucial for understanding the behavior of electrons in atoms, as it dictates that each electron must have a unique set of quantum numbers (n, l, m_l, and m_s). For example, in an atom, if two electrons are in the same orbital, they must have opposite spins, ensuring that their overall quantum state remains distinct. The exclusion principle is fundamental to the structure of the periodic table and the properties of matter, as it explains why electrons fill atomic orbitals in a specific order and prevents atoms from collapsing under the electromagnetic force. Unlike fermions, bosons are not subject to this principle and can share quantum states freely, leading to phenomena such as Bose-Einstein condensation[46][47][48].
What Are Identical Fermions
Identical fermions are particles that share the same intrinsic properties, such as mass, charge, and spin, making them indistinguishable from one another in a quantum system. Examples of identical fermions include electrons, protons, and neutrons. In quantum mechanics, these particles must obey the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. This requirement leads to the construction of antisymmetric wave functions for systems of identical fermions, ensuring that the overall state of the system changes sign when two particles are exchanged. As a result, while identical fermions can exist in different external states (like varying positions or momenta), they cannot be in identical quantum states, which is a defining characteristic that influences the behavior of matter at the atomic and subatomic levels.[51][52][53][54][55]
Superconductors and Macroscopic Quantum Effects
We can observe superconductors floating in mid-air over magnets. Superconductors are materials that can conduct electricity without resistance when cooled below a critical temperature. This behavior is a macroscopic quantum effect known as superconductivity. In this state, superconductors exhibit remarkable properties, such as the expulsion of magnetic fields (the Meissner effect), allowing them to levitate above magnets. This phenomenon not only demonstrates the principles of quantum mechanics on a larger scale but also has practical applications in technologies like magnetic levitation trains and advanced medical imaging devices.
What Experiments have shown
Schrodinger’s Cat experiment is a famous thought experiment in quantum mechanics that illustrates the concept of superposition. In this experiment, a hypothetical cat is placed in a sealed box with a mechanism that can potentially kill it based on the decay of a radioactive substance. Until the box is opened and the cat is observed, it exists in a superposition state where it is considered both alive and dead simultaneously. This experiment highlights the idea that quantum systems exist in all possible states until observed, demonstrating the concept of quantum superposition[2][3][4].
The Measurement Problem
What counts as a measurement in the thought experiment was not clearly defined. This is known as the measurement problem in quantum physics. Proposed solutions to the measurement problem in quantum mechanics have been a subject of intense debate and exploration within the scientific community. Here are some key proposed solutions based on the provided sources:
1. Unitary-Only Approaches: Wallace argues that only unitary-only approaches to the measurement problem are currently viable, but they face serious epistemic challenges. These approaches aim to extend solutions to relativistic quantum mechanics and quantum field theory[15]. The measurement problem in quantum mechanics arises from the question of how and when quantum states collapse into definite outcomes. Unitary-only approaches suggest that the evolution of quantum states is continuous and deterministic until measurement occurs.
2. Decoherence: Some researchers, like Zeh and Schlosshauer, suggest that quantum decoherence plays a crucial role in resolving the measurement problem. Decoherence explains how interactions with the environment lead to the classical appearance of macroscopic objects, providing a bridge between the quantum microworld and the classical world[17]. Decoherence explains how quantum systems lose their superposition due to interactions with the environment, leading to classical behavior. This process helps to understand why we do not observe macroscopic superpositions in everyday life.
3. Objective-Collapse Models: Objective-collapse models propose modifications to the Schrödinger equation with stochastic nonlinear terms that induce wave function collapse for macroscopic objects. These models make falsifiable predictions and offer an alternative perspective on the collapse of the wave function[17]. Objective-collapse models propose that wave function collapse is a physical process triggered by specific conditions, rather than being dependent on observation.
4. Single-World Realist Approach: A proposed solution emphasizes a single-world realist approach that reproduces the predictions of relativistic quantum mechanics without supervening on precisely-defined microscopic beables. This approach suggests that observable reality may be emergent or not microscopically defined[15]. This approach suggests that there is only one reality, and quantum mechanics describes the probabilities of different outcomes rather than multiple realities.
5. Hidden Variables Theories: Hidden variables theories, such as those proposed by Everett interpretations, attempt to reproduce quantum mechanics but may fail for highly entangled particles. These theories could potentially allow for a quantum computer to fail without observable deviations in less entangled systems[5]. These theories posit that underlying hidden variables determine the outcomes of quantum measurements, providing a deterministic view of quantum mechanics.
These proposed solutions represent different perspectives and attempts to address the measurement problem in quantum mechanics, highlighting the complexity and ongoing research in this fundamental area of physics.
Is Concsiouness an All Powerful Creator of Reality?
If you close your eyes, does the world disappear? No. While closing your eyes alters your immediate sensory experience of the world, it does not make the world disappear. The external reality continues to exist independently, and your mind retains the capacity to recall, imagine, and reflect on it. Consciousness, the integration of senses and memories to guide behavior, does not negate the existence of an objective reality that operates independently of individual perceptions. While your thoughts are important because they influence your actions and feelings, they do not have direct influence on the external physical world, as far as anyone has been able to show with a repeatable valid experiment. Thoughts do have a direct influence on the external physical world, but not without corresponding actions. The relationship between thoughts, feelings, and behaviors is complex, but scientific evidence supports the idea that tangible change requires active engagement with the world rather than mere thought alone.
Thought as A Super Spiritual Power
If you want to be popular, tell people their thoughts can manifest anything they want. The belief that thoughts can influence the universe is a popular notion, often associated with concepts like the Law of Attraction, manifestation, and various spiritual or metaphysical philosophies. While thoughts may not directly influence external reality, they can significantly impact behavior and decision-making. Positive thinking can lead to increased motivation, resilience, and proactive behavior, which can, in turn, create opportunities and changes in one’s life. This indirect influence is often conflated with direct influence. Some might argue that it does not matter, that feeling powerful is fun, so no harm in it. While embracing empowerment can be beneficial, for best practical results, mental manifestation and the like should ideally be linked with realistic expectations and actionable steps.
Scope Error?
Could this above conclusion be an error of scope? What if, for example, we are in a simulation? In that cause, while our thoughts would not influence the physical material of the simulation without action, there could be a back door, whereby things we visualize do manifest. Some theories suggest that consciousness itself could play a fundamental role in shaping the simulated reality. While the simulation hypothesis is intriguing, it remains speculative. There is currently no empirical evidence to support the idea that we live in a simulation or that thoughts can manifest in such a context. On the other hand, I have my personal examples, which to me seem to reach well beyond interpretation after the fact and wishful thinking. Ultimately, each person must puzzle this out, this key question about existence, because the truth of it should dictate to some extent what we do with our time.
Consciousness Is Not Required
This is where people get into conflicts and get confused. The word measurement implies observation by a conscious living human being. Indeed the cat experiment is set up in those terms. The experiment, however, does not require consciousness for measurement. Rather, any interaction that conveys information is considered a form of detection in quantum mechanics. The concept of measurement in quantum mechanics is defined as any interaction that provides information, allowing for a narrowing down of possibilities or refining of probabilities. This interaction can be between any entities, not necessarily involving conscious observers[14].
Therefore, in Schrödinger’s Cat experiment, what constitutes a measurement is crucial, and it does not rely on consciousness but rather on interactions that convey information and lead to the collapse of quantum superpositions into definite states[15].
The conclusion drawn from modern interpretations is that consciousness does not play a role in the measurement process. Instead, it is the interactions that convey information that lead to the collapse of quantum superpositions.
Conclusion
In conclusion, Schrödinger’s Cat experiment illustrates the complexities of quantum mechanics. The thought experiment highlights the significance of measurement and interaction in determining the state of a quantum system. It is crucial to understand that the measurement does not rely on consciousness but rather on physical interactions that lead to the collapse of quantum superpositions into definite states. This understanding is essential for grasping the nature of reality at the quantum level and the implications it has for both theoretical and practical applications in modern physics.
More Reading
[1] https://wtamu.edu/~cbaird/sq/2013/07/30/what-did-schrodingers-cat-experiment-prove/
[2] https://builtin.com/software-engineering-perspectives/schrodingers-cat
[3] https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat
[4] https://www.techtarget.com/whatis/definition/Schrodingers-cat
[5] https://www.youtube.com/watch?v=UjaAxUO6-Uw
[6] https://wtamu.edu/~cbaird/sq/2013/07/30/what-did-schrodingers-cat-experiment-prove/
[7] https://www.livescience.com/schrodingers-cat.html
[8] https://www.reddit.com/r/askscience/comments/2f84yu/if_the_common_understanding_of_schr%C3%B6dingers_cat/
[9] https://science.howstuffworks.com/science-vs-myth/everyday-myths/scientists-prove-schrodingers-cat-can-be-two-places-once.htm
[10] https://en.wikipedia.org/wiki/Schr%C3%B6dinger%27s_cat
[11] https://www.scientificamerican.com/article/this-twist-on-schroedingers-cat-paradox-has-major-implications-for-quantum-theory/
[12] https://wtamu.edu/~cbaird/sq/2013/07/30/what-did-schrodingers-cat-experiment-prove/
[13] https://www.askamathematician.com/2011/06/q-what-is-a-measurement-in-quantum-mechanics/
[14] https://physics.stackexchange.com/questions/506695/is-schrodingers-cat-itself-an-observer
[15] https://arxiv.org/abs/2301.06192
[16] https://link.aps.org/doi/10.1103/RevModPhys.38.453
[17] https://en.wikipedia.org/wiki/Measurement_problem
[18] https://iopscience.iop.org/article/10.1088/2399-6528/ac96cf
[19] https://physics.stackexchange.com/questions/23163/solution-to-the-quantum-measurement-problem
[20] https://en.wikipedia.org/wiki/Quantization_%28signal_processing%29
[21] https://www.open.edu/openlearn/digital-computing/exploring-communications-technology/content-section-3.3
[22] https://docs.taichi-lang.cn/en/docs/quant/
[23] https://soulpageit.com/ai-glossary/quantizationp-explained/
[24] https://www.khanacademy.org/computing/computers-and-internet/xcae6f4a7ff015e7d:digital-information/xcae6f4a7ff015e7d:bits-and-bytes/a/byte-sized-bits
[25] https://courses.lumenlearning.com/chemistryformajors/chapter/the-bohr-model-2/
[26] https://periodicos.ufv.br/jcec/article/download/13960/7199/63918
[27] http://vergil.chemistry.gatech.edu/notes/quantrev/node5.html
[28] http://hyperphysics.phy-astr.gsu.edu/hbase/Bohr.html
[29] http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/qangm.html
[30] https://www.youtube.com/watch?v=7V6j4sZ7w_E
[31] https://www.livescience.com/schrodingers-cat.html
[32] https://scienceexchange.caltech.edu/topics/quantum-science-explained/quantum-superposition
[33] https://en.wikipedia.org/wiki/Quantum_superposition
[34] https://www.quantum-inspire.com/kbase/superposition-and-entanglement/
[35] https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Quantum_States_of_Atoms_and_Molecules_%28Zielinksi_et_al%29/05%3A_Translational_States/5.03%3A_Linear_Combinations_of_Eigenfunctions
[36] https://en.wikipedia.org/wiki/Quantum_state
[37] https://pennylane.ai/qml/demos/tutorial_lcu_blockencoding/
[38] https://mathforquantum.quantumtinkerer.tudelft.nl/4_vector_spaces_QM/
[39] https://www.physicsforums.com/threads/a-linear-combination-of-states-that-diagonalize-the-hamiltonian.997020/
[40] https://www.britannica.com/science/wave-particle-duality
[41] https://en.wikipedia.org/wiki/Uncertainty_principle
[42] https://quantumatlas.umd.edu/entry/uncertainty-principle/
[43] https://plato.stanford.edu/entries/qt-uncertainty/
[44] https://scienceexchange.caltech.edu/topics/quantum-science-explained/uncertainty-principle
[45] https://www.youtube.com/watch?v=luvf_9EaJ0w
[46] https://en.wikipedia.org/wiki/Pauli_exclusion_principle
[47] https://www.youtube.com/watch?v=8IMAduR1niM
[48] https://byjus.com/jee/pauli-exclusion-principle/
[49] https://phys.libretexts.org/Bookshelves/Quantum_Mechanics/Advanced_Quantum_Mechanics_%28Kok%29/12:_Multiple_Particle_States/12.5:_The_Pauli_Exclusion_Principle
[50] https://courses.lumenlearning.com/suny-physics/chapter/30-9-the-pauli-exclusion-principle/
[51] https://physics.stackexchange.com/questions/322839/when-are-two-fermions-considered-identical
[52] https://www.grandinetti.org/resources/Teaching/Chem4300/LectureCh21.pdf
[53] https://www2.ph.ed.ac.uk/~ldeldebb/docs/QM/lect16.pdf
[54] https://ocw.mit.edu/courses/8-06-quantum-physics-iii-spring-2016/6e02558ecf4b7af37d2cdff550fc0f71_MIT8_06S16_chap4.pdf
[55] http://www.tcm.phy.cam.ac.uk/~bds10/aqp/lec11_compressed.pdf
[56] https://www.livescience.com/schrodingers-cat.html
[57] https://www.britannica.com/science/Schrodingers-cat
[58] https://www.techtarget.com/whatis/definition/Schrodingers-cat
[59] https://www.newscientist.com/definition/schrodingers-cat/
[60] https://www.nationalgeographic.com/science/article/130812-physics-schrodinger-erwin-google-doodle-cat-paradox-science
