#### QM Basics 3 : Particle Superposition

<< Val Baganza, Italy, AUG 8 2024 >> NOTE: This is a first cut to get to press. This subject is so complicated that it may take a few updates to get this article correct. Quantum superposition is a basic principle in quantum mechanics that describes how particles, such as electrons or photons (particles with no mass), can exist in multiple states (called "basis states" ) simultaneously. Unlike classical physics, where an particle must be in a single state at any given time, quantum superposition allows a particle to be in a combination of states at any given time. For instance, an electron in superposition might be described as being in several positions or possessing multiple energies simultaneously.This concept challenges our normal intuition. Understanding superposition is crtical to fathoming the strange behavior observed in the quantum world. The idea of superposition is often illustrated using thought experiments like Schroedinger's cat. In this scenario, a cat is placed in a sealed box with a mechanism that has a 50% chance of killing the cat when the box is opened. According to quantum mechanics, until the box is opened and the cat is observed, the cat is considered to be in a superposition of being both alive and dead. This thought experiment highlights the bizarre nature of quantum superposition, where the act of measurement plays a crucial role in determining the state of a system. Here at TDM, we dont like this cat in the box metaphor. We prefer a more real world analogy. So later we will use the TDM quantum Coin to describe superposition. WAVES,WAVES Again... As described earlier, quantum superposition can be represented using wave functions, which are mathematical descriptions of the quantum state of a system. A wave function can be a linear combination of multiple possible states, with each state having a certain probability amplitude. The square of the probability amplitude gives the likelihood of the system being found in a particular state upon measurement. Again, we MUST emphasize these are NOT physical waves, like at the beach. These are cycling of the probabilities of a basis state with respect to time. The waves are in the data sets. The schroedinger equation is used to sample a particle property probability at any point in time. The equation ONLY works at the time of "wave collapse" (also called "actualization). After the sampling, the partile goes back into superposition. The Shcroedinger equation ONLY works on particles that are boxed in by something, like an electron bound to an atomic nucleus. It does not work on free particle flying through space. This mathematical framework allows quantum superposition to be precisely defined and calculated, making it a powerful tool in predicting the behavior of quantum systems.Quantum superposition has significant implications for military technology, particularly in the field of quantum computing. In a classical computer, bits are the basic units of information and can be either 0 or 1. However, in a quantum computer, qubits can be in a superposition of both 0 and 1 simultaneously. This ability to represent multiple states at once allows quantum computers to perform certain calculations exponentially faster thanclassical computers. Superposition, combined with other quantum phenomena like entanglement, is what gives quantum computers their potential to revolutionize computing. We will look at Quantum Computing in detail in a future article. Quantum Superposition remains a topic of intense research and debate. The exact nature of superposition, especially how and why a quantum system "chooses" a particular state upon measurement, is still not fully understood. This mystery is at the heart of various interpretations of quantum mechanics, such as the classic wave based "Copenhagen Interpretation" ,the "Bohmian Interpretation " and the "Many Worlds Interpretation". Each offers a different perspective on how to reconcile the counter intuitive aspects of quantum superposition with our understanding of reality.For now we will stick the with Copenhagen Interpretation which views superposition as as summation of probability waves. This interpretation is often referred to as the "Shut up and just do the math" method. This approach just deals with how it works, not why it works. This avoids long and mind bending meta physical pondering. To understand quantum superposition we will use what we call the TDM Quantum Coin. The Quantum Coin has only 2 basis states ,head or tail. Each basis state has a 50% probability. So if you toss the Quantum coin a hundred times, you will get 50 heads and 50 tails. Now if we toss the Quantum Coin, what state is the Quantum Coin in as it tumbles ?? It is cycling through head, tails, head, tails, etc. This is analogous to superposition. Only when the Quantum Coin is caught in your palm and slapped down (in effect sampled) does it "choose" a basis state (head or tails). Under the "Copenhagen Interpretation", when a particle chooses a basis state, it is called "wave collapse". This means the particle stops cycling and MUST choose an absolute basis state (head or tails). So if a particle has 35 basis states in can be in, while in superposition it is cycling thru them all. When the particle runs into something or is observed by a sensor, it must choose a basis state based on its probability density. This choosing can be desribed by the schroedinger equation. It is important to understand that this equation only gives the probability of the basis state at the TIME of sampling. It is just a snap shot at time T. After being sampled, the particle goes back into cycling through its basis states in superposition. This has actually been proving by experiments. Lets use the TDM quantum coin again. Say we build a machine that seperates quantum coins into ones that show head and ones that show tails at the point of sampling. This machine has one opening where we put in quantum coins. The machine sorts the quantum coins into 2 outputs, one for head and one for tail. If we pour in 100 quantum coins we get the expected 50 head coins in the first output and 50 tail coins in the second output. But here is where it gets wierder. If we take the all head coins from output one and pour it back into the machines input what do we get ? Intuition tells us that if we pour in 50 head coins, we would get all 50 head coins out output one again. NOT SO! WE actually get 25 head coins and 25 tail coins again. This is because on the first sort each coin is sampled and chooses a state. Immediately after the sampling, ALL coins go back into superposition. When its sampled on the second sort, we get the 50% probabilty of the basis states again. Very odd to say the least. We hope you now have at least a rudimentary understanding of this most important Quantum property. Now, on to Entanglement. References Stephen Hawking & Leonard Mlodinow, The Grand Design, Bantam Books,2012 Jakob Schwictenburg, No-Nonsense Quantum Mechanics, No-Nonsense Books,2020 https://en.wikipedia.org/wiki/Quantum_superposition - accessed on AUG 7,2024