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Quantum Mechanics
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information from http://www.quantumphysicslady.org/glossary/quantum-superposition/
The term “superposition” is used in both classical physics and quantum physics. In this article, “superposition” is addressed primarily as a quantum phenomenon.
Classical Superposition
The term “superposition” was first used in classical physics. There, waves are said to be in a superposition when they meet and run through each other. When they do so, they are on top of each other. This is called a “superposition.” When in a superposition, they can change each other in a number of ways. But upon parting, amazingly, they return to their original forms.
In the accompanying video, two waves approach each other from opposite directions. These might be, for example, waves in water or sound waves in the air. Upon meeting, they form a superposition–two waves superimposed on top of each other. In this case, they amplify their heights—the heights of the two waves add together to make a taller wave. I find the next bit quite magical: once they’ve passed each other, they emerge unscathed as if nothing had happened. They return to their original heights.
In this video the waves are perfectly in sync (technically “in phase”). That is, both waves go up into crests and go down into troughs at exactly the same moment. As noted, in this situation, they amplify each other before parting ways.
But, of course, waves might meet that are out of phase. That is, they might crest at different times. If they were perfectly out of phase so that one crested exactly at the moment that the other bottomed out into a trough, they would cancel each other. Upon meeting, the water would go flat. In this superposition, it would appear that there were no waves at all. Then, once the waves had passed each other, they would emerge again, in the same forms that they had assumed prior to meeting–just as if nothing had happened.
Quantum Superposition
Quantum mechanics took the term “superposition” to describe a quantum state analogous to classical superpositions but even more magical. The quantum state of Schrodinger’s cat is called a “superposition.” The cat ends up in a state of being both dead and alive; it’s in a superposition of being both dead and alive. Sometimes, people say that an electron is in a superposition of being in more than one place at the same time.
Or it’s in a superposition of spinning both clockwise and counter-clockwise at the same time. No, I’ve not seen an attempt to make a still image of that! But below is a video of an atom in a superposition of being in an excited state (when it enlarges) and a less excited state (when it shrinks).
To say that a quantum particle is in more than one state at the same time is a quick and dirty way to describe a “superposition.” And it gets across the general idea. But it’s not really accurate, and we can’t wrap our minds around it. How can an electron spin both clockwise and counterclockwise at the same time? How can a cat be both dead and alive? What is really going on?
Example of a Quantum Superposition
To explain what’s really going on, consider an experiment in which an electron is trapped in a box. The electron is magnetic and is repelled by the magnets which surround it on all sides—this is an electron trap. The box also holds an electron detection screen. This might be a screen treated with chemical phosphor. A tiny pixel of phosphor in the screen lights up when an electron interacts with it.
Let’s say that experimenters would like to calculate where the electron is. They calculate the behavior of the electron in the box using an equation derived from the Schrodinger Wave Equation. This derived equation is called a “wave function.” (A function is a common type of equation, often referred to in algebra.)
If the electron were like a baseball, the wave function would tell us where the electron is at any moment in time. Staying with the baseball, if a batter were to hit it with a known amount of force, physicists could calculate the position of the baseball at any particular moment in time. They would apply the laws of force originally developed by Isaac Newton in the 1600’s. Every moment, the baseball would occupy a different position in spacetime. When it was caught, it would be in spacetime too. It never disappears from spacetime. This is not the way quantum particles behave.
The wave function derived from Schrodinger’s Equation doesn’t tell us where the electron is. Nor does it tell us that the electron is in many places at the same time. Instead, the wave function tells us a set of probabilities as to where the electron will appear if it is detected. The wave function assigns a probability to each spacetime position in which the electron could possibly be detected. While the experimenters would like to know where in the box the electron is at any one moment, the best that they can do is calculate the probabilities of where it will be detected.
Probability amplitudes quantum mechanics
Now we can return to the term “superposition.” The electron is in a superposition until detected. When not detected, it isn’t considered to be in position in spacetime. Rather, it’s in a quantum superposition of probabilities. Physicists describe the electron as being in a “probability state” or a “probability wave” or an “electron cloud.” This superposition can be described mathematically. But it cannot be described as an object or energy in a particular position in spacetime or even in a group of positions in spacetime.
The accompanying image is an imaginary graph of the probabilities as to where the electron might be detected in the magnetic box. This is a graph of a superposition. Each wave peak represents a probability of an experimental result rather than representing the position of a physical object or energy. According to this graph, the electron might be found in six different positions when it is detected (A, B, C, D, E, F). In this case, due to the particular set-up of the magnets, the electron has an equal probability of being detected as a particle in each position. This is indicated by the equal heights of the wave peaks. This graph shows what’s going on in “Quantumland.”
Quantumland
This explanation of “superposition,” that it is a state which is not in spacetime, comes from the Transactional Interpretation of quantum mechanics. In this interpretation, quantum particles are in Quantumland, and Quantumland is a level of reality underlying spacetime.
The wave function, not Newton’s Laws, are used to calculate the wavy, apparently insubstantial, possibilities of where the electron will be detected.
While Quantumland may seem insubstantial, it determines what happens in spacetime. True, Quantumland only sets the probabilities, but the behavior of quantum particles which are detected in spacetime must conform with the probabilities...
Superpositions in the Copenhagen Interpretation
The original interpretation of quantum mechanics, the Copenhagen Interpretation, however, interprets “superposition” differently. This interpretation was developed in the 1920’s and 30’s by the founders of the field of quantum mechanics. Like the Transactional Interpretation and most other interpretations of quantum mechanics, it derives the wave function from the Schrodinger Equation to describe the superposition.
But it’s mum on the issue as to whether there is any reality to the wavy probabilities calculated by the wave function. It declines to address the issue, describing the question as “unscientific.” This is due to a philosophy that was current at the time that the Copenhagen Interpretation was developed, a philosophy of science called “logical positivism.” According to logical positivism, science should address only those things which can be measured and should stay clear of everything else.
In summary, in the Copenhagen Interpretation, the physical nature of quantum superpositions cannot be described. They are a set of probabilities calculated by the wave function, and nothing more can be said about superpositions.
from https://builtin.com/software-engineering-perspectives/superposition
Superposition is a quantum principle that refers to a physical system that exists in multiple states simultaneously based on a specific set of solutions. The most commonly used set of solutions is all possible solutions, also known as Hilbert space. In quantum physics, the Hilbert space is the mathematical representation of all the possible states the system can take. If my system is a spinning electron, its Hilbert space is spin up and spin down, since these are the two possible options for the spin direction.
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