a) Superposition in Quantum Mechanics:
In quantum mechanics, the principle of superposition allows a particle (such as an electron or photon) to exist in multiple states simultaneously until it is observed or measured. This means that before a measurement is made, the particle can exist in a combination of different possible states, each with a certain probability amplitude. These probability amplitudes are represented by complex numbers, and they describe the likelihood of finding the particle in a particular state when measured.
Mathematically, superposition is represented using the wave function (usually denoted by the Greek letter Ψ), which is a mathematical function that describes the quantum state of a system. The wave function includes all possible states the particle can be in, and its squared magnitude gives the probability of finding the particle in each state upon measurement.
b) Schrödinger's Cat Thought Experiment:
Schrödinger's cat is a thought experiment proposed by Austrian physicist Erwin Schrödinger in 1935. It is used to illustrate the apparent paradox between quantum superposition and our classical macroscopic world. The thought experiment goes as follows:
Imagine a cat inside a sealed box along with a radioactive atom, a Geiger counter, a vial of poison, and a hammer. The release of the poison and the hammer's fall are triggered by the decay of the radioactive atom, as detected by the Geiger counter.
According to the laws of quantum mechanics, the radioactive atom can be in a superposition of decayed and not decayed states until it is observed. As a result, the cat's fate is also in superposition—it is both alive and dead—until the box is opened and the cat is observed.
This leads to a paradox when applying quantum principles to the macroscopic world because we don't observe everyday objects like cats in superpositions of states. The question then arises: When and how does the quantum superposition become a definite, classical outcome (the cat being either alive or dead) through the process of measurement?
c) Copenhagen Interpretation and Many-Worlds Interpretation:
The Copenhagen interpretation, proposed by Niels Bohr and his colleagues, is one of the earliest and most widely known interpretations of quantum mechanics. It suggests that the act of measurement causes the wave function to collapse, and the system takes on a definite state with the probabilities determined by the squared magnitudes of the wave function. In this interpretation, the superposition is considered a state of potentiality until it interacts with an observer, and the act of measurement brings about a specific outcome.
The Many-Worlds interpretation, proposed by Hugh Everett III, offers a different perspective. It suggests that the wave function never collapses. Instead, when a measurement occurs, the universe splits into multiple branches, one for each possible outcome. In this view, all possibilities described by the wave function are realized in different branches of the universe, creating a "multiverse" of parallel realities.
d) Quantum Decoherence as a Solution to the Measurement Problem:
Quantum decoherence is a process by which a quantum system interacts with its environment, leading to the suppression of interference effects between different states of the system. When a quantum system is in superposition and becomes entangled with its surrounding environment, the different branches effectively lose their ability to interact with each other coherently.
Decoherence explains why macroscopic objects, like Schrödinger's cat or any larger system, do not seem to exhibit quantum superposition in our everyday experience. The interactions with the environment cause the system to quickly settle into one of the classical states (e.g., alive or dead cat) due to the overwhelming number of entangled particles involved.
Quantum decoherence does not necessarily solve the measurement problem entirely, but it offers a possible explanation for why we observe classical behavior in our macroscopic world while retaining the formalism of quantum mechanics for describing the behavior of microscopic particles. It is important to note that the interpretation of quantum mechanics is still a topic of active debate among physicists and philosophers, and no single interpretation has been universally accepted.