"A measurement is the testing or manipulation of a physical system to yield a numerical result."
The measurement problem, quantum decoherence, and the role of the observer.
Wave-particle duality: The idea that particles can behave like waves and vice versa.
Uncertainty principle: The principle that it is impossible to simultaneously measure certain pairs of physical properties, such as position and momentum, with arbitrary precision.
Schrödinger equation: The fundamental equation of quantum mechanics, which describes how the state of a quantum system changes over time.
State vectors and wave functions: Mathematical representations of the state of a quantum system, which allow us to calculate probabilities of different outcomes.
Superposition and entanglement: Two key features of quantum systems that allow them to exhibit behaviors that are impossible in classical physics.
Observables and operators: Quantities that can be measured in a quantum system, and the mathematical tools used to describe them.
Quantum measurement: The process by which a measurement is made on a quantum system, and the effects it can have on the system.
The role of the observer: The question of how measurements are actually made in the quantum world, and whether consciousness plays a special role.
Decoherence: The phenomenon whereby quantum systems become "entangled" with their environment, leading to the loss of quantum behavior.
Quantum computing: The use of quantum mechanics to perform computation, which has the potential to revolutionize many areas of technology.
projective measurements: Projective measurements in quantum physics involve determining the state of a quantum system by performing measurements on the projection operators associated with the eigenstates of the observable being measured.
non-projective measurements: Non-projective measurements in quantum physics refer to measurement methods that do not collapse the quantum state into one of the eigenstates of the observable being measured.
weak measurements: Weak measurements in quantum physics refer to a method used to obtain partial information about a quantum system without strongly disturbing its state.
continuous measurements: Continuous measurements in the context of Physics and Quantum Measurement refer to the process of observing and quantifying a physical quantity in a continuous manner over a certain period of time rather than obtaining discrete values.
"A fundamental feature of quantum theory is that the predictions it makes are probabilistic."
"The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system."
"The formula for this calculation is known as the Born rule."
"Applying the Born rule to these amplitudes gives the probabilities that the electron will be found in one region or another when an experiment is performed to locate it."
"The best the theory can do; it cannot say for certain where the electron will be found."
"The uncertainty principle implies that, whatever the quantum state, the range of predictions for the electron's position and the range of predictions for its momentum cannot both be narrow."
"Measuring a quantum system generally changes the quantum state that describes that system."
"The mathematical tools for making predictions about what measurement outcomes may occur, and how quantum states can change, were developed during the 20th century and make use of linear algebra and functional analysis."
"Quantum physics has proven to be an empirical success and to have wide-ranging applicability."
"On a more philosophical level, debates continue about the meaning of the measurement concept."
"A quantum particle like an electron can be described by a quantum state that associates to each point in space a complex number called a probability amplitude."
"The same quantum state can also be used to make a prediction of how the electron will be moving if an experiment is performed to measure its momentum instead of its position."
"Furthermore, the fact that nature violates the statistical conditions known as Bell inequalities indicates that the unpredictability of quantum measurement results cannot be explained away as due to ignorance about "hidden variables" within quantum systems."
"Measuring a quantum system generally changes the quantum state that describes that system."
"The mathematical tools for making predictions about what measurement outcomes may occur, and how quantum states can change, were developed during the 20th century and make use of linear algebra and functional analysis."
"Quantum physics has proven to be an empirical success and to have wide-ranging applicability."
"This is a central feature of quantum mechanics, one that is both mathematically intricate and conceptually subtle."
"The procedure for finding a probability involves combining a quantum state, which mathematically describes a quantum system, with a mathematical representation of the measurement to be performed on that system."
"The best the theory can do; it cannot say for certain where the electron will be found."