The Edge of Knowledge: Unsolved Mysteries of the Cosmos by Lawrence M. Krauss

Author:Lawrence M. Krauss [Krauss, Lawrence M.]
Language: eng
Format: epub
ISBN: 9781637588574
Publisher: Post Hill Press
Published: 2023-02-15T14:35:54+00:00

1.Many states at once: For me, the key distinction between the quantum picture of reality and the classical picture has to do with the configurations of systems governed by quantum mechanics. Classically, if I throw a ball, it takes some well-defined trajectory determined by Newton’s laws. If many electrons are emitted by a cathode ray tube, their average trajectories will mimic those of the ball. But the specific trajectory of each electron is completely undetermined in advance. In fact, it doesn’t even make sense to talk about the trajectory in advance of measuring it. That is because the electron acts as if it is taking many trajectories at once. Every measurement one can make to try and demonstrate that it actually took a specific path in advance of directly measuring its position, instead finds that no single trajectory is consistent with the data. This picture, promoted by Richard Feynman in his “path integral” formulation of quantum mechanics, most concisely captures the heart of quantum theory in my opinion.

2.The fundamental quantity in quantum mechanics is the wavefunction of an object, which, succinctly, allows an exact prediction of the probability of measuring the object in any one of the allowed states it may be measured to be in, for all times. One of the many misstatements about quantum mechanics is that it is not deterministic. This is incorrect. Quantum mechanics is based on an equation that describes the time evolution of the wavefunction. This means that if one specifies the value of a wavefunction at some initial time, its value at all subsequent times can be determined exactly, at least in principle. The wavefunction, defined more precisely, gives the probability amplitude (a complex number) of finding the system in a certain state. The square of the wavefunction gives the probability (a real number between zero and one) of measuring the system to be each of its many possible allowed states. Quantum mechanics determines these probabilities exactly. By the same token, it tells us that it is only these predicted probabilities that we can ever compare with experiments. The initial state of the system can never be determined exactly because the system can be in a combination of many states at once, a phenomenon called superposition. Such a superposition is another way of framing the fact that a particle can follow many different trajectories as it traverses from A to B, as long as we do not measure it between those two points.

3.The order in which one measures properties of a system can determine the properties one measures. Put another way, for some properties, reversing the order in which you measure them, for example the momentum and position of a particle, will give a different result than will the original measurements. This translates into the famous Heisenberg uncertainty principle, examples of which include the fact that one cannot measure with 100 percent accuracy both the position and momentum of a quantum object, or the precise value of its energy at a given time.

4.Once

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