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this chapter, we’ll lay out the basic principles that are central to understanding quantum physics: wavefunctions, allowed states, probability, and measurement. We’ll introduce a key example system, and talk about a simple experiment that demonstrates all of the essential features of quantum physics. We’ll talk about the essential randomness of quantum measurement, and the philosophical problems raised by this randomness, which are disturbing enough that even some of the founders of quantum physics gave up on it entirely.
WHAT DOES A WAVEFUNCTION MEAN? INTERPRETATION OF QUANTUM MECHANICS
    Most of the philosophical problems with quantum mechanics center around the “interpretation” of the theory. This is a problem unique to quantum mechanics, as classical physics doesn’t require interpretation. In classical physics, you predict the position, velocity, and acceleration of some object, and you know exactly what those quantities mean and how to measure them. There’s an immediate and intuitive connection between the theory and the reality that we observe.
    Quantum mechanics, on the other hand, is not nearly so obvious. We have the mathematical equations that govern the theory and allow us to calculate wavefunctions and predict their behavior, but just what those wavefunctions
mean
is not immediately clear. We need an “interpretation,” an extra layer of explanation, to connect the wavefunctions we calculate to the properties we measure in experiments.
    The central elements of quantum mechanics can be presented in many different ways—as many different ways as there are books on the subject—but in the end, they all rest on four basic principles.You can think of these as the core principles of the theory, the basic rules that you have to accept in order to make any progress. *
    CENTRAL PRINCIPLES OF QUANTUM MECHANICS
    1. Wavefunctions: Every object in the universe is described by a quantum wavefunction.
    2. Allowed states: A quantum object can only be observed in one of a limited number of allowed states.
    3. Probability: The wavefunction of an object determines the probability of being found in each of the allowed states.
    4. Measurement: Measuring the state of an object absolutely determines the state of that object.
    The first principle is the idea of wavefunctions. Every object or system of objects in the universe is described by a wavefunction, a mathematical function that has some value at every point in space. It doesn’t matter what you’re describing—an electron, a dog treat, a cat in a box—it has a wavefunction, and that wave-function has some value no matter where you look. The value could be positive, or negative, or zero, or even an imaginary number (like the square root of -1), but it has a value everywhere.
    A mathematical formula called the Schrödinger equation (after the Austrian physicist and noted cad † Erwin Schrödinger, who discovered it) governs the behavior of wavefunctions. Givensome basic information about the object of interest, you can use the Schrödinger equation to calculate the wavefunction for that object and determine how that wavefunction will change over time, similar to the way you can use Newton’s laws to predict the future position of a dog given her current position and velocity. The wavefunction, in turn, determines all the observable properties of the object.
    The second principle is the idea of allowed states . In quantum theory, an object will only ever be observed in certain states. This principle puts the “quantum” in “quantum mechanics”—the energy in a beam of light comes as a stream of photons, and each photon is one quantum of light that can’t be split. You can have one photon, or two, or three, but never one and a half or pi.
    Similarly, an electron orbiting the nucleus of an atom can only be found in certain very specific states. * Each of these states has a particular energy, and the electron will always be found with one of those energies,