Through Two Doors at Once Quotes

“A cartoon captioned “At home with the Heisenbergs” was stuck on the bathroom door outside the apartment, with Mrs. Heisenberg saying, “I can’t find my car keys,” and Mr. Heisenberg replying, “You probably know too much about their momentum.”)”
― Anil Ananthaswamy, Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

“Bohr wanted to make wave-particle dualism—the idea that nature has two faces and only shows one or the other at any one time—a key component of any interpretation of reality; Heisenberg put his “trust in the newly developed mathematical formalism,” to see what meanings it suggested, rather than presupposing any particular view of reality.”
― Anil Ananthaswamy, Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

“The advantage of wave mechanics, in Schrödinger’s opinion, was the idea that nature even at the smallest scales was continuous, not discrete. There were no quantum jumps.”
― Anil Ananthaswamy, Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

“If this sounds like the probabilities of matrix mechanics, you are not mistaken. Schrödinger himself, in another stroke of insight, showed that wave mechanics and matrix mechanics are mathematically equivalent (in hindsight, it was a mathematician called John von Neumann who would really prove the equivalence a few years later).”
― Anil Ananthaswamy, Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

“In classical physics, solving a wave equation for, say, a sound wave can give you the pressure of the sound wave at a certain point in space and time. Solving Schrödinger’s wave equation gives you what’s called a wavefunction. This wavefunction, denoted by the Greek letter ψ (psi, pronounced “sigh”), is something quite strange. It represents the quantum state of the particle, but the quantum state is not a single number or quantity that reveals, for example, that the electron is at this position at this time and at that position at another time. Rather, ψ is itself an undulating wave that has, at any given moment in time, different values at different positions. Even more weirdly, these values are not real numbers; rather, they can be complex numbers with imaginary parts. So the wavefunction at any instant in time is not localized in a region of space; rather, it is spread out, it’s everywhere, and it has imaginary components. The Schrödinger equation, then, allows you to calculate how the state of the quantum system, ψ, changes with time. Schrödinger”
― Anil Ananthaswamy, Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

“The fact that we are now dealing in probabilities is not, presumably, because we do not know enough about the particle. Matrix mechanics says you have all the information you can possibly have. Yet, if you take a million identically prepared particles in the same state (the same combination of states A and B) and perform a million identical measurements, then, on average, x2 number of times you will find the particle in state A, y2 of the time you’ll find it in state B. But you can never predict the answer you’ll get for any single particle. You can only talk statistically. Nature, it seems, is not deterministic in the quantum realm. Recall that something similar happens with the double slit. We cannot predict where exactly a single photon will land on the screen—we can only assign probabilities for where it might go.”
― Anil Ananthaswamy, Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

“The fact that we are now dealing in probabilities is not, presumably, because we do not know enough about the particle. Matrix mechanics says you have all the information you can possibly have. Yet, if you take a million identically prepared particles in the same state (the same combination of states A and B) and perform a million identical measurements, then, on average, x2 number of times you will find the particle in state A, y2 of the time you’ll find it in state B. But you can never predict the answer you’ll get for any single particle. You can only talk statistically. Nature, it seems, is not deterministic in the quantum realm.”
― Anil Ananthaswamy, Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality

“What Born realized was that the symbols Heisenberg was manipulating in his equations were mathematical objects called matrices, and there was an entire field of mathematics devoted to them, called matrix algebra. For example, Heisenberg had found that there was something strange about his symbols: when entity A was multiplied by entity B, it was not the same as B multiplied by A; the order of multiplication mattered. Real numbers don’t behave this way. But matrices do. A matrix is an array of elements. The array can be a single row, a single column, or a combination of rows and columns. Heisenberg had brilliantly intuited a way of representing the quantum world and asking questions about it using such symbols, while being unaware of matrix algebra.”
― Anil Ananthaswamy, Through Two Doors at Once: The Elegant Experiment That Captures the Enigma of Our Quantum Reality