Taking Quantum Mechanics Seriously

The advent of modern quantum mechanics marked a profound shift in how we view the fundamental laws of nature: it was not just a new theory, but a new kind of theory, a dramatic shift from the prevailing Newtonian paradigm.

One obstacle is that, notwithstanding the enormous empirical success of quan­tum theory, we human beings still tend to think in classical terms. Quantum theory

Submitted to the Foundational Questions Institute Essay Competition, “What Is Fundamental?”

S. M. Carroll (B) • A. Singh

Walter Burke Institute for Theoretical Physics, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA

e-mail: seancarroll@gmail.com

A. Singh

e-mail: ashmeet@caltech.edu

© Springer Nature Switzerland AG 2019 95

A. Aguirre et al. (eds.), What is Fundamental?, The Frontiers Collection,

https://doi.org/10.1007/978- 3-030-11301-8_10 describes the evolution of a state vector in a complex Hilbert space, but we populate our theories with ideas like “spacetime,” “particles,” and “fields.” We typically con­struct quantum theories by starting with some classical theory and then “quantizing” it. Presumably Nature works the other way around: it is quantum-mechanical from the start, and a classical limit emerges in the right circumstances.

In this essay we ask how far we can take the idea that the world is fundamentally quantum, with a minimal plausible ontology: a space of quantum states (Hilbert space) H, a particular state ) within it, and a Hamiltonian U, which tells how the state evolves over time. This is a version of the Everettian (Many-Worlds) approach to quantum mechanics, in which the quantum state is the only variable and it smoothly evolves according to the Schrodinger equation with the given Hamiltonian,

Our approach is distinguished by thinking of that state as a vector in Hilbert space, without any preferred notion of “observables,” and without necessarily representing Hilbert space in terms of particular classical variables. All of the additional elements familiar in physical theories, we will argue, can be emergent from the state vector (cf. [1]). We call this approach “Mad-Dog Everettianism,” to emphasize that it is as far as we can imagine taking the program of stripping down quantum mechanics to its most pure, minimal elements.^[20]

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