[Paper Review] What if Time Really Exists?

Sean M. Carroll|ArXiv.org|Nov 23, 2008

Quantum Mechanics and Applications12 references22 citations

TL;DR

This paper argues that time is real and fundamental, proposing a quantum mechanical universe governed by a time-dependent Schrödinger equation with a time-independent Hamiltonian. By taking this perspective seriously, the authors derive a Heraclitean cosmology in which the universe evolves eternally in an infinite-dimensional Hilbert space, naturally explaining the arrow of time through continuous entropy increase, with no equilibrium state and a symmetric time evolution across past and future.

ABSTRACT

Despite the obvious utility of the concept, it has often been argued that time does not exist. I take the opposite perspective: let's imagine that time does exist, and the universe is described by a quantum state obeying ordinary time-dependent quantum mechanics. Reconciling this simple picture with the known facts about our universe turns out to be a non-trivial task, but by taking it seriously we can infer deep facts about the fundamental nature of reality. The arrow of time finds a plausible explanation in a "Heraclitean universe," described by a quantum state eternally evolving in an infinite-dimensional Hilbert space.

Motivation & Objective

• To challenge the widespread philosophical and physical view that time is an illusion or emergent, by arguing instead that time is fundamental and must be taken seriously in quantum cosmology.
• To reconcile the existence of time with quantum gravity, particularly the Wheeler-DeWitt equation, which appears to eliminate time by setting the Hamiltonian to zero.
• To explain the observed arrow of time not as a low-entropy initial condition, but as a consequence of eternal, irreversible evolution in a quantum system with no equilibrium.
• To propose that the universe’s current de Sitter phase is unstable, allowing for eternal entropy growth both forward and backward in time, leading to a symmetric multiverse.
• To explore how a quantum state evolving under a time-independent Hamiltonian can produce a universe with a clear arrow of time, despite the absence of a preferred initial moment.

Proposed method

• Assumes the universe is described by a quantum state evolving unitarily in time via the standard Schrödinger equation: $ irac{d}{dt}| ilde{\Psi}\rangle = \hat{H}|\tilde{\Psi}\rangle $, with a time-independent Hamiltonian.
• Requires the Hilbert space to be infinite-dimensional to allow for continuous energy eigenvalue accumulation, enabling eternal evolution without equilibrium.
• Applies the concept of duality in string theory to argue that time may be emergent in some formulations but must be fundamental in others, especially in quantum gravity.
• Uses the idea of quantum tunneling and baby universe creation (Farhi-Guth-Guven) to model transitions from high-entropy de Sitter space to even higher-entropy configurations.
• Proposes that entropy can increase both into the future and the past, leading to a time-symmetric multiverse where the arrow of time is not tied to a low-entropy beginning.
• Analyzes the geometry of two particles in 3D space as an analogy: closest approach is not a special point, just as minimum entropy in the universe need not be low.

Experimental results

Research questions

• RQ1 Can a universe governed by time-dependent quantum mechanics with a time-independent Hamiltonian still be consistent with known physics, including quantum gravity?
• RQ2 How can the arrow of time emerge in a quantum system that evolves eternally without reaching equilibrium?
• RQ3 What constraints does eternal evolution place on the structure of the Hilbert space, particularly regarding energy eigenvalue spectra?
• RQ4 Is the de Sitter phase of the universe, currently dominant, a stable endpoint or a transient state in a larger, time-symmetric multiverse?
• RQ5 Can entropy increase both into the future and the past, and what would that imply for cosmological initial conditions and the nature of time?

Key findings

• A quantum universe governed by a time-dependent Schrödinger equation with a time-independent Hamiltonian requires an infinite-dimensional Hilbert space with at least one accumulation point in the energy eigenvalue spectrum.
• The arrow of time arises naturally from eternal, irreversible evolution in a system with no equilibrium, where entropy can always increase, rather than from a special low-entropy initial condition.
• The current de Sitter phase of the universe is likely unstable, suggesting mechanisms like quantum creation of baby universes or vacuum transitions that allow for continued entropy growth.
• The universe may exhibit a symmetric time evolution: entropy increases both into the far future and the far past, implying that the arrow of time could be reversed in the distant past.
• The absence of a unique initial state or equilibrium in such a cosmology makes the observed arrow of time a robust feature of eternal quantum evolution, not a contingent boundary condition.
• Duality in string theory supports the idea that time may be emergent in some formulations, but the paper argues that a fundamental, real time is necessary to explain the observed flow of time and entropy.