Singularities, Firewalls, and Complementarity

Almheiri, Marolf, Polchinski, and Sully, recently claimed that once a black hole has radiated more than half its initial entropy (the Page time), the horizon is replaced by a "firewall" at which infalling observers burn up, in apparent violation of the equivalence principle and the postulates of black hole complementarity. In this paper I review the arguments for firewalls, and give a slightly different interpretation of them. According to this interpretation the horizon has standard properties, but the singularity is non-standard. The growing entanglement of the black hole with Hawking radiation causes the singularity to migrate toward the horizon, and eventually intersect it at the page time. The resulting collision of the singularity with the horizon leads to the firewall. Complementarity applies to the horizon and not to the singular firewall. Almheiri, Marolf, Polchinski, and Sully conjecture that firewalls form much earlier then the Page time; namely at the scrambling time. I argue that there is no reason to believe this generalization, and good reason to think it is wrong. For most of this paper I will assume that the firewall argument is correct. In the last section before the conclusion I will describe reasons for having reservations.Comment: 28 pages, 8 figure

Complexity and Newton's Laws

In a recent note I argued that the holographic origin of gravitational attraction is the quantum mechanical tendency for operators to grow under time evolution. In a followup the claim was tested in the context of the SYK theory and its bulk dual---the theory of near-extremal black holes. In this paper I give an improved version of the size-momentum correspondence and show that Newton's laws of motion are a consequence. Operator size is closely related to complexity. Therefore one may say that gravitational attraction is a manifestation of the tendency for complexity to increase. The improved version of the size-momentum correspondence can be justified by the arguments of Lin, Maldacena, and Zhao constructing symmetry generators for the approximate symmetries of the SYK model.Comment: 13 figure

Addendum to Fast Scramblers

This paper is an addendum to [arXiv:0808.2096] in which I point out that both de Sitter space and Rindler space are fast scramblers. This fact naturally suggests that the holographic description of a causal patch of de Sitter space may be a matrix quantum mechanics at finite temperature. The same can be said of Rindler space. Some qualitative features of these spaces can be understood from the matrix description.Comment: 16 pages, 2 figure

Is Eternal Inflation Past-Eternal? And What if It Is?

As a result of discussions with Bousso and Vilenkin I want to return to the question of whether the multiverse is past-eternal or if there was a beginning. Not surprisingly, given three people, there were three answers. However, the discussions have led to some common ground. The multiverse being past-eternal, or at least extremely old has content and potential phenomenological implications. I will discuss how the oldness of the multiverse is connected with recent speculations of Douglas.Comment: 13 pages, 4 figure

Addendum to Computational Complexity and Black Hole Horizons

In this addendum to [arXiv:1402.5674] two points are discussed. In the first additional evidence is provided for a dual connection between the geometric length of an Einstein-Rosen bridge and the computational complexity of the quantum state of the dual CFT's. The relation between growth of complexity and Page's ``Extreme Cosmic Censorship" principle is also remarked on. The second point involves a gedanken experiment in which Alice measures a complete set of commuting observables at her end of an Einstein-Rosen bridge is discussed. An apparent paradox is resolved by appealing to the properties of GHZ tripartite entanglement.Comment: 11 pages, 1 figur

PiTP Lectures on Complexity and Black Holes

This is the first of three PiTP lectures on complexity and its role in black hole physics.Comment: Lectures, PiTP summer school, 2018. Superseded by arXiv:1810.1156

Butterflies on the Stretched Horizon

In this paper I return to the question of what kind of perturbations on Alice's side of an Einstein-Rosen bridge can send messages to Bob as he enters the horizon at the other end. By definition "easy" operators do not activate messages and "hard" operators do, but there are no clear criteria to identify the difference between easy and hard. In this paper I argue that the difference is related to the time evolution of a certain measure of computational complexity, associated with the stretched horizon of Alice's black hole. The arguments suggest that the AMPSS commutator argument is more connected with butterflies than with firewalls.Comment: Additional citations and substantive additions. All additions indicated in boldfac

Why do Things Fall?

This is the first of several short notes in which I will describe phenomena that illustrate GR=QM. In it I explain that the gravitational attraction that a black hole exerts on a nearby test object is a consequence of a fundamental law of quantum mechanics---the tendency for complexity to grow. It will also be shown that the Einstein bound on velocities is closely related to the quantum-chaos bound of Maldacena, Shenker, and Stanford.Comment: 6 pages, 1 figur

Was There a Beginning?

In this note I respond to Vilenkin's claim that there must have been a beginning.Comment: 4 pages, 2 figure

Dear Qubitzers, GR=QM

These are some thoughts contained in a letter to colleagues, about the close relation between gravity and quantum mechanics, and also about the possibility of seeing quantum gravity in a lab equipped with quantum computers. I expect this will become feasible sometime in the next decade or two.Comment: Letter to Colleague