Category Archives: Physics

Question: How is the existence of a graviton consistent with the GR paradigm of gravity as a purely geometrical effect? Answer: Ontologically, it’s not! Gravitons are predicated on a quantum field-theoretic formulation of gravity, while spacetime curvature is the corresponding … Continue reading →

Consider a scalar field in dimensions with the standard decomposition into creation and annihilation operators, Then the commutation relations between the creation/annihilation operators, where , imply exact commutativity of spacelike separated fields: where the last step follows from the fact … Continue reading →

Black hole thermodynamics In 1973, Jacob Bekenstein observed that black holes must be endowed with an entropy in order to preserve the second law of thermodynamics; otherwise, one could decrease the entropy of the universe by simply throwing subsystems with … Continue reading →

Why is the universe comprehensible? Wigner referred to this as the “unreasonable effectiveness of mathematics in the natural sciences”, and even Einstein is famous for writing, in 1936, that “[t]he eternal mystery of the world is its comprehensibility… The fact … Continue reading →

In an earlier post, we sketched the basic mathematical description of quantum mechanics, culminating in the general description of quantum states as (reduced) density matrices. We also claimed that generic measurements are not orthogonal projections, and evolution is not unitary. … Continue reading →

There’s a fundamental problem in gauge theory known as Hilbert space factorization. This has its roots in the issue of how local quantities (e.g., operators) are defined in quantum field theory, and has consequences for everything from entanglement and holographic … Continue reading →

Reference: John Preskill’s notes on Quantum Information and Computation. In quantum mechanics, a state is a complete description of a physical system. Mathematically, it is given by a ray (an equivalence class of vectors) in Hilbert space, , which is … Continue reading →

The derivation of Ryu-Takayanagi (RT) put forward by Lewkowycz and Maldacena (LM) is essentially an extension of the (boundary) replica trick into the bulk. The basic idea of the replica trick is that entanglement entropy is generally hard to calculate, … Continue reading →

There’s a marvelous — and by now quite well-known — paper (paywalled) by Gibbons and Hawking, in which they compute the entropy of black holes from what is essentially a purely geometrical argument. This relies on the fact that the … Continue reading →