Using Cosmology to Establish the Quantization of Gravity

A short article that I’ve read today (via @seanmcarroll).

arXiv:1309.5343 [hep-th]

Title: “Using Cosmology to Establish the Quantization of Gravity”

Authors: Lawrence M. KraussFrank Wilczek

Here is the abstract:

While many aspects of general relativity have been tested, and general principles of quantum dynamics demand its quantization, there is no direct evidence for that. It has been argued that development of detectors sensitive to individual gravitons is unlikely, and perhaps impossible. We argue here, however, that measurement of polarization of the Cosmic Microwave Background due to a long wavelength stochastic background of gravitational waves from Inflation in the Early Universe would firmly establish the quantization of gravity.

The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics

One of the latest books I’ve read: “The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics”, a book by Stanford well-known professor Leonard Susskind. I say “well-known” because anybody with some interest in Theoretical Physics may find his lectures on iTunes or YouTube (of course, for free). A great communicator Mr Susskind, one of my favourites, and also one of the fathers of String Theory.

In this book, a book that I think I will read again in some near future, Professor Susskind tells us the story about a theoretical dispute between him (“Is information lost when something falls into a black hole?“) and dutch physicist Gerard ‘t Hooft (1999 Nobel Prize in Physics), on one side, vs. the most famous physicist to the general public, Stephen Hawking, on the other.

The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics

The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics (image:


This is the book description from the publisher:

A mind-bending book about modern physics, quantum mechanics, the fate of stars and the deep mysteries of black holes. What happens when something is sucked into a black hole? Does it disappear? Three decades ago, a young physicist named Stephen Hawking claimed it did–and in doing so put at risk everything we know about physics and the fundamental laws of the universe. Most scientists didn’t recognize the import of Hawking’s claims, but Leonard Susskind and Gerard t’Hooft realized the threat, and responded with a counterattack that changed the course of physics. This is the story of their united effort to reconcile Hawking’s revolutionary theories with their own sense of reality–effort that would eventually result in Hawking admitting he was wrong, paying up, and Susskind and t’Hooft realizing that our world is a hologram projected from the outer boundaries of space.

A great book I strongly recommend to anyone interesting in this challenging and profound topics. You can find it, for example, on, here.

You can get a grasp of what is explained in this book in this short YouTube video: Hawking vs Susskind.

The original 2005 publication by Professor Hawking entitled: “Information Loss in Black Holes” can be found here.

Strings and Extra Dimensions

Chapter #21 of the course “Dark Matter, Dark Energy: The Dark Side of the Universe” by Prof. Sean Carroll. An interesting chapter to talk about these topics:

  • String theory: according to Wikipedia’s entry, “String theory is an active research framework in particle physics that attempts to reconcile quantum mechanics and general relativity. It is a contender for a theory of everything (TOE), a self-contained mathematical model that describes all fundamental forces and forms of matter”. I am pretty sure that if you are reading this blog from time to time, you must have heard of String theory (this could be another “coincidence scandal“, be reading this blog, I mean… or this expression is reserved for other stuff? 🙂
  • Quantized gravity: “Quantized Gravity or Quantum Gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity”. This model should be able to produce the same results that are currently known in the following two limits: a) when there is weak gravity (when we use QM and not GR), and b) when we use only GR at much larger distances than h bar (Planck’s reduced constant, i.e., when we do not take into consideration quantum phenomena). In addition to this, it should be able to explain physical situations in which both QM and GR are involved. The most famous quantum gravity theories are String Theory and Loop Quantum Gravity. I am pretty sure that I will be posting about them in future entries of this blog.
  • QED: relativistic QFT (quantum field theory) of electrodynamics. It describes how matter and light interact and involves both quantum mechanics and the special theory of relativity. The founder (one of the founders) of this theory was Richard FeynmanSurely You’re Joking, Mr. Feynman!
  • Planck length: length scale at which the structure of spacetime becomes dominated by quantum effects. In some theories, it is proposed that the structure of spacetime is discrete and its smallest distance is the Planck length.

    Planck length

    Planck length

  • M-theory: this refers to the theory proposed by Edward Witten who in 1995 said that the 5 viable string theories were nothing but different aspects of the same theory. Please, don’t ask me what the M stands for. We Physicists don’t know! (mother? magic? mistery? matrix? master?… the W in Witten’s surname but inverted? Choose the one that you like best).
  • QCD: quantum chromodynamics is the theory that explains the strong interaction that binds together quarks and gluons to form hadrons (i.e., protons and neutrons). One of the fathers of this theory was Murray Gell-Mann. If you want to see Gell-Mann in action, I strongly recommend you this TED Talk about “Beauty and Truth in Physics“. Gell-Mann, you are an incredible man, you know! 
  • Branes: mathematical concept that appears in string and related theories such as the M-theory. Enough for the moment…

Although I recommend purchasing the original videos from The Teaching Company, this chapter can be seen on YouTube here (part 1) and here (part 2) and here (part 3).

David Tong: Lectures on Quantum Field Theory

I wish I was born in 2000 or later, I must confess. Why? Because when I was younger (let’s express it this way), there was no YouTube, no lectures on the Web, no nothing but plain text, etc. Nowadays you can follow, for example, a really interesting course on QFT (introductory level) from a Cambridge Professor, for free… This course is the one that I’ve started following. At the moment I’ve only seen the first class of it and hope it doesn’t get very complicated for me with respect to mathematics (not in its best shape of all time at the moment). Professor David Tong explains quite clearly the concepts, so I think I will enjoy the course.

The content of the course (please visit his webpage if you want to know it in detail) treats the following points:

  1. Preliminaries.
  2. Classical Field Theory:   
    Table of Contents; Introduction; Lagrangian Field Theory; Lorentz Invariance; Noether’s Theorem and Conserved Currents; Hamiltonian Field Theory.
  3. Canonical Quantization:   
    The Klein-Gordon Equation, The Simple Harmonic Oscillator; Free Quantum Fields; Vacuum Energy; Particles; Relativistic Normalization; Complex Scalar Fields; The Heisenberg Picture; Causality and Propagators; Applications; Non-Relativistic Field Theory
  4. Interacting Fields:   
    Types of Interaction; The Interaction Picture; Dyson’s Formula; Scattering; Wick’s Theorem; Feynman Diagrams; Feynman Rules; Amplitudes; Decays and Cross Sections; Green’s Functions; Connected Diagrams and Vacuum Bubbles; Reduction Formula
  5. The Dirac Equation:   
    The Lorentz Group; Clifford Algebras; The Spinor Representation; The Dirac Lagrangian; Chiral Spinors; The Weyl Equation; Parity; Majorana Spinors; Symmetries and Currents; Plane Wave Solutions.
  6. Quantizing the Dirac Field:   
    A Glimpse at the Spin-Statistics Theorem; Fermionic Quantization; Fermi-Dirac Statistics; Propagators; Particles and Anti-Particles; Dirac’s Hole Interpretation; Feynman Rules
  7. Quantum Electrodynamics:   
    Gauge Invariance; Quantization; Inclusion of Matter — QED; Lorentz Invariant Propagators; Feynman Rules; QED Processes.

Notes to the course can be found in this pdf (149 pages). The videos that I’m currently watching, in this link.

I want to thank Prof. Tong and the University of Cambridge for this wonderful initiative. By the way, I also hope they extend this (the publishing of the videos) to other courses by Mr Tong (String Theory, Solitons, etc.).