The Black Hole War

Recommended by Mr. Rip after From the Big Bang to Black Holes. It goes deeper into black holes and the universe. It really does that and goes deep into the subject, explaining black hole evaporation, why Hawking’s assumptions are so unsettling, with solid physics foundations and deep dives into string theory and the holographic principle. I admit I got lost toward the end, it gets very technical, but it stays approachable on many other topics.

I am not sure I would recommend it. He tries to challenge Hawking, but I did not really grasp his arguments; they are very theoretical, and he ends up suggesting that information can leave black holes in some universes, not all. I struggled to follow parts of it. The question remains open. What is valuable is the early overview of the subject and the precise explanations of various points. A book for physicists. Fortunately I had some background.

At times the arguments feel overly elaborate. The author’s barbs at Hawking can be distracting (even if they are friends). As some comments note, the lack of practical testability is frustrating, though the question “what happens if I fall into a black hole” is engaging.

Notes

Notes taken from Goodreads, a good recap chapter by chapter. Note how it becomes harder to follow toward the end.

Chapter 1 - In 1981, Hawking postulates that information is lost in black holes.

Chapter 2 - Black holes and the horizon at the Schwarzschild radius described. Einstein rejected black holes. Tidal forces are less at the horizon of large black holes. Einstein’s equivalence principle states that the effects of gravity and acceleration are indistinguishable.

Chapter 3 - Riemann proposed that space may be curved, an idea incorporated into general relativity. Minkowski space incorporates space and time, with a world line representing the path of an object. Einstein discovered time dilation where rapidly moving clocks slow down. General relativity states that objects move along geodesics in spacetime. If space is curved, the object follows the curvature. Gravitational force is the curvature of spacetime. John Wheeler proposed wormholes but they would stay open for so short a time that even light could not pass through. Einstein discovered gravitational redshift where clocks slow down near a heavy mass.

Chapter 4 - Duality of light - not only wavelike but particle-like - Einstein 1905. Planck’s constant h ~ 6.62 x 10^-34 J s. Information conservation, or reversibility, states that given the present, one can construct the future and the past. Quantum mechanics respects the conservation of information. Heisenberg’s uncertainty principle states that the greater the certainty of velocity, the lesser the certainty of position. m delta v delta x > h. When a system is deprived of all energy it is in ground state. QM, however, states that particles are still in motion - zero point motion or the quantum jitters. Energy of a photon E = h f. In quantum field theory, the path of a particle is a propagator. A split, such as in the release of a particle, is a vertex.

Chapter 5 - Planck found that if c, G (Newton’s gravitational constant) and h are set to one, three fundamental Planck units result. The Planck length is very small (10^-35 m), much smaller than a proton. Planck time (10^-42 s) is very small, being the time it takes light to traverse the Planck length. Planck mass is about that of a dust mote. The energy equivalent is about equal to a tank of gasoline. The Planck length, time and mass are the size, half-life and mass of the smallest possible black hole.

Chapter 6 - The question of how black holes decay. A possibility is that quantum fluctuations would allow a piece of the horizon to fly away.

Chapter 7 - Equivalence of chemical, potential, kinetic and thermal energy. Conservation of energy is the First Law of Thermodynamics. The Second Law states that entropy always increases. Entropy is a measure of the number of arrangements that conform to some specific recognizable criterion. Entropy is hidden information. Entropy increases because we lose track of the details over time. The smallest size containing a bit of information is a Planck length. Maximum amount of information that can be put into a region of space is equal to the area of the region, not the volume.

Chapter 8 - John Wheeler stated that black holes have no hair, meaning the horizon was smooth. Adding one bit of information to a black hole increases its horizon by one square Planck length. Entropy of a black hole is proportional to the area of the horizon.

Chapter 9 - Black holes have temperature which is inversely proportional to their size. Black holes are black bodies - they reflect no light. Black holes emit photons and therefore evaporate. A black hole the mass of the moon would be 1 K. One the mass of a boulder would be a billion billion degrees. Photon emission from a BH is Hawking radiation. Hawking calculates that the entropy of a BH equals one quarter of the horizon area, measured in Planck units.

Chapter 10 - Hawking states that when a BH evaporates, the trapped bits of information disappear from the universe.

Chapter 11 - Particle collisions are described by an S or scattering matrix, which is reversible. Hawking invented the not-S matrix or dollar matrix which is not reversible.

Chapter 12 - Surrounding space is warmer than astronomical BHs, so they are still gathering mass rather than evaporating, although the evaporation rate is very slow. Einstein’s equivalence principle - the effects of gravity and acceleration are indistinguishable from one another.

Chapter 13 - Susskind’s Antigravity Pill paradox where characters fall through a BH horizon. Apparently they are destroyed and emitted as evaporation products as required by QM. But apparently they also pass safely through the horizon as predicted by the equivalence principle.

Chapter 14 - The possibility that a BH horizon is covered with quantum copying machines so that evaporation and passage are both possible. However, a quantum copying machine is not possible as it would violate Heisenberg’s uncertainty principle.

Chapter 15 - A BH stretched horizon is one Planck distance above the horizon. It is an energetic, hot layer. Susskind proposes complementarity whereby both alternatives of the paradox are true. No paradox because the observers on the inside and outside can never meet, so each story is true in its own zone of reference.

Chapter 16 - It requires increasingly short wavelength (high energy) photons to observe smaller particles. As an atom falls closer to a horizon, it requires increasingly high energy photons to resolve them. So as the atom falls to the horizon, it becomes increasingly blurred and appears to spread out over the horizon.

Chapter 17 - About Cambridge, religion and Hawking.

Chapter 18 - The Holographic Principle - the contents of space are actually a holographic representation of the information on the area bounding that space. Perhaps all space and the universe is a hologram, coded on a distant two dimensional space.

Chapter 19 - String theory - we do not know whether this model actually represents the real world. However, it is consistent with the real world and does allow theories to be tested for consistency.

Hadrons are nucleons, mesons and glueballs. Nucleons are protons and neutrons.

As you spin a nucleon, the energy increases in proportion to the angular momentum, but in steps. An electron cannot be spun.

Energetic nucleons are stringlike objects, made up of quarks and gluons. The simplest hadron is a meson, composed of a quark and an anti-quark joined by a stringlike gluon. Open strings, such as mesons, have ends, but there can also be closed strings. Nucleons are 3 quarks joined by a Y shaped string. Another hadron, the closed string or glueball, has no quarks.

The mathematical theory of quarks and gluons is quantum chromodynamics (QCD). Quarks are elementary particles with six flavors - up, down, strange, charmed, bottom and top. All quarks come in three colors - blue, green and red.

Gluons have positive and negative poles, and each has a color - R, B or G. Therefore, nine types of gluon are possible. The propagator of a gluon has two sides corresponding to the two poles - each side is R, B or G. At a vertex, or split, each side must be consistent - e.g. a BR can split into BG - GR.

While string theory applied to hadrons is well accepted, fundamental strings associated with gravity at Planck scales are not. The graviton is the primary fundamental string.

Electrical and gravitational forces create waves. Hence, gravitational waves. Gravitons are conjecture. Any particle can emit a graviton, even other gravitons.

Possibly, fundamental and QCD strings are the same objects at different scales.

Fundamental strings require 9 dimensions. The 6 extra dimensions are compacted into geometric spaces called Calabi-Yau manifolds.

Feynman theorized that electrical force is due to particles continually emitting and absorbing photons - photon exchange. Also, all matter continually emits and absorbs gravitons. Fundamental strings spawn off and absorb tiny strings - these are the gravitons.

The string theory of gravity is not fully described but appears to be the best mathematical model of quantum gravity.

Chapter 20 - As things slow down, more structure comes into view. Much structure cannot be seen due to cosmic jitter. Perhaps particles are much larger than thought.

Chapter 21 - Going up the mass scale beyond elementary particles are conjectural collections called superpartners, grand unification partners and string excitations. These range to the Planck mass. The Large Hadron Collider (LHC) should see superpartners. T’ Hooft speculates that the spectrum of particles extends beyond the Planck mass in the form of black holes. A 1 kg BH is a trillion times smaller than a proton.

Strings, such as those making up photons, have temperature and entropy.

The entropy of a BH is proportional to the area of the horizon, and therefore the square of the mass.

Strings can cross each other, normally passing through each other. A small probability (the string coupling constant) exists that they split and re-arrange. This is how small strings are formed at a horizon, producing Hawking radiation.

If an electron is dropped into a BH, the BH becomes charged. A charge on a BH pushes the horizon out from the singularity. If enough charge exists to balance gravity, you have an extremal BH.

Polchinski discovered D-branes, a membrane on which fundamental strings can end. These turn out to fill a large mathematical hole in string theory. The use of D-5 branes for the extra dimensions, D-1 branes for the normal dimensions, and fundamental strings allowed the math to be developed for an extremal BH showing that the entropy = one quarter of the horizon area. Also allowed the math of the evaporation process to be developed. This clinched the argument that BH are storage containers for information, not eaters of information.

Chapter 22 - De Sitter space is a four dimensional (4 + 1) space with positive curvature that satisfies Einstein’s equations. It is becoming important in cosmology.

Anti-de Sitter (AdS) space is similar, but with negative curvature. The spacetime curvature in AdS creates a gravitational field that pulls objects back to the center even if there is nothing there. If matter is added to an AdS space, a BH trapped in the space (like a box) results - a BTZ black hole.

Strings on a stack of D-branes are governed by the same rules as those that govern gluons in QCD. Maldacena showed that a three dimensional world with gravity is equivalent to a two dimensional quantum hologram on the boundary of space.

Witten showed that a BH in AdS must be equivalent to something on the surface bounding the space - a hot fluid of gluons.

Chapter 23 - The Holographic Principle states that everything that takes place in AdS (4+1) is describable by a mathematical theory with fewer dimensions. Quantum gravity in AdS is mathematically equivalent to QCD.

If an AdS space is modified to a Q space with both a UV (small scale) brane and an IR (large scale) brane, particles near the UV brane act like fundamental strings while those near the IR brane act like nuclear particles. The possibility is that fundamental particles and nuclear particles are really the same objects in different areas of space. The hot quark soup produced in nuclear collision events has an unexpected very low viscosity, as does a BH horizon.

Nuclear physics may allow string theory to be tested. Conversely, string theory may be applicable to nuclear events.

Chapter 24 - It appears that the cosmological constant is non zero - 10^-123 in Planck units. Einstein had originally included an extra term in his equations, called the cosmological term. The constant (Greek lambda) creates a repulsive force if negative; attractive if positive. Eventually, Einstein set it to zero, eliminating it from his equations, and calling it his biggest mistake.

A cosmic horizon exists at 15 billion light years where the universe is receding from Earth at the speed of light. This cosmic horizon may be analogous to a BH horizon.