### How much Information can you Store on the Surface of a Black Hole?

In the currently best understood theory of gravity, spacetime is a physical entity which curves, bends, dips and expands. In some regions where gravity is so strong, light can't escape and the region has formed a black hole. When one just skims through any physics journal there are a plethora of papers published on the "entropy" of black holes, on Hawking radiation and on "holograms". But why do so many cosmologists believe in the holographic principle? The arguments in favor are really rather convincing, so lets try and follow the logic behind it. The radius of a black hole is

The energy of any given photon that cuts across the even horizon is given as

Normally, the formula includes the Greek symbol Lambda for wavelength but in our case, we are throwing in photons with a wavelength equal to the radius of the black hole. Such that

We use this equivalence because we only want one bit of information to be associated with each photon, a photon with much smaller wavelength will have a position. It's then simple to rearrange some of the equations, to find the change in wavelength of the photon

One small step for a mathematician is sometimes a big step for physics.

What we have now on the left side of the equation is the change in area, which is about equal to the Planck area.

Planck's area is derived from Planck's constant, the Newton constant and the speed of light. Which tells us that quantum gravitational effects become important at that scale. But also the equation tells us that when a bit of information falls into the black hole and the entropy increases, it increases the area of the black hole. So that the entropy of a black hole is equal to the information of one bit multiplied by the number of bits.

The entropy then, is the area of a black hole divided by the Planck area. Thus obviously, the entropy of a black hole is proportional to the area, not its volume. We can go further and find the universal upper limit of entropy that can be contained in a black hole. Which was done famously by Jacob Bekenstein.

Through indirect arguments you can show an equivalent relationship with any region of space, by imagining that region engulfed in a black hole. The amount of entropy in any given region of space cannot be bigger than the area of that region in Planck units. This we call the "Holographic principle" because it suggests that spacetime is a hologram (if it wasn't information would be proportional to volume, not area). This relationship has been beautifully worked out in the AdS/CFT correspondence but that's for another time.

### William Lane Craig and the Hartle-Hawking No Boundary Proposal

Classical standard hot Big Bang cosmology represents the universe as beginning from a singular dense point, with no prior description or explanation of classical spacetime. Quantum cosmology is different in that it replaces the initial singularity with a description in accord with some law the "quantum mechanical wave function of the universe", different approaches to quantum cosmology differ in their appeal either to describe the origin of the material content of the universe e.g., Tyron 1973, Linde 1983a, Krauss 2012 or the origin of spacetime itself e.g., Vilenkin 1982, Linde 1983b, Hartle-Hawking 1983, Vilenkin 1984.

These last few proposals by Vilenkin, Hartle-Hawking and others are solutions to the Wheeler-DeWitt equation and exist in a category of proposals called "quantum gravity cosmologies" which make cosmic applications of an approach to quantum gravity called "closed dynamic triangulation" or CDT (also known as Euclidean quantum gravity). I&#…

### How Should Thatcherites Remember the '80s?

Every now and again, when I talk to people about the '80s I'm told that it was a time of unhinged selfishness, that somehow or other we learned the price of everything but the value of nothing. I can just remember that infamous line from Billy Elliot; 'Merry Christmas Maggie Thatcher. We all celebrate today because its one day closer to your death'. If it reflected the general mood of the time, one might wonder how it is she won, not one but three elections.

In an era when a woman couldn't be Prime Minister and a working class radical would never lead the Conservative party, Thatcher was both and her launch into power was almost accidental owing in part to Manchester liberals and the Winter of Discontent. Yet I'm convinced her election victory in '79 was the only one that ever truly mattered. Simply consider the calamity of what preceded it, the 1970s was a decade of double-digit inflation, power cuts, mass strikes, price and income controls, and the three…

### Creation Of Universes from Nothing

The above paper "Creation of Universes from Nothing" was published in 1982, which was subsequently followed up in 1984 by a paper titled "Quantum Creation of Universes". I decided it would be a good idea to talk about these proposals, since last time I talked about the Hartle-Hawking model which was, as it turns out, inspired by the above work.
Alexander Vilenkin also explains in a non-technical way the essential idea in his book; Many World's in One – one of the best books I've ever read – it mostly covers cosmic inflationary theory but the 17th chapter covers how inflation may have begun. In fact Vilenkin is one of the main preponderant who helped develop inflation along with Steinhardt, Guth, Hawking, Starobinsky, Linde and others.
Although I won't talk about it here, Vilenkin also discovered a way of doing cosmology by using something called "topological defects" and he has been known for work he's done on cosmic strings, too.
In ex…