**What is space-time made of?**

https://plus.google.com/u/0/109667384864782087641/posts/YYV1UmbfRVb

This was a really informative lecture. Fay goes from the Laws of Thermodynamics to Hawking's Laws of Black Hole Dynamics and explains the fundamental nature of space-time through the logic that follows. There are a lot of examples of unification and she presents the information so that most people can understand it. The Q&A is also excellent.

She explains the underlying concepts first, so it doesn't get really good until after 30m in.

The main thing that I took away from this was that the key part of the black hole is surface area of the event horizon and not actually the black hole. And that this event horizon is really only empty space-time.

This leaves us on the threshold of an understanding of quantum gravity. She also goes on to marry the granularity of space-time causality and how it illustrates causal horizons including black hole horizons which are only one type.

Fay proposes that entropy counts the number of simplest causal relations that straddle the horizon.

Around 50m in she goes into the expanding universe & the cosmological constant (λ) or the energy density of empty space-time. Einstein originally postulated the cosmological constant and after Hubble's observations, Einstein thought his constant was his greatest error. But we now know that Einstein was wrong about being wrong. Rafael Sorkin predicted that the cosmological constant would be non-zero. Some unknown mechanic of the universe pushes this towards zero but it cannot be non-zero because of Werner Heisenberg's Uncertainty Principle. She restates this principle in the context of space-time and energy density by saying that the smaller the fluctuations in space-time volume, the larger the fluctuations in

**λ.**

She suggests that we can prove the atomicity of space-time by looking at how Brownian motion gave us a clue that lead to a greater understanding as to the existence of atoms.

Richard Feynman said,

*"All things are made of atoms."*Fay suggests that this includes space-time. I think it only makes sense, space-time must be quantized by a relationship to the Planck unit. Perhaps gravity is the Brownian motion clue that proves the atomicity of space-time.

*Sorkin believes that the successful solution of quantum gravity will involve both a reevaluation of gravity in terms of a discrete structure underlying continuous spacetime, and also a reformulation of quantum mechanics. He also hypothesises that the phenomena of topology change and the thermodynamics of the black hole structure provide important clues to the formation of the final synthesis. In this framework he has examined the quantum properties of topological geons (particles created directly from the spacetime topology). His findings include that the topological geons can exhibit remarkable statistical properties. He also discovered evidence that topology change is a required feature of any consistent quantum gravity theory. He has hunted the origin of a black hole's entropy to discover more about how it relates to the synthesis of quantum mechanics and the theory of general relativity.*

http://en.wikipedia.org/wiki/Rafael_Sorkin

http://www.perimeterinstitute.ca/index.php?option=com_content&task=view&id=30&Itemid=72&pi=1254

http://arxiv.org/find/grp_physics/1/au:+Sorkin_R/0/1/0/all/0/1

http://www.phy.syr.edu/~sorkin/

http://www.einstein-online.info/spotlights/causal_sets

A lot of great lectures on the Perimeter Institute Recorded Seminar Archive (PIRSA), including Fay Dowker and Rafael Sorkin.

**An Invitation to Causal Sets - Lecture 1**

http://pirsa.org/10100038/

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- +Cliff Harvey If you had two black holes of the same mass, does that really mean they hold the same entropy? Or, could one be more complex than the other as far as the information encoded into the event horizon?

Or, if you had a older black hole that was evaporating and reduced to the same size as a brand new black hole of the same radius/mass, would they too have the same entrophy?

Or is there more or less entrophic matter that could fall into a black hole making it be more or less complicated but of the same radius/mass?Apr 28, 2012 - Hey, Im glad you're asking the easy questions tonight. :] A black hole should always represent the maximum entropy that can occupy a given region. So that should answer all 3 of the questions.

The entropy is always proportional to the area. Aside from the mass/radius, momentum and angular momentum, the only kinds of distinguishing characteristic you can give the black holes is its charge. (the 'No-hair theorem') But this wont effect the entropy. Its easy to list all the possible types of black holes:

http://en.wikipedia.org/wiki/Rotating_black_hole

http://en.wikipedia.org/wiki/No-hair_theorem

So the charges are the main distinguishing feature, and in the stringy picture they can be charged under different kinds of gauge fields. One really interesting aspect is that in more than 4 dimensions you can have more complicated types of horizons: like "black strings" in 5 dimensions, and in general we can talk about "black p-branes". Im sure I couldn't really answer too many specific questions on these, but its something that I find insanely interesting. Just reading the abstract of this paper ought to give a flavor: http://arxiv.org/abs/1006.5960v3Apr 28, 2012 - +Cliff Harvey But does that mean that two black holes of the same radius and mass are perfectly identical?

They both have an equal maximum entropy, but can one black hole just be all 0's (or formed form the same atoms) and the other be complicated mix?

Or, for them to be different would they have to have somewhat different mass/energy?Apr 28, 2012 - Yeah. You can define a black hole to be any configuration of matter that sits inside its Schwarzschild radius, which is a function only of the mass. So pretty much by definition, same mass means the same radius and the same entropy. If a black hole is old enough that it has radiated away some of its mass, that must translate into the corresponding reduction of its radius.Apr 28, 2012
- Given that atoms are all of different mass, that would obviously mean a difference. But in that you could have the same total mass and you want to preserve that either a bunch of one atom type contributed vs some mix of equal total mass.

It would seem that the black hole that was formed entirely from gold atoms might be more ordered requiring less use of the maximum entropy possible and a mix would have higher entropy?Apr 28, 2012 - Oh yeah, so I was a bit confused by the logic you're hinting at here. Anything that falls into a black hole will be in an environment where "atoms" will no longer be a useful concept. But anyway I cant say much because I don't understand your reasoning.

The main mystery of black hole thermodynamics, since we can infer the entropy, is to figure out in what physical way we can count the internal states to agree with that entropy. Atoms wont provide the right counting, their entropy is volume- rather than area-extensive, but string theory does when you consider all the higher-dimensional objects – the branes – that it describes.

Heres one review Ive been looking at a bit. Some of the explanations might help. (its a bit old, but the explanations are pretty clear overall, or at least better than any other reference Ive found yet.) http://arxiv.org/abs/hep-th/9711153Apr 30, 2012