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What is space-time made of?

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.

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
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I need the podcast of this so I can listen to it on my phone!
Often it is forgotten time is often a tool of measurement in repeat patterns. There is also the mind how it uses time differentley than what is measured in the physical world. There is more than one state of time in a sense but they can coexist (almost is dimensional in a way).
I count myself with Hawking in thinking that all of this is the wrong approach. Quite literally all of physics is based on smooth symmetries and smooth manifolds, which are not easily reconcilable with any hoped-for discreteness. Maybe discreteness cannot strictly be ruled out, but there is certainly no evidence – theoretical or experimental – suggesting any kind of discrete structure of spacetime.

There is only one framework in which all of physics has actually been successfully unified: M-theory, which is a unique and completely fixed structure despite having a few distinct faces. Hawking and myself think that its spectacular successes in unifying all the logic of physics motivate it as the single real candidate for the theory of everything. No exaggeration: In his exact words "M-theory is the only candidate for a complete theory of the universe." (emphasis in original). M-theory owes this success to being a framework that subsumes the principles on which existing physics is based, namely quantum mechanics and smooth symmetries , not demolishing them and attempting to start over. But that is what will be necessary if the line of reasoning in this video is taken seriously.

Discreteness of spacetime is a backwards step, because the Lorentz symmetry reduced the number of independent concepts in physics: there is no longer such a thing as a "preferred frame". There is no absolute concept of being "stationary". I think its clear this is a pretty deep and vital principle, and there is absolutely no good reason to discard it unless there is a very good reason. But I dont think there is a good reason, more precisely, there is no reason.

(Not directly related, but among the many reasons I implicitly refer to for taking M-theory seriously is the resolution of many conceptual questions in QG, including one that you mentioned, the issue of topology change. It has shown that topology change can occur without physical singularities...)
+Cliff Harvey Are you saying that Hawking has stated that he disagrees with his former student? I'm not familiar with what Hawking has said about quantum gravity or this idea of space-time atomicity. Is he still butt-hurt that Susskind proved he was wrong?

Fay Dowker was awarded the Tyson Medal in 1987 and completed her Doctor of Philosophy under the supervision of Stephen Hawking in 1990.

According to Hawking, is Sorkin wrong too?
Yes, thats what I said. Its why I was pretty surprised to find that she studied under Hawking, but apparently the apple sometimes falls very far from the tree.

By the way I think Hawking's butt is doing just fine because he himself has contributed important understandings to the holographic principle and the preservation of information. ...I think any potential butt-aches are probably comparable to when he lost the bet that black holes don't exist. :] i.e. the'yre probably negative butt aches! :]

As I said when I referenced the quote from the Grand Design, Hawking considers M-theory the single viable candidate theory of everything, and this fundamentally goes against the train of logic presented here. Because M-theory subsumes the fundamental organizing principles of physics, namely smooth symmetries. Smooth symmetries only make sense on smooth manifolds, not on discrete spaces. In particular it subsumes the gauge symmetries of particle physics along with general relativity's symmetry under arbitrary smooth coordinate transformations (diffeomorphisms). If there was a fundamental discreteness, these principles could not hold exactly. We would have to live in a preferred reference frame where the pixels could mimic the smooth manifolds, because under extreme enough Lorentz transformations, say, the pixels would become so distorted that they could no longer keep up the act.

The Lorentz transformations are really the most important example. Because there are very fast things moving around the universe all the time, very huge relative accelerations (Lorentz transformations) are relevant in a lot of cases. In one extreme example, where a 31 GeV(!) photon was observed, we were able to set an upper limit on the characteristic scale of any Lorentz invariance violation to below the Planck scale. This relates to the general problem that discrete space violates the principle of relativity, the fact that there is no such concept as "absolute rest"; all inertial frames are equally good. Pixels necessitate the introduction of a preferred frame. So it would then just be a coincidence that special relativity can be formulated in terms of the principle of relativity. But the principle of relativity itself is actually very important insight, not just as a model for computing length contractions and stuff, but for the conceptual unification between space and time.

So basically anyone barking up this tree is hoping to find a discrete space that might mimic a smooth manifold, and hoping that they can reconstruct a very big pyramid of physics logic on top of it, which is completely based on smooth symmetries. Its pretty ambitious. I might entertain the idea if there was a good reason to, but I don't think there is a single good reason to, or even any reason. The main motivation you may hear is that discretizing space is a way to regulate the ultraviolet divergences in QFT. A much more effective, successful and insightful regulation scheme is to consider the basic objects as extended rather than point-like.

I think the biggest reason people are interested in discrete space is that its just an intuitive concept for humans.
Well that's pretty interesting. Fay seems to say much of their proposal is built on Hawking's notions of causal information being able to construct spatial geometry.

So, just to be clear, you saying that a theory of a granularity of space-time as opposed to a continual one is wrong? And that Hawking is openly against this theory of granularity?

I'm going to have to lookup more recent stuff on Hawking. Is he actively working on quantum gravity?
+Cliff Harvey It's my understanding that Gerard 't Hooft and Susskind resolved the black hole information loss paradox, not Hawking? That paper by Hawking is from 2005. Susskind came up with a formulation of M-theory using the holographic principle in 1995. Ed gave his M-theory presentation in 1995 as well. In 1997, Juan Maldacena gave the first holographic descriptions of a higher dimensional object, the 3+1 dimensional type IIB membrane, which resolved a long-standing problem of finding a string description which describes a gauge theory.

The bet was in 1997. Hawking conceded in 2004.

This is from 1994.

Hooft 1993

"The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional."

Did Susskind/Hooft resolve the paradox or did Hawking do it with Feynman's Euclidean path integral?

This doc gives the idea that Susskind & Hooft resolved it, more so that Susskind did.
BBC Horizon 2005: 5/7 The Hawking Paradox

Hawking U-turns, says he solved it and that Susskind is wrong.

Who is right? Is Susskind really wrong? Is this resolved or still up in the air? Summing over all possibilities of the black hole using Feynman's idea seems like cheating. Hawking is only correct if there are parallel universes.
"you saying that a theory of a granularity of space-time as opposed to a continual one is wrong?" - It depends on what you mean by granularity. What Im saying is that discreteness is almost certainly wrong. (and more importantly that there is no motivation for it connected to established physics) But even in the smooth picture of the stringy approach to quantum gravity, space becomes, in a sense, "granular" because there are quantum fluctuations of the metric – the geometry – around the Planck scale. So by this wording, Im inclined to disagree with your statement. Spacetime develops a granular or foamy structure based all the approaches to quantum gravity.

You're also right that Hawking did not resolve the information paradox. Im unclear about the exact chronology (but Im familiar with Hawkings paper) but my understanding is that this 2005 paper is mostly about discussing/examining the resolution of the paradox by formulating it in its natural setting – a euclidean scattering problem from infinity in an AdS spacetime. It might not be the most historically important, but I think its a very insightful read.

Im also curious about exactly how or why Fay got on the discrete bandwagon after working with Hawking....
I wonder how Hawking is doing so far on a new paper too. I gather from his 70th that he is in Cambridge now...

+Cliff Harvey I was calling granular the idea that space-time could be quantized at the planck scale, rather empty space-time could be divided up in discrete segments?

If the Uncertainty Principle holds, wouldn't it be near impossible to ever tell?

And if the universe is expanding or that the expansion could ever be measured locally to a high accuracy, would that be a continual growth or would that growth be quantized?

Assume you had a measurement of the expansion of spce from one moment to the next, it would seem to be measured in planck time and grow in some sort of planck length as opposed to any infinitely small amount depending on time.

It would seem to follow that this would have something to do with why the speed of light is what it is, and also maybe start to explain General Relativity as Fay/Sorik hints (the threshold of quantum gravity).

If you increase space with negative energy by an infinitely small amount (less then Planck), would that cause problems? Virtual particles couldn't pop in and out in the vacuum using non-quantized energies?
Those PI guys seem to be big on discrete spacetime.

What is space made of? 1/25/2012 2pm by Daniele Oriti

Quantum gravity is about finding out what is the more fundamental nature of spacetime, as a physical system. Several approaches to quantum gravity, suggest that the very description of spacetime as a continuum fails at shorter distances and higher energies, and should be replaced by one in terms of discrete, pre-geometric degrees of freedom, possibly of combinatorial and algebraic nature. Space, time and geometry would be emergent concepts, valid at macroscopic scales, whose emergence is the result of a collective dynamical process (a phase transition) of the fundamental degrees of freedom. This process has been sometimes dubbed ‘‘geometrogenesis’’. We illustrate this set of ideas, focusing on one framework that attempts to realize it: group field theory, itself incorporating insights and tools from various other approaches.
Be careful with the word "quantized". To any physicist, quantization means the process of applying the postulates of quantum mechanics. It cant be universally identified with the word "discrete"; under quantization some things take on discrete values but many remain continuous.

So in the stringy approach to quantum gravity, the spacetime geometry is still "quantized", in that its treated quantum mechanically, and every physical degree of freedom undergoes quantum fluctuations, but it is not discrete.

You're statement that we can never tell is correct, but just in the same we we always knew it to be true: our ability to know always has certain limits. We don't have infinite energy to probe the smallest distances and even if we did, you can never resolve sub-Planckian distances because it requires enough energy-density to create micro-black holes. This is reflective of a deeper insight from quantum gravity, that at this scale the conventional notions of spacetime geometry break down, because the geometric fluctuations become too great for them to be meaningful.
she had a hard time trying to explain things in lamans terms or trying to get her head around stuff that she wasnt ready for, like how to measure the temperature of a black hole, "the same way that you would measure the temperature of a heater, it radiates"

im not sure she satisfied the question :P
Well, we still don't know how to measure the temperature of a black hole (: I thought she did okay. But, wouldn't two black holes of the same mass have the same temperature? Or could it differ? I'm guessing Hawking's equation means it has to be the same.
I agree +Shannon Fitzgerald, there were a few areas like that I found unsatisfactory.

The correct answer would have been that we really cant measure the temperature of a black hole in that same way, at least not in practice. Its just a theoretical insight thats taken extremely seriously because it fits so well into the overall web of understanding on black holes & their thermodynamics.

We can only really measure the temperature by measuring the radius, or equivalently, the mass.
+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?
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:

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:
+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?
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.
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?
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.)
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