But what would such a program be like? Somehow all these things have to emerge from something much lower level and more fundamental. But even though such a structure works well for models of many things , it seems at best incredibly implausible as a fundamental model of physics. I thought about this for years, and looked at all sorts of computational and mathematical formalisms. A network—or graph —just consists of a bunch of nodes, joined by connections. So could this be what space is made of? But do we in fact know that space is continuous like this? In the early days of quantum mechanics, it was actually assumed that space would be quantized like everything else.

But what if space—perhaps at something like the Planck scale—is just a plain old network, with no explicit quantum amplitudes or anything? But how could this be what space is made of? First of all, how could the apparent continuity of space on larger scales emerge? On a small scale, there are a bunch of discrete molecules bouncing around. But the large-scale effect of all these molecules is to produce what seems to us like a continuous fluid. It so happens that I studied this phenomenon a lot in the mids—as part of my efforts to understand the origins of apparent randomness in fluid turbulence.

What about all the electrons, and quarks and photons, and so on? In the usual formulation of physics, space is a backdrop, on top of which all the particles, or strings, or whatever, exist. But that gets pretty complicated. As it happens, in his later years, Einstein was quite enamored of this idea. He thought that perhaps particles, like electrons, could be associated with something like black holes that contain nothing but space.

But within the formalism of General Relativity, Einstein could never get this to work, and the idea was largely dropped. That was a time before Special Relativity, when people still thought that space was filled with a fluid-like ether. Meanwhile, it had been understood that there were different types of discrete atoms, corresponding to the different chemical elements. And so it was suggested notably by Kelvin that perhaps these different types of atoms might all be associated with different types of knots in the ether.

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It was an interesting idea. Maybe all that has to exist in the universe is the network, and then the matter in the universe just corresponds to particular features of this network. Even though every cell follows the same simple rules, there are definite structures that exist in the system—and that behave quite like particles, with a whole particle physics of interactions. Back in the s, there was space and there was time. Both were described by coordinates, and in some mathematical formalisms, both appeared in related ways. It makes a lot of sense in the formalism of Special Relativity, in which, for example, traveling at a different velocity is like rotating in 4-dimensional spacetime.

So how does that work in the context of a network model of space? And then one just has to say that the history of the universe corresponds to some particular spacetime network or family of networks. Which network it is must be determined by some kind of constraint: our universe is the one which has such-and-such a property, or in effect satisfies such-and-such an equation. And, for example, in thinking about programs, space and time work very differently. In a cellular automaton, for example, the cells are laid out in space, but the behavior of the system occurs in a sequence of steps in time.

How does this network evolve? But now things get a bit complicated. Because there might be lots of places in the network where the rule could apply. So what determines in which order each piece is handled? In effect, each possible ordering is like a different thread of time. And one could imagine a theory in which all threads are followed—and the universe in effect has many histories. Needless to say, any realistic observer has to exist within our universe. So if the universe is a network, the observer must be just some part of that network.

## Understanding gravity—warps and ripples in space and time

Now think about all those little network updatings that are happening. If you trace this all the way through —as I did in my book, A New Kind of Science —you realize that the only thing observers can ever actually observe in the history of the universe is the causal network of what event causes what other event. Causal invariance is an interesting property, with analogs in a variety of computational and mathematical systems—for example in the fact that transformations in algebra can be applied in any order and still give the same final result. So what about spacetime and Special Relativity?

In other words, even though at the lowest level space and time are completely different kinds of things, on a larger scale they get mixed together in exactly the way prescribed by Special Relativity. But because of causal invariance, the overall behavior associated with these different detailed sequences is the same—so that the system follows the principles of Special Relativity.

At the beginning it might have looked hopeless: how could a network that treats space and time differently end up with Special Relativity? But it works out. OK, so one can derive Special Relativity from simple models based on networks. The whole story is somewhat complicated. First, we have to think about how a network actually represents space. Now remember, the network is just a collection of nodes and connections. Just start from a node, then look at all nodes that are up to r connections away.

If the network behaves like flat d -dimensional space, then the number of nodes will always be close to r d. One has to look at shortest paths—or geodesics—in the network. One has to see how to do everything not just in space, but in networks evolving in time. And one has to understand how the large-scale limits of networks work. But the good news is that an incredible range of systems, even with extremely simple rules, work a bit like the digits of pi , and generate what seems for all practical purposes random.

I think this is pretty exciting. Which means that these simple networks reproduce the features of gravity that we know in current physics. There are all sorts of technical things to say, not suitable for this general blog. Quite a few of them I already said long ago in A New Kind of Science —and particularly the notes at the back.

A few things are perhaps worth mentioning here. All these things have to emerge. When it comes to deriving the Einstein Equations, one creates Ricci tensors by looking at geodesics in the network, and looking at the growth rates of balls that start from each point on the geodesic. The Einstein Equations one gets are the vacuum Einstein Equations. One puts remarkably little in, yet one gets out that remarkable beacon of 20th-century physics: General Relativity.

Another very important part is quantum mechanics. But then their behavior must follow the rules we know from quantum mechanics—or more particularly, quantum field theory. A key feature of quantum mechanics is that it can be formulated in terms of multiple paths of behavior, each associated with a certain quantum amplitude. But what about in a network? Because everything is just defined by connections. And the tantalizing thing is that there are indications that exactly such threads can be generated by particle-like structures propagating in the network.

How might we set about finding such a model that actually reproduces our exact universe? The traditional instinct would be to start from existing physics, and try to reverse engineer rules that could reproduce it. But is that the only way? What about just starting to enumerate possible rules, and seeing if any of them turn out to be our universe? So what happens if one actually starts doing such a search?

They just freeze after a few steps, so time effectively stops. Or they have far too simple a structure for space. Or they effectively have an infinite number of dimensions. Or other pathologies.

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Telling if they actually are our universe is a difficult matter. There are plenty of encouraging features, though. For example, these universes can start from effectively infinite numbers of dimensions, then gradually settle to a finite number of dimensions—potentially removing the need for explicit inflation in the early universe.

In the end, though, one needs to reproduce not just the rule, but also the initial condition for the universe. But once one has that, one will in principle know the exact evolution of the universe. So does that mean one would immediately be able to figure out everything about the universe?

Absolutely not. But it would raise plenty of other questions.

- Communications in Mathematical Physics.
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Like: why this rule, and not another? And why should our particular universe have a rule that shows up early enough in our list of all possible universes that we could actually find it just by enumeration? But these are all speculations. This publication documents an extraordinary chapter in experimental gravitation. First articles published June General relativity predicts the existence of black holes, fascinating objects made of pure spacetime fabric.

Understanding the strong-gravity interaction between black holes and fundamental fields has become a crucial tool to gain insight into beyond-standard model physics, and to constrain dark matter. In this issue, we will collect a number of exciting contributions covering many aspects of this emerging, multifaceted field.

## What Is Spacetime, Really?—Stephen Wolfram Writings

The year marks the centenary of Einstein's general relativity. CQG celebrates this historic anniversary by publishing special review articles on 13 key events that occurred during the years following publication of the theory. Each of these events was a 'game changer' in that it had an immediate impact on the field, and continues to spur research today.

The milestones span the breadth of areas—experiment, pure theory, quantum gravity, astrophysics, cosmology—that make gravitational physics so exciting today, years after the birth of the theory. Dense stellar systems such as galactic nuclei and stellar clusters are unique laboratories, not only for astrophysics, but also for general relativity. The complexity of these systems is such that in spite of a huge theoretical, observational and numerical effort, there are still a large number of open key questions.

This focus issue brings together an array of invited articles on important aspects of these questions. This focus issue summarizes recent developments in computing relativistic effects in cosmology. The first part examines general relativistic formulations of the observed over-density of galaxies, and the second discusses relativistic effects on large-scale structure formation. The authors pioneered the development of our understanding of general relativistic effects in cosmological observations, and we hope this issue will provide the basis for further advancement of the field.

Recent years have seen a flourishing of interest in the role that entanglement entropy plays in the physics of spacetime. Insights have been obtained into the role of entanglement for the entropy for black hole thermodynamics, and new ideas have been explored connecting entanglement to holography, wormholes, the structure of semiclassical spacetime itself and others. This issue collects a number of articles on this topic, offering a partial overview of these new developments.

The quest to detect gravitational waves directly has accelerated in the past decade with the successful operation of a first generation of large interferometric detectors. The lessons learned from the first-generation detectors fed into the design of advanced detectors that are now being constructed and commissioned and will soon begin collecting data. This special issue examines the advanced techniques and detectors currently being assembled, tested and prepared.

For this focus issue, 13 prominent researchers were asked to summarize recent developments in the observational and theoretical understanding of black holes, both stellar mass and supermassive, as well as black holes in alternate theories of gravity. The context is astrophysical; that is: how black holes form in, and interact with, their stellar and galactic environments, and the observational consequences of that interaction. This issue begins with a description the fundamental techniques of pulsar timing and the effects of gravitational radiation, followed by the current challenges: searches for suitable pulsars, noise limitations and data analysis techniques, the current status of the PTA consortia, along with that of the Square Kilometer Array, and the astrophysics of sources of GWs in this frequency band and the potential for testing general relativity using PTA.

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- Devils Dream: A Novel About Nathan Bedford Forrest.
- The Columbian Covenant: Race and the Writing of American History;

This focus issue presents several active directions of research where the interplay between scalar fields and gravity is essential. Scalar fields can affect gravity in two ways. The concept of mass has been central in many areas of physics. Gravitation is not an exception, and it has been one of the long-standing questions whether the graviton, a spin-2 particle that mediates gravity, can have a non-vanishing mass or not.

This is relevant from not only theoretical but also phenomenological viewpoints, since a nonzero graviton mass may lead to late-time acceleration of the universe and thus be considered as an alternative to dark energy. The principles of quantum mechanics and relativity impose rigid constraints on theories of massless particles with nonzero spin.

- A step closer to a theory of quantum gravity | Cosmos?
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These higher spin gravity theories are therefore of great intrinsic interest, since they, along with supergravity, provide the only known field theories generalizing the local invariance principles of Yang—Mills theory and General Relativity. This site uses cookies.

By continuing to use this site you agree to our use of cookies. To find out more, see our Privacy and Cookies policy. Close this notification. Classical and Quantum Gravity. Focus issues Quicklinks: current focus issues completed archive Current focus issues Classical and Quantum Gravity 's focus issues are collections of high-quality invited articles.

New focus issues Focus Issue: Numerical Investigations in Non-Perturbative Quantum Gravity Editors Bianca Dittrich and Parampreet Singh In recent years, the importance of numerical techniques has increasingly been felt in the quantum gravity community. Focus Issue: Magnetic fields at cosmological scales Editors Tina Kahniashvili and Lawrence Widrow This focus issue will include articles that cover the observations and signatures of cosmic magnetic fields, the mechanisms to generate them, and the evolution of magnetic fields in astrophysical systems and during the expansion of the universe.

Focus issue: Black holes and electromagnetic fields Editor Maria Rodriguez How do electromagnetic fields change the behavior and physics of black holes? Focus issue: Computational issues in mathematical cosmology Editors Alan A Coley and David L Wiltshire New developments are currently being made to include general relativity in computational cosmology. Focus issue: The causal set approach to quantum gravity Editors Fay Dowker, Rafael Sorkin and Sumati Surya The causal set approach to the problem of quantum gravity is based on the proposal that the deep structure of spacetime is atomic and takes the form of a discrete partial order.

Focus issue: Approaches to the two-body problem Editors Alexandre Le Tiec, Bernard Whiting and Eric Poisson The two-body problem has always played a central role in gravitational physics. Focus issue: Gravitational waves Editors P Shawhan and D Shoemaker The direct detection of a signal from merging black holes by LIGO launched gravitational waves as an experimental science, but one which depends crucially on theory, accurate modeling, and astrophysics for both discovery and interpretation.

Focus issue: Rattle and shine: the signals from compact binary mergers Editors Luis Lehner and Stephan Rosswog This special focus is issue dedicated to the many physical facets of those compact binary mergers that contain at least one neutron star. Focus issue: Applications of loop quantum gravity to cosmology Editor Parampreet Singh The unification of quantum theory and Einstein's theory of general relativity is one of the most fundamental problems of theoretical physics.

Focus issue: Hairy black holes Editors Carlos Herdeiro and Eugen Radu This issue collects some of the models of alternative compact objects to the paradigmatic Kerr black hole of general relativity, with focus on hairy black holes. Focus issue: Black holes and fundamental fields Editors Paolo Pani and Helvi Witek First articles published June General relativity predicts the existence of black holes, fascinating objects made of pure spacetime fabric. Focus issue: Astrophysics and general relativity of dense stellar systems Editors Pau Amaro-Seoane and Clifford M Will Published December —February Dense stellar systems such as galactic nuclei and stellar clusters are unique laboratories, not only for astrophysics, but also for general relativity.