Wednesday, October 09, 2013

The Universe Is Bigger on the Inside: Tardis regions in spacetime and the expanding universe

From Gizmag:

Fans of the Doctor Who will be very familiar with the stupefied phrase uttered by all new visitors to his Tardis: "It's...bigger...on the inside." As it turns out, this irrational idea may have something to contribute to our understanding of the universe. A team of cosmologists in Finland and Poland propose that the observed acceleration of the expansion of the universe, usually explained by dark energy or modified laws of gravity, may actually be the result of regions of spacetime that are larger on the inside than they appear from the outside. The researchers have dubbed these "Tardis regions."
Perhaps the most surprising cosmological observation of the past few decades was the 1998 discovery by Perlmutter, Schmidt and Riess, that the expansion of the universe has been accelerating for the past five billion years. This result, which won the 2011 Nobel Prize, was quickly corroborated by observation of independent phenomena such as the cosmic background radiation.
Why the acceleration is occurring is not currently understood, although it can be described. In terms of conventional cosmological theory, it calls for the existence of a "dark energy," an energy field permeating the universe. However, because gravity attracts normal mass-energy, dark energy would have to have a negative energy density, something unknown as yet in nature. In addition, roughly 75 percent of the contents of the universe have to be made up of dark energy to get the observed acceleration of expansion. Even though dark energy provides a reasonable description of the universal acceleration, its value as an explanation is still controversial. Many have the gut reaction that dark energy is too strange to be true.
Professors Rasanen, and Szybkab, of the University of Helsinki and the Jagellonian University at Krakow, together with Rasanen's graduate student Mikko Lavinto, decided to investigate another possibility.
The "standard cosmological model," which is the framework within which accelerated expansion requires dark energy, was developed in the 1920s and 1930s. The FLRW metric (named for Friedmann, Lemaître, Robertson and Walker, the major contributors) is an exact solution to Einstein's equations. It describes a strictly homogeneous, isotropic universe that can be expanding or contracting.
Strict homogeneity and strict isotropy means that the universe described by an FLRW metric looks the same at a given time from every point in space, at whatever distance or orientation you look. This is a universe in which galaxies, clusters of galaxies, sheets, walls, filaments, and voids do not exist. Not, then, very much like our own Universe, which appears to be rather homogeneous and isotropic when you look at distances greater than about a gigaparsec, but closer in it is nothing of the sort.
Rasanen's research team decided to examine a model universe having a structure closer to ours, in an attempt to look for alternate explanations of the accelerating expansion we see. They took an FLRW metric filled with a uniform density of dust, and converted it into a Swiss cheese model but cutting random holes in it. This has the effect of making the model inhomogeneous and non-isotropic (except very far away), and hence the Swiss cheese model looks more like our own Universe, save for the fact that our Universe does not seem to be full of holes.
While Swiss cheese is delicious, a universe with holes is not. To rectify this, Rasanen's team filled in the holes with plugs made from dust-filled exact solutions of Einstein's equation. These plugs are a reasonable model of the region near a sizable body, such as a galaxy. By putting the plugs in the holes, and then smoothing the intersections between them, they obtained a rather uniform spacetime with a lot of smaller blobs of matter dispersed throughout it – a (very) simple analog to the structure of the universe in which we live.
Rasanen's team made the plugs from a model in which the spatial parts essentially fold in on themselves as the spacetime evolves. As suggested by the figure above, such folds increase the length of a path passing through the plug without changing the external dimensions of the plug. For some such plugs, the length of a path through the plug becomes longer throughout the life of the Universe.
The team calls such a plug a Tardis region, and a spacetime containing Tardis regions is called a Tardis spacetime. As seen in the figure below, the proper diameter and volume of a properly configured plug starts somewhat larger than the apparent quantities, but then grows to much larger sizes.
Let's get to the story about Tardis regions and expansion of the universe. Because gravity is universally attractive, in an inhomogeneous universe a denser region will tend to expand more slowly than will a less dense region – there is less gravitational interaction holding the less dense region together.
Although the Tardis regions expand faster than the surrounding dust space, this does not change their apparent size from outside, so at first glance it is difficult to see how this accelerates the expansion of the universe. The key is that when an observer looks at a distant object in a plugged Swiss cheese space, the light they see has passed through a number of plugs, the number increasing the further away the object. As the length of a path through a Tardis region rapidly becomes larger as time goes by, the total length of the path the light followed from an object increases faster than does the space outside the plugs. The result is that the expansion of the universe appears to be accelerating with time, without additional influences such as dark matter.
To sum up, a space with a large number of relatively small Tardis regions will appear initially to expand at roughly the same rate as does the dust space in which the Tardis regions are embedded. As time goes on, however, the Tardis regions expand faster than the Swiss cheese, and as they fill larger fractions of the photon paths between objects and observers, the expansion of the universe as measured by optical tests over large distances will appear to accelerate.
The effect can be made large enough to reproduce the observed acceleration, so the idea isn't silly. But is this the explanation? It is too early to tell. The model is very artificial and simplistic, but does suggest that there is at least one possible alternate to dark energy within the bounds of classical general relativity.

Monday, October 07, 2013

Quantum black hole study opens bridge to another universe

From Gizmag:

Physicists have long thought that the singularities associated with gravity (like the inside of a black hole) should vanish in a quantum theory of gravity. It now appears that this may indeed be the case. Researchers in Uruguay and Louisiana have just published a description of a quantum black hole using loop quantum gravity in which the predictions of physics-ending singularities vanish, and are replaced by bridges to another universe.

Singularities, such as the infinitely strong crushing forces at the center of a black hole, in a physical theory are bad. What they tell you is that your description of the universe fails miserably to explain what happens as you approach the singularity. Tricks can sometimes resolve what appears to be singular behavior, but essential singularities are signs of a failure of the physical description itself.

General relativity has been summed up by the late John Wheeler's phrase: "Spacetime tells matter how to move, matter tells spacetime how to curve." Relativity is riddled with essential singularities, because gravity is both attractive and nonlinear – curvature in the presence of mass tends to lead to more curvature, eventually leading to trouble.

The result is rather similar to a PA system on the verge of producing a feedback whistle. If you whisper into the microphone (small gravitational fields) the positive feedback isn't enough to send the PA into oscillation, but talking at a normal volume (larger gravitational fields) produces that horrible howl.

Whispering is the comparable to the familiar actions of gravity that keep the planets and stars in their courses. The howl is the process that eventually leads to a singularity as the end result of gravitational collapse.

Let's follow this analogy a bit further. On a PA system, the volume of the feedback is limited by the power capacity of the amplifier, so it can't reach truly destructive levels (other than to our eardrums.) However, gravity as described by general relativity doesn't have such a limit. Since gravity is always attractive, and eventually becomes stronger than all the (known) forces that normally give volume to matter, there is nothing to keep gravitational collapse from proceeding until the curvature of the spacetime tends toward infinity – i.e. a singularity.

Remember that this is the prediction of the classical theory of gravity, general relativity. Classical physical theories contain no fundamental limitation on mass-energy density or on the size of spacetime curvature.

While this may be (and probably is) incorrect, we rarely run into a problem caused by this error, so have largely ignored the problem for centuries. Then along came gravitational collapse and black holes. First proposed by geologist John Mitchell in 1783, a black hole is a region of spacetime from which gravity prevents anything, even light, from escaping.

Black holes are formed when large stars run out of fuel. When a star's core cools, the star shrinks. As the star's layers fall inward, they are compressed by the unbalanced force of gravity, and heat up until a new balance is established. This can only go on so long, as the star (on average) gets smaller at each step of the process of collapse. Eventually the heating driven by this gravitational collapse becomes too small to hold the star up.

At this point, the size of the star depends mostly on its mass, as the force of gravity is only balanced by the ability of the star's material to resist pressure. If a star is heavy enough (8-10 times the mass of our Sun), there is no known source of material pressure which is large enough to resist gravity.

In that case, the star collapses without end, and forms a black hole, from which even light cannot escape. Black holes really began to be understood in the late 1950s, when David Finkelstein, then a professor at the Stevens Institute of Technology, found that the odd behavior at the Schwartzchild radius was actually "... a perfect unidirectional membrane: causal influences can cross it but only in one direction."

In other words, what falls into a black hole stays there. In the spacetime diagram below, known as a causal diagram, the exterior and interior of a classical black hole are sketched. The yellow lines outside and the blue lines inside the black hole show the paths along which light travels. All particles have to follow slower paths that are sandwiched between these "light cones." The red line at the center of the black hole is a curvature singularity.