A Crinkle in the Wrinkle of Space-time

Albert Einstein’s revolutionary general theory of relativity describes gravity as a curvature in the fabric of spacetime. Mathematicians at University of California, Davis have come up with a new way to crinkle that fabric while pondering shockwaves.

“We show that spacetime cannot be locally flat at a point where two shockwaves collide,” says Blake Temple, professor of mathematics at UC Davis. “This is a new kind of singularity in general relativity.”

Temple and his collaborators study the mathematics of how shockwaves in a perfect fluid affect the curvature of spacetime. Their new models prove that singularities appear at the points where shock waves collide. Vogler’s mathematical models simulated two shockwaves colliding. Reintjes followed up with an analysis of the equations that describe what happens when the shockwaves cross. He dubbed the singularity created a “regularity singularity.”

“What is surprising,” Temple told Universe Today, “is that something as mundane as the interaction of waves could cause something as extreme as a spacetime singularity — albeit a very mild new kind of singularity. Also surprising is that they form in the most fundamental equations of Einstein’s theory of general relativity, the equations for a perfect fluid.”

The results are reported in two papers by Temple with graduate students Moritz Reintjes and Zeke Vogler in the journal Proceedings of the Royal Society A.

Einstein revolutionized modern physics with his general theory of relativity published in 1916. The theory in short describes space as a four-dimensional fabric that can be warped by energy and the flow of energy. Gravity shows itself as a curvature of this fabric. “The theory begins with the assumption that spacetime (a 4-dimensional surface, not 2 dimensional like a sphere), is also “locally flat,” Temple explains. “Reintjes’ theorem proves that at the point of shockwave interaction, it [spacetime] is too “crinkled” to be locally flat.”

We commonly think of a black hole as being a singularity which it is. But this is only part of the explanation. Inside a black hole, the curvature of spacetime becomes so steep and extreme that no energy, not even light, can escape. Temple says that a singularity can be more subtle where just a patch of spacetime cannot be made to look locally flat in any coordinate system.

“Locally flat” refers to space that appears to be flat from a certain perspective. Our view of the Earth from the surface is a good example. Earth looks flat to a sailor in the middle of the ocean. It’s only when we move far from the surface that the curvature of the Earth becomes apparent. Einstein’s theory of general relativity begins with the assumption that spacetime is also locally flat. Shockwaves create an abrupt change, or discontinuity, in the pressure and density of a fluid. This creates a jump in the curvature of spacetime but not enough to create the “crinkling” seen in the team’s models, Temple says.

The coolest part of the finding for Temple is that everything, his earlier work on shockwaves during the Big Bang and the combination of Vogler’s and Reintjes’ work, fits together.

There is so much serendipity,” says Temple. “This is really the coolest part to me.
I like that it is so subtle. And I like that the mathematical field of shockwave theory, created to address problems that had nothing to do with General Relativity, has led us to the discovery of a new kind of spacetime singularity. I think this is a very rare thing, and I’d call it a once in a generation discovery.”

While the model looks good on paper, Temple and his team wonder how the steep gradients in spacetime at a “regularity singularity” could cause larger than expected effects in the real world. General relativity predicts gravity waves might be produced by the collision of massive objects, such as black holes. “We wonder whether an exploding stellar shock wave hitting an imploding shock at the leading edge of a collapse, might stimulate stronger than expected gravity waves,” Temple says. “This cannot happen in spherical symmetry, which our theorem assumes, but in principle it could happen if the symmetry were slightly broken.”

Image caption: Artist rendition of the unfurling of spacetime at the beginning of the Big Bang. John Williams/TerraZoom

Dark Energy Ignited By Gamma-Ray Bursts?

An artistic image of the explosion of a star leading to a gamma-ray burst. (Source: FUW/Tentaris/Maciej Fro?ow)


Dark energy… We’re still not exactly sure of what it is or where it comes from. Is it possible this mysterious force is what’s driving the expansion of the Universe? A group of astronomers from the universities in Warsaw and Naples, headed by Dr. Ester Piedipalumbo, are taking a closer look at a way to measure this energetic enigma and they’re doing it with one of the most intense sources they can find – gamma-ray bursts.

“We are able to determine the distance of an explosion on the basis of the properties of the radiation emitted during gamma-ray bursts. Given that some of these explosions are related to the most remote objects in space that we know about, we are able, for the first time, to assess the speed of space-time expansion even in the relatively early periods after the Big Bang,” says Prof. Marek Demianski (FUW).

What spawned this new method? In 1998, astronomers were measuring the energy given off by Type Ia supernovae events and realized the expelled forces were consistent. Much like the standard candle model, this release could be used to determine cosmic distances. But there was just one caveat… The more remote the event, the weaker the signature.

While these faint events weren’t lighting up the night, they were lighting up the way science thought about things. Perhaps these Type Ia supernovae were farther away than surmised… and if this were true, perhaps instead of slowing down the expansion of the Universe, maybe it was accelerating! In order to set the Universal model to rights, a new form of mass-energy needed to be introduced – dark energy – and it needed to be twenty times more than what we could perceive. “Overnight, dark energy became, quite literally, the greatest mystery of the Universe,” says Prof. Demianski. In a model put forward by Einstein it’s a property of the cosmological constant – and another model suggests accelerated expansion is caused by some unknown scalar field. “In other words, it is either-or: either space-time expands by itself or is expanded by a scalar physical field inside it,” says Prof. Demianski.

So what’s the point behind the studies? If it is possible to use a gamma-ray burst as a type of standard candle, then astronomers can better assess the density of dark energy, allowing them to further refine models. If it stays monophonic, it belongs to the cosmological constant and is a property of space-time. However, if the acceleration of the Universe is the property of a scalar field, the density of dark energy would differ. “This used to be a problem. In order to assess the changes in the density of dark energy immediately after the Big Bang, one needs to know how to measure the distance to very remote objects. So remote that even Type Ia supernovae connected to them are too faint to be observed,” says Demianski.

Now the real research begins. Gamma-ray bursts needed to have their energy levels measured and to do that accurately meant looking at previous studies which contained verified sources of distance, such as Type Ia supernovae. “We focused on those instances. We knew the distance to the galaxy and we also knew how much energy of the burst reached the Earth. This allowed us to calibrate the burst, that is to say, to calculate the total energy of the explosion,” explains Prof. Demianski. Then the next step was to find statistical dependencies between various properties of the radiation emitted during a gamma-ray burst and the total energy of the explosion. Such relations were discovered. “We cannot provide a physical explanation of why certain properties of gamma-ray bursts are correlated,” points out Prof. Demianski. “But we can say that if registered radiation has such and such properties, then the burst had such and such energy. This allows us to use bursts as standard candles, to measure distances.”

Dr. Ester Piedipalumbo and a team of researchers from the universities in Warsaw and Naples then took up the gauntlet. Despite this fascinating new concept, the reality is that distant gamma-ray bursts are unusual. Even with 95 candidates listed in the Amanti catalogue, there simply wasn’t enough information to pinpoint dark energy. “It is quite a disappointment. But what is important is the fact that we have in our hands a tool for verifying hypotheses about the structure of the Universe. All we need to do now is wait for the next cosmic fireworks,” concludes Prof. Demianski.

Let the games begin…

Original Story Source: University of Warsaw Press Release. For Further Reading: Cosmological models in scalar tensor theories of gravity and observations: a class of general solutions.

Astronomy Without A Telescope – Is Time Real?

Time is an illusion caused by the passage of history (Douglas Adams 1952-2001).

The way that we deal with time is central to a major current schism in physics. Under classic Newtonian physics and also quantum mechanics – time is absolute, a universal metronome allowing you determine whether events occur simultaneously or in sequence. Under Einstein’s physics, time is not absolute – simultaneity and sequence depend on who’s looking. For Einstein, the speed of light (in a vacuum) is constant and time changes in whatever way is required to keep the speed of light constant from all frames of reference.

Under general relativity (GR) you are able to experience living for three score and ten years regardless of where you are or how fast you’re moving, but other folk might measure that duration quite differently. But even under GR, we need to consider whether time only has meaning for sub-light speed consciousnesses such as us. Were a photon to have consciousness, it may not experience time – and, from its perspective, would cross the apparent 100,000 light year diameter of the Milky Way in an instant. Of course, that gets you wondering whether space is real either. Hmm…

Quantum mechanics does (well, sometimes) require absolute time – most obviously in regards to quantum entanglement where determining the spin of one particle, determines the spin of its entangled partner instantaneously and simultaneously. Leaving aside the baffling conundrums imposed by this instantaneous action over a distance – the simultaneous nature of the event implies the existence of absolute time.

In one attempt to reconcile GR and quantum mechanics, time disappears altogether – from the Wheeler-DeWitt equation for quantum gravity – not that many regard this as a 100% successful attempt to reconcile GR and quantum mechanics. Nonetheless, this line of thinking highlights the ‘problem of time’ when trying to develop a Theory of Everything.

The winning entries for a 2008 essay competition on the nature of time run by the Fundamental Questions Institute could be roughly grouped into the themes ‘time is real’, ‘no, it isn’t’ and ‘either way, it’s useful so you can cook dinner.’

The ‘time isn’t real’ camp runs the line that time is just a by-product of what the universe does (anything from the Earth rotating to the transition of a Cesium atom – i.e. the things that we calibrate our clocks to).

How a return to equilibrium after a random downward fluctuation in entropy might appear. First there was light, then a whole bunch of stuff happened and then it started getting cold and dark and empty.

Time is the fire in which we burn (Soran, Star Trek bad guy, circa 24th century).

‘Time isn’t real’ proponents also refer to Boltzmann’s attempt to trivialise the arrow of time by proposing that we just live in a local pocket of the universe where there has been a random downward fluctuation of entropy – so that the perceived forward arrow of time is just a result of the universe returning to equilibrium – being a state of higher entropy where it’s very cold and most of the transient matter that we live our lives upon has evaporated. It is conceivable that another different type of fluctuation somewhere else might just as easily result in the arrow pointing the other way.

Nearly everyone agrees that time probably doesn’t exist outside our Big Bang universe and the people who just want to get on and cook dinner suggest we might concede that space-time could be an emergent property of quantum mechanics. With that settled, we just need to rejig the math – over coffee maybe.

I was prompted to write this after reading a Scientific American June 2010 article, Time Is An Illusion by Craig Callender.

What is Space?

First, some simple answers: space is everything in the universe beyond the top of the Earth’s atmosphere – the Moon, where the GPS satellites orbit, Mars, other stars, the Milky Way, black holes, and distant quasars. Space also means what’s between planets, moons, stars, etc – it’s the near-vacuum otherwise known as the interplanetary medium, the interstellar medium, the inter-galactic medium, the intra-cluster medium, etc; in other words, it’s very low density gas or plasma (‘space physics’ is, in fact, just a branch of plasma physics!).

But you really want to know what space is, don’t you? You’re asking about the thing that’s like time, or mass.

And one simple, but profound, answer to the question “What is space?” is “that which you measure with a ruler”. And why is this a profound answer? Because thinking about it lead Einstein to develop first the theory of special relativity, and then the theory of general relativity. And those theories overthrew an idea that was built into physics since before the time of Newton (and built into philosophy too); namely, the idea of absolute space (and time). It turns out that space isn’t something absolute, something you could, in principle, measure with lots of rulers (and lots of time), and which everyone else who did the same thing would agree with you on.

Space, in the best theory of physics on this topic we have today – Einstein’s theory of general relativity (GR) – is a component of space-time, which can be described very well using the math in GR, but which is difficult to envision with our naïve intuitions. In other words, “What is space?” is a question I can’t really answer, in the short space I have in this Guide to Space article.

More reading: What is space? (ESA), What is space? (National Research Council of Canada), Ned Wright’s Cosmology Tutorial, and Sean Carroll’s Cosmology Primer pretty much cover this vast topic, from kids’ to physics undergrad’ level.

It’s hard to know just what Universe Today articles to recommend, because there are so many! Space Elevator? Build it on the Moon First illustrates one meaning of the word ‘space’; for meanings closer to what I’ve covered here, try New Way to Measure Curvature of Space Could Unite Gravity Theory, and Einstein’s General Relativity Tested Again, Much More Stringently.

Astronomy Cast episodes Einstein’s Theory of Special Relativity, Einstein’s Theory of General Relativity, Large Scale Structure of the Universe, and Coordinate Systems, are all good, covering as they do different ways to answer the question “What is space?”

Source: ESA