What Big Bang?

By Amanda Gefter
New Scientist, June 30, 2012

Edited by Andy Ross

Paul Steinhardt: "We thought that inflation predicted a smooth, flat universe. Instead, it predicts every possibility an infinite number of times. We're back to square one."

Max Tegmark: "Inflation has destroyed itself. It logically self-destructed."

Sean Carroll: "Inflation is still the dominant paradigm. But we've become a lot less convinced that it's obviously true."

Alan Guth proposed inflation in 1980. The cosmic microwave background radiation seems to confirm the big bang theory but it troubled theorists. Some 12 teraseconds after the big bang, the cosmos had expanded and cooled enough for the first atoms to form. Photons have been flying free through the cosmos ever since. Now, some 14 billion years later, we see them as a background radiation that suffuses the sky at an almost uniform temperature of 2.7 K.

You can measure the cosmic background 10 billion light years away in one direction and 10 billion light years in the other and still observe that pleasing uniformity. But these patches of space apparently never meet. So that uniformity is a suspicious coincidence. Also, the universe is extremely flat, with a nearly Euclidean geometry, which is also unlikely, given that gravity warps space.

The inflationary story is that in the beginning was a quantum field called the inflaton. It was in a temporarily stable "false vacuum" energy state. It could rest there undisturbed, but the slightest quantum jiggle would collapse it to the true vacuum below. A random quantum fluctuation later, a kind of repulsive gravity inflated space at much more than light speed.

When the inflaton hit rock bottom, all that kinetic energy turned into matter and radiation, and eventually us. In a decillionth of a second, the observable universe ballooned over 20 orders of magnitude in size. Inflation solved the horizon problem and the flatness problem. Also, by inflating tiny quantum fluctuations in the density of the cosmos to astronomical proportions, it provided seeds for the galaxies we see today.

The problem is that inflation is hard to stop. Quantum fluctuations ensured that the inflaton field had different energies in different places. Each collapse kicks off the inflation of a different region of space, which blows up faster than light. These regions bud off to independent existences in an infinite multiverse. And in an infinite multiverse there are no definite predictions, only probabilities. Every conceivable value of dark energy or anything else will exist an infinite number of times among the infinite number of universes. The odds of observing any particular value are infinity divided by infinity.

At first, cosmologists hoped to take a snapshot of the multiverse and then extrapolate the relative probabilities of various observations out to ever later times and ever more universes. But relativity says there is an infinite number of ways to take snapshots of the multiverse, each giving different probabilities. This measure problem destroys all predictions.

In 2001, Paul Steinhardt, Justin Khoury, Burt Ovrut, and Neil Turok reinterpreted the big bang as a recent event in a much longer history. Their inspiration came from string theory, in which all elementary particles are vibrations of tiny strings, including one for a graviton. It also predicts the existence of extra dimensions beyond the four of spacetime.

Maybe our 4D cosmos is situated on a "brane", a lower-dimensional object floating in a higher-dimensional space. Two branes floating near each other can sandwich a 5D space in between. The idea is that every few trillion years or so neighboring branes collide. The fifth dimension briefly goes pop and reappears as the branes bounce apart. Our 4D brane gets a huge hit of energy, a.k.a. the big bang.

This "cyclic model" of the big bang does much of what the inflationary big bang was invented to do. The branes are flat and hit all at once, solving the flatness problem and creating a nearly uniform cosmos. Small quantum energy fluctuations are enough to seed galaxies. No multiverse, no measure problem. But we must explain how the fifth dimension survives its pop.

In quantum physics, when a particle travels from A to B it can pass along two or more paths simultaneously, interfering with itself at the other end as if it were a wave. To find out which path we are most likely to observe, we must add together the wave functions for each possible path, working out how they cancel and amplify each other. In this total wave function is everything we need to know about the quantum particle at B.

Three decades ago, Stephen Hawking and James Hartle argued that a similar approach could be applied to the universe as a whole. Point B is the universe we see today. Looking back towards its origin, we can trace many valid histories of its expansion back towards point A where semiclassical physics breaks down and quantum spacetime foams up. This point is a timeless zone where a superposition of all possible historical universes pops into existence from nothing with all its laws of physics intact. This was the no-boundary proposal.

Adding up all the possible histories that began in a universe with no boundary and ended in the universe we see today, we get a single universe with multiple histories. The resulting wave function gets rid of the measure problem, as it encodes a unique set of probabilities for anything we might observe. The horizon and flatness observations are not problems but inputs to the theory.

As Hartle, Hawking, and Thomas Hertog showed in 2008, inflation crops up naturally along many paths the universe could have taken to get here. Hertog: "You can calculate the probability that inflation occurred, and it turns out that probability is very high."

The holographic principle says that the physics of a 4D universe including gravity is mathematically equivalent to the physics on its 3D boundary without gravity. The world is a holographic projection of information from the edge of reality. The principle appears both in string theory and in almost any approach to unifying relativity and quantum theory dreamed up so far.

The no-boundary proposal says the universe has a boundary in the infinitely far future. Hertog calculated the probabilities of all the possible universes that can emerge as its holographic projections and found that the probabilities for the homogeneity of the cosmic background or the amount of dark energy are the same as those from the no-boundary wave function, so there is a direct connection between string theory and the no-boundary proposal. Hawking, Hartle, and Hertog showed how in a recent arXiv paper (blog June 8).

Brian Greene on inflation, dark energy, strings, and the multiverse

Alan Lightman on the contingency of the anthropic string multiverse

Sean Carroll on an idea to merge the multiverse with quantum branching

Stephen Hawking, Roger Penrose, and Jeremy Bernstein on cosmology

Inflation and Infinity

By Amanda Gefter
New Scientist, August 17, 2013

Edited by Andy Ross

Mathematics as we know it is riddled with infinities. Georg Cantor argued that sets containing an infinite number of elements were themselves mathematical objects. Within set theory, the continuum of the real numbers is treated as an actual infinity.

The standard model of particle physics was long beset by pathological infinities. Decades of work banished most of them, but gravity resists unification. Einstein's field equations predict states where matter becomes infinitely dense and hot, and spacetime infinitely warped.

Big bang infinity is worst. Cosmic inflation explains essential features of the universe, but it continues inflating other bits of spacetime long after our universe has settled down, creating an infinite multiverse where everything that can happen will happen an infinite number of times. It predicts everything and nothing. This is the measure problem.

MIT cosmologist Max Tegmark: "Inflation is saying, hey, there's something totally screwed up with what we're doing ... All of our problems with inflation and the measure problem come immediately from our assumption of the infinite."

The holographic principle makes the maximum amount of information that can fit into any volume of spacetime proportional to the area of its horizon. Given the principle, there is no room for infinity.

Rutgers mathematician Doron Zeilberger wants to do away with infinity altogether. There is a largest number. Start at 1 and just keep on counting and eventually you will go to a kind of limit. Zeilberger: "I call it N0." If you try to add 1 to N0, you get either an overflow error or a reset to zero. Zeilberger: "We can redo mathematics postulating that there is a biggest number and make it circular."

Tegmark says the calculations and simulations that physicists use to check a theory against the hard facts of the world are all done on a finite computer: "That already shows that we don't need the infinite for anything we're doing. There's absolutely no evidence whatsoever that nature is doing it any differently, that nature needs to process an infinite amount of information."

MIT quantum physicist Seth Lloyd: "We have no evidence that the universe behaves as if it were a classical computer, and plenty of evidence that it behaves like a quantum computer."

Quantum physics has difficulties with Schrödinger's cat. When no one is watching, the cat can be both dead and alive at the same time. Mathematically, its state can only be depicted using infinities. The same is true of qubits. Lloyd: "If you really wanted to specify the full state of one qubit, it would require an infinite amount of information."

Tegmark: "When quantum mechanics was discovered, we realized that classical mechanics was just an approximation. I think another revolution is going to take place, and we'll see that continuous quantum mechanics is itself just an approximation to some deeper theory, which is totally finite."

AR  In 1975, I tried to reconstruct set theory on finitist foundations but it didn't work. My supervisor said my big new idea (of "horizonal numbers") was "not crazy enough" and so I redid it on constructivist foundations instead. Even then I got into deep water with the Gödel's work on V = L and the GCH and I foundered on Cohen's independence proof of the GCH.

Now, in physics, I think finitist spacetime based on Planck-scale quanta (including quantum loop gravity and similar approaches) is the way to go, but the mathematical foundations can go to discrete infinity.