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 selfdestructed."
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
lowerdimensional object floating in a higherdimensional 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 noboundary
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 noboundary 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
noboundary wave function, so there is a direct connection between string
theory and the noboundary 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 Planckscale quanta (including quantum loop gravity and similar
approaches) is the way to go, but the mathematical foundations can go to
discrete infinity.
