What is Loop Quantum Gravity?（原声文稿）

It seems perfectly smooth. You can cut a distance in half and in half again, forever.

Einstein's general relativity agrees.

Space is a smooth, flexible fabric that bends and ripples. But zoom in.

Past atoms, past nuclei, past anything we have ever measured, down to about 10 to the minus 35 meters.

Here, gravity and quantum physics collide, and one idea says, the fabric stops being a fabric.

It becomes a network, tiny, indivisible grains of space, stitched together by threads.

Not things in space, the grains are space.

This is loop quantum gravity, and if it is right, there is a smallest possible area.

Black holes have a countable inner structure, and the Big Bang may not have been the beginning at all.

Physics runs on two great theories.

Quantum mechanics describes the very small.

Electrons, photons, quarks, all jittering and uncertain, coming in discrete lumps called quanta. General relativity describes gravity.

Mass bends spacetime, and bent spacetime tells mass how to move. Each works brilliantly in its own domain.

The trouble starts where both matter at once.

– the first instant of the Big Bang or the center of a black hole.

The obvious move is to treat gravity like the other forces.

Light has a quantum particle, the photon, so give gravity 1, 2, the graviton, and add up how gravitons interact.

For light, this recipe works to astonishing precision.

For gravity, it fails.

The calculations produce infinities, and every attempt to absorb them demands new ones without end.

In 1986, Mark Gorov and Augusto Sagnotti showed that even pure gravity, with no matter at all, breaks down at two loops.

At the plank scale, the recipe predicts nothing.

Loop quantum gravity takes this as a hint that the recipe itself is wrong for gravity. Here's why.

Every other force plays out on a stage, a fixed background of space and time.

To quantize the photon, we assume space is already there, with distances already defined.

But in general relativity, gravity is the geometry of space and time. There is no stage separate from the actors.

Treating gravity as tiny ripples on a fixed background quietly sneaks the stage back in.

So the loop approach sets a strict rule, background independence.

Quantize the geometry itself with no space laid down in advance.

Already in 1936, the Soviet physicist Matve Bronstein suspected this might force us to give up our ordinary ideas of space and time.

Fifty years later, a change of variables made it possible to try.

For decades, general relativity was written in terms of the metric, a rule that gives the distance between any two nearby points.

Quantizing it directly led to equations so tangled that almost nothing could be solved.

In 1986, Abhay Ashtakar, building on work by Amitabh Hussain, found a different way to write the very same theory.

Instead of measuring distances, his central variable describes how directions change as you move from point to point. Mathematicians call it a connection. Here's the idea.

Stand at the north pole of a sphere, holding an arrow.

Walk down to the equator, a quarter of the way around it, and back up to the pole, never twisting the arrow. When you return, it points in a different direction.

It rotated, not because you turned it, but because the surface is curved.

The connection is the rule for carrying arrows, and the rotation around a closed path measures the curvature inside it.

Its partner is a set of three little perpendicular rulers at every point, called a triad, which encodes the shape of space.

Connection and triad are to gravity what position and momentum are to a particle. Why does this matter?

Because the strong force, the weak force, and electromagnetism are all described by connections.

Ashdekar's variables made gravity look, mathematically, like a cousin of the other forces.

Same language, same tools, with one crucial difference kept intact. There is still no fixed background.

His original variables were complex numbers, which made the quantum theory hard to interpret.

In 1995, Fernando Barbero found a real version at the cost of a new free number.

Giorgio Immirzi studied that number and it carries his name, the Immirzi parameter written gamma.

Remember it, it comes back when we count the states of a black hole.

With gravity written as a connection, an old tool from particle physics became available.

In the 1970s, Kenneth Wilson studied the strong force by asking a simple question. If you carry a quark around a closed loop, how much does it turn?

These Wilson loops capture everything about a connection, one loop at a time. Apply the same idea to gravity.

Take any closed loop in space, carry an arrow around it, and record the rotation, called the holonomy.

Know the holonomy around every loop, and you know the geometry.

In 1988, Ted Jacobson and Lee Smolin found that loops do more than describe the classical field, they solved the central equation of quantum gravity, the Wheeler -DeWitt equation.

Bryce DeWitt had published that equation in 1967, and it had resisted almost every attempt at a solution.

Carla Rovelli and Smolin then turned this into a new way to write quantum gravity, the loop representation, and found an infinite family of exact solutions.

Then, something remarkable happened.

Because the theory has no background, it cannot care where a loop sits, only how it is tied, how it whines, how it links with other loops.

Sliding a loop smoothly changes nothing physical. What survives is the not.

Not theory, a branch of pure mathematics, turned out to control the physical states of the gravitational field. So picture quantum space this way.

Not a sheet with ripples, but threads.

A surface that no thread crosses has no area at all.

Weave enough loops together, densely enough, and from far away, the weave looks like smooth space, the way fine fabric looks continuous until you hold it under a magnifying glass.

Loops alone turned out to be too many. Different collections of loops could describe the same state.

The clean answer came from an idea Roger Penrose had in the 1960s and published in 1971.

Spin Networks A spin network is a graph, points called nodes joined by lines called links, and every link carries a number called a spin, one half, one, three halves, and so on.

In 1994, Revelli and Smolin asked what happens when you measure geometry in this quantum theory.

They built the operators for area and volume, and computed their possible values. The answer? Both come in discrete steps.

Here is what a spin network means physically. Each node is a tiny grain of volume, a quantum chunk of space.

Each link is where two grains touch, and its spin sets the area of the face they share.

Think of the nodes as atoms of space, and the links as the walls between them.

A surface gets its area only from the links that cross it, and each crossing adds a quantum. Bigger spin, bigger quantum.

In a formula, the area is 8 pi times gamma times the plank length squared times a sum over the lengths that cross the surface.

The plank length is about 10 to the minus 35 meters, and gamma is the Amirzi parameter.

Crucially, there is a smallest area that is not zero, an area gap, about 10 to the minus 69 square meters. Nothing in the theory can be smaller. This is not the same as space being a grid.

grid. A grid would be laid down in advance and would pick out special directions.

A spin network is not in space. It IS space.

There is no between the nodes. And the discreteness is not put in by hand.

It comes out of the mathematics, just as the energy levels of a hydrogen atom do. That is the boldest claim of loop quantum gravity.

Geometry itself is quantized.

Area and volume, like energy in an atom, can take only certain values.

So far, we have a snapshot, a quantum state of space at one moment. But what about time?

Here, loop gravity runs into one of the deepest puzzles in physics.

The Wheeler -DeWitt equation contains no time at all.

In general relativity, time is part of the geometry.

So when you quantize geometry, there is no outside clock left ticking in the background.

Physicists call this the problem of time.

The loop answer is that change is real, but it is always change of one thing relative to another, the hands of a clock relative to the position of a planet. Time is not a stage, it is a relation. How does a spin network change?

Nodes split into merge and links reconnect.

Now stack these moments and look at the whole history at once.

Each node traces out a line and each link sweeps out a surface.

The result is a foam of faces, edges and vertices, like the foam in a sink.

Physicists call it a spin foam and it is a quantum spacetime, a history of space built out of quanta.

The vertices of the foam, where the network changes, are the elementary events of spacetime.

Quantum mechanics says to add up every possible history, history, each with its own weight, called an amplitude.

In 2007, Jonathan Engel, Roberto Pereira, Carlo Rovelli, and Etara Levine proposed the vertex amplitude used in most work today, known as EPRL. There is a parallel with Richard Feynman.

In particle physics, Feynman diagrams add up the histories of particles.

A spin foam is a Feynman diagram of space itself.

At everyday scales, the hope is that the sum over foams reproduces Einstein's smooth, curved space -time, the way countless swirling molecules make up a smooth -flowing river.

Black holes are where any theory of quantum gravity gets tested on paper.

In the 1970s, Jacob Beckenstein and Stephen Hawking showed that a black hole has entropy, a measure of its hidden microscopic states, equal to a quarter of its horizon area in plank units. Entropy is supposed to count something. But what microscopic states can a black hole have?

It looks completely featureless from outside. Loop gravity offers a picture.

The horizon is a surface, so its area comes from the links of the spin network that pierce it. Each puncture is a tiny patch of area with its own spin.

A black hole the mass of the sun is pierced roughly 10 to the 77 times.

Count the ways those punctures can be arranged for a given total area and you get the entropy.

In 1996, Rovelli made the first such count.

In 1997, Abhay Ashdekar, John Baez, Alejandro Corici and Kirill Krasnov made it rigorous. The result? Entropy proportional to area.

The same law Beckenstein and Hawking found, now from counting quanta of geometry.

There is a catch, and honesty requires saying it.

The number in front depends on the Amirzi parameter.

To get exactly one quarter, gamma has to be set to one particular value, about 0 .24.

Supporters point out that once gamma is fixed with one black hole, the same value works for others too, such as black holes with electric charge.

Critics answer that a free number tuned to fit is not a prediction.

Both points are fair, and the debate is still open.

Some loop researchers go further and ask what happens at the center where the classical theory predicts a singularity.

The same quantum geometry may stop the collapse there too, which is exactly what happens to the whole universe in the next chapter.

Run the expanding universe backwards.

Galaxies crowd together and matter grows denser and hotter.

General relativity says that about 13 .8 billion years ago, everything was squeezed to infinite density. – the Big Bang Singularity.

But infinite density isn't a physical result. It is the theory telling us it has stopped working.

Loop quantum cosmology applies the ideas of loop gravity to the universe as a whole.

Martin Boyovald began this program in 2001.

In 2006, Abhay Ashtakar, Tomasz Pawlowski and Parampreet Singh solved the quantum equations of a simple model universe on a computer and found something striking.

Far from the beginning, the quantum universe follows Einstein's equations exactly.

But as the density approaches the Planck scale, the discreteness of geometry takes over.

Space can't be squeezed below its smallest quanta, and the quantum geometry produces an effective repulsion.

Gravity, normally always attractive, turns repulsive. The collapse halts and reverses. The big bang becomes a big bounce.

In the simplest models, the bounce always happens at the same critical density, about 0 .41 of the Planck density, roughly 10 to the 96 kg per cubic meter. Enormous, but finite.

And before the bounce, there was a contracting universe, a cosmos collapsing toward us, which then rebounded into the expansion we see today.

So the time before the Big Bang may not be ruled out by physics.

It may only have been hidden by our equations breaking down. Is this real?

These are simplified models of perfectly uniform universes, and connecting them to the full theory is still an open problem. But they make the bounce testable in principle.

A bounce may leave fingerprints in the cosmic microwave background, the oldest light in the universe, and several groups are calculating exactly what those fingerprints would look like.

Like, loop quantum gravity is almost four decades old.

It's fair to ask, what has it delivered and what is still missing? The open problems first.

The biggest is showing that at large scales, the theory really reproduces Einstein's smooth spacetime.

That the weave of loops truly looks like the world we see. Progress is real, but incomplete. The dynamics has ambiguities.

Different ways of writing the quantum equations give different theories, and it is not settled which one nature uses.

And unlike string theory, loop gravity is not a theory of everything.

It quantizes gravity and geometry, and adds the particles of the standard model by hand. Then the tests.

If space is grainy, light might travel at slightly different speeds depending on its energy, a little like light in glass.

Over billions of light years, even a tiny difference would add up.

On the 10th of May 2009, NASA's Fermi telescope caught a gamma -ray burst whose light had traveled about 7 billion years, including a single photon with about 31 billion electron volts of energy. It arrived less than a second after the burst began.

That rules out the simplest energy -dependent speed of light, up to beyond the Planck scale.

loop gravity doesn't necessarily predict such an effect, but the measurement shows that Planck scale physics is not completely out of reach. And strings? The two approaches start from opposite ends.

String theory starts from particle physics, quantize the graviton and aim to unify every force.

Loop gravity starts from general relativity, keep background independence sacred and quantized geometry itself.

Strings gave us ADS, CFT, and M theory.

Loops gave us atoms of space and a bouncing universe. Neither has yet been confirmed by experiment. Perhaps the deepest lesson is one they share.

In both, space and time stop being the bottom layer of reality. Something more basic lies beneath.

Threads, grains, strings, or something no one has imagined yet.

Space may not be the stage after all. It may be part of the play.