Emergent Space-Time?

A few weeks ago, Quanta Magazine released a fantastic and fascinating series of articles examining the concept of emergent space-time.  Since it’s been awhile since we did a dedicated science post, and the topic has been boggling my mind ever since, I figured I would share, or attempt to share, a little of what is as much science philosophy as it is theoretical physics.  The core concept is not all that difficult to explain.  Consider a fluid, like water.  The particles of which the fluid is composed are not themselves fluid – they are particles, and have no state of matter – but rather, the fluidic properties arise from the behavior of those particles in combination.  In other words, fluids are emergent from a more basic substance.  It’s when we start trying to apply that idea to space-time that things get mind-bending.

Defining space-time has long been a struggle.  Channeling Shakespeare, perhaps, Newton gave us an understanding of space-time akin to “all the world’s a stage,” in which space-time served as an immutable and absolute backdrop upon which the action of the universe takes place.  He was building on the work of previous thinkers like Descartes, who, aside from giving us “cognito ergo sum,” gave us the idea for Cartesian coordinates.  Given the ubiquity of graphs, charts, coordinates, and measurements in our modern world, it is easy to forget the revolutionary significance of developing a way to discretely define every point in a continuous space-time, and the insights and mathematical concepts that must underpin such a mechanism.

Of course, the Newtonian rigid space-time stage didn’t last.  Einstein modified it almost past recognition with his special and general relativity.  In relativity, space-time is not a stage, but an actor in the drama of the universe.  Neither points in space nor time can be defined absolutely under relativity.  This is how most people probably think about space-time today, if they think about it at all; a relativistic, curving medium contributing to this grand play called existence.  Except that, even in relativity’s early days, there was a suggestion that this could not be the final explanation.  It was there, in the mathematics of zeros and infinities, though it wasn’t taken seriously until an appropriate name was applied: black holes.

Black holes arise from the mathematics of relativity.  They are singularities, implied by the behavior of fractions when the denominator goes to zero, and they are an example of what is sometimes referred to as “tortured” space-time geometry.  By itself, this would not be enough to suggest a fundamental flaw in the entire concept of space-time, but that’s before we consider the other revolutionary theory of the twentieth century: quantum physics.  Quantum physics introduces chaos, randomness, into the universe, including the idea that, at the smallest of levels, space-time itself would break down due to the severity of spontaneous behaviors, called quantum foam, with particles popping in and out of existence to the point that space-time would exist about as often as it would not exist.

To be a little less vague, quantum physics and general relativity have resisted every attempt to develop a quantum theory of gravity.  The mathematics of general relativity can’t accommodate the chaos quantum physics suggests at the smallest of scales, and quantum physics doesn’t provide an explanation for the macroscopic effects observed.  Furthermore, Hawking’s work with black holes led to the idea that black holes have entropy, which, if they are truly singularities, they should not be able to possess.

All of this is apparently leading many physicists to conclude that space-time is insufficiently fundamental.  Like the properties of fluids, they are asserting that the properties of what we perceive as space-time emerge from some more basic components – the atoms of space-time, if you will.  Easy enough to say, perhaps, especially with the fluid analogy to help us visualize it, but what does it really mean?  For that matter, what really is the space-time that we are attempting to replace?

In truth, physicists aren’t quite certain, and describing these concepts using written language, rather than mathematics, is almost hopelessly imprecise (going back to the quote about describing the deepest secrets of the universe using grunts intended to tell each other where to find the best fruit). The leading theory is that the “bulk” four-dimensional space-time we experience is an emanation from a lower dimensional state, like a hologram. The example frequently invoked is the idea of CFT/AdS correspondence, in which a conformal field theory describing reality on a two dimensional spherical surface can be translated into the physics of a bulk universe arising within that two dimensional sphere, called an Anti-de Sitter space, which is a little like our own universe, except ours lacks a boundary, and AdS space has negative energy instead of our positive energy.

Then again, there are other physicists and mathematicians who think our current understanding of space-time may not be fatally flawed, and are instead looking for ways to patch the holes. Indeed, the question I kept wondering as I read these articles was how physicists can be so confident in the math and the limited experimental data we have that they are prepared to pursue a completely new paradigm of understanding for the very essence of the universe. What if black holes are not truly black holes, but rather black stars or some similar object which has nearly identical properties but is not a true singularity? What if dark energy and dark matter are not some missing physics, but a problem with our current theories of physics? Indeed, dark energy and dark matter have, to me, long been indicative of a problem with our understanding of gravity, not or some mysterious, non-interactive universe existing alongside us. Unfortunately, I lack of the physics and mathematics knowledge to tackle revising relativity.

In a word, reading these articles is humbling. It can be easy sometimes to start to think I have some idea about how the universe works, with all the science papers I read and the books I study and the work I do, but reading about and wrestling with the ideas surrounding emergent space-time are a quick cure. We might discuss these ideas further in the future, perhaps do a dedicated post on the idea of the Planck scale, but for now, I hope you’ll consider bending your brain on Quanta’s excellent articles about the end of space-time as we know it.