Spacetime on its smallest scales is a  seething ocean of black holes and wormholes   flickering into and out of existence—or  so many physicists think has to be the   case.

But why should we take this spacetime foam  seriously if we’ve never seen any evidence of it?

A while ago we started talking about the  fundamentalness of space—is it the most   elementary stage that holds all of the complexity  of physics?

Or is it just the way our brains make   sense of something that’s nothing like the space  of our experience.

Well, we have good reason to at   least doubt that the fundamental building block  of space is just more space.

And that’s because   our best theory of the nature of space—Einstein’s  general theory of relativity—is incomplete.

It   comes into severe conflict with the other great  pillar of modern physics: quantum mechanics.

We’ve spoken in the past about the source of  this conflict, and about some of the speculative   solutions such as string theory and loop quantum  gravity.

In both of these theories, space gives   way to something rather different—something  more fundamental at the tiniest scales.

But these theories have proved damnably difficult  to test, and so we can’t say what the most   elementary building block of space really is.

But  that doesn’t mean we can’t say something about   what space looks like at close to the smallest  scales.

By using a little logical deduction,   we can combine general relativity and  quantum mechanics just well enough to   trick nature into giving us an answer.

And  that answer is that spacetime is … foamy.

It was John Archibald Wheeler who worked  this one out.

Wheeler was a central figure   in the development of both general relativity  and quantum mechanics, and adviser to Richard   Feynman and Hugh Everett and Kip Thorne and many  many others.

Here’s the analogy that Wheeler came   up with to describe his conclusions about the  minutest scales of the fabric of spacetime.

Imagine you're flying in a plane over the Atlantic  ocean.

From a regular cruising altitude, looking   down, the surface of the ocean appears smooth  and relatively featureless.

But, if your plane   lowered its altitude and got closer you may start  to see the waves—from here just tiny disturbances   in the surface of the water.

But if you got  even close, perhaps on a large ship sailing   through the waters you'd see the foam and white  caps of waves forming and breaking, and you’d   feel their effect on your motion.

And if you’re  in a rowboat the wave would be everything—you’d   be moving through a space that was far from flat,  but rather dominated by ever changing geometries.

In this analogy, the 2-D surface of  the ocean is 3-dimensional space.

For large creatures like us humans,  we’re flying high above and see smooth,   flat, and perfectly continuous spatial dimensions.

But “descending” closer to the Planck scale,   we would see ubiquitous tiny fluctuations as  distances and geometries became warped.

And at   the Planck scale, spacetime would become  so curved that black holes and wormholes   would be popping into existence, only to vanish  again—as if our ocean were now violently boiling.

This is Wheeler’s “spacetime foam’’, and  there’s good reason to think that spacetime   really does look like this when you’re close to  the smallest scales—regardless of your preferred   theory of quantum gravity.

We need the latter  to say what spacetime is made of—to understand   the analogous level of the water molecules in  our ocean.

However, the behavior of a quantum   spacetime just above that level can perhaps be  understood regardless of its underlying theory,   just as we can describe the behavior  of water without knowing its chemistry.

Today we’re going to see where the  idea of spacetime foam came from,   and also how it might be tested.

Now we'll do this by combining two of the fundamental   ideas in each theory of the fundamental theories the uncertainty of quantum mechanics and the geometry   of general relativity.

Because spacetime foam is what you get when geometry itself becomes uncertain.

Let’s start with the bit about uncertainty.

The Heisenberg uncertainty principle is   one of the foundational concepts in quantum  mechanics.

One version tells us that we can’t   simultaneously know both the position and the  momentum of a particle to arbitrary precision.

The product of their uncertainties will always  be larger than a particular very small number.

This is a very deep relationship that  we get into in detail in this episode.

But let me also remind you of a simpler way to  think about the Heisenberg uncertainty principle that we covered more recently—the   Heisenberg microscope.

Imagine you try to measure  the position of an object by bouncing a photon   off it.

You’ll get a more precise position  measurement with a shorter wavelength photon.

That photon will transfer some of its momentum  to the object, as will any measurement attempt.

The shorter the wavelength, the more momentum  the photon can transfer.

So the more precisely   you measure position, the less certain you  become about the final momentum of the object.

But there’s a limit to the precision of  our position measurement, even if we’re   happy with absolute uncertainty in momentum.

That limit is a consequence of us bringing   general relativity into the picture.

GR  tells us that mass and energy changes   the geometry of space.

This is described  by the Einstein field equations, with the   mass-energy content of space completely  determining the geometry of that space.

So as our measuring photon gains  momentum and therefore energy,   it introduces uncertainty into the geometry  of space between you and the object,   which increases our uncertainty in the distance to  the object.

So as the photon gets more energetic,   the Heisenberg uncertainty goes down but the  uncertainty in the geometry goes up.

They equal   each other when the uncertainty is equal to the  Planck length, which is a tiny 1.6x10^-35 meters.

So the absolute limit of our ability to  pinpoint objects in space is the Planck length.

But what does that mean for the  structure of space on that scale?

Let’s say we now want to measure the size of  a little block of space.

The measuring photon   needs to have a wavelength at least  smaller than the width of that block.

That photon also warps our chunk of space.

The  Einstein field equations bv can tell us roughly   when the introduced curvature is equal to the  size of the space we’re trying to measure.

It turns out that if we try to measure the size  of a 1-Planck-length block of space, the curvature   introduced is equal to a Planck length.

We can  express our curvature uncertainty with a new   version of the uncertainty principle that combines  quantum mechanics and general relativity.

Here we have our first glimpse of the spacetime  foam.

As we peer closer and closer at the fabric   of spacetime, we see that its curvature at  any point becomes more and more variable;   its geometry more uncertain,  until the curvature dominates.

What does that mean?

Well, geometries that have a  radius of curvature similar to their size include   spheres, cylinders, and black holes.

So those are  the geometries that emerge at the Planck scale.

Space at that scale curves completely back on itself, infinitesimal black holes appear,   and wormholes connect nearby regions.

But such  Planck scale black holes would likely rapidly   evaporate due to Hawking radiation and the  wormholes would be unstable and collapse in   a very short amount of time.

The quantum foam  is as transitory as any quantum fluctuation.

To better understand the dynamics of  the spacetime foam, let’s think about   quantum fluctuations.

For that it’s  helpful to turn to the other popular   version of the Heisenberg uncertainty  principle, which tells us that we can’t   simultaneously know both the energy  and the time or duration of an event.

So if you try to measure the energy  of a system at a very precise time,   or over a very short duration, then your  energy measurement becomes highly uncertain.

But if energy can be fundamentally  uncertain, that means there can   be a fundamental uncertainty in the physical  contents of the universe.

To understand that,   let me give you a quick refresher on our best  theory of stuff in the universe.

Quantum field   theory and in particular the standard model of  particle physics nicely describes all matter and   3 of the 4 forces as excitations in different  quantum fields that permeate all of space.

But because of the time-energy uncertainty  principle, we can never know the exact energy   present in a particular patch of space.

We can’t  even know that the energy is precisely zero even in the   complete absence of real particles.

What should  be a complete vacuum might be observed to have   non-zero energy, and that becomes more likely  the shorter the timescale of our observation.

This manifests as an underlying buzz of rapid  energy fluctuations in the quantum vacuum.

This is sometimes described as an ocean of virtual particles constantly appearing and vanishing,   although it’s way more complicated than that.

Now, this isn’t quite our spacetime foam,   because it says nothing about the shape  of the fabric of spacetime on its own.

But let’s bring general relativity back into  it.

This fluctuating energy of the vacuum can be   thought of as an uncertainty in whatever’s sitting  on the right side of the Einstein equations.

The   mass-energy content of a tiny chunk of space  is uncertain, so the corresponding geometry   should be uncertain also.

If we think about this  in terms of virtual particles, then every time one   appears, we should see an accompanying tiny  gravitational field that lasts just for an   instant.

But because these quantum fluctuations  are extremely complex and constantly changing,   the effect on the geometry of space  is also complex and ever-changing.

Virtual particles aren’t even restricted to the  normal rules that real particles have—for example,   negative masses —which means  exotic objects like wormholes can appear   and vanish amid the general roiling  mess of spacetime at the Planck scale.

And because these quantum fluctuations are  actually in a superposition of many different   states, we need to think of the geometry  of spacetime as also being in a quantum   superposition at that scale.

Many, and perhaps  every possible geometry exists simultaneously.

What we see on the macroscopic  scale is the washed out sum of   all Planck-scale configurations—and  it ends up conveniently nice and flat.

We can think of the quantum foam as  being due to an intrinsic uncertainty   in either the stuff space contains or  in the geometry of spacetime itself.

These are two ways to get at the same conclusion:  as long as the uncertainty principle holds in some   reasonable way for gravity, then on the Planck  scale the fabric of spacetime should be foamy.

So now we have a picture of what space might  look like on scales well below our experience,   or even below the experience of atoms or nuclei.

How do we test this?

If the standard picture is right, then quantum fluctuations of spacetime only  become significant near the Planck scale,   which is far, far smaller than any of our  direct probes of spacetime structure—and   that’ll probably be the case until we’re  a super-advanced galactic civilization.

But indirect tests are possible now.

Remember  Wheeler’s analogy of spacetime foam as a choppy   ocean surface.

A gigantic ship doesn’t  notice the waves, but a rowboat does.

A vessel in between may have a relatively smooth  ride, but might be deflected or impeded over   time on a wavy ocean versus a still one.

If  spacetime foam is real, then we might expect   a particle traveling very long distances  to experience a slight shift in its course.

And we can test this with a  surprisingly simple experiment.

A distant point of light can produce diffraction  patterns, for example these diffraction spikes and airy rings if we observe through a telescope aperture or  diffraction fringes through a pair of slits.

Those   patterns are due to individual photons interfering  with themselves after interacting with the gap.

Photons that reach us traveling in the same  direction will experience the same interference.

By catching many such photons, we slowly  build up a single interference pattern.

But two photons coming at even slightly  different angles will land on our detector   according to different interference  patterns.

If we look at many such photons,   those different patterns will be overlaid  on each other and result in just a blur.

That’s why we see diffraction spikes  around stars in Hubble or even JWST images,   but we only see a blurry blob from even our best  ground-based telescopes.

In the latter case,   light from the star is bounced around by our  atmosphere so that it arrives traveling in   slightly different directions.

Well, if spacetime  is foamy then we might expect a similar effect for   light arriving from very great distances.

Stars in our own galaxy are not far enough away,   but some objects like quasars and gamma ray  bursts can be billions of light years distant.

A number of studies have tried to detect the  effect of spacetime foam on the diffraction   patterns of distant objects in Hubble Space  Telescope data.

Hubble is particularly good   because it’s very sensitive to ultraviolet  light—a short wavelength light that should be   more influenced by a turbulent spacetime fabric  compared to, say, the long-wavelength infrared   light that JWST is sensitive to.

So far the best these studies   have been able to do is to rule out certain  models which produce a particularly strong   spacetime foam.

But some of the measurements are tantalizingly close to the needed sensitivity,   so perhaps a bigger ultra-violet-sensitive space  telescope will be able to detect this effect.

More work is needed.

Only then could we really be sure that a tempestuous   ocean of uncertain geometries underlies  our deceptively placid spacetime.