If the universe is expanding, are we expanding too?

The fabric of expanding space means that the farther away a galaxy is, the faster it appears to ... [+] recede from us. The space between individually bound objects is surely expanding; that much we can measure. But what about bound objects in that space itself?

NASA, Goddard Space Flight Center

One of the most revolutionary discoveries of the past century was the fact that the Universe is not eternally static and unchanging, but rather is actively in the process of expanding. Some 13.8 billion years ago, in the earliest stages of the hot Big Bang, our observable Universe was no bigger than the size of a city block, and may have been as small as a soccer ball; today, it extends for more than 46 billion light-years in all directions. If the Universe is expanding, then what does that means for the objects in it? Are galaxies expanding? What about stars, planets, human beings, or even atoms themselves? That’s what Harald Hick wants to know, writing in to ask:

“In the ‘raisin bread’ model of the expanding Universe, do the raisins expand as well? Which means, do all atoms grow in size as the universe is expanding?”

It’s a deep question, and its answer might not be what you expect. Here’s how to figure it out.

We often visualize space as a 3D grid, even though this is a frame-dependent oversimplification when ... [+] we consider the concept of spacetime. In reality, spacetime is curved by the presence of matter-and-energy, and distances are not fixed but rather can evolve as the Universe expands or contracts.

ReunMedia / Storyblocks

When Einstein first put forth his new theory of relativity, it forever changed how we think of space and time. Space isn’t fixed like a three-dimensional grid, with universally agreed-upon distances between any two points. Nor is time a continuously flowing entity, where you can sync up your clocks, move anywhere you like, and be confident that your clock reads the same as anyone else’s. Instead, we experience space and time as relative: your motion through space affects your motion through time, and vice versa.

This was the core idea behind Special Relativity, which led us to discard our older ideas of “absolute space” and “absolute time,” instead replacing them with the notion of spacetime. As you move through space relative to another observer, your clocks appear to run differently, according to Einstein’s laws. Special Relativity works perfectly for all observers whether they’re at rest or in motion, and represented an enormous leap in understanding our Universe over Newton’s original laws of motion.

A light-clock, formed by a photon bouncing between two mirrors, will define time for any observer. ... [+] Although the two observers may not agree with one another on how much time is passing, they will agree on the laws of physics and on the constants of the Universe, such as the speed of light. A stationary observer will see time pass normally, but an observer moving rapidly through space will have their clock run slower relative to the stationary observer.

John D. Norton

But this idea, brilliant though it was, didn’t include gravity. The old Newtonian picture of gravity was inherently tied to absolute notions of distances and times, and was incompatible with the notion of spacetime. It took over a decade for Einstein to bring gravity into the fold, taking us from Special Relativity to General Relativity: incorporating matter and energy into the equation.

Instead of the flat spacetime of Special Relativity, the presence of matter and energy allowed for space-and-time to be dynamic entities. No longer bound to be static, the Universe could expand or contract, depending on what was in it. Matter and energy told spacetime how to curve, and that curved spacetime dictated how matter and energy would move.

The gravitational behavior of the Earth around the Sun is not due to an invisible gravitational ... [+] pull, but is better described by the Earth falling freely through curved space dominated by the Sun. The shortest distance between two points isn't a straight line, but rather a geodesic: a curved line that's defined by the gravitational deformation of spacetime.

LIGO/T. Pyle

This relationship, first put forth more than 100 years ago, has been tested by an enormous suite of experiments and observations, with Einstein’s theory passing each and every one. General Relativity applies not only to the gravity we find on Earth and elsewhere in the Solar System, but on vast cosmic scales that dwarf our own: galaxies, clusters of galaxies, and even to the entire Universe itself.

This last part is particularly fascinating: if we take a Universe that’s (on average) uniformly filled with matter and/or energy — including a combination of different forms of matter and/or energy — that Universe must either expand or contract. It cannot remain in a static state for more than an instant, even if it starts off in one. In 1922, Alexander Friedmann demonstrated this, deriving from Einstein’s theory the Friedmann equations: the equations that govern the expansion of the Universe.

A photo of the author at the American Astronomical Society's hyperwall, along with the first ... [+] Friedmann equation (in modern form) at right. Dark energy could either be treated as a form of energy with a constant energy density or as a cosmological constant, but exists on the right-hand side of the equation.

Perimeter Institute / Harley Thronson / E. Siegel

The very next year, Edwin Hubble measured the distance to Andromeda, determining that this “spiral nebula” was in fact its own galaxy far beyond and outside the Milky Way. Subsequently, we measured distances to large numbers of galaxies while also independently obtaining measurements of the light coming from them. What we found, almost universally, was the following.

1. The farther away a galaxy was, the redder its light was.
2. That this was true even though the stars inside the more distant galaxies were, on average, intrinsically “bluer” than the stars we seen in nearby galaxies.
3. The explanation for this was consistent with the idea that light — emitted by galaxies with the same frequencies and wavelengths that light is emitted by here in our own galaxy — was being redshifted by the expansion of the Universe.

Alternative explanations such as “tired light” disagreed with the observations, leaving only those explanations that included the expanding Universe as viable. When taken all together, there was no escaping that conclusion: the Universe itself was expanding, and that expansion was responsible for the observed redshift of light that originated from far away.

This simplified animation shows how light redshifts and how distances between unbound objects change ... [+] over time in the expanding Universe. Note that the objects start off closer than the amount of time it takes light to travel between them, the light redshifts due to the expansion of space, and the two galaxies wind up much farther apart than the light-travel path taken by the photon exchanged between them.

Rob Knop

While many popular conceptions show the expanding Universe as balloon-like, this analogy has its flaws. For one, our Universe has three dimensions of space (and one of time, making up a four-dimensional spacetime), not two. A balloon has a meaningful “center” where putting air into it causes the two-dimensional surface to expand. Contrariwise, our Universe has no well-defined center, but, in accord with Einstein’s relativity, depends on the observer.

Instead, perhaps the best analogy is a leavening ball of dough with raisins in it: raisin bread. If you imagined this ball of dough as the fabric of (our three-dimensional) space and the raisins as objects within it, you could identify any “raisin” as yourself: the observer. From your perspective, the raisins would appear to move away from you, with the more distant raisins appearing to recede more rapidly and severely than the closer ones. In reality, the raisins themselves aren’t moving relative to the space they occupy, but rather the space between those raisins is expanding, causing their emitted light to redshift before reaching our eyes.

The "raisin bread" model of the expanding Universe, where relative distances increase as the space ... [+] (dough) expands. Note that the raisins themselves are not expanding, only the dough is. However, individual raisins will appear to move away from all other raisins dependent on the distance between them.

NASA / WMAP science team

But what about the objects that the raisins themselves represent? Does the space that’s inside them expand as well? We can do a calculation to determine what that expansion would look like.

The expansion rate of the Universe, as we measure it (even with our current ongoing controversies), is somewhere around 70 km/s/Mpc, which means that for every Megaparsec away a “raisin” is, we’ll see it appear to recede at 70 km/s. Unfortunately, Megaparsecs are enormous: about 3.3 million light-years. If we scaled that down to the size of planet Earth — which is more like 12,700 km in size — we’d expect to see the Earth expanding by about 0.1 millimeters-per-second. Over time, that would add up significantly, and we’d notice.

Our detailed measurements show that, at least on Earth, objects aren’t expanding. Even with the enormous scale of the Universe and the relatively tiny size of the planet and the objects on it, it’s possible to do experiments to tell. The LIGO gravitational wave detectors are sensitive to changes in distance as small as less than 0.1% the width of a proton. Quantum mechanical experiments can measure the properties of atoms down to precisions of 1-part-in-billions, and precise measurements from decades or even a century apart can be compared. The answer is in, and we know: neither the Earth nor the atoms on it are changing in this fashion over time.

Aerial view of the Virgo gravitational-wave detector, situated at Cascina, near Pisa (Italy). Virgo ... [+] is a giant Michelson laser interferometer with arms that are 3 km long, and complements the twin 4 km LIGO detectors. If the Earth were changing in size due to the expanding Universe, these gravitational wave detectors would have seen it.

Nicola Baldocchi / Virgo Collaboration

This is expected if you think about what the expanding Universe is working against: actual forces. On the one hand, we have the forces between objects: the electromagnetic, gravitational, or any other fundamental force you’d like to consider. If the Universe weren’t expanding at all, you’d be able to calculate the size of anything — atoms, the Earth, the galaxy, a group/cluster of galaxies etc. — just by understanding the physical forces at play and the dynamics of the particles/objects involved.

In these systems, and in fact in any bound system (regardless of what force binds it), the forces involved cause dynamics that are greater in magnitude than the expanding Universe can cause. It’s an excellent approximation to state what you’ll frequently hear physicists say: that it’s only the space between bound objects that expands. For bound objects themselves, the forces at play overwhelm the dynamics of the otherwise expanding Universe, and the expansion is overcome.

This snippet from a structure-formation simulation, with the expansion of the Universe scaled out, ... [+] represents billions of years of gravitational growth in a dark matter-rich Universe. Even though the Universe is expanding, the individual, bound objects within it no longer expand. Their sizes, however, may be impacted by the expansion; we do not know for certain.

Ralf Kähler and Tom Abel (KIPAC)/Oliver Hahn

But that doesn’t mean the expanding Universe isn’t playing any role at all. If we consider a point mass in an otherwise empty, non-expanding Universe, it would behave as an uncharged, non-rotating black hole: a Schwarzschild black hole. There would be an event horizon of a fixed radius: the Schwarzschild radius, which is solely determined by its mass. But if you throw in an additional ingredient — such as a bit of dark energy (or a cosmological constant), one of the forms of energy present in our realistic Universe — things change in a slight but important way.

That outward “push” causes the Universe outside the event horizon to expand, but it also causes the location of the event horizon to be pushed out just a little bit over where it would be in an otherwise empty Universe. The difference is extremely tiny, imperceptible with realistic values for the energies and masses found in our Universe, but it illustrates an point: the expansion of the Universe does affect the objects within it, but it does so by changing the value of their “equilibrium” size, not by causing them to expand.

Both inside and outside the event horizon of a Schwarzschild black hole, space flows like either a ... [+] moving walkway or a waterfall, depending on how you want to visualize it. Placing a black hole in a spacetime that is expanding doesn't cause the event horizon to expand, but simply pushes its horizon out to a slightly greater radius.

Andrew Hamilton / JILA / University of Colorado

We still don’t know whether the space that’s here on Earth — from the space in our atoms to the space surrounding our planet to the space throughout our galaxy — is affecting the equilibrium values of the size of the objects within it. We measure objects as they are, and any differences that may arise from the expansion of the Universe do not affect what we measure at the precision we’re capable of measuring them. The effects of the expanding Universe only begin appearing in what you might consider a transition zone: at the outskirts of structures that are very close to the border of being bound versus unbound.

But we can be certain that atoms, humans, planets, stars, and galaxies aren’t expanding along with the expansion of the Universe. The only effect that the expanding (or contracting) Universe can have on already-bound structures is to slightly change their sizes: by increasing (or decreasing) it from the additional effect introduced by expanding space. As astrophysicist Katie Mack so beautifully put it:

“The Universe is expanding the way your mind is expanding. It's not expanding into anything; you're just getting less dense.”

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