Space is big, and it’s getting bigger. But where does all that new space actually come
from? And is it popping into existence all around you right now? Is that why the remote
control is always further away than I thought?
Nearly a hundred years ago, a collection of observations and theoretical ideas came together
to reveal the universe is expanding on the largest scales. The distant galaxies are all
racing away from us, and interpreted through the lens of Einstein’s general theory of
relativity, this only makes sense if all distances everywhere are increasing evenly. This revelation
led us to the discovering of the beginning of the universe at the big bang, and lets
us predict its future - it’ll probably expand forever, FYI.
We know the effect of cosmic expansion on the most enormous scales, but what about the
here and the now? If space is expanding everywhere,
is it expanding inside the solar system, inside
you? And what does it even mean for space to be expanding? Does that stretching stretch
space thin? Will it eventually snap like overdrawn taffy? Or does new space get created on the
fly - in which case, where does it come from?
Objects in space tend to move around due to nearby gravitational influences - planets
orbit stars, stars orbit in the mutual gravity of their galaxies, galaxies whirl and collide
in local groups and clusters. But if you expand your view to large enough scales, that local
motion or “peculiar velocity” is small compared to the fact that distant points are
moving apart - receding - and the further distant the faster the recession. We call
this the Hubble flow, after Edwin Hubble, the guy who first measured the rate of expansion.
The Hubble flow could be interpreted as everything moving THROUGH space, but there’s a cleaner
picture. Soon after Einstein finished general relativity, four scientists independently
solved its equation for the entire universe, giving us the Friedman-Lemaitre-Robertson-Walker
or FLRW metric. You can think of a metric as the coordinate system of a patch of spacetime.
Similar to how longitude and latitude and the coordinate system of the 2-D surface of
the Earth, a metric in GR is the coordinate system of a chunk of spacetime with 3 spatial
and 1 temporal dimensions.
And just as latitude and longitude describe the spherical geometry of the surface of the
Earth, the FLRW metric gives the geometry or shape of the universe. The spatial part
of that geometry could be the 3-D analog of our surface of a sphere, which would be a
space that loops back on itself in all directions. Or it could be an infinite plane, either flat
or hyperbolic. These shapes can be thought of as 2-D slices of 3-D spaces. But those
3-D spaces are also just slices out of 4-D spacetimes - representing single instants
in time. If you use general relativity to track how the FLRW metric changes over time,
you find that it has to change - either growing or shrinking in size everywhere evenly.
The FLRW metric makes some pretty big assumptions - that the matter in the universe is perfectly
evenly spread out - homogeneous, and it looks the same in all directions - isotropic. That
seems to be a good representation of the universe on its largest scales. But keep this assumption
in mind. It’ll be important to notice when it’s wrong.
OK, just for laughs let’s look at the math. This is the FLRW metric - it’s basically
Pythagorus for 4-D spacetime - the squared proper distance between two points is the
sum of the squares of x, y & z, but here adding the dimension of time. And this thing is the
scale factor, which represents the overall size of the universe, and this is the thing
that has to change. In our universe it’s getting bigger. When we say “the universe”
or “space” is expanding, we mean the scale factor is getting bigger. But what does that
mean beyond the math? What’s physically happening?
There’s a classic classroom representation of the expanding universe that’s actually
pretty useful here. Glue galaxies to a balloon and inflate. The galaxies recede from each
other with apparent speeds that are proportional to distance. But the balloon analogy isn’t
even really an analogy - at any one instant it’s a fair representation of a 2-D slice
out of a closed universe,
and its growth represents the increase in the scale factor over time.
The FLRW metric - the coordinate grid of this slice could be represented in spherical polar
coordinates. In that case it looks a lot like latitude and longitude. Those lines are smooth
because of our founding assumptions of homogeneity and isotropy. But if we zoom in we can see
that the shape of the gridlines change. They pull towards massive objects like galaxies.
In fact the shape of spacetime around massive objects is NOT the FLRW metric because the
matter isn’t spread out evenly. For example, near a compact massive object the correct
description of the spacetime is the Schwarzschild metric. The space in the Schwarzschild metric
by itself doesn’t expand - in fact space is pulled inwards - pinched - and it’s completely
static over time. But what about if it's embedded in a larger FLRW spacetime? Does the underlying
expanding sphere fight against the inward pull of gravity? Is the space inside, say,
a galaxy growing but overcome by the gravitational attraction between the stars?
The answer is no. Space within any gravitationally bound system is unaffected by the surrounding
expansion. In the balloon analogy it’s tempting to think of the galaxy as being held together
despite the expanding material that it's attached to. But that’s not what’s happening. The
gravitational field isn’t somethin,g that lies on top of the fabric of spacetime. The
gravitational field IS the fabric of spacetime. If the gravitational field of the galaxy is
this static, inwardly-pinched grid of the Schwarzschild metric, then that’s it. That’s
the spacetime in that area. There isn’t another underlying expanding grid that this
field has to fight against. In fact, the spacetime inside the Milky Way doesn’t even know that
the universe is expanding.
The other way the balloon analogy fails is that the fabric of spacetime doesn’t get
stretched in the way the rubber gets stretched - it doesn’t thin out and it doesn’t build
up tension in a way that can pull against these embedded static fields. It’s as though
the balloon adds more rubber as it inflates, always maintaining the same level of stretch.
Let's try something else. Lose another dimension of space so the universe becomes an expanding
ring instead of a ,sphere, with grid points instead of gridlines. But then we can add
the dimension of time into our picture so that the expanding ring traces a sort of cone,
and the points trace lines. This is nice because you can show the changing rate of expansion
- perhaps a period of rapid accelerating growth during inflation, then the expansion slows
under the influence of gravity, then dark energy takes over and expansion accelerates
again.
The expansion of space is seen in the divergence of our FLRW coordinate gridlines. Now the
distance between those lines represents the growing scale factor. Let’s zoom in again.
What does an individual galaxy look like? If the galaxy causes gridlines to be pulled
together on a sphere, then on the ring it causes points to be pulled together, and they
maintain that separation as the ring expands. So on our expanding cone, we see distant gridlines
diverging, but nearby lines in a gravitational field remain parallel.
So there is no constant tug of war between the expanding universe and the gravitationally
bound systems it contains. That tug of war did happen, but it happened a long time ago.
In certain regions expansion won, and threw apart objects and the spacetime grids they
trace. But in sufficiently dense regions gravity won and there the only evidence of the greater
expansion comes from the receding view of distant galaxies.
I told you that space doesn’t get stretched out like rubber. In a sense new space gets
created as it expands. But what does that actually mean? Well this is a tough one - in
fact an impossible
one because we don’t have an accepted theory for what that the fabric of space is actually
made out of, if anything. That’s the province of a long-sought theory of quantum gravity.
But let’s see what we can say.
In general relativity, space can be infinitely divided. That means we can start with a universe
that’s small and grid it up and watch it expand. The grid lines diverge, but we can
choose to re-grid it at any point. What was once a millimeter might become a meter and
the meter becomes a kilometer, but we can just redefine everything and start again.
We’ll never run out of subdivisions. Similarly, we can take the universe of the present and
define a grid of space - or a grid of points on our 1-D ring universe. Then we rewind the
universe and every single one of those points traces a path back to the big bang. We can
make the starting grid as fine as we like and get the same result. Every point in the
modern universe can be traced back to a point at the big bang.
This is related to the idea of geodesic completeness,
which we’ve talked about before. All spacetime
paths can be traced to the infinite future or past until they hit a singula,rity - the
big bang or a black hole. As the universe expands, we don’t have new patches of space
appearing between the old ones to fill out the universe. Geodesics don’t just pop out
of nowhere.
This all works if space is infinitely divisible. But we know that at the smallest scales, general
relativity comes into conflict with quantum mechanics. There is a smallest measurable
length called the Planck length. When space expands, what happens to this smallest length?
Does it expand too? Well the Planck length stays the same - it’s just defined as a
combination of the Gravitational constant, the Planck constant, and the speed of light
- so if those aren’t changing - and there’s no evidence that they change -then the Planck
length remains the same. But as the universe expands it adds more and more of these “Planck
lengths” which must expand out of the old Planck lengths. That implies an infinitely
divisible space emerging from within each Planck length.
This apparent conundrum is related to something called the transplanckian problem, which is
to do with how Hawking radiation seems to emerge from sub-Planck-wavelength radiation
at the event horizon of a black hole. Its solution takes us to the realm of the holographic
principle, and so we can’t go there today. But long story short - even with a quantized
fabric of space, it’s still possible to expand it or condense it infinitely without
changing its fundamental nature. Empty space can be rescaled infinitely.
And that’s even true if empty space contains something. Like dark energy. Empty space has
a very weak energy density, even in the absence of particles. As space expands, that density
doesn't change - remember, the balloon skin doesn’t thin out. The result of this is
that the total dark energy content of the universe depends on the amount of space in
the universe, which means dark energy increases as the universe expands. But again, this will
never have any effect inside bound gravitational systems. Its effect only manifests when there’s
an enormous amount of empty space compared to the amount of matter. But the ratio of
empty space to matter inside galaxies doesn’t change. Now if the level of dark energy per
unit volume were to increase, that would be a different matter - and we talked about the
resulting cataclysm in our episode on the big rip.
So there’s your answer. The infinite scalability of space means the universe can and probably
will expand forever with no effect on this little bubble of relatively static space that
we call the Milky Way. Well, except for permanently
isolating our bubble from all of the others.
Let’s just be grateful that we came into being soon enough to catch a glimpse of those
receding galaxies - they will spend most of cosmic time far beyond the horizon, in which
case we never would have even known that we live in an infinitely expanding spacetime.
Today we’re looking at your comments for the last two episodes - there was the one
on John Archibald Wheeler’s Participatory Universe, and the episode on the Higgs mechanism
and the mass of the W boson. Let’s do the latter first.
247tubefar asks How the heck do you weigh a subatomic particle? Good question. Riley
Schroeder quips “carefully and hypothetically” - which is correct in the sense that you don’t
measure it not directly, like, not with a subatomic set of scales. Fernando, who was
one of the three of us who pulled our hair out writing this episode, gave the correct
answer: when a charged particle is created in a particle collider it travels through
the powerful magnetic fields of the detector. The amount by which its path is deflected
by that field depends on its mass. In the case of the W boson, the particle actually
decays too quickly to measure its mass “directly”, but you can measure the masses and kinetic
energies of its decay products and determine the mass of the W.
Some of you reasonably point out
that it is potentially misleading to use terms like “observation” or “conscious awareness”
as the causal event that collapses the wavefunction,
or in this case manifests the universe. Rather
than for example saying that “interaction” is doing the work. It’s very true that the
choice
of phrasing has led to all sorts of misunderstanding
and quantum charlatanry. But I think the reason
people like Wheeler and Bohr used these terms is because their conscious observation of
the system is literally the only event that they can be sure actually happened. They were
being philosophically honest by adhering to pure, stripped down logical inference in the
style of Descartes. They felt it dishonest to start their train of reasoning with statements
about external factors that they couldn’t directly observe. Unfortunately, practitioners
of quantum woo are not so careful and definitely not so honest.
Lyman Brown-Whitehill reminds us that the participatory isn’t the first of Wheeler’s
wacky-sounding ideas. The other famous one is the one-electron universe, in which all
electrons are actually the same electron bouncing back and forward in time. Wacky as they are,
they tend to have legs these ideas. In his Nobel prize acceptance speech, Richard Feynman
admitted to
stealing the time-traveling electron thing from his advisor, and using it to help develop
quantum electrodynamics. So what can we build using ideas from the participatory universe?
Meatsauce Z asks us to address the elephant in the room. If the participatory universe
interpretation is true,
then what are entities that initiated the first interaction that brought everything
into being? Actually, I think this is exactly the issue the Wheeler was trying find his
way around - the issue of infinite regress. How to you identify a founding cause by tracing
the causal chain backwards? In Wheeler’s mind, the only universe that can exist is
the one that causes itself. That’s what he meant by a “self-excited circuit”.
It put me in mind of the way the electron in the admittedly outdated Bohr model of the
atom in a sense “creates itself” by constructive interference - only electrons whose wavefunction
peaks and valleys line up on each orbit can exist. Maybe the universal wavefunction is
the just that wavefunction in the space of
infinite possible wavefunctions that constructively
interferes to reinforce its own existence.
Speaking of which, several of you notice that this video was posted on 4/20. I swear that
was a coincidence. Like whoah dude.