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.
