Thank you to Brilliant for supporting PBS.
We can all be a little self-absorbed sometimes, acting like we’re the center of the universe
or something.
Well first let me tell you where the center of the universe actually is before you decide that’s
where you are.
For most of history all of humanity has been pretty self-absorbed, astronomically speaking.
We imagined the earth the center of the cosmos until Nicolaus Copernicus shoved us from our
pedestal onto a random rocky planet orbiting an ordinary star in the outskirts of an unremarkable
galaxy.
Ever since then, astronomers have embraced the Copernican principle, which states that
we are NOT in a special place in the universe.
At least, once you factor out the selection biases of needing to be somewhere moderately
hospitable.
And the Copernican principle inspired another important idea - not only are we not the center
of the universe, but the universe doesn’t have a center.
Once you zoom out far enough, the universe looks basically the same everywhere.
This is called the Cosmological principle.
But neither the Copernican principle nor the Cosmological principle are actual laws of
physics - they’re philosophical positions - guiding principles that so far have not
led us astray.
I think both must be right - but I don’t know for sure.
And it sure would be nice to feel special again.
Today we’re going to ask a simple-seeming question that will lead to so pretty wacky
places.
The question is this: If the universe has a center, where is it?
You might imagine that the center of the universe is the place where the Big Bang happened.
The origin of the explosion that created everything. This would be wrong, but it’s easy to understand
the misconception.
Thanks to Edwin Hubble, we know that distant galaxies are racing away from us - and the
further we look, the faster they’re moving.
It looks like the Milky Way is at the center of an colossal explosion, or as Calvin more
poetically named it - a horrendous space kablooie.
But the Big Bang isn’t an explosion emanating from one point in space.
The recession of the galaxies is just as well explained if all of space is expanding evenly
everywhere.
Galaxies appear to be receding due the space between them stretching.
Most importantly, this looks the same no matter what galaxy you’re in.
In this picture the Big Bang isn’t something that happened at a single point in space,
instead it happened everywhere at the same time.
All space was created at that instant.
Google “where is the center of the universe”, or “where did the big bang happen” and
you’ll get this basic story for the first 50 pages.
And that’s because this story is probably right.
But today I want to dig deeper and see what assumptions are behind this interpretation,
and also ask what it would mean if those assumptions are wrong.
But before we mess with the standard narrative, let’s make sure we understand what it is.
As with much, it starts with Einstein.
His general theory of relativity explains gravity as the warping of space and time due
to the presence of mass and energy.
Explains gravity as the warping of space and time due to the presence of mass and energy.
General relativity can be used to calculate the spacetime curvature produced by the Earth
or the Sun to determine their gravitational effects.
It can also give us the gravitational field of the entire universe, which tells us the
shape of all of spacetime.
It wasn’t actually Einstein who worked this out.
The first to solve this was Alexander Friedman - he ignored all those little gravitational
bumps - doing the mathematical equivalent of grinding up everything into the universe
into a fine paste and spreading it evenly through space.
That gave him equations of motion that described how the universe must evolve.
And a shape, defined by something called the Friedman-Lemaitre-Robertson-Walker metric,
also named for those three other guys who came up with it right after Friedman.
This simplification really paid off.
For one thing it predicted that the universe could not be static - it had to be contracting
or expanding, and that as more than a decade before Hubble discovered it was the latter.
The FLRW metric also predicts that there are only three possible global shapes to 4D spacetime,
determined entirely by one number- the curvature.
Depending on whether the average curvature is positive, negative, or zero, we get one
of three shapes- which we call ‘closed’, ‘open’, and flat.’
The exact shape is determined by the relative amounts of matter and dark energy in the universe.
The presence of matter increases the curvature and the presence of dark energy decreases
the curvature.
We can’t visualize the center of a geometry if we can’t fit it in our heads.
In order to do that we need to lose a dimension.
Positively curved 3D space is the easiest.
First imagine the surface of a sphere.
That surface is 2-dimensional.
But for a 2-D being living on that surface, those two dimensions are all that exists.
The surface is finite, but there’s no edge and there’s no center - or at least, no
center that’s part of the 2-D universe.
A closed 3-D universe is like the 3-D surface of a 4-dimensional hypersphere.
And just like it’s 2-D analog, it’s finite and center-less.
If I were to ask a denizen of the surface of the sphere to point to the center of the
universe, they couldn’t do it.
They can’t point “down” to the center of the sphere, because to them there is no
down.
But from our perspective that direction exists.
So could it be that there’s a higher dimensional space in which our 4-D hypersphere lives?
Could there be an equivalent of “down” in that space that we are just too dimensionally-challenged
to point to?
Not necessarily.
Space can have curvature without there being anything for it to curve into.
And that’s the most straightforward interpretation of the FLRW metric for a closed universe.
Those three spatial dimensions just loop back on themselves.
But actually, we can sort of give a location for this expanding hypersphere - because at one point we were
at that center.
So far we’ve ignored the dimension of time.
Our universe is expanding.
In the case of the closed universe, that means it started out as a very, very tiny hypersphere
surface and got bigger.
So, very crudely, we can think of the radial direction as the dimension of time.
It would be more accurate to say that the radial dimension of this expanding hypersphere
is represented in the math by the scale factor - and the scale factor increases as time increases.
But it’s fun to think of the center of the expanding hypersphere as being a location
in time.
That means we really CAN point to the location of the Big Bang - by pointing to the past.
And conveniently, you can point to the past - by pointing in any direction whatsoever.
I’m serious, hear me out.
You can point at, say, the moon by ensuring that a line drawn from your outstretched finger
intersects would intersect the moon.
Of course your wouldn’t be pointing at the moon of the present - it would be the moon
of the past, because you’re aligning your finger with the light that only now reached
you from the moon, and that light has been traveling one second ago.
Now imagine that 2-D dweller points at a random direction.
Draw a line in that direction and at the same time reverse the flow of time to see what
it intersects.
The line loops around the closed universe as the sphere shrinks, until eventually all
points in the universe, including the pointed line, coincide with the center.
It’s the same with our universe - point in any direction and you’re pointing at
the Big Bang.
And if the universe really is closed, you’re also pointing at the point where all space
occupied the geometrical center of the hypersphere.
A lot of this stuff is also true for a flat or open universe.
The 2-D analog of the flat universe is an infinite flat plane, while the open universe
corresponds to a sort of saddle shape - what we call a hyperbolic plane - which also stretches
on forever.
In both of these cases there is no geometrical center, even in a fictional higher dimension.
However you can still point at the Big Bang by pointing in a random direction, because
the line traced from you finger also ends up at the beginning of time.
These lines we’ve been tracing have a name - they’re called null geodesics.
They’re the grid that defines the fabric of space time in general relativity, and correspond
to the paths followed by light.
No matter the geometry of our FLRW universe, all geodesics converge to a single point in
the past, and end there.
In the language of GR, we call this ending of spacetime paths “geodesic incompleteness”.
Geodesic incompleteness is just a fancy way to say “singularity”.
There is literally no direction that you could point that would not intersect the Big Bang
if traced backwards, and that’s true anywhere in the universe.
We say that the Big Bang is a past, space-like singularity - which means it occupies all
space at t=0 and is in the past of all paths through spacetime.
OK, so maybe the location of the Big Bang isn’t at one point in this universe.
But can we still say that the Big Bang happened at one point?
I mean, if all points converged onto the same point at the beginning - if all geodesics
emerged from that point - does that mean the universe started out point-like?
In the case of the closed universe that’s easier to imagine - rewind the growing sphere
and it approaches a single point at t=0.
But what about an infinite universe?
The math of the FLWR metric and the Friedman equations tell us that as time approaches
zero, the distance between any two points approaches zero.
But at the same time there are infinite points.
So did the universe start out pointlike at t=0 and then suddenly become infinite in size?
Well the size of the universe at t=0 is zero times infinity … which is neither zero nor
infinity - it’s the point where the math breaks.
And that’s the nature of singularities - they are discontinuities in the math we use to
describe the universe.
They probably also represent places where our understanding of physics breaks apart.
Stand by for our theory of quantum gravity to resolve that one.
By the way, there are close parallels with the singularity of the black hole.
We might ask whether the Big Bang is a reverse black hole - also called a white hole.
We might, but we won’t.
That’s a topic worth it’s own video - although as a spoiler, the answer isn’t as obviously
in the negative as you might think.
OK, so we have the state of the current wisdom on the shape of the universe, and the non-existence
of its center.
But I promised to tell you how this might not be true.
Remember that Alexander Friedman came up with his solution for the shape of the universe
by assuming that matter and energy are evenly spread out everywhere.
He assumed a homogeneous universe and assumed the cosmological principle.
But what if he was wrong?
It turns out there are ways to make sense of Hubble’s observation of the receding
galaxies that doesn’t require an infinite universe, nor a hyperspherically looping universe.
And you can do it without breaking Einstein’s general relativity.
One of the alternative solutions was discovered by Georges Lemaitre, the L in the
FLRW metric.
Lemaitre asked what the universe might look like if it was NOT homogeneous.
He sought solutions to the Einstein equation for a universe that is lumpy on the largest
scales.
In one of his solutions, matter was distributed with constant density across a spherically
symmetric cloud, but beyond that cloud the density could change, or space could be empty.
He found that an observer in a sufficiently large cloud that was expanding or contracting
would observe an expanding or contracting universe that looks exactly like a FLRW universe.
At around the same time, Richard Tolman made the same discovery, and so we have the Lemaitre-Tolman
metric. Such a universe would have a center - the
center of the cloud, assuming the cloud is finite.
I should point out that this doesn’t necessarily break the Cosmological principle because it
could still be that our bubble is small on the most ridiculously gigantic scales, and
that if you zoom out to many, many, many times larger than the observable universe, everything
evens out smoothly.
So you can find a Lemaître-Tolman universe inside a greater FLRW universe.
And there’s even a scenario where this might be the case: that’s eternal inflation, which
proposes that our universe is just one bubble of relatively slowly expanding space embedded
within an unthinkably colossal region of exponentially accelerating space.
Check out our episode on that for that insane-seeming proposition.
Long story short: the universe probably doesn’t have a center, and if it does we may never
know - the evidence of there being a boundary to our bubble is very likely far beyond our
cosmic horizon.
In that case then as far as we know there could be a center and we could be at it.
So go ahead and get right back on that pedestal - we know it’s almost certainly not true,
but no one is ever going to prove that the earth, humanity, even you personally, are
not at the very center of a very non-Copernican spacetime.
Thank you to Brilliant for supporting PBS.
To understand astrophysics, Brilliant believes it helps to have a solid understanding of
relativity.
Brilliant has a lesson on special relativity that includes interactive challenges and problems
to solve.
A hands-on approach can guide you through thinking strategies for challenging subjects
like relativity.
It starts out explaining relativity in terms of boats passing by each other on a river,
then goes into some puzzles that require changing perspective (like the ball stack bounce),
and then goes into the speed of light and even time travel!
To learn more about Brilliant, go to Brilliant.org/Spacetime.
Today we’re answering questions from the last two episodes - the one where we explored
the Proxima system in search of habitable worlds, and the other one where we asked whether
electric charge really is a fundamental property of nature.
Starting with Proxima.
Palindromeordnijap asks whether the massive tides that the Proxima planets experience
might be ideal for life due to the rich biodiversity of Earth’s intertidal zones.
I’m no expert, but I do remember that for a while tidal pools where thought to be a
likely location for abiogenesis - the origin of life.
That seems to have fallen out of favor, with geothermal vents and hot springs providing
more promising temperature gradients and general chemistries.
But even if life didn’t start in tidal pools on Earth, who’s to say it couldn’t have
happened that way elsewhere?
Relatedly, dmaxcustom asks whether the tidal force wouldn’t resulted in strong tectonic
activity.
Tidal squeezing should indeed help keep the planet’s interior hot, just like it does
on the volcanic moons of Jupiter and Saturn.
For a planet that would presumable help drive tectonic activity.
On Earth, tectonic activity is essential for life due to its role in the carbon cycle.
Life draws carbon from the atmosphere and sequestered in the crust.
As the crust is pulled into the hot mantle, that carbon is released again in volcanic
activity.
Without that recycling Earth would have frozen due to the absence of greenhouse effect.
A hot interior may also have been essential for abiogenesis - if life really did first
start around geothermal vents or hot springs.
So in short those tidal forces on those Proxima planets may make it more likely that there's life.
Al H asks what particles and interactions existed before the electroweak force split
into electromagnetism and the weak force.
Well, the big one is that the elementary particles were massless back then due to the absense of the Higgs mechansism.
Also, before that split, particles could transfer their isospin a lot more easily.
That means there was not much of a difference between Up and Down quarks or between electrons
and their neutrinos.
Just like it makes no sense to distinguish electrons with up or down spin as different
particles.
In fact the universe seemed to be made of only six particles, three quarks and three
leptons.
When the universe cooled down and the electroweak symmetry was broken, particles were locked in whatever isospin state
they happened to be in.
They gained different properties depending on their isospin state and on their the newly gained
mass.
TheGundeck asks whether chirality depend on the observers reference frame, given that
it’s defined in reference to the momentum vector of the particle.
For example, if a particle races past you you observe its chirality based on its direction
of motion.
What happens if you then you accelerate and overtake the particle so it appears to be moving in the reverse
direction.
Does its chirality flip?
Does that mean it stops interacting with the weak force?
The answer is that chirality isn’t as simple as a projection of spin onto the momentum
vector.
That spin projection is actually called helicity, and it does change depending on your reference
frame.
But chirality is what we call Lorentz invariant - it’s fundamental and doesn’t change.
It’s only equal to helicity for particles that you can’t overtake - aka light speed,
massless particles.
Sorry we didn’t have time to dig deeper on this.
Another time.
And back to Proxima for one last comment.
Anarchy Antz asks if there’s any update on the radio signal from the direction of
Proxima detected by the Breakthrough Listen project.
Yes, there’s an update.
Radio astronomer Sofia Sheikh found around 60 similar signals that were not clearly
associated with stars and had radio frequency spacing similar to Earthly oscillators.
So it looks like local interferenced.
Or in other words, the Proximans realized we were onto them and hacked the database
and injected fake signals to put us off their tracks.