Thank you to Brilliant for supporting PBS. We can all be a little self-absorbed sometimes,
acting like weâre the center of the universe or something. Well first let me tell you where the center of the universe actually is before you decide thatâs 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 doesnât 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 - theyâre philosophical positions
- guiding principles that so far have not led us astray. I think both must be right - but I donât
know for sure. And it sure would be nice to feel special
again. Today weâre 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 itâs 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 theyâre 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 isnât 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 youâre in. In this picture the Big Bang isnât 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 âwhere is the center of the universeâ,
or âwhere did the big bang happenâ and youâll get this basic story for the first
50 pages. And thatâs 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,
letâs 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 wasnât 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 âclosedâ,
âopenâ, and flat.â 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 canât visualize the center of a geometry
if we canât 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 thereâs no edge
and thereâs no center - or at least, no center thatâs 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 itâs 2-D analog, itâs 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 couldnât do it. They canât point âdownâ 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 thereâs a higher dimensional
space in which our 4-D hypersphere lives? Could there be an equivalent of âdownâ
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 thatâs 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 weâve 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 itâs 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. Iâm 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 wouldnât be pointing at the
moon of the present - it would be the moon of the past, because youâre 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. Itâs the same with our universe - point
in any direction and youâre pointing at the Big Bang. And if the universe really is closed, youâre
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 weâve been tracing have a name
- theyâre called null geodesics. Theyâre 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 âgeodesic incompletenessâ. Geodesic incompleteness is just a fancy way
to say âsingularityâ. There is literally no direction that you could
point that would not intersect the Big Bang if traced backwards, and thatâs 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
isnât 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 thatâs
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 - itâs the point where the math
breaks. And thatâs 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 wonât. Thatâs a topic worth itâs own video - although
as a spoiler, the answer isnât 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 Hubbleâs observation of the receding galaxies that doesnât require an infinite
universe, nor a hyperspherically looping universe. And you can do it without breaking Einsteinâs
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 doesnât 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 LemaĂŽtre-Tolman universe inside a greater FLRW universe. And thereâs even a scenario where this might
be the case: thatâs 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 doesnât
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 itâs 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 weâre 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 Earthâs intertidal zones. Iâm 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 didnât start in tidal pools
on Earth, whoâs to say it couldnât have happened that way elsewhere? Relatedly, dmaxcustom asks whether the tidal
force wouldnât resulted in strong tectonic activity. Tidal squeezing should indeed help keep the
planetâs 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 itâs 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 isnât 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
- itâs fundamental and doesnât change. Itâs only equal to helicity for particles
that you canât overtake - aka light speed, massless particles. Sorry we didnât have time to dig deeper
on this. Another time. And back to Proxima for one last comment. Anarchy Antz asks if thereâs any update
on the radio signal from the direction of Proxima detected by the Breakthrough Listen
project. Yes, thereâs 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.
I love this channel so much. Thank you to everyone that contributes behind the scenes as well.
Always challenging, satisfying and engaging while weaving together previous episodes. It's just superbly done.
This episode was so interesting and the setup for a white hole discussion to boot!
The 3D animations with the null geodesics spiraling back in time to the big bang was absolutely beautiful
I hope it's not too gauche to joke about cosmological theories, but the "pool of locally non-inflating space" theory really reminds me of the flat earth theory where the entire earth is nearly flat, but resides on a large sphere of ice