Hey Crazies. We’re gonna cover some big questions today.
Is the universe really infinite? Does it have an edge?
How can it be flat? What’s up with this mole on my...
Ok, maybe not that last one. Before we even try to answer these, we’re
gonna need to clarify some things.
First, the word “Universe” can mean a bunch of different things.
Merriam-Webster says the scientific definition is:
“All of space and everything in it including stars, planets, galaxies, etc.”
But when most people refer to the universe, they’re only talking about all the stuff
that we can see. That’s what astronomers call the “Observable
Universe” and it’s definitely not infinite. In every direction, we see a blotchy shell
of hydrogen atoms completely enclosing us. The light from these atoms is called the cosmic
microwave background, or CMB, and it’s coming from a distance of about 13.8 billion light-years
away. So you might be inclined to say the observable
universe is: 27.6 billion light-years across. But the speed of that light is finite, so
the farther out we look, the further back in time we look.
If this was emitted from 13.8 billion light-years away,
then it was emitted from there 13.8 billion years ago.
So it gives us a good estimate for the age of the observable universe, but not its size.
Just, just stop and think about this for a minute.
What you’re looking at is the formation of the first ever hydrogen atoms.
This is what the whole observable universe looked like 13.8 billion years ago.
Eh OK, to get the current size, we need to adjust for the time difference.
Space has expanded since that light was emitted, so the edge is now 46.5 billion light years
away. Meaning the observable universe is 93 billion
light-years across. Very big, but still finite!
However, the observable universe is probably not the entire universe.
Everything we’re capable of observing must be within our past light-cone.
The rest is behind a cloak of invisibility known as the cosmic horizon.
Since that horizon grows over time, you’d expect it to reveal more things to us.
Unfortunately, the universe seems to be accelerating in its expansion,
so the galaxies are moving farther apart faster than the cosmic horizon grows.
The observable universe is getting lonelier as time goes on.
But what about the entire universe? Is that infinite?
Well, that depends on a few things.
We're going deep!
Since we can’t measure anything beyond the cosmic horizon,
we're going to have to be creative with the stuff inside it.
Two things will help with this: curvature and topology.
Basically, we need to know both local and global properties.
and, since local stuff is easier to understand, let’s start with curvature.
How local?
Infinitesimally local!!
Considering the scale of the observable universe, you might think this box is pretty local,
but that’s far too big for fundamental physics. o then you might make the box smaller like
this. Not small enough!
If there’s any kind of real size to that box, then all you’ll ever see is an average
curvature and you all know how I feel about averages.
It's a number that only exists on paper. It has no physical meaning.
What we need is an “Infinitesimal” box
a size that’s infinitely small, yet still not zero.
When it comes to representing curvature those infinitesimals come packaged in something
we call a “Metric.” and each metric can be written using a wide
variety of coordinates. Meh, let me just show you.
If you want to take spacetime and divide it into infinitesimal pieces
those pieces will have 4 dimensions: 3 for space and 1 for time.
A different choice of coordinates can change the shape of those pieces
but curvature can change their shape and size. A metric puts all this information in one
place and gives us everything we need to develop
concepts about: length, distance, volume, or even the passage
of time. This is what we need to understand what the
universe looks like. Just keep in mind, these little pieces aren’t
necessarily real physical pieces. They’re just imaginary pieces that help
us write equations.
Speaking of which.
Behold! The Friedmann–Lemaître–Robertson–Walker metric.
or FLRW metric for short.
Yes, there’s a lot going on here, so let’s try to make better sense of it.
We could actually write it as simple as this, where this “a” is called the scale factor
representing the universe's expansion. So, basically, this tells us that space expands,
but time doesn’t. If we wanted to get more information out of
it, we could write it like this, which tells us the overall curvature of spacetime
is inward and outward. That means the universe is “spherically
symmetric” or “isotropic,” but a better way to put that is that it looks
the same in all directions.
So, what does this mean for the size of the universe?
I’m getting there, Ok?
The size of the universe hinges on wherever
this “k” falls on the number line. If it’s exactly zero, the universe is called
“Flat.” Side note! Flat doesn’t mean like a piece
of paper. It just means that any shape in any slice
of the spacetime has the same properties as that shape if it
were on a piece of paper. The universe is most definitely not a piece
of paper. End of side note!!
The easiest shape to consider is a triangle.
Angles in a flat triangle add to be exactly 180 degrees,
so that’s what they’ll do in a “flat” spacetime.
If the “k” is positive though, angles in a triangle will add to be more than 180
degrees. The universe could have sphere, ellipsoid,
or even donut shaped slices. If the “k” is negative, angles in a triangle
will add to be less than 180 degrees. Slices could be shaped like a hyperboloid.
So what does this mean for the size of the universe!?!
Alright alright!
If the universe has positive curvature, it
cannot be infinite. It must curve back on itself and be finite
with no edges. If the universe is “flat” or has negative
curvature, it could be either finite or infinite. It depends on topology!
We mentioned earlier that a sphere and a donut have the same type of curvature.
but they don’t have the same topology because of this giant gaping hole.
To know the shape of the universe completely, we need to know its topology.
This is where things get super tricky.
We can only take measurements in our observable part of the universe,
so it might be impossible to measure topology, but we can definitely do curvature.
And if the universe has positive curvature, we know it’s finite regardless of topology.
We can draw a triangle, measure the angles, add them up, and we get exactly 180 degrees.
Grrrrr, I refuse to accept the universe is flat!
We’re gonna need a bigger triangle. Let’s use the CMB from earlier. The Earth
can be one corner. Then we’ll pick the other two corners to
be in hydrogen emitting the CMB. We know the lengths of all the sides, so we
can get the angles too. Yeah trig!
Adding up the angles we get exactly 180 degrees.
[Groaning Noises]
OK, using an unimaginable amount of data collected
from the Planck space telescope, we see that the universe is pretty flat.
That doesn’t mean the universe is infinite though.
This is an example of a flat finite universe. It’s kind of like a soccer ball with flat
faces. But most cosmologists don’t get behind topologies
like that. This is one of those places that Occam’s
Razor becomes important. Which says: When presented with two competing
hypothesis explaining an observation. You should err on the side of caution and
start with the one with the fewest assumptions. In other words, start with the simplest one.
So, while this soccer ball shape might be possible, it is most definitely not simple.
Cosmologists stick to what they call “Trivial Solutions.”
Which means simple shapes and no edges. In which case, a flat universe must be infinite.
The Planck telescope isn’t perfect though. There’s still a 0.4% margin of error.
There could still be some curvature to the overall universe
as long as it’s unimaginably larger than the observable part.
I’m still holding out for that finite universe with positive curvature.
But just because your universe is finite in size, it doesn't mean it's totally finite.
Physics still needs a lot of infinities to support it.
I'll explain why getting Achilles from "A" to "B"
requires you to assume that there are way more numbers in this distance than you might have imagined.
Hmmm that sounds interesting. You should check that out.
Alright, crazies that’s it for today. Thanks for liking and sharing this video.
Don’t forget to subscribe if you'd like to keep up with us.
And until next time, remember, it’s ok to be a little crazy.
In the last video, we learned about how far apart things are in space.
Comment response time! Antares was impressed that the moon was so
far away but that it still affected the tides. Yeah, I know, right?! How crazy is that?!
In all fairness though, it’s not the only reason that tides happen.
The oceans also need a lot of fluid pressure, so it helps that they’re all connected to
each other. So, while the moon is the primary cause for
the tides, it’s not the only reason they happen.
Kahandran guessed that, if we wanted to put the next closest star to the Sun in our scale
model, it would have to be in outer space and, indeed, it would.
A little over 4 light-years away there’s a star system with 3 stars in it.
The closest of the 3 is a little red dwarf named Proxima Centauri.
On our scale, it would only be the size of a small car,
but located twice as far as the real actual Moon.
That Mr. T C wants faster-than-light travel but says Einstein is standing the way with
a barbed-wire baseball bat. A barbed-wire baseball bat? Really?!
Einstein is German and he’s smart, so obviously he’d be using a two-handed long-sword known
as a Zweihänder.
Also, the Alcubierre Drive might be a way to out maneuver him.
Alexandro Ochoa said he wishes the Moon were closer.
I don’t think that’s such a good idea. If the Moon were as close as most people think,
it would orbit the Earth every 8.3 hours and, as Thomas Jackson said we’d have a hard
time keeping satellites in orbit. Also, I’m not sure how that would affect
the tides.
Elliot Grey brought up the game Majora’s Mask and, honestly, it kept popping into my
head the whole time I was editing. He wondered what would happen if the Moon
crashed into the Earth. If it came in fast enough, it could stay in
one piece, but the Moon in Majora’s Mask took days
to come down. That’s plenty of time for gravitational
tidal forces to break up the Moon. Probably turning it into a ring in orbit around
the Earth. Well, until the pieces finally came crashing down.
You Can Science It pointed out that the Moon reflector isn’t just for NASA.
If you have a strong enough signal, then you can use it too.
It’s a retro reflector, so it returns the light back to exactly where it came from,
no matter what angle you're at.
Anyway, thanks for watching and don’t forget to go check out Looking Glass Universe.
See you next time!