Asking how big the universe is seems like a silly question.
I mean- like- it’s big.
Really big.
How big, you might ask?
Oh, I dunno, there’s probably a 'your momma' joke in there somewhere, but suffice it to
say that it’s ginormous.
But ginormous isn’t really a scientific term- although it should be.
So, seriously now, how big is the universe?
Well the first thing you need realize is that many people misunderstand exactly what that
question is asking.
We first need to distinguish between the entire universe and the universe visible from Earth.
Those are different things.
So how much of the universe can we see from our vantage point here on Earth?
Well light has a finite speed, specifically about 300,000 kilometers per second, or about
186,000 miles per second, which means that when you see an astronomical object, you’re
seeing it like it was in the past.
For instance, it takes light from the Sun eight minutes to get to the Earth.
You probably knew that.
But that has bigger implications.
For instance, that means that there is a sphere around the Earth with the radius of the Earth/Sun
distance where light takes eight minutes to travel to us.
And that sphere idea is true in general.
There is a sphere around the Earth with a radius of a light year.
If we could somehow send lots of super bright lights a light year away to surround the Earth
and briefly blinked them, what would happen is that the light pulse would take a year
to get to Earth and they’d arrive at the same time.
When we saw them, we’d be seeing a blink that was a year old from objects located a
lightyear away.
We can take this idea to the extreme and ask what is the oldest thing in the universe,
and that is, by definition, the moment the universe began.
That happened 13.8 billion years ago.
If the universe wasn’t expanding, the farthest thing we could see would be a sphere, centered
on the Earth, with a radius of 13.8 billion light years.
This is what we call the visible universe.
Inside that sphere, light has had time to get to us.
Outside that sphere, it hasn’t.
We can’t see anything outside that sphere.
Now I should caution you and point out that the numbers I quoted for the visible universe
are true only if the universe isn’t expanding.
Of course, it is expanding, so the situation is a little more complicated.
I made a video about how that changes things and you might even want to take a look at
it.
But the bottom line is that there is a sphere centered on the Earth that is the extent of
the visible universe.
Is that how big the entire universe is?
The answer to that is almost certainly no.
The universe is bigger than we can currently see right now.
And you already kind of knew that.
For instance, as we look out and see the light from the beginning of the universe today,
we can see out to some distance.
If we look again tomorrow, we will be able to see out to that distance, plus an additional
light day.
That’s because light traveling over the course of those 24 hours will just be getting
to us tomorrow.
And, inexorably, day after day, we will be able to see a larger and larger sphere of
the universe.
There are locations that we cannot see today because the light simply hasn’t had time
to get to us, that we will be able to see tomorrow.
Again, this ignores the complications due to the expansion of the universe.
We’ll get to that in a minute.
So if the entire universe is larger than the portion we can see, how big is it?
Well, to answer that question, we need to back up and be a bit more careful.
Let’s start with talking about the oldest and most distant thing we can see.
As it happens, we can’t see the moment the universe began.
That’s because the early universe was so hot that light couldn’t pass through it.
You can sort of think of it like a fog.
However, there was a moment about 380,000 years after the Big Bang when the universe
cooled enough to become clear.
The temperature at which that happened is about 3,000 degrees centigrade or about 5,400
degrees Fahrenheit.
Everywhere in the universe the temperature was identical.
And, at 3,000 degrees, it was glowing hot.
So you’d think that when we looked out with our telescopes, we’d see a glow about like
what you’d see in a steel mill.
But this is where the expansion of space comes in.
Since that moment, the universe has been expanding and cooling and even stretching space.
The upshot of that is that what once would have been viewed by the human eye as white,
is now no longer visible and can only be seen by radio antennas capable of detecting microwaves.
For that reason, this oldest thing that we can actually see is called the cosmic microwave
background, or CMB, and the temperature of the universe in the current day is now 2.7
kelvin, or -270 degrees centigrade, or -455 degrees Fahrenheit.
Pick your favorite units.
So that’s the first big thing.
This microwave radiation that measures that the current temperature universe as 2.7 kelvin
is a fossil remnant of light emitted when the universe was about 3,000 degrees.
This temperature is almost the same everywhere, but we’ve learned that there are very small
variations in the universe’s temperature.
These variations really are incredibly tiny.
The hottest and coldest spots are only a hundredth of a percent different from the average.
Our current best measurement of these variations comes from a telescope in space called Planck.
Astronomers using the Planck observatory have measured the entire sky and their map of these
temperature variations is what we see here.
The blue spots are colder than average and the red ones are hotter.
So those temperature differences are pretty and all, but what do they have to do with
the size of the universe?
It turns out that these variations were caused by sound waves in the hot universe just before
it became transparent.
And because we know the temperature the universe was at the time, and we have measured the
total amount of matter we can see in the universe, we can calculate the wavelength of those sound
waves.
It’s a complicated calculation, but a straightforward one.
And I want to emphasize that there is no guesswork on this.
We have heated matter to these temperatures and we’ve measured the matter we see in
the visible universe.
We know a great deal about the wavelengths of sound that were present.
Sound in the early universe is pretty much the same as the sound you use to hear me.
Sound is transmitted through variations in the density of air and you can hear a variety
of frequencies.
In the early universe, the regions of higher and lower density due to the sound waves result
in hotter and colder spots in the cosmic microwave background.
And, given that we know the wavelength of the loudest sound in the universe before it
became transparent, we can calculate the angular size of the most common sizes of hot and cold
spots in the microwave background.
Further, we can calculate what size is the most likely and it should be one degree as
viewed from Earth.
Okay- so now we’re getting somewhere.
We have a firm prediction of the size of the hot and cold spots.
This brings us closer to our question, which I remind you is the size of the universe.
Now that prediction of one degree depends on the shape of the universe.
Remember that Einstein’s theory of relativity says that space and time can bend and morph.
Space could be one of a variety of different shapes.
It’s hard to imagine this in the three dimensions that we know space really is, so we have to
substitute a two dimensional analogy.
Bear with me.
A flat two-dimensional space is like the surface of a table.
Flat means flat.
But a two-dimensional space could be like the surface of a globe, where, if you kept
on walking you could, in principle, end up back where you started.
This is called a closed space.
Another possibility is space could be shaped like a saddle.
This is an example of what is called an open space.
So those are the three basic possibilities of the shape of space.
How does that fit into our question?
It comes down to the fact that light travels in a straight line in space.
But, if space is curved, then we can get fooled.
Let’s use the hot and cold spots in the microwave background to see what I mean.
If space is flat and a distant spot in the microwave background is one degree wide, then
we will measure its size as one degree.
This is the simple mathematics of triangles that you learned in geometry class, where
straight lines travel in – well straight lines.
But that behavior doesn’t have to apply.
Let’s see why.
For instance, if two ants were in flat space and they were separated by a certain distance
and started walking parallel to one another in a straight line in that flat space, they
will always stay the same distance apart.
If you do the same thing on a closed or spherical space, the two ants will eventually run into
one another because straight lines in curved space are curved.
This is like lines of longitude on a globe, where they are parallel at the equator, but
intersect at the pole.
And the opposite is true in an open space like the saddle space.
There, the two ants, initially a fixed distance apart from one another and walking in straight
lines, will eventually diverge and get farther apart.
That’s just curved space for you.
So this has consequences when measuring the apparent size of these distant spots of the
microwave background.
If space is flat, the line that crosses the spot you’re looking at and the two lines
that go from the edges of the spot to your telescope form a common triangle.
But in an open or closed curved space, the triangles are distorted.
Let me be more specific, because this is super important.
In a closed, or spherical, space, what one would expect to be a straight line is curved
in a specific way.
The crucial effect is that the angle of the triangle near your eye is >>bigger<< than
if space wasn’t curved.
The opposite is true for a closed, or hyperbolic, space.
Here, the curvature is in the opposite direction.
We see that the angle of the triangle near your eye is smaller than if space isn’t
curved.
Now the telescope can’t see the whole path travelled by the light.
All it sees is the angle of the light coming into your eye or the telescope.
All you see is the angle of light coming into your eye, with the closed, or spherical, space
angle being bigger than expected and the angle seen in the open, or saddle-shaped, space
being smaller.
And if we apply this to the spots in the microwave background, this means that a spot that is
one degree wide in flat space will be different in a curved space.
So this is a perfect way to test whether space is flat or curved.
In a flat space, the dominant size of the spots should be one degree.
If space is curved and closed, the spots should look bigger.
If space is curved and open, the spots should look smaller.
So what did Planck and other experiments find?
A drum roll please, maestro?
The measurements found that the size of the spots is one degree.
From that, we conclude that space is flat.
Or can we?
Well, yes, sort of.
But that is an incautious statement.
Physics is an experimental science.
When we say that the Earth is flat, what we mean is that the measurement is consistent
with being flat.
But that also means that the measurement is consistent with a tiny bit of curvature.
For example, if we’re at the beach on the ocean and look at the horizon, it surely looks
flat.
But, in spite of the claims of some people, the Earth most certainly isn’t flat.
It’s a sphere.
So, you have to keep this in mind.
What appears to be flat can, indeed, be curved.
And when we measure space, we can only say that it appears to be flat.
And that is true of space as well.
Space appears to be flat.
If, and I repeat if, space is flat, then the universe is infinite in extent.
Our visible universe just a small bubble in an infinite sea.
Similarly, if space is shaped like a saddle…what scientists call a hyperbolic or open space…space
is also infinite.
But what if space is closed and shaped like a sphere, but so big that it looks flat, like
the Earth can look flat?
Well, in that case, space is not infinite.
It has a finite size.
So now we’re getting somewhere.
If the universe is closed, how big is it?
Well if you do a careful analysis, using the maximum possible curvature allowed by the
best measurements, you find that the universe can be no smaller than 250 times bigger than
the visible universe.
So that’s your answer.
I mean we’ve always kind of thought that the universe is big, but now we can hang a
number on that.
The visible universe, meaning the part of the universe we can see using our instruments,
is a sphere, centered on the Earth and taking into account the effects of expansion, with
a diameter of 92 billion lightyears.
However the entire universe, including the parts we can’t see, is at least 250 times
wider than that.
And the universe could indeed be infinite in size.
We’ve come a long way from simple speculation about the universe.
Seemingly intractable questions are now getting answers and, that, is your fascinating fact
for the day.
Okay, so that was a very cool topic.
The thought that we can actually constrain such things as the size of the universe, including
the bits we can’t see is just mind-blowing.
You should realize that there is even more to the conversation because this video didn’t
include simply- versus multiply-connected topologies.
But, you know, I had to leave something for future videos.
If you liked what you saw, be sure to like, comment, and share.
And please subscribe to the channel, because the fact that you’re watching this means
that you’re probably my kind of people – the kind of people who realize that physics is
everything.