Thanks to Brilliant for helping support this episode.
Hey Crazies.
We all know that things are smaller when they're farther away, right?
The size of familiar objects gives us a way to tell distance.
Except it doesn't always work.
I mean, you're still good if the distance is less than, like, nine and a half billion light years.
But there are plenty of galaxies more distant than that and they look bigger than the closer ones.
This demonstration is an example of angular diameter.
It's the idea that if something is farther away, it'll look smaller in our field of view.
Imagine there's a sphere around your head.
There are 360 degrees all the way around in any direction, regardless of the sphere’s size.
If you see a ball at some distance, it'll take up a fraction of those 360 degrees,
meaning you can measure its diameter as an angle.
Hence, angular diameter.
If the ball is closer, the angle will be larger.
If the ball is farther away, the angle will be smaller.
That's why one of these clones looks farther away than the other.
His angular diameter is smaller.
Of course, our brains aren't precisely measuring these angles and doing calculations.
Instinctively, you only need a vague idea of distance.
So your brain cheats by using visual cues from the environment, like perspective.
If I replace this background with one that has less depth, your brain gets confused.
It looks like I have a mini clone.
We call this forced perspective.
They took advantage of this trick in Lord of the Rings to make the Hobbits look smaller.
We run into a similar problem in astronomy.
Environmental cues don't exist in outer space.
We only have the vast emptiness between objects.
So it turns out that angular diameter is not a great judge of distance in astronomy.
But when we measure distance in other ways, the pattern still holds up...
kind of.
Say we've cataloged a bunch of identical galaxies at various distances.
From what we just learned about angular diameter,
we'd expect the pattern to look like this.
An object's apparent size should be proportional to one over its distance.
What we actually see is this.
They match up at first, but quickly begin to deviate.
The strangest part of the pattern occurs here at about 9.6 giga lightyears.
That's where the angular diameter takes a u-turn.
Galaxies start appearing larger again.
What? What?! What?!?!
I know, I know. It sounds unbelievable, but it's true.
We call it angular diameter turnaround.
And I'll admit it's weird AF.
I've heard it described as watching galaxies sink into a pool of diluted blood.
And given the redshift, that makes complete sense.
Are they actually being diluted, though? Well, no.
I just thought it would be a nice metaphor.
Anyways!
Angular diameter turnaround is just an optical illusion. And like any optical illusion, it comes down to the behavior of light.
The first thing we need to know is that light has a finite speed.
It's about 300,000 kilometers per second or 186,000 miles per second,
give or take.
That might seem instantaneous on human scales.
It's even pretty fast when you consider the entire Earth.
But one step out in scale and we start to see the problem.
Another step, and it looks as if it's standing still.
Light takes time to get places and space is big. Really big.
Units can be misleading.
Kilometers and miles are terrible units in outer space.
It would be more helpful to say that light travels at one lightyear per year.
Alpha Centauri is the closest star system to the Sun and it's a little over four light years away.
That means light takes over four years to travel that distance.
Four years! And that's the closest one.
We can certainly draw the angular diameter triangle on this image
and Alpha Centauri is close enough that this simple rule applies.
But in general, it's becoming clear that time is going to be a major factor.
Let's incorporate that factor now before things get too heavy.
If you haven't guessed it already,
I'm going to use a spacetime diagram.
Why is time on the vertical axis?
I mean, we had to pick a direction. Why not vertical?
I mean, as Michael Stevens would say:
It's a choice. It's a choice.
That choice was made a long time ago. It’s just tradition now.
Tradition!
Anyway, the Alpha Centauri system won't move much in four years, at least relative to Earth.
So in a spacetime diagram, they'll be on parallel paths.
Your first instinct might be to think star light moves like this.
But remember, light travels at a finite speed: one lightyear per year.
So we don't get to see this star as it is now.
We only get to see it as it was four years ago.
There's a delay.
Light has to travel along diagonal paths in a spacetime diagram.
We call them null paths,
for mathy reasons I'm not prepared to get into today. Just go with it.
The long sides of that triangle defining angular diameter are null paths.
For some perspective, that same triangle looks like this in a spacetime diagram.
I know, I snuck an extra dimension in there on you, but I promise there's a payoff at the end of all this.
Light from either side of Alpha Centauri A travels along 45 degree diagonals to reach Earth.
But if we consider all the 45 degree diagonals, we get something special:
a light cone.
Specifically, Earth's past light cone.
Every event that could possibly have affected the present day Earth is inside it.
All light that could possibly have arrived at Earth travels along its edge.
But this video is not about nearby stars.
It's about distant galaxies.
Which means we need to extend this light cone
much further into the past.
In fact, we'll be extending this cone so far into the past that it won't even look like a cone anymore.
At least not like anything a rational person would call a cone.
Anyway, this brings us to the second thing we need to know.
Space is getting bigger as time passes. It's expanding.
That means light isn't the only thing moving here.
In the time it takes that light to arrive at Earth from a distant galaxy,
that galaxy and ours will have moved farther apart.
We're not seeing that distant galaxy.
We're seeing an image of that galaxy from when space was smaller.
In other words, an image of that galaxy from when it was closer.
For a nearby star, the spacetime paths look like this: parallel.
For distant galaxies, it looks more like this.
The paths diverge.
In an expanding universe, the distances between most galaxies get larger over time.
But we don't see them as they are now.
We see them as they used to be.
Light from those galaxies has to travel along the edges of our past light cone.
That's those null paths I was talking about.
The farther the galaxy, the further into the past we see.
So, the reason they look closer is because they were closer.
Yep. But it's more interesting than that.
If we could extend the past light cone indefinitely like this,
we wouldn't actually get the pattern we see.
Our angular diameter graph would look like this instead.
It would deviate from the simple one over distance rule.
But galaxies would still continue to get smaller.
There wouldn't be an angular diameter turnaround, like in our real universe.
Something else is going on here.
Which brings us to the third and final thing we need to know.
Light is also affected by the expansion of space. Yes, really.
And I'm not just talking about redshift, though that does happen.
Light is dragged along just like the galaxies are.
Light just happens to be so fast that it's better at overcoming that expansion than galaxies.
Our past light cone isn't actually a cone.
The null paths gradually curve toward the big bang singularity.
Would you call this shape a cone? I wouldn't.
But then again, I'm not sure what else to call it either.
It's giving me serious Taj Mahal vibes, though.
Anyway, the turnaround point is right here.
Light coming from beyond that hump spent some time moving away from us at first.
The distance was increasing faster than the light could move.
What? What?! What?!?!
This is the detail that makes angular diameter turnaround possible.
Even before the turnaround point, galaxies begin appearing larger than they should,
but they still continue to get smaller the farther they are.
It's not until 9.6 giga lightyears that we see them start to get larger again.
Why this happens is perfectly clear from the spacetime diagram.
All light currently arriving at Earth is coming from a point along the edge of this shape.
If it's coming from a galaxy, then it's coming from when that galaxy crossed those null paths.
Beyond the hump, looking at further galaxies means looking at closer images of galaxies.
All we ever get to see are images of the distant past, filled with illusions of cosmic proportion.
[Dramatic Music]
Now, I'll admit, I did gloss over how we measure distances in outer space.
If you want to learn more, you should check out Brilliant.
Working with a problem yourself is the best way to learn skills in math, science, and computer science.
Brilliant is a tool for learning STEM interactively.
They have thousands of lessons with new content added monthly.
Learning a little bit every day can have a huge impact.
If you like this video, I bet you'll like their astrophysics course.
Brilliant has several lessons on how to measure the vast distances between the stars.
But maybe you're looking for something a little more advanced.
They also have a course on special relativity where you can learn the basics of spacetime diagrams.
Brilliant is college-level content for everyone.
If you want to get started with a free trial,
go to Brilliant dot org slash Science Asylum or click the link in the description below.
The first 200 of you will get 20% off Brilliant’s annual premium subscription.
It’ll also let Brilliant know you heard about them from me, which helps out the channel.
So do you know any mind-blowing facts about cosmology?
Please share them in the comments.
Thanks for liking and sharing this video.
A special thanks goes out to all my Patreon patrons and YouTube members for their generous support.
Don't forget to subscribe if you'd like to keep up with us.
And until next time, remember: It's okay to be a little crazy.
Since a bunch of you were asking, the Star Trek transporter does allow for cloning in extreme circumstances.
But a real-life transporter would not.
Quantum information must be conserved.
That information is either in the old you, caught up in the entanglement,
or in the new you, but never more than one place.
Anyway, thanks for watching!