Most galaxies are moving away from us over time.
In fact, the farther away they are, the faster they're moving away.
If space is big enough, some galaxies should be moving away from us faster than light.
But how is that possible? Doesn't light travel at the universal speed limit?
This episode was made possible by generous supporters on Patreon.
Alright. Let's establish two things about light before we get into this.
One! Light is actually pretty slow astronomically speaking.
I mean, it seems pretty instantaneous to us.
We flip a switch and BAM! The room is immediately filled with light.
Fast fast!
But that's only because rooms aren't actually that big.
It still seems fast even on the scale of the Earth, but you can begin to see isn't infinitely fast.
Light from the Moon takes 1.3 seconds to get here.
Light from the Sun takes 8.3 minutes.
Wait, is that even moving?
Oh, yep, there it is.
Anyway, the Alpha Centauri system, the closest stars to the Sun, are over 4 light-years away.
That means their light takes over 4 years to get here.
Light from the Andromeda galaxy, the closest spiral galaxy, takes 2.5 million years.
The farther away the source, the longer the time.
The cosmic microwave background, or CMB, has taken 13.8 billion years to get here.
That's billion with B.
It's the oldest light in the universe.
The point is, light takes time to get places, sometimes a long time
So, in a way, we shouldn't be that surprised there's something going faster.
Two! The speed of light isn't actually a speed limit for all speeds.
There are, in fact, plenty things that go faster.
Say we're outside one night and we decide to point a laser at the Moon.
This isn't going to work. We wouldn't be able to see the laser dot.
True, but this doesn't affect my main point, so assume we could see it.
The dot would be pretty big by the time it got there. Even laser light spreads out.
If we start on one edge of the Moon and suddenly move it to the opposite edge,
the laser dot will move across the surface of the Moon faster than light.
Wait, what?!
For realsies.
This isn't even a problem, because the speed of light isn't a universal speed limit.
It's just the speed limit of causality, of cause and effect.
Hear me out.
You know how you can get the distance between things using Pythagorean theorem?
A squared plus B squared equals C squared?
Well, if you make time one of those dimensions, it still kind of works.
This equation governs the order of cause and effect.
It’s kind of a big deal.
All thanks to Pythagoras.
Pith-ah-gore-as?
Whatever.
This is the speed of light right here.
It represents how quickly parts of space can communicate across time.
The speed of light isn't really about light.
It's about causality, about cause and effect.
If one event causes another, everyone agrees on the order of those events.
The cause must come before the effect.
With the laser on the Moon, it's perfectly fine for the dot to move faster than light.
The events on either side of the Moon aren't causally connected,
so there's no speed limit.
The cause is all the way back on Earth with the laser.
The photons from the laser still can't get to the Moon faster than light,
so there's a delay between you moving the laser and the dot moving on the Moon.
As long as causality is maintained, things can go as fast as they want.
And that's a rule that applies even in cosmology.
It's perfectly fine for distant galaxies to be going faster than light
as long as they're not causing anything faster than light.
So thanks for liking and...
[Off Camera] What is this? 2013?!
I answered the original question!
But how did they get going that fast in the first place?
Oh, well, that's a much deeper question.
You've probably heard something like this:
The faster you go, the more and more kinetic energy you need to keep going faster.
You would need an infinite amount of energy to accelerate to the speed of light.
Right, so how can distant galaxies break that rule?
That simple rule is only a special case, which is why we call the model Special Relativity.
Is there a general case?
Yep! We call it General Relativity and it's absolutely necessary for cosmology.
Let’s get back to this causality equation from earlier.
It isn't quite enough.
In fact, in general relativity, what it looks like depends on the circumstances
and it can get pretty complicated sometimes.
This is what it looks like near a rotating black hole.
Yikes!
Thankfully, on cosmological scales, the universe is extremely uniform and simple.
We only need to take our special case and smash an extra factor in there.
It's called the scale factor. It represents the scale of space.
As space expands, the scale factor gets bigger.
That's the reason distant galaxies can move away faster than light.
They're just carried along as space expands.
The distance where galaxies are expanding away at exactly the speed light is called:
The Hubble Horizon.
It's 14.5 billion light years away,
which is about 14.4 billion farther than our brains could ever hope to comprehend.
But that's not even the most surprising bit about this.
You might expect the Hubble horizon to be the limit of our vision,
but it isn't.
We can actually see past it!
There are two more horizons beyond it.
One is our vision limit of the present.
The other is our vision limit of the past.
That last one is three times farther than the Hubble horizon.
If you want to learn more about those horizons, I have a video on them,
but let's get back to the expansion of space.
This time right here is not the time measured by Earth.
It's what we call "cosmic time."
It's the time measured by someone who isn't moving relative to the source of the CMB.
You know, this stuff.
This is just a map though. It gives you the wrong impression.
The CMB is actually the inside surface of a sphere.
In its raw form, it's red-shifted in one direction and blue-shifted in the other.
That tells us the Earth is moving relative to whatever stuff is emitting that light.
Which isn't the most convenient point of view for cosmology.
If we adjust the CMB data to remove that color shift,
then we have a better point of view.
We call this the comoving frame.
Oh yeah! We're going there.
What is it comoving with?
The expansion!
Let's say we're dealing with a bunch of events across space
that all happen at the same cosmic time.
Our new version of causality simplifies to this.
We already know "a" is the scale factor, the thing that grows when space expands.
The other two things are different measures of distance:
Proper distance and comoving distance.
Proper distance is called proper because it's the kind of distance we’re used to.
You take space, slap down a static grid, and you're good to go.
As space expands, galaxies and everything inside them are taken along for the ride.
The proper distance between galaxies increases.
This is the distance we actually see when we look out into the universe.
But the comoving distance is actually much more convenient in cosmology.
It’s called "comoving" because it co-moves with the expansion of space.
As space expands, the grid goes with it.
Distant galaxies remain roughly the same comoving distance from each other as time passes.
This coordinate doesn't change with the expansion. The scale factor does.
That gives people the impression galaxies can't move in comoving coordinates and they can.
Hmm, I suppose you’re right.
As two galactic clusters expand away from each other with the grid,
the galaxies inside those clusters can also move around locally a little bit.
Both of these can change.
It's just that a change in the scale factor represents the expansion
and a change in the comoving coordinate represents actual local motion.
And that's the loophole in physics that distant galaxies exploit to go faster than light.
Since both of these can change, there are actually two different velocities:
A recession velocity because it measures things receding from us
and a peculiar velocity because I don't know why it's called that.
Don't get on my case, ok? I don't get to name these things.
Anyway, the recession velocity is the one that's bigger than the speed of light.
The peculiar velocity is the one that must be slower.
Why though?
Because causality!
Remember, this all started with causality, with the order of cause and effect.
The speed of light isn't the upper limit on how fast things can move.
It's the upper limit on how fast two points in space can communicate with each other.
Only the peculiar velocity lets parts of space communicate,
so only that velocity has the speed of light limit.
I should also point out here that recession velocity isn't really a velocity.
At least not in the way we usually understand it.
It's not actually a change in distance over time.
It's a change in scale over time.
It's the scale factor that changes, not the coordinate.
The recession velocity is kind of an illusion created by the expansion of space.
The rate of expansion isn't even measured as a speed.
It's measured as speed a distance.
It's about 70 kilometers per second per mega parsec,
also known as the Hubble parameter.
That just means that galaxies are moving away at 70 kilometers per second
for every mega parsec they are distant.
The more space there is to expand between us,
the faster they'll seem like they're moving away.
In fact, the difference between these two speeds actually explains the difference between two different types of redshift.
Doppler redshift and cosmological redshift.
I realize someone, who will go unnamed, just released a video arguing that all redshifts are the same.
I disagree.
While I'm comfortable saying that Doppler redshift and gravitational redshift are the same,
cosmological redshift is entirely its own beast.
These two different velocities result in two different redshifts.
The second one gives us the Doppler redshift because it's an actual velocity.
The first one gives us cosmological redshift, the redshift caused by the expansion of space.
It's not actually a velocity though, so it can't be the same as Doppler.
It just can’t.
Seriously. If you graph out Doppler and cosmological redshift against velocity,
the patterns are approximately true for small redshifts,
but they diverge wildly for large redshifts.
Doppler redshift maxes out at the speed of light. Cosmological redshift does not.
They're not the same! They're just not!
[Calming Exhale]
Are you ok?
Yeah, I think I got it out of my system.
Sorry. I haven't ranted on camera in while.
Anyway, to summarize. Distant galaxies go faster than light by cheating.
When measuring how far away distant objects are, there are two factors that matter:
The scale factor and the comoving coordinate.
They create a grid that grows with the expansion of space.
As a result, there are two different types of motion taking place.
Only one of those motions has a speed limit though.
The speed of light is only the limit of cause and effect, not of everything.
It's the maximum speed that two different parts of space can communicate.
Only this velocity lets parts of space communicate, so it's the only one with a speed limit.
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.
I know many of you were expecting part 2 of the Wife Reacts video.
It's just that this video has been on the schedule for a while. It had to happen.
Wife Reacts Part 2 is next, probably.
And thanks for watching!