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- Over many videos now, we've been talking about
- how every interstellar object is moving away from Earth.
- We've also been talking about how the further something is
- away from Earth, the faster it's moving.
- What I want to do in this video
- is to put a few numbers behind it,
- or even better conceptualize what we've been talking about.
- So, one way to think about it
- is that, if at an early stage in the Universe,
- I were to pick some points,
- so that's one point,
- another point, another point
- another point,
- let me just pick 9 points so that I have a proper grid.
- So this is an early stage in the Universe
- if we fast-forward a few billion years,
- and I'm clearly not drawing it to scale.
- All of these points
- have all moved away from each other.
- So this point is over here,
- and actually let me draw another row,
- actually another column,
- just to make it clear.
- So if you fast-forward a few billion years
- the Universe has expanded,
- and so everything has moved away from everything
- and let me color code a little bit,
- let me make this point magenta.
- So this point, the magenta point is now here.
- This green point
- has now moved away from the magenta point.
- And now this blue point
- has now moved away from the magenta point
- in that direction,
- and we can keep going,
- this yellow point is maybe
- over here now.
- I think you get the general idea.
- And I'll just draw the other yellow points,
- so they've all moved away from each other.
- So there's no center here
- everything is just expanding away
- from things next to it.
- And what you can see here,
- is not only did this thing expand away from this,
- but this thing expanded away from this
- even further,
- because it had this expansion plus this expansion.
- Or another way to think about it is
- the velocity with which,
- the apparent velocity with which something is expanding
- is going to proportional to how far it is.
- Because every point in between is also expanding away.
- And just to review a little bit of the visualiztion of this,
- one way to think of this, if you think of the Universe
- as an infinite flat sheet.
- You could imagine that we are just taking a sheet of
- I don't know
- some type of sheet of stretchy material and just stretching it out
- we're just stretching it out,
- that's if we kind of imagine a more infinite Universe,
- that just goes off in every direction.
- We're just stretching that infinite sheet out,
- so it has no boundaries, but we're still stretching it out.
- Another way to visualize it, and this is what we did earlier on,
- is you could imagine that this --, that the Universe is the
- three-dimensional surface of a four-dimensional sphere,
- or the three-dimensional surface of a hyper-sphere.
- Sort of an early stage in the Universe,
- the sphere looked like this, and these points here
- the magenta point is right over here
- the green point is right over there,
- then we had the blue point up here,
- and then let me just draw the rest of the yellow points.
- And the yellow points are here, they're all on the surface of this sphere.
- They're all on the surface of the sphere.
- Obviously, I'm only dealing with two-dimensions right now,
- and it's nearly impossible, or maybe impossible to imagine
- a three-dimensional surface of a four-dimensional sphere,
- but then the analogy holds.
- If is the surface of a balloon, or the surface of a bubble,
- if the bubble were to expand,
- so if the bubble were to expand over a few billion years,
- and once again - not drawn to scale.
- So now we have a bigger bubble here
- This part of the surface is all going to expand,
- so once again, you have your magenta
- you have your blue dot,
- you have your green dot,
- and then let me just draw the rest in yellow.
- So they will have all expanded away from each other on the surface of this sphere.
- Just to make it clear that this is a sphere, let me draw some contour lines.
- So this is a contour line,
- just to make it clear that we are on the surface,
- we are on the surface of an actual sphere.
- Now with that out of the way, let's think about
- how fast or what is the apparent velocity with which things are moving away.

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