Radius of Observable Universe

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Radius of Observable Universe

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Right now, the best estimate of when the Big Bang occurred -
and once again, I don't like the term that much, 'cause it kind of implies
some type of explosion, but what it really is is kind of an expansion of space
- when space really started to expand from a singularity
but our best estimate of when this occurred is
13.7 billion years ago, and even though we're used to
dealing with numbers in the billions, especially when we talk about
large amounts of money and whatnot, this is an unbelievable amount
of time. It seems like something that is tractable, but
it really isn't. And in future videos, I'm actually going
to talk about the time scales, so you can really appreciate
how long, or even start to appreciate, or appreciate
that we CAN'T appreciate how long 13.7 billion years is.
And I also want to emphasize that this is
the current best estimate. Even in my life time, even in
my life time that I actually new about the big bang and
that I would pay attention to what the best estimate was,
this number's been moving around, so I suspect
that in the future, this number might become more accurate
or might move arround some.
But this is our best guess. Now, with that said, I want
to think about what this tells us about the size
of the observable universe.
So, if all of the expansion started 13.7 billion years ago...
[and] all of everything we know in our 3 dimensional universe
was in a single point,
the longest that any photon of light could be traveling
that's reaching us right now...
(so, our eye is right...)
(so, let's say that's my eye right over there)
(that's my eyelashes, just like that)
the longest - so, some photon of light,
is just getting to my eye, or maybe
it's just getting to the lense of a telescope -
the longest that that could have been traveling
is 13.7 billion years.
So when we looked at that depiction
(this, I think, was 2 or 3 videos ago)
of the observable universe,
I drew - it was a circle.
It was this circle.
And, when we see light coming from these
remote objects, that light is getting to us right here
this is where we are. This is where, I guess,
in the depiction, the remote object was,
but the light from that remote object is just now getting to us.
And that light took 13.7 billion years to get to us.
Now, what I'm going to hesitate to do,
because we're talking over such large distances
and such large time scales ...over which
space itself is expanding, we're going to see
that you cannot say that this object over here -
this is not necessarily...
this is NOT
(I'll put it in caps.)
This is NOT 13.7 billion light years away!
If we're talking about smaller time scales,
or, I guess, smaller distances,
you could say aproximately that.
The expansion of the universe itself
would not make as much of a difference.
And let me make it even more clear.
I'm talking about an object over there,
but we can even talk about that coordinate in space.
And that coordinate in (and actually I should say,
"That coordinate in space-time."
'Cause we're viewing it at a certain instant as well.)
But that coordinate is not 13.7 billion light-years
away from our current coordinate.
And there are a couple of reasons to think about it.
First of all, think about it.
That light was emmitted 13.7 billion years ago.
When that light was emmitted, we were much closer to that coordinate.
This coordinate was much closer to that.
Where we are in the universe now
was much closer to that point in the universe.
The other thing to think about is, as this - let me actually draw it.
So let's say that - let's go three hundred thousand years
after that initial expansion of that singularity.
So, we're just 300,000 years into
the universe's history, right now.
So this is roughly 300,000 years into
the universe's... life, I guess we could view it that way.
And let's say at that point - well, first of all
at that point, things haven't differentiated
in meaningful ways yet, right now.
We'll talk more about this when we talk about
the cosmic microwave background radiation,
but at this point in the universe
it was kind of this almost uniform
whitehot plasma of hydrogen.
And we're going to talk about - it was emmiting
microwave radiation, and we'll talk more about that
in a future video.
But let's just think about two points in this early universe.
So, in this early universe, let's say you have that point,
and let's say you have
the coordinate where we are right now.
I won't make it the center.
'Cause I think it makes it easier to visualize
if it's not the center.
And let's say that very early stage in the universe
if you were able to just take some rullers
instantaneously and measure that,
you would measure this distance
to be 30 million light-years.
And let's just say right at that point,
this [magenta] object over here
emits a photon. Maybe in the microwave
frequency range, and we'll see
that that was the range it was emmitting in.
But, it emits a photon.
And that photon is traveling at the speed of light!
It IS light!
And so, that photon says, "Oh, you know..."
"I only got 30 million light-years to travel."
"That's not too bad. I'm gonna get there"
"in thirty-million years."
And so - and I'm going to do it descrete.
The math is really more complicated than what I'm doing here,
But I really just want to give you the idea
of what's going on, here.
So, let's just say, that photon says,
you know, "In about ten million years, I should be"
"right about at that coordinate."
"I should be about one third of the distance."
But what happens over the course of those ten million years?
Well, over those 10 million years,
the universe has expanded some.
The universe has expanded, maybe, a good deal.
So let me draw the expanded universe
So after ten million years, the universe...
...might look like this.
(Actually, it might even be bigger than that.)
(Let me draw it like this.)
After ten million years,
the universe might have expanded a good bit.
So, this is ten million years into the future.
Still, on a cosmological time scale,
still almost at the infancy of the universe,
'cause we're talking about 13.7 billion years.
So let's say 10 million years go by.
The universe has expanded.
This coordinate where we're sitting at present
is now all the way over here.
That coordinate where the photon was
originally emitted is now
going to be sitting right over here.
And that photon has said, "Ok,"
"After ten million light-years [sic] I'm going to get"
"over there,"
And, you know, I'm aproximating and I'm doing it
in a very descrete way - I really just want to give you the idea.
So that coordinate, roughly where the photon
gets in ten million light years
Is about right over here.
The whole universe has expanded.
All the coordinates have gotten further apart.
Now what just happened here?
The universe has expanded.
This distance that was 30 million light-years
now - and I'm just making rough numbers -
now it is actually - this is really just for the sake of
giving you the idea of why... giving you the intuition
of what's going on -
This distance now is no longer 30 million light-years
Maybe it's a hundred million.
So this is now a hundred million light-years.
The universe is expanding.
The space is actually spreading out.
You can imagine it's kind of a trampoline,
or the surface of a baloon - getting stretched thin.
And so this coordinate where the light happens to be
after ten million years,
it has been traveling for ten million years,
but it's gone a much larger distance!
It has now gone - that distance might be
on the order of maybe 30 million light years.
And the math isn't exact, here.
I haven't done the math to figure it out.
But the point here - so, it's done 30 million light-years.
And actually, I shouldn't even make it
the same proportion, because the distance it's gone
and the distance it has to go,
because of the stretching, it's not going to be
completely linear. At least, when I'm thinking about it
in my head, it shouldn't be, I think.
But I'm not going to make a hard statement
about that.
But the distance that it traversed - maybe
this distance right here is now 20 million light-years
...because every time it moved some distance,
the space that it had traversed is now stretched.
So even though it's travelled for 10 million years,
the space that it traversed is no longer just
10 million light-years.
It's now stretched to 20 million light years.
And the space that it has left to traverse
is no longer only 20 million light-years.
It might now be 80 million light-years.
And so, this photon might be getting frustrated.
There's an optimistic way of viewing it, is like,
"Wow! I was able to cover 20 million light-years"
"in only ten million years."
"It looks like I'm moving faster than the speed of light."
The reality is, it's not, because the space coordinates themselves
are spreading out.
Those are getting thin. So, the photon is just moving
at the speed of light. But the distance that it actually
traversed in ten million years is more than
ten million light-years.
It's 20 million light-years.
So, you can't just multiply rate by time
on these cosmological scales, here.
Especially when the coordinates themselves
are actually moving away from each other.
But I think you might see where this is going.
Now this photon says, "Oh,"
"In another 40 million light years [sic],"
"maybe I'm going to get over here."
But the reality is over that next 40 million years,
it might get right over here,
'cause this is 80 million light years.
The reality is, after 40 million years,
so, another 40 million years go by...
Now, all of a sudden, the universe has expanded
even more!
I won't even draw the whole bubble,
but the place where the photon was emitted from
might be over here,
and now our current position is over here,
where the light got after ten million years
is now over here,
and now where the light is after 40 million years,
is maybe over here.
So, now this distance between these two points:
when we started, it was 10 million light years,
then it became 20 million light-years
maybe now it's on the order of - I dont' know
maybe it's a billion light years!
And maybe this distance over here,
and I'm just making up these numbers,
in fact, that's probably too big for that point...
Maybe this is now a hundred million light-years.
And now, this distance maybe is, I dunno
500 million light-years.
And maybe now the total distance between the two points is a billion light years.
So, as you can see, the photon might be getting frustrated.
As it covers more and more distance, it looks back,
and says, "Wow, in only 50 million years, I've been able to cover 600 million light-years,"
"That's pretty good."
But it's frustrated, because what it thought
it had to cover - 30 million light-years -
that keeps stretching out.
'cause space itself is stretching.
So the reality, just going to the original idea,
this photon that is just reaching us
that has been traveling for, let's say, 13.4 billion years
so, it's reaching us just now, so let me just fast-forward 13.4 billion years
from this point now to get to the present day.
So if I draw the whole visible universe right over here
this point right over here is going to be where it was emitted from.
We are sitting right... over there. And actually...
Let me make something clear. If I'm drawing the whole observable universe,
the center actually should be where we are, 'cause we can observe an equal distance
- if things aren't really strange - we can observe an equal distance in any direction.
So, actually, maybe we should put us at the center.
So, this is the entire observable universe. And the photon was emitted from here
13.4 billion years ago. So 300,000 years [sic] after that initial big bang.
And it's just getting to us.
It is true that the photon has been traveling for 13.7 billion years [sic].
But, what's kind of nutty about it is, this object, since we've been expanding away from eachother
this object is now, in our best estimates
46 billion light-years away from us.
And I want to make it very clear:
This object is NOW 46 billion light-years away.
So when we just use light to observe it, it looks like
just based on light years, hey, this light's been traveling 13.7 billion years to reach us,
that's our only way, kind of, with light, to think about the distance, so maybe it's 13.4
*chuckle* (I keep changing the decimal)
but, [maybe it's] 13.4 billion light-years away.
But the reality is, if you had a ruler today
and, you know, light-year rulers
this thing, the space has stretched so much
that this is now 46 billion light-years.
And just to give you a hint of when we talk about
the cosmic microwave background radiation,
what will this point in space look like?
This thing that's actually 46 billion light-years away
but the photon only took 13.7 [sic] billion years to reach us.
What will this look like?
Well, when we say, "look like," it's based on
the photons that are reaching us right now.
Those photons left 13.4 billion years ago.
So, those photons are the photons being emitted
from this primitive structure, from this white-hot
haze of hydrogen plasma.
So what we're going to see is this white-hot haze
- so we're going to see this kind of
white hot plasma.
Undifferentiated, not differentiated into proper stable atoms, much less stars and galaxies.
But white-hot - we're going to see this white hot plasma.
The reality today is that that point in space that's 46 billion years from now [sic]
it's probably differentiated into stable atoms and stars and planets and galaxies.
And frankly, if that person - if there is a civilization there right now, and they're sitting right there
and they're observing photons being emitted
from our coordinate, from our point in space right now [sic]
They're not going to see us. They're going to see
us 13.4 billion years ago. They're going to see
the super primitive state of our region of space
when it really was just a white-hot plasma.
And we're going to talk more about this in the next video, but think about it.
ANY photon that's coming from that period in time,
so, from any direction, that's been traveling for
13.4 billion years, from any direction,
is going to come from that primitive state, or,
it would have been emitted when the universe was in
that primitive state, when it was just that white-hot
plasma, this undifferentiated mass.
And hopefully, that'll give you a sense of where
the cosmic microwave background radiation comes from.