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PROFESSOR: So I want to begin
by reviewing a little bit what
I said last time in terms
of this overview lecture.
And then we'll finish
the overview lecture.
So summary of last lecture
is actually on five slides.
It's not all on this one slide.
We started by talking about the
standard Big Bang, by which I
mean the Big Bang without
thinking about inflation.
And I pointed out that
it really describes
only the aftermath of a bang.
It begins with the
description of the universe
as a hot, dense soup of
particles which more or less
uniformly fills the
entire available space,
and the entire system
is already expanding.
Cosmic inflation is a prequel
to the conventional Big Bang
story.
It describes how
repulsive gravity, which
in the context of
general relativity,
can happen as a consequence
of negative pressure.
This repulsive
gravity could have
driven a tiny patch
of the early universe
into a gigantic burst of
exponential expansion.
And our visible
universe would then
be the aftermath of that event.
As this happened, the
total energy of this patch
would be very small and
could even be identically 0.
And the way that's possible
is caused by the fact
that the gravitational
field that fills the space
has a negative
contribution to the energy.
And as far as we can tell
in our real universe,
there are about
equal to each other.
They could cancel each other
exactly as far as we can tell.
So the total energy
could in fact
be exactly zero,
which is what allows
one to build a huge
universe starting
from either nothing
or almost nothing.
Inflation.
The next item is
evidence for inflation.
Why do we think there's
at least a good chance
that our universe
underwent inflation?
And I pointed out three items.
The first was that inflation
could explain the large scale
uniformity that we
observe in the universe
and that large
scale uniformity is
seen most clearly in the
cosmic microwave background
radiation, which is observed
to be uniform to one
part in $100,000, that is same
intensity all across the sky
no matter what direction
you look, once you account
for the Earth's motion,
to an accuracy of one part
in 100,000.
Secondly, inflation can explain
a rather remarkable fact
about this quantity
omega, where omega
is defined as the actual
mass density of the universe
rho divided by rho critical,
the critical mass density which
is the density that would make
the universe precisely flat.
The statement that that
ratio is equal to 1 we know
is accurate to about 15
decimal places at one second
after the Big Bang.
And prior to inflation,
we didn't really
have any explanation
for that at all.
But inflation
drives omega to one
and gives us an explanation
for why, therefore,
started out so
extraordinarily close to 1.
And in fact, it
makes a prediction.
We'd expect that if
inflation is right,
omega should still be one today.
And we now have measured omega
to be 1.0010 plus or minus
0.0065, which I
think is fabulous.
Finally, inflation
gives an explanation
for the inhomogeneities
that we see in the universe.
It explains them as
quantum fluctuations which
happened during the inflationary
process and, most importantly
really, as inflation was
ending, the quantum fluctuations
cause inflation to go
on for a little bit
longer in some
regions than others.
And that sets up
these inhomogeneities.
Today, we can see
these inhomogeneities
most accurately.
inhomogeneities, of course, are
huge at the level of galaxies,
so they're obvious.
But it's hard to connect
them to the early universe.
So we can make our most
precise comparison between what
we observe and theories
of the early universe
by making careful observations
of the cosmic background
radiation itself, which has
these ripples in the intensity,
It is not quite uniform.
There really are ripples at the
level of one part in 100,000,
which can now be observed.
And inflation makes
a clear prediction
for the spectrum
of those ripples,
how the intensity should
vary with wavelength.
And I showed you this graph last
time from the Planck satellite.
The agreement between the
prediction and the theory
is really marvelous.
So we'll be coming back to that
near the end of the course.
Finally, in the last
lecture, I began
to talk about inflation and
the possible implications
for a multiverse, the idea that
our universe might be embedded
in a much larger
thing consisting
of many universes, which
we call a multiverse.
And the key point is that
most inflation models
tend to become eternal.
And that is once inflation
starts, it never stops.
And the reason for
that, basically,
is that the metastable
material, this repulsive gravity
material that's causing
the inflation, decays,
but it also
exponentially expands.
And for typical models,
the exponential expansion
completely overpowers the decay.
So even though it's an
unstable material that decays,
the total volume of it actually
increases exponentially
with time rather than decreases.
Decays happen however,
and wherever decay happen,
it forms what we call
a pocket universe.
We would be living in one
of those pocket universes.
And the number of
pocket universes
grows exponentially with time as
the whole system grows and goes
on, as far as we
can tell, forever.
And that is the picture
of the multiverse
that inflation tends to lead to.
Finally, this is my
last summary slide
and then we'll
start new material.
At the very end of
lecture, I talked
about a problem, which is very
important in our present day
thinking about
physics and cosmology,
and that is the nightmare that
this discovery of dark energy
leads to.
What was discovered
at about 1998
is that the expansion
of the universe
is not slowing down under
the influence of gravity
as one might expect,
but Instead, it's
actually accelerating.
The universe is expanding
faster and faster.
And that indicates
that space today
is filled with some repulsive
gravity material, which
we call the dark energy.
And the simplest interpretation
of the dark energy
is that it simply vacuum energy,
the energy of empty space.
Space does have an
energy density that
have exactly the
properties that we observe,
so it seems natural to
draw that connection.
Vacuum energy, at first,
might seem surprising.
If a vacuum's empty, why should
it have any mass density?
But in a quantum field theory,
it's really not surprising
because in a quantum
field theory,
the vacuum is really not empty.
In a quantum field
theory, there's
no such thing as
actual emptiness.
Instead, in the vacuum, one has
constant quantum fluctuations
of fields.
And in our current theory
of particle physics,
the standard model
of particle physics,
there's even one particular
field called the Higgs field,
which has a non-zero
mean value in the vacuum
besides fluctuations.
So the vacuum is a
very complicated state.
What makes it the
vacuum is simply
that it's alleged to be the
state of lowest possible energy
density, but that
doesn't have to be zero
and doesn't even
look like there's
any reason why it
should be zero.
So there's no problem
buying the fact
that maybe the vacuum does
have a non-zero energy density.
The problem comes
about though when
we try to understand the
magnitude of this vacuum
energy.
If it was going to have
a vacuum energy density,
we'd expect it to be
vastly larger than what
is observed in the
form of the expansion
acceleration of the universe.
So a typical order of magnitude
in the particle physics
model for the vacuum
energy is, in fact,
about a full 120
orders of magnitude
larger than the
number that's implied
by the acceleration
of the universe.
So that is a big problem.
I began to talk about a possible
resolution to that problem.
It's only a possible resolution.
Nobody has really
settled on this.
But there's a
possible resolution
which comes out
of String theory,
and in particular
from this idea, which
is called the landscape
of String theory.
Most String theorists believe
that String theory has
no unique vacuum,
but instead, there's
a colossal number, perhaps
something like 10 to the 500,
different metastable
states, which
even though they are metastable,
are incredibly long-lived,
long-lived compared to the age
of the universe as we know it.
So any one of these 10 to
the 500 different states
could serve as effectively
the vacuum for one
of these pocket universes.
And the different
pocket universes
would presumably fill the
whole set of possible vacua
in the landscape, giving reality
to all these possibilities
that come about
in String theory.
And in particular, each
different type of vacuum
would have its own
vacuum energy density.
And because there are
both positive and negative
contributions-- I think I
didn't read that out loud--
but there are both positive
and negative contributions
that arise in quantum
field theories.
So the vacuum energy
of a typical state
could be either
positive or negative.
And what we would
expect of these 10
to the 500 different
vacua is that they
would have a range
of energy densities
that would range from something
like minus 10 to the 120
to plus 10 to the 120
times the observed value.
So the observed value
would be in there,
but would be an incredibly
small fraction of the universes.
Yes?
AUDIENCE: Does this mean that
so many pocket universes could
be closed and opened as well
in terms of their geometry?
Or--
PROFESSOR: They're
actually predicted
to be open due to complications
about how they form,
which I'm not going to go into.
But they should all be open, but
very close to flat for the ones
that under a lot of inflation.
So they'd be
indistinguishable from flat,
but technically, they'd be open.
Yes?
AUDIENCE: Is the minus 10 to
the 120 plus 10 to the 120 just
chosen because we're off
520 orders of magnitude,
or is it predicted
somewhere else?
PROFESSOR: Well,
when we say we're off
by 120 orders of magnitude,
the more precise statement
is that the estimate of what
a typical range of the energy
should be is 10 to 120
times the observed value.
So this is basically just
a restatement of that.
And you might
wonder why I didn't
put 5 times 10 to the
120, but in fact, the 120
itself is only accurate
to within a few orders
of magnitude, so 5
times that wouldn't
have made any difference
in the way one
actually interprets
those numbers.
10 to the 123 is probably
slightly more accurate number
actually.
But this is good enough
for our purposes.
Yes?
AUDIENCE: Just a
general question
about inflation properties.
We think of attractive
gravity as driving
the motion of objects
through space.
So why do we think
of repulsive gravity
like to drive the
expanse of space itself?
PROFESSOR: Well, for one
thing, it does actually
behave differently.
Repulsive gravity,
repulsive gravity
that appears in
general relativity,
is not just ordinary gravity
with the opposite sign.
Ordinary gravity
has the property
that if I have two objects to
attract each other with a force
proportional to the
masses of those objects.
This repulsive
gravity is actually
an effect caused by the negative
pressure in the space between.
So if I have two
objects, they will
start to accelerate apart
by the amount that's
totally independent
of the masses.
This is not really the
masses that's causing it.
So the whole force was
completely different,
so we can't really
just compare them.
In either case, when
everything is moving apart,
it's really a
matter of viewpoint
when you think of the
whole space as expanding
or whether you think
of the particles
as moving through space.
In relativity, there's no
way to put a needle on space,
put a pen in it and
say this is stationary.
So we really can't say that
the space is moving or not.
In cosmology, we usually
find that the simpler picture
and the one that we
will generally use
is that space expands
with the matter.
It gives a much
simpler description
of how things behave.
Good question.
Yes?
AUDIENCE: I have a question
going back a few slides.
PROFESSOR: Sure, you
want me to go back.
AUDIENCE: How the energy
of the early universe
seemed to be close to zero.
Are there theoretical
models that would explain
or that would say it
should be exactly 0?
PROFESSOR: Yeah, there are.
I didn't mention it.
But if the universe is closed,
which is a possibility.
Even if it's very nearly flat,
it could still be closed.
If it were closed, it would
have exactly zero energy.
Yes?
AUDIENCE: So the
cosmic background,
microwave background,
picks ups that it's
pretty similar in all
directions once correct for it.
And this leads to the thought
that the cosmological principle
all over the universe
is pretty identical.
Is it possible that
we are actually
located in just a smaller
like circular pathway
and it may be different
than [? allowed. ?]
And there's many
of these patches,
so we-- there's actually
like a speckled form.
PROFESSOR: OK.
So if you didn't
hear the question,
I was asked if it's possible
that the universe is not
really homogeneous on
a very large scales,
but really speckled, just
that speckles are large
and our speckle might
look very different
from other speckles
that are far away.
And that was the question.
And the answer is certainly
if the multiverse picture
is right.
That is exactly the case
that's being predicted.
These other pocket
universes could
be viewed as other
speckles in your language,
and they'd be very different
from what we've observed.
So inflation actually
changes one's attitude
about this particular question.
Back in the old days,
before inflation,
the uniformity of the
universe had no explanation,
so it became a postulate.
And nobody postulates
that something
is uniform on that scale.
If you are going to
make a postulate,
you just postulate that
the universe is uniform.
So that was the postulate
that was in use.
But now that we think of the
homogeneity of the universe
as being generated by a
dynamical process, inflation,
then, it's a natural
question to ask,
what is the scale
of the homogeneity
that that generates.
And it's certainly
a scale that's
much larger than
what we can observe.
So we don't really expect
to see inhomogeneity
as caused by different
pockets of inflation,
but the model seems to
make it very plausible that
is what we would see if
we could see far enough.
Any other questions while
we're on a little break here?
Yes?
AUDIENCE: If the
universe is expanding,
then I think like we are
expanding as well, so how can
we observe the change
from a distance,
in particular everything
is increasing scale?
PROFESSOR: OK.
That's a very good question.
The question was if the
universe is expanding,
then the universe is everything.
So everything is expanding.
And if everything's expanding,
when you compare things
with rulers, they
have the same length.
So how would you even observe
that everything was expanding?
And the answer to
that is that when
we say the universe
is expanding,
we're not really saying that
everything is expanding.
When we say the
universe is expanding,
we really are saying that the
galaxies are getting further
apart from each other,
but individual atoms
are not getting bigger.
The length of a
ruler, determined
by the number of atoms
and how those atoms move
to ground state, does not
expand with the universe.
So the expansion is
now partially driven
by the repulsive
gravity that exists
now, which is causing the
universe to accelerate.
But most of the expansion is
really just a residual velocity
from the Big Bang,
whatever caused it then.
I would assert inflation.
And it's just a matter
of coasting outward, not
being pulled outward,
and that coasting outward
does not cause
atoms to get bigger.
Yes?
AUDIENCE: Is the current
idea that the expansion,
like the acceleration,
is indefinite or are we
going to reach a stop point?
PROFESSOR: OK.
What will be the ultimate
future, I'm being asked here.
And the answer, as you might
guess, is nobody really knows.
But in the context of the kind
of models I'm talking about,
there is a pretty
definite answer,
which is that our
pocket universe--
I'll answer at the level
of our pocket universe
and I'll answer at the level
of the multiverse as a hole.
At the level of our
pocket universe,
our pocket universe
will thin out.
Life will eventually
become impossible
because matter density
will be too low.
It will probably decay.
Our vacuum is probably
not absolutely stable.
Very few things 2
String theory are,
if something like String
theory is the right theory.
But even though it
will be decaying,
it will be expanding still
faster than it decays.
So the decay will cause
holes in our universe.
It will become
like Swiss cheese.
But the universe, as
a whole, will just
go on exponentially
expanding, perhaps
forever, as far as
we can tell, forever.
The multiverse is a
more vibrant object.
The multiverse,
as I always said,
would continue to generate
new pocket universes forever.
So the multiverse
would forever be alive
even though each pocket
universe in the multiverse
would form at some time
and then ultimately die,
die of thinning out
into nothingness.
Yes?
AUDIENCE: Just to add to that.
Do you believe that maybe
it's a cyclic process?
So it expand and decay and
then come back [? yet again ?]
and then happen all over again?
PROFESSOR: OK.
The question is could it
be a cyclic process that
expands, reaches maximum,
comes back and crunches,
and expands again.
That is certainly a
possibility, and there
is some people who
take it very seriously.
I don't see any evidence for it.
And furthermore, there
never really was and still
really isn't a reasonable
theory of the bounce
that would have to be
a part of that theory.
Yeah?
AUDIENCE: But would it be
the expansion overtaking
the decay in our own vacuum
that our universe exists
in, our own little pocket
vacuums of ultimate decay
within our system create more
little pocket universes--
[INTERPOSING VOICES]
PROFESSOR: Within.
Yes.
Yeah, that's correct.
They would not be a big fraction
of the volume of our universe,
but, yes.
The pieces in our universe
that might decay in the future
would produce new
pocket universes.
Most of them would be very low
energy pocket universes that
would presumably not create
life, but some of them
could nonetheless have a high
enough energy to create life.
So we would expect
new, thriving universes
to appear out of our
own pocket universe
as it reaches this
expansion death.
Yes?
AUDIENCE: What does
distinguishes different vacua
besides the
cosmological constant?
PROFESSOR: The question
is what distinguishes
the different vacua besides
the cosmological constant.
And the answer is that they can
distinguish in many, many ways.
What fundamentally
distinguishes them
is the rearrangement
of the innards
within the space, maybe a little
bit more precise without trying
to get into details
which I probably
don't understand either.
But what's going on is that
String theory fundamentally
says that space has nine
dimensions, not the three
that we observe.
And the way the
nine becomes three
is that the extra
dimensions get twisted up
into tiny little knots, so
they occupy too small a length
to ever be seen.
But there are many
different ways
of twisting up those
extra dimensions,
and that's really what leads
to these very large numbers
of possible vacua.
The extra dimensions are
twisted up differently.
So that means that as
far as the low energy
physics in these
different vacua--
practically everything
could be different,
even the dimension of
space could be different.
You could have different numbers
of dimensions compactified.
And the whole particle
spectrum would
be different because what we
view as a particle is really
just the fluctuation of vacuum.
And if you have a different
structure to the vacuum itself,
the kinds of particles
that exist in it
could be totally different.
So the physics inside
these pocket universe
could look tremendously
different from what
we observe even though
that we're predicating
the whole description
on the idea
that, ultimately, it's
the same laws of physics
that apply everywhere.
Other questions?
Yes?
AUDIENCE: [INAUDIBLE]?
PROFESSOR: OK.
I think you're asking about
if we have a small patch, then
that goes inflation and the rest
doesn't, how does the patch end
up dominating because
it started out
with just a small
fraction of the particles.
Doesn't it still have the same
small fraction of particles?
Is that what you're asking?
AUDIENCE: Well, I guess.
If you start out with the
smooth particles being
the excessive matter,
and one of the particles
behaves and the other
two particles [INAUDIBLE]
even if it's still
just two particles?
PROFESSOR: Right.
It isn't the number of
particles conserved, basically,
as all this happens, is I
think what you're asking.
AUDIENCE: Well, even if it
eventually [? is called ?]
expanded wave because the
second part will [INAUDIBLE]
PROFESSOR: Well, let's see.
I'm having a little
trouble hearing you.
But let me make a definite--
let me make a broader statement,
and you can tell
me if I've answered
what you're asking about or not.
When one of these
patches undergoes
the exponential
expansion of inflation,
the energy is really
not very well described
as particles at all.
It's really described
in terms of fields.
And fields sometimes behave
like particles, but not always.
And in this case-- in principle,
there's a particle description
too, but it's not
nearly as obvious
as the field description.
So you have energy stored in
fields and the region grows.
The energy stored
in those fields
actually increases
as the region goes.
The energy density remains
approximately constant.
And that sounds like
it would violate
the conservation of energy,
but we discussed the fact
that what saves
conservation of energy
and allows this to happen in
spite of conservation of energy
is that as the
region expands, it
is filled by a gravitational
field, which is now occupying
a larger and larger volume, and
that gravitational field has
a negative energy density.
So the total energy, which
is what has to be conserved,
remains very small
and perhaps zero,
and the region can
grow without limit
while still having this very
small or zero total energy.
Then, eventually it
decays and when it decays,
it produces new particles,
and the colossal number
of new particles, and
those would be the stuff
that we would be made out of.
And that number is vastly larger
than the number of particles
that may have been
in this region
when the inflation started.
Yes?
AUDIENCE: So does the emergence
of [INAUDIBLE] just purely
a conservation of energy?
Like, what do you need to
make these [? an organism ?],
the negative energy,
zero [INAUDIBLE] I guess.
PROFESSOR: Are you saying
the conservation of energy
maybe controls the whole
show, and that this is really
the only thing consistent
with conservation of energy?
I think that's probably
an exaggeration
because if nothing happened,
that would conserve energy too.
So I think one needs more than
just the conservation of energy
to be able to describe how the
universe is going to evolve.
OK.
Let me continue.
Get back to the beginning
there, back to the end.
OK.
So I just finished talking about
the landscape of String theory
and how it offers all
these possible vacua.
So in particular, and this is
now the new stuff, if there
are 10 to the 500 vacua of
String theory, for example.
We don't really know the number,
but something crazy like that.
And if only one part in
10 to the 120 of them
have this very small energy,
thus the energy densities
are spread from plus
10 to the 120 times
what we observe to minus 10 to
the 120 times what we observe.
That would mean that
what we observed
would be a narrow slice in the
middle there occupying about 10
to the minus 120th of the
length of that spread.
We would then expect--
and all this, of course,
is very crude estimates.
It's not really the
numbers that's important,
it's whether or not
you believe the ideas.
But we'd expect then that
about 10 to the minus 120
of the different vacua would
have an acceptably low vacuum
energy density.
But that's still a
colossal number because 10
to the minus 120
times 10 to the 500--
you add the exponents--
is 10 to the 380.
So we would still predict
that even though they'd
be very rare, there might be
10 to the 380 different kinds
of vacua, all which would
have a vacuum energy density
as well as what we observe.
So there's no problem finding,
in the landscape, vacua
whose energy density is
as low as what we observe.
But then there's the question
if they're so incredibly rare,
wouldn't it take
a miracle for us
to be living in one of these
incredibly unusual vacua
with such an extraordinarily
low vacuum energy density.
That then leads to
what is sometimes
called Anthropic considerations
or perhaps a selection effect.
And to see how that works and
make it sound not as crazy
as it might sound
otherwise, I want
to begin by giving an example
where I think one could really
say that this effect happens.
And that is suppose we just
look at our own position
in our own visible
universe and look at,
for example, the mass density.
Where we're actually
living is incredibly
unusual in many ways, but one
of the ways we could talk about,
which is just simple
and quantitative,
is the mass density.
The mass density of the
things around this room
is on the order of one gram per
centimeter cubed give or take
a factor of 10.
The factor of 10 is
not very important
for I'm talking about here.
The point is that
the average mass
density of the universe, the
visible universe, is about 10
to the minus 30 grams
per centimeter cubed.
It's really unbelievable
how empty the universe is.
It's actually a far lower mass
density than is possible for us
to achieve in laboratories
on Earth with the best vacua
that we can make in
our laboratories.
So where we're living
has a mass density of 10
to the 30 times the average
of the visible universe.
So we're not living in a typical
place in our visible universe.
We're living in an
extraordinarily atypical place
within our visible universe.
And we can ask how
would we explain that.
Is it just a matter
of chance that we're
living in a place that's
such a high mass density?
Doesn't seem very likely
if it's a matter of chance.
Is it luck?
Is it divine
providence, whatever?
I think most of us would admit
that it's probably a selection
effect.
That that's where life happens.
Life doesn't happen throughout
most of the visible universe,
but in these rare
places, like the surface
of our planet, which is
special in more ways than just
the mass density, but
the mass density alone
is enough to make it
extraordinarily special.
We're off by a factor
of 10 to the 30
from the average
of our environment.
So if we're willing
to explain why
we live in such an unusual place
within our visible universe
and explain that as simply
a requirement for life,
then it doesn't seem to be such
a stretch to maybe imagine--
and it was Steve Weinberg who
first emphasized this in 1987.
Certainly not the
first person to say it,
but the first person to
say it and have people
sometimes believe him.
He pointed out that may be the
low energy-- the low vacuum
energy density could be
explained the same way.
If we're not living
in a typical place
within our visible
universe, there's
no reason for similar
ideas to expect
that we should be living
in a typical place
in the multiverse.
Maybe only a small fraction
of these different types
of pocket universe's
can support life.
And maybe the only
way to have life
is to have a very small value
for the vacuum energy density.
And there is some
physics behind that.
Remember this vacuum energy
density drives expansion--
acceleration, I should say.
So if the vacuum energy density
were significantly larger
than what we
observe, the universe
would accelerate
incredibly rapidly
and would fly apart
before there'd
be any time for anything
interesting to happen
like galaxies forming.
Weinberg based his arguments
here on the assumption
that galaxies are a
necessity for life.
Yes?
AUDIENCE: So that's
what I was going to ask.
Why do we assume that our
universe is the only one that
could have like-- why couldn't
just all the multi-universes
have like--
PROFESSOR: Right.
Right.
Well, that's OK.
That is what I am talking about.
I'm trying to answer it.
So if the vacuum energy density
were significantly larger
than what we observe,
the universes
would fly apart so fast
that there could never
be galaxies and therefore
never planets, none of things
that we think of as being
associated with life as we know
it.
Conversely, if the vacuum energy
density were negative, but had
a magnitude large compared
to what we observed,
that would be a large negative
acceleration, an implosion.
And those universes would
just implode, collapse,
in an incredibly short amount
of time, much too fast for life,
of any type that we
know of, to form.
So there is a physical argument
which suggests that life only
forms when the vacuum
energy density is very low.
And Weinberg and his
collaborators-- and this
is the same Steve Weinberg who
wrote the First Three Minutes
that we're reading-- calculated
what the requirements would
be for galaxy formation.
And they decided that, within
about a factor of 5 or so,
the vacuum energy
density would have
to be about the same as
what we observe or less
in order for galaxies to form.
So it seems like a
possible explanation.
It's certainly not a generally
accepted explanation.
These things are very
controversial one.
I guess that's, in
fact, what I was
going to talk about
on my next slide.
Some physicists by this
selection effect idea.
I tend to buy it.
But a number of physicists
regard it as totally
ridiculous, saying you
could explain anything
if you except
arguments like that.
And there's some truth to that.
You can explain a lot
of things if you're
willing to just say,
well, maybe that's needed
for life to happen.
So because of that, I would
say that these selection effect
arguments or anthropic
arguments should always
be viewed as the
arguments of last resort.
That is, unless we
actually understand
the landscape of
String theory, which
we do not in detail,
and once we actually
understand what it
takes to create life,
we really can't do more than
give plausibility arguments
to justify these
anthropic explanations.
But these anthropic
arguments do sound sensible.
I think there's nothing
illogical about them,
and they could very well be the
explanations for some things.
As I pointed out, I think it
is the explanation for why
we are living in
such an unusual place
within our own visible universe.
And it means that these
selection effect arguments
become very attractive when the
search for more deterministic
explanations have failed.
And in the case of trying to
explain the very small vacuum
energy density, I think
other attempts have failed.
We don't have any calculational,
deterministic understanding
for why the vacuum energy
should be so small.
So is it time to accept this
explanation of last resort
that the vacuum energy
density is small
because it has to be
for life to the evolve?
Your guess is as good as mine.
I don't really know.
But I would say that, in the
case of the vacuum energy
density, people have
been trying very, very
hard for quite a
few years now to try
to find a particle physics
explanation for why the vacuum
energy has to be small, and
nobody's really found anything
that anybody has found-- that
any large number of people
have found to be acceptable.
So it is certainly a
very serious problem.
And I think it is
time to take seriously
the argument of last resort,
that maybe it's that way only
because in the parts of the
multiverse where it's not
that way, nobody lives there.
So I would say it's
hard to deny, as of now,
that the selection
effect explanation is
the most plausible of
any explanation that
is known at the present time.
To summarize things--
I'm actually done now,
but let me just
summarize what I said
to remind you where we're at.
I've argued that the
inflationary paradigm
is in great shape.
It explains the large
scale uniformity.
It predicts the mass
density of the universe
to better than about 1% accuracy
and explains the ripples
that we see in the cosmic
background radiation,
explaining them as a result
of quantum fluctuations
that took place in the
very early universe.
The picture leads
to three ideas that
at least point towards
the idea of a multiverse.
It certainly doesn't prove that
we're living in a multiverse.
But the three ideas that
point in that direction
are, first of all, the
statement that almost
all inflationary models
lead to this feature
of eternal inflation, that
the exponential expansion
of the inflating material,
generally speaking,
out runs the decay
of that material
so that the volume grows
exponentially forever.
Second point is that, in 1998,
the astronomers discovered
this rather amazing fact
that the universe is not
slowing down as it expands,
but in fact, is accelerating.
And that indicates
that there has
to be some peculiar material
in the universe other than what
we already knew was here,
and that peculiar material is
called the dark energy.
And we don't have any simple
interpretation of what it is,
but it seems to most
likely be vacuum energy.
And if it is, it
leads immediately
to the important
question of can we
understand why it has
a value that it has.
It seems to be much smaller
than what we would expect.
And then three, the
String theorists
give us an interesting
way out here.
The String theorists tell
us that maybe there's
not unique vacuum to
the laws of physics,
but maybe there's a
huge number, which
seems to be in fact what
String theory predicts.
And if there is, then of
the many different vacua
you expect there to be,
in fact perhaps even
a large number, that would have
this very small vacuum energy
density, a tiny fraction of
the total different vacua,
but nonetheless a
large number of vacua
that would have this property.
And then this
selection effect idea
can provide a
possible explanation
for why we are living in one of
those very unusual vacua which
has this incredibly tiny
vacuum energy density.
So finally, I'd
just like to close
with a little sociological
discussion here.
Do physicists really
take this seriously?
And I'd like to tell you about
a conversation that took place
at a conference a few years ago.
Starting with Martin Rees, who I
don't know if you know the name
or not, but he's an Astronomer
Royal of Great Britain,
former president
of Royal Society,
former master of
Trinity College as well,
a very distinguished person,
nice guy, too, by the way.
And he said that
he is sufficiently
confident in the multiverse
to bet his dog's life on it.
Andrei Linde, from Stanford,
a real enthusiastic person
about the multiverse, one of the
founders of inflation as well,
said that he's so
confident that he
would bet his own life on it.
Steve Weinberg was not
at this conference,
but he wrote an article
commenting on this discussion
later which became known.
And I always considered
Steve Weinberg
the voice of reason,
which is why we're
reading the First Three Minutes.
And he said that I have
just enough confidence
in the multiverse to
bet-- guess what's
coming-- the lives of both
Andrei Linde and Martin Rees'
dog.
That's it for the
summary, or the overview.
Anymore overview type
questions before we get back
to the beginning, actual
beginning of the class?
Yes?
AUDIENCE: You said-- so
selection effect argument says
that it's because life
exists within these certain
constraints, omega being one
and low energy larger than it
generally is allowed, that
life could exist in this way.
But we're considering
carbon-based life.
What if there's some
other [INAUDIBLE] life
forms out there that gives
us different energies
and radiation and
stuff like that?
PROFESSOR: Yeah, what
you're pointing toward
is certainly a severe weakness
of these selection effect
arguments, that we really know
about carbon-based life, life
that's like us, and we can
talk about what conditions
are needed to make life
like us, but maybe there's
life that's totally
different from us
that we don't know
anything about that
might be able to
live under totally
different circumstances.
That is a real weakness.
However, I would argue-- and
this is also controversial.
Not everybody would agree
with what I'm about to say.
But I would argue that if
we're willing to explain
the unusual features of
the piece of the universe
that we live in by
selection effect arguments--
the fact I used, the
example is simply
that we're living a place
where the mass density is
10 to the 30 times
larger than the mean.
If we're willing to use the
anthropic arguments to explain
that, then I think all those
same issues arise there also.
If life was really teem--
if the universe was really
teeming with a different
kind of life that
thrived in vacua,
then we'd be much more
likely to be one of them,
extremely unusual creatures
living on the
surfaces of planets.
So I think it's a
possible weakness
that one has to
keep in mind, but I
don't think it should
stop us from using
those arguments completely.
But it is certainly a
cause for skepticism.
Yes?
AUDIENCE: Isn't the point
of the selection principle
just the fact that exist--
the universe selected for us.
Does it matter for the general
of just for like carbon-based
[? organisms? ?] Is the fact
that we exist [INAUDIBLE]
that we've been selected
for [INAUDIBLE]?
PROFESSOR: You're
asking about, I
think, how peculiar
to carbon-based life
should we expect these selection
effect arguments to be.
AUDIENCE: Doesn't the selection
affect where [INAUDIBLE]?
PROFESSOR: Now that's
an important point,
and certainly one that's not
settled among philosophers,
probabilist,
physicists, or anybody.
What you're asking-- if
I'm summarizing it right--
is when we're thinking
of the selection effects,
should we may be only talk
about carbon-based life
because, after all, we know
that we are carbon-based life.
So what does it matter if
there's other kinds of life
out there?
That's one way of
looking at it, certainly.
Or, maybe we should think
about all kinds of life.
That's something
else that people say.
The problem I would--
I tend to be by the way
the kind of person that thinks
that all life is relevant,
not just carbon-based life.
Because we happen
to be carbon-based,
and we happen to
have fingernails
that have a certain
length, and we
happen to have hair
that's a certain length
or a certain
thickness, does that
mean we should only
think of those things
as being relevant
when we're thinking
about selection effects?
And I would say
that they're not.
If our hair had a
different thicknesses,
we would still be able to
make measurements and so on.
So from my point
of view, when one
thinks about these issues
of selection effects,
one should precondition
only on the elements that
are necessary to ask the
question in the first place.
And what I would like to
think-- and as I point out,
this is controversial,
not everybody
agrees with me-- is that
a good theory should
be a theory in which you could
say that most of the people who
ask this particular question
will get the answer that we
say.
If only a tiny fraction of
people who ask that question
will get that answer, but
that same tiny fraction
happens to have hair
of a certain color
and you have hair
of that color, to me
that's still not an explanation
because you don't know why you
have hair of that
color or why you're
living in such an unusual place.
OK that strikes up a
lot of conversations.
Yes?
AUDIENCE: You
mentioned last time
that the different
pocket universes
that comprise the multiverse
are disconnected from each other
though they start out as patches
within the preceding vacua.
What starts to disconnect
them fundamentally
from the vacuum
which they formed?
PROFESSOR: The question is
what is it that separates these
different pocket universe's.
If they start out all
in the same space,
don't they remain all
in the same space?
And the answer is they do, but
the space they started out in
was expanding at
a very rapid rate.
So in most cases,
but not all actually,
two pocket universes will
form far enough apart
from each other
that they will never
touch each other as they grow
because the space in between
will expand to fast to
ever allow them to meet.
However, collisions
of pocket universities
will occur if two pocket
universes form close enough
to each other, the expansion
of space in between
will not be enough to keep them
apart, and they will glide.
How frequent one should
think of that as being
is an incredibly tough
question to which
nobody knows the answer.
There are actually--
at least there
is at least one
astronomical paper
in the literature by
a group of astronomers
who have looked for possible
signs of a collision of bubbles
in our past.
They did not find
anything definitive.
But it is something
to think about,
and it's something people
are thinking about.
There really are
quite a few papers
about collisions of
bubbles in the literature.
Yes?
AUDIENCE: How long
is long-lived?
So if the energy density was
too large and too negative
would that still
be long-lived if it
were to collide upon itself?
PROFESSOR: Talking about the
lifetime of these universes
that I said would
collapse very quickly.
How quickly do I mean?
AUDIENCE: Like the
metastable long-lived.
PROFESSOR: I used
the word long-lived
at least twice in what I've
talked about-- I talked
about the long-lived
metastable vacua.
And there, by long-lived
I mean anything
that's long compared to the age
of our universe since the Big
Bang.
Long means long
compared to 10 to the 10
years in that context.
I also said that if the
vacuum energy of a universe
were large and negative, it
would very rapidly collapse.
That could be as fast as
10 to the minus 20 seconds.
It could be very fast
depending on how large
the cosmological constant was.
Yes?
AUDIENCE: So I have read
that there's an effect such
that if you're vacuum
can be seen differently
by different observers.
For example, inertial--
there's something
that I read in effect it says
that if one inertial observer
sees vacuum, another
observer that's
accelerating with
respect to that observer
would see like a number
of particles [INAUDIBLE]
a warm gas.
So how much of the effect we
observe are due to the fact
that perhaps we believe the
universe is accelerating,
and we're accelerating perhaps
with respect to some vacuum
and we're just observing that.
That's just a fact of our
motion not necessarily the--
PROFESSOR: You're
touching on something
that is in fact very confusing.
What is your name?
AUDIENCE: Hani.
PROFESSOR: Hani?
What Hani said was
that he had heard--
and this is correct--
that if one had simply
a region of ordinary
vacuum-- and I am now
going to talk about
special [INAUDIBLE] vacuum.
You don't even need relativity.
You don't general relativity,
you just need this.
If you had an accelerating
observer moving
through that vacuum, the
accelerating observer
would not see something
that looked like vacuum,
but rather would see particles
that in fact would look
like they had a finite
temperature which you can
calculate, a temperature that's
determined by the acceleration.
So the question is,
how much of what
we see should we think
of as really being there
and how much might be caused
just by our own motion.
And there's not a terribly
great answer to that question
that I know of except that we--
when these questions come up,
we tend to just
adopt the philosophy
that an observer
who's freely moving,
which really means moving
with the gravitational field,
a geodesic observer as the
word phrase is sometimes used,
essentially defines what
you might call reality
and then if you calculate what
accelerating observers might
see in terms of that reality.
And we are almost
geodesic observers.
The Earth is exerting a
force on our feet, which
violates that a little bit,
but by the overall cosmic scale
of things where
the speed of light
is what determines
what's significant,
we are essentially inertial
or geodesic observers.
Yes, Aviv?
Aviv first and then
the one in front.
AUDIENCE: So I'm wondering
about the philosophical approach
to this discussion and why
the very-- by the definition,
we can't possibly
observe another universe.
And so maybe we
have a theory that
makes a lot of great
predictions like inflation.
But it may also make
predictions about multiverse.
We can't possibly empirically
determine whether that's true
or not, so a
nonfalsifiable question.
And so I feel like
[INAUDIBLE] who [INAUDIBLE]
essentially never
going to be answered.
And if we're going to
be strict empiricists,
should we not be concerned
with this question?
PROFESSOR: The question is if we
could never see another pocket
universe, is it even
a valid question
to discuss whether
or not they exist,
a valid scientific question.
That is also a question
which is generally
debated in the community, and
people have taken both sides.
There certainly is
a point of view,
which I think I
tend to take, which
is that we never really
insist that every aspect
of our theories can be tested.
If you think about any theory,
even Newtonian gravity,
you can certainly
imagine implications
of Newtonian
gravity that you can
calculate that
nobody's ever measured.
So I think in practice we
tend to accept theories
when they have made enough
measurements that we've tested
so that the theory
becomes persuasive.
And when that happens, I think
we should, at the same time,
take seriously whatever
those words mean,
the implications that the theory
has for things that cannot be
directly tested.
As far as the other
pocket universes,
some people think
it's important,
and maybe I do too,
that even though it's
highly unlikely, incredibly
unlikely, unbelievably unlikely
that we'll ever acquire
direct observational evidence
for another pocket universe,
it's not really in principle
impossible because of the fact
that pocket universes can,
in principle, collide.
So we could, in principle,
describe with evidence
that our universe has had
contact with another pocket
universe in the past.
Yes.
AUDIENCE: What
determines the stability
of a particular vacuum state?
Is it simply things with higher
vacuum energies are less stable
and things with lower vacuum
energies are more stable?
PROFESSOR: The question
is what determines
the stability of
the different vacua.
Is it simply that
higher energy ones
are more unstable and lower
energy ones are more stable
or is it more
complicated than that?
And the answer,
as far as I know,
is that there is a trend
for higher energy ones
to be more unstable and lower
energy ones to be more stable.
But it's not as simple as that.
There are also wide
variations that
are independent of
the energy density.
AUDIENCE: If the one
that we're living in
is incredibly is really
ridiculously close to zero
in a city that seems to make
it incredibly unlikely that we
would pay anything else I soon
PROFESSOR: Right.
The question is if
our universe has
such has such a
small energy density
relative to the average.
Wouldn't that mean
that we should also
expect to be much more
long-lived than average?
And the answer is I guess so.
But as far as the effect
on the Swiss cheese
picture that I described
for the ultimate future,
it doesn't change the
words that I used.
It just changes how frequent
those decays would be.
But since the future of
this pocket universe,
if this picture is
right, will be infinite,
decays will happen no matter
how small the probability is.
An infinite number of
decays will happen in fact.
OK we should probably
go on now even
if there are more questions.
We have a whole term to
discuss things like this.
The next thing I
want to do is handle
some housekeeping details.
I'd like to arrange
office hours.
And the problem sets
are due on Friday,
so what [? Tsingtao ?]
and I thought
was that a good time
for office hours
would be on Wednesdays
and Thursdays.
One of us on each of those days.
It turns out that I can't
really do Thursdays,
so one of us on
each of those days
ends up meaning
that I'll probably
be having office
hours on Wednesdays.
This is all
provisional depending
on how it works with you folks.
And [? Tsingtao ?]
will probably be
having office
hours on Thursdays.
Generally speaking, if one
wants to have an office
hour that most
people can come to,
I think it should be
in the late afternoon.
So maybe we'll start by
discussing my office hours
since it comes before
[? Tsingtao's, ?] Wednesday
versus Thursday.
So on Wednesday, I
can do an office hour
in the late, normal afternoon,
which might mean 4:00 to 5:00
I think after five some
people have sports activities
and things.
We're told to try to
avoid those hours.
So 4:00 to 5:00 would be
a reasonable possibility
for my office hour on Wednesday.
If that doesn't
work, I could stay
and have the office
hour in the evening.
That's actually what
I did two years ago.
I had an office hour
from 7:30 to 8:30.
It was also
Wednesdays-- I forget.
But it was in the evening,
and that's a possibility.
So let me ask if I have my
office hour from 4:00 to 5:00
on Wednesdays, how
many of you who
might be interested in coming
would not be able to come?
1, 2, 3, 4, 5, 6,
7, 8, 9, 10, 11, 12.
A significant number, but
most of you can come at least.
Let me ask the corresponding
question for the evening.
Suppose I made the office
hour from 7:30 to 8:30
in the evening on Wednesdays.
In that case, how many of
you who might want to come
would not be able to come?
1, 2, 3 5, 6, so it's a smaller
number, but not vastly smaller.
OK I think I'll do it in
the evening for the benefit
of the difference
between those two groups.
And the evening also has
the little slight advantage
that it can be a little more
open-ended if people still
have questions after
the normal time is over.
So I will make my office hour on
Wednesday's from 7:30 to 8:30.
Is that particular hour as good
an hour as any on Wednesday
evening.
Would people want to
move it earlier or later?
Any suggestions for moving
it earlier or later?
AUDIENCE: I know people have
sports til technically at least
7:00, but if it's 6:30 to
7:30 might be a little--
PROFESSOR: 6:30?
You'll be starting at 6--
starting at 6:30 versus-- 6:30
to 7:30, starting at 6:30.
Well, I'd be happy
to do that, but I
suspect we might run
into problems with people
who have sport
activities, but let's see.
How many of you would
be inconvenienced
if I started at 6:30
instead of 7:30?
3, 4, 5, 6, a number.
So I think we'll honor
that and start at 7:30.
I assume 7 is also a bit of
a problem for those people.
We'll say 7:30.
Now, I have to announce
that this week is going
to unfortunately have to be
an exception because I already
have plans for Wednesday night.
So for this week, I
think the best thing--
the only possible
thing, probably
the best-- it's almost
the only possible thing
would be 4:00 to
5:00 on Wednesday.
Wednesday's bit tomorrow.
I'll send you all an email
when I find a room for that.
I think I'll probably
not have it in my office,
but maybe it will
be in my office.
Comment up there?
AUDIENCE: Oh, I was just
going to ask where, but you--
PROFESSOR: Where?
OK, I guess then the
fourth option's my office.
I was hoping to put
a sign of my office
if we're someplace
other than my office.
So should put this
on the board too.
Tomorrow 4:00 to 5:00 PM.
So be at my office
or I'll send email.
Yes?
AUDIENCE: How will we be turning
in the Thursday problem set?
PROFESSOR: We're going
to talk about that now.
For Thursday, for
[? Tsingtao, ?] I remember
you had some constraints.
So what was possible?
TSINGTAO: Yeah.
So I usually leave
around 7:00 PM,
so I have appointment
[? meeting ?],
and today is probably
not very good at 4:00 PM.
PROFESSOR: So 4:00 to 5:00 is a
possibility for [? Tsingtao ?]
on Thursday, and I
guess later than that.
But should be over by
5:00-- by 7:00 either
or do you want it to
be over before then.
TSINGTAO: Oh, 6:00 to 7:002
Oh, 6:00 to 7:002 I guess.
PROFESSOR: 6:00 to
7:00 would be OK?
TSINGTAO: Yeah, that's OK.
PROFESSOR: OK, so let's
start with 4:00 to 5:00.
If [? Tsingtao ?] was to have
an office hour from 4:00 to 5:00
on Thursdays, how many of you
think you might want to go
would be unable to?
Wow, tons!
OK, that seems more than
half of you I think.
So I guess we try to avoid that.
This impact's probably
an athletic region,
but maybe we'll have to do that
for lack of an alternative.
Suppose it were 5:00 to 6:00.
How many of you who would be
interesting in coming-- who
might be interesting
in coming, I should say
I guess because it'll
vary from week to week--
but how many of you
who think you might
be interested in
coming would not
be able to come from 5:00
to 6:00 on Thursdays.
OK, a small group.
1, 2, 3, 4, 5, 6, 7.
Looks to me like 7.
And let's say, I
said 4:00-- That
was at 6:00-- that
was 5:00 to 6:00.
So maybe we should next try 5:30
to 6:30 in smaller increments
here.
If we're 5:30 to
6:30, how many of you
would not be able to come?
Looks like pretty
much the same people.
And if it were 6:00 to
7:00, how many of you
would not be able to come?
Same people, I think it is
literally the same people.
OK.
So it looks like 4:00
to 5:00 is very bad.
And all other times
are about equivalent.
So I think if all other
times are bad equivalently,
we probably might as well
make it 5:00 to 6:00.
And that way
[? Tsingtao ?] can get off
to an earliest possible start
to wherever he's going at 7:00,
and it also means a little
more flexibility in the end
if there are more questions.
AUDIENCE: Where is that located?
PROFESSOR: That
also, I think, will
require us to get a room
which will be announced.
So I will try to
arrange rooms tomorrow
morning and send
it by email, and I
guess I'll post it on
the website as well.
Any other organizational--
and questions
limited to organizational
questions now?
Get back to physics later.
Any organizational
questions before we
start on Doppler shifts?
Yes?
AUDIENCE: If I can't make
a single office hour,
how should I field questions
when I have questions?
PROFESSOR: A good question.
Yeah, there may be some
people, and apparently there is
at least one who cannot
make either of these times,
even though we tried
to optimize things.
So by all means,
don't feel like you
don't have a channel
for questions.
If you have a question,
send an email to
either me, or
[? Tsingtao, ?] or both.
And we'll either answer
it together with you
or answer you by email depending
on what the question is
and what seems useful.
And that goes for everybody.
In that case, if
everybody's on board,
we will now start the actual
material for the term.
Well, the overview
is an overview
of the material for the term,
but not at the standard pace
and the standard
level of detail.
So what I want to
talk about this week--
and I guess I'll only get
to start today and finish
on Thursday-- I had
planned to tell you
everything you need to know
for the problem set by today,
but that's not going to happen.
So I don't-- if people complain,
we could consider postponing
the due date of the problem
set, so consider that an option.
But probably you could
do the problem set anyway
because it is all
described in lecture notes.
But if any of you have
difficulties meeting
that deadline, it will be a
somewhat flexible deadline
this week because of
the fact that I'm not
covering the material
today as I had planned.
And I'll admit that's not
necessarily a good thing
to do in terms of problem set.
So we're going to begin
the course, in principle,
by talking about Hubble's law,
although Hubble's law will
rapidly lead us to the
question of the Doppler shift,
which is what I'll
mainly be talking
about for the rest of today
and for most of Thursday.
Hubble's law itself
is a simple equation
that v is equal to h r,
where v is the recession
velocity of any typical galaxy.
Hubble's law is
not an exact law,
so individual galaxies will
deviate from Hubble's law.
But in principle,
Hubble's law tells you
what the recession velocity
is of a galaxy, at least
to reasonable accuracy.
Where h is what is often
called Hubble's constant.
Sometimes, it is called
the Hubble parameter.
I like actually-- it's called
the Hubble expansion rate.
The problem with calling
Hubble's constant
is that it's not
really a constant
over the lifetime
of the universe.
It's a constant over the
lifetime of an astronomer,
but not a constant over the
lifetime of the universe?
And we'll be talking about
universes, not astronomers,
at least for the most part.
And even over history,
it's not a constant
because the estimate
of Hubble's constant
has actually changed by a
factor of about 10 or so
since Hubble's
original estimate.
And the r that appears here
is the distance to the galaxy.
And if you look at the lecture
notes from two years ago,
they start out by saying
that Hubble's law was
discovered by Hubble in 1929.
When I looked at that
first sentence in my notes,
and when I started to
revise them for this year,
I realized that I heard
that that statement has
become controversial.
Almost everything in
cosmology is controversial,
so even that statement
is controversial.
There are claims
that Lemaitre really
deserves credit for Hubble's
law rather than Hubble.
And there's some
validity to that claim.
There's also some
[? intrigued ?] that happens,
if you want to read about this.
It was discovered by
several of-- I think
amateur historians I think is
what they are often referred
to in the press-- that we know
mainly of Lemaitre's work-- we
being the Western speaking,
the Western English speaking
world-- know mainly
of a Lemaitre's work
through a 1931 translation
in a 1927 paper
he wrote about the
foundations of cosmology.
And it turned out that several
significant seeming paragraphs
in the 1927 French
article somehow
didn't make it to the 1931
English translation, paragraphs
about the Hubble constant.
And for a while, that
seemed like dirty play
and there were accusations that
Hubble, or friends of Hubble,
had suppressed those
paragraphs when
the article was translated.
The truth finally was
discovered a couple years ago
by a physicist named Mario Livio
who actually was on the Daily
Show a couple nights
ago by the way.
He has a book out now, not about
this, but about other things.
But anyway, he
discovered by going
through the archives of the
monthly notices of astronomy,
which is where the article
was published in English.
And turned out it
was Lemaitre himself
he removed those paragraphs.
The paragraphs basically
gave a numerical estimate
of the Hubble constant, but by
1931 Hubble's papered already
been published, so Lemaitre
felt that it was only
a less accurate estimate
of the same quantity
that Hubble had estimated, so he
cut it out of his translation.
What certainly is
true is that Lemaitre
knew about Hubble's law
on theoretical grounds.
Lemaitre was building a model
of an expanding universe.
I don't know if he is
really the first person
to know that an expanding
universe model gave rise
to a linear relationship
between velocity and distance,
but he certainly did know about
it and understood Hubble's law
and give an estimate
of it based on data.
What he did not
do, however, is try
to use data to actually
show that there
was a linear relationship.
What Lemaitre did,
in those paragraphs
that were not
translated, was simply
to look at a large
group of galaxies,
figure an average value for
v and an average value of r
and determine h from
dividing those two averages.
And he admitted
that there was not
really good enough data to tell
if the relationship is linear
or not.
I think it is definitely
fair to say that Hubble
is the person who deserves
credit for arguing first really
with a fairly weak argument,
but then got stronger over time,
that there really is
astronomical evidence
for this linear relationship
between velocity and distance.
So probably it will continue
to be called Hubble's law.
If you look in
Wikipedia, it tells you
either one is acceptable
at the moment,
but Wikipedia articles
change rapidly,
so we'll see what
it says next year.
It's also mentioned
that we should probably
root for Lemaitre since
Lemaitre, it turns out-- well,
he was a Belgian priest,
it was often described,
but he was also an MIT
student, had a Ph.D. for MIT,
which he received in 1927.
You can actually
read his thesis.
When I was writing
my [INAUDIBLE] book,
I remember going
to the MIT archives
and actually picking up
his thesis and reading it.
It's not that well-written
actually, but it's interesting.
Although he got
his Ph.D. from MIT,
it also turns out that
he did most of his work
down Mass Ave at the
Harvard College Observatory,
but the Harvard
College Observatory
did not give degrees
in those days.
It was just an observatory.
So he wanted to get a
degree, so he signed up
at MIT for the Ph.D.
Program and wrote a thesis,
received a Ph.D.
Onward, what I really
want to talk about
is, after mentioning
Hubble's law--
so Hubble's law as an indication
that the universe is expanding.
And we'll talk more about the
history of all this later,
and it actually is very
well-described in Steve
Weinberg's book.
But initially, Einstein
proposed a model
of the universe that was
static, and it was really
Hubble who convinced
Einstein that observationally
the universe does not appear
to be static, but does
appear instead to obey
this expansion law.
So that gave rise to the theory
of the expanding universe.
But what I want to
talk about today
is how one measures the
v that appears here.
There's also a big
discussion about how
one measures r, the distance.
And that is, I think, rather
well-done in Steve Weinberg's
book, and I'm going to
pretty much leave it
to your reading of
Steve Weinberg's book
to learn about how distances to
distant galaxies are estimated.
Roughly-speaking,
I might just say
that they are estimated
by finding objects
in those distant galaxies
whose brightnesses you think
you know, by one
means or another.
And a complicated story
is what objects are there
in brightnesses
we think we know.
But once you find an
object whose brightness
you think you know, those
go by the general name
of standard candles,
a standard candle
being an object whose
brightness you know,
then you can tell
how far the object is
by how bright it appears.
And that becomes a very
straightforward way
of estimating distances,
and that is the only way
we really have of estimating
distances of distant galaxies.
So it's a much longer story than
what I just said, and you'll
read about it in
Weinberg's book.
The velocity is measured
by the Doppler shift,
and that's what lecture
notes one are mainly about,
and that's what I'll be
talking about for the remaining
few minutes of today's class.
And what we want to do in the
course of this set of lecture
notes, this week of
class I guess it will be,
is understand how to
calculate the Doppler
shift both non-relativistically
and relativistically,
and we'll just work out the
primary cases of observer
stationary source moving, source
stationary observer moving,
and all in a line, for
both the relativistic and
non-relativistic cases.
So I think I'll launch into
the first calculation, which
you might even have
time to finish.
I'd like to consider
a case where
the observer is stationary
and the source is moving,
which is normally how we
think of the distant galaxies.
We work in our own reference
frame, so we're stationary,
the galaxy is moving.
How do we calculate
this redshift
I should say at the
asset here, however--
I don't know if I said
it in the lecture notes--
that the cosmological
redshift is actually
a little bit different from what
we're calculating this week.
This week, we're calculating
the special relativity redshift.
But cosmology is not controlled
by special relativity
because special relativity
does not describe gravity,
and gravity plays a
major role in cosmology.
So the cosmological redshift,
we will talk about a little
later in the course,
in a more precise way.
But for now, we, like Hubble--
Hubble didn't know any better--
are ignoring gravity, which
is OK for the nearby stars,
and the further away they
are, the more important
these gravitational influences
are, and ignoring gravity one
could just use special
relativity or even
Newtonian kinematics
to calculate
the relationship between
v and the redshift.
And that's what we'll
be talking about.
So the first problem that
we want to talk about--
and I guess I'll just set it up
and that's as far as we get--
will be a problem where there's
a source of radiation, which
is moving to the right in our
diagram with a velocity, v,
and an observer
who is stationary.
Now of course, all these are
frame dependent statements,
but we're working
in a frame where
the observer is stationary.
And we're also going to assume
for the non-relativistic case,
that the air-- we'll be talking
about sound waves-- but the air
is stationary in this frame.
So the frame of backboard is not
only the frame of the observer,
but it's also the
frame of the air
when we're talking about the
non-relativistic sound wave
calculation.
So to define our
notation, we're going
to let u be equal the
velocity of the sound wave.
And that would normally be
measured relative to the air,
but the air will be at
rest in this picture,
so u will be the velocity
of the sound wave
relative to the diagram.
v is the velocity of the
source already shown.
And we'll be interested
in two time periods,
delta t sub s where
s stands for source,
which will be the period of
the wave at the source, which
is the same as talking
about the period of the wave
as it would be
measured by the source.
And delta t sub
O-- that's supposed
to be a capital O, not a zero.
It is the period of the wave
at the observer or as observed.
And the important point, which
is maybe obvious qualitatively,
is that these two times,
or time intervals,
will not be equal to each other.
And the reason, basically,
is that because the source is
moving-- and I've defined
positive v the way
astronomers would as moving away
from us-- because the source is
moving away from us,
each successive wave that
goes from the source to us has
to travel a little bit further.
And that means that each wave
crest is slightly delayed
from when it would
have gotten here
if everything were stationary.
And if you delay
each wave crest,
it means the time
between crests is larger.
And that means
that we expect here
that delta t sub O will be
larger than delta t sub s
because of this extra distance
that each wave crest has
to travel.
And what we'll be
doing next time--
I think I will just
leave the calculations
for next time-- is
calculating that.
And then doing the same
thing for the case where
the observers moving and
the source is stationary,
and then talking a little
bit about special relativity,
and then repeating
both calculations
with a special relativity
situation where
we'll be talking about light
rays and velocities that
might be comparable
to the speed of light.
So see you folks on
Thursday, but maybe I'll
see some of you at my
office hour tomorrow.
And I will send an email about
where exactly that office
hour will take place.
