# Fine Tuning

[From Bruce Gregory (2005.0401.0758)]

There seems to be some question as to what is meant by fine tuning. Here is one example. There is a number called Omega in General Relativistic models of the universe. The value of Omega determines the geometry of the universe, values less than one mean that spacetime has a negative curvature; values greater than one means that the spacetime has a positive curvature. Only a value of Omega = 1 predicts that spacetime will be flat, i.e., Euclidean. Recent observations show that Omega = 1.012 +0.018, -0.022. The problem is that in the standard big bang cosmology Omega is unstable. If Omega was slightly less than one in an early stage of the universe, it would rapidly go to zero. (An Omega of 0.9 one second after the big bang would yield an Omega today of .00000000000001.) If Omega was slightly greater than one in the early universe, the universe would rapidly collapse. (An Omega of 1.1 one second after the big bang means that the universe would have collapsed 45 seconds later.) So Omega had to be incredibly close to exactly 1 immediately after the Big Bang. Nothing in the physics we know today predicts that Omega should have any particular value (except for a family of theories involving a putative process called inflation, which predict Omega should be almost exactly one. This is one reason that inflation has become an integral part of our understanding of the history of the universe.)

So while it might sound like "weasel wording" to some, fine tuning is quite quantitative. Of course everything we know in physics could be wrong so there really wouldn't be any problem at all, would there?

A true believer knows the solution before he understands the problem.

[From Bill Powers (2005.04.01.0850 MST)]

Bruce Gregory (2005.0401.0758) –

Only a value of Omega = 1
predicts that spacetime will be flat, i.e., Euclidean. Recent
observations show that Omega = 1.012 +0.018, -0.022.

Perhaps you or others on the net know or can find out the answer to a
question that has bugged me for years. If space-time is Eudlidean or
anything like it, why does the microwave radiation from the Big Bang come
from all directions? In a three-dimensional Euclidean universe where a
Big Bang occurred, some parts of the universe would be in the direction
where the explosion originated, and some parts would be in the opposite
direction where, supposedly, there is still nothing. But that’s not what
we see. We are looking toward the origin of the Bang no matter where we
are looking.
The explanation I’ve always heard is is that the universe is curved into
a closed hypersphere by the mass within it, so space is curved not in
Euclidean geometry but in a higher dimension. The usual analogy is that
it’s like living in the skin of an expanding balloon. Our lines of sight
in this surface seem straight, but they are curved in the dimension that
lies ouside the skin, so if we could see far enough we would see the
backs of our own heads (a rather long time ago). We see everything around
us getting farther away, just as spots on an expanding balloon would all
be receding from each other no matter where on the balloon you look. But
that is only because space is curved into a hypersphere.
I was more or less satisfied with that, but now you seem to be indicating
that the space may, after all, be Eudlidean. Maybe I don’t know what
Euclidean means, but I can’t see how a flat space would be consistent
with the facts – particularly the fact that no matter in what direction
we look, we are looking back toward the center of the Big Bang.
If space is indeed flat, then mass does not curve it, and we can start
dismantling the whole fabric of General Relativity, can’t we?
Whatever the case, I think that the value of Omega we come up with will
be whatever it is, perhaps exactly 1. You know that when you cause an
object to accelerate, the reaction force you feel is exactly -1.0
times the force you apply. If it were even the tiniest bit different,
objects would accelerate without limit or grind to a halt: energy would
appear or disappear. Does that mean that some Divine Intelligence saw to
it that the ratio is exactly -1.0? And what about all those
inverse-square laws? Why isn’t the power 1.99999… or 2.000001? Why is
anything the way it is? You can use absolutely any firm fact of nature to
deduce that Intelligent Design exists. If you want to. The fact that you
want to counts a lot more than the particular reasoning you use.

This is why I am suspicious of the illustrious Astronomer Royal’s notion.
Why did he stop with six numbers? There are scads more. People have seen
Intelligent Design in the fossil record – those fossils were put there
to test our faith, and belief in evolution simply shows that the test
successfully exposes those whose faith is insufficient. Goody, let’s
torture them to death.

Best,

Bill P.

···

The problem is that in the
standard big bang cosmology Omega is unstable. If Omega was slightly less
than one in an early stage of the universe, it would rapidly go to zero.
(An Omega of 0.9 one second after the big bang would yield an Omega today
of .00000000000001.) If Omega was slightly greater than one in the early
universe, the universe would rapidly collapse. (An Omega of 1.1 one
second after the big bang means that the universe would have collapsed 45
seconds later.) So Omega had to be incredibly close to exactly 1
immediately after the Big Bang. Nothing in the physics we know today
predicts that Omega should have any particular value (except for a family
of theories involving a putative process called inflation, which predict
Omega should be almost exactly one. This is one reason that inflation has
become an integral part of our understanding of the history of the
universe.)

So while it might sound like “weasel wording” to some, fine
tuning is quite quantitative. Of course everything we know in physics
could be wrong so there really wouldn’t be any problem at all, would
there?

A true believer knows the solution before he understands the
problem.

[From Bruce Gregory (2005.0401.1155)]

Bill Powers (2005.04.01.0850 MST)

Bruce Gregory (2005.0401.0758) --

Only a value of Omega = 1 predicts that spacetime will be flat, i.e., Euclidean. Recent observations show that Omega = 1.012 +0.018, -0.022.

Perhaps you or others on the net know or can find out the answer to a question that has bugged me for years. If space-time is Eudlidean or anything like it, why does the microwave radiation from the Big Bang come from all directions? In a three-dimensional Euclidean universe where a Big Bang occurred, some parts of the universe would be in the direction where the explosion originated, and some parts would be in the opposite direction where, supposedly, there is still nothing. But that's not what we see. We are looking toward the origin of the Bang no matter where we are looking.

I know that it is not easy to envision, but here are a few suggestions. Remember that the Big Bang did not occur anywhere _inside_ the observable universe, the Big Bang _created_ the observable universe. That is to say, the Big Bang occurred "everywhere" in the observable universe. One way to think of it is that everywhere in the universe the density began to rapidly fall 13.7 billion years ago. As the density fell, structure formed, including the galaxies we see today. The cosmic microwave background radiation (CMB) is the light left over from the Big Bang. At the time it was emitted, it had the characteristics of a 3000 K black body. (That's the temperature at which electrons and protons combine to form hydrogen. Before this the universe was opaque because free electrons scatter photons very readily.) The CMB now has a temperature slightly less than 3 K. This means that the average distance between galaxies (the scale factor) is now 1000 times larger than it was when the radiation start streaming toward us. Another way to say this is that the the observable universe has expanded 1000 fold since the time the CMB was emitted. The CMB we see today has been traveling toward us for 13 billion years. The region we are seeing today was not always 13 billion light years away because of the expansion of the universe the region emitting the radiation was once much closer to us, but that is just a further detail.

If space is indeed flat, then mass does not curve it, and we can start dismantling the whole fabric of General Relativity, can't we?

No, fraid not. The overall curvature of space is determined by the average density of the matter and energy it contains. GR still applies, and spacetime is curved in the vicinity of matter. So while the Milky Way curves spacetime, the average curvature throughout the the observable universe is zero.

Whatever the case, I think that the value of Omega we come up with will be whatever it is, perhaps exactly 1.

Yes. But that is like winning the lottery. Someone will win, but the changes that it is you are very small.

You know that when you cause an object to accelerate, the reaction force you feel is exactly -1.0 times the force you apply. If it were even the tiniest bit different, objects would accelerate without limit or grind to a halt: energy would appear or disappear. Does that mean that some Divine Intelligence saw to it that the ratio is exactly -1.0? And what about all those inverse-square laws? Why isn't the power 1.99999... or 2.000001? Why is anything the way it is? You can use absolutely any firm fact of nature to deduce that Intelligent Design exists. If you want to. The fact that you want to counts a lot more than the particular reasoning you use.

The inverse square law is exactly as it is because space has three dimensions. At least thats what we believe. (Of course string theorists are convinced there a six more but they are curled up out of sight and don't effect the argument.)

This is why I am suspicious of the illustrious Astronomer Royal's notion. Why did he stop with six numbers? There are scads more. People have seen Intelligent Design in the fossil record -- those fossils were put there to test our faith, and belief in evolution simply shows that the test successfully exposes those whose faith is insufficient. Goody, let's torture them to death.

The six numbers Rees is referring to are constants in the laws of nature. It turns out that if these constants (which are arbitrary as far as we know) had somewhat different values, the universe would look nothing like it does today. Either stars could not form, or the heavy elements could not be created inside stars. Those sort of problems. Of course to take this argument seriously, you have to believe that we understanding something about the laws of nature. If you're not convinced of that, all bets are off.

A true believer knows the solution before he understands the problem.

[Martin Taylor 2005.04.01.14.11]

[From Bill Powers (2005.04.01.0850 MST)]

Bruce Gregory (2005.0401.0758) --

Only a value of Omega = 1 predicts that spacetime will be flat, i.e., Euclidean. Recent observations show that Omega = 1.012 +0.018, -0.022.

Perhaps you or others on the net know or can find out the answer to a question that has bugged me for years. If space-time is Eudlidean or anything like it, why does the microwave radiation from the Big Bang come from all directions? ...

The explanation I've always heard is is that the universe is curved into a closed hypersphere by the mass within it, so space is curved not in Euclidean geometry but in a higher dimension. The usual analogy is that it's like living in the skin of an expanding balloon. ...

I was more or less satisfied with that, but now you seem to be indicating that the space may, after all, be Eudlidean. Maybe I don't know what Euclidean means, but I can't see how a flat space would be consistent with the facts -- particularly the fact that no matter in what direction we look, we are looking back toward the center of the Big Bang.

If space is indeed flat, then mass does not curve it, and we can start dismantling the whole fabric of General Relativity, can't we?

Teo different issues here: How come everywhere is in the middle of a space with Euclidiean large-scale geometry? and How can mass curve the space and yet the Universe can still be flat?

Second question first: Take a 2-D analogy. In fact, take an essentially 2-D object, like a sheet of soft paper. Now put dents in it. The dents represent masses in the 3-D space, the sheet of paper represents the space as a whole. The sheet is locally non-Euclidean around the mass points, but is still Euclidean on the large scale. It's an experimental question as to whether the sheet retains its globally Euclidean character when you put more and more dents in it, since there's no mathematical reason why it should or shouldn't.

Same with the real universe. For a long time it was assumed that the universe might be closed, and the Big Bang might eventually be mirrored by a Big Crunch. Now, observations of amny different kinds agree that not only is the universe essentially flat (globally), but that its expansion seems to be accelerating so that there will never be a Big Crunch.

Of course, all that is extrapolation from the mesoscale to times and distances far beyond our ability to test through perceptual control, so our intuitions may be as wrong as they are on the nanoscale of quantum mechanics.

First question second: We can't see the edge of the universe in any direction. That statement is independent of whether the global curvature of the universe is spherical, Euclidean, or hyperbolic. Wherever within the Big Bang the stuff that makes us started out, the place instantly lost light-wave contact with any edge there might have been. In fact, we are only just now getting to see light waves that started near the edge of what was then the accessible part of the Bang. Of course, they are stretched so that waves that probably were very hard gamma radiation then, now come to us streatched out to microwaves.

You could say that the stretching is simply a manifestation of the expansion of the Universe, if you want to look at it in terms of naive intuition. But however you look at it, the Universe then and now extended beyond the reach of sight from the place that we now call home. Whether the Universe is finite or infinite, whether it is flat or curved, none of that matters as to why every place seems to be the place from whch everything in the distance is receding. We were in the middle of the (presumably) intense gamma radiation then, and are still surrounded by that same radiation we now see as microwaves.

Everyday analogy: If you stand in the middle of a cloud, which way do you see the most water droplets?

Martin

[From Bill Powers (2005.04.01.1251 MST)]

Bruce Gregory (2005.0401.1155) –

I know that it is not easy to
envision, but here are a few suggestions. Remember that the Big Bang did
not occur anywhere inside the observable universe, the Big Bang
created the observable universe. That is to say, the Big Bang occurred
“everywhere” in the observable universe.

In all such 3-dimensional situations of which I know, the center of the
explosion is contained within all the material it generated, and from the
standpoint of any one piece, there is a vector you can draw back to where
the original explosion was centered. A vector 180 degrees from that
vector points away from the center, in a direction toward empty
space.

But that’s not the case for the Big Bang; the geometry is clearly not
that of an ordinary explosion.

One way to think of it is that
everywhere in the universe the density began to rapidly fall 13.7 billion
years ago. As the density fell, structure formed, including the galaxies
we see today.

It seems to me that this description deliberately omits any mention of
size – the description makes it sound as if there is a fixed volume
within which the density of matter is decreasing. But the amount of
matter (-energy) in the universe is not decreasing – it is the volume
that is increasing, the distances between the objects in the universe.
Some matter may be falling through black holes into other universes, but
that’s a different question not related to expansion.

I don’t think there is any way to get the effects we observe in a
Euclidean universe. For the apparent center to be visible in all
directions, there HAS to be some sort of nonEuclidean curvature. I think
that what the omega constant must refer to is a departure from a uniform
curvature, not the curvature itself. In other words, I suspect that omega
= 1 means a universe with the same curvature everywhere, and departures
from that value mean that the curvature increases or decreases as the
hyper-radius grows. That is a totally uninformed guess, but it’s the
nearest I can get to making sense of this stuff.

The region we are seeing today
was not always 13 billion light years away because of the expansion of
the universe the region emitting the radiation was once much closer to
us, but that is just a further detail.

Are you really satisfied with that? “Just a further detail”
seems to be the whole problem. How can the region emitting the radiation
be closer or farther from us – in every direction? That is not
Euclidean space as I know it.

If space is indeed flat, then
mass does not curve it, and we can start dismantling the whole fabric of
General Relativity, can’t we?

No, fraid not. The overall curvature of space is determined by the
average density of the matter and energy it contains. GR still applies,
and spacetime is curved in the vicinity of matter. So while the Milky Way
curves spacetime, the average curvature throughout the the observable
universe is zero.

But that requires that mass cause negative curvature elsewhere to
compensate for positive local curvature, and I don’t think there’s any
provision in General Relativity for that. AQlso what you say denies
itself: if curvature is determined by the average density of
matter-energy, then the universe contains a very large amount of that and
it has to be curved. If there is curvature anywhere, then the average
curvature is positive.

Whatever the case, I think that
the value of Omega we come up with will be whatever it is, perhaps
exactly 1.

Yes. But that is like winning the lottery. Someone will win, but the
changes that it is you are very small.

Well, the chances of holding a particular bridge hand, even a bust hand,
are small – but after the deal their probability is 100%.

The inverse square law is
exactly as it is because space has three dimensions. At least that’s what
we believe. (Of course string theorists are convinced there a six more
but they are curled up out of sight and don’t effect the argument.)

That’s in Euclidean geometry. So it’s not true in our universe, if
general relativity holds.

The problem is that we’re talking about theoretical notions that people
are still arguing about. These are propositions, not facts. We’re
exploring the implications of certain theories as they would apply under
extreme conditions, which is one good way of testing theories. One reason
the old theories of the electron as a point-charge were abandoned was
what happened in thought-experiments when you carried calculations to an
extreme condition, arbitrarily close to the singularity. The self-energy
of the electron, instead of being finite, went to infinity. So there was
clearly something wrong with the theory, even though nobody knew at the
time just what was wrong.

I think we’re finding that when you take the basic concept of a Big Bang
and an expanding universe to extreme conditions (small or large
distances) you start seeing contradictions. That’s why people are still
arguing. If all the questions like the ones I raise, and those raised by
clear and wouldn’t rely on analogies – illegimitate analogies, since
they propose similarities to perceptions in an ordinary intuitive
three-dimensional universe.

The six numbers Rees is
referring to are constants in the laws of nature. It turns out that if
these constants (which are arbitrary as far as we know) had somewhat
different values, the universe would look nothing like it does today.
Either stars could not form, or the heavy elements could not be created
inside stars. Those sort of problems. Of course to take this argument
seriously, you have to believe that we understanding something about the
laws of nature. If you’re not convinced of that, all bets are
off.

Yes, that’s my point. The ideas behind his proposals are nowhere near
fully-developed enough to count as “laws of nature.” When the
dust settles, we will see what we have then. When you say “arbitrary
as far as we know” you point directly at the weak link in the
deductions: hidden premises. What this phrase does is say that there are
arbitrary assumptions behind these constants, so the conclusions remain
true only as long as the assumptions are not modified or disproven. The
fact that we are being led into absurdities and contradictions could be
interpreted to mean that pure physics is vastly superior to human
intuition. But it could also be interpreted as a “reductio ad
absurdum” proof that there is something wrong in the premises –
especially those we are using without being aware of using them.

Best,

Bill P.

[From Bruce Gregory (2005.0401.1615)]

Bill Powers (2005.04.01.1251 MST)

Bruce Gregory (2005.0401.1155) --

I know that it is not easy to envision, but here are a few suggestions. Remember that the Big Bang did not occur anywhere _inside_ the observable universe, the Big Bang _created_ the observable universe. That is to say, the Big Bang occurred "everywhere" in the observable universe.

In all such 3-dimensional situations of which I know, the center of the explosion is contained within all the material it generated, and from the standpoint of any one piece, there is a vector you can draw back to where the original explosion was centered. A vector 180 degrees from that vector points away from the center, in a direction toward empty space.

But that's not the case for the Big Bang; the geometry is clearly not that of an ordinary explosion.

That's true, and the reason is that an ordinary explosion takes place within an existing space and time. The Big Bang fills the space and time it creates.

One way to think of it is that everywhere in the universe the density began to rapidly fall 13.7 billion years ago. As the density fell, structure formed, including the galaxies we see today.

It seems to me that this description deliberately omits any mention of size -- the description makes it sound as if there is a fixed volume within which the density of matter is decreasing. But the amount of matter (-energy) in the universe is not decreasing -- it is the volume that is increasing, the distances between the objects in the universe. Some matter may be falling through black holes into other universes, but that's a different question not related to expansion.

At the beginning the entire observable universe was smaller than an atom. After inflation it was roughly the size of grapefruit. That does not say that the observable universe is all there is. The observable universe is presumably embedded in a much much larger, possibly infinite universe. The density decreases because the volume is increasing as you say.

I don't think there is any way to get the effects we observe in a Euclidean universe. For the apparent center to be visible in all directions, there HAS to be some sort of nonEuclidean curvature. I think that what the omega constant must refer to is a departure from a uniform curvature, not the curvature itself. In other words, I suspect that omega = 1 means a universe with the same curvature everywhere, and departures from that value mean that the curvature increases or decreases as the hyper-radius grows. That is a totally uninformed guess, but it's the nearest I can get to making sense of this stuff.

Well you are creating a new physics, but there is nothing wrong with that. I have been describing the picture generated by the existing physics. You may have trouble imagining the effects we observe in a Euclidean Universe, but that's what the physics calls for.

The region we are seeing today was not always 13 billion light years away because of the expansion of the universe the region emitting the radiation was once much closer to us, but that is just a further detail.

Are you really satisfied with that? "Just a further detail" seems to be the whole problem. How can the region emitting the radiation be closer or farther from us -- in every direction? That is not Euclidean space as I know it.

Well, just imagine that we are in the center of the expansion. Then the emitting region was once closer to us, but the universe is expanding, so the emitting region is now much further from us.

If space is indeed flat, then mass does not curve it, and we can start dismantling the whole fabric of General Relativity, can't we?

No, fraid not. The overall curvature of space is determined by the average density of the matter and energy it contains. GR still applies, and spacetime is curved in the vicinity of matter. So while the Milky Way curves spacetime, the average curvature throughout the the observable universe is zero.

But that requires that mass cause negative curvature elsewhere to compensate for positive local curvature, and I don't think there's any provision in General Relativity for that. AQlso what you say denies itself: if curvature is determined by the average density of matter-energy, then the universe contains a very large amount of that and it has to be curved. If there is curvature anywhere, then the average curvature is positive.

In fact the total energy of the universe is exactly zero. The positive energy of mass and energy is exactly balanced by the negative energy of gravity. That's another way of saying that Omega is exactly 1.

Whatever the case, I think that the value of Omega we come up with will be whatever it is, perhaps exactly 1.

Yes. But that is like winning the lottery. Someone will win, but the changes that it is you are very small.

Well, the chances of holding a particular bridge hand, even a bust hand, are small -- but after the deal their probability is 100%.

The inverse square law is exactly as it is because space has three dimensions. At least that's what we believe. (Of course string theorists are convinced there a six more but they are curled up out of sight and don't effect the argument.)

That's in Euclidean geometry. So it's not true in our universe, if general relativity holds.

General relativity holds, as far as we know, and space is Euclidean. Those two statements are perfectly compatible.

The problem is that we're talking about theoretical notions that people are still arguing about. These are propositions, not facts. We're exploring the implications of certain theories as they would apply under extreme conditions, which is one good way of testing theories. One reason the old theories of the electron as a point-charge were abandoned was what happened in thought-experiments when you carried calculations to an extreme condition, arbitrarily close to the singularity. The self-energy of the electron, instead of being finite, went to infinity. So there was clearly something wrong with the theory, even though nobody knew at the time just what was wrong.

I think we're finding that when you take the basic concept of a Big Bang and an expanding universe to extreme conditions (small or large distances) you start seeing contradictions.

Well, the community of folks who study these things see no contradictions.

That's why people are still arguing. If all the questions like the ones I raise, and those raised by much smarter people, had been answered, the explanations would be clear and wouldn't rely on analogies -- illegimitate analogies, since they propose similarities to perceptions in an ordinary intuitive three-dimensional universe.

No. People are not arguing about the Big Bang. It is confirmed by a host of independent measurements. The unresolved issues are the nature of dark matter and dark energy. There are plenty of ideas but a paucity of data. Other questions are the exact nature of inflation (we have a hope of getting a handle on this from gravity-wave experiments), and what happened before inflation, which may always remain speculation. The only analogies involved are in attempts to relate the mathematics of the theory to everyday experience. The mathematics is perfectly consistent and unambiguous, just as the mathematics of QM is perfectly consistent and unambiguous. As Martin says, the problem is trying to think of this mathematics on a scale (everyday life) very different from the scale under investigation.

The six numbers Rees is referring to are constants in the laws of nature. It turns out that if these constants (which are arbitrary as far as we know) had somewhat different values, the universe would look nothing like it does today. Either stars could not form, or the heavy elements could not be created inside stars. Those sort of problems. Of course to take this argument seriously, you have to believe that we understanding something about the laws of nature. If you're not convinced of that, all bets are off.

Yes, that's my point. The ideas behind his proposals are nowhere near fully-developed enough to count as "laws of nature."

That simply is not true. We is talking about constants associated with well-established physics, not with speculation. Let me give you an example, Newton's gravitational constant G is perfectly well determined. However, it cannot be derived from first principles. As far as we know it is arbitrary. If you want to win a Nobel Prize, derive G from first principles. In other words, show, in Einstein's words, that "God had no choice" in determining the value of G. Once you accept the conservation of energy and the laws of thermodynamics, say, G _must_ have the value it does.

When the dust settles, we will see what we have then. When you say "arbitrary as far as we know" you point directly at the weak link in the deductions: hidden premises. What this phrase does is say that there are arbitrary assumptions behind these constants, so the conclusions remain true only as long as the assumptions are not modified or disproven. The fact that we are being led into absurdities and contradictions could be interpreted to mean that pure physics is vastly superior to human intuition. But it could also be interpreted as a "reductio ad absurdum" proof that there is something wrong in the premises -- especially those we are using without being aware of using them.

More than one Nobel Prize for the person who pulls this off. Needless to say, I'm not holding my breath.

A true believer knows the solution before he understands the problem.

[From Bill Powers (2005.04.01.1338 MST)]

Martin Taylor 2005.04.01.14.11 –

Two different issues here: How
come everywhere is in the middle of a space with Euclidiean large-scale
geometry? and How can mass curve the space and yet the Universe can still
be flat?

The problem here is simple: trying to work from the theoretical universe
back to the intuitive experiential one.
Try starting with the assumption that the universe as a whole is flat –
i.e., that Euclidian geometry applies, with perhaps some local
distortions that we can ignore. Now imagine a very dense concentration of
matter-energy appearing in this space and expanding like a hydrogen bomb
explosion. Bang. What happens? The individual particles of the explosion
travel in all directions away from the center, getting farther and
farther apart. It doesn’t matter whether there are local changes in
density or not. Seen from any one particle, all the other particles will,
on the average, seem to be receding, but that’s just because of velocity
sorting; the slower particles are closer to the origin of the explosion,
the faster ones are farther from it. If we look back toward the center,
we may not be able to see all the way to ground zero, but we will see
that the slower particles are closer to the center than we are. We are
moving faster than they are, so they seem to be moving the other way.
Add Doppler shift to this, and we can see that light coming to us from
all particles in all directions will be red - shifted; the farthest
particles will be red-shifted the most. I assume that this red-shift will
be anisotropic: when the radius of a volume increases at a constant
speed, all points within it have the same velocity relative to others in
all directions. Is that so? I think so.
Now what about the ages of the particles we see in different directions?
Clearly, they are all the same age, but those farther away are seen as of
some time ago, so they look younger. When we look back far enough, we see
light that has been doppler-shifted to the limit, and we can see no
farther even without interstellar extinction. This is true in all
directions, of course. We see light from far enough away, in all
directions, that it forms an almost uniform background of very
low-frequency radiation in which no objects can be distinguished any
more. This has nothing to do with where the center of expansion is.
(*Ding!)*There is a question about the distribution of velocities. For
example, if slower particles predominated, we would see a larger
population of particles in a certain direction than in any other
direction. That would tell us the direction to the location of the
original explosion. If high-velocity particles predominated, the greatest
population would be away from the center. If there is no difference
in populations in different directions (save for random local anomalies),
we could conclude that the initial distribution of particle speeds was
uniform – or that the center of the explosion was very far away,
indeed.

Now, suppose that the Big Bang actually injected an infinite amount of
matter-energy into space, or anyway a great deal more than we can see
now, and that it did so much longer ago than we have calculated. How
would this change the situation? I think it would make no difference,
because we would still be able to see only to a distance where the
Doppler shift reduced the light to barely-detectable microwaves. We would
see a “Little Bang” and think it was the Big one.

Look what this gives us. It gives us an infinite universe that is
infinitely old, in which we perceive a bubble bounded by the limiting
velocity of light.

Or, to be more modest, a much bigger and older universe than the one we
currently experience.

OK, this is where I get by ignoring the curvature of space and the two
relativies. This is sort of a baseline picture, barring reasoning errors,
of the way the universe would look if there were no funny business going
on. I have, in fact, answered my big question as to why the microwave
radiation comes equally from all directions. If it’s really
“equally,” then the velocity distribution of particles is
uniform. We don’t see “the center” in all directions; we just
see particles receding from us close to the velocity of light, a long
time ago. The uniform distribution alone suggests that the distribution
extends beyond the velocity of light (remember, no funny business in this
strictly Euclidean view).

So – where from here? First, correct all the mistakes I’ve made. Then,
of course, start introducing the modifications that are forced on us by
phenomena like the constancy of the velocity of light and the bending of
light rays near large masses (well, small masses, too, but not enough to
see). I think that the Euclidean picture tells us the largest part of the
story; the other effects may warp this picture considerably, but we’ve
handled at least one of the biggest questions that has bugged me and
maybe others. Without miracles, to quote a friend of ours.

I didn’t know this was going to come out. I’m as surprised as you
probably are. Have at it.

Best,

Bill P.

[Martin Taylor 2005.04.01.17.18]

[From Bill Powers (2005.04.01.1338 MST)]

Martin Taylor 2005.04.01.14.11 --

Two different issues here: How come everywhere is in the middle of a space with Euclidiean large-scale geometry? and How can mass curve the space and yet the Universe can still be flat?

The problem here is simple: trying to work from the theoretical universe back to the intuitive experiential one.

Try starting with the assumption that the universe as a whole is flat -- i.e., that Euclidian geometry applies, with perhaps some local distortions that we can ignore. Now imagine a very dense concentration of matter-energy appearing in this space

We run into teh first problem right here, with the words "in this space". The concentration of matter-energy of interest isn't "in this space" it is part of what creates this space. There's no concept of a space that contains it.

Also, as Bruce pointed out, in terms of General Relativity the content of the universe (matter+energy+dark matter+dark energy) is exactly zero, at least within our current measurement ability. If that's true there's nothing strange about creation at all. New universes could be being created all around us, in diffeent dimensions, and we wouldn't notice.

and expanding like a hydrogen bomb explosion. Bang. What happens? The individual particles of the explosion travel in all directions away from the center, getting farther and farther apart. It doesn't matter whether there are local changes in density or not. Seen from any one particle, all the other particles will, on the average, seem to be receding, but that's just because of velocity sorting; the slower particles are closer to the origin of the explosion, the faster ones are farther from it.

You are talking a Newtonian language, here. You are giving some place in the Universe a privileged position. From even a special relativistic viewpoint, there's no such thing. You are at the centre, and the velocity sorting is that the faster objects are moving away from you (but so is everyone else in other galaxies at the centre).

If we look back toward the center, we may not be able to see all the way to ground zero, but we will see that the slower particles are closer to the center than we are. We are moving faster than they are, so they seem to be moving the other way.

You can look in any direction you want, and you are looking toward the centre of the Big Bang. It took all those gigayears for the light from those places to get to you, and there's still more to come (and will be, until all other matter has passed outside our light-horizon -- the boundary past which we will never see.

....
Look what this gives us. It gives us an infinite universe that is infinitely old, in which we perceive a bubble bounded by the limiting velocity of light.
Or, to be more modest, a much bigger and older universe than the one we currently experience.

No, not so. Bigger, yes. but not older. The age is now "known" to within a percent or so, because of a whole constellation of converging observations in different domains.

OK, this is where I get by ignoring the curvature of space and the two relativies. This is sort of a baseline picture, barring reasoning errors, of the way the universe would look if there were no funny business going on. I have, in fact, answered my big question as to why the microwave radiation comes equally from all directions. If it's really "equally," then the velocity distribution of particles is uniform. We don't see "the center" in all directions; we just see particles receding from us close to the velocity of light, a long time ago. The uniform distribution alone suggests that the distribution extends beyond the velocity of light (remember, no funny business in this strictly Euclidean view).

What does the last sentence mean? Are you contrasting a "strictly Euclidean view" with General Relativity? Or are you talking about how Euclid might have conceived the Universe as compared to how we perceive it since Einstein wrote?

So -- where from here? First, correct all the mistakes I've made.

If we correct the opening one, in which you imagine an observer standing in a space within which the Big Bang occurred, I think the rest ought to follow, depending on how much maths and how much observational detail you would need. I'm certainly no authority, but I do read Science, Physics Today, and journals like that. Those are where I get this stuff, mostly.

By the way, don't even demand that space-time be continuous. Some people think it may not be. Others suggest that on the nanoscale, it might be like a foam, in which "Big Bangs" can happen, just as bubbles coalesce in a foam. Remember what Bruce G said -- If Omega = 1, the total energy in the Universe is zero. It sounds counter-intuitive, but that shouldn't pose a problem, should it?

Martin

[From Bill Powers (2005.04.01.1615 MST)]

Martin Taylor 2005.04.01.17.18–

[From Bill Powers
(2005.04.01.1338 MST)]

Martin Taylor 2005.04.01.14.11 –

Two different issues here: How
come everywhere is in the middle of a space with Euclidiean large-scale
geometry? and How can mass curve the space and yet the Universe can still
be flat?

The problem here is simple: trying to work from the theoretical universe
back to the intuitive experiential one.

Try starting with the assumption that the universe as a whole is flat –
i.e., that Euclidian geometry applies, with perhaps some local
distortions that we can ignore. Now imagine a very dense concentration of
matter-energy appearing in this space

We run into teh first problem right here, with the words “in this
space”. The concentration of matter-energy of interest isn’t
“in this space” it is part of what creates this space. There’s
no concept of a space that contains it.

I was starting with non-spooky assumptions. In simple Euclidean space,
space is infinite whether there is anything in it or not. The fact that
some matter and energy suddenly appear in it doesn’t alter the geometry
of empty Euclideanspace.

Also, as Bruce pointed out, in
terms of General Relativity the content of the universe
(matter+energy+dark matter+dark energy) is exactly zero, at least within
our current measurement ability. If that’s true there’s nothing strange
about creation at all. New universes could be being created all around
us, in diffeent dimensions, and we wouldn’t notice.

That’s only in the spooky version, which I am not starting with. I start
with simple 19th-Century physics and see where it takes us.

As to the overall energy budget, doesn’t that depend on the signs you
arbitrarily assign to the different components? I thought gravitational
energy was equivalent to mass like any other energy, but Bruce G. said it
has a negative sign. Anyway, my little picture wouldn’t include those
considerations.

You are talking a Newtonian
language, here. You are giving some place in the Universe a privileged
position. From even a special relativistic viewpoint, there’s no such
thing.

No, I didn’t say where in the universe this center was. I just said that
if the explosion took place there, then all the particles are flying away
from that center. Do you disagree with that?

You are at the centre, and
the velocity sorting is that the faster objects are moving away from you
(but so is everyone else in other galaxies at the
centre).

No, I am on one of the particles. That’s why I said that particles closer
to the center (wherever it is) are moving away from it less fast than I
am and so appear to be moving the other way, toward the center relative
to me.

If we look back toward the
center, we may not be able to see all the way to ground zero, but we will
see that the slower particles are closer to the center than we are. We
are moving faster than they are, so they seem to be moving the other
way.

You can look in any direction you want, and you are looking toward the
centre of the Big Bang.

But that gets spooky again, by which I mean it’s not Euclidean geometry.
If the big bang was an explosion that took place at a given arbitrary
coordinate in this simple 3-D space, then we can express the motions of
all particles relative to that coordinate. And there is only one
direction toward the location of the explosion from any given
particle.

However, an occupant of one of the particles may not see any preferred
direction, and I deduced that that would be because the velocities are
uniformly distributed. In that case it would not be possible for anyone
on one of the particles to determine in which direction the original
explosion took place. That was my answer as to why the 3-degree microwave
radiation seems to be coming from every direction.

It took all those
gigayears for the light from those places to get to you, and there’s
still more to come (and will be, until all other matter has passed
outside our light-horizon – the boundary past which we will never
see.

Look what this gives us. It
gives us an infinite universe that is infinitely old, in which we
perceive a bubble bounded by the limiting velocity of light. Or, to be
more modest, a much bigger and older universe than the one we currently
experience.

No, not so. Bigger, yes. but not older. The age is now “known”
to within a percent or so, because of a whole constellation of converging
observations in different domains.

Why isn’t that simply the age to the event horizon of our universe, as
seen from our point of view, which we have mistaken for the beginning of
everything? What would look the same if it were, and what would look
different? The event horizon in Euclidean space is simply the distance at
which the rate of recession is the velocity of light, ignoring special
relativity as I am doing. That will tell us when everything
appears to have started, but that may be an illusion due to the
fact that we can’t see anything moving as fast as or faster than light.
Euclidean, non-spooky, remember. Things can move faster than light, but
of course we can’t see them.

The uniform distribution alone
suggests that the distribution extends beyond the velocity of light
(remember, no funny business in this strictly Euclidean
view).

What does the last sentence mean? Are you contrasting a “strictly
Euclidean view” with General Relativity? Or are you talking about
how Euclid might have conceived the Universe as compared to how we
perceive it since Einstein wrote?

I’m omitting both relativities and the apparent constancy of the speed of
light with respect to the emitter and absorber. That’s the “funny
business.” If all velocities are equally represented, assuming a
cutoff at the velocity of light would create an abrupt discontinuity in
the distribution, which would be at least surprising. It could be that
all velocities from zero to infinity are represented. Well, “could
be” is a relative term.

So – where from here? First,
correct all the mistakes I’ve made.

If we correct the opening one, in which you imagine an observer standing
in a space within which the Big Bang occurred, I think the rest ought to
follow, depending on how much maths and how much observational detail you
would need. I’m certainly no authority, but I do read Science, Physics
Today, and journals like that. Those are where I get this stuff,
mostly.

I meant mistakes in applying the simple Euclidean view. In order for the
Big Bang to occupy the entire volume of space from the very beginning, we
have to think of space being curved around the point of origin. The more
concentrated the matter-energy, the greater the curvature. So this
immediately contradicts the idea that the average density of
matter-energy in the universe is zero. If it were zero there would be no
curvature, would there? As the universe expands the density drops and
simultaneously the curvature drops – that is what we mean by
“expand;” the radius of curvature increases.

Anyway, in the higher-dimensioned space or the simple 3D one, there is
still a place that is the center of the (hyper)sphere that is the
universe. All velocities are directed away from that center, in however
many dimensions. But if the velocities are uniformly distributed (just as
many particles moving with one velocity as with any other) an occupant of
a particle might not be able to determine the direction of the
center.

By the way, don’t even demand
that space-time be continuous. Some people think it may not be. Others
suggest that on the nanoscale, it might be like a foam, in which
“Big Bangs” can happen, just as bubbles coalesce in a foam.
Remember what Bruce G said – If Omega = 1, the total energy in the
Universe is zero. It sounds counter-intuitive, but that shouldn’t pose a
problem, should it?

No, but “counter-intuitive” isn’t a recommendation in itself,
unless you’re a very committed science-fiction fan. People are suggesting
all sorts of things, which is what suggests to me that the dust hasn’t
settled yet. Who is there to ask about these things who really doesn’t
care how it comes out? What I see going on is a very hot competition and
a lot of overblown claims. Of course everyone insists that he or she
knows what the score really is. Not very confidence-inspiring.

Best,

Bill P.