An Einsteinian Thought Experiment.

[Prairieboy]

I seem to like to think about things on extremely small or extremely large scales, so here goes my second foray into this forum...

Imagine, if you might, that the expansion of the universe were temporarily halted at this exact moment in time. Then imagine that you could leave the earth and travel in any direction at, say, the speed of light. If the expansion of the universe then remained halted indefinitely, what would you eventually run into? Or would you be back where you started (4th/5th dimension hyperspheres and all that)?

I believe the consensus is that the universe is in fact finite (otherwise, how could it be 13.7 billion years old).

I'm positive I'm far from the first person to wonder about this, but I'm curious about what some of the members here might think.

Thanks!

[grapes]

Is the question essentially, "What's outside the universe?"

[WayneFrancis]

The age of the universe has nothing to say about the question whether the universe is finite or infinite.

All it says is that over 13 billions years ago all the matter/energy we see was in a much smaller region. Popular science often says that at the big bang the universe was "smaller then an atom" or something like that but all we can say is the "visible universe" was that size. As far as the universe as a whole? Who knows. The universe may or may not be infinite but there is no indication as of yet that it is either finite or bounded.

I believe that if at T₀ the universe was finite then it is finite now, if it was infinite then it is infinite now. The science into the manifold of the universe is interesting but right now inconclusive on the actual size of the universe but the age....we've got very good evidence on and it is independent of the size.

[01101001]

I believe the consensus is that the universe is in fact finite [...]

No.

Sean Carroll's Cosmology Primer FAQ: Is the universe finite or infinite?

[...] Up to the limits of the observable universe, what we observe is consistent with a uniform distribution of matter and energy that could easily extend forever. On the other hand, it might eventually turn into something very different, beyond what we can see [...]

[Jeff Root]

I agree with Prairieboy. The Universe as a whole might be infinite, but the
part of it that participated in the Big Bang and is only 13.7 billion years old
cannot be infinite. If all of the Universe participated in the Big Bang, then
it is not infinite. If the Universe is infinite, then only one infinitesimal part
of it participated in the Big Bang.

-- Jeff, in Minneapolis

[Ken G]

In my opinion, the answer to the OP is, "if we were massless particles that never interacted with anything, so length contracted everything in our path to nothing, then we'd find out how childishly oversimplified are all of our models, and how irrelevant is the question of whether the universe is infinite or finite." But then, if we were photons, we'd be quite different than we are, and our universe would too.

[WayneFrancis]

I agree with Prairieboy. The Universe as a whole might be infinite, but the
part of it that participated in the Big Bang and is only 13.7 billion years old
cannot be infinite. If all of the Universe participated in the Big Bang, then
it is not infinite. If the Universe is infinite, then only one infinitesimal part
of it participated in the Big Bang.

-- Jeff, in Minneapolis

Just curious what reasoning there is to think that if the universe infinite that everywhere couldn't have had a Big Bang about 13.7 billion years ago? Is this simply an argument of causally separated points in space sense of time would be different? Or that in an infinite universe you'd expect variation?

I honestly don't see what the being infinite or finite in size has to do with how we define time since the universe had a much higher energy density.

[DrRocket]

I seem to like to think about things on extremely small or extremely large scales, so here goes my second foray into this forum...

Imagine, if you might, that the expansion of the universe were temporarily halted at this exact moment in time. Then imagine that you could leave the earth and travel in any direction at, say, the speed of light. If the expansion of the universe then remained halted indefinitely, what would you eventually run into? Or would you be back where you started (4th/5th dimension hyperspheres and all that)?

I believe the consensus is that the universe is in fact finite (otherwise, how could it be 13.7 billion years old).

I'm positive I'm far from the first person to wonder about this, but I'm curious about what some of the members here might think.

Thanks!

It is not the consensus that the universe is finite.

In fact, it is not known whether the universe is finite or not. If there is even a "majority opinion" it is probably that the universe is infinite. But no one really knows.

Whether or not, in the case that the universe is finite, you might return to a starting point is a question as to the toplogy of space, and has nothing to do with any additional dimensions. Three spatial dimensions are quite enough. The question is whether or not "space: is a closed 3-manifold. Again, nobody knows.

[DrRocket]

I agree with Prairieboy. The Universe as a whole might be infinite, but the
part of it that participated in the Big Bang and is only 13.7 billion years old
cannot be infinite. If all of the Universe participated in the Big Bang, then
it is not infinite. If the Universe is infinite, then only one infinitesimal part
of it participated in the Big Bang.

-- Jeff, in Minneapolis

This is simply wrong. There is no reason that the result of the big bang could not be an infinite universe. This has been explained to you before.

It is not known whether the result was an infinite space or not, but there is most certainly no justification to state that it cannot be infinite.

[DrRocket]

In my opinion, the answer to the OP is, "if we were massless particles that never interacted with anything, so length contracted everything in our path to nothing, then we'd find out how childishly oversimplified are all of our models, and how irrelevant is the question of whether the universe is infinite or finite." But then, if we were photons, we'd be quite different than we are, and our universe would too.

The real question is the topology of "space". I don't think tha tis particularly irrelevant. On the other hand, it is not of immediate importance in describing physics in that portion of the universe that is causally related to us. What is quite clear is, independent of the global topology of space, it is REALLY big.

[Jeff Root]

Just curious what reasoning there is to think that if the universe [is] infinite
that everywhere couldn't have had a Big Bang about 13.7 billion years ago?

It is way, way, way too big a coincidence for everything in an infinite Universe
to spontaneously exhibit the same behavior simultaneously. There is no need
to suppose such an absurd coincidence to describe the Big Bang if it was finite.

Is this simply an argument of causally separated points in space sense of time
would be different?

It is an argument that when something happens to a large number of things, it
is because they are causally connected.

Or that in an infinite universe you'd expect variation?

I would not expect any similarity whatsoever between places that are not or
have not been causally connected. If electrons, for example, exist in two places,
then those two places are causally connected. The combination of properties
that constitute electrons would not independently appear in infinitely many places
simultaneously just by chance. Vast numbers of water droplets in a rain cloud
do not all become raindrops simultaneously by chance. They do it because they
are causally connected.

-- Jeff, in Minneapolis

[Prairieboy]

The real question is the topology of "space". I don't think tha tis particularly irrelevant. On the other hand, it is not of immediate importance in describing physics in that portion of the universe that is causally related to us. What is quite clear is, independent of the global topology of space, it is REALLY big.

Indeed, my question was more concerned with topography than with the finiteness or infiniteness of space, though these questions are clearly related. I suppose I'm more curious about how the hypothetical journey described above would be perceived by the observer.

The being said, I'm going to take a stab at arguing for the finiteness of the universe nonetheless. The expansion since the big bang has been taking place for 13.7 billion years, but it has not been taking place at an infinite speed (though quite possibly faster than light). If it had been, we would never have been able to see anything. Since the volume of the universe and its rate of expansion would seem to be related, a finite rate of expansion could not have produced an infinite volume.

[Prairieboy]

Honestly, I wish it was, since I wish there was an answer to this, though I highly doubt it. I guess I understand theoretically that everything, including space (i.e. the distance between two points), is contained within the universe, but my tiny human brain still has trouble intuitively understanding what this means in terms of perception.

Is it possible, though obviously entirely hypothetical, that, if such a thing as the "edge of the universe" exists, it is simply an inability to move, since there is no "space" within which this movement could take place?

[Ken G]

The real question is the topology of "space". I don't think tha tis particularly irrelevant.

What is the real question, and what is relevant, is the topology of space as perceived by us, i.e., which is testable by the experiments we are now capable of, or will ever be capable of. A relatively recent physics principle is that the means of perceiving is not separable from what is perceived, and what is surprising is that we ever thought anything else. Thus, there is no reason to think that a massless particle like a photon, if it could perceive, would perceive like we do. Thus, there is no reason to think it would perceive the same topology that we do. That's the problem with labels like "finite" and "infinite" or "closed" and "open"-- they seem to extrapolate from our way of interacting with the universe, to the universe itself. That's a mistake we've made so many times in the history of science, we should know better by now. But I agree with your conclusion-- however general or specific is our concept of the topology of the universe, the concept only works in a model where the universe is far larger than anything we can hope to see a limit to.

[Ken G]

It is way, way, way too big a coincidence for everything in an infinite Universe
to spontaneously exhibit the same behavior simultaneously. There is no need
to suppose such an absurd coincidence to describe the Big Bang if it was finite.

If one looks at the history of science, the clearest lesson is that what seems "absurd" is very much a moving target! You are simply underestimating the imagination of physicists in coming up with models that make the impossible seem plausible. Though it was absurd, Copernicus made a model where stars could be a million times farther than the Sun. Though it was absurd, Einstein came up with a model where time was mutable to the conditions of the observer. Though it was absurd, de Broglie came up with a model where particles could share attributes with waves. And though it is absurd, some theorists (like Hawking) already talk about models wherein the Big Bang began when a four dimensional space underwent a phase transition which turned one of the dimensions into time. If time only emerged when one of the dimensions was turned into it (giving meaning to "when"), then it could have happened everywhere, as there would be no concept of causality or evolution separate from the existence of that dimension, one dimension just "turned into time". I can imagine another possibility, where space was infinite and 3-D, and a time axis was "born" everywhere in that space (which is possible, since without time, there is no concept of causality or the speed of light). With the birth of the time axis came causality, expansion, freezing out the forces, inflation, and the rest of the show.

Of course, I only point these out to show how easy it is to create models that are consistent with observations and encounter no difficulty with an infinite universe and causality. I'm not suggesting these models capture what the universe is really doing, as any such assertion is the height of hubris-- with or without vast experimental support.

I would not expect any similarity whatsoever between places that are not or
have not been causally connected.

The problem with this philosophical stance is that it brings us back into contact with that question that we thought we had done away with: if there are electrons within a causal sphere, but not outside it, then "what is outside the universe?"

[captain swoop]

Jeff Root, you seem to be teetering on the edge of ATM, please think about your posts in the Q&A Forum

[Jeff Root]

Captain swoop,

Is it ATM to assert that infinitely many particles throughought an infinite space
could not and would not all simultaneously start doing exactly the same thing?

If so, why?

-- Jeff, in Minneapolis

[Ken G]

Is it ATM to assert that infinitely many particles throughought an infinite space
could not and would not all simultaneously start doing exactly the same thing?

Because if there is no time, then "simultaneously" does not carry the meaning you intend. Your argument puts the cart before the horse-- you claim it is impossible for an infinite number of things to start doing the same thing when time begins, on the grounds that there hasn't been enough time for them to get into causal contact, yet you cannot even define what causality would mean in the context of the beginning of time. I wouldn't say it is ATM, I would say it is flawed logic. You can certainly choose to imagine that the universe is finite, and no one can tell you that you are wrong (it is "mainstream" to allow each individual to believe what they like on that score), but what you are presenting as a logical argument of same is not actually a logical argument.

Let's look at the flaw closer, because you might imagine that your argument is reminiscent of the need for inflation to understand why the CMB is all the same temperature. The latter argument is that after time begins, and a concept of causation appears, a tiny region of what must be thought of as the rest of universe comes into causal contact (which was not previously) and establishes a common temperature, after which inflation spreads that common temperature over everything we can see. Even in that standard argument (which is already somewhat speculative), there is a "coming into causal contact of that which was not previously in causal contact." Your argument rests on the claim that what I put in quotations is actually impossible, because there is no "universe" there to come into causal contact if it were not already in causal contact from the start.

[Incomplete]

Is it ATM to assert that infinitely many particles throughought an infinite space
could not and would not all simultaneously start doing exactly the same thing?

Imagine an infinite straight line, with evenly spaced tick marks along it. Now imagine that as time proceeds, the space between each pair of tick marks expands, so that at any given time the marks are moving away from each other with a velocity proportional to the distance between them.

Now run that back in time. The marks get closer and closer together. At some time they're so dense the laws of physics break down and no one knows what happens. That's a spatially infinite big bang.

[DrRocket]

The being said, I'm going to take a stab at arguing for the finiteness of the universe nonetheless. The expansion since the big bang has been taking place for 13.7 billion years, but it has not been taking place at an infinite speed (though quite possibly faster than light). If it had been, we would never have been able to see anything. Since the volume of the universe and its rate of expansion would seem to be related, a finite rate of expansion could not have produced an infinite volume.

That line of reasoning does not work. It is not that simple.

Consider this function F(t,X),= tX where X is a vector and t a scalar with t in the interval [0,1]. Then F(0,X) = 0 and F{1,X)=X for any X. Note also that F is continuous and in fact smooth on the open interval (0,1). F is what is called in homotopy theory a strong deformation retract of Euclidean space to a point.

Now, the mechanisms of general relativity and the big bang are a more complex than this, but does serve to illustrate how one might describe the evolution of a point (zero volume) to an n-dimensional Euclidean space (infinite volume), in not only finite time, but actually in zero time, in a continuous manner. Note that the "rate of expansion", which is reflected in the parameter "t" is not an issue here.

[DrRocket]

Honestly, I wish it was, since I wish there was an answer to this, though I highly doubt it. I guess I understand theoretically that everything, including space (i.e. the distance between two points), is contained within the universe, but my tiny human brain still has trouble intuitively understanding what this means in terms of perception.

Is it possible, though obviously entirely hypothetical, that, if such a thing as the "edge of the universe" exists, it is simply an inability to move, since there is no "space" within which this movement could take place?

What you are missing is the concept of an intrinsic manifold, which is how the universe is modeled in general relativity.

1. The universe does not move. It has no place to go anyway.

2. The spacetime manifold of GR is the whole enchilada. It contains all of "space" and all of "time", all mixed together in a manifold with curvature.

3. The meaning of "expanding space" is somewhat subtle. If one assumes that spacetime is, on the largest scales, homogeneous and isotropic, then one can decompose spacetime as a one-parameter foliation of space-like hypersurfaces. That parameter, though not really time, serves as a surrogate for time. Those hypersurfaces serve as a surrogate for space, and can be shown to be spaces of constant curvature. One then asks what topologies are admitted for such spaces, It is the topology of those hypersurfaces, and in particular whether they are compact topological spaces, that is asked when one asks if the universe is "infinite" or "finite". In all cases these manifolds are manifolds without boundary -- there is no such thing as an "edge", anymore than there is an edge to surface of a sphere (like the Earth).

4. Spacetime in general relativity is an intrinsic manifold. It is not embedded in anything larger. There is nowhere "else".

To understand this stuff you either have to read hard-core mathematics and physics texts or there is one popularization that might help. That popularization is a book by Roger Penrose, The Road to Reality, A Complete Guide to the Laws of the Universe. In that book you will find a treatment of manifolds and other mathematics and some pictures that may help with your understanding. It is not the easiest of popularizations, but it is a very good and very deep book. You can skip any parts that are too difficult in terms of the mathematics and still benefit from the book.

If you are interested in some hard-core titles, ask and ye shall receive. But the do tend to be pretty demanding.

[Prairieboy]

Thanks DrRocket, my brain hurts, but in a good way :-)
I had to give myself a crash course on intrinsic vs. extrinsic manifolds, but I think I'm starting to get the picture (stats camp at the University of Michigan wasn't quite cutting it, but at least your function equation made some sense to me).

Am I completely off base to be thinking of travelling through space-time as analogous to moving along the surface of a sphere, which appears to me as two-dimensional, but is in fact three-dimensional, then adding another dimension? In other words, I'm moving through 4 dimensions, but perceive it as three dimensions?

I'll definitely take a look at Roger Penrose's book, since I'm by no means qualified to dive into the more "hard-core titles." Thanks for the reference!

Full Disclosure: I'm actually a social scientist, and our dirty little secret is that all social scientists are really frustrated physicists who aren't good enough at math to have gone to grad school for that. So please be patient with what must seem like terribly innane questions to our hard-scientific role models.

[Jeff Root]

Is it ATM to assert that infinitely many particles throughought an infinite space
could not and would not all simultaneously start doing exactly the same thing?

Because if there is no time, then "simultaneously" does not carry the meaning
you intend.

If there is no time is a very, very big assumption.

It assumes that the Big Bang was instantaneous, rather than occurring over an
interval of time. In that regard it is different from all observed phenomena.

It assumes that there was no time before that instantaneous event, which may
be possible, but is not required by any observation.

Your argument puts the cart before the horse-- you claim it is impossible for
an infinite number of things to start doing the same thing when time begins,
on the grounds that there hasn't been enough time for them to get into causal
contact, yet you cannot even define what causality would mean in the context
of the beginning of time.

It is not putting the cart before the horse. The idea that you can assume
anything you like as long as you first assume that there is no time is patently
ridiculous. I assume that the known laws of physics applied at the beginning,
and I assume that the known laws of physics are not sufficient to describe
the beginning. I do not assume that because there was no time, anything
you can think up could happen.

I wouldn't say it is ATM, I would say it is flawed logic. You can certainly choose
to imagine that the universe is finite, and no one can tell you that you are wrong
(it is "mainstream" to allow each individual to believe what they like on that score),
but what you are presenting as a logical argument of same is not actually a
logical argument.

Let's look at the flaw closer, because you might imagine that your argument is
reminiscent of the need for inflation to understand why the CMB is all the same
temperature.

I do.

The latter argument is that after time begins, and a concept of causation appears,

Interesting choice of term, "concept".

a tiny region of what must be thought of as the rest of universe comes into causal
contact (which was not previously) and establishes a common temperature, after
which inflation spreads that common temperature over everything we can see.
Even in that standard argument (which is already somewhat speculative), there is
a "coming into causal contact of that which was not previously in causal contact."
Your argument rests on the claim that what I put in quotations is actually
impossible, because there is no "universe" there to come into causal
contact if it were not already in causal contact from the start.

Yes. If there is no causal connection between two places, there is no reason
for them to have anything in common. Inflation describes why a large region
of the Universe can be at the same temperature: Everything that inflated was
in causal contact, and at roughly uniform temperature to begin with. Inflation
does not describe how places which are not in causal contact can inflate
simultaneously and identically.

You did not point out any flaw in my logic. You only asserted that there is one.

-- Jeff, in Minneapolis

[Jeff Root]

Is it ATM to assert that infinitely many particles throughought an infinite space
could not and would not all simultaneously start doing exactly the same thing?

Imagine an infinite straight line, with evenly spaced tick marks along it. Now
imagine that as time proceeds, the space between each pair of tick marks
expands, so that at any given time the marks are moving away from each
other with a velocity proportional to the distance between them.

I made an animation to illustrate exactly that:

http://www.freemars.org/jeff2/expand3e.htm

Now run that back in time. The marks get closer and closer together. At some
time they're so dense the laws of physics break down and no one knows what
happens. That's a spatially infinite big bang.

There is no reason to think that the matter in the Universe was ever so dense
that causality could be ignored. Looking backward in time, at some point the
known laws of physics are not sufficient to describe what is happening. So we
don't know what was happening at that time. It might be that the matter was
so dense that some of the known laws of physics did not apply. That is a
possibility, not a requirement. Even if some of the known laws of physics
didn't apply, I see no value in throwing away the "concept" of causality in
order to allow the Big Bang to have affected an infinite volume of space and
an infinite quantity of matter.

In the analogy of the imaginary infinite straight line with infinitely many tick
marks, the tick marks start out with some particular spacing because I gave
them that spacing. The tick marks were all causally connected to me. In the
actual Universe, an infinte volume and infinite quantity of matter cannot be
causally connected that way.

-- Jeff, in Minneapolis

[DrRocket]

Am I completely off base to be thinking of travelling through space-time as analogous to moving along the surface of a sphere, which appears to me as two-dimensional, but is in fact three-dimensional, then adding another dimension? In other words, I'm moving through 4 dimensions, but perceive it as three dimensions?

No you are moving through 4 dimensions and perceive it as four dimensions. When you go to a meeting you go to a specific spatial location at a specific time -- 4 parameters are required, and that is 4 dimensions. When you say "moving through" that more or less implicitly implies some change in the time coordinate, so you move through 3 spatial dimensions and also experience a change in the time dimension.

But general relativity show us that the picture above is only local. More globally, space and time are intertwined by the curvature of spacetime. One observer's time is another observer's space. In fact there is no global notion of either space or time. This takes a lot of getting used to. The Penrose book will probably help. But even many physicists have trouble with the abstraction, and I don't know of any texts that make this truly clear except those in the "hard-core" category. Relativity turns out to be a study in geometry, but it takes some significant mathematical background to understand that statement.

[DrRocket]

Captain swoop,

Is it ATM to assert that infinitely many particles throughought an infinite space
could not and would not all simultaneously start doing exactly the same thing?

If so, why?

-- Jeff, in Minneapolis

It is absolutely ATM. You are asserting that the position of mainstream cosmologists is wrong. That position is that there is a tentative explanation for the "horizon problem" in terms of inflation theory, which is compatible with either an infinite or a finite universe.

See for instance books on physical cosmology ; ;

Principles of Physical Cosmology -- P.J.E. Peebles

The large scale structure of space-time --- Hawking and Ellis

Cosmological Inflation and large-scale structure -- Liddle and Lyth

Physical Foundations of Cosmology -- Mukhanov

[Incomplete]

I made an animation to illustrate exactly that:

http://www.freemars.org/jeff2/expand3e.htm

Good.

There is no reason to think that the matter in the Universe was ever so dense
that causality could be ignored.

Who said there was?

Looking backward in time, at some point the
known laws of physics are not sufficient to describe what is happening. So we
don't know what was happening at that time. It might be that the matter was
so dense that some of the known laws of physics did not apply. That is a
possibility, not a requirement.

It's pretty much a requirement if you go all the way back, because the density goes to infinity and the known laws cease to be predictive.

Even if some of the known laws of physics
didn't apply, I see no value in throwing away the "concept" of causality in
order to allow the Big Bang to have affected an infinite volume of space and
an infinite quantity of matter.

In the analogy of the imaginary infinite straight line with infinitely many tick
marks, the tick marks start out with some particular spacing because I gave
them that spacing. The tick marks were all causally connected to me. In the
actual Universe, an infinte volume and infinite quantity of matter cannot be
causally connected that way.

-- Jeff, in Minneapolis

That's where your problem is. You're assuming the big bang "caused" all this, and then on top of that assuming that is impossible. Neither assumption is justified. It also sounds like you think those tick marks are causally connected, which is also wrong. They're not. If one suddenly fires a rocket, it has no effect on the rest (until later at least).

"Causality" in physics means that if I change something here, now, it can only affect anything that's inside the future lightcone of here and now. It doesn't tell us a thing about the initial conditions, or what's going on outside my current lightcone, or anything else.

[Ken G]

If there is no time is a very, very big assumption.

Not at all, we are talking about the origin of time. There could be many theories for that, none very easy to test, but the actual point is that there is no correct logical argument that says "any model of the origin of time has to involve a finite universe or there is a logical inconsistency in the model around the issue of causality." That is what I showed. What's more, I showed that your picture is itself the one with a logical inconsistency, because you imagine that the universe must always be in causal contact with its own entirety, and I don't know of any models that do that. Certainly not standard Big Bang with inflation.

It assumes that there was no time before that instantaneous event, which may
be possible, but is not required by any observation.

So what is the logic here, that no time before is not required by observation, but time before is? Given that we are attempting to discover the meaning of the origin of time as we know it and use it in physics, we have no idea if it was there "before", nor does any of our observations have anything to say on the issue. There is simply not a "similar observation" you can point to to support your logic, it is all guesswork. That's why no one can say it is wrong or right, all they can say is that it is not a logical necessity.

The idea that you can assume
anything you like as long as you first assume that there is no time is patently
ridiculous.

This is very curious logic. You are simply disallowing (via labeling as "ridiculous") any assumptions other than the ones you yourself choose to make. How convenient, I suppose I can argue anything that way! But logic doesn't work like that, there are no logical or illogical assumptions, there are only assumptions that prove, via logic, to disagree with what we observe. It will be interesting to see how you will argue that the assumption that time itself has a beginning disagrees with what we observe!

I assume that the known laws of physics applied at the beginning..

Now that is a ridiculous assumption, because we already know that it is not the case. Or do you mean some ethereal "actual laws of physics" that we are not yet privy to, that unite GR and QM and have no Planck length? Do you mean laws that refer to time in an absolute way, not subject to the limitations of our own operational definitions involving periodic phenomena that we can model or at least hope to describe in our current language? Because that's what most physicists mean by "time", and they already know this concept is going to break down at some point early in the Big Bang unless one goes to great lengths to preserve it (by inventing all kinds of additional unconstrained physics that is just as bizarre and unobserved as a beginning to time).

If there is no causal connection between two places, there is no reason
for them to have anything in common. Inflation describes why a large region
of the Universe can be at the same temperature: Everything that inflated was
in causal contact, and at roughly uniform temperature to begin with.

Yet you have not understood my point. Prior to inflation, there would need to have been regions of the universe that were not in causal contact, coming into causal contact. Were that not so, there'd be no point for inflation, you could just claim everything was always in causal contact! But GR without inflation doesn't do that, so whenever you don't have inflation, you have new regions coming into causal contact, and they are all participating in the expansion or else you have a very different theory. Your core thesis here is that it is impossible for there to be a universe, participating in the Big Bang, that is outside of the causal contact of other parts of the universe, also participating in the Big Bang. You have not understood that your core thesis is in violation of the most basic tenet of inflation theory, and indeed Big Bang theory with or without inflation.

Inflation
does not describe how places which are not in causal contact can inflate
simultaneously and identically.

See again my point about inflation, which was not that.

You did not point out any flaw in my logic. You only asserted that there is one.

I described it in detail, and repeated it here.

[DrRocket]

What's more, I showed that your picture is itself the one with a logical inconsistency, because you imagine that the universe must always be in causal contact with its own entirety, and I don't know of any models that do that. Certainly not standard Big Bang with inflation..[/I]

True. But you don't need to go even that far.

Just an expanding universe based on Hubble's observations and some basic observations results in parts of the universe that are receding superluminally and are causally disconnected from us.

[DrRocket]

Yes. If there is no causal connection between two places, there is no reason
for them to have anything in common. Inflation describes why a large region
of the Universe can be at the same temperature: Everything that inflated was
in causal contact, and at roughly uniform temperature to begin with. Inflation
does not describe how places which are not in causal contact can inflate
simultaneously and identically.

-- Jeff, in Minneapolis

You quite clearly do not understand the problems that are addressed by inflation.

One of the most critical problems is the "horizon problem", which is the question of how it is possible that parts of the universe that are now widely separated and not causally related could have been causally relatied near the time of the big bang. The bottom line is that there are no points that were not in causal contact sufficiently near the time of the big bang. You are worrying about the empty set.

If you begin to talk about possible parts of the universe that were never in causal contact then you are venturing in to the lala world of the "multiverse". That is an entirely different subject.