Big Bang and The Edge of The Universe?

[WayneFrancis]

The issue of 2 causally disconnected points having similar properties I don't see as a problem. I don't see why some other point in the universe that isn't causally connected to us shouldn't have similar properties.

For example take the gravitational constant. Why should a spot that isn't causally connected to us have a different value for the gravitational constant besides your say so? My logic being that while there are points that are not causally connected to us there are points which are causally connected to us and that other spot. So if points A & C are not causally connected and B is causally connected to A & C then you can't complain that A & C have the same value for a property because since they are not causally connected "there would be no reason to be the same" but the fact that A & B are causally connected and have the same value and B & are causally connected then C can have the save value as A.

Or is my logic flawed some how?

Note the in a torus the amount of curvature averages out to zero. So there isn't a problem with saying the universe is flat even if it was a 2 torus. It would be like complaining that since there is mass in the universe and it causes curvature that the universe isn't 'Flat'

The way to think about it is the outside of the torus is sphere like, positive curvature, and the inside of the torus is saddle like, negative curvature. But if you add it all up the curvature is still zero.

[noncryptic]

If we live on a 2d universe and we measure it as flat (as we do) we wouldn't be able to distinguish between a plane and a large enough cylinder. Not that i'm saying we live on a cylinder, it just seemed easier to see that it's flat than a torus, but perhaps i was wrong.

No, you're correct. It made me realize that apparently according to theory spacetime can have intrinsic curvature that is such that it can not be detected - at least not by the sort of measurements that WMAP did. Speedfreek's remarks re geometry / topology make more sense now.


I do agree with Jeff regarding "the singularity";

Here is the view of another expert - NASA astronomer Dr Sten Odenwald:
An infinite universe can have an origin at a finite moment in the past because, in general relativity, one can have a 'singularity' condition in which the volume of 3-d space vanishes at a finite moment in the past.

Imo that's taking GR as Truth instead of taking it as a model.

As far as i know it is a mainstream school of thought that says the fact that GR produces zeros and infinities at certain scales means GR is not valid/does not work at those scales.

I suppose that's why the standard cosmological model does not include the first few fractions of a second after the BB (thereby excluding the 'point of origin'), nor does it include the 'inside' of a BH.

[Jeff Root]

The idea of the Universe possibly having a sphere-like topology
seems entirely plausible to me. Observations suggest that it
would have to be vastly larger than the observable part in order
to have a sphere-like topology.

You are referring to a 3-sphere here, where the 3 dimensions are
positively curved. A 3-sphere is something we never see anywhere
in nature!

Any particular reason you point that out? It seems like something
I would say, and you would respond, "So?"

Of course, if the curvature were negative rather than positive, we
might have a "saddle shaped" universe.

Also never seen in nature, of course.

With a 3-sphere, if you look in any direction in what you think of
as a straight line, that line is actually part of a great circle that
circumnavigates the whole universe and its path comes right
back around and hits you in the back of the head. This applies
to all spatial directions.

With a 3-torus, if you look in any direction in what you think of
as a straight line, it is a straight line!

No more so than in the spherical case. In both cases, every
line is "straight" in some ways and "curved" in other ways.

But only in certain directions does it loop back around and hit
you in the back of the head.

In every direction, it goes away and then comes closer again.
It amounts to the same thing: an indication that the line curves.

A torus-like or pac-man-like topology also seems plausible, but
a torus-like or pac-man-like geometry seems wildly unrealistic.
Can the Universe have such a topology without having the
corresponding geometric shape? A spherical geometry would
be perfectly natural. A toroidal geometry for the Universe would
be about as freaky as a toroidal planet: theoretically possible
but absurdly unlikely.

I have never heard of a 3-spherical planet. So, in what way is a
3-sphere more perfectly natural than a 3-torus?

Mass-energy gives space positive curvature. That results in a
sphere-like geometry according to general relativity. The greater
the mass-energy density, the greater the curvature. The Universe
has very low density overall, so very low overall curvature.

I have no idea how you could get a toroid-like geometry.

Of course, we see objects with the topology of a 2-sphere all the
time, but then again we also see 2-tori. Consider, for instance,
the magnetic field of the Earth, and remember we aren't talking
about the shape of a solid object when considering the shape of
the universe.

As to the rest of your post, we have had this discussion at least
twice before and there is no point going over it all again as it
always ends badly.

It does? I'd say it hasn't ever come to any conclusion. I made
an assertion which you don't accept, but also don't disprove.
That's as far as it's gone.

Neither of us fully understands the principles involved here, but
I am willing to accept what the experts in this field have been
saying for decades.

Here is the view of another expert - NASA astronomer Dr Sten Odenwald:

An infinite universe can have an origin at a finite moment in the
past because, in general relativity, one can have a 'singularity'
condition in which the volume of 3-d space vanishes at a finite
moment in the past.

I would require evidence of the last part of that statement before
accepting it: That the volume of 3-d space can vanish (or appear)
instantaneously. It strikes me as completely unphysical.

Even if the 3-d space was still infinite at that moment, the
separations between nearby and distant points reached a
limit of zero separation at the same time.

This also strikes me as being completely unphysical. If the
separation between all places is zero, then those places do
not constitute infinite space. The assertion has no basis in
observation.

-- Jeff, in Minneapolis

[caveman1917]

I would require evidence of the last part of that statement before
accepting it: That the volume of 3-d space can vanish (or appear)
instantaneously. It strikes me as completely unphysical.

The term "vanish" has a technical meaning in mathematics, it means "become zero", not "vanish" as in "disappear".

This also strikes me as being completely unphysical. If the
separation between all places is zero, then those places do
not constitute infinite space. The assertion has no basis in
observation.

They don't, it says the exact same thing as the above, the volume vanishes so the seperation vanishes (ie becomes zero).

[Jeff Root]

The issue of 2 causally disconnected points having similar
properties I don't see as a problem. I don't see why some
other point in the universe that isn't causally connected to
us shouldn't have similar properties.

And there is no reason why it should have similar properties.

If there were some reason, that reason would indicate a causal
connection.

Unfortunately for our ability to discuss this, we don't (and can't)
have any actual examples of causally-disconnected things to
examine and consider. That would be tremendously helpful.

For example take the gravitational constant. Why should a spot
that isn't causally connected to us have a different value for the
gravitational constant besides your say so?

I wouldn't say exactly that. I would say that there is no reason
to assume that such a spot would have a gravitational constant.

I say that everything which has ever participated in the cosmic
expansion of the Big Bang is causally connected. Anything
which has never participated in the cosmic expansion or Big
Bang may be causally disconnected from us, and may not have
any of the properties of spacetime, matter, and energy that we
are familiar with. Or it may. But there is no reason to assume
that it would.

The more similar things are, the more likely that the similarity
is due to a causal connection. That is not a hard and fast rule
of course, but I think it is a very good rule of thumb.

If two spots have the same gravitational constant, I'd guess
that it is because they are causally connected.

My logic being that while there are points that are not causally
connected to us there are points which are causally connected
to us and that other spot. So if points A & C are not causally
connected and B is causally connected to A & C then you can't
complain that A & C have the same value for a property because
since they are not causally connected "there would be no reason
to be the same" but the fact that A & B are causally connected
and have the same value and B & C are causally connected
then C can have the same value as A.

Or is my logic flawed some how?

If A and B are similar *because* they are causally connected,
and B and C are simllar because they are causally connected,
then A and C are similar because they are causally connected.

On the other hand, if A and B are similar because they are
causally connected, but B and C are similar just by chance,
even though they are causally connected, then A and C are
similar just by chance, and we don't have enough info to say
whether A and C are causally connected or not.

A, B, and C are toymakers. A and B know each other, and B
and C know each other. But A and C know nothing of each
other's existence.

Toymaker B makes xylophones that he invented. Toymaker A
makes xylophones that he copied from toymaker B. Toymaker
C makes xylophones that he copied from toymaker B. So the
xylophones of toymakers A and C are causally connected.

In the second scenario, Toymaker B again makes xylophones
that he invented, and toymaker A again makes xylophones that
he copied from toymaker B. But toymaker C makes zylophones
that he invented, and which just happen to be identical to the
xylophones made by A and B. So the xylophones of toymaker
A are not causally connected to the zylophones of toymaker C,
even though they are identical, and even though toymakers A
and C happen to be causally connected via toymaker B.

None of the above implies that A ever affects C, or that C ever
affects A. Toymaker B may have died before toymakers A and
C were born.

Note that in a torus the amount of curvature averages out to zero.
So there isn't a problem with saying the universe is flat even if it
was a 2 torus. It would be like complaining that since there is
mass in the universe and it causes curvature that the universe
isn't 'Flat'.

I haven't complained that there is a conflict between the observed
flatness and a toroidal geometry. To do that I would have to study
the details of how toroidal curvature might affect observations,
which I haven't done. What I have complained is that I don't see
how or whether a toroidal topology can exist without a toroidal
geometry, and that a toroidal geometry seems utterly unlikely.

-- Jeff, in Minneapolis

[Selfsim]

And there is no reason why it should have similar properties.

If there were some reason, that reason would indicate a causal
connection.

Unfortunately for our ability to discuss this, we don't (and can't)
have any actual examples of causally-disconnected things to
examine and consider. That would be tremendously helpful.
…

I wouldn't say exactly that. I would say that there is no reason
to assume that such a spot would have a gravitational constant.

I say that everything which has ever participated in the cosmic
expansion of the Big Bang is causally connected. Anything
which has never participated in the cosmic expansion or Big
Bang may be causally disconnected from us, and may not have
any of the properties of spacetime, matter, and energy that we
are familiar with. Or it may. But there is no reason to assume
that it would.

The more similar things are, the more likely that the similarity
is due to a causal connection. That is not a hard and fast rule
of course, but I think it is a very good rule of thumb.

If two spots have the same gravitational constant, I'd guess
that it is because they are causally connected.

Jeff;

What happens to a very early hydrogen cloud, when it moves beyond our Cosmic Horizon ?

Does it suddenly loose its physical properties just because it is no longer causally connected to our observable universe? Do the photons it once produced, cease to exist? With your rationale, what happens if it enters the domain of a realm having different adopted physical properties ? What happens during its approach to this realm ?

Whilst I agree that there is no reason to assume the same values of the fundamental 'constants' we measure, there are still abstracted parameters, which we can infer might be applicable, regardless of the precise conditions of their origins. (Eg: the concept of Inflaton Fields, comes to mind). If this principle is accepted, then there would seem to be 'causality' everywhere throughout the universe, with the Big Bang as one possible evidence-based, universally common phenomenon, possibly capable of producing different outcomes.

This also does not exclude other origin events either, but inferences can be drawn from what we have observed, in order to encroach upon the boundaries of the presently causally disconnected.

Regards

[speedfreek]

I'd say it hasn't ever come to any conclusion. I made
an assertion which you don't accept, but also don't disprove.
That's as far as it's gone.

Fair enough.

Your assertion is that the universe cannot be infinite, and all have taken part in the same Big-Bang, isn't it? Your objection is based on a lack of causal connection, rather than the concept an infinite universe itself. You do not object to the concept of an infinite universe, only to the concept that it could all have taken part in the same Big-Bang as the part we live in. Is that a fair summation of the situation?

My take is that we do not know what the Big-Bang actually is. We represent it with a singularity, which is generally taken to mean "we don't know". I ask myself, if the Big-Bang is the cause of our observable universe, how large a universe could it possibly be the cause of? What would limit the amount of universe it could cause?

If we assume the whole Big-Bang universe is larger than our observable part of it, then we must also assume it has always been larger by the same proportion. If it is 100 times larger now, then it has always been 100 times larger. This works all the way back, until we reach the singularity, when the universe becomes singular. So either the universe can go from being singular to having more volume than our observable part of it, or it was never actually a singularity ("we don't know").

So, if it is the case that the universe went from being singular to having volume, what limits the volume that can be produced from a singularity? I know it is a circular argument to say that if the Big-Bang caused an infinite volume, then the infinite volume is all causally connected to the Big-Bang, but I see no reason why, if the universe make a transition from zero size to some size larger than our observable part of it, that there has to be a causal limit to the size of the volume produced in that transition - it was all caused by the same thing ("we don't know"), however much of it there is.

Either that, or it was never a singularity in the first place, in which case it already had volume and could already have had infinite volume. Whatever caused it to be in that state, "we don't know".

Perhaps, and this is completely idle speculation of course, at the "we don't know" the contents of the universe, whether finite or infinite, were in the most fundamental state - the most extreme state of matter possible. From this state, only one thing can happen, however much of it there is. I think what I am saying is here is that causal connection at the Big-Bang might be considered an initial condition.

[Jeff Root]

Jeff;

What happens to a very early hydrogen cloud, when it
moves beyond our Cosmic Horizon ?

It loses its causal connection to events here from that time
forward. It retains the causal connection to past events.

Ancestors of mine lived a thousand years ago. I can have
no effect on their lives, and they can do nothing more to
affect mine. But I inherited their genes. They caused me.
I am causally connected with them, via the intervening
generations. That causality cannot go away.

Does it suddenly loose its physical properties just because it
is no longer causally connected to our observable universe?
Do the photons it once produced, cease to exist?

Obviously not. When you get such a peculiar interpretation
of a statement, you can assume that you have misinterpreted
it, and try again.

With your rationale, what happens if it enters the domain of a
realm having different adopted physical properties ? What
happens during its approach to this realm ?

I've never really thought about such a situation. I have no
reason to think that such a thing is possible. I expect that it
is not possible. My rationale from my previous post has no
relevance to the question.

Whilst I agree that there is no reason to assume the same
values of the fundamental 'constants' we measure, there
are still abstracted parameters, which we can infer might be
applicable, regardless of the precise conditions of their
origins. (Eg: the concept of Inflaton Fields, comes to mind).

The concept of inflation fields is a particularly wooley one.
I expect that you can come up with something more likely
to be real, and more closely connected to observables.

If this principle is accepted, then there would seem to be
'causality' everywhere throughout the universe, with the
Big Bang as one possible evidence-based, universally
common phenomenon, possibly capable of producing
different outcomes.

I'm not going to argue with that because it is such a vague
and nebulous statement, it could mean almost anything.
I can easily interpret it in a way that I agree with, or not.

This also does not exclude other origin events either, but
inferences can be drawn from what we have observed, in
order to encroach upon the boundaries of the presently
causally disconnected.

I can't puzzle out the meaning of that last clause.

By "other orgin events" I'm guessing you mean "other
events similar to but independent of the Big Bang." That
is a notion I accept as entirely reasonable. One Big Bang
happened, so others seem likely. I agree that there must
be fundamental, universal parameters which describe
such events. They might even include known physics.

-- Jeff, in Minneapolis

[Jeff Root]

Your assertion is that the universe cannot be infinite,
and all have taken part in the same Big-Bang, isn't it?

That's close. I assert that the Big Bang and resulting
cosmic expansion cannot be infinite. If the Universe is
infinite, then only a finite portion of it was involved in
the Big Bang.

Your objection is based on a lack of causal connection,
rather than the concept an infinite universe itself. You do
not object to the concept of an infinite universe, only to
the concept that it could all have taken part in the same
Big-Bang as the part we live in. Is that a fair summation
of the situation?

Yes.

My take is that we do not know what the Big-Bang actually is.
We represent it with a singularity, which is generally taken to
mean "we don't know".

I take the term "singularity" in this case to refer to a point in
time when everything was in the same place. That's the result
of extrapolating back in time with general relativity, and I think
it is what Roger Penrose meant by the term.

I ask myself, if the Big-Bang is the cause of our observable
universe, how large a universe could it possibly be the cause
of? What would limit the amount of universe it could cause?

If we assume the whole Big-Bang universe is larger than our
observable part of it, then we must also assume it has always
been larger by the same proportion. If it is 100 times larger
now, then it has always been 100 times larger.

I don't see any reason why the proportion couldn't change.
I expect that it would change, even if only trivially.

This works all the way back, until we reach the singularity,
when the universe becomes singular. So either the universe
can go from being singular to having more volume than our
observable part of it, or it was never actually a singularity
("we don't know").

I don't know any of the details of Stephen Hawking's
argument of recent years that there was no singularity,
but in very general terms, that best accords with my own
thinking: Unknown physics at the beginning is needed
to replace the otherwise-assumed singularity.

So, if it is the case that the universe went from being singular
to having volume, what limits the volume that can be produced
from a singularity? I know it is a circular argument to say that
if the Big-Bang caused an infinite volume, then the infinite
volume is all causally connected to the Big-Bang, but I see
no reason why, if the universe make a transition from zero size
to some size larger than our observable part of it, that there has
to be a causal limit to the size of the volume produced in that
transition - it was all caused by the same thing ("we don't
know"), however much of it there is.

There are limits on everything else ever observed. Although
the Big Bang was clearly a unique event (as far as we can
actually see), and clearly involved physics not yet known to
us, it would pretty much violate all known physics for it to go
from finite size or nonexistence to infinite size in finite time
or instantaneously. Nothing else behaves anything like that.

Either that, or it was never a singularity in the first place, in
which case it already had volume and could already have
had infinite volume. Whatever caused it to be in that state,
"we don't know".

If it already had a large or infinite volume, the simultaneous
initialization of the expansion throughout that volume would
be what I object to as violating causality. I would, instead,
suggest a beginning with very small (essentially zero) size
and finite energy density, rapidly growing. Every part of the
result having causal contact with that initial event.

Perhaps, and this is completely idle speculation of course,
at the "we don't know" the contents of the universe, whether
finite or infinite, were in the most fundamental state - the most
extreme state of matter possible. From this state, only one
thing can happen, however much of it there is. I think what I
am saying is here is that causal connection at the Big-Bang
might be considered an initial condition.

I think my ideas and your ideas can get along just fine.

-- Jeff, in Minneapolis

[Selfsim]

Obviously not. When you get such a peculiar interpretation
of a statement, you can assume that you have misinterpreted
it, and try again.

Well, apparently not.
It seems you don't accept the inflation mechanism as part of the Standard Model, for instance.
Is there anything else you don't consider to be part of the model ?

I've never really thought about such a situation. I have no
reason to think that such a thing is possible. I expect that it
is not possible. My rationale from my previous post has no
relevance to the question.

Fascinating ...
Others seem to be pondering such questions ... and searching for evidence.
If one doesn't consider the possibility, how is progress ever made ?

The concept of inflation fields is a particularly wooley one.
I expect that you can come up with something more likely
to be real, and more closely connected to observables.

As mentioned above, Inflaton Fields (hypothesised), have resulted in predictions and plausible explanations.
I'm having real difficulties in understanding which parts of the Standard Model you do, and don't, consider acceptable ...

What mechanism do you consider 'works' as a cause of the 'Bang' ?

I can't puzzle out the meaning of that last clause.

By "other orgin events" I'm guessing you mean "other
events similar to but independent of the Big Bang." That
is a notion I accept as entirely reasonable. One Big Bang
happened, so others seem likely. I agree that there must
be fundamental, universal parameters which describe
such events. They might even include known physics.

Fair enough .. my last paragraph could have been worded more clearly (apologies for that). I'll try again ..

This also does not exclude other origin events either, but inferences can be drawn from what we have observed, in order to understand what we cannot confirm by direct observation. Theory enables us to extrapolate beyond those observational limitations, whilst maintaining consistency.

How do you define, quantify and describe: 'known' physics ?

Regards

[Shaula]

What I have complained is that I don't see how or whether a toroidal topology can exist without a toroidal geometry, and that a toroidal geometry seems utterly unlikely.

Why? With no evidence what intuitive model are you using to make this judgement? How many universe geometries that you have observed/measured are you basing this statement on? I think this is a totally non-scientific call.

You are posting an opinion and then passionately arguing it despite there being no evidence for or against it. I am not sure what place that has in this thread? It is why I stopped contributing before - the OP seemed to want to believe in a subset of possibilities that have been speculated on within the standard framework. That is fine. Believe what you like. But defending beliefs with no evidence and nothing more that "I think this is unlikely" or "I want to believe this" is not a tenable position in science.

If two spots have the same gravitational constant, I'd guess that it is because they are causally connected.

And that would be a complete guess. Without knowing the basis of the value of that constant you cannot rule out:
1) There is only one solution to the real theory of everything and that fixes G
2) All other values of G are much more unlikely due to some mechanism (such as symmetry breaking)
3) The value of G is actually set by the shared geometry/metric the universe is in or is embedded in
... ...

[Van Rijn]

Believe what you like. But defending beliefs with no evidence and nothing more that "I think this is unlikely" or "I want to believe this" is not a tenable position in science.

Yes, I read them as multiple arguments from personal incredulity.

[Van Rijn]

This describes the fallacy well, I think. From:

http://rationalwiki.org/wiki/Argument_from_incredulity

The general form of the argument is as follows.

Major premise: One can't imagine (or has not imagined) how P could be so.
Minor premise (unstated): If P were so, one could imagine (or would have imagined) how.
Conclusion: Not-P.

As a syllogism this is valid. The fallacy lies in the unstated minor premise. If a state of affairs is impossible to imagine, it doesn't follow that it is false; it may only mean that imagination is limited.

(Emphasis added).

[Cougar]

...it would pretty much violate all known physics for it to go
from finite size or nonexistence to infinite size in finite time...

Infinity is not a size. It's a process.

[Astron]

IF there is no point of beginning then the scenario of Big Crunch ends in what point?
Everything are compressed everywhere?
Shouldn't be one single point of singularity to exist?

[Shaula]

Shouldn't be one single point of singularity to exist?

We don't know there will be a big crunch. The singularity may not correspond to everything being at one point - we need more complete theories to describe what is going on as our physical models break down before we reach that point.

[Strange]

No more so than in the spherical case. In both cases, every
line is "straight" in some ways and "curved" in other ways.

The meaning of "what you think of as a straight line" is a line which is the shortest distance between two points. This will appear straight to the observer in curved space even though it is more correctly a geodesic (I know, we have had that discussion before). As opposed to a line which appears curved to the observer and is not the shortest distance between two points (and therefore not a geodesic).

[noncryptic]

To me the issue is not so much whether or not the universe is infinite, but whether or not the universe originated from an infinitesimal small/dense point.

GR says it did, but we know GR to be incomplete and it's generally thought that the zeros and infinities that math can produce are not real. Rather they mean the math does not work under those circumstances.

As i previously stated: afaik the notion that the universe originated from an infinitesimal small/dense point is not part of the standard model.

It is of course part of mainstream science in that it is a product of GR - but it's also one of a few predictions of GR that have not been confirmed by observation. In that respect the singularity is not nearly as 'true' as other consequences of GR.

I see no basis for firm claims about anything that happened during a time where we know conditions were such that "the laws of physics break down".

You can't have both GR break down -and- conclude from GR what the conditions are when it has broken down. All we know is the limit at which GR still does work, but that's a long way off from a singularity.

[Jeff Root]

It seems you don't accept the inflation mechanism as part of
the Standard Model, for instance.

I don't know which posts of mine you got that from, but it is
true that I question whether inflation should be part of the
standard model. Whether it *is* part of the standard model
is a question I've never considered.

Is there anything else you don't consider to be part of the model ?

You ask such amusing questions.

With your rationale, what happens if it enters the domain of a
realm having different adopted physical properties ? What
happens during its approach to this realm ?

I've never really thought about such a situation. I have no
reason to think that such a thing is possible. I expect that it
is not possible. My rationale from my previous post has no
relevance to the question.

Fascinating ...
Others seem to be pondering such questions ... and searching
for evidence.

Really? Searching for evidence of distant matter moving out
of our Universe and into another Universe with different laws
of physics? Really? If so, I wish them luck. They'll need it.

If one doesn't consider the possibility, how is progress ever made ?

By asking better questions.

The concept of inflation fields is a particularly wooley one.
I expect that you can come up with something more likely
to be real, and more closely connected to observables.

As mentioned above, Inflaton Fields (hypothesised), have resulted
in predictions and plausible explanations.
I'm having real difficulties in understanding which parts of the
Standard Model you do, and don't, consider acceptable ...

If you say so.

What mechanism do you consider 'works' as a cause of the 'Bang' ?

Although I, too, frequently change the direction of discussion
when a comment suggests a new line of inquiry, I'm not going
to follow you on this one. You mentioned inflaton fields as an
example of possible fundamental "abstracted parameters"
which might apply to everything, not just the part of the Universe
in which the Big Bang occurred. I replied that inflaton fields are
extremely hypothetical. They are far removed from observation.
There is no direct evidence for such fields. I suggested that you
could come up with a better example of "abstracted parameters"
than inflation fields. Now you want to morph that into a question
about causes of the Big Bang. Essentially a new subject.

This also does not exclude other origin events either, but
inferences can be drawn from what we have observed, in
order to encroach upon the boundaries of the presently
causally disconnected.

I can't puzzle out the meaning of that last clause.

By "other orgin events" I'm guessing you mean "other
events similar to but independent of the Big Bang." That
is a notion I accept as entirely reasonable. One Big Bang
happened, so others seem likely. I agree that there must
be fundamental, universal parameters which describe
such events. They might even include known physics.

Fair enough .. my last paragraph could have been worded
more clearly (apologies for that). I'll try again ..

This also does not exclude other origin events either, but
inferences can be drawn from what we have observed, in
order to understand what we cannot confirm by direct
observation. Theory enables us to extrapolate beyond those
observational limitations, whilst maintaining consistency.

How do you define, quantify and describe: 'known' physics ?

What odd questions you ask.

I didn't want to pass over your post without responding,
but the questions you're asking are mostly unanswerable
and not particularly useful.

-- Jeff, in Minneapolis

[Jeff Root]

What I have complained is that I don't see how or whether
a toroidal topology can exist without a toroidal geometry,
and that a toroidal geometry seems utterly unlikely.

Why? With no evidence what intuitive model are you using
to make this judgement? How many universe geometries
that you have observed/measured are you basing this
statement on? I think this is a totally non-scientific call.

You are posting an opinion and then passionately arguing
it despite there being no evidence for or against it.

Which opinion of mine do you refer to here? The one I
expressed in the quote? That a toroidal geometry for the
Universe seems utterly unlikely? I have scarcely argued
that opinion *at all*, much less argued it passionately.

I asked whether a toroidal (pac-man) topology can exist
without a corresponding toroidal geometry, but have not yet
got an answer. I said I don't understand what a "3-torus" is.
The term seems to have come into cosmology discussion
quite recently. I find no mention of it in either 'The Big Bang'
(second edition, 1989) by Joseph Silk, or 'The Origin of The
Universe' (1994) by John D. Barrow. The one thing that I
know a toroidal geometry has going for it is that it can be
considered in some sense "flat" -- having some properties
similar to those of a Euclidean space -- so it doesn't conflict
with the observation that the observable Universe appears
to have a nearly "flat" overall geometry. I'm not aware of
any other advantages it might have. It's basic problem, from
my point of view, is that it is a more complex geometry than
Euclidean or spherically-curved space, without providing
any apparent advantages over those simpler geometries.

The opinion I *have* been passionate about (though I also
have not said much to support it) is the opinion that everything
involved in the Big Bang and resulting cosmic expansion must
be causally connected, so cannot have infinite extent. That
seems apparent on its face, so it isn't clear how to argue for it.

I am not sure what place that has in this thread?

The question of the geometric shape of the Universe bears
directly on the question of whether it has an "edge". I said a
toroidal topology is plausible to me, but a toroidal geometry
seems utterly unlikely, and asked whether a toroidal topology
can exist without a toroidal geometry. Pretty straightforward.

It is why I stopped contributing before - the OP seemed to want
to believe in a subset of possibilities that have been speculated
on within the standard framework. That is fine. Believe what
you like. But defending beliefs with no evidence and nothing
more than "I think this is unlikely" or "I want to believe this" is
not a tenable position in science.

I didn't make any attempt to argue that toroidal geometry is
unlikely. I merely said that it seems utterly unlikely. It does.
If that opinion bothers you, then it is your cue to explain why
a toroidal geometry is not unlikely, or why it isn't required for
a toroidal topology.

If two spots have the same gravitational constant, I'd guess
that it is because they are causally connected.

And that would be a complete guess. Without knowing the
basis of the value of that constant you cannot rule out:
1) There is only one solution to the real theory of everything
and that fixes G

Does this theory have a mechanism, or is it just descriptive
of the results? If it is only descriptive, how do you know it
describes parts of the Universe which are not causally
connected to ours? You don't. If it has a mechanism, ...

2) All other values of G are much more unlikely due to
some mechanism (such as symmetry breaking)

Which means the "mechanism" causally connects the
"values of G".

3) The value of G is actually set by the shared
geometry/metric the universe is in or is embedded in... ...

Which means the "value of G" is causally connected to
the "shared geometry/metric".

Any mechanism which causes things to be the same
in different locations causally connects them.

Without a mechanism, then you can't know whether
things are the same in places which are not causally
connected.

-- Jeff, in Minneapolis

[Shaula]

Any mechanism which causes things to be the same in different locations causally connects them.

That is an interesting definition of casually connected. One I would not subscribe to at the moment as it dives deeply into areas not covered by current theory, as of yet. In this context I was talking about light cones, basically. If something is outside the future light cone it is not causally connected to that event.

This is all at the highly speculative end of physics but may serve as an example of what I was talking about:
Suppose M-theory is right. Suppose the universe was created by two branes colliding. There is nothing to stop them colliding in several places along their extent. If the underlying geometry of space-time is set by the properties of the colliding branes then they universes, despite never having been in contact, will share certain rules of physics, particle families and so on.

The opinion I *have* been passionate about (though I also have not said much to support it) is the opinion that everything involved in the Big Bang and resulting cosmic expansion must be causally connected, so cannot have infinite extent. That seems apparent on its face, so it isn't clear how to argue for it.

So are you making the assumption that the volume we see that was part of the Big Bang was all of it? Say we can trace the observable universe back to a volume the size of an atom. Why should that be all of the bang? We don't know enough about the initial event. For all we know when it happened an infinite expanse of spacetime was created, all filled with 'bang' that all expanded out to create the universe. The initial conditions might have been deterministically created by the initial event as the only solution to the basic laws, which in turn might be basic laws because they are the only laws that work, or were imposed on us by a higher dimensional interaction, or by the topology of whatever.

We don't know - the argument "This seems too obvious to argue" doesn't work with things when there are so many unknowns that you have to eventually admit that there simply is not enough data to reason reliably from.

Without a mechanism, then you can't know whether things are the same in places which are not causally connected.

This is interesting - your argument is somewhat difficult to counter in that it is fairly obvious that without knowing how physical laws were set we cannot know if they vary outside our light cone. It all comes down to what you mean by causally connected. And that is embedded heavily in whether you link causality to spacetime. How it is related to spacetime and the earliest conditions is very likely part of the deeper theory of everything and hopefully something that will come out in further work. But at the moment the underlying causal structure of spacetime at these epochs is not well understood.

[speedfreek]

I asked whether a toroidal (pac-man) topology can exist
without a corresponding toroidal geometry, but have not yet
got an answer. I said I don't understand what a "3-torus" is.
The term seems to have come into cosmology discussion
quite recently. I find no mention of it in either 'The Big Bang'
(second edition, 1989) by Joseph Silk, or 'The Origin of The
Universe' (1994) by John D. Barrow. The one thing that I
know a toroidal geometry has going for it is that it can be
considered in some sense "flat" -- having some properties
similar to those of a Euclidean space -- so it doesn't conflict
with the observation that the observable Universe appears
to have a nearly "flat" overall geometry. I'm not aware of
any other advantages it might have. It's basic problem, from
my point of view, is that it is a more complex geometry than
Euclidean or spherically-curved space, without providing
any apparent advantages over those simpler geometries.

Joseph Silk is one of my primary sources - there is a chapter about the possible topologies of the universe in his book "The Infinite Cosmos", and there are only two possible topologies for a flat universe.

Here is Joseph Silk, talking on the subject:

We do not know whether the Universe is finite or not. To give you an example, imagine the geometry of the Universe in two dimensions as a plane. It is flat, and a plane is normally infinite. But you can take a sheet of paper [an 'infinite' sheet of paper] and you can roll it up and make a cylinder, and you can roll the cylinder again and make a torus [like the shape of a doughnut]. The surface of the torus is also spatially flat, but it is finite. So you have two possibilities for a flat Universe: one infinite, like a plane, and one finite, like a torus, which is also flat.

http://www.esa.int/esaSC/SEMR53T1VED_people_0_iv.html - The whole interview is about this.

If flat, the universe is either infinite, or a 3-Torus.

I think you might appreciate what he says about comparing the universe to an explosion, too.

[Jeff Root]

Thanks for the link, SpeedFreek. Of course, in that very short
interview, Silk didn't go deep enough into describing toroidal
geometry to help me understand it better.

You're right about the explosion! That is usually what I mean!
I'll probably add it to the list of quotes I've collected.

-- Jeff, in Minneapolis

[Jeff Root]

Any mechanism which causes things to be the same in
different locations causally connects them.

That is an interesting definition of causally connected.
One I would not subscribe to at the moment as it dives
deeply into areas not covered by current theory, as of yet.

It is completely straightforward. It can't be any other way.
You and I have similar DNA because we are causally
connected by our common ancestors. Without those
common ancestors it would be extremely unlikely that
we would be anything alike.

In this context I was talking about light cones, basically.
If something is outside the future light cone it is not
causally connected to that event.

If two things are both inside the future light cone of an
event, they are both causally connected to that event.
One event can cause multiple things to have common
properties. Perfectly straightforward.

This is all at the highly speculative end of physics but
may serve as an example of what I was talking about:
Suppose M-theory is right. Suppose the universe was
created by two branes colliding. There is nothing to
stop them colliding in several places along their extent.
If the underlying geometry of space-time is set by the
properties of the colliding branes then the universes,
despite never having been in contact, will share certain
rules of physics, particle families and so on.

The universes are each causally connected to the
same branes. The branes are the DNA which tells
the universes what properties they will have.

The opinion I *have* been passionate about (though I
also have not said much to support it) is the opinion that
everything involved in the Big Bang and resulting cosmic
expansion must be causally connected, so cannot have
infinite extent. That seems apparent on its face, so it isn't
clear how to argue for it.

So are you making the assumption that the volume we
see that was part of the Big Bang was all of it?

I'm having trouble parsing that question.

I assume that the volume we see is less than everything
that was involved in the Big Bang. I haven't examined
it quantitatively to have an estimate of how much less.
I know that others have done so. I neither accept nor
reject their figures until I get around to examining them
in greater depth.

I do think it is very notable that there is no hint of any kind
of edge in any observations. I don't take that as conclusive
evidence that there is no edge.

I do not make any assumption as to whether the Big Bang
was the beginning of Everything, or only the beginning of
our own Universe, with other universes also existing. As I
said, though, since one Big Bang happened, others can
probably happen.

Say we can trace the observable universe back to a volume
the size of an atom.

I'm not sure it makes any difference for your question, but
"the observable Universe" can mean either "the currently
observable part of the Universe, traceable back through
time", or "the observable part of the Universe at any given
time". Distant parts of the Universe may enter or leave the
observable part depending on how the expansion goes.

Why should that be all of the bang?

Your question probably needs a quantitative answer, which
I don't have. I say that everything involved in the Big Bang
is causally connected. I don't know exactly how to do that.
I don't know the relationships between time, volume, speed,
and whatever, that must be required for everything to be
causally connected and to appear as it does.

We don't know enough about the initial event. For all we
know when it happened an infinite expanse of spacetime
was created, all filled with 'bang' that all expanded out to
create the universe. The initial conditions might have been
deterministically created by the initial event as the only
solution to the basic laws, which in turn might be basic laws
because they are the only laws that work, or were imposed
on us by a higher dimensional interaction, or by the topology
of whatever.

Perhaps I am assuming that the known laws of physics
should not be thrown out to make the Big Bang work. Some
unknown physics happened, but I assume that that unknown
physics is in addition to known physics, and doesn't replace
it wholesale. Laws of physics are essentially descriptions
of the limits of what is possible. I assume that most of the
limits we know of applied even to the Big Bang. Causality
is a particularly important limitation. Change requiring time
to occur is an equally important limitation. Changes over
large volumes of space -- or the creation of a large volume
of space -- should require more time than small changes.
We never observe anything change instantaneously except
at the very limit of the smallest detectible changes. Perhaps
the very largest detectible change was also instantaneous,
but that would be bucking the trend more violently than any
ATM idea ever. It doesn't fit in with anything ever observed.

We don't know - the argument "This seems too obvious to
argue" doesn't work with things when there are so many
unknowns that you have to eventually admit that there
simply is not enough data to reason reliably from.

I assume that big changes never happen instantaneously.
Creation of an infinite Universe is an infinitely big change.

So I expect that the Universe created in the Big Bang is
finite, and took some time to come into existence. That
is not obviously true. But I think it is obviously true that
everything which resulted from the Big Bang is causally
connected. It all has one common cause.

(I'll add that since everything was necessarily causally
connected from the beginning, I'm skeptical of the need
for later inflation to even out the temperature.)

Without a mechanism, then you can't know whether things
are the same in places which are not causally connected.

This is interesting - your argument is somewhat difficult to
counter in that it is fairly obvious that without knowing how
physical laws were set we cannot know if they vary outside
our light cone. It all comes down to what you mean by
causally connected. And that is embedded heavily in
whether you link causality to spacetime. How it is related
to spacetime and the earliest conditions is very likely part
of the deeper theory of everything and hopefully something
that will come out in further work. But at the moment the
underlying causal structure of spacetime at these epochs
is not well understood.

I came up with a little aphorism a couple of decades ago:
"Time is a factor in everything that happens, but it isn't the
only factor in anything." That could probably be extended
to refer to spacetime. It embodies my view that change
requires time. Bigger changes tend to require more time.
That's what I observe in the visible Universe. I have no
good reason to think it isn't valid for the biggest change
we can observe: the beginning of the Universe.

If distant parts of the Universe are similar to ours in many
details, then it can only be because we are connected by
a common ancestor, whether that ancestor is the Big Bang
or something which preceeded it.

-- Jeff, in Minneapolis

[Van Rijn]

It is completely straightforward. It can't be any other way.

I disagree. I don't accept your arguments from incredulity.

[Van Rijn]

Joseph Silk is one of my primary sources - there is a chapter about the possible topologies of the universe in his book "The Infinite Cosmos", and there are only two possible topologies for a flat universe.

Here is Joseph Silk, talking on the subject:


http://www.esa.int/esaSC/SEMR53T1VED_people_0_iv.html - The whole interview is about this.

If flat, the universe is either infinite, or a 3-Torus.

Heh, I was just thinking about this in regards to Astromark's thread.

[Selfsim]

I disagree. I don't accept your arguments from incredulity.

Ha ! Beat me to it ! Couldn't have expressed it better.

I've never conducted the experiment, but I'm also told that if one removes the lid of a jar containing fleas, they will continue jumping to the exact height of where the lid previously was (??)

Cheers

[Selfsim]

This is all at the highly speculative end of physics but may serve as an example of what I was talking about: Suppose M-theory is right. Suppose the universe was created by two branes colliding. There is nothing to stop them colliding in several places along their extent. If the underlying geometry of space-time is set by the properties of the colliding branes then the universes, despite never having been in contact, will share certain rules of physics, particle families and so on.

The universes are each causally connected to the same branes. The branes are the DNA which tells the universes what properties they will have.

As it turns out, in higher dimensional space, photons and charged objects cannot necessarily be located just anywhere. The extra dimensions introduce a way to separate particles. Distinct particle types might be restricted to separate regions of space occupied by different branes. Because not all points in extra dimensions look the same, extra dimensions introduce a way to separate particles by confining different particle types, to separated branes.¹

For example, grouping certain particles on certain branes types, might explain why particles have different masses, and why proton decay doesn't occur in extra dimensional models.¹

As another example: flavour changing amongst groups of leptons, (electrons and muons), and quark flavours, (up, charm and top), has also been explained by interactions with particles in the 'bulk'², (full higher dimensional M-theory space). Given that these three quarks have exactly the same gauge interactions, in the Standard Particle model, so far, it is unexplained as to why they all have different masses. Other models can be constructed, but it has been found that invariably, these models also contain unwanted interactions that change flavour identities. Distinguishing the flavours without producing these problematic interactions, required an M-theory model including branes and 'Sequestered Supersymmery'.^1,2

These examples highlight the way M-Theory can be used as a model for explaining issues, (or 'troubles' in Cougar's terminology), so far unexplained in the Standard Particle Model.

In these examples, 'causality' can be attributed to interactions amongst particle classes and physical brane properties (eg: dimensionality, charge, shape and tension¹). In other words, 'causality' is still governed by the known laws of Physics, and measured parameters throughout all dimensions (up to, and including, the higher dimensional space of the 'bulk').

In this sense, there is also no question about String and M-Theory being firmly embedded in, and adding value to, mainstream Physics !

Regards
1. Warped Passages - Lisa Randall (2005): Chapter 9: internal Symmetries, Chapter 17: Sequestering and Shining Masses, Chapter 15 Nascent Branes. (Not exact wording ... summarised and compacted by myslef)
2. Nima Arkani-Hamed and Savas Dimiopoulos.

[Shaula]

Yeah, sorry Jeff - as far as I can see all you are doing is presenting the same assertions. Your first paragraph is an absolutely perfect example of it. It can be many other ways. Causality is not as simple as you make out and is being investigated as a fundamental aspect of the space time it is linked to. Theories other than String theory seem to be probing deeply into what is mean by causality and how it can be used to 'build' spacetime. So if they turn out to be better than Strings then we would have the situation where any universe with causality would end up with the same spacetime structure as our own. So by your logic that would mean everything with causality would be causally connected.

In the brane example - while it is true that the two universes created would lie within the world volume of the branes colliding the fundamental conjecture of causal set theory suggests that if the two manifolds are different enough causal sets are not mappable between the two. This means that you cannot say that they are causally related any more than you can say what is going on inside a black hole using the co-ordinate system of an external observer.

Your assumptions about how the universe formed basically drive your thinking and conclusions - I am not sure if any argument will touch them because the basic premises seem to hardwired into your reasoning. Your point about the Big Bang is a case in point. You assume it was finite to preserve your ideas about causal connections and the way time works which in turn reinforce your belief that it was finite.

[speedfreek]

I missed this earlier.

Mass-energy gives space positive curvature. That results in a
sphere-like geometry according to general relativity. The greater
the mass-energy density, the greater the curvature. The Universe
has very low density overall, so very low overall curvature.

I have no idea how you could get a toroid-like geometry.

Mass-energy can also give the universe negative curvature, as here we are talking about the global curvature. If the average density is greater than the critical density we have positive global curvature and a spherical geometry (omega>1 = a closed universe), whereas if the average density is less than the critical density we have negative global curvature and a hyperbolic geometry - the "saddle shape" (omega<1 = an open universe). If the average density is equal to the critical density, we have a flat universe (omega=1).

So, when we say the universe is close to being flat, we have to acknowledge that if it isn't flat, it is just as likely to be negatively curved as positively curved. It is just as likely to be a saddle as it is to be a sphere!

Now it seems, from what I have read, that the geometry and topology of the universe are not exactly the same thing, but it will take someone better acquainted with these principles than I to explain why, exactly.