Closed or open universe?

[johngalt]

I was watching Event Horizon the other day, and it got me thinking about the universe. The villian in the movie said that he had gone to another universe, blah blah blah....

Well, here is my first of 2 related questions:

1) Is the universe infinite in volume, or is it a finite size? I am leaning toward an infinite volume because of the billions of galaxies and such. Now if the universe is closed, though, that would be weird. I just have this thought about spaceships in the future billions of light-years away from earth that end up running into a solid surface, being the end of the universe.

2) Is their a significant amount of research suggesting that there could be 2, 3, or an infinite amounts of universes( i guess what would be called a multiverse)?

All comments welcome

[Seraphim]

1) Is the universe infinite in volume, or is it a finite size? I am leaning toward an infinite volume because of the billions of galaxies and such. Now if the universe is closed, though, that would be weird. I just have this thought about spaceships in the future billions of light-years away from earth that end up running into a solid surface, being the end of the universe.

Ever thought the Universe could have be round or sphere-shaped (like an egg)?
The Galaxies could be on the "surface" and the surface is round so there will be no beginning or the end. The middle portion could be a big black space where earlier galaxies were form and died out.

Where I got this idea? From Big Bang. They did say it expanded from a central point, so it should be like a sphere instead of spread like a jam on a piece of bread.

I seems to remember an Episode from Space 1999 - if not mistaken (for you kids who are born after 1980s, the show was somewhere around 1970s so some of you couldn't remember). The Moon (with a lunar base) was blown of the orbit due to a large nucklear explosion and send flying through space. And those who did survived it on the Moon base, made it like something like a spaceship and explore the space as they went along.

In one episode, the Moon was getting close to a system which was very close resemble to Earth and everyone thought that they are coming back home. Some people doubt it because they were travelling in one direction and it will take hundreds of years to return back to the Solar system (assuming the Universe was round).

2) Is their a significant amount of research suggesting that there could be 2, 3, or an infinite amounts of universes( i guess what would be called a multiverse)?

Multiverse could exist but I don't believe that you can find another you there.

The reason why I said that Multiverse could exist is simply theorical. IF the event of Big Bang which created us happened here, WHY shouldn't we believe that it couldn't happen somewhere else?

[Wounded King]

1. Nobody knows. Our visible universe is certainly finite, its range being restricted by the speed of light.

2. There is a lot of theoretical research and philosophical work on the possible forms a multiverse might take. A recent article in Scientific American discussed this recently and there is a thread on that topic on this forum. Some advocates of the many worlds (MW) interpretation of quantum mechanics say that quantum computing provides evidence for MW, but I think this is a fairly controversial conclusion.

[eh]

Originally posted by johngalt

1) Is the universe infinite in volume, or is it a finite size? I am leaning toward an infinite volume because of the billions of galaxies and such. Now if the universe is closed, though, that would be weird. I just have this thought about spaceships in the future billions of light-years away from earth that end up running into a solid surface, being the end of the universe.

Cosmologists would say there is no edge or center to the universe, so travelling far enough in a spaceship will eventually take you back to your starting point. But it's a little more complicated, so here's a link: http://www2.corepower.com:8080/~relfaq/centre.html

2) Is their a significant amount of research suggesting that there could be 2, 3, or an infinite amounts of universes( i guess what would be called a multiverse)?

Depends on the kind of multiverse. Run out and grab the latest copy of Sci American, as it has the article Wonded King mentioned. An universe of infinite volume is consistent with the evidence, but is not really a testible model. A finite but large universe will still always be an option.

There is the multiverse as a result of eternal inflation, where pre-existing regions of space-time end up producing universes for eternity. I don't know of any testible predictions made by these models. The same goes for others, such as MWI, so research would be limited to the theoretical aspect of physics.

[johngalt]

IF the event of Big Bang which created us happened here, WHY shouldn't we believe that it couldn't happen somewhere else?

My question to this is where would another explosion happen? What it be in our universe, or what?

[Friar Bellows]

"Open" and "closed" refers to the curvature of space, a local quantity which can vary from point to point. The term "open universe" refers to a universe where the spatial curvature is negative and constant everywhere, but only on the large scale. If you drew a triangle on 2D surface which had a negative constant curvature, you would find that the sum of the interior angles would add up to less than 180 degrees. A "closed" universe has a positive, constant, spatial curvature everywhere. The sum of the interior angles of a triangle on a closed 2D surface add up to greater than 180 degrees. A "flat" universe has zero, constant, spatial curvature everywhere, and the sum of the interior angles of a triangle drawn on a 2D flat surface adds up to exactly 180 degrees (so all of Euclid's axioms hold true in flat space).

"Open" and "closed" are not to be confused with "unbounded" and "bounded", "infinite" and "finite", or "non-compact" and "compact", which refers to the topology of space, a global quantity about which Einstein's field equations (which are used to model the expansion of space) have nothing to say. For example, an open or a flat universe could be finite in volume. The 3-torus is one example of a topology which is flat everywhere but is still bounded. Astronomers are studying the cosmic background radiation and the large-scale distribution of galaxies to determine the topology of the universe, but it's not an easy task (it might even be impossible). So the question of whether the universe is finite or infinite is still undecided and likely to remain so.

As for there being more than one universe, it's all just speculation at this point. Good for popular science articles. :)

[Shadowy Man]

"The universe is a big place, perhaps the biggest."

- Kilgore Trout

[Seraphim]

by johngalt

My question to this is where would another explosion happen? What it be in our universe, or what?

Well ... there are Supernovaes ... smaller scale explosion which destroys everything and when things colds down, elements forms and new solar system and masses forms. That could be a good study model (if someone could live long enough to witness it all).

I always viewed the Universe as a large, blank white painting canvas (except it is black). The explosion which caused the Big Bang could actually like a painter spread a color onto the white canvas.

Anyway, if the space is indeed huge and empty, then the same explosion which created this Universe could create others. To me, that's logical.

[eh]

Well Seraphim, there are inflation models which consist of a large canvas in which an eternity of big bangs take place. The problem is, even that empty canvas itself is expanding. Logically, if you wind back the clock the painted universe gets smaller and smaller until reaching a singular point. So it would seem that anything happening before this initial singularity is a problem, since there would no canvas at all for the painter to work with.

[Seraphim]

by eh

Well Seraphim, there are inflation models which consist of a large canvas in which an eternity of big bangs take place. The problem is, even that empty canvas itself is expanding. Logically, if you wind back the clock the painted universe gets smaller and smaller until reaching a singular point. So it would seem that anything happening before this initial singularity is a problem, since there would no canvas at all for the painter to work with.

Maybe the canvas is expanding because the Universe (which is forming from atoms and energy to taking solid shapes) pushing the the space to expand.

Like a inflated ballon, flat and without a shape or size, and when air is forced into it, it slowly increase in size and shape and take room which was occupied by the empty air out the ballon before.

Both forms (the Universe and the empty space) is consists of air BUT only difference between them is ONE (the Universe, or the ballon if you may) has shape and dimension while the other is empty.

As for the event before the Singularity ... well, that is beyond Science (no offence attended). Even if a scientist (like another Einstein) appeared and created a model of what happened before the Singularity occured, one have to witness an actual Big Bang to prove it.

Hmmm ... that reminds me .... anyone knows any theory of what happens to those elements and matter absorbed by the Black Hole? Does energy (which Science says cannot be destroyed) actually get destroyed? Does Singularity formed back like that before the Big Bang, occured within the Black Hole?

[Answerer]

Originally posted by Wounded King
Some advocates of the many worlds (MW) interpretation of quantum mechanics say that quantum computing provides evidence for MW, but I think this is a fairly controversial conclusion.


Sorry, I just don't get it. In what ways do quantum computing prove MWI?

[Wounded King]

Not very convincing ones. David Deutsch is the main proponent of this argument that I am aware of, you can find some stuff by him at www.Qubit.org.

[JGL53]

Here's the link to the Scientific American article previously mentioned:

http://www.sciam.com/article.cfm?ar...umber=1&catID=2

[Anachronix]

There has been some speculation (that I can't seem to track down ATM) that postulates the 'boundaries' of our universe are one big singularity that, if touched or crossed, could transport the object through time or space. Much the same theories have been put forward as to the centre of black holes.

[Bob K]

John Galt:

RE: 1) Is the universe infinite in volume, or is it a finite size?

Check out

http://www.bobkwebsite.com/invriabletimeintrvls.html

Summary: When we define space to be an unbounded volume, a void in which things/events comprised of matter/energy float, then we find that there is no limit to the dimensions nor the duration of the volume/void which is space, that it is essentially a pure vacuum except for those areas in which are found matter/energy, then we find that space is open, that space cannot possibly be closed.

From observations in laboratories conducted concerning thermodynamics, we can extrapolate what is the universe.

A closed energy system is one from which energy cannot be taken and to which energy cannot added.

The matter/energy of the universe is a closed system. Matter/energy cannot be taken from it (where would it go?); and matter/energy cannot be added to it (where would it come from?).

From thermodynamics we learn that in a closed energy system:

1. matter/energy cannot be destroyed but only changed in form, matter <-> energy, as expressed by E = mc2 and m = E/c2;
2. the sum total of matter/energy is a constant.

Because matter/energy cannot be destroyed but only changed in form, matter/energy is infinite in duration, never had a beginning, is present now, and will never have an ending.

Because in a closed system the sum total of matter/energy is a constant, the sum total of matter/energy is a finite number.

Infinity is not a number. If you think it is, then tell us what it is, but don't be surprised if I add one more to your number and therefore come up with a bigger number. Infinity, at best, is a condition of having no mathematical or physical limits.

A finite quantity of matter/energy cannot be dispersed into an infinite volume/void without practical limits to the finite quantity of matter/energy beyond which is a pure vacuum. There will be, therefore, points in space which will have no quantity of matter/energy present.

Matter/energy includes force fields, including electromagnetic fields and gravitational fields. Thus, matter/energy is not one 'thing' and force fields another 'thing'; they are the same.

Time is the use of time-intervals for the measurement of the occurrences of events in sequences of events.

When time-intervals are invariable, then Absolute/Universal Time is established. Absolute Space is likewise established, and spacetime is destroyed as a physical or theoretical concept. [When constructed using invariable time-intervals, a Spaceclock returned to Earth and its Earthclock twin will show identical face readings/time measurement and therefore no time dilation; only Spaceclocks and Earthclocks constructed using variable time-intervals will show differences in their face readings/time measurement and an illusion of time dilation, but, because of the fact that invariable time-intervals produce the practical and theoretical effect of Absolute Time, there can be no time dilation in reality.]

When invariable time-intervals are used for measuring time, time can be measured from the present/now timepoint, T0 (Timepoint Zero) forwards into the future and backwards into the past with no limit to the face readings/time measurements:

Infinity Past <- ... T-2 <- T-1 <- T0 -> T+1 -> T+2 -> ... -> Future Infinity

Thus, there was no beginning of time, there is the present, the Now, in which there is a configuration of matter/energy which is different from previous configurations at past timepoints and subsequent configurations at future timepoints, and there will be no ending of time. Time travel is not possible because there is only the present, the Now, the current configuration of matter/energy present in time and space, and, therefore, there will never be a way in which a person could return to a previous configuration nor advance to a future configuration.

The universe, consisting of space, time and matter/energy, with space being infinite in volume and in duration, time being infinite in duration, and matter/energy being a closed system and infinite in duration but finite in quantity, has always existed, was never created, will never end, and, therefore, could not have been created in a Big Bang and cannot be destroyed in a Big Crunch.

There never was a first cause, nor will there ever be a final effect.

Causality, things/events as causes causing (creating) other things/events as effects, has a source, matter/energy, thus, there never was a first cause/never will be a final effect, but, instead, there is a source of causality from which sequences of causes and effects emerge.

By the way, gods, if they exist, are comprised of matter/energy, of some kind, perhaps of a kind not currently observed--they certainly cannot be comprised of time, and they certainly cannot be comprised of space, be pure vacuums, therefore the only possibility is being matter/energy of some kind. But until we can capture a god and torture it until it confesses that it is a god and performs stunts that prove it has more knowledge and capabilities than man individually or collectively, then we have no reason to claim we know gods exist, and we actually have no rational reason to believe they exist, and, therefore, we have no reason to include them in social, political or scientific decision-making and problem-solving.

In short, the universe is infinite in spatial size, infinite in temporal duration, and infinite in physical (matter/energy) duration (matter/energy being finite in quantity).

RE: 2) Is [there] a significant amount of research suggesting that there could be 2, 3, or an infinite [amount] of universes ... ?

The universe, defined as consisting of space, time and matter/energy, with space being infinite in volume and in duration, time being infinite in duration, and matter/energy being a closed system and infinite in duration but finite in quantity, has always existed, was never created, will never end, and is the one-and-only universe there could possibly be.

Thus, there cannot be another universe. Where would it be? What would it consist of? (We have all the matter/energy that exists here in our universe, so there could be no matter/energy for another universe.)

Thus, there can be no parallel or multiple universes.

If someone claims space is curved, and therefore closed, every point in space must have a quantity of energy, etc., or space = gravitational field, then their definitions/conceptions do not match those presented herein because they do not conform to the observable facts presented herein.

Space is not a gravitational field because a gravitational field is a form of matter/energy and space is a volume, and that volume would be a void, a pure vacuum except for the presence of matter/energy, but matter/energy is finite in quantity, and you cannot disperse a finite quantity into an infinite volume/void, therefore there are areas of space in which there is no matter/energy present and therefore no gravitational fields.

Space cannot be curved because it is a pure vacuum except for those limited areas in which matter/energy is present, and you cannot curve a pure vacuum. In free space, space in which there is no matter/energy present and therefore no gravitational fields (no force fields), then a spaceship can and will travel in a straight line, not in or on a geodesic about a center of gravity (there is no gravity and therefore no center of gravity in free space).

All of the above is based upon these fundamental observations which serve as premises for Operational Physics:

1. Time is the use of time-intervals to measure the occurrences of events in sequences of events.
2. Invariable time-intervals create Absolute Time and Absolute Space.
3. The matter/energy of the universe is a closed system and therefore a finite quantity.
4. A finite quantity of matter/energy cannot be dispersed into an infinite volume.
5. Space is a pure vacuum except for those limited areas in which matter/energy is present.
6. A force field is a form of matter/energy. Gravitational and electromagnetic fields are force fields and therefore are forms of matter/energy.
7. Infinity is not a number; it is a condition of not being mathematically nor physically limited.

Anyone who wants to refute the conclusions of Operational Physics must refute the premises of Operational Physics.

[Wounded King]

This just seems to be based on a confusion of our visible universe with the actual universe. Obviously a universe constituting everything that exists is going to have nothing outside of it by definition. This doesnt mean however that our visible universe is a closed system and hence all that ever was and ever more shall be.

In the Sci Am article one of the assumptions for a Type 1 model is that space is isotropic. Isotropy coupled with infinite volume would allow for a large number of verses whose light cones have not intersected and which might constitute parallel visible universes. I dont see any reason to believe space is isotropic but the conclusions from it seem reasonable even on a limited scale. Not every possible universe has to be true for there to be more than one visible universe, visible from that particular universe that is.

Im also not sure how this adresses the MWI, or are you suggesting that MWI violates the second law?

[Bob K]

WK: This just seems to be based on a confusion of our visible universe with the actual universe. Obviously a universe constituting everything that exists is going to have nothing outside of it by definition. This doesn't mean however that our visible universe is a closed system and hence all that ever was and ever more shall be.

In the universe, space is open--infinite in volumetric measurement, time is open--infinite in temporal measurement, but matter/energy is a closed system--finite in quantity and limited in dispersion/presence in space.

WK: In the Sci Am article one of the assumptions for a Type 1 model is that space is isotropic.

If isotropic = without direction, then 'direction' is imposed by organisms/machines which are 'aware' of 'direction.'

But if isotropic = homogeneous = everywhere the same, then the universe is not homogeneous/isotropic because of the fact that the matter/energy of the universe is a finite quantity that cannot be dispersed homogeneously into an infinite volume and because of the observed fact that there are clumps of matter/energy in the visible part of the universe in which the concentration of matter/energy is clearly more dense than in other visible parts.

WK: Not every possible universe has to be true for there to be more than one visible universe, visible from that particular universe that is.

We get into word salads when we talk about 'universes' as if there would be more than one universe.

For each and every Now, each and every timepoint, there is a configuration of matter/energy which exists regardless of whether or not we can observe it/see it. That Now configuration is 'true' because it is the ONLY configuration possible at a timepoint. Thus, for every timepoint, there is only the 'true' actual configuration of matter/energy; there are no 'false' configurations.

WK: I'm also not sure how this addresses the MWI, or are you suggesting that MWI violates the second law?

If MWI = Multiple Worlds Interpretation, then there cannot be multiple worlds because there is one and only one universe.

The second law of thermodynamics in which the ability to do work decreases over time in a closed system [and the reciprocal entropy increases] appears to be 'violated' by the increase in the use of energy by life forms and by the concentration of energy by plasma fields--when conditions are favorable, then the concentrated energy in a plasma field can exert a force and therefore 'do' work, which would not be possible if the entropy in the plasma field increased.

[Wounded King]

I may not know much about physics and plasmas Bob but Id like an example of a lifeform which violates the 2nd law of thermodynamics, or indeed any lifeform which is a closed energetic system.

You still havent said why our visible universe must be all the universe that exists.

I see no reason why your TRUE now couldnt encompass more than one visible verse in a larger universe.

I fail to see how the MW interpretation of quantum mechanics is invalidated by there being only one universe. Obviously there is only one universe again by definition, it is the nature of that universe that is in dispute. All I am saying is that our visible universe does not have to be the be all and end all of everything.

[Bob K]

WK: I may not know much about physics and plasmas Bob but I'd like an example of a lifeform which violates the 2nd law of thermodynamics, or indeed any lifeform which is a closed energetic system.

You can read more about plasma physics in The Big Bang Never Happened by Eric Lerner.

Essentially, those spatial areas within the universe in which matter/energy are found contain plasmas, gasses of ions in which electromagnetic currents flow--energy currents flow, and in the natural/normal flow of electromagnetic currents the electromagnetic effect pulls the currents together and increase the energy concentration in a plasma, and thereby decrease the entropy and increase the work potential of the energy within the plasma.

Life forms take energy from other systems and return energy to those other systems and are therefore not isolated energy systems, and by this process they thereby concentrate energy within themselves.

WK: You still haven't said why our visible universe must be all the universe that exists.

I see no reason why your TRUE now couldn't encompass more than one visible verse in a larger universe.

I never said--never intended to say--that the visible universe is all there is; the theory shows that because matter/energy is a finite quantity and the finite quantity of energy cannot be dispersed into an infinite volume there must be areas of space in which no matter/energy is present, and those areas are outside of our view of our visible part of the universe when we define the visible universe to be only those areas we can presently see and we observe the currently visible part of the universe to be rather large and we suspect that we have not yet viewed the entirety of it.

I need your definition of 'verse.' I have not seen that term used in physics, only in poetry/music [among my trades I am a professional musician].

There is only one universe, and if by 'verse' you mean only the part(s) of it that is (are) visible, assuming our vision is not infinite, then, yes, we are only seeing our 'verse' within the universe.

WK: I fail to see how the MW interpretation of quantum mechanics is invalidated by there being only one universe. Obviously there is only one universe again by definition, it is the nature of that universe that is in dispute. All I am saying is that our visible universe does not have to be the be all and end all of everything.

There is only one universe, which is comprised of (A) one spatial reality/space--the infinite volume/void, (B) one temporal reality/time--the infinite measurement of time-intervals (time-periods), and (C) one physical reality/the finite sum total of all matter & energy of infinite duration, all of which encompass all there was, is, and ever will be, with parts of it outside our current vision (assuming our current vision to not be infinite). There is therefore no other possibility for a universe. Someone' s misconception of 'another universe' would have to fit within the one-and-only universe, therefore we would have to continue to use the term 'universe' to mean the one-and-only universe within which all matter/energy must fit. Otherwise, we would have to create a new term, such as 'superuniverse,' to mean 'all there was/is/will be,' but we already use 'universe' to mean 'all there was/is/will be,' so we do not need another term to mean 'all there was/is/will be.' This confusion is what results when we rapidly grow word salads because we have no operational definitions of terms we use, such as 'universe.'

[paul30]

1. Apparently the universe is finite, though expanding.

2. The current issue of Scientific American has a cover story about multiple universes. This is not based on empirical research but on mathematical probability. Go figure.

[eh]

Actually, whether or not the universe is finite or infinite has not been settled. The BBT does not say which is correct. While either is consistent with the evidence, there is no reason space must be infinite. But hey, who wants to read about a boring, finite spacetime with few lifeforms in it? A infinite volume of space with countless populated worlds is more interesting, and will sell more magazines.

Either way, the evidence will still always be consistent with a finite yet large universe. However, discovery of a closed spacetime might put an end to sensationalist articles like the recent one from Sci American, but then we'd have physicists talking about infinite 5D spacetimes.

[Wounded King]

Hey Bob,

I admit that using verse to signify a specific portion of the universe, such as 1 visible universe, was just a bit of poetic license on my part.

With regard to lifeforms, what you say in no way shows anything contadictory to the second law. And from your description of them the plasmas are not closed systems and dont violate the 2nd law either.

There already is such a term in common usage and it is 'multiverse'. All you seem to be doing is reiterating my point that there is a confusion between visible universes and 'The Universe'. All you are really saying is that we need a specific term for distinct visible universes in 'The Universe'. That was why I used 'verse' to signify such a thing, I thought the usage was relatively appparent given the context.

TTFN,

Wounded

[Bob K]

paul30 : Apparently the universe is finite, though expanding.

What 'part' of the universe is finite and expanding?

A. Space--the already infinite volume/void?

B. Time--the already infinite measurement of time-intervals?

C. Matter/Energy--the physical reality, things/events comprised of matter/energy, which is infinite in duration but finite in quantity?

Rhetorical Question: How can that which is finite in quantity expand?
Rhetorical Answer: The spatial distance between 'bits' of matter/energy can expand, but not the quantity, and not space nor time.

[Bob K]

eh:Actually, whether or not the universe is finite or infinite has not been settled. The BBT does not say which is correct. While either is consistent with the evidence, there is no reason space must be infinite.

When space = volume/void, the volumetric aspect of the universe, there can be no limits to its dimensions, meaning any attempt to measure its size will result in infinite measurement, therefore space = infinite in size/volume/etc.

When time = the use of time-intervals to measure the occurrences of events in sequences of events, there can be no limit to the measurement of time-intervals, therefore time, the temporal aspect of the universe, is infinite/cannot be finite and had no beginning and has no ending.

When physics = the matter/energy of the universe, the physical aspect of the universe, which includes force fields [gravity/electromagnetism/etc.], there is no known limit to the duration of matter/energy [matter/energy being indestructible], and, the matter/energy of the universe being a closed system, no energy can be removed (where would it go?) and no energy can be added (where would it come from?), then the sum total of matter/energy in the universe is a constant, a finite number [infinity is not a number but a condition of having no limits], and cannot be expanded in quantity, although the spatial distance between 'bits' of matter/energy can be expanded, which is not, however, to mean that space itself, already infinite in volume, can be expanded/is expanding.

eh:Either way, the evidence will still always be consistent with a finite yet large universe.

What part/aspect of the universe--space/time/physics--is 'finite and yet large'?

The volume of space occupied by physics--by matter/energy? [But not the volume of space itself, when space = the volume/void.]

What evidence supports a 'finite yet large universe'?

[Bob K]

Wounded King:I admit that using verse to signify a specific portion of the universe, such as 1 visible universe, was just a bit of poetic license on my part.

Your poetic license is both accepted, and appreciated.

I recognize that miscommunications can occur when people do not hammer out definitions, particularly operational definitions, of the terms they use. I therefore prefer to clarify communication by either offering paraphrases of what I thought they said/intended so that people can confirm or rectify those paraphrases or by asking for re-statements and paraphrases so I can confirm or rectify my understanding of what they said/intended.

Perhaps this is perceived as stickiness/nit-picking, but miscommunication occurs when people are (A) not specific and (B) do not offer or ask for paraphrases, and, therefore, the reciprocal, miscommunication can be avoided/corrected by (A) being specific and (B) offering/asking for paraphrases.

WK:With regard to lifeforms, what you say in no way shows anything contradictory to the second law.

Life forms are unusual in that (A) they organize energy and use it and thereby decrease their entropy, and perhaps they thereby decrease the overall entropy of the universe, and (B) they give us an arrow of time, because life evolves through time in one direction in a physical process that cannot be reversed, adults regressing to 'earlier stages' including birth and egg stages, to previous adults, etc.

WK:And from your description of them the plasmas are not closed systems and don't violate the 2nd law either.

The matter/energy of the universe in all its forms is a closed system and therefore a finite quantity.

Plasmas, being forms of matter/energy, are part of the closed matter/energy system of the universe.

Plasmas are energetic in the sense that they organize and reorganize matter/energy and thereby reorganize the work-production/anti-entropy aspects of matter/energy and thereby suspend/violate the second law of thermodynamics. Stuff in the universe (matter/energy = 'stuff') keeps bouncing around with no known observable universal entropy, meaning we do not observe 100% homogeneity of matter/energy present in the universe, with every point in space having a finite quantity of matter/energy, but, instead, we observe that some points of space have more stuff than others, and because the stuff is finite in overall/total quantity and cannot be dispersed infinitely into an infinite volume there are points in space which have zero matter/energy, therefore the universe cannot be and never will be 100% homogeneous, and with discrepancies in the quantities of matter/energy present at different points in space and the work-potential/anti-entropy they represent, perhaps that is the explanation of why we do not observe universal entropy.

In the sense of the 'energetics' of plasmas, they are not closed systems, as you have observed, but are open subsystems that can exchange energy with other subsystems, and, perhaps, thereby keep the overall entropy of the entire system of matter/energy from reaching a final limit that would suggest the death of the 'energetics,' the movements, of matter/energy in the universe.

WK:There already is such a term in common usage and it is 'multiverse'. All you seem to be doing is reiterating my point that there is a confusion between visible universes and 'The Universe'. All you are really saying is that we need a specific term for distinct visible universes in 'The Universe'. That was why I used 'verse' to signify such a thing, I thought the usage was relatively apparent given the context.

I fear that there is too much potential confusion when we try to distinguish 'visible universes' from 'The Universe.'

By 'visible universe' you mean a limited area/volume of space which can be observed, but perhaps verbal clarity can be better established and maintained by the usage of a phrase such as 'a visible volume of space' rather than the potentially confusing 'visible universe.'

I prefer 'universe to mean 'universe' = space/time/physics (all three aspects/realities combined comprise and therefore define the universe) and 'visible universe' to not be used for 'visible volume of space' because of the narrowing of 'universe' to mean 'space' as in 'visible volume of space.'

I did in fact recognize your intended general meaning of 'verse' = 'visible universe' = 'visible volume of space,' and yet I wanted to be sure what I thought I understood was what you intended, which is why I offered a paraphrase and asked you for your confirmation or rectification.

[Wounded King]

I don't feel that 'a visible volume of space' is a good phrase for what we are discussing, it could easily refer to my bedroom.

I think we would need to decide on some arbitrary definition such as regions of space whose light cones do not intersect over a certain period of time, such as a 1000 billion years. This would be a reasonable definition for the type 1 and 2 models in the Sci-Am article. It wouldn't help with multidimensional or other more abstruse concepts such as the Many Worlds, a world being not a universe but a particular subset of the universe, interpretation of quantum mechanics however.

I think we should drop the side questions about thermodynamics, neither of your examples appear to violate the 2nd law. There are a number of non-living systems which evolve through time in an asymmetric fashion, such as stars or a breaking vase. Many people consider it is entropy itself which gives us the arrow of time.

Are your only objections to the ideas discussed in this thread based on the terminology?

Your initial assumption is that the universe is infinite, what is this based on?

[NearNihil Experience]

Hawking's "Theory of Everything" puts forth the idea of a finite but boundry-less universe. This allows for expansion and agrees with what we know from previous observation. check out the book for an easy, clear, informative, and enjoyable read.

[Bob K]

Wounded King:I don't feel that 'a visible volume of space' is a good phrase for what we are discussing, it could easily refer to my bedroom.

I think we would need to decide on some arbitrary definition such as regions of space whose light cones do not intersect over a certain period of time, such as a 1000 billion years. This would be a reasonable definition for the type 1 and 2 models in the Sci-Am article. It wouldn't help with multidimensional or other more abstruse concepts such as the Many Worlds, a world being not a universe but a particular subset of the universe, interpretation of quantum mechanics however.

How about 'a finite volume of space' or 'a local area of space' for a phrase referring to a limited subset of space without producing the confusion that all of space is a finite volume?

WK:Are your only objections to the ideas discussed in this thread based on the terminology?

My objections to many conclusions of theoretical and practical physics are based upon the lack of operational definitions of physics terms.

You challenge a theory by challenging its premises and showing how they lead to false conclusions.

You challenge a premise by demanding physical evidence which serves for proof which supports the validity of the premise.

The topic of this thread is the question of whether the universe is open or closed, and what evidence exists to support an answer to the question.

For the universe to be labeled open or closed, there must be \operational definitions of the aspects/realities which comprise the universe and their relevant supporting evidence.

See below.

WK:Your initial assumption is that the universe is infinite, what is this based on?

Whenever I read a statement that is a claim of fact that is a conclusion from a logical argument describing scientific 'facts' as premises and the conclusion as logically following from and therefore relevant to the premises and their supporting evidence I challenge the premises that supposedly lead to the conclusion.

I want to know if the terms used in scientific premises are operationally defined and if physical evidence is available which serves as proof of their validity.

A finity is a specific number, whatever it is, no matter what it is, no matter what mathematical or physical condition it describes; an infinity is not a number but a mathematical or physical condition of having no limits, being unbounded.

When I observe a finite quantity of space, a measurable local area of space no matter how small or large, whether my room, my real estate, etc., I see the finity of its spatial/physical limits and I see the infinity beyond the finity; i.e., I see both the limits of the finity and the nonlimits of the infinity.

When I extrapolate the finity of my observable space/local area of space to the next higher level of finite dimensions, and the next level beyond, and continue this process, through intuitive thought, then it is clear to me that there can be no finity to the spatial dimensions of the volume/void of spatial reality of the universe, to space.

Thus, the spatial reality of the universe is open.

The temporal reality, when measured using invariable time-intervals which eliminate time-dilations, is also an infinity, and, therefore, the temporal reality of the universe is also open.

The duration of the physical reality, the matter/energy, of the universe is infinite in duration in space and in time, but the sum total of the physical reality, the quantity of the matter/energy of the universe, is a finite number, a finity, and, therefore, the duration of the physical realty is infinite and therefore open while the quantity is finite and therefore closed.

Thus, the universe is infinite in three realities, (1) the infinite volume of the spatial reality--space, (2) the infinite duration of the temporal reality--time, and (3) the infinite duration of the physical reality--matter/energy.

The universe is finite and therefore closed in only one aspect--the quantity of the physical reality, of matter/energy, because the matter/energy of the universe is a closed system because matter/energy cannot be taken from it (where would it go?) and cannot be added to it (where would it come from?).

Any claim that because of gravity there is a curvature to space that defines a limit, a finity, to the volume of space and therefore the universe is closed is absolutely silly.

All we have to do to prove how silly such a claim is is to require anyone making such a claim to tell us what lies beyond the claimed volumetric/spatial finity of the universe.

Another illogical claim is that there are infinite pathways over the surface of a closed universe.

I require/demand that each point on the surface of any claimed closed universe to have physical dimensions, either spherical or cubical, and that once traversed a point cannot be traversed again, and thereby eliminate forever the possibility that there could be an infinite number of pathways over the surface of that claimed closed universe and prove, therefore, the fact that the claimed closed universe nevertheless is a finity which has an infinity beyond it, outside of it, which then proves, again, that the claimed closed universe never was a closed universe.

The claim of relativity that gravity imposes a limit to the dimensions of space and therefore a limit to the universe and therefore creates a closed universe ignores the fact that any finity, any finite number, imposed upon the spatial or temporal realities and the durational reality of matter/energy is instantly bogus/false/illogical due to the fact that infinity is not a number but a condition of being mathematically and/or physically without limits, unlimited.

Summary: We need clarity in communciations and one way to be clear is to create operational definitions of terms being used, operational definitions being definitions which require that the observable/measurable people/things/events relevant to a term being defined be specified so the term can be made concrete and therefore valid.

From operational definitions of 'universe,' space,' 'time,' 'physics' (matter/energy), 'finity,' 'finite,' 'infinity,' 'infinite,' and 'open' vs. 'closed,' we can conclude that there are no premises which support the conclusion that the universe is closed/finite and that there are premises which support the conclusion that the universe is open/infinite in its spatial, temporal and physical realities.

[Bob K]

ContraTheos:Hawking's "Theory of Everything" puts forth the idea of a finite but boundry-less universe. This allows for expansion and agrees with what we know from previous observation. check out the book for an easy, clear, informative, and enjoyable read.

I have read Hawking's A Brief History of Time but only browsed through his Theory of Everything and conclude from my own operational definitions, observations and intuitions (gedankenexperiments--thought experiments) that space/time/physics (matter/energy) did not begin/were not created by a Big Bang (what existed before the Bang?) nor will be destroyed by a Big Crunch (what will exist after the Crunch?), that space/time/physics have existed without a beginning, exist now, and will continue to exist without an ending, and that the universe is not expanding except for the spatial dimensions between bits of matter/energy (space itself, being a pure vacuum of unbounded/infinite volume, cannot expand, but the distances between/among the bits of the physical reality can expand).

Moreover, there is a logical contradiction between the concept of a finite universe and the concept of a boundary-less universe.

The only finity of the universe is the quantity of matter/energy; all other realities/aspects of the universe--space/time/physics (duration of matter/energy)--are infinities, therefore the universe is infinite, open, without mathematical or physical limits except for the finite quantity of matter/energy.

[eh]

Originally posted by Bob K
eh:
When space = volume/void, the volumetric aspect of the universe, there can be no limits to its dimensions, meaning any attempt to measure its size will result in infinite measurement, therefore space = infinite in size/volume/etc.

Not quite. If the universe is closed and finite, then someone travelling in a spaceship in one direction will eventually end up back where they started. In that sense, only a finite volume would be measured. This is only possible if the geometry of spacetime is non-Euclidean.

But forget matter and energy for the time being. Let's just try to focus on space. In fact, picture of a universe completely empty of matter, and absolute void. From there, the question is whether or not space itself must be infinite. I say no, since logically either finite or infinite will suffice. Furthermore, there is no logical reason why the geometric structure of space must be the flat Euclidean space we are familiar with. A non-Euclidean universe is just as viable, and is really just a matter of geometry.

What part/aspect of the universe--space/time/physics--is 'finite and yet large'?

I am arguing that space itself, the void, can be finite. That is to say, while it is possible to be infinite, it is not necessarily so. A finite volume of space is just as likely. But I'm not arguing space must be finite either, only that it is logically possible.

However, science could uncover evidence of a closed finite universe. How? If astronomers find multiple images of the same galaxies at different locations in the sky, then a closed non-Euclidean spacetime geometry would probably be the only explanation for it. So far, it hasn't been found though.

What evidence supports a 'finite yet large universe'?


The same evidence that supports a flat, infinite universe. Meaning, cosmological observations. They can't argue for infinite, since the same evidence is equally consistent with a finite universe.

There are also some misconceptions that need to be cleared up. You wrote,

Any claim that because of gravity there is a curvature to space that defines a limit, a finity, to the volume of space and therefore the universe is closed is absolutely silly.

Actually, curvature does not imply a finite volume of space. You can have an infinite volume of 3D space, while it is curved in the 4th dimension. While we can not imagine what a curved 3D volume looks like, we can look to lower dimensions for a mental picture to work with. With a flat 2D sheet of paper, we can imagine it stretching to infinity in the X,Y coordinates. But there still is the 3rd dimension to deal with, and if we crumple regions of the sheet, the regions will be curved instead of flat. However, the sheet as a whole, while curved in 3 dimensions, still remains an infinite 2D entity.

A closed universe is a result of a high average density (curvature) to space. This type of closed universe is as viable as an infinite volume, and no one has ever been able to show a logical inconsistency with the idea.

All we have to do to prove how silly such a claim is is to require anyone making such a claim to tell us what lies beyond the claimed volumetric/spatial finity of the universe.

This one is easy. Since you cannot have a location without space, there can be no beyond a finite spacetime. That just means there is no such thing as an outside to the universe. So the answer to the question of what would lie beyond a finite universe - is that there is no beyond.

Another illogical claim is that there are infinite pathways over the surface of a closed universe.

Actually, this is only a matter of basic geometry. In plane geometry, a surface (curved or not!) contains an infinite number of lines. Thus, you get an infinite number of pathways on any surface, even in Euclidean geometry. But using 2D surfaces as analogies helps with the mental picture, since we can't actually percieve a 4D volume.

[eh]

Originally posted by Bob K
Moreover, there is a logical contradiction between the concept of a finite universe and the concept of a boundary-less universe.


No there isn't. Does the surface of a balloon have a boundary in 2 dimensions? No, it only has a boundary in 3 dimensions. That seems to be the analogy here. A closed universe is like the surface of a 2 dimensional balloon, but in 3 dimensions. Thus if you travel along any axis (X,Y,Z) you will never find a boundary. Much like the 2D balloon, you need to go up a dimension to find a boundary. In cosmology, that boundary is the big bang, with the 4th dimension being time.

The no boundary proposal by Hawking is a little different, and a little more complicated.

[JGL53]

I concede that my own coal-burning brain might not be up to the standards of the nuclear-powered brains of others on this thread:D - but in my own personal 'thought experiment' I envision our observable universe as finite (about 24 billion light years in diameter) and unbounded (you can't get out, you're stuck here), and merely a teeny tiny fairly unimportant part of an infinite, eternal or timeless, and unbounded multiverse.

Hard if not impossible to prove, I know, but I'm a-thinking such a view answers both the design and the 'fine-tuned' questions with less of a violation of Occam's Razor than an imagined god does.

I'm very opened to consideration of any ideas on this subject (I gotta be - my expertise is in pharmacy, for christ's sake!), but until I'm exposed to a theory that resonates with my relatively low IQ more so than my aforementioned 'thought experiment', I'm going to stick with it, out of sheer necessity (i.e, everybody has to believe in something, and having another beer doesn't do it for me). :D

[paul30]

Newton was disturbed by the thought that the universe was infinite. If it were, there would be an infinite number of stars, and (a) the night sky would be as bright as the day sky, and (b) the infinity of mass would cause all the stars to come together.

Nevertheless, he believed the universe is infinite.

Einstein did not.

I think it would be well to define "infinite." An infinite set is one that is not reduced if any number of its constituents are removed.

I think that cannot be said of the universe.

(Although I am not absolutely sure.)



;)


I think it would also be well to define "space." Space is not just emptiness in which things exist or move. Space is a relationship.

[Bob K]

eh

Bob K:When space = volume/void, the volumetric aspect of the universe, there can be no limits to its dimensions, meaning any attempt to measure its size will result in infinite measurement, therefore space = infinite in size/volume/etc.

eh:Not quite. If the universe is closed and finite, then someone travelling in a spaceship in one direction will eventually end up back where they started. In that sense, only a finite volume would be measured. This is only possible if the geometry of spacetime is non-Euclidean.

What is the universe? It is the combination of (A) the spatial reality--space, (B) the temporal reality--time, and (C) the physical reality--matter/energy.

Is the universe closed and finite?

It is not.

The notion of a closed universe with spaceships unable to travel in true straight lines because of a curvature of space due to the gravitational force field created by the mass of the matter/energy of the universe is a GR conclusion that is illogical.

Infinity is not a specific number; instead, it is a condition of having no known mathematical or physical limits, of being unlimited, unbounded.

That which is open is infinite--it has no known mathematical or physical limits.

That which is closed is finite/not infinite--it has known mathematical/physical limitations.

Space is an infinite volume, because it has no known mathematical/physical limits to its volume.

Space is therefore open--there will always be another area of space to which you can go.

Time is an infinite process of the measurement by time-intervals of the occurrences of events in sequences of events.

Because the measurement of time is infinite, time is therefore open.

Physics is the matter/energy of the universe.

Matter/energy is indestructible and therefore is infinite in duration and therefore is open re: its duration.

In a closed energy system, matter/energy cannot be taken away (where would it go?) and matter/energy cannot be added (where would it come from?), and in a closed energy system the quantity of matter/energy is a finite quantity.

The quantity of matter/energy in the universe, present in space, is a finite quantity, because the matter/energy of the universe is a closed system, because matter/energy cannot be taken away from it (where would the removed matter/energy go?) and cannot be added to it (from where would the additional matter/energy come?).

The matter/energy of the universe is a finite quantity and is therefore a closed system.

Space is a volume, not matter/energy; matter/energy is independent of space.

Time is not space nor matter/energy.

A gravitational field is a force field and consists of, is a form of, matter/energy because only matter/energy can produce force fields.

A gravitational field, being a form of matter/energy, is therefore not space.

Space, being open and being not a gravitational field, cannot change the trajectories of things moving within it.

The universe, comprised of three realities which are open--space, time and physics (the duration of matter/energy) and having only a single closed system--the quantity of matter/energy within the physical reality, is open--there will always be another place within space for things to go, there will always be another timepoint in which things can exist and events can occur, and there will always be matter/energy of which things/events can be comprised.

[Bob K]

eh:But forget matter and energy for the time being. Let's just try to focus on space. In fact, picture of a universe completely empty of matter, [an] absolute void. From there, the question is whether or not space itself must be infinite. I say no, since logically either finite or infinite will suffice. Furthermore, there is no logical reason why the geometric structure of space must be the flat Euclidean space we are familiar with. A non-Euclidean universe is just as viable, and is really just a matter of geometry.

What lies outside a finite space?

Can you logically conceive of a volume of space of dimension X, being limited/finite without also conceiving of a volume of space of dimension X + 1 which contains the space which is X and the additional space which is + 1 that lies outside/beyond the limited/finite X-dimensioned volume of space?

From our personal experience, we see volumes of space limited by their physical dimensions, and we see larger volumes of space which include the smaller volumes. If we extrapolate our experience of larger volumes encompassing smaller volumes, as soon as anyone claims space is a volume of specific dimensions we can add to those dimensions and create a larger volume, and we can do so without limits, without either mathematical or physical limits, the definition of infinity, therefore, from our experiences of volumes, we can easily conceive of the logical extension of a volume to the condition of having no mathematical or physical limits, which is infinity, and, therefore, we can imagine that the spatial reality, space, is an infinite volume, an unbounded volume, a volume with no mathematical/physical limits.

Space, therefore, is a pure vacuum and is infinite in dimensions, unlimited, unbounded, etc.

[Bob K]

Bob K:What part/aspect of the universe--space/time/physics--is 'finite and yet large'?

eh:I am arguing that space itself, the void, can be finite. That is to say, while it is possible to be infinite, it is not necessarily so. A finite volume of space is just as likely. But I'm not arguing space must be finite either, only that it is logically possible.

No, any conception of a finite volume of space immediately is clouded by the conception of a volume beyond/outside. There will never be a human being who, or a machine which, will create a logical conception of a finite volume of space which eliminate any possibility of its being surrounded by still another volume of space with larger dimensions which will ultimately be surrounded by a volume of space which has no dimensions because it is infinite, because it has the condition of having no mathematical or physical limits.

[Bob K]

eh:However, science could uncover evidence of a closed finite universe. How? If astronomers find multiple images of the same galaxies at different locations in the sky, then a closed non-Euclidean spacetime geometry would probably be the only explanation for it. So far, it hasn't been found though.

A closed/finite universe is a logical impossibility.

Space is infinite in mathematical and physical dimensions and therefore open.

Time is infinite mathematical measurements of time-intervals/periods and therefore open.

Physics--matter/energy--is infinite in having no mathematical/physical limits to its duration and is therefore open.

Physics-matter/energy--does have mathematical/physical limitations to its quantity, but that quantity can exist without durational limits within the opennesses of space and time, therefore physics is also open.

Multiple images of the same ___ (?) viewed at different locations in the sky are multiple imagies of the same ___ (?) viewed at different locations in the sky. The ___ (?) remains the ___ (?).

[Bob K]

Bob K:What evidence supports a 'finite yet large universe'?

eh:The same evidence that supports a flat, infinite universe. Meaning, cosmological observations. They can't argue for infinite, since the same evidence is equally consistent with a finite universe.

What is your definition of 'universe'? Or, what is the definition of 'universe' of the individuals who conducted the 'cosmological observations' you cite?

What are the 'cosmological observations' you cite which support both the finite and the infinite 'universe'?

There is no logical interpretation of any 'evidence' resulting from cosmological observations that supports a conception of a finite universe because the universe IS infinite in its spatial/temporal/physical realities.

Infinity is not a finity. Infinity is not a number; it is a condition of having no mathematical or physical limits. A finite universe would be a finity, therefore there could be no infinity associated with its dimensions.

[Bob K]

Bob K:Any claim that because of gravity there is a curvature to space that defines a limit, a finity, to the volume of space and therefore the universe is closed is absolutely silly.

eh:Actually, curvature does not imply a finite volume of space. You can have an infinite volume of 3D space, while it is curved in the 4th dimension. While we can not imagine what a curved 3D volume looks like, we can look to lower dimensions for a mental picture to work with. With a flat 2D sheet of paper, we can imagine it stretching to infinity in the X,Y coordinates. But there still is the 3rd dimension to deal with, and if we crumple regions of the sheet, the regions will be curved instead of flat. However, the sheet as a whole, while curved in 3 dimensions, still remains an infinite 2D entity.

Problem: Space/volume requires a 3D model and therefore three axes of X/Y/Z, or East<->West axis = X axis, North<->South axis = Y axis, and Up<->Down axis = Z axis.

Whenever we are dealing with space, the infinity of all three axes leads us to an understanding that the volume of space is infinite, without physical or mathematical limits, provided that we are dealing with axes that are in fact striaght lines, not curvable, and therefore not curved.

The 3D model I use for intuiting the infinity of the volume of space is the grid/latticework of lines constructed of rigid rods of fixed length and absolutely straight/absolutely uncurved and placed parallel to some lines and at ninety degrees to other lines. When traveling upon one line, an individual would never come to its end, for there would always be one more rigid rod to traverse. This neverending measurement of straight rigid rods proves the infinity of space, the unbounded volume, the limitless void.

[Bob K]

eh:A closed universe is a result of a high average density (curvature) to space. This type of closed universe is as viable as an infinite volume, and no one has ever been able to show a logical inconsistency with the idea.

From our previous exchanges, you expressed the opinion that space = gravitational fields.

Space n= gravitational fields. [n= means is not equal to/]

Space is a pure vacuum for those areas in which matter/energy is not present, because matter/energy, being a finite closed system and therefore a finite/limited quantity, which is a constant number, cannot be dispersed infinitely into an infinite volume, and in those areas into which the finite quantity of matter/energy cannot be/is not dispersed there is no matter/energy present and therefore there is no gravitational field present.

Therefore, space cannot possibily be a gravitational field.

Space not being a gravitational field, it is not possible for space to either be a curved volume or to impose a curvature to itself which would impose a curvature to the trajectories of physical things/objects within it.

[Bob K]

Bob K:All we have to do to prove how silly such a claim [of the universe being closed and finite] is to require anyone making such a claim to tell us what lies beyond the claimed volumetric/spatial finity of the universe.

eh:This one is easy. Since you cannot have a location without space, there can be no beyond a finite spacetime. That just means there is no such thing as an outside to the universe. So the answer to the question of what would lie beyond a finite universe - is that there is no beyond.

Your answer is a logical absurdity.

Imagine whatever has to be the dimension(s) of the volume of a finite spacetime, then add + 1 to the dimension(s), and you have a conception of what lies beyond the finite spacetime.

Remember, infinity is not a number; it is a condition of having no mathematical/physical limits.

Remember also that the concept of the invariable time-interval (time-period) destroys time-dilation and spacetime because it creates the independence of time from space and therefore re-establishes Absolute Time and therefore Absolute Space, hence there is no possibility of a spacetime when invariable time-intervals/periods are used.

If you want to challenge these conclusions, then prove that invariable time-intervals/periods cannot and do no exist, either (1) as realities when (A) clocks are constructed to be motion-sensing and self-adjusting or (B) clocks are synchronized by radio signals from a master clock or (2) as imaginings when (C) our intuitive thinking constructs clocks which are not affected by/impervious to the effects of changes of velocity/gravity.

Once you accept the reality of invariable time-intervals/periods which can be used for the measurement of the occurrences of events in sequences of events, time being the use of time-intervals/periods to measure the occurrences of events in sequences of events, then you must accept the destruction of time-dilation and the destruction of spacetime.

Your conception of spacetime is a finity, a finite quantity of matter/energy present in a finite volume of space. This finite quantity of matter/energy creates a force field, a gravitational force field, which may curve the trajectories of things/objects comprised of matter/energy but cannot curve space itself, which is a pure vacuum, because matter/energy cannot curve a pure vacuum--matter/energy can only be present within space and impose a gravitational field, a form of matter/energy, which causes the curvature of the trajectories of objects within the gravitational field.

[Bob K]

Bob K:Another illogical claim is that there are infinite pathways over the surface of a closed universe.

eh:Actually, this is only a matter of basic geometry. In plane geometry, a surface (curved or not!) contains an infinite number of lines. Thus, you get an infinite number of pathways on any surface, even in Euclidean geometry. But using 2D surfaces as analogies helps with the mental picture, since we can't actually percieve a 4D volume.

I require a point on a curved surface to have physical dimensions and therefore to be finite.

And I require that once a point on a curved surface is traversed it cannot be traversed again.

With these two requirements, for a point on a curved surface to have physical dimensions and once traversed a point on a curved surface cannot be traversed again, then there cannot be an infinite number of pathways on a curved surface.

Thus, within a finite curved volume of space, there is a finite number of points and therefore a finite number of lines/pathways.

Thus, the volume of a curved volume of space is a finite number, and, therefore, that volume of space is not an infinity, because an infinity is not a finite number but instead is a condition of having no mathematical/physical limits.

For an uncurved volume of space, as described the the 3D grid/latticework model, with no mathematical/physical limits to the X/Y/Z axes, the volume of space is uncurved and infinite, having no curvature and no mathematical/physical limits.

[Bob K]

Bob K:
Moreover, there is a logical contradiction between the concept of a finite universe and the concept of a boundary-less universe.

eh:No there isn't. Does the surface of a balloon have a boundary in 2 dimensions? No, it only has a boundary in 3 dimensions. That seems to be the analogy here. A closed universe is like the surface of a 2 dimensional balloon, but in 3 dimensions. Thus if you travel along any axis (X,Y,Z) you will never find a boundary. Much like the 2D balloon, you need to go up a dimension to find a boundary. In cosmology, that boundary is the big bang, with the 4th dimension being time.

There is no such thing as a 2D balloon.

There are only 3D balloons.

The surface of a balloon which is not expanding has definite boundaries:

1. It has the physical limit imposed by its diameter/radius.
2. When each point upon its surface has specific physical dimensions, then the total number of points on the surface is a finite number, is bounded, and when once a point is traversed it cannot be traversed again, the total number of pathways upon the surface of a balloon is a finite number.
3. When each point within the volume encompassed by the surface has specific physical dimensions, then the total number of points within the volume is a finite number; and when a point within the volume is traversed it cannot be traversed again, the total number of pathways within the volume is a finite number.
4. Outside the physical limits imposed by the diameter/radius of a balloon are additional points which have specific physical dimensions but the number of such points is without mathematical limit, therefore the number of points outside the surface of an expanding balloon.

A non-expanding balloon is not subject to change and therefore at all timepoints the diameter/radius and volume and number of physical points on its surface and within its volume are the same/never change.

The surface of a ballon which is expanding also has definite boundaries because at any timepoint there is a finite limit to its diameter/radius and a finite limit to the number of points with specific physical dimensions on its surface and within its volume and a finite limit to the number of pathways on its surface and within its volume. and there is an infinite number of points with physical dimensions outside the surface and volume of the expanding balloon.

The keys herein to understanding the finity of a closed space/volume and its surface are (1) the concept of time as the use of invariable time-intervals/periods for the measurement of the occurrences of events in sequences of events and (2) the concept of an imaginary point which has a specific physical dimensions which immediately imposes a mathematical and physical value to the number of points possible upon its surface and within its space/volume.

(1) Time when measured by the use of invariable time-intervals establishes timepoints at regular time-intervals which can be used to determine the rate at which a balloon is expanding [zero rate of expansion = non-expanding balloon]. [Time when measured by variable time-intervals cannot give us the stability of timepoints, the stability of the establishment of timepoints at regular intervals, and, hence, we cannot get an actual rate of change which would give us the actual rate of expansion.]

(2) The concept of the imaginary point of specific physical dimensions destroys forever the concept of an actual point of infinite smallness or largeness; and it destroys any conclusion that there are an infinite number of actual physical points on the surface of a closed volume.

Because at any timepoint the diameter/radius is frozen at that timepoint and therefore at that timepoint is not expanding, the surface/volume of the balloon is finite/of limited physical dimensions/not infinite.

[Bob K]

eh:The no boundary proposal by Hawking is a little different, and a little more complicated.

Hawking is wrong if he has no conception of (1) time as measured by invariable time-intervals/periods and (2) imaginary points of specific physical dimensions.

Questions for you:

1. Was space created at the beginning of the Big Bang, or did space exist prior to the Bang?

2. Was time created at the beginning of the Big Bang, or did time exist prior to the Bang?

3. Was matter/energy created at the beginning of the Big Bang, or did matter/energy exist prior to the Bang?

If you claim matter/energy was created at the beginning of the Big Bang, where did it come from? Something from nothing?

[paul30]

Where did matter/time/space come from?

This may be a nonsense question.

Time is not a reality but a concept, based on our perception of change and regularity.

If there were no change there could be matter, but we would not think there was time. (Yes, I know, there would not be US, either.)

[Bob K]

JGL53

JGL:I concede that my own coal-burning brain might not be up to the standards of the nuclear-powered brains of others on this thread - but in my own personal 'thought experiment' I envision our observable universe as finite (about 24 billion light years in diameter) and unbounded (you can't get out, you're stuck here), and merely a teeny tiny fairly unimportant part of an infinite, eternal or timeless, and unbounded multiverse.

Hard if not impossible to prove, I know, but I'm a-thinking such a view answers both the design and the 'fine-tuned' questions with less of a violation of Occam's Razor than an imagined god does.

I'm very opened to consideration of any ideas on this subject (I gotta be - my expertise is in pharmacy, for christ's sake!), but until I'm exposed to a theory that resonates with my relatively low IQ more so than my aforementioned 'thought experiment', I'm going to stick with it, out of sheer necessity (i.e, everybody has to believe in something, and having another beer doesn't do it for me).

The essence of intelligence is adaptibility, using what you know. The chances are excellent that you are much smarter than you realize.

Infinity is not a number; instead, it is a condition of having no mathematical or physical limitations.

We know of, nor can we logically conceive, of any mathematical/physical limitations to the dimensions of space, therefore space is infinite and open.

When time = the use of time-intervals to measure the occurrences of events in sequences of events, then we know of no mathematical/physical limitations to the measurement of time-intervals, therefore time is infinite and open.

When physics = matter/energy, we know from thermodynamics that matter/energy has no mathematical/physical limitations to its duration, therefore matter/energy, physics, is infinite in duration and therefore open.

We know from thermodynamics that the quantity of matter/energy in a closed system is finite, a finite quantity, and, therefore not open.

The finite quantity of matter/energy can exist infinitely within the infinity of space and the infinity of time, therefore physics, matter/energy, is infinite and therefore open.

When universe = space, time and physics, it is infinite in volume--space, infinite in duration in time, and infinite in duration of matter/energy.

If you define universe to be anything other than the combination of space/time/physics, then anything goes, and all is lost.

[Bob K]

http://www.iidb.org/vbb/showthread.php?s=&threadid=54104&perpage=25&pagenumber=2#newpost

paul30

Paul30:Newton was disturbed by the thought that the universe was infinite. If it were, there would be an infinite number of stars, and (a) the night sky would be as bright as the day sky, and (b) the infinity of mass would cause all the stars to come together.

Nevertheless, he believed the universe is infinite.

Einstein did not.

Niether Newton nor Einstein proposed nor proved that the quantity of matter/energy in the universe is a closed system, but it is.

The Matter/Energy of the Universe = Closed Energy System:

Premise: If an energy system is a closed energy system, then matter/energy cannot be taken away from it (where would it go?) nor added to it (where would it come from?); if an energy system is an open energy system, then matter/energy can be taken away from it (there would be a place for it to go) and matter/energy can be added to it (there would be a place from where it would come).
Premise: No matter/energy can be taken away from (where would it go to?) or added to the matter/energy of the universe (from where would it come?).
Conclusion: The matter/energy of the universe is a closed energy system.

The Quantity of Matter/Energy in the Universe = Finite:

Premise: If an energy system is a closed energy system, then the sum total of matter/energy is a constant/the quantity of matter/energy is a finite number/is not infinite.
Premise: The matter/energy system of the universe is a closed energy system.
Conclusion: The sum total of the matter/energy of the universe is a constant/the quantity of matter/energy in the universe is a finite number/is not infinite.

Paul30:I think it would be well to define "infinite." An infinite set is one that is not reduced if any number of its constituents are removed.

I think that cannot be said of the universe.

(Although I am not absolutely sure.)

Infinity

Infinity is not a specific number, instead, it is a condition of having no mathematical or physical limits.

Finity

Finity is a condition of having mathematical and physical limits which can be expressed by specific numbers.

Paul30:I think it would also be well to define "space." Space is not just emptiness in which things exist or move. Space is a relationship.

Space

Space = Infinite Volume:

Premise: If a volume has no mathematical or physcal limits, then it is infinite.
Premise: The volume which is space has no known mathematical/physical limits.
Conclusion: Space is infinite/Space is an infinite volume.

The Matter/Energy of the Universe = Closed Energy System:

Premise: If an energy system is a closed energy system, then matter/energy cannot be taken away from it (where would it go?) nor added to it (where would it come from?); if an energy system is an open energy system, then matter/energy can be taken away from it (there would be a place for it to go) and matter/energy can be added to it (there would be a place from where it would come).
Premise: No matter/energy can be taken away from (where would it go to?) or added to the matter/energy of the universe (from where would it come?).
Conclusion: The matter/energy of the universe is a closed energy system.

The Quantity of Matter/Energy in the Universe = Finite:

Premise: If an energy system is a closed energy system, then the sum total of matter/energy is a constant/the quantity of matter/energy is a finite number/is not infinite.
Premise: The matter/energy system of the universe is a closed energy system.
Conclusion: The sum total of the matter/energy of the universe is a constant/the quantity of matter/energy in the universe is a finite number/is not infinite.

The Volume of Space = Infinite; The Quantity of Matter/Energy in the Universe = Finite:

Premise: If a volume or quantity has no mathematical or physical limitations, then the volume/quantity is infinite; but if a volume/quantity has mathematical/physical limits, then the volume/quantity is finite.
Premise: The volume of the universe, space, has no mathematical/physical limits; the quantity of matter/energy in the universe has mathematical/physical limits.
Conclusion: The volume of universe, space, is infinite; but the quantity of matter/energy in the universe is finite.

The Finite Quantity of Matter/Energy in the Universe Cannot Be Dispersed Infinitely into the Infinite Volume of Space:

Premise: A finite quantity of matter/energy cannot be dispersed infinitely into an infinite volume. [A mathematically/physically limited quantity cannot be dispersed without limits/infinitely into a mathematically/physically infinite/unlimited volume.]
Premise: The sum total of matter/energy in the universe is a constant, a finite quantity.
Conclusion: The finite quantity of matter/energy in the universe cannot be dispersed infinitely into the infinite volume of space.

Space = Areas in Which No Matter/Energy Is Present & Areas in Which Matter/Energy Is Present.

Premise: If a finite quantity of matter/energy cannot be dispersed infinitely into an infinite volume, then there are areas of the infinite volume which are pure vacuums in which no matter/energy is present and there are areas of the infinite volume in which matter/energy is present.
Premise: The quantity of matter/energy of the universe is a finite quantity and the volume of the universe is an infinite volume.
Conclusion: In the infinite volume which is space, there are areas in which no matter/energy is present and there are areas in which matter/energy is present.

Space = Pure Vacuum [The Nature of Space = Pure Vacuum]:

Premise: In the infinite volume which is space, there are areas in which no matter/energy is present.
Premise: A pure vacuum is a volume which contains no matter/energy.
Conclusion: Space is an infinite pure vacuum in those areas in which no matter/energy is present; Space is an infinite pure vacuum except for those areas of it which contain matter/energy.
Conclusion: Space is not matter/energy.

[Bob K]

Paul30:Where did matter/time/space come from?

This may be a nonsense question.

Time is not a reality but a concept, based on our perception of change and regularity.

If there were no change there could be matter, but we would not think there was time. (Yes, I know, there would not be US, either.)

So far you have created a definition of time:

Time = A concept based upon our perception of change and regularity.

From OpPhys (Operational Physics):

Time = The use of time-intervals to measure the occurrences of events in sequences of events.

Thing = Object, a unity which retains its identity over a longer time period than related events.
Examples: Jane, a ball, Dick.

Event = Relationship between/among things.
Example: Jane throws the ball to Dick.

Causality = People/things who/which are causes cause/create people/things/events who/which are effects.

Regularity in OpPhys = Invariable time-intervals/periods = (Initially) Regularly recurring periodic motions which, once chosen, are standards for invariable time-intervals, are independent of the original periodic motions used to define/model them, and are not affected by changes of velocity/gravity [as used in clocks constructed to be (A) motion-sensing and self-adjusting or (B) synchronized by radio signals from a master clock].

Change = Events in which people/things who/which are causes cause/create people/things/events who/which are effects (and potential future causes of future events).

Time is therefore the measurement of change in events by the use of invariable time-intervals.

How about developing your definition of time and see how yours compares to the definition of time in OpPhys?

[eh]

Bob K,

Wow, long post. From past experience, it seems these discussions become very long and time consuming. With the subject of spacetime it's very easy to get sidetracked into quantum mechanics, singularities, vacuum energy and other off topic areas. Since that is only going to take focus away from the original topic, I'm going to try and stick with the subject of an infinite or finite universe.

That's not to say the other subjects aren't worth discussing. I know you think space, matter and time each have seperate existence of their own, and I would obviously argue that they do not. But let's save that topic for another thread, if only because it will save us from having to deal with a thousand page thread. While the issue of general relativity comes up often in topics abut space and time, I don't feel it's really important here. That's because even if GR were to be disproven tommorrow, the argument of finite vs. infinite space would remain. I will argue that space can be either finite or infinite, and without relying on any arguments from modern physics. So this is really only a matter of geometry, and that's the same Euclidean geometry of the ancient Greeks thousands of years ago. So....

The notion of a closed universe with spaceships unable to travel in true straight lines because of a curvature of space due to the gravitational force field created by the mass of the matter/energy of the universe is a GR conclusion that is illogical.

Infinity is not a specific number; instead, it is a condition of having no known mathematical or physical limits, of being unlimited, unbounded.

Now I want to stay with Euclidean geometry, but what is logically inconsistent about curved spaces? In terms of logic, they are as consistent as flat spaces.

And I just want to clarify something here. A closed universe is not taking a pre existing infinite space and making it finite. That would be illogical. The idea is that the space would already be finite to start with. But even further, this is not the reason space can be finite. The idea of a spacetime with hyperspherical geometry is based on the cosmological principle. That is, the geometry of space is on average, the same everywhere. But if this principle is not true (and only appears to in our region of a much bigger universe) then it is possible that the universe has an edge and center. I only brought up the hypersphere to show it as the only example of being able to prove whether space is finite or infinite.

Space is an infinite volume, because it has no known mathematical/physical limits to its volume.
Space is therefore open--there will always be another area of space to which you can go.


This is not quite true. There is nothing that stop us from defining an infinite volume of space. But then, there is also nothing that prevents us from defining a volume of finite size. Mathematics in this case can explain all logically possible worlds, but it cannot tell us which world we actually live in. That is up to science and observations.

A gravitational field is a force field and consists of, is a form of, matter/energy because only matter/energy can produce force fields.

Just another clarification. The gravitational field is not made of energy. In fact, it's not made of anything, as it is just space. The idea is that what Newton saw as a mysterious force field is nothing but space - but the so called force of gravity is due to the curvature of this space. The only reason I've said vacuums can't exist in past threads, is because of quantum mechanics.

A gravitational field, being a form of matter/energy, is therefore not space.

How do you explain the fact the gravity is everywhere? Are you saying Newton's inverse square law is incorrect? It would seem that if space really does have independent existence of gravity, then the gravitational field would be like icing on a cake - completely filling up space. It would just be rather redundant. But then, this is probably good for another thread.

[eh]

What lies outside a finite space?

Can you logically conceive of a volume of space of dimension X, being limited/finite without also conceiving of a volume of space of dimension X + 1 which contains the space which is X and the additional space which is + 1 that lies outside/beyond the limited/finite X-dimensioned volume of space?

Yes I can, quite easily. In geometry, a volume of space is defined entirely by it's own points. That means you do not need any external space to define a volume. Likewise, the size of an object is defined without any notion to what is outside. So logically we certainly can talk about a finite space.

What would lie outside? As I said, there is no outside, as that would be a contradiction. If you take a volume of finite size and add to it, you are increasing the size of the manifold itself.

From our personal experience, we see volumes of space limited by their physical dimensions, and we see larger volumes of space which include the smaller volumes. If we extrapolate our experience of larger volumes encompassing smaller volumes, as soon as anyone claims space is a volume of specific dimensions we can add to those dimensions and create a larger volume, and we can do so without limits, without either mathematical or physical limits, the definition of infinity, therefore, from our experiences of volumes, we can easily conceive of the logical extension of a volume to the condition of having no mathematical or physical limits, which is infinity, and, therefore, we can imagine that the spatial reality, space, is an infinite volume, an unbounded volume, a volume with no mathematical/physical limits.

Space, therefore, is a pure vacuum and is infinite in dimensions, unlimited, unbounded, etc.

Be careful not to commit a logical fallacy here. Just because we can't imagine a volume of space that is not embedded in some larger space, does not logically follow that space is therefore actually infinite. What we imagine does not equal logic.

And just to clarify again, I'm not arguing that space cannot be infinite. I'm only arguing that logically, finite is also a possibility.

No, any conception of a finite volume of space immediately is clouded by the conception of a volume beyond/outside. There will never be a human being who, or a machine which, will create a logical conception of a finite volume of space which eliminate any possibility of its being surrounded by still another volume of space with larger dimensions which will ultimately be surrounded by a volume of space which has no dimensions because it is infinite, because it has the condition of having no mathematical or physical limits.

You are mistaking logic and imagination. I can logically define a volume that is all the space that exists, without being able to perceive it. And in actual, we only ever percieve a finite volume at a time, so it's not so hard to imagine a finite space at all. You just have to imagine it from the inside.

Also, some clarification is needed on the definition of a dimension. In geometry, when an object has 3 dimensions, we are not talking about the size. It is just the X,Y,Z coordinates that are possible in a volume of space. No matter what the size of space, there will always be the X,Y,Z axis to move about. An infinite universe would have 3D dimensions, but the size would be infinite. In other words, there would be an infinite number of possible coordinates.


A closed/finite universe is a logical impossibility.

Why? Where is the logical contradiction? Mathematicians would like to know.

Multiple images of the same ___ (?) viewed at different locations in the sky are multiple imagies of the same ___ (?) viewed at different locations in the sky. The ___ (?) remains the ___ (?).


I'll see if I can get an article that explains it in detail. The basic idea is that in a hyperbolic (or flat multiply connected) universe, light from the same galaxy will have made several trips around space. Since the galaxy is itself moving throughout the universe, those images from the light will then be in different locations in the sky. If this is detected, I don't know of anything else that could explain it. In fact, that might be the only way that proof of a finite universe can ever be found.

What is your definition of 'universe'? Or, what is the definition of 'universe' of the individuals who conducted the 'cosmological observations' you cite?

What are the 'cosmological observations' you cite which support both the finite and the infinite 'universe'?

It's all based on general relativity and the cosmological principle. It has to do with the average geometry of spacetime, which will never be able to disprove one (finite or infinite) while proving the other. But since GR isn't really a big deal with the basic question, don't worry about it for now.

There is no logical interpretation of any 'evidence' resulting from cosmological observations that supports a conception of a finite universe because the universe IS infinite in its spatial/temporal/physical realities.

How do you know? What logic says that the volume of space must be infinite? The only way you can show that, is if you can show a logical contradiction in the concept of finite space. It would be quite an accomplishment, since no one has been able to do so in over 5000 years. But that is all it would take. If finite space is logically inconsistent, then infinite space is the only alternative and would be true by default. But you will have to show this contradiction first.

Problem: Space/volume requires a 3D model and therefore three axes of X/Y/Z, or East<->West axis = X axis, North<->South axis = Y axis, and Up<->Down axis = Z axis.

Whenever we are dealing with space, the infinity of all three axes leads us to an understanding that the volume of space is infinite, without physical or mathematical limits, provided that we are dealing with axes that are in fact striaght lines, not curvable, and therefore not curved.

The 2D models are just analogies, since we cannot imagine curved 3D space. In Euclidean geometry, lines are straight and not curved, correct. But Euclidean geometry is not the only logically consistent geometry there is.

The 3D model I use for intuiting the infinity of the volume of space is the grid/latticework of lines constructed of rigid rods of fixed length and absolutely straight/absolutely uncurved and placed parallel to some lines and at ninety degrees to other lines. When traveling upon one line, an individual would never come to its end, for there would always be one more rigid rod to traverse. This neverending measurement of straight rigid rods proves the infinity of space, the unbounded volume, the limitless void.

Whatever works. But you could just as easily imagine a finite 3D Euclidean grid. Try to visualize a finite 3D grid, where an individual comes to the edge. Now what happens if he goes any further? Well, if you visualize him crossing it, you'll see that there is now an increased volume - the distance between the individual and the former edge. Thus, the volume of the grid itself has increased - and the space has expanded.

But if we were ever to do this kind of experiment in the real world (ignoring curved spacetime) we could not tell the difference between an infinite space, and a finite expanding space. That is because real space does not have grid lines painted on it to guide us.

[eh]

Your answer is a logical absurdity.

Imagine whatever has to be the dimension(s) of the volume of a finite spacetime, then add + 1 to the dimension(s), and you have a conception of what lies beyond the finite spacetime.

Where is the logical contradiction in this? If you add + 1 to the the dimensions, you are increasing the size of the manifold. That hardly can be used as proof for infinite space. It would be like someone arguing the amount of matter in the universe is infinite, because if you take a finite quantity and add +1 to it, you can see there is no limit to the quantity.

Your conception of spacetime is a finity, a finite quantity of matter/energy present in a finite volume of space. This finite quantity of matter/energy creates a force field, a gravitational force field, which may curve the trajectories of things/objects comprised of matter/energy but cannot curve space itself, which is a pure vacuum, because matter/energy cannot curve a pure vacuum--matter/energy can only be present within space and impose a gravitational field, a form of matter/energy, which causes the curvature of the trajectories of objects within the gravitational field.

No, I do not believe in any mysterious force fields. Nor do I believe that energy is a substance at all. I would actually argue that the geometry of space is non-Euclidean and constantly evolving. These evolving geometric relations give rise to the what we percieve as matter, and is really all there is to space and time. Thus what we see as 3 seperate realities, is really part of the same fundemental thing.

I require a point on a curved surface to have physical dimensions and therefore to be finite.

And I require that once a point on a curved surface is traversed it cannot be traversed again.


But that isn't the definition of a point in geometry, and applies to flat surfaces as well. A point is just a location. In the case of lines, they are only 1 dimensional, with no width or breadth. So you can see how in any finite volume will contain an infinite number of pathways, whether curved or not.


With these two requirements, for a point on a curved surface to have physical dimensions and once traversed a point on a curved surface cannot be traversed again, then there cannot be an infinite number of pathways on a curved surface.

Thus, within a finite curved volume of space, there is a finite number of points and therefore a finite number of lines/pathways.

Thus, the volume of a curved volume of space is a finite number, and, therefore, that volume of space is not an infinity, because an infinity is not a finite number but instead is a condition of having no mathematical/physical limits.

See above, as this is just the definition of geometric terms. A single line has only length, but contains an infinite number of points. A plane has length and width, and an infinite number of lines. And to complete the picture, a volume contains an infinite number of planes. This isn't really an issue of curved space, as it applies to flat Euclidean space as well.

There is no such thing as a 2D balloon.

There are only 3D balloons.

Correct, but I am talking about the 2D surface of the balloon. It's just an analogy to show how a finite flat space becomes unbounded when curved enough. That is to say, to a 2D stick person running around on the surface, he will not find an edge or center.

The surface of a balloon which is not expanding has definite boundaries:

1. It has the physical limit imposed by its diameter/radius.
2. When each point upon its surface has specific physical dimensions, then the total number of points on the surface is a finite number, is bounded, and when once a point is traversed it cannot be traversed again, the total number of pathways upon the surface of a balloon is a finite number.
3. When each point within the volume encompassed by the surface has specific physical dimensions, then the total number of points within the volume is a finite number; and when a point within the volume is traversed it cannot be traversed again, the total number of pathways within the volume is a finite number.
4. Outside the physical limits imposed by the diameter/radius of a balloon are additional points which have specific physical dimensions but the number of such points is without mathematical limit, therefore the number of points outside the surface of an expanding balloon.

This just seems to be a matter again of definitions. Since a point is merely an X,Y,Z (Or X,Y in the case of the balloon) coordinate with no size itself, you get an infinite number of them in any manifold. And from the same logic, you have an infinite number of lines on a surface.

You can take an area of space, and divide it into sections that each have their own finite size. If each section is called a point, then indeed, the number of points on that area would be finite. The problem is, within each finite section of area, there are still an infinite number of smaller areas that make it up. That just means you can cut space as arbitrarily small as you want.


Questions for you:

1. Was space created at the beginning of the Big Bang, or did space exist prior to the Bang?

2. Was time created at the beginning of the Big Bang, or did time exist prior to the Bang?

3. Was matter/energy created at the beginning of the Big Bang, or did matter/energy exist prior to the Bang?

If you claim matter/energy was created at the beginning of the Big Bang, where did it come from? Something from nothing?

Here is the problem in cosmology. The universe is expanding. Logically, if you wind the clock back on the expansion, the universe gets much denser as you go further back in time. Eventually, you hit a singularity where the density reaches a maximum, assuming the quantum structure of space avoids an infinitely dense state. A static universe is not allowed, so the universe either had a beginning at the big bang, or is cyclic. If there is some kind of mechanism to allow for the big bang to have merely been a phase change from a contracting dense state to an expanding one, then the universe may have existed forever.

Of course there are other solutions to the beginning of time problem, but that's another topic entirely.

[Bob K]

eh:

Bob K:What lies outside a finite space?

Can you logically conceive of a volume of space of dimension X, being limited/finite without also conceiving of a volume of space of dimension X + 1 which contains the space which is X and the additional space which is + 1 that lies outside/beyond the limited/finite X-dimensioned volume of space?

eh:Yes I can, quite easily. In geometry, a volume of space is defined entirely by it's own points. That means you do not need any external space to define a volume. Likewise, the size of an object is defined without any notion to what is outside. So logically we certainly can talk about a finite space.

What would lie outside? As I said, there is no outside, as that would be a contradiction. If you take a volume of finite size and add to it, you are increasing the size of the manifold itself.

No, the way the brain works, when you conceive of a limited space then you immediately become aware of a space outside of it and surrounding it. Gestalt psychology. Figure/ground images. When you limit spatial dimensions you create a figure that has a ground around it. The brain is actually working in this case to create a map of the real world, the real universe, because of the fact/logic of X + 1, which is the principle that when someone claims he knows the limits of space, the spatial reality of the universe, to be X, then someone else only has to add 1 to that X to get X + 1 to show the ground/space beyond/outside/surrounding X.

Again, infinity is not a specific number; instead, it is a condition of having no mathematical or physical limits.

Any spatial/volumetric X is a limit.

X + 1 shows the fallacy of the limit, that there is a spatial/volumetric beyond/outside represented by + 1.

The mathematical expression to be used for describing infinite space surrounding a limited/finite space of dimension X is X + i where i = infinity = infinite measurement; thus, for any claim that the universe/space = volume x, a limited/finite volume, the reality is X + i, meaning the volume X exists in/floats in and is surrounded by + i.

If by 'manifold' you are referring to the straight/rigid rod grid/latticework used to describe/imagine/intuit the infinity of space, then the manifold never increases; it is present always, and without limit to the number of straight/rigid rods an individual could traverse from a point of origin.

Once again, the manifold never increases, only our traversing of it, and our neverending measurement of it.

Similarly, the volume of space never increases; it is present as it is in its unlimited infinity.

A vacuumetric volume of infinite size cannot be increased nor decreased.

Observing a limited volume within an infinite volume does not decrease the infinite volume, but only limits the area of space under observation.

[Bob K]

Bob K:From our personal experience, we see volumes of space limited by their physical dimensions, and we see larger volumes of space which include the smaller volumes. If we extrapolate our experience of larger volumes encompassing smaller volumes, as soon as anyone claims space is a volume of specific dimensions we can add to those dimensions and create a larger volume, and we can do so without limits, without either mathematical or physical limits, the definition of infinity, therefore, from our experiences of volumes, we can easily conceive of the logical extension of a volume to the condition of having no mathematical or physical limits, which is infinity, and, therefore, we can imagine that the spatial reality, space, is an infinite volume, an unbounded volume, a volume with no mathematical/physical limits.

Space, therefore, is a pure vacuum and is infinite in dimensions, unlimited, unbounded, etc.

eh:Be careful not to commit a logical fallacy here. Just because we can't imagine a volume of space that is not embedded in some larger space, does not logically follow that space is therefore actually infinite. What we imagine does not equal logic.

And just to clarify again, I'm not arguing that space cannot be infinite. I'm only arguing that logically, finite is also a possibility.

There is no logical fallacy inherent in imagining/intuiting reality as it actually is.

Again, infinity is not a specific number; instead, it is a condition of having no mathematical or physical limits.

The spatial reality of the universe--space--the vacuum/void within which all people/things/events exist--is infinite in being without volumetric boundaries, being without mathematical or physical limits.

And, again, any attempt to claim that the universe/space has a finite volume, X, is destroyed by the expression Universe/Space = X + i.

By X + i, any attempt to imagine/intuit a universe of finite volume/volumetric measurements is illogical.

[Bob K]

Bob K:[Any] conception of a finite volume of space immediately is clouded by the conception of a volume beyond/outside. There will never be a human being who, or a machine which, will create a logical conception of a finite volume of space which eliminate any possibility of its being surrounded by still another volume of space with larger dimensions which will ultimately be surrounded by a volume of space which has no dimensions because it is infinite, because it has the condition of having no mathematical or physical limits.

eh:You are mistaking logic and imagination. I can logically define a volume that is all the space that exists, without being able to perceive it. And in actual, we only ever perceive a finite volume at a time, so it's not so hard to imagine a finite space at all. You just have to imagine it from the inside.

Also, some clarification is needed on the definition of a dimension. In geometry, when an object has 3 dimensions, we are not talking about the size. It is just the X,Y,Z coordinates that are possible in a volume of space. No matter what the size of space, there will always be the X,Y,Z axis to move about. An infinite universe would have 3D dimensions, but the size would be infinite. In other words, there would be an infinite number of possible coordinates.

You are kidding yourself if you seriously believe that you can imagine a spatial reality component of the universe that is limited to a volume describable by a specific number X [whatever that number may be].

Once again, to your X I can add + 1 and increase your volume, which proves that your volume was not a final limit to the spatial reality of the universe.

Infinity being a condition of having no mathematical or physical limits, there are no mathematical or physical limits to the increasing of the volume you define by the specific number X.

Thus, there is no X that can describe the infinite volume of the spatial component of the universe--space. By Universe/Space = X + i, for any finite volume X, the real Universe/Space is described as X + i.

I agree that each point in space would have an x/y/z coordinate as a function of being part of a 3D grid extending everywhere without mathematical/physical limit, hence extending infinitely.

Concerning points on surfaces, within volumes and upon/within grids, I require that each and every point have a set of dimensions which describe its size, otherwise points become useless, lines have no dimensions, etc., and any conclusions based upon manifolds which have points of infinite, actually, indefinite, size, are illogical and therefore useless.

[Bob K]

Bob K:A closed/finite universe is a logical impossibility.

eh:Why? Where is the logical contradiction? Mathematicians would like to know.

Mathematically, the spatial reality--space--of a closed/finite universe would itself be closed/finite and describable by a specific number, such as X.

The spatial reality, however, of the real/actual/true universe is describable by X + 1 + 2 + ... + i where i = infinity, the condition of having no mathematical or physical limits hence no specific final number to i.

Thus, outside/beyond any closed finite space describable by X is the additional space describable by X + 1 + 2 + ... + i.

The simplified mathematical expression is thus: Universe/Space = X + i; for every claimed finite space of X dimensions, the real Universe/Space = X + i.

Therefore, the concept of a closed/finite spatial reality of a closed/finite universe being the only spatial reality in the real/actual/true universe is nonsense/illogical/fallacious.

I am describing and articulating the same concepts and principles that I have said before but in a different way.

The universe has three components, three realities, space/time/physics, and the spatial reality is without mathematical/physical limits and therefore infinite in volume, as describable by X + 1 + 2 + ... + i, or, practically, X + i, and, ultimately i.

Now mathematicians can know why the concept/principle of a closed/finite space/spatial reality component of the real/actual/true universe is impossible and why, therefore, the concept/principle of a closed/finite universe is a logical impossibility, an absurdity, etc.

Other bones to pick with mathematicians:

I require a point on a surface, within a volume, or upon/within a grid to have physical dimensions whatever we wish to assign but which then limit the number of points upon/within a limited surface/volume/grid [manifold].

Mathematicians have for years gotten away with happy horsecrap such as claiming an infinite number of points upon a finite surface or within a finite volume or grid.

By requiring each point to have physical dimensions, no matter how large or small, the principle of an infinite number of points upon a finite surface or within a finite volume or grid is now shown to be logically absurd because it is mathematically/physically impossible.

For example, if I draw an equatorial geodesic consisting of contiguous points on the surface of a sphere and require each point on the geodesic to have physical dimensions and stipulate that once traversed a point cannot be traversed again, then we can intuit that the geodesic divides the sphere into two halves and limits the number of points upon each half and therefore the number of pathways upon each half.

Similarly, regardless of where I draw a geodesic upon the surface of a sphere, with contiguous points of finite dimensions which once traversed are no longer traversable, the geodesic will limit the number of pathways upon each section of the sphere sectioned by the geodesic.

Similarly, within the volume encompassed by a sphere of a finite diameter/radius, when each point within is required to have/be assigned physical dimensions, then the physical dimensions limit the number of points which can be found within the volume of the sphere, and, therefore, the points within the volume of the sphere cannot possibly be infinite in number mathematically or physically, therefore, there cannot ever be an infinity within the volume of a finite sphere.

Moreover, when points are required to be assigned physical dimensions, and once traversed cannot be traversed again, then the number of pathways within a finite volume of any shape is limited/finite and definitely not infinite.

Therefore, under the rules that dimensionless points in space are nonsense and not allowed, and that, the reciprocal, all points in space are to be assigned physical dimensions, whatever they may be, then a closed/infinite space is not possible because of the fact that the physical dimensions of each point will limit the number of points/pathways possible within the finite volume of the closed space, hence a closed space cannot ever be infinite [except in duration in time, another matter/issue/consideration/etc.].

Notice what happens when points in an infinite space are assigned physical dimensions: there is still no limit to the number of points possible in an infinite space.

By the way, if you are having a problem with physical dimensions = mass, then consider the dimensioned points to have no mass, and all will be well.

[Bob K]

Bob K:Multiple images of the same ___ (?) viewed at different locations in the sky are multiple images of the same ___ (?) viewed at different locations in the sky. The ___ (?) remains the ___ (?).

eh:I'll see if I can get an article that explains it in detail. The basic idea is that in a hyperbolic (or flat multiply connected) universe, light from the same galaxy will have made several trips around space. Since the galaxy is itself moving throughout the universe, those images from the light will then be in different locations in the sky. If this is detected, I don't know of anything else that could explain it. In fact, that might be the only way that proof of a finite universe can ever be found.

Lightwaves/rays/etc. can be bent by gravitational fields, which are forms of matter/energy because they cause forces which cause changes of inertia and only matter/energy can cause forces which can cause changes of inertia.

Lightwaves can be bent into continuous circles within a gravitational field created by a clump of matter/energy and yet there will always be the spatial reality that lies outside/beyond the volume X defined by the gravitational field, such volume describable by, and understood, intuited, by X + 1 = 2 + ... + i, or Universe/Space = X + i.

The sum total of matter/energy in a closed energy system is a constant, a finite number, and, therefore, the matter/energy in a closed energy system is a finite quantity, and that the matter/energy of the real/actual/true universe is a finite quantity; moreover, remember always that a finite quantity of matter/energy cannot be dispersed infinitely into an infinite volume, hence the finite quantity of matter/energy in the real/actual/true universe will have boundaries, edges, limits. And there is the possibility that the matter/energy of the universe is not clumped into one singular clump but, instead, is separated into clumps which may be beyond visual observation and out of contact with each other via gravitational/electromagnetic force fields.

This insight into reality shows us that there will be areas of the spatial reality--space--in which there will be no matter/energy present, in which there will be no gravitational or electromagnetic force fields, hence gravity and electromagnetism will not be found everywhere and anywhere in the spatial reality--space--of the real/actual/true universe.

[Bob K]

Bob K:There is no logical interpretation of any 'evidence' resulting from cosmological observations that supports a conception of a finite universe because the universe IS infinite in its spatial/temporal/physical realities.

eh:How do you know? What logic says that the volume of space must be infinite? The only way you can show that, is if you can show a logical contradiction in the concept of finite space. It would be quite an accomplishment, since no one has been able to do