Is the Universe Precisely Flat and Infinite?

[charon]

David -

I can’t comment further on this, without seeing the discussions. Are they no longer online? You can’t link to them?

Don't be intense, David, they're long gone. You'll just have to take my word for it. Waffling means skirting round the subject and generally prevaricating. In any case, it's not really pertinent to this discussion, is it?

It is indeed a terminological dispute

Well, in that case it's not of my making. If you science chappies clarified your terms we'd all be better off.

if you wish to define “universe” as all that there is, anywhere, at any time, ever

That is the dictionary definition, as I keep saying. Do I really have to paste it in? The word comes from Latin meaning 'all together, all in one, whole, entire, relating to all'.

https://www.etymonline.com/search?q=universe

the Many Worlds are, indeed, different “worlds” within the same universe

What Many Worlds? Do you know of any?

It makes no difference to the science whether you say that the two different cats, one dead and the other alive, are in two different “universes,” or that they now occupy two different “worlds” within the same universe.

But there aren't two worlds or universes. Cats in a box are of this world alone. I take reality, not a conceptual idea created by the mind. The mind can invent anything it likes, but that mind is of this world!

Who cares?

Well, obviously we do, otherwise we wouldn't be discussing it. In any case, they should care. What sort of mind is it that can't differentiate between reality and an invented concept? Generally the answer is those illusory religious ones but we better not go there!

Consider, for example, that there are many different locations in the universe, and many different moments. Are each of these different spatial and temporal locations just subsets of a singe universe? Or would you wish to define them each as an individual universe?

You said it - 'many different locations in the universe'. Of course there are. I'm here and you're wherever you are. Why on earth should I say that we inhabit different universes? A poet might, but it's not supposed to be literal. Science is supposed to deal with facts, not romantic, poetical metaphors.

We know that locations in space and time are indexicals — basically, point-of-view dependent. Wherever I am, I call it “here.” Whenever I am, I call it “now.”

Absolutely. I'm writing this now and. when you read it, it'll still be now! It's always now. There probably only ever is now at any time. That's the interesting thing about time...

There is a “world,” according to Lewis, actual to its own inhabitants but not actual to us, in which pigs actually fly. There is another in which donkeys actually talk. There is another in which the ancient Greek gods are literally real. Basically, on this doctrine, everything that is logically possible, is actual. (There is no Lewisian world with four-sided triangles, for example, since that is not logically possible and hence cannot be actual.)

No, that is invention - as above re. the mind.

Lewis specifies that these actualities are spatiotemporally isolated from one another

His inventions, you mean? There's no point is ascribing qualities to inventions. There are many 'worlds' in this world but they're all in the same world, i.e. this one. Therefore they cannot be isolated from each other. Everything is related to everything else, however vaguely. That's what life is, what reality is.

The upshot is, there cannot both be one universe, and many universes, at the same time.

I know, I keep saying that.

If the universe is flat it is infinite

'Flat' as in your definition, presumably. But apparently it's not clear whether it is or not. Apparently it's merely the preferred choice out of three. I know that's a bit mean because the evidence seems to point that way, but it's certainly not settled.

Expansion means that cosmic distances — basically, distances between galaxies — increase over time. This can happen perfectly well whether the universe is spatially infinite or spatially finite but unbounded (curved). In the deep past, all objects in a spatially infinite universe could have been infinitely close together. The universe would still be spatially infinite.

Ah, now we get to something.

I can blow up a balloon. It expands. Lots of things expand. Peoples' waistlines expand! Such growth - things getting bigger and therefore altering relative spacial dimensions - are part of life, they're a reality. Things also diminish in size too, of course. But all this doesn't affect 'the universe', that stays as it is.

Galaxies, star-systems, may move around and change - everything changes all the time - but it doesn't affect the whole we call the universe. I'd say that was a fundamental facet of reality, that there is change within changelessness.

I think it's that that really interests me, how there is constant and unaltering change yet nothing changes. You and I have gone through innumerable changes in our short time yet we're still here.

I have to say I find that interesting.

[davidm]

*Sigh* I can see that this is yet another online waste of time. It’s why I almost never post on the internet anymore. And yet, from time to time, I creep back, hoping for a different result, the definition of insanity … NOTE TO SELF: Someone is wrong on the internet! Don’t try to correct him/her — IGNORE them!

It astonishes me how you could have so breathtakingly missed the point, completely missed the point, of what I just wrote. Wow! Congrats! If Missing the Point were a Nobel Prize category, you win!

[charon]

It was only a matter of time.

There's nothing wrong with what I've said, quite the contrary. Unfortunately it doesn't tie in with your knowledge and theories, that's the trouble. But your knowledge is not only limited but largely untested; it's incomplete.

That's true, isn't it?

[davidm]

There is everything wrong with what you said. The problem is that you have no knowledge base, and cannot even grasp the simplest, most elementary things that are written to you. You are so lacking in knowledge and education that you assumed that the description of a "flat" universe in cosmology meant that people advocating this were saying the the universe is 2D rather than 3D. When you were corrected on this, you thanked precisely no one for the correction, which makes me doubt even now that you even grasp the point.

All knowledge is incomplete. But the idea that the universe is spatially infinite is as probably true as anything can be. Another thing you don't understand, apparently, is that science does not ever deal in absolute proof, but only in probability proofs.

I suggest you take a class or read a book.

[davidm]

I should also add again -- though admittedly, doing so is redundant -- that you completely missed the point of my post. It's as if you were not reading it at all, or reading something I did not write. It's bizarre.

[charon]

I forgot, the other thing they did when all was said and done was to attack me personally. I'm immune :-)

The point I'm trying to make is simple. I'm not trying to join a science class, nor enter that world, nor indulge in theories and concepts. I'm a layman and make no apology for it. If you think I'm a lesser being because my head isn't stuffed with technicalities that are mostly entirely conceptual and, as you say, not wholly proven, then you've certainly missed the point.

I don't believe for one instant that, to understand the world we live in, or the universe in which we exist, we need to go to college and take some very complicated courses. If that were so anyone outside of the science world
could be immediately classed as ignorant. I'm afraid it isn't true. They may be ignorant of the specialised knowledge but they are not necessarily ignorant at all.

I'm not having a go at anyone nor am I trolling, as I said before. You'll notice I said that right at the beginning... prior experience talking!

I think most of this stuff is common sense. The universe can't be limited because what would be beyond that? The very word limitation implies something more. Time, as we know, is always 'now'. Do we have an explanation for that?

Incidentally, you haven't told me what the point is that I'm supposed to have completely missed. Perhaps you should.

[charon]

reading something I did not write

Nonsense, I went through it point by point, with full explanations and a link.

What you're objecting to is that I'm not answering it as a scientist would, with correct terms, knowledge, and all that. That's too bad, I'm not a scientist. If you can only converse with those in the same 'club' then that's a closed society. And I would never subscribe to a closed society.

[A_Seagull]

The universe in not infinite, for reasons posted previously.
It may be very large or even very very large, but never infinite.

[charon]

Anyway, Davidm isn't the only poster here so perhaps someone else might care to answer my points.

It's quite interesting. Positor gave me a link about the 'flat' question. This one:

http://curious.astro.cornell.edu/about- ... d-beginner

If one also explores other questions on the same site, other people are making the same points I am. I hadn't seen any of this before so I wasn't copying them. Obviously quite a few people have had the same thoughts and asked the same questions.

So either we're all thick as pudding or there's a point to this. It has to be said that all the answers from the specialists and experts are speculative. That is, they begin with 'if' most of the time. So actually it seems no one really knows.

Now that is another interesting point. There's a vast difference between simply not knowing and keeping knowledge open for updating. As David said (before he lost his rag!) nothing in science is considered 'proven'. I know. He thought I didn't, but I do. It's very old, basic stuff.

So again I ask, if your universe is something IN space then it can be measured, etc, etc. But if 'universe' means Absolutely Everything then it must include space. In which case things aren't so simple.

But no one wants to answer that. They couldn't on the other site either. Or, rather, they could, but started with the word 'if' and posed two different scenarios. And then said:


'However, because we are, by definition, stuck within the space that makes up our universe and have no way to observe anything outside of it, this ceases to be a question that can be answered scientifically.'

Well, that was the first point I made, quite independently. So apparently not so ignorant after all... But I knew that, which is why I am largely unmoved.

Anyway, let's leave it because I know where this goes. I better think of something else to do.

[charon]

The universe in not infinite, for reasons posted previously.
It may be very large or even very very large, but never infinite.

The universe as something existing in space (and therefore measurable)? Or the universe as the totality of everything including space?

[Positor]

The universe as something existing in space (and therefore measurable)? Or the universe as the totality of everything including space?

The Wikipedia article on "the Universe" states:

The Universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy.

[davidm]

The Weirdest Idea in Quantum Physics is Catching On

[BurtJordaan]

They put the scale function a(t) as the curve of the trumpets long cross section (i.e. varying perpendicular to time's arrow).

I don't follow what you mean. As I understand the "trumpet diagram", Ethan Siegel shows the "trumpet"

with a cross-sectional diameter representing the proper diameter of the observable universe at cosmological time t. This value is obviously just a scaled version of the expansion factor at time t, i.e. some multiple of a(t). The flat piece, where "Space" is indicated, represents the rest of the flat universe, in principle going to infinity in all 3 spatial directions, of which 2 is shown. I think that was his original purpose of this particular diagram.

This fact is also indicated in the cylindrical coordinate diagram at the bottom of his page

which is just a plot of a snapshot in time, with the yellow sphere indicating our presently observable universe, with the cylinder just a truncation of the rest of the flat universe. In both these views, the circumference of the circle (sphere) means nothing more than pi*observable diameter.

I'm showing all this, because in my opinion, your non-standard representations are bound to confuse readers here who try to understand what the mainstream says.

[charon]

The universe as something existing in space (and therefore measurable)? Or the universe as the totality of everything including space?

The Wikipedia article on "the Universe" states:

The Universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy.

Just what I've been saying all along.

So you see the problems that creates now? I've already spelt them out but I'll just re-post this quote from the link you gave me (on another page). It's not so much fun but...

'However, because we are, by definition, stuck within the space that makes up our universe and have no way to observe anything outside of it, this ceases to be a question that can be answered scientifically.'

http://curious.astro.cornell.edu/104-th ... JzcGFjZSJd

Or am I preaching to the converted?

[BurtJordaan]

The universe as something existing in space (and therefore measurable)? Or the universe as the totality of everything including space?

The latter and therefore in principle measurable (from within). Just like we cannot measure the diameter of the solar sysyem directly, we can deduce if from the measurements we make from within, using general relativity (or for all practical purposes Newtonian theory due to the weak gravitational fields).

In cosmology, the main tool that we use for measuring the size of the total universe is the CMB radiation and the observed absence of spatial curvature, to within experimental limits. Since we still can't figure on which side of flatness it lies, we use flat and infinite as the most likely case.

If it happens to be precisely flat, it will require weird science to explain why its not infinite. After all, what is the length of a perfectly straight line?

[charon]

The Weirdest Idea in Quantum Physics is Catching On

Ah, the Many Worlds thing...

This is the sort of idea it's fascinating to play with, and we love toying with ideas. I really can't see any point at all in there being multiple versions of oneself.

I can see a case for multiple facets of consciousness incarnating at different points in time and space. That may be possible. It would give experience to a species, if you see what I mean. We ourselves may be facets of a group consciousness but whether that means multiple clones of exactly the same person is highly doubtful. There wouldn't be any point to it.

Everything we do may be contributing to a greater whole, indeed it must do - like an aggregation of the findings of different scientists contributing to the general understanding - but they are from different scientists with different capacities. There'd be little point in the same one repeating his/her own investigations in the same way. Like making music on the same instrument all the time.

So I don't go for it. Not as stated, anyway.

[BurtJordaan]

The Weirdest Idea in Quantum Physics is Catching On

Now that's a whole new can of worms (for this thread, at least).

If we don't kill those worms now, think about the infinite number of copies of this thread, which within itself will be infinitely lengthy before the end of time...

[charon]

Burt -

The latter and therefore in principle measurable (from within)

In principle. But space, which you're saying includes our universe (let's say our universe), is illimitable. As I keep asking, if it's limited then what is beyond that limitation? More space?

Another word for illimitable is immeasurable. How can one measure something that is infinite, that has no boundaries? Apart from saying it's infinite, of course.

[BurtJordaan]

Charon, indirectly measurable is still measurable or determinable, if you want. From the inside.

E.g. how would you determine that a straight line is in fact unlimited in length, i.e. infinitely long.

Before we go into an infinite loop, let me say this:

I posted this thread and am hence responsible for all the "conflict". My objective was only to show that we as scientists use the equations for the spatially flat (i.e. infinite in size) cosmos simply because it simplifies our equations somewhat, and it is not in conflict with observations.

If we ever obtain irrefutable evidence for some curvature (positive or negative) that rules out "flat", we will just switch to the more accurate set of Friedmann equations and "suffer" the more difficult equations - which we had at our disposal for most of the last century. In the meantime, we listened to Occam.

And if the curvature is still very, very close to zero (as we currently observe), cosmologists will probably carry on with the "flat" equations for most of their work - many of the cosmological parameters are not presently even known to the accuracy of the "flatness parameter".

[charon]

Burt -

I posted this thread and am hence responsible for all the "conflict".

There's no conflict, at least not with me. It's an animated discussion! Thank god for it too.

Forgive my pointing it out, but you haven't actually answered my question. If by universe we mean literally everything, including space, and that space is limitless, how are we to measure it?

indirectly measurable is still measurable

But if you say it's measurable, even indirectly, what is it you're measuring (or determining)?

[A_Seagull]

The universe in not infinite, for reasons posted previously.
It may be very large or even very very large, but never infinite.

The universe as something existing in space (and therefore measurable)? Or the universe as the totality of everything including space?

The latter.

[Faradave]

The latter.

Yes. In my experience, in academic literature "universe" most often means all time and all space, which is in principle traversable. "Cosmos" means all space at any given time (typically "now"). Thus, there is "cosmic expansion" over time.

The "observable universe" is hybrid in that it refers to the (spatial) size of the cosmos as determined from signals (such as light, neutrinos and gravity waves) which have been traveling for a very long time. I usually interpret that as all space and all time from the Big Bang until now, often depicted as the "trumpet" images above.

Of course, I defer to any adjustment Jorrie (a.k.a. Burt) would make.

[charon]

The universe in not infinite, for reasons posted previously.
It may be very large or even very very large, but never infinite.

The universe as something existing in space (and therefore measurable)? Or the universe as the totality of everything including space?

The latter.

Well, this is it. Some say one thing, some say the other.... I say nothing :-)

[charon]

The latter.

Yes. In my experience, in academic literature "universe" most often means all time and all space, which is in principle traversable. "Cosmos" means all space at any given time (typically "now"). Thus, there is "cosmic expansion" over time.

The "observable universe" is hybrid in that it refers to the (spatial) size of the cosmos as determined from signals (such as light, neutrinos and gravity waves) which have been traveling for a very long time. I usually interpret that as all space and all time from the Big Bang until now, often depicted as the "trumpet" images above.

Of course, I defer to any adjustment Jorrie (a.k.a. Burt) would make.

In that case - that trumpet thing... what is that? That's not limitless space! It looks suspiciously like something IN space to me.

[BurtJordaan]

But if you say it's measurable, even indirectly, what is it you're measuring (or determining)?

I have tried to say this many times: we measure the spatial curvature (flatness) of the observable universe. Then the mathematics tells us that, if the observed result is either "flat" or negatively curved, the universe must be endless, i.e. infinite.

If this was not so, we would have had an even bigger problem to solve, i.e. we don't have any theory that could tell us where the end is, nor what would lie farther than the end.

Even if we would find the spatial curvature to be positive and hence the universe must be extremely large, but closed in on itself, it would (given enough time) observationally repeat itself over and over an infinite number of times. Fortunately, the cosmic size and expansion dynamics spare us that riddle - we can never look that far...

[A_Seagull]

The universe as something existing in space (and therefore measurable)? Or the universe as the totality of everything including space?[/quote]

The latter.[/quote]

Well, this is it. Some say one thing, some say the other.... I say nothing :-)[/quote]

Perhaps the best model is to consider that space and time were created along with matter at the Big Bang.

The expansion of space is not limited to the speed of light and hence the universe may be considerably larger than the 'observable universe'.

[BurtJordaan]

I usually interpret that as all space and all time from the Big Bang until now, often depicted as the "trumpet" images above.

FD, I guess that you have now come to terms with the idea that the trumpet shape usually represent the observable universe only. Here and there a mainstream cosmology author sloppily writes "universe", leaving out the "observable" qualifier, but it is usually clear from the context that the observable universe is pictured and discussed.

Most practical cosmologists are only interested in what the astronomers can observe, because that's the data they have and there are still enough unknowns there to keep them in work for a long time.

[charon]

Burt -

I have tried to say this many times: we measure the spatial curvature (flatness) of the observable universe. Then the mathematics tells us that, if the observed result is either "flat" or negatively curved, the universe must be endless, i.e. infinite.

In your very first post here, to the question 'Is the Universe Precisely Flat and Infinite?', you said 'The short answer to this question is, we do not know'.

Have you revised that? Sorry, I'm not trying to catch you out.

[charon]

Incidentally, don't think I don't understand all this. I do. They thought the earth was flat once because they didn't know it was round. In other words, what looked flat locally was, at larger scales, actually not.

Similarly, the idea that the Total Universe (beyond the observable) is either round or some other defined shape doesn't work because, if it were, that globe or other shape would still have to exist 'in' something. So we can say, at least logically, that the Total Universe is 'flat' (in the sense it's not round, etc). In other words, it's just 'there', and therefore presumably infinite.

So far so good. Where are we now then? Have we solved the problem?

[Faradave]

FD, I guess that you have now come to terms with the idea that the trumpet shape usually represents the observable universe only.

To be sure! When I presented my 3-Ring Circus as analogous to the cosmic heart diagram, only one trumpet was meant to represent the universe observable by us. The rest fill in the rest of the universe, observable only by aliens we can never hope to contact.


Left: The observable universe. Right: With three dimensions of space compacted into any circumference (i.e. 3-ring), a curved-space, radial-time model accommodates a cosmos much greater than what we can ever hope to observe.

None of this rules out flat depictions, but I seek models with explanatory power for things like limit c and dark energy. I believe curved-space, radial time offers this while simplifying to only one kind of dimension, time emanating as a 4-field from a central Big Bang event.

The scale factor as a function of time a(t) gives the shape of the trumpet's profile. Space can be straight for a flat cosmos or an arc if positively curved.