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Lower dimensional universe

I just saw this on PhysOrg.com. It sounds kind of mind blowing, and I'm not sure I really have any thoughts about it yet. It seems that some physicists have proposed that our universe may have started out as just one dimension. Then as that dimension expanded and the energy level dropped it switched to 2 dimensions. As the expansion continued and the energy level continued dropping it switched up to the current 3 dimensional universe. The time dimension of course has to be added to all 3 configurations. So the 1 dimensional universe had 1 space dimension and 1 time dimension (1+1). They claim to have detected what could be a signature of the 2+1 version.

As an aside I just finished reading "The Black Hole War" by Leonard Susskind. In it he tells how they did a lot of theoretical research using 1 and 2 dimensional universes, since the physics is a lot simpler. Whether that would work in with this subject is open for question.

Bill Gill

Well, now I have been thinking some more about this story. This is my idea, not in any way to be suspected of having any reality to it.

The story suggests that our universe started out as a 1+1 dimensional universe, then switched to a 2+1 and then a 3+1 dimensional universe. My idea is that they don't really mean that the universe grew a whole brand new dimension on each switch. I suspect they they are working from a string theory perspective. When string theory was first developed it turned out that it would not work in a universe with 3 + 1 dimensions. They had to add more dimensions to make it work. However, since we don't see any more dimensions they decided the the extra dimensions were compact. That is, they are rolled up into very small bundles that were too small for us to detect them. An analogy from "Warped Passages" by Lisa Randall is the garden hose analogy. If you are sitting up in the nosebleed section at the stadium and you look at the far side of the field and see a hose that the groundskeepers left out it will look like just a one dimensional line. You have to get much closer to see that it has more than one dimension. So having said that I suspect that in the story on PhysOrg.com the original authors assumed that all the current dimensions of our universe were already there, but they were all compact dimensions, except the 1 spacial dimension that they think the universe started with. Then when the temperature of the universe dropped far enough the second dimension unrolled, and the universe became a 2+1 universe. Then as the temperature dropped further another dimension unrolled to give us our current universe. I have absolutely no idea why the dimensions would unroll as the temperature dropped. At first thought I would think that they would roll up as the temperature dropped. A drop in temperature would imply a reduced energy density, and therefore a reduced pressure. So I'm not sure how it works. But then I also have absolutely no idea how the math they use for all this works.

Bill Gill

Interesting read, Bill, thanks. It's going to need a bit of thought, I struggle with the idea of rolled up dimensions, possibly because I lack the maths to get a handle on it without a mental image.

However, I think your suggestion that the three dimensions are there all the time is easier to work with than imagining the Universe suddenly sprouting new dimensions.

Observers could be in for something of a shock if the fourth spatial dimension suddenly unfurls.

Well, I finally thought of that myself. I'm not sure what kind of range we would have to be talking about to make the change. The article said the change from 1 + 1 to 2 + 1 would have happened at about 100 TEV (10^14 EV), and the change from 2 +1 to 3 + 1 happened at about 1 TEV, or a ratio of 100 to 1. That is 2 orders of magnitude. The universe now has a temperature of about 10^3 EV. Now that is a ratio of about 15 orders of magnitude. That seems to be an awful big gap for the change. Let's asssume the same amount of energy in the 1 + 1 universe as in the 2 + 1 universe. I think that is a safe assumption, since the conservation of energy is one of the fundamentals in any universe. Then the energy that was concentrated in a single line would be spread through an area that is the square of the length of the line. That would cause a huge decrease in energy density. In fact I wouldn't be surprised if the decrease was greater than the 2 orders of magnitude that they say would be the trigger point for the change to a 3 + 1 universe. So in a way the change might be almost a direct change from 1 + 1 to 3 + 1. But the volume of the 3 + 1 universe would be very much higher than the area of the 2 + 1 universe. At first glance it looks like the volume would be the area of the 2 + 1 multiplied by the length of the 1 + 1. But of course the 2 + 1 volume is zero, so I'm not sure how you would calculate it. But that might explain the very low energy density we have now. And thinking about it, but very carefully not trying to figure anything out, you might consider that to be the explanation of the inflationary stage of the Big Bang.

Now that should give everybody something to think about for a few minutes. I think I will go away and try to think about something that isn't totally insane for a while.

Bill Gill

That could just be a stroke of genius! No comments about the thin line between genius and insanity.

I've done a little thinking about lower dimensions. I suspect that the problems I have had with these lower dimensions is that I have been trying to visualise them in a 3+1D environment. In order to exist in a 3+1D environment anything would have to have 3 spatial dimensions, otherwise it would not be there. However, if the environment has only 2+1D or 1+1D, I suppose that would be OK.

There is always a problem trying to visualize any system that has a different number of dimensions than we are used to. It is worst for more, but there is still a problem with less. If you can find a copy of "Flatland: A Romance in Many Dimensions" it might help. Flatland is over a 100 years old, but is still in print. I have seen it in book stores fairly recently.

Bill Gill

I have a copy of Flatland, which I thoroughly enjoyed. Abbott was way ahead of his time, and not even a scientist. I suspect he wrote Flatland essentially as a social comment, but it will undoubtedly continue to be used by popular science writers.

Just for those who might be reading this and might want to read "Flatland". You don't necessarily have to buy a copy of it. It is available for free download from Gutenberg.

Bill Gill

0 dimension of space + 1 dimension of time.... 1D formed...
then dimension of space starting from 1... 2D
3D
4D(us)
0 dimension of space?
Yes....

We have 0 dimension of time too....
In string theory... We called it as the eleventh dimension...
Different physicist and philosopher have different concept on this...
So............
My concept is that...

gan, I think you have the idea there. However, I'm not sure that anybody has considered a 0+1D universe, that is one consisting only of time. I'm not sure that such a universe could exist even theoretically. The lowest that I am aware of that anybody has worked with is a 1+1D universe. This has been used as a theoretical construct to test some ideas with. It makes the math much simpler to work with only one space dimension, and when they have that worked out they can then start generalizing to a higher dimensional space.

Bill Gill

Hi, folks; I'm back after a few days without access to the internet.

Perhaps no one has really considered a 0=1D universe because:
1. There would be no one around to observe it.
2. If time is a measure of change, there would be no change to measure.

0=1D. Of course, that should have been 0=1D, but you all knew that.

I've been looking again at the link in the OP, the following quote leads to a train of thought which I seem unable to get beyond.

“In other words, the universe is a straight line that is “wrapped up” in such a way so that it appears (3 + 1)-dimensional at today’s higher energy scales, which is what we see”.

A 3D object has extension in 3 directions, at right angles to one another.
A 1D object has extension in 1 direction and zero extension in any other direction.
If you fold a 1D object in two it has extension in its original direction, but its extension in the second direction is 0 X 0 = 0.
However you “wrap up” your 1D object you cannot do more than multiply zero by zero in any other direction.
Your 1D object will never have more than one dimension.

Bill, as I said before, your interpretation is easier to cope with, but you say “But of course the 2 + 1 volume is zero, so I'm not sure how you would calculate it” which raises the same problem. How do you get from zero volume to a positive volume?

Well Bill S. I'm not sure just how to reply. The problem to me is that what intuitive feel I have for 1+1D and 2+1D universes is very contaminated by my automatic understanding of a 3+1D universe, since that is what I am living in. But I will try to interpret what I have read about String Theory, and its requirements for more dimensions.

They say that the extra dimensions are there, but that they are "compactified", so that they are too small to be detected. The normal way they present it is that the compact dimensions are rolled up so that their extent is very small. Actually it may not be 'rolled" which implies something like a roll of cloth, but that is the way it is usually explained. They have some ideas about the way it is actually folded, but saying rolled is a shorthand way of describing it in a non-mathematical way. Now a rolled up dimension is kind of hard to visualize. I have had a hard time myself figuring out what it means to have it rolled up. I look at what I mean when I say something about the dimensions of something. I mean that I can travel along one dimension, for example North, then make a turn and travel off in a different dimension maybe East, or along a different dimension which would be up or down. So basically a dimension is a direction in space. Now they tell me that there is another dimension at right angles to all three of the dimensions I have been traveling, but I can't see or travel in that dimension because it is too wrapped up in itself. This is not intuitive, we just have to accept it because we are told it is so.

Now let me see if I can figure out what it would mean to "get from zero volume to a positive volume". Let's just forget the time dimension for this discussion. Well, for one dimension the energy of the universe would be concentrated in a straight line with no thickness. That is a lot easier to say than it is to visualize. But the only interactions would be between adjacent blobs of energy. I'm not sure how differentiated the energy would be. If we assume that an uncertainty principle existed, and I think it probably would, then the energy would exist in very small blobs. Presumably at the Planck scale. I can visualize this as knots in a string, but of course my visualization is a 3 dimensional visualization of a 1 dimensional universe. Anyway the energy density of the universe would determine the size and spacing of the blobs. If it was high they would be large and close together, as the universe expanded they would be able to spread out more. I envision the addition of the second dimension as the unfurling of a sail from a mast with a roller boom. That is a boom that has the sail wrapped around it. When you want to furl the sail you rotate the boom so the sail wraps around it. To unfurl it you just turn the boom the other way and the sail spools off. So for 1 dimension the energy would be running back and forth along the boom. As the second dimension unfurled the energy would get to jump off of the boom and spread itself all over the sail. So now instead of just running back and forth the energy could spread out over the second dimension. So now we have to talk about the energy density of an area, rather than a line. In going from 2 to 3 dimensions the sail analogy breaks down, because we have to picture the 3rd dimension rolling out from the first 2 dimensions. I think maybe the transition to the 3rd dimension can be envisioned as a ballon. Before you blow up a baloon you can lay it out flat and it will look kind of like a 2 dimensional surface. Of course the 3rd dimension is there, it is just kind of rolled up or "compactified" so that there is no access from the 2 dimensional surface. But as soon as it starts to inflate then you can suddenly discern the 3rd dimension and the energy that was trapped in the 2 dimensional universe can spread out into 3 dimensions.

Ok, let's see if that helps at all. And keep in mind that this is only my mostly uninformed raving. So if that isn't how it is don't blame me.

Bill Gill

Of course! Now I understand what I had in mind when quite awhile ago I wrote: In the beginning G0D--that is, the no-thing ('0') from which the things of existence got (G)generated, evolved and (D)delivered as we now experience them.

Sometime ago, a member of the last church I served, senior to me and long since in the dimension we call death, an engineer and a friend of mine loaned me his copy of Flatland. We often had open-minded dialogues about the nature of things.

Is my recollection correct when I say that I recall that in a "flatland" Flatland observers would experience a globe passing through their system first as a dot, then as a straight line?

Is this interesting talk about serious science? Or it is just science fiction? Me? I am open to anything the human mind can imagine. With Rene Descartes' famous, "I am, therefore I think" in mind, I like to say: I am, therefore I have the power to imagine anything, for better or for worse, I choose to think.

Thanks, Bill. It's great to see someone else working through the same sort of logical processes I struggle with.

Perhaps I can best explain my difficulty using your balloon analogy. It works because, as you pointed out, the third dimension is there all the time. However, in a genuinely 2D situation the the extent of the third dimension is zero. The only 2D thing I can think of is a shadow. Now I try folding the shadow, and that is where I run into trouble.

I think your recollection is correct. Of course Abbott had to think of a clever way in which to make 2D objects visible in a 2D environment, as he was aware of the fact that his illustration using a coin on a table needed a third dimension. A shadow on a flat tabletop would not give the same result.

Would this mean that in Flatland the N/S Poles would simply be the centre point on a straight line?

Theologically speaking: I imagine that in the beginning G0D was like an involved ("compactified") ball of matter. Then GOD, as the space/time continuum, began to evolve (unfold) to what it is now.

Eventually, the point came when I became aware of my personal involvement and role in the whole process. With the help of my imagination I became aware that I have the power to chose to be (heaven), or not to be (hell), to evolve, or not to evolve. I chose to be a willing participant. So can anyone.

I haven't actually read "Flatland", sorry about that. But Rev's remembrance that a globe passing through Flatland would appear as a line isn't quite right. Actually it would appear as an expanding and contracting circle. I read something about this in, I believe, "Warped Passages" by Lisa Randall. She pointed that out and said that we could detect extra-dimensional objects that passed through our 3 space by seeing a 3 dimensional object that appeared as a dot then
expanded to its maximum size, then contracted back to a dot. The way I read it she expected the objects to be very small and to appear in collider experiments. I'm not absolutely sure that is where I read it, but that is how I remember it.

And as far as your comment about folding a pure 2 dimensional flatland, well, in fact you could fold it all you want to. As far as I can see an occupant of the flatland would never notice it. It might have some of the same characteristics as a gravitational warp in 3-space does for us, but that is pure conjecture on my part. Essentially though warping flatland doesn't make it become 3 dimensional. For a pure flatland to become 3 dimensional would require what I would think of as magic, since there is nothing there to expand into.

Bill Gill