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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

Surely, it would appear as a circle only if you had a third dimension from which to view it; in which case it would appear as a sphere!



Would the same not apply to the universe?
Probably that is why you said that the extra dimension would have to be there all the time, but then you run into the problems of compactification, folding shadows etc.

No, in flatland it would appear as a circle, a round area completely enclosed by a line, with no entrance or exit. It would be possible to go completely around it and see that it had a continuous smooth curve. That is it would have the same curvature at all points. That may not be the standard definition of a circle, but it would define it for flatlanders who couldn't see it from above.

I'm not sure what to say about your other comment. I don't have a problem with the universe that we know, because it presumably had at least 3 dimensions right from the start. I have no idea how a dimension could be created from nothing. Of course I have no idea how our universe was created from nothing. But then not even the theorists studying it really have any idea.

And I don't have much faith in the so called String Theory. It just seems to be to be over complicated, with no way to find out where our universe would fit into it. So as far as compactification of dimensions is concerned I have my doubts that it really happens. I would feel much better about a theory of everything that just had our standard 3 + 1 dimensions. Which obviously hasn't kept me from talking about other ideas.

Bill Gill

Precisely my point: Flatlanders would not be able to see it as a circle. The only way they would know it was a circle would be to feel its roundness.

Of course, there are "vertical" versions of 2D space in which it is easy to suppose that a circle would be visible, but a little reflection establishes that such is not the case. A third dimension would still be needed to see the circle.

This seems to be a point on which we agree entirely.

I too have problems with the idea of creating dimensions, but I also have problems with rolling them up, or compacting them.

Well, seeing its roundness is exactly how a flatlander would see a circle. That is how a flatlander would define a circle. To them the view of a 3 dimensional sphere passing through would be what they would interpret as an expanding and contracting circle. It doesn't matter how we would see it, they see it as a continuous, equally curved impenetrable "wall". After all they wouldn't be able to "see" a square, or a rectangle, or a triangle, or any randomly shaped form except by sensing it's shape. After all in the book that is how they tell the difference between people, by their shape.

Bill Gill

So, how many Flatlanders can dance on the circumference of a circle? And would they believe in a flat heaven, hell, and god?

Precisely; that's what made women so dangerous.

However, unless you had time and opportunity to "walk" round the shape, any shape, all you would see would be either a straight line or a point.

I think you could make an interesting analogy between God and the occupant of Pointland, if you wanted to.

I look forward to hearing Kallog's take on that.

There is some very important things you miss in this discussion.

If our standard model of physics is right we have a mesh on the fabric of spacetime at plank distance and plank time units.

Now consider a particle moving at an angle like 45 degree to the mesh ... this is the jaggies problem of computer graphics display (http://en.wikipedia.org/wiki/Jaggies)

How does a particle pull off this trick of doing right angle jaggie movement on the plank time and plank distance fabric.

One view is thats why we have quantum mechanics because it has temporarily disappear off the spacetime mesh to come back again.

Another is the mesh is actually an illusion itself.

Ask any computer gamer who has played world of warcraft, rifts, or second life if you can have an illusion of 3D. If all you senses fed back in your visual illusion it would become hard to pick it from reality.

This problem goes back to the cave allegory from plato (http://en.wikipedia.org/wiki/Allegory_of_the_Cave)

Well, Orac, you have come up with some interesting views. As far as the movement of particles on the fabric of spacetime. Some people have speculated that the particles are actually just configurations of the mesh, and their movement is an evolution of the mesh. Actually this is one of the areas where I don't have a great deal of faith in what anyone says. I think that everybody is kind of stabbing in the dark hoping to hit on something that will provide a good description of the way the universe works at the smallest (Planck) scales.

Bill Gill

Even with string theory they don't really deal with how you conserve energy and momentum of particles when it is crossing at some angle to the 3D flywire plank distance mesh we are supposedly dragging through a higgs particle ocean.

Unfortunately for me I have to try and model this stuff and this nasty little side effect of having a grid really hasn't hit the radar of the physicists.

Basically you end up at one of three places

1.) We have a 3D mesh at plank distances universe and something like string theory, higgs oceans etc exist.

Explains gravity easily but motion on the grid is problematic.


2.) We have a universe that is fractal based and you can zoom in indefinitely.

Very difficult to factor gravity in but easy to have particle motions at angles because nothing changes

3.) The universe is a hologram.

Strangely this is the easiest to model because 3D worlds on computer programs are very very common. I am not convinced it's reality but it feels like home sometimes :-)

One thing about which I am unclear where the holographic universe is concerned is what its supporters actually mean. There seem to be two possible interpretations:

1. The Universe really is a hologram.

2. The holograms we produce are in some way analogous to the way in which the Universe works.

I am inclined to think that the second of these is more likely to be correct, but I would be interested to hear what others think.

That sounds interesting. It may not actually be physics, but it is physics related, so could you give us some idea of what you do?

Bill Gill

Yes I don't really like number 1 it's really easy to create and model because it really is nothing more than a 3D computer game but that is also it's weakness it implies that there is something and/or someone behind the illusion.
Maybe the matrix was right :-) Number 1 is not really a physics world interpretation.

There are a couple of theories that produce number 2.

D-Branes in string theory is probably the most compelling interpretation I have seen. It is probably the hologram version I feel most at home in.

I am not sure my english will hold up to explaining it but can have a go if you really want. It's probably best to read up on it, Briane Greene does a reasonable job in the book "The Fabric of the Cosmos: Space, Time, and the Texture of Reality". Be warned I really dislike his discussion of the spinning bucket in the book for me he never covers it's importance. It does create for me some degree of confidence in that you can get gauge theory, gravity a 3 dimensional world and all the basics I am familar with.

On the reverse I find the interpretation in quantum gravity the most contrived. They are so pre-occupied with gravity that some of the other basics end up sort of tagged in and by the old occam's razor they don't look right to me.

That's sort of my view on it in my best english I can muster ... sorry.

I am not sure it's that exciting .... :-)

String theory analysis for example is almost entirely a mathematically excercise. I have still yet to see M-string theory incorporated properly it is just so dam complex.

Some of the more basic ones like MOND (http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics) are much easier to model but I really can't see where this goes with Quantum Mechanics it's sort of still there like the ugly duckling it is with GR.

In my area there is much more work around trying to model conditions in and around the big bang or inflationary period depending on your view of which theory.

The reason is simple much bigger discoveries to be made ... Nobel prizes await.

My world of modelling is much more mundane we are looking closely at the operation of the theory at the plank distance because thats the key distance things get interesting. No nobel prizes given for proving or disproving someone elses theory usually :-)

Much more interesting boundaries for theories exist such as black holes and the boundary of the universe but they are even more inaccessible to us.

At the end of the day I am however a computer programmer with a physics background not a physicist who does programming so some of the stuff gets way beyond my ability at physics.

Mine physics knowledge is made usually from trying to help physicists feed model simulations into the computers and I usually end up asking a lot of questions.

There are a rare few who are great physics theorists and very good on computer programming.

My real work usually looks like trying to decipher weird drawings and scribbles on rather tattered and torn paper, drinking lots of coffee and pulling lots of hair out as either the simulation wont run or the phycisist doesn't liek the result :-)

Well,Orac you may not be a physicist, but it sounds like you are plugged into the physics community. I have a BS in physics, but that doesn't get me very far. Most of what I have been spouting has been what I have tried to understand in a lot of reading I have been doing for the last 30 years. I hope you can keep on helping us understand what we are trying to talk about.

I expect that your physicist co-workers learn from trying to explain it to you. Explaining what you are doing is a great way to learn more about what you think you already know.

Bill Gill

Leonard Susskind did explain String Theory. I am so happy that Stanford University post it up in youtube. It is a good guide.

SUSY and most of string theory looks to being read it's last rites from the LHC.

Quantum loop gravity is gone ... it's getting pretty light on for theories left standing :-)

I have had serious doubts about string theory ever since I read Brian Green's "The Elegant Universe". He explained it in pretty good detail, except that nobody could figure out how to make it apply to the universe as it is. All they had was a huge bunch of possible universes. And since then nobody has been able to come up with anything better. I think the only thing they ever came up with that seemed to intersect with this universe was that it had a spin 2 particle, which matches what QM theorists have said the graviton would have. Unless they come up with something more than that they are going to have a hard time convincing me.

Bill Gill

Conference is on today

http://www.physorg.com/news/2011-08-lhc-latest-results-mumbai-conference.html
http://www.science20.com/quantum_diaries_survivor/new_atlas_limits_higgs_mass-81880


Thats most of string theory gone leaves only light higgs possible around 135 GEV but unlikely which is a few weird variants and a few light higgs models.

Otherwise you are up to a very heavy Higgs but the air is getting very stratified.

So the LHC says

no string/brane exotica,
no sparticles,
no WIMPs,
no supersymmetry exotica,
no extra-dimensions,
no mini-black holes,
no Randall-Sundrum gravitons,
no heavy Higgs,

Standard model holding.

So, where have the extra dimensions gone?

Bill G ate them ... FB :-)

Delicious, with a side order of branes.

Bill Gill

Not the brains that Rede might be parting with, I'm first in line for those.

Just when we thought those other dimensions might have vanished we find this:

New Scientist 21 August 2011

"Black holes and pulsars could reveal extra dimensions"

LOL yeah I saw that on "Not Even Wrong" website that gave it a bashing (http://www.math.columbia.edu/~woit/wordpress/).