Energy in Space Time: Where Does it Come From?

[wolram]

I can imagine that space time is made up of some (spin foam) or some other
abstract unit, but if that (unit) is (all there is )where does the energy come from to give us the Hubble ?

 

[Chronos]

Einstein's maligned, but often discussed vacuum energy. Mainstream models currently favor a tiny, but omnipresent cosmological constant [i.e., dark energy].

 

[wolram]

Einstein's maligned, but often discussed vacuum energy. Mainstream models currently favor a tiny, but omnipresent cosmological constant [i.e., dark energy].

That would mean that dark energy was some how built into the (unit) of
space time, is this allowed for in QG ?

 

[marcus]

That would mean that dark energy was some how built into the (unit) of
space time,...

YES! that is a fundamental insight

a good QG theory should tell us how the dark energy, or the cosmological constant, arises from the basic building-blocks

this is a big item on the agenda for people working on spin network theories and they don't have the answer! It is something to keep asking---not to be satisfied with a theory until it explains the dark

the paper I'm reading currently, and which selfAdjoint said yesterday he has been also looking at, has some brief discussion of this. It is an overview paper largely written in words rather than equations and I think it gives an excellent overview. Mentions all the hard questions and indicates current ideas being explored for answers.

Your particular unresolved question is discussed on page 10. but that seems too technical to tackle straight on so I will go roundabout some

The paper is "Generic Predictions"
http://arxiv.org/hep-th/0605052

He may have a line on it. something promising to try anyway. I will explain a little

 

[marcus]

In physics one way to measure progress towards explanation is where you can explain two or three numbers using only one number and some mechanism whereby the one can determine the many.

it is an idea of economy.

this is not in answer to your question, it is a different question. How do observed features of the CMB arise from the model? I will get to your question in a post or two. this is warm-up or illustration.

In the last couple of paragraphs on page 18 he discusses a possible notion that ONE number----the fraction of non-local links in the network (which he denotes by the letter "p" but that doesn't matter) could determine for us several things: the fluctuation specs of the CMB, the rough similarity in all directions of the CMB temperature.

the physicists strategy would be to look for several different things that the value of "p" determines, use one measurment to determine a value for "p" and then test to see if that is consistent with other measurments. If there are two measurments that you think are determined by p, then the SAME VALUE of p should WORK FOR BOTH.

It is a simple logical strategy: a tried and true workhorse. he doodles around with this on page 17---section 5.4 "disordered locality and the CMB spectrum". He hasnt quite got it but you can see him fishing for it.

He gets a rough rough rough estimate for p of 10^-56.

 

[marcus]

here is the basic idea.
look at figure 2 on page 5, it shows a couple of moves by which graphs can evolve, one is an EXPANSION MOVE where one vertex is replaced by 3 vertices in a triangle

in smolin's type theory (what he calls "causal spin network" (CSN) theory) the graphs are the quantum states of spacetimematter

1. the graphs evolve by the occurrence of local moves that expand or reconnect nearby verts-----each kind of move has a certain probability

2. matter is tangles, like knots and braids, in the graphs----stuff which is not easily undone by the simple local moves, so matter persists

3. the expansion of space is taken care of by the expansion-type moves (which always replace one vert by a triangle or a tetrahedron, so one vert becomes 3 or 4)

4. at bang-time Nature provided us with a graph that is CONNECTED RANDOMLY EVERY WHICH WAY! maybe not perfectly random but it had a high proportion of non-local links which are like the ancient "wormhole" idea of John Wheeler----they go silly places instead of just around in the neighborhood. but intuitively you can see that eventually EXPANSION MOVES TEND TO SMOOTH THAT OUT!

5. the network begins to look more and more like an ordinary lattice approximation to smooth space, more and more regular, it just has these rare occasional links which JUMP, they are left over from bang.
see figure 6 on page 17.

he estimates the fraction of these links that JUMP is one in 10^56.

I think that normal routine expansion processes can create more of these in a subtle way by stretching out the space between two connected verts. But to a rough approximation the local moves don't create or destroy these things. to me, they represent a kind of curvature but this is just a dim intuition.

6. Smolin estimates the number of ordinary links in the Hubble volume as 10^180.

so if one out of 10^56 of these are crazy nonlocal links, that means the number of nonlocal links in the Hubble volume (more or less same size as the currently observed universe) would be 10^124

he actually does the calculation twice, once very roughly at the beginning at the top of page 16 but then a bit less roughly at the bottom of page 17----dont be confused by the fact there are different numbers.
I am focusing on the second set of numbers, bottom of page 17.

he isn't saying he has the answer. but it is an example of trying to see how observed phenomena can arise from the graph itself.

that is the main idea, in a particular theory, how do you get the interesting stuff to be intrinsically built right into the theory, and not just something laid on as an afterthought. the interesting stuff, like Lambda, should be organic to the most basic nodes and links nuts and bolts of the model

======HERE'S WHERE I START RESPONDING TO YOUR QUESTION=====

I think your question "Where is the dark energy" is a type of fundamental question that QG people have to address.

What would be the natural way for the Cosmological Constant LAMBDA to be present in the picture. What is a natural role for LAMBDA?

As I mentioned a couple of posts back LAMBDA is touched on at page 10, it is built into the way the links are labeled. Section 3.4 "Heat and the Cosmological Constant". this is more technical.

You know of the Lorentz group. It is symmetries of an empty flat spacetime that does not expand. (1905 special relativity)

the simplest picture of a space that expands like our space is deSitter with a positive Lambda. That is the flattest picture you can have that still has accelerating expansion. All detail washed out, all bumps (like galaxies) ironed smooth.

But that is not "LORENTZ INVARIANT"----the deSitter space has just enough curvature that the symmetries of 1905 special rel will not fit any longer. So they have a DEFORMED Lorentz algebra of symmetries which fits deSitter.

then there is a key "What if" idea. What if we took this approximate symmetry in the large and used IT for our symmetries in the small?

the custom with causal spin networks has been to label links with representations of a symmetry group. But what if we labeled links with representations of a deformed symmetry which looks, in the small (down at Planck scale where the nodes and links are) like a miniature image of the grand deSitter symmetry of the whole universe? What then?

this turns out to be an inspired guess. It has a lot of consequences some of which are mentioned on page 10.
One thing it does is affect the links in the graph so that they can register twists. I would not have expected this---it is not intuitive for me, at least for now, but here it is on page 10:

"A consequence of the quantum deformation of the label set is that the graphs are framed, so edges are represented by ribbons or tubes[21, 29, 32]."

I find this rough going. I studied group theory and abstract algebra before "quantum groups" became popular. the gist of it, to my limited understanding, is that there is a deformation parameter that SKEWS THE GROUP and gets you a different algebraic structure which is almost but not quite the same. Like a stiff drink, and the world is slightly modified. It expands, maybe. or some other weird stuff.

if you are in this deformed symmetry world and you let the deformation parameter go to ZERO then ahhhhh! everything is cold sober flat and normal. Einstein's 1905 Poincaré group again!
Sometimes they call an exponentiated version of the deformation parameter by the name KAPPA and they call the distorted group of symmetries the "kappa-Poincaré". It's essentially the same information---like a number and its logarithm. For the deformation parameter itself, they often use the overworked ordinary lowercase letter k, and write 1/k (for the very small number) or 1/(k+2). Notation not important here.
The way to think about it is that the deformation parameter is a very small number that YOU THINK REALLY OUGHT TO BE ZERO but isn't.Smolin suggests that you can tell what the deformation parameter is simply by MEASURING THE COSMOLOGICAL CONSTANT. that is the gist of page 10.

And it is the deformation parameter, for example, that causes the slight variation in the speed of light with energy that they hope to look for using GLAST.

and technically, just focusing on causal spin network models, it is the deformation parameter with makes the links be (in effect "tubes or ribbons") so that you can twist them. I think all that means is there is a PERIODICITY in the representations of the deformed symmetry group.

I regret not being able to explain the stuff on page 10 better, and also must admit that it looks like it would be pretty hard even with a better explainer. there is a whole wagon-load of high-tech verbiage that goes along with page 10, ominous terms like "chern-simons" (I heard Chern lecture when I was in school and it went over my head and left me with dim inexpressible notions which are probably of the wrong sort. but he was a warm affable guy with assured precision like a firm handshake)

So over and above all the confusion and doubt we suffer from, it dimly emerges that THERE IS A ROLE in causal spin network theories FOR THE COSMOLOGICAL CONSTANT. there is some handle on it. it is not just some number that appears one day in a flaming chariot. it is a working number that belongs in the model of how spacetimematter is put together.
it appears at the largest scale, in the acceleration of expansion, but it also appears at the smallest scale in the character of the microscopic SYMMETRIES that constitute the links in the microscopic web.

beyond saying this, I don't think I can help more with your question.
best if you read Smolin's new paper yourself, find the 60 or 70 percent you can understand and get some feel from it where the field is going. It is the best overview I know of, to date.