Two World-theories (neither one especially stringy)

marcus · Dec 19, 2004

The two that look most promising to me are Lorentzian DT and Loop.
To look at the raw numbers---sheer quantity of research papers written per year---you'd say LQG was growing rapidly and DT was flat.

Lorentzian DT was first proposed in 1998 (a paper by Ambjorn and Loll), here are some preprint numbers:

http://arxiv.org/find/grp_physics/1...gravity+AND+Lorentzian+quantum/0/1/0/1998/0/1

http://arxiv.org/find/grp_physics/1...gravity+AND+Lorentzian+quantum/0/1/0/1999/0/1

http://arxiv.org/find/grp_physics/1...gravity+AND+Lorentzian+quantum/0/1/0/2000/0/1

http://arxiv.org/find/grp_physics/1...gravity+AND+Lorentzian+quantum/0/1/0/2001/0/1

http://arxiv.org/find/grp_physics/1...gravity+AND+Lorentzian+quantum/0/1/0/2002/0/1

http://arxiv.org/find/grp_physics/1...gravity+AND+Lorentzian+quantum/0/1/0/2003/0/1

http://arxiv.org/find/grp_physics/1...gravity+AND+Lorentzian+quantum/0/1/0/2004/0/1

LORENTZIAN DT (etc.) PREPRINTS

Code:

Code:

The 2004 figures are up through 19 December, which is close enough to yearend so one gets an idea.

I have been reading nothing but DT papers this morning. the approach has some unique and impressive advantages working in its favor. I would like to be able to compare these two quantum spacetime theories on an equal footing.
Their most noticeable disagreement is apt to concern the area and volume operators. As yet no indication that in DT these will have discrete spectra.

I would like to know why the research output in DT is essentially flat. Given its apparent promise and the recent (2004) success, why arent more people getting into DT?

marcus · Dec 20, 2004

I will quote some about Lorentzian path integral from
the most pedagogical paper I know----Renate Loll
http://arxiv.org/hep-th/0212340

----quote from "A Discrete History"----
The desire to understand the quantum physics of the gravitational interactions lies at the root of many recent developments in theoretical high-energy physics. By quantum gravity I will mean a consistent fundamental quantum description of space-time geometry (with or without matter) whose classical limit is general relativity. Among the possible ramifications of such a theory are a model for the structure of space-time near the Planck scale, a consistent calculational scheme to compute gravitational effects at all energies, a description of (quantum) geometry near space-time singularities and a non-perturbative quantum description of four-dimensional black holes. It might also help us in understanding cosmological issues about the beginning (and end?) of our universe, although it should be said that some questions (for example, that of the “initial conditions”) are likely to remain outside the scope of any physical theory.
---end quote---

I guess anyone interested in this thread already has realized this: one of the unusual things about this approach is there are no coordinates.
That was the headline on Regge's 1961 paper that set things up for Renate Loll and friends------"General Relativity Without Coordinates".

they can consider the space Geom(M) of all spacetime geometries on some manifold-----each geometry is described by listing interconnections between uniformsized simplexes, some kind of computer data structure.

that is a point in Geom(M), it is real elementary barebones
there is no "gauge" or chaff of arbitrary choice (as when things are presented using coordinates)
and that barebones reality is what the quantum mechanics is about

I have always appreciated the spareness of LQG----it doesn't seem to have anything in it that isn't needed to describe a quantum theory of 4D spacetime. But to get started, LQG does employ a differentiable manifold and connections thereon. That takes in a batch of arbitrary mathematical equipage (physically meaningless "gauge" accessory) which then has to be factored out later. But I thought that LQG kept gauge to a bare miniumum. After all, how could one ever get started without an underlying smooth manifold?

Systems of coordinates are an arbitrary physically meaningless choice but how do you get started without them?

Well the framework for Lorentzian path integral, or DT, is even more stripped down nitty. No coordinate system. It seems right. have to go, will try to get back to this later.

nightcleaner · Dec 20, 2004

Code:

                             0                                            1
                             1  

                           1     1                                     1    1     
                           0     1

                        2     2     2                             1      2       1
                        0     1     2

                     3     3     3     3                    1        3        3        1
                     0     1     2     3
  
                  4     4     4     4     4           1         4        6         4       1
                  0     1     2     3     4     
                           n pick k                                pascal

marcus · Dec 20, 2004

bravo Cleaner
I will go over to the other thread and do an example
============
some side comments
since the essential thing about space is relations (next-to, between, around) so that space is in some sense a compendium of all those spatial relations then it is intuitive to me that a basic piece of space would be a simplex.

and it seems reasonable that global geometry would consist of saying HOW THEY ARE GLUED

but the minimal element of space, I could see, might be a tetrahedron---basically just 4 points

and for a path integral describing the evolution of space one would want to build it of the fivepointer analog (the simplex with 5 points and 5 tetrahedral walls)

OR, if that one would get a quantum model of spacetime by TAKING THE LIMIT with smaller and smaller simplices.

I mean that space is not actually to be imagined as diced up into little simplices, because maybe there IS no minimal distance. Maybe we just THINK that Planck length indicates some fundamental minimal length and it really doesnt! But even so it could be that the right approach to quantizing is to divvy up into simplexes and then make the simplexes smaller and smaller. Because the simplex approximation is a good approximation to how space behaves.

marcus · Dec 21, 2004

two kinds of simplexes in 4D

suppose we go along with Loll and Ambjorn and we say OK
simplexes are basic
and we are going to have a "path integral"

then we are going to get to recognize two kinds of fivepoint simplexes
or, if you'd rather, two types of orientation.
that is because CAUSALITY layers spacetime
a simplex can stand like a pyramid with 4 points in one spatial layer and the remaining 5th point upstairs in the next layer
or it can be upside down with the 5th point in the prior layer
(that is really the same kind)

in this case there are 6 spacelike edges and 4 timelike edges (connecting the 5th point to the other 4)

but there is another kind of fivepointer you maybe did not expect that may be thought of as dual to this one----it has 4 spacelike edges and 6 timelike!
this kind has 3 points on the ground and 2 points upstairs in the next layer (or turning it over) downstairs in the prior layer.

In Ambjorn and Loll's path integral approach each 4simplex has a piece of MINKOWSKI space in it. What could be a nicer material for them to be made of? All the simplexes are chunks cut out of the familiar 4D flat space of 1905 special relativity.

The two types of 4simplexes----call them (4,1) and (3,2) and remember there are flipped versions (1,4) and (3,2) that are so similar to the first two that we don't make a point of distinguishing----are two ways that Minkowski space can be oriented so as to sit in the simplex.

when these little lego-bricks are glued together to make a spacetime PATH (from some initial to some final geometry of space)
then the GLUING HAS TO RESPECT the lightcones in each block. The fitting of face to face has to respect the way Minkowski space sits in each simplex.

that is why Renate Loll tells us about the two types of 4simplex. So we won't forget and try to stick two faces together in a way that disrespects the Minkowski causality, or lightcones, in the two neighbor pieces.

the two types are shown in her picture Figure 5 on page 11
of
http://arxiv.org/hep-th/0212340
this paper I esteem more and more because of its
occasional kindergartenness
I just wish it were that way all the time
the simpler the better. amen.

marcus · Dec 21, 2004

All Geometry Is In The Gluing

On page 10:
"... no local curvature degrees of freedom are suppressed by fixing the edge lengths; deficit angles in all directions are still present, although they take on only a discretized set of values. In this sense, in dynamical triangulations all geometry is in the gluing of the fundamental building blocks. This is dual to how quantum Regge calculus is set up, where one usually fixes a triangulation T and then “scans” the space of geometries by letting the l_i's run continuously over all values compatible with the triangular inequalities..."

This is just a reminder that after all spacetime is nothing but a PATH between two geometries of space---the way it is now and the way it will be later (or was earlier)

In the Feynman path integral spirit, one says that the path a particle follows in getting from here to there DOES NOT EXIST. the path does not exist and there is no unique path that it follows!
It just somehow gets from here to there, and to calculate a quantum mechanics amplitude of it doing so, we make a weighted sum over all the paths. An integral that mooshes together all the paths from here to there, even crazy ones.

OK now SPACETIME DOES NOT EXIST EITHER
there is just the way space was shaped before
and the way it is shaped now
and there are LOTS OF PATHS of geometry to connect from then to now.
And we have to be prepared to average---to take a weighted sum including all the paths even ones that seem quite unlikely
this is the Feynman path integral philosophy (which has a pretty good track record so probably isn't totally out of step with nature)

Now what Ambjorn and Loll need is a machine that will generate a random geometry path from spatial shape A to spatial shape B.
And all geometry is in the gluing this means the machine
has to be able to output a random 4D TRIANGULATION that gets from shape A to shape B
which means it has to find ways of gluing uniformsize fivepointer simplexes
of those two orientation types together, so as to connect from A to B (3D conditions of space before and after)----and do it in an orderly layered way.

the more I read of this explanation by Loll the more I think that this is actually what a quantum theory of gravity ought to look like.

I mean that it ought to provide a path integral in the space of geometries.
Or a measure on the space Geom(M) of 4D geometries.
I DONT CARE IF IT IS SIMPLICIAL or not. Simplexes and gluing is just one way of describing a point in Geom(M)-----just one way of specifying a 4D geometry-----i.e. a path from A to B.

If someone can find a general way of describing a 4D geometry that is less messy than with simplexes that would be great! however my experience with coordinates is that the minute you try to do it with coordinates and metrix and ten-sores and coneckshuns, in that moment you have opened the closet of the nineteenth century and it is very difficult to close the door back up.

Another nice thing is that it doesn't matter if the path is jagged and zigzag because its QUANTUM so it gets blurred with other paths.
this is a great thing, and it is reminiscent of the original Feynman path integrals with were zigzag piecewise linear jagged and thus completely unrealistic paths---- the real particle wouldn't behave like that but it DOESNT MATTER you still calculate good results because the jagged things are blurred together in the weighted average. Well the same thing happens here: the Ambjorn Loll approach is intrinsically quantum because when you glue simplexes together, especially these uniformsized ones, you almost never get anything FLAT you get something which a PF poster has called a "broken glass" look. But all that averages out and the overall effect can be smooth.

Renate mentions that somewhere. i will try to find the page.

nightcleaner · Dec 21, 2004

marcus said:

I mean that space is not actually to be imagined as diced up into little simplices, because maybe there IS no minimal distance. Maybe we just THINK that Planck length indicates some fundamental minimal length and it really doesnt!.

Maybe. But consider the Compton wavelength, where for example the Compton wavelenght of an electron is calculated from the energy of the electron. If a universe has a measurable amount of energy, then it should have a minimum Compton wavelength. Since more energy means smaller wavelength, the Compton wavelength of a universe should be the smallest length possible in that universe.

You could substitute "measurment" for "universe" in the case of any real world observational system.

If there is a minimal length, then there is a minimal time, given the maximum velocity c where c= minimum length/minimum velocity. All the other units, such as energy, power, voltage, current, resistance, etc can be calculated from these base unitis, see Wikipedia, Natural units.

http://en.wikipedia.org/wiki/Natural_units

I would like to challenge the assertion found in Kaku (Hyperspace p. 10) and elsewhere that humans cannot visualize in four dimensions. I base my proposition on my personal experience of discovering binocular vision at a delayed age, so that I can remember vividly the experience of "seeing" the world in 3d for the first time, when before I had "seen" only in the flat, monocular view. I can tell you it was a very exciting experience, given to me originally by my opthamologist through the careful selection of lenses and mirrors. I was sixteen years old.

Since I have had the distinct pleasure of "popping up" into the 3d vision from the 2d world, I see no reason why a further progression should not be possible from our usual and common 3d vision into a 4d vision. Or five or six or any required number of dimensions. It just takes careful thought and practice. I see regularly in 3d now, using both eyes at once, because once I had seen how beautiful it is, I practiced it until I could do it without mirrors and lenses.

Vision in four dimensions is not much more difficult. Anyone who can catch a baseball should have no trouble with it. A catcher has to know where the object is, where it was a moment ago, and where it will be by the time of interception. Moving across a field to catch a ball on the run is clearly a four dimensional activity. Why should we have difficulty seeing what we are already able to do?

nightcleaner · Dec 21, 2004

marcus said:

but there is another kind of fivepointer you maybe did not expect that may be thought of as dual to this one----it has 4 spacelike edges and 6 timelike!
this kind has 3 points on the ground and 2 points upstairs in the next layer (or turning it over) downstairs in the prior layer.

Ok so by upstairs and downstairs here you are meaning in the instant next in the future or in the past? Please confirm this so I know I have gotten your point.

nightcleaner · Dec 21, 2004

marcus said:

This is just a reminder that after all spacetime is nothing but a PATH between two geometries of space---the way it is now and the way it will be later (or was earlier)

In the Feynman path integral spirit, one says that the path a particle follows in getting from here to there DOES NOT EXIST. the path does not exist and there is no unique path that it follows!
It just somehow gets from here to there, and to calculate a quantum mechanics amplitude of it doing so, we make a weighted sum over all the paths. An integral that mooshes together all the paths from here to there, even crazy ones.

OK now SPACETIME DOES NOT EXIST EITHER
there is just the way space was shaped before
and the way it is shaped now

I have to challenge this view of the Feynman path integral. This interpretation depends on the idea that "really" the particle can only follow one path, no matter what the math says, no matter what the two slit experiment says. One particle, one path.

However, there is another interpretation, one which is fully consistant with the Feynman path intergral, as described in Quantum Electrodynamics. That is the many worlds interpretation of Everette, Deutsch and others, or in my idiosyncratic formulation, the many times interpretation. In this paradigm, the particle does indeed follow every path available to it, just as a single photon is shown to reflect off of every part of a mirror in QED, which is an unavoidable result. This is what the photon or the particle actually does. What we see in our 3d 1t vision is only one edge of the simplex which the object occupies.

This view makes all the path integrals real, as opposed to the method you have chosen, which says only one can be real, while all the others are some sort of statistical trick, a mathematical illusion. Why not use Occam? You already have huge evidence that the other dimensions are present, and that they have a definable geometry, and that our usual vision is limited to 3d in space and one in time.

Four pick three, Marcus. There are four dimensions in spacetime, of which we pick three to hold our view of space, leaving one of time. How many ways are there to do this? Four ways, Marcus. Four possible paths of time from any instant. You choose.

When we move through four dimensional spacetime, at any instant there will be three dimensions of choice (space) and immediately beyond them but still in our quantum view a fourth dimension, which is time. The fourth in this case is not unique, but one of four possible time dimensions. The fifth point of the simpex? You are standing upon it. You the observer, three space, one time, five points.

marcus · Dec 21, 2004

nightcleaner said:

Ok so by upstairs and downstairs here you are meaning in the instant next in the future or in the past? Please confirm this so I know I have gotten your point.

yes.
I am picturing spacetime as (they often say) folliated
that is to say "leaved", or layered
like philo dough
this is still at an intuitive stage for me and I cant
answer any very rigorous questions

but we do seem to be seeing it similarly
so on a visual level things are ok.

this folliation is a kind of representation of causality or
temporal ordering, as I see it, deeper down is into the past

marcus · Dec 21, 2004

nightcleaner said:

...
Four pick three, Marcus. There are four dimensions in spacetime, of which we pick three to hold our view of space, leaving one of time. How many ways are there to do this? Four ways, Marcus. Four possible paths of time from any instant. You choose.

When we move through four dimensional spacetime, at any instant there will be three dimensions of choice (space) and immediately beyond them but still in our quantum view a fourth dimension, which is time. The fourth in this case is not unique, but one of four possible time dimensions. The fifth point of the simpex? You are standing upon it. You the observer, three space, one time, five points.

this is witty and entertaining but...
well and provocative too, but...
I probably am not going to respond because of a deeply engrained
intellectual laziness.
besides my wife is playing an Elvis Presley's greatest hits collection which she does whenever she sews (it helps regress back to the 1950s when women DID sew and it all seems to fit) and how can I think philosophy under the circumstances

marcus · Dec 21, 2004

I liked your reasoning about the Compton wavelength
It is a little like the Zen experiment of dropping a drop of ink into
a glass of water and watching it until...

As I recall, the Planck mass is 22 micrograms
so if the mass of the universe is a billion Planck masses (of course it is really much more, since that is only 22 kilograms!)
then the compton of the universe is one billionth of the Planck length.

nightcleaner · Dec 21, 2004

marcus said:

Now what Ambjorn and Loll need is a machine that will generate a random geometry path from spatial shape A to spatial shape B.
And all geometry is in the gluing this means the machine
has to be able to output a random 4D TRIANGULATION that gets from shape A to shape B
which means it has to find ways of gluing uniformsize fivepointer simplexes
of those two orientation types together, so as to connect from A to B (3D conditions of space before and after)----and do it in an orderly layered way.

This is what I have been trying to give you. Consider the Compton wavelength of the universe. Consider a sphere of radius one universal Compton wavelength (call it a Planck, it is shorter to spell and afaik it is the same thing). Consider a dense stack of these spheres. That is what 4d spacetime looks like.

Now consider the observer as if the observer could occupy a single sphere. I know we are too big to fit into a single sphere of that size, but suspend your disbelief on this point for a moment and I will try to remember to come back to it. For now, just accept that there are larger spheres which we do fit into, and they behave the same way as the Planck size spheres I am describing.

If the observer occupies one sphere, then there are twelve spheres around the observer. Each of these spheres is a next instant. In a sense, they make a layer around the observer, a layer of events that are infalling at the speed of light. The observer in the one sphere must wait until the next instant to know what is happening in the next layer. In a sense, the universe of the observer is growing one layer per instant.

But the observer is always moving. I can tell you why the observer has to move in a moment, but stay with me here. Because the observer is moving, there are some spheres which are left behind. No information from those spheres can catch up to the moving observer. Altho all twelve spheres are anext to any spacetime instant, the observer only "sees" the ones directly in the path of the movement. The others are left behind.

Hence, the observer seems to occupy a four dimensional spacetime universe in which there are three visable spatial dimensions and one time dimension. The observer follows a path, and sees all other objects following paths. The real higher dimensional structure is not seen, but only the path edges of the simplices. But it exists and we know it exists because 1. The math requires it (eg string theory); and 2. Observations in the laboratory confirm it (eg 2 slit wave particle duality experiments); and 3. Cosmological observations confirm it (eg, GR and dark energy/ dark matter).

Now for gluing simplices. Yes, you can build spaces by gluing simplices. Not all spaces that are possible in geometry are possible in our universal conditions. AJL seem to want to use the octet space formed by building entirely with tetrahedrons. I have explained elsewhere why this is not the optimal space for modeling our univerese. One must ask where the tetrahedrons come from? I have given a derivation from Planck lengths. It does not involve only tetrahedrons, but also includes cubes. It can be seen to hold both triangular simplices and tetrahedral ones, as well a cubic forms.

The isomatrix. The cubeoctahedron. Face Centered Cubic. Please look at the link.

nc

nightcleaner · Dec 21, 2004

Hi Marcus. I just now saw that you were online and replying. By all means be with your family. We have to keep our priorities straight, and this stuff here is all starlight on a distant sea. I trust you will return again, refreshed and ready to trade points with me? Be well, on this longest of nights.

nc

nightcleaner · Dec 21, 2004

marcus said:

I liked your reasoning about the Compton wavelength
It is a little like the Zen experiment of dropping a drop of ink into
a glass of water and watching it until...

As I recall, the Planck mass is 22 micrograms
so if the mass of the universe is a billion Planck masses (of course it is really much more, since that is only 22 kilograms!)
then the compton of the universe is one billionth of the Planck length.

The Planck mass is derived in a different way from the Planck length, but I value your attempt to quantify this, since I work easier with words and images than with numbers. I hope we can work through this so I can see if the ideas match up with the observations. At first glance you have provided a challenge. Thanks!

I have been studying this for a while now and let's see if I can get it right in one go.

The Planck length and Planck time were given in pretty much their current form by Max Planck about a hundred years ago. No one seems to know how he came on the right numbers, but the Planck length is about 10^-34 cm, and the Planck time is about 10^-43 seconds, which when divided should give the speed of light in cm per second at about c=10^9cm/s. I'll have to check and see if I got those numbers right.

The Planck mass is derived by considering how much mass can be crammed into a small space before it collapses into a Schwartzchilde singularity. I think if memory serves that the small space is a proton diameter. The mass that can be crammed into a proton diameter is about the mass of a small flea.

So, your estimate may not be based on first principles.

I am going to go look up the numbers and derivations. Maybe I'll even find out how to calculate the Compton Wavelength while I am at it.

Thanks,

nc

nightcleaner · Dec 21, 2004

marcus said:

yes.
I am picturing spacetime as (they often say) folliated
that is to say "leaved", or layered
like philo dough
this is still at an intuitive stage for me and I cant
answer any very rigorous questions

but we do seem to be seeing it similarly
so on a visual level things are ok.

this folliation is a kind of representation of causality or
temporal ordering, as I see it, deeper down is into the past

just have to answer this first. Jumping to the end of my line of reasoning without going over the middle ground, when we get to our current spacetime, the universe we find ourselves in is very nearly flat, and we are very nearly large. The past is in, the future is out, and we exist in a thin layer. The layer is very nearly regular, but has some flaws in it which come from the difference between the close pack face centered cubic form and the curvature of spacetime at our distance, quite a large distance, from the origin. This is a spacetime distance and is reflected in our observations of the cosmos, eg CMBE, but is not to be thought of as distant from us in space. The origin now and always is within. The flaws are matter and energy, the very regular areas are "vacuum" or empty space, and the vacuum fluctuations come about because of the uncertainty of position of the flaws. You could think of the Planck spheres as being very nearly perfectly densely packed, but not quite perfectly. The little bit of slop in the fit accounts for all the phenomena we observe. We never observe the spacetime directly.

nc

nightcleaner · Dec 21, 2004

From this source:

http://en.wikipedia.org/wiki/Natural_units

I get this derivation:

<tr><td>'''[[Planck mass]]'''</td>
<td>[[Mass]] (M)</td>
<td><math>m_P = \sqrt{\frac{\hbar c}{G}}</math></td>
<td>[[1 E-8 kg|2.17645 × 10<sup>-8</sup>]] [[kilogram|kg]]</td>
</tr>

but I see it does not show the formula in this forum. I'll have to review my latex skills.

[tex]m_p=\sqrt{\frac{\hbar c}{G} [/tex]

That was easy. Just replace math with tex and <> with []

so

[tex]m_p=\sqrt{\frac{\hbar c}{G} [/tex] = 2.17645 x 10^-8 kilogram

I guess that's about 2.2x10^-5 grams, or 2.2x10^-2 micrograms, or .02 micrograms? Anyway within a couple orders of magnitude.

Now to find out how to calculate Compton wavelength.

I find the Compton wavelength of the electron to be listed at :

http://en.wikipedia.org/wiki/Physical_constant

as

[tex]\lambda_e=h/m_e c[/tex]

This is not helpful. I see that the Compton wavelength already assumes the value of the Planck length, h, is known. If we write

[tex]\lambda_U=h/m_U c[/tex]

then lambda_U=h when m_U c =1. Since c is 1 in base units, then m_U is just 1 also. But what if we go back to CGS units? When is the mass of the universe times the speed of light equal one? When the mass of the universe is the inverse of the speed of light. c = 3x10^8 meters/second so 1/c = 3x10^-9 seconds per meter. What kind of a mass is that?

Lets try a different tack. I interpret Lambda_e as the radius of the region in which an electron is most probably found. (Since an electron is a point particle, this radius is really the radius of the area in which the electron is most likely to interact with photons via quantum fluctuations and virtual particles.) So Lambda_U would be the likely radius of the universe. We can get that from cosmological data. But should we use the inflation value of 78 billion light years, or the age of the universe data of 13 billion light years? Well they are only an order of magnitude or so apart.

Anyway the radius of the universe is equal to the smallest possible length in the universe divided by the mass of the universe times the speed of light. Sounds easy enough. Solving for h, h equals the radius of the universe times the mass of the universe times the speed of light. Ooops. That looks like a big number.

But the extremely small is the inverse of the extremely large. Can we be justified to say then that the formula should be inverted on one side? Then we would have radius universe = mass universe times speed of light, divided by smallest possible length. So smallest possible length equals mass of universe times speed of light, divided by radius of universe.

[tex]\lambda_U=1/\lambda_p[/tex]

[tex]\lambda_U=m_U c/h[/tex]

[tex]h=m_U c/\lambda_U[/tex]

nightcleaner · Dec 22, 2004

ok I think I see it better now. A Compton wavelength is not a length at all, but a frequency, T^-1. So to recover a length from the Compton wavelength, it is necessary to divide a velocity by that frequency.

working on it. Have to sleep. nc

marcus · Dec 22, 2004

nightcleaner said:

[tex]m_p=\sqrt{\frac{\hbar c}{G} [/tex]
= 2.17645 x 10^-8 kilogram

I guess that's about 2.2x10^-5 grams,..

that is the same as 22 x 10^-6 grams

that is the same as 22 micrograms

because a microgram is a millionth of a gram----that is, 10^-6 gram

I am glad to see you using Latex

in many discussions you will find h standing for a version of Planck's constant (not Planck length) and hbar standing for a reduced version of Planck's constant, namely h divided by 2 pi.

the formulas defining the Planck quantities customarily use hbar, as you did when you wrote:
[tex]m_p=\sqrt{\frac{\hbar c}{G} [/tex]
but the formula for the Compton sometimes uses h and sometimes hbar, so what people call the compton can vary by a factor of 2 pi.
humans, imperfect as they are, sometimes waffle a bit in their notation
requiring tolerance and goodwill on everyone's part

marcus · Dec 22, 2004

montecarlo method: find the answer by random wandering

in the path integral approach to quantum spacetime
one has an integral which is an average over all geometries

(a weighted sum of 4D geometries that get you from one 3D condition of space to another one later on, but we have quantum uncertainty about what went on in between)

now Geom(M) the vast warehouse of all possible 4D geometries is a huge place to wander around in
and actually summing or integrating over all those possibilities (as a very dutiful conscientious person would do when asked to find the average) is next to impossible
(there are more degrees of freedom in the geometry of a whole spacetime than, for instance, in the mere path of a single particle going from here to there----so the vastness of the possibilities is vaster)

nevertheless that is the idea of quantizing, you have a bigspace of all possibilities and you define wavefunctions on the bigspace and you define quantum states and you integrate and so on----you have to be able to describe a blur of possibilities and an indefiniteness about how you got from one situation to another

so what to do? the Monty approach says to define a small set of MOVES which allow you to do a RANDOM WALK in the vast warehouse of geometries------and go for a walk, and get lost, and wander about AVERAGING AS YOU GO

this is very zen because it uses the vastness in order to overcome the vastness----because it is very huge you can wander randomly and be sure of not coming back or getting caught in a loop---and therefore you can make a RANDOM SAMPLE and the average of a random sample is a good estimate of the real average.

So Renate "the Fox" Loll defines what she calls the Monte Carlo moves, which are rearrangements of the simplex-gluings which get you from one geometry to another "nearby" geometry

these moves are socalled "ergodic" which means that if you do them enough you will eventually pass thru every configuration in the warehouse.
ergodic is an idea about mixing which means THOROUGH
the moves are very little but but they thoroughly stir the geometry
so if you do enough of these little moves you will completely stir things up.

Jan Ambjorn should be praised for this too. And it goes back to 1980s and 1990s when people applied it to "euclidean" (not lorentzian) path integrals and dynamical triangulations. but even though the Monty method did not originate with Ambjorn and Loll I find it admirable and they are the ones that finally applied this approach to the Lorentzian setup and finally, in 2004, made it work right.

nightcleaner · Dec 22, 2004

Thanks Marcus. I see I need to brush up on my metric prefixes. I really am being dragged away from here by commitments. Be well, I'll be back tomorrow or later today if I can manage. Richard.

marcus · Dec 22, 2004

nightcleaner said:

Thanks Marcus. I see I need to brush up on my metric prefixes. I really am being dragged away from here by commitments. Be well, I'll be back tomorrow or later today if I can manage. Richard.

no rush
take care of the commitments
the green arrow in the title of my previous post was an accident of the fingers

marcus · Dec 22, 2004

Bianca Dittrich did her Diploma thesis on dynamical triangulations approach to quantum gravity, back in 2001.
then she moved over to Loop and working with Thiemann.

she could move back.

Renate Loll has also migrated between Loop and DT.

they are kindred approaches, even though they do not agree about the
discrete spectrum of area and volume (which I think makes it likely that only one can be successful in the long run)

Bianca's 2001 (undergrad? masters?) thesis was in German and is probably on file in Univ. Potsdam, and is called
Dynamische Triangulierung von Schwarzloch-Geometrien

marcus · Dec 22, 2004

...

so what to do? the Monty approach says to define a small set of MOVES which allow you to do a RANDOM WALK in the vast warehouse of geometries------and go for a walk, and get lost, and wander about AVERAGING AS YOU GO
...
these moves are socalled "ergodic" which means that if you do them enough you will eventually pass thru every configuration in the warehouse.
ergodic is an idea about mixing which means THOROUGH
the moves are very little but but they thoroughly stir the geometry
so if you do enough of these little moves you will completely stir things up.
...

in lower dimension versions of the theory the moves are few and comparatively easy to visualize. I want to get more familiarity with the Monty moves in 4D (where there are more moves and harder to visualize)

In 4D the authors (hep-th/0105267) give us a set of 10 moves
but some are just the REVERSE of others so, depending how you count there are really only 5 (or maybe 6) different moves

these can be given names which are just a couple of numbers like for example these:

(2,8)
(4,6)
(2,4)
(3,3)

The move called (4,6) takes a cluster of 4 chunks and redivides it so it becomes 6 chunks

the reverse of that could be named (6,4) and simply does the reverse.
the authors have a picture of how this redividing is done---Figure 7 on page 25---and they also spell it out by listing the vertices of the chunks---on page 24. It is actually pretty simple.

This redividing up of clusters of chunks RESPECTS the layering, or causality, or foliation, or Lorentzianity-----whatever you want to call it. If some tetrahedron starts out purely spatial and it gets divided up then the resulting things are purely spatial and so on.

I guess I would like to run down the list of these moves and try to say in words what they do.

Remember that Geom(M) is the bunch of all the 4D geometries of the universe from bang to crunch (so far in their simulations they have a finite life universe with a crunch)
We want to see how the geometry of the universe works---quantum style---and so we are exploring this huge Geom(M) set of possibilities by doing a random walk in it. We make little bitty steps from one 4D geometry to another by just changing some detail of some cluster of simplexes.

the marvel is if we make enough of these moves, take enough of these little bitty steps, we get a representative random sample of how the geometry of the universe works

check out some of their graphics, like Figure 5 of hep-th/0411152

On page 2 of hep-th/0105267 the authors refer to Geom(M) as
"the mother of all spaces" and also as the "space of geometries" which
seems reasonable since it contains all the possible spacetimes as its elements-----a spacetime geometry is a POINT in Geom(M)

this means that wandering around in Geom(M), the space of geometries, means visiting many different spacetimes geometries in turn.

these Monty moves may seem very weak and insignificant, each one changes just one cluster somewhere in the universe, and not by very much either. but the effect of the steps is cumulative

Anyway, I want to review these 5 or so Monty moves

marcus · Dec 22, 2004

marcus said:

...
In 4D the authors (hep-th/0105267) give us a set of 10 moves
but some are just the REVERSE of others so, depending how you count there are really only 5 (or maybe 6) different moves

these can be given names which are just a couple of numbers like for example these:

(2,8)
(4,6)
(2,4)
(3,3)

The move called (4,6) takes a cluster of 4 chunks and redivides it so it becomes 6 chunks

...

Instead of saying 4D simplex I will say "chunk"
A chunk has 5 points and 5 tetrahedron for its sides.
the easiest way to picture a chunk is to put down a tetrahedron as a base
(like the base of a pyramid, sort of) and then put a new apex point "up in the air" and imagine drawing lines from each point of the tetrahedron base up to the the new point.

here is something you can visualize because it is in ordinary 3D:
take a tetrahedron and put a point in the middle of it and connect the 4 orig points to the centerpoint. Presto you have divided the orig tet
into FOUR tets.

each of the four orig. faces becomes like the base of one of the four new tets and the centerpoint becomes like the common apex
Now to business:

(2,8)
now we are in 4D and we have a spatial tetrahedron in the present and two apexes one up in the future and one down in the past. So we have a CLUSTER OF TWO CHUNKS meeting at a shared tet.

put a centerpoint into that shared tet, dividing it into FOUR tets, and connect each of them to the two (future and past) vertices.
pretty clearly we now have a CLUSTER OF EIGHT CHUNKS.
so that is what is called the move (2,8)
and there is an obvious reverse move (8,2)

(4,6)

there is a 3D thing that is easy to visulize where you start with TWO tets butting together at a shared triangle, like two pyramids base-to-base with one's apex out East and the other's apex out West. And you erase that triangle and draw a line between the east and west apex points and suddenly you see that you have THREE tetrahedrons.

well now in 4D suppose you have two tets in the present, butted together like that, and each connected to an apex up in the future and to an apex down in the past-----so you have a cluster of FOUR chunks

if you do that 3D redivision of the spatial pair of tetrahedrons so you now have 3 tetrahedrons in the present----and then connect each of them up and down to the future and past apexes as before, then you have a
cluster of SIX chunks. that is the (4,6) move and the reverse move is obvious.

The (3,3) and the (2,4) moves involve cluster of fewer chunks. I guess I will take a break here and describe them later.
These are spelled out and depicted around page 23 of hep-th/0105267

selfAdjoint · Dec 23, 2004

Marcus, I just found http://yolanda3.dynalias.org/wb/whoiswb.html ; check him out.

marcus · Dec 23, 2004

Marcus, I just found
http://yolanda3.dynalias.org/wb/whoiswb.html
check him out.
-----------
thanks, I will do so at once
strange URL
-----------

with Fahrenheit near zero by Lake Winnebago
you are well situated to appreciate the photo album
of life in the Bahamas. Wolfgang Beirl has a nice
offshore lifestyle.

his real business appears to be modeling financial markets
like the US stock market
his most recent lattice gravity posting (that he gives a link to)
is mid 2003

marcus · Dec 23, 2004

http://arxiv.org/find/hep-lat/1/au:+Beirl_W/0/1/0/all/0/1

19 simplicial/lattice quantum gravity papers

3 in 1996 but only two since then

Here is Beirl's record of some communications with Lubos Motl
http://yolanda3.dynalias.org/tsm/tsm.html
that began with Lubos comment on the recent AJL paper

nightcleaner · Dec 23, 2004

Marcus, in regard to LQG and DT, you said:
"they are kindred approaches, even though they do not agree about the
discrete spectrum of area and volume (which I think makes it likely that only one can be successful in the long run)"

Marcus could you take a moment to expand on this? I would like to understand more about what is meant by discrete spectrum of area and volume. I think I know what area and volume are. I have a notion of discrete spectrum but need to verify. And then, in what respects do not agree?

Thanks

nc

nightcleaner · Dec 23, 2004

marcus said:

Instead of saying 4D simplex I will say "chunk"
A chunk has 5 points and 5 tetrahedron for its sides.
the easiest way to picture a chunk is to put down a tetrahedron as a base
(like the base of a pyramid, sort of) and then put a new apex point "up in the air" and imagine drawing lines from each point of the tetrahedron base up to the the new point.

here is something you can visualize because it is in ordinary 3D:
take a tetrahedron and put a point in the middle of it and connect the 4 orig points to the centerpoint. Presto you have divided the orig tet
into FOUR tets.

each of the four orig. faces becomes like the base of one of the four new tets and the centerpoint becomes like the common apex
Now to business:

(2,8)
now we are in 4D and we have a spatial tetrahedron in the present and two apexes one up in the future and one down in the past. So we have a CLUSTER OF TWO CHUNKS meeting at a shared tet.

put a centerpoint into that shared tet, dividing it into FOUR tets, and connect each of them to the two (future and past) vertices.
pretty clearly we now have a CLUSTER OF EIGHT CHUNKS.
so that is what is called the move (2,8)
and there is an obvious reverse move (8,2)

(4,6)

there is a 3D thing that is easy to visulize where you start with TWO tets butting together at a shared triangle, like two pyramids base-to-base with one's apex out East and the other's apex out West. And you erase that triangle and draw a line between the east and west apex points and suddenly you see that you have THREE tetrahedrons.

well now in 4D suppose you have two tets in the present, butted together like that, and each connected to an apex up in the future and to an apex down in the past-----so you have a cluster of FOUR chunks

if you do that 3D redivision of the spatial pair of tetrahedrons so you now have 3 tetrahedrons in the present----and then connect each of them up and down to the future and past apexes as before, then you have a
cluster of SIX chunks. that is the (4,6) move and the reverse move is obvious.

The (3,3) and the (2,4) moves involve cluster of fewer chunks. I guess I will take a break here and describe them later.
These are spelled out and depicted around page 23 of hep-th/0105267

Marcus,
You said
"here is something you can visualize because it is in ordinary 3D:
take a tetrahedron and put a point in the middle of it and connect the 4 orig points to the centerpoint. Presto you have divided the orig tet
into FOUR tets."

Are you accounting here for the condition that the new point has to be non-co-spatial with the original 4 of the tetrahedron?

You said
"each of the four orig. faces becomes like the base of one of the four new tets and the centerpoint becomes like the common apex"

The four new tets each have a 2-simpex base, and these four bases share a common 3-space. The apex however is in 4d, and is not really in the common 3-space of the bases. The apex is best thought of as being infinitely removed from the 3-space of the bases, which is to say it is not in the common 3-space of the bases at all. So the lines that join the points of the bases to the apex are infinitely long parallel time-like lines, and the apex itself is not a point, but another 3-space tetrahedron offset an infinite distance, so that it could be represented as a point anywhere in the 3-space of the bases. You chose to represent it as if it were in the center of the original tetrahedron, which is a good choice since it represents each of the infinitly long timelike lines as equal in length in the 3-space, but of course infinity does not equal infinity, so the apparent equality does not hold, but is best remembered as an artifact of the visualization process, much as in a two dimensional drawing of a three dimensional object two points that seem to be close together in the drawing can actually represent points that are far apart in the 3-space. Think of a drawing of a cube. The near corner and the far corner can seem to be in the same place on the drawing, but we mentally recall that they are really in separate planes.

I am trying to follow your analysis of the chunks and moves, but have worked myself into some kind of a cross-eyed cross-legged 4-d stance and need to take time out for sugar and protien to balance the caffeine fix. As the Arnold says, with a steely gleam in his android eye, "I'll be back."

nc

281 views of this thread as of this posting

marcus · Dec 23, 2004

in ordinary 2D, on a sheet of paper, draw an equilateral triangle.

then put a point in the middle and connect it to each of the orig. vertices.
this divides the triangle into 3 triangles (still on the orig. 2D piece of paper)
everything is "co-spatial"

do the same with a tetrahedron,

marcus · Dec 23, 2004

nightcleaner said:

Are you accounting here for the condition that the new point has to be non-co-spatial with the original 4 of the tetrahedron?
...

no I am counting on the new point being actually inside the tetrahedron
and so part of the same 3D space that the tetrahedron occupies

[clarification: in this case we are not making a 4simplex, we are
DIVIDING UP an existing tet to make 4 smaller tets, by placing a point in the center]

marcus · Dec 23, 2004

nightcleaner said:

Marcus, in regard to LQG and DT, you said:
"they are kindred approaches, even though they do not agree about the
discrete spectrum of area and volume (which I think makes it likely that only one can be successful in the long run)"

Marcus could you take a moment to expand on this? I would like to understand more about what is meant by discrete spectrum of area and volume. ..., in what respects do not agree?
...

Here is a brief response to this question. I would be glad if anyone wants to explain it in more detail.
this issue points to a crucial difference between LQG and DT.

DT is fairly new and i do not know of the area and volume operators being studied yet. I suspect that when they are defined they could turn out NOT to have discrete spectrum.

But in LQG associated with any material surface, like a desktop, there is an operator on the hilbert space (the quantum states of geometry) which corresponds to measuring the area of that surface----it is an operator called an "observable" and it has a discrete set of possible values, including a smallest positive value.

the language is a bit technical, even a bit awkward, and gives the impression of more difficulty than there really is.

the essential is that from LQG one has learned to expect that measuring the area will give discrete levels of area, like the energy levels of an atom.

as an atom can be excited and made to go up into a higher energy level (or an electron of the atom can, however you think about it)
so also the gravitational field can be excited and go up into a stage where things have more area, and also more volume.

but the areas and volumes only go up in little "jumps"
(too small to measure with today instruments)

and this is a characteristic of LQG-------indeed in LQG COSMOLOGY even the size of the universe goes up in miniscule "jumps" and at the time of the bigbang this turns out to be significant (even tho the steps are very very small it still matters)

But I have not seen any hints that when they get DT more developed and get area and volume operators, that they will have a discrete set of possible values---a discrete spectrum---and that areas and volumes will increase and decrease in jumps (as the gravitational field changes).
So this could be a serious disagreement between DT and LQG

nightcleaner · Dec 24, 2004

Hi all

Some more on 4d visuals.

We have seen how the 3d simplex is a tetrahedron. Now we wish to consider the shape of things in the 4th dimension. We have discussed how logical development by geometric principles lead us to think that the 4d simplex will have five points. Moreover, these five points consist of a 3d simplex tetrahedron, and one point which is not in the same 3d space as the tetrahedron. This follows from the condition placed on upper dimensional points that they not be part of the lower dimensional simplex.

One way to model the 4space simplex, which will have five points, is to place the fifth point somewhere in the same 3space as the tetrahedron and then try to remember that it is not really a part of the same 3space. We then draw lines from each point of the tetrahedron through 3space to the new point. One convenient way to do this is to place the point at the center of the tetrahedron, thus dividing the tetrahedron into four 3spaces which are interior to the tetrahedron.

This model may prove useful, but we need to remember that the central point is not allowed to be in the same space as the original tetrahedron. I have suggested that we think of the fifth point as being offset in time, or alternately, offset to another 3space which is at a sufficient distance so that there can be no contact with the original 3 space. This offset distance is, for any practical purpose, infinite. This means that the interior lines to the central point in the tetrahedron are infinite. We could represent this infinity either by a gauge variance or by a space-like curvature.

Infinities are not welcome in physics problems because they lead to divergent conclusions. In the math sense, infinity is not equal to infinity so calculations are nearly impossible, making any theory which relies on infinities non-physical. Most serious physics reasearchers rule out any such theory on the grounds that it cannot describe the physical processes we find around us in this universe. I would like to suggest that we hold on to the tetrahedron with its infinitely removed center for a moment, if for no other reason than it gives us the most symmetric possible 3space model of this 4space system.

Meanwhile, let us return to the idea that the offset is not in space, but is in time. This has the advantage of allowing us to place the fifth point in the same space as the tetrahedron but offset one unit of time, thereby removing the infinities. We can still use our model of the tetrahedron with a central point, with a few modifications.

First, we must keep in mind that this central point is a representative point, and our choice of placement at the center is merely a convenience. The point could equally well be placed anywhere in the 3space of the model, because it is not really in the 3space of the model at all, but is offset by one unit of time. The only limitation to the placement comes from the speed of light, which causes the set of possible placements in the next unit of time to be limited to a three dimensional sphere. Any placement outside the limits of the sphere results in a discontinuity between time units, and perhaps it would be best for now to regard time as continuous.

Now we can take our tetrahedron simplex in 3space, and displace it one unit of time, and regard them side by side, as if they were two tetrahedrons side by side in 4space. We can say that the tetrahedron has not actually moved at all in 3space, so all of its points in the offset space are in the same relationship to each other as they were in the original 3space tetrahedron.

But what relationship do the two tetrahedrons have, in the 3space model, to each other? That is, if we represent the original tetrahedron, call it tet1, and the offset tetrahedron, call it tet2, in the same 3space, do we have any justification for saying that the lines in tet1 are parallel to the lines in tet2? It would be convenient for visualization purposes if we could say that tet2 is not rotated compared to tet1 in the 3space model, but is it justified?

We have to remember that tet2 can be placed anywhere in the 3space model. It could be placed offset to the right of the viewer and then up, and then forward or back, with no preferred position. A sequence of these moves can result in any desired rotation, at any desired location, so we cannot justify the convenient proposition that the two tetrahedrons should have parallel lines in the 3space model

Moreover, tet2 can have any size compared to tet1, within the 3space limits set by the continuity provision as determined by the spacetime ratio, c. Tet2 could be represented as entirely within or entirely outside of tet1, and any size from a single point to the full extension of 3space surrounding tet1. Within the limits of the tet1 3space set by the discrete unit of time, every point has to be considered as equal in terms of representation for the offset.

The model now seems rather blurry, and of little use in visualization. However, we can make some improvements. We can justify some preferred conditions. For example, no matter where we place tet2, and no matter what rotation, there is always a one to one correlation between the four points in tet1 and the four points in tet2. From any apex in tet1, there are four lines leading to tet2. Likewise from any apex in tet2, there are four lines leading to tet1. We can count these lines. There are sixteen lines leading from tet1 to tet2, and sixteen lines leading from tet2 to tet1. Can we say that the sixteen lines 2=>1 are the same sixteen lines 1=>2? No.

We have to remember that there is no preferred orientation. All rotations must be considered. The lines from 2 to 1 are therefore not simple one dimensional lines. They are cones. They start as a single point in the tet of origin, but by the time they arrive at the tet of destination, they are no longer zero dimensional in cross section. Because of this fact, we cannot say that a line from tet1 to tet2 is matched by any line from tet2 to tet1. We are left with the unavoidable conclusion that there are thirty two cones.

These cones are not without structure. They expand from the origin to the offset, and moreover, they are not of consistant internal density. Rather, there is a spectrum of preferred densities within the cone. This results from the fact that the offset tetrahedron can take any rotated position. To draw the cone, we must consider all possible rotations. A moment of consideration will convince you that not all points in three space will be equally represented in these rotations.

The tet2 can be represented, in its own 3space, as unchanged in any way from tet1, except for the offset in time. This identity can be asserted as long as we keep the two 3spaces apart in our mind. The blurring of the model only comes about when we try to represent the two tets as if they were in one 3space. But it is allowed, for example, to indicate the two tets on one sheet of paper, so long as we keep in mind that they are separated by one unit of time. We can do this by drawing a circle around one of the tets to remind is that it is not in the same space as the other tet. In fact it might be a good idea to draw circles representing their spaces around each of the two tets. Then we could label one circle 3space1 and it contains tet1, and the other circle is 3space2 containing tet2. Now when we draw the lines, we have to draw not from point one tet1 to point one tet2, but from point one tet1 to the entire circle containing tet2. Each resulting cone then represents all four lines from point one to the four apexes of tet2.

Now let's consider all the possible rotations of one tet in 3space.

First we have to choose a point of origin for the rotation. The simplest choice would be the center point of the tetrahedron. This choice gives us a sphere when the tet is rotated in every possible way around it. The sphere is equal density everywhere on its surface, but the interior of the sphere has a density structure.

This density structure is definable from the existence of edge lines and surfaces of the tetrahedron. Consider for example the density of the region close to the center. This density is defined only by lines radial from the center point to the apexes of the tet. Then consider a region near to the interior surface of the sphere formed by the rotated apex points. The density of this region is also defined by the rotation of the radial lines, but in addition has definition provided by the existence of lines between the apexes. These lines are the edges of the tet. When rotated, these lines define a region limited to the difference between the radial distance to the center of the cord defined by two apexes and the radial distance to the apex itself. The center of the cord is closer to the center of the tet (origin of rotation) than is the apex.

This results in a density of definition which is not merely a spherical surface of points equidistant from the center, but is a sphere with a surface that has thickness, an inner and an outer surface with an incremental space defined between them.

But we also have to consider rotating the tet around the apex points. This gives another equal surface density sphere, but one which is larger than the rotation from the center point. It is larger because the distance from the center of the tet in the first rotation is less than the distance of each apex from the other three apexes. The sphere also has its own internal density structure formed in a similar manner to that described above. Then we have to rotate the tet around each of the other apex points.

Now we begin to see the 4d stucture in some detail. There are spheres within spheres, and spheres intersecting spheres. There are unique definable points within this 4d structure, and it has a spectrum of densities in different regions.

In this discussion, I have tried to show the limitations and conditions which can be placed on a three dimensional model of a four dimensional structure. The simplest model in three dimensions, that of a tetrahedron with a central point, is certainly useful, as long as we keep the conditions in mind.

I have also shown that a four dimensional structure is not merely an undifferentiated space, a blur of 3space, but can be shown to have definable geometric points, lines, planes, surfaces, densities, and spectra.

I have shown that mappings from points in one 3space to their corresponding points in another 3space, even when there is a one to one correspondance between the points, can not be taken as one dimensional lines but have to be considered as three dimensional objects (cones) with internal structure.

In conclusion, this discussion has application to the Regge calculus in that it shows that it is not sufficient to model 4space objects in 3space by a dynamic triangulation with variable but discrete side lengths. I suggest that a better fit to physical measurements can be achieved by spectral analysis of rotated 3space objects.

Richard

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marcus · Dec 24, 2004

I am still working on the small project of reviewing the 4D Monte Carlo moves. BTW other sets of moves would probably be OK, the moves just have to be simple and easy to program in a computer and ergodic in the sense that if you do them enough it thoroughly explores the space of geometries Geom(M).

Part of this is a re-edit of post #25 to make it clearer. In that post I got halfway thru the list of moves and then got distracted, so i will review that and then try to proceed further with it.

To have fewer syllables to say: Instead of saying 4D simplex I will say "chunk" and instead of tetrahedron I will sometimes say "tet"
A chunk has 5 vertices and 5 sides, which are tets.
the easiest way to picture a chunk is to put down a tetrahedron as a base
(like the base of a pyramid, sort of) and then put a new apex point "up in the air" and imagine drawing lines from each point of the tetrahedron base up to the the new point.

As preliminaries, here is some things you can visualize in ordinary 3D and THEY DONT REQUIRE 4D:
take a tetrahedron and put a point in the middle of it and connect the 4 orig points to the centerpoint. Presto you have divided the orig tet
into FOUR smaller tets.
(each of the four orig. faces becomes like the base of one of the four new tets and the centerpoint becomes like the common apex)

here is another 3D thing where 4D IS NOT REQUIRED. You start with TWO tets butting together at a shared triangle, like two pyramids base-to-base with one's apex out East and the other's apex out West. And you erase that triangle and draw a line between the east and west apex points and suddenly you see that you have THREE tetrahedrons. they all share that eastwest line.

we will use these two maneuvers----one is a purely 3D way to divide ONE tet into FOUR (by adding a point) and the other is a purely 3D way to divide TWO tets into THREE (by adding a line)

Now let's consider some 4D moves:

(2,8)
Suppose we have a CLUSTER OF TWO CHUNKS meeting at a shared tet. Imagine it is a spatial tet in the present plus two apexes one up in the future and one down in the past.

Put a centerpoint into that shared tet, dividing it into FOUR tets.
(as described earlier)
Then connect each of them to the two (future and past) vertices.
We now have a CLUSTER OF EIGHT CHUNKS.
That is what is called the move (2,8)
and there is an obvious reverse move (8,2)

(4,6)

Now suppose you have two spatial tets in the present, butted together at a common triangle. Suppose each is connected to an apex up in the future and to an apex down in the past-----so you have a cluster of FOUR chunks

Purely in 3D, we can redivide the spatial pair of tets to make 3 tets (as described earlier). So we now have 3 tetrahedrons in the present, and we connect each of them up and down to the future and past apexes as before, so that we have have a cluster of SIX chunks. That is the (4,6) move and the reverse move is obvious.

-----------that finishes that, the rest is just a comment------

I still have to review the (3,3) and the (2,4) moves.
All these are spelled out and depicted around page 23 of hep-th/0105267

Maybe it is worth mentioning that the moves discussed already both require 7 points. In the case of the move (2,8) the initial cluster needed only 6 points to define but one had to add a point, and in the other move (4,6) the initial cluster already needed 7 points to define-----5 for the pair of abutting tets in the present, plus two apexes in future and past.

But the moves I still have to describe, namely (2,4) and (3,3),
are simpler in the sense that they take place in the context of just 6 points.
Also these moves are interesting because THEY DONT CHANGE THE PRESENT AT ALL. More is true: they don't change spatial layer triangulation either in the present or in the future. They only change HOW YOU GET FROM ONE LAYER TO THE NEXT.

they just change the timework links that are sandwiched between spacework layers.

so these two remaining types of moves are in a way more simple, but actually I had more struggle visualizing them from the pictures in
http://arxiv.org/hep-th/0105267
maybe this is their fault (the moves really arent simpler) or else my fault, or maybe the picture's fault (maybe better pictures could be made, say by coloring)

Two World-theories (neither one especially stringy)

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