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December 23, 2014

CATEGORY: Blog [back]
TOPIC: Nonlocality versus nonreality, by H. Dieter Zeh [refresh]
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FQXi Administrator Zeeya Merali wrote on Nov. 28, 2008 @ 12:08 GMT
One of our new bloggers, Vlatko Vedral, has been posting a lot on the subject of “reality”—raising the hackles of FQXi’s Dieter Zeh in the process. In a guest post, Zeh responds to Vlatko and defends the maligned concept of reality.

From Dieter Zeh:

Vlatko Vedral has recently published three blog posts that are concerned with the central interpretational dilemma that has...

view entire post


this post has been edited by the forum administrator

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amrit wrote on Jan. 6, 2009 @ 17:39 GMT
Dear Prof. Zeh

Regarding your statement

""""The most important prejudice about reality is that it must be defined in space and time.""""

i agree deeply. We can not imagine physics without time. For new understanding of time there is an elegant and practical solution:



1. cosmic space (vaccum) in which move massive objects and elementary particles is atemporal

2. with clocks we measure duration and numerical order of their motion

3. time is a coordinate of motion

4. time exists only when we measure it



In this way we keep time in science, but time is not any more fundamental physical reality as matter, energy, space and motion are.



yours Sincerely amrit sorli





- Sorli A. (2008) The Theory of Atemporality

http://www.fqxi.org/data/forum-attachments/THE_THEORY_OF_ATE
MOPORALITY.pdf



- Sorli A. (2008) The Concept of Atemporality into The Theory of Relativity

http://www.fqxi.org/data/forum-attachments/1_The_Concept_of_
Atemporality_into_The_Theory_of_Relativity__amrit_2008.pdf

attachments: 4_In_The_Theory_of_Relativity__Time_is_a_Coordinate_of_Motion__Sorli__FOUNDATIONS_OF_PHYSICS_2009.doc

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String time averaging wrote on Feb. 24, 2009 @ 09:55 GMT
Does it help to think of time as follows?

Every superstring experiences the changing of its shape; it wiggles or slips around curled dimensions, etc. But it changes its shape as slow or as fast as it can based on its environmental conditions (energy density) and its own inherent characteristics. But what we see are the averaged out dyanmics of avagadros of strings.

Could we describe time as a function of the string's density and rigidness properties? String time for string i is a function of local energy scalar, and how quickly the string can change shape (maybe because a wave is moving along it).

We don't look at individual strings (we couldn't if we wanted to). We measure time based on macroscopic clocks, lasers over known distances, chemical reaction times, etc. We see time averaged out but never see the phenomena that produces time: strings change their shape ... in string time.

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amrit wrote on Feb. 24, 2009 @ 13:21 GMT
String, time is a function of measurment.

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Jason Wolfe/wulphstein@gmail.com wrote on Feb. 24, 2009 @ 17:50 GMT
Measurements are just relationships between avagadros of strings. Superstrings are reality. You and I, computers, clocks, Kg weights under glass jars, meter sticks, atomic clocks are all google-clusters of superstrings. By google cluster, I mean that strings -> particles -> protons/Neutrons ->atoms -> molecutles -> measuring equipment.

I want to define a Primary Reality, but I will mangle my definititon initially. If you take away the ultimate cause/effect phenomena, everything else vanishes. If I take away my ruler stick and my clock, I can't measure velocity, but everything in the universe exists. If I take away all the superstrings, what are you left with? Nothing. So strings must be the primary reality, not measurements.

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amrit wrote on Feb. 26, 2009 @ 20:43 GMT
Sure strings are primary reality and measurements (time) are secondary.

Time is in strings and strings are not in time. Strings are timeless.

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Georgina Parry wrote on Feb. 26, 2009 @ 23:32 GMT
Jason,

do you consider what you can observe and measure as your primary reality? Many people would claim that only the observable and measurable can be called real. I assume most scientists would be included, because the scientific method is based on observation and experiment.

This is what I call subjective reality. This reality in all of its manifestations is the playground of science.

Or do you consider primary reality to be those factors that are beyond observation and measurement, by and of which observable and measurable reality is formed.

Which I call objective reality.

A scientific model of such a reality can be formed but its validity can not be confirmed by science. It can only be deemed acceptable to scientists if it corresponds to other scientifically verified facts and agrees with some other accepted scientific and mathematical models.

This is the realm of metaphysics, religion, theoretical speculation, and philosophical debate. Where no measurement, observation, and verification are possible there is can be no scientific enquiry. Enquiry here is the domain of those other afore mentioned disciplines.

So which reality do you consider to be primary?

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Jason Wolfe/wulphstein@gmail.com wrote on Feb. 27, 2009 @ 10:58 GMT
A primary reality should lead you to the actual mechanism, in a complicated system, that controls what you're trying to control. You want to get to the actual cause/effect part of the system so you can expand humanities technical capabilities.

Yes I think that measurements and subjective reality approaches are extremely important. But, eventually, someone has to look beyond the data at what might be possible in physics; even if it's just to get more average people excited about physics who will, in turn, ask Congress to allocate more money for science. Yes, I like objective reality a little more. But keep taking measurements, it helps me refine my creative ideas.

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Georgina Parry wrote on Feb. 27, 2009 @ 12:29 GMT
Jason,

Have fun with your creative ideas. I have only had just a little time on this site and already I feel that you are not alone in your ambition.

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Jason Wolfe/wulphstein@gmail.com wrote on Feb. 28, 2009 @ 02:32 GMT
I'm just curiuos. In the last 24hours, has anybody put together string theory, relativity, and quantum mechanics in a really mathematically easy way? With a really easy simplification and the really easy concept that goes with it? Just curious.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 1, 2009 @ 18:50 GMT
I thought I had something cool. I spent the last two days playing around with an idea; but I'm ready to pass it on now. Starting with causality, the past and the future are walled off by infinite potential walls. The present is a thin layer of temporal thickness, Tp which is the Planck time (the time it takes light to cross the radius of a Scwartzchilde sphere, about 10^-44 sec). I propose that inside a Planck time, causality cannot be guaranteed.

Then, I said that particles within space time actually stretch out along this Planck time as superstrings. By the way, I'm assuming zero potential energy within the Planck time region and in all spatial directions. I also made the further assumption that within Planck time, space and the speed of light become unreliable.

Next, I looked up the vibrating string equation. Transverse displacements are in a spatial direction, longitudinal displacements are "special". But the tension becomes a temporal tension (with undetermined units). I assume that the string has some mass m. But, to use the vibrating string analog, the mass density of the string, along the Planck time, becomes a temporal mass density.

Within the Planck time, photons would start as point sources in the past, at - Tp/2 and expand to conical cross sections at +Tp/2; photons are more like rigid sticks in this picture because there are no photons lagging behind or getting ahead of c.

From this picture, it seemed to predict that sub atomic particle decay should occur if the particle is not a standing wave.

Does anybody think this is a possible description of nature? Did I invent Temporal Physics? Or did I spend two days farting around on some silly physics? I think I might add it to my blog at

http://ufo-technology.blogspot.com/

I'm trying to invent FTL Warp drive physics. At the very least, it'll be fun to read.

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Georgina Parry wrote on Mar. 2, 2009 @ 09:59 GMT
Jason,

there are aspects of this that I would agree with because there is some correspondence with the Prime Quaternion model.

Re. "Walled off past and future", I see what you are saying in that these "regions" are inaccessible to matter from visible 3D vector space. However according to the Prime Quaternion model they are not inaccessible to sub atomic particles that can move through all regions of quaternion space and can pop into and dissappear from visible 3D vector space.

The terms past, present and future are very problematic because they belong to a "historical or time line" concept of time where past and future actually exist, which leads to the time travel paradoxes. These concepts arise from observation of change, brain function and imagination. They do not exist in objective reality according to the Prime Quaternion model.

If I were you I would be extremely careful about how you define and use definitions and concepts involving time. As comprehension of time is the problem that Einstein, Godel, and many others have struggled to overcome without success.

The present is particularly problematic as a term. The subjective present experienced by an individual is constructed from a patchwork of inputs that have taken various lengths of time to reach the observer. These inputs are processed to generate the experience of that moment. Every person receives unique input and it is processed by their unique biology.

Therefore there is no such thing as the present. This leads on to relativity and associated mathematics.

However, in objective reality there is a continuous sequence of slices of 4 dimensional space and I assume that you may be referring to one of these slices when you refer to the present.

I could go on but I think this is probably enough to think about for now. By the way, in my opinion, there are not enough people who actually take the trouble to think for themselves. So no you have not wasted your time, keep thinking.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 2, 2009 @ 11:39 GMT
I decided to set aside brain function and consciousness and stick to particle-waves and superstrings when I talk about time. While I do beleive that consciousness has certain "special" attributes, it's too mushy to build any physics with.

I was actually prepared to admit that a +/- 1/2 Planck time is an arbitrary temporal thickness. While I guess that people in the UK like watching Dr.Who, the TV series about a time traveler, I can't say that I think it's possible. There are just too many opportunities to muck things up. But in a temporal slice of 10^-45 seconds, there may be too few information transmission opportunites to create any paradoxes.

While I like the Planck time idea for large scale time, I also like the idea that superstrings transition between two configurations, A->B in a time delta t; and large scale time is the averaging out of googles of these strings.

Is it possible that the fourth spatial dimension you're talking about is a short dimension of a Planck length?

I'm delighted that a famous author is taking the time to chat with me. Thank you.

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Georgina Parry wrote on Mar. 2, 2009 @ 21:38 GMT
Jason,

all perception can be misleading. Assumptions can lead to incorrect conclusions whether you still attend primary school or you are a 60 year old professor.

It is a mistake to set aside brain function. That is why the fundamental questions are still being asked.

The subjective reality in which you experience your life and in which the mathematics of relativity apply is the product of observation and interpretation.



Dimensions do not have length. Up and down, forward and backward,side to side and afore and aft along the 4th dimension, non of these dimensions have a length.

The size of the change in position along the 4th dimension of a sub atomic particle will be determined by the environment in which that particle exists i.e. which forces are acting on the particle and their strength. For a macroscopic object the "forth" of the object will be the difference between the potential energy at the surface of the object compared to the potential energy at the most interior position, at the centre of gravity . This in turn will be related to the radius of the object in 3D vector space.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 2, 2009 @ 23:32 GMT
Hi Georgina,

I set brain function and consciousness aside because the physical universe has been operating since before there were any observers (biological or otherwise). Personally, it would give me great joy to find a proof that consciousness has always existed or is a necessary ingredient to physics; it is something that I suspect but can't definitively prove. But the problem with starting with that assumption is that it opens the door to unlimited creativity which is good for happiness and fulfillment, but is bad for building mathematical physics models that require limitations and strict definitions to isolate mechanisms.

If you know of such a definite proof, then I'd like to read it. But I suspect that if consciousness exists independent of the brain (I believe it does), then it interacts with our physical universe through many different mechanisms, not just one isolateable mechanism. This would explain why skeptics always poo poo metaphysical research; not because it doesn't exist, but because the interactions with the ion pumps (nerve cells, brain tissue)in people's brains cannot be isolated down to a single mechanistic event. Psychic flashes, when they really do occur, involve entire sections and networks in the brain. You can't just look at one firing nerve and find mathematical proof.

Through all of our subjective measurements, which is like a common human scientific experience of repeatable events, we begin to see pieces of a larger objective reality. But if the larger objective reality includes biologically independent consciousness, then mathematics and logic is the wrong approach. I think that's what happening.

I think subjective measuremtns and experimentation will pin down a lot of the deterministic qualities of the objective reality. But consciousness, in my view, cannot be guaranteed to be determistic. In fact, the opposite is probably true.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 2, 2009 @ 23:54 GMT
Georgina,

In your paragraph, "The size of the change in position along the 4th dimension ..."

Are you saying that 1 more dimension is added/required to account for a the potential energy (Potential versus(x_4D)between the surface and the center of mass?

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Georgina Parry wrote on Mar. 3, 2009 @ 01:26 GMT
Jason,

No.Change in position along the 4th dimension is equivalent to change in potential energy, according to the Prime Quaternion model.

All macroscopic objects must have 4th dimensional thickness, even if it is extremely small, since a zero value for any dimension would not permit the object to exist. If you insist on calling the 4th dimension time, which I do not agree with, that would translate as saying the object must exist within time as well as space. Hence it has a 4 dimensional volume being spread not only within 3 vector space dimensions but also along the 4th dimension. The "spread" of the object along the 4th dimension is the difference in potential energy between the surface and the most interior point at the centre of gravity.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 3, 2009 @ 02:31 GMT
Georgina,

Let's say that we can hypothetically add(account for) another spatial dimension (either spread out or curled up). And let's consider a static system (no time evolution).

Since the potential energy is a scalar, we can talk about a scalar potential field V (x, y, z, q) where q is the additional dimension. I have a sneaking suspicion that this will only describe a 3D object.

When you say, "change in position ... change in potential energy", it sounds like your saying delta Phi/delta q = k const --> delta q = 1/k delta Phi --> delta q ~ delta phi; this would be true for Phi (x) = kq, a linearly changing potential.

But let's ignore whether or not Phi (x) changes along x or not. I don't get the relationship between the surface of the object and it's center. Are you referring to the divergence theorem?

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Georgina Parry wrote on Mar. 3, 2009 @ 03:34 GMT
Jason,

I will have to leave you to think about this for a while.

Please do not be hasty to reply.

There is no need for another dimension. The Quaternion structure is all that is required. What you (and most other people) are currently thinking of as a time dimension is another spatio-energetic dimension.

Within 3D vector space we observe change in position along the 4th dimension as a change in potential energy. Movement along this dimension not only gives rise to the subjective experience of time but also gravity. Gravity reveals the connection with change in potential energy.

Yes, I am talking about a change in potential that can be visualised as a linear change. The dimensions can be visualised as spatial or considered purely in energetic terms. As both apply, a spatial change of position can be regarded as an energetic change and vice versa.

The relationship between the surface of the object and its most interior point at the centre of gravity is the orientation of the 4th dimension. Which can be visualised as running from every point on the exterior surface, through to the centre of gravity, where it does not stop but continues on into afore 4D space, beyond visible 3D vector space. It arrives at the surface of the object from aft 4D space which is also space beyond visible 3D vector space. This takes some getting used to. It does mean that the interior of an object is further afore along the 4th dimension than the exterior and the direction of motion of all matter along the 4th dimension is from all of the exterior of an object to the interior of the object not directly through any one of the 3 vector space dimensions. No,it does not collapse on itself in 3D space.

When you can visualise this motion, gravity is no longer mysterious.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 3, 2009 @ 04:19 GMT
Just curious, is there a formula for mapping points from three space into four space through a center of mass point? I was looking at Brilluoin zones, but that's still 3D to only 3D.

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John Merryman wrote on Mar. 3, 2009 @ 10:56 GMT
Georgina,

You are trying to define dynamic process as a static measurement, but a version of Zeno's paradox applies. There can be no defined limits to this fourth dimension for the same reason it isn't a dimensionless point in the first place. The result is that it is fuzzy, because you are trying to define the dynamic as static and that is contradictory. When it is fully defined, it is no longer dynamic.

As you point out, "All macroscopic objects must have 4th dimensional thickness, even if it is extremely small, since a zero value for any dimension would not permit the object to exist." Since we can't define its parameters, it could be smeared across the universe.

It is the essential conflict between a wholistically dynamic reality and our reductionistic thought processes. If we could truly stop the dynamic, reality would vanish. It would be a featureless non-fluctuating vacuum, or void, in that case. We want to project some exact understanding on a fluid system and it just runs through our fingers.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 3, 2009 @ 18:47 GMT
All,

The Many Worlds Interpretation of the "multi-verse" has a problem with it. When I apply reductionism to the many worlds interpretation, it also seems to grab determinism by the tail and drags it into the debate.

MWI basically says that there are an infinite number of universes that are distinguished by the selection of each possible choice made. I had cereal for breakfast. In another universe, I made pancakes. This was also a strategy for understanding how probability amplitudes and densities could be understod. In one universe, a particle physicist found his electron at point A, in another universe, it was found at point B, and so on...

But if every choice, not just by us, but at the quantum particle level, splits the universe into two separate universes, each with a total energy E, then there are not an infinity of universes, there are 2^infinity; there are googles of infinities of universes, each with energy E, but no Big Bang!

Using reductionism, maybe there is just one universe with one of you and one of me, and determinism, while it makes phyicists feel better, is not entirely perfect. Furthermore, maybe there is no way to gaurantee that you will always detect your particle at point A because its not a particle, its a particle-wave or a string that (to abuse the priviledge of using metaphors) has a moving target on it that moves along the string; and you can't always hit a moving target. Is it really such a disaster for physics if we disprove determinism; that we have to make up a multiverse with bazillions of universes in which Elvis is still alive in some of them?

Let's just metaphorically harpoon the infinite universe idea and just accept that determinism is a useful tool, but it's not true. Don't let physics and determinism prevent you from choosing between cereal and pancakes for breakfast.

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georgina Parry wrote on Mar. 3, 2009 @ 19:03 GMT
John,

I absolutely am NOT trying to define a dynamic process as a static measurement. That is your own misunderstanding. When a point is defined in 3D vector space it is a point only from the 3D vector space perspective.I have explained before now to you that all macroscopic objects are in continuous motion along the 4th dimension, so any point will in fact be a continuously moving change of position.

Likewise subatomic particles are always in motion but are not obliged to move continuously afore along the 4th dimension.

I do feel a little disappointed when I have taken the trouble to be precise in my explanations but you take your own or other peoples misunderstandings and tell me that is what I am saying.I have not put any limits in the 4th dimension, have had to explain that a dimension has no length to Jason and have said nothing about it being a dimensionless point. That is Jason confusing an explanation of the orientation of the 4th dimension from a 3D vector space perspective with the behaviour of matter in 4D space in relation to the dimension. I told him to take some time to think about it and not be hasty.

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Lawrence B. Crowell wrote on Mar. 3, 2009 @ 19:57 GMT
If you want to consider Brilluoin zones in spacetime physics consider spacetime in some chosen frame as tessellated by Planck units of volume. In flat spacetime this is the 24-cell which has F_4 Lie alegebraic content. For cosmology the AdS spacetime can be tessellated by the 120-cell, which is the 1/2-root space for E_8.

The Brilluoin zone structure defines noncommutative coordinates. This operates best in the AdS-E_8 system, since the root space is the Lie group. So there is a transition operator T(x) which is periodic T(x + d) = T(x), for d an edgelink distance. Since the root space = E_8 group the Bloch-like wave functions contain the symmetries of the E_8 field.

My essay #370 discusses some of this structure.

Lawrence B. Crowell

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John Merryman wrote on Mar. 3, 2009 @ 20:05 GMT
Jason,

I would agree that MWI means the model is imperfect, but that faith in the model is preferable to not knowing for some people.

Georgina,

I'm sorry if it seems I've come to conclusions that are in error. It certainly wouldn't be the first time. I tend to see the fourth dimension as narrative projection, i.e. defining all activity as serial. This makes sense to us because it is how our brains function. Out of the sea of input, we manufacture a series of perception, so we think reality is similarly linear. What if in your three dimensional space, every action resulted in a consequent reaction by the rest of the frame? There would be no need for an additional dimension, since the activity is in fundamental equilibrium. Since space is effectively infinite and action does cause reaction, there isn't clear proof or evidence of this fourth dimension, especially if the effect of time is emergent, rather than fundamental.

As for the original three dimensions, I see them as the coordinate system of the center point and any number of different such coordinate systems can occupy the same space. For reference consider how two observers moving relative to one another perceive spatial dimensions, as well as time, as having different measurements. In everyday life, consider how two people, or two different groups of people, might view the same situation from completely different perspectives and both be completely sure of their own truth. Space is infinitely dimensional.

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Georgina Parry wrote on Mar. 3, 2009 @ 20:09 GMT
John,

Please read my last post above if you have not already done so. Then this one.

I do think there may be another ambiguity in my explanation of dimensions. However I have assumed basic comprehension of physics and mathematics and did not expect to have to explain, in detail, very basic concepts. When I say a dimension has no length, I mean that it is just not a term that applies to a dimension. It does not have a beginning and end, so its extent can not be measured and therefore it does not have a length.It is an orientation.

There is no limit to up or down. Likewise forward and backward and side to side. These are the dimensions of 3D vector space. Likewise the 4th dimension has no length because it is an orientation, not because it is a point.

That is easy. Thinking in 4 dimensions rather than 3 is considerably harder and as I have said before takes some getting used to.

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Georgina Parry wrote on Mar. 3, 2009 @ 20:19 GMT
John,

Sorry for the overlap of our posts. I think we will just have to agree that we have a very different take on how the universe is structured and functions.

I have tried to explain how the Prime quaternion model is able to simply answer all of the fundamental questions.

If you would prefer infinite complexity to a simple solution, so be it. A biblical proverb linking the porcine beast with a shellfish product springs to mind.

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John Merryman wrote on Mar. 3, 2009 @ 21:42 GMT
Georgina,

"All macroscopic objects must have 4th dimensional thickness, even if it is extremely small, since a zero value for any dimension would not permit the object to exist."

"When I say a dimension has no length, I mean that it is just not a term that applies to a dimension. It does not have a beginning and end, so its extent can not be measured and therefore it does not have a length.It is an orientation. "

?

I understand dimension is orientation, but my reading of your first statement is stating the distance of this fourth dimension is very short, thus having a beginning and end.

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Georgina Parry wrote on Mar. 3, 2009 @ 22:30 GMT
John,

the thickness of an object in particular dimension may be large or small. A sheet of tissue paper is extremely thin in one of its 3 dimensions but it must still have that thickness.It can not exist as a 2 dimensional object in 3 dimensional space. I am talking about thickness of the object not length of the dimension, which would be nonsense. It would be nonsense because length simply does not apply to dimensions. That is why I thought it necessary to clarify this basic concept with the second sentence that you have posted above. The first sentence is only ambiguous and open to misinterpretation if you do not really understand the concept of a dimension.In my opinion.

I was hoping to discuss the foundational questions and get feedback on my work but it is not possible if even the most basic of scientific concepts are not grasped,leading to such misinterpretation.I am sorry if this sounds at all rude or intolerant,it is not my intention. I am new to this site and came here with high expectations, that is perhaps the biggest mistake that has been made.

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John Merryman wrote on Mar. 3, 2009 @ 22:37 GMT
Georgina,

No problem. I'll refrain from further discussion.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 4, 2009 @ 09:38 GMT
If were going to disagree on what a dimension is, then maybe we are using different definitions.

The standard 3D, height, lenght and depth extending in either direction are infinite distance; their orientations are perpendicular; obeying i.i=1, j.j=1, k.k=1, i.j = 0, etc.

Time can be described as a dimension ct. As far as we know, it started at the Big Bang and its orientation is into the future. So far, it's 13.7 billion light years long, but that's close enough to infinity for me.

String theorists speak of rolled up dimensions that strings will wrap themselves around some integer number of times. Since strings are about a Planck length long, then a distance around this dimension is 2pi x Planck length (which is a very small distance). Its orientation is angular, 0 to 360 degrees; radius is constant, r.

I defined my own dimension as a short segment of length along the time orientation. It's center is at the present, and it extends 1/2 Planck length into the future and into the past. At those edges, I'm putting up an infinite potential wall. I'm going to put superstrings in it, and I don't want them escaping into the past or the future. I defined it.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 4, 2009 @ 09:58 GMT
Lawrence,

The only reason I brought up Brilluouin zones was because I was looking for some way to map 3D points into 4D space. I suppose even in a static 4D space, there are infinite orientations, similar to mapping a 2D geometric circle into three space, etc...

I had been thinking about Brilluoin zones lately. I think the emergent properties of periodically spaced atoms in crystals are so fascinating: conduction and valence bands, phonons, etc. I've been looking for a better way to explain space-time. Crystals are not it.

As for tesselated Planck unit volumes and F_Lie algebra, I'll keep that in mind. Right now, I'm contemplating "micro-verses". I define a "micro-verse", in my thought experiment, as a simplistic d-brane with a 2D surface. I'm trying to figure out how much energy it takes to (1) create a "micro-verse" of radius R (in 3D), (2) add information per bit, (3) add superstrings, (4) add space as a bit (here or there) (5) add time as a bit (before/after). I want to see if anything helpful pops out.

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Lawrence B. Crowell wrote on Mar. 4, 2009 @ 13:13 GMT
A four dimensional flat space can be tessllated by the 24-cell (octahedrachoron), which is a Coxeter-Dynkin representation of B_4, D_4 and F_4, where the latter is the most interesting. The 24-cell is self dual, and so the entire system has 48 roots. F_4 is a rank 4 group which adds the 16 roots of B_4 with the 36 roots of spin(9). The coset space F_4/B_4, for B_4 ~ SO(9) defines the sequence

F_4/B_4: 0 --- spin(9) --- F_{452} --- OP^2 --- 0.

So the 52 dimensional representation contains the 26-dimensional bosonic string, the string modes and their Fourier transformations.

As for 3-d tessellations, the boundary of this polytope consist of octahedra. Of course this polytope has diffeomorphic freedom, which correspond to a freedom of frame choice one imposes on the spacetime. By imposing that choice one restricts this diffeomorphic freedom by imposing "cross struts," so the octahedra are composed of tetrahedra. This is of course related to Regge calculus.

The root space is not the group itself, but since this is a tessellation of flat 4-dim space then in any frame the same tesselation holds with imposed cross struts. For a curved spacetime however, this really fails. So what do we do next? The curved spacetime we really want to tessellate is the AdS spacetime or AdS_2xS^2. The Maldecana duality AdS ~ CFT then appears as the duality between the group of quaternions on the 120-cell which tesselates the AdS and the eqivalent group structure on the elementary tessellation element = 120-cell.

For the hyperbolic AdS the tessellation are given by the octahdedrachoron. The three dimensional reduction is the tessellation of a hyperbolic space by octahedra, and the boundaries of the 120-cell are octahedra.

Quantum gravity is then a system of quantum bits on the lattice. The Bloch wave will have a periodic structure for an integral which around any sub-polyhedra, such as a line integral "oint" around a strut or an area integral around a triangular face and so forth. The quantum "flux" through any of these chains will then have some representation

|Y) = P_0|0) + P_1e^{i@_1}P_1 + ... + P_ne^{i@_n}|n),

for P_i projectors and @_i phase terms determined by the connection ("quantum flux") on any chain in the entourage around the chain of integration. I use | ) for the Feynman "bra-ket" since this editor does not like carrot symbols. The quantum states are then determined by the root space E_8, which in this duality gives E_8xE_8, or ther heterotic string.

I hope this makes a few things clear. I tend to agree that the foundations of quantum gravity and quantum cosmology should have a solid state physica appearance. This is the way I think that string/M-theory and loop space quantum gravity can be made to "talk to each other."

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Mar. 4, 2009 @ 13:19 GMT
erratum: the equation above written as

|Y) = P_0|0) + P_1e^{i@_1}P_1 + ... + P_ne^{i@_n}|n),

should be

|Y) = P_0|0) + P_1e^{i@_1}|1) + ... + P_ne^{i@_n}|n).

L. C.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 4, 2009 @ 18:42 GMT
Lawrence,

From reading your last post, I got the impression that I might be able to find something I was looking for. I expect to find additional forces (above the present 4), that should exist in higher dimensional branes, and are, of course, bosonic fields. When you brought up heterotic strings, you caught my attention.

If I describe space-time by tesselating octahedrachors, I eventually get a 52 dimensional geometric object that represents bosonic strings in 26D. I should be able to get a wave function out of that for a boson and its field. Since I don't have a 26D boson generator handy with adjustable parameters, then the bosons will be in whatever state they happen to be in. Is there anyway to take two bosons, each with their own parameters, and somehow add them mathematically and physically in an attempt to get a third boson whose parameters are a reliable and repeatable function of the first two? Boson A + Boson B = Boson c?

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Jason wrote on Mar. 4, 2009 @ 19:20 GMT
Jason,

we most definitely are. We can agree on the vector dimensions but not the scalar dimension.Coiled up dimensions are to my mind a case of the overly enthusiastic wagging of the mathematical tail unbalancing the equilibrium of the whole animal.

4 dimensions were enough for Einstein. Quantum physics took its own path, rather than ascertaining what the 4th dimension really represents, after Einstein had already shown that time is an emergent phenomenon not fundamental. Time was the question that tormented Godel and consumed Einstein and Godel in their later years. This is the fundamental question that if it had been answered then would have allowed Einstein's work to be continued. This is the Question that has lead to the Prime Quaternion model.

If we can not agree on the basics of what a dimension is, we can not really have a meaningful dialogue. Have fun with your recipe.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 4, 2009 @ 20:59 GMT
I admit to not having a sufficient understanding of F_4 Lie algebra from which the Prime Quaternion model is a subset. As for the overly enthusiastic mathematical tail waggers, it's helps us figure out what the animal is.

Since you constructed (tesselated) curved space time with these octahedrachors, that must mean that time is already included in this geometric object. So, are octahedrchors just a fancy accounting system for physics or do you believe that these are real building blocks of the universe?

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Georgina Parry wrote on Mar. 4, 2009 @ 22:11 GMT
No time is not included in the geometric object. Time is not part of objective reality. The geometric object that gives rise to the universe exists within 4 spatio-energetic dimensions only. Yes it is stationary. Time is experienced within subjective reality due to motion of all matter of the universe along the 4th spatio-energetic dimension of the geometric entity, a hypersphere which is called the Quaternion megauniverse or 4D Megauniverse.That is according to the Prime quaternion model. You and I are not working with the same concepts of time. It is a very fundamental difference of opinion.

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Lawrence B. Crowell wrote on Mar. 5, 2009 @ 02:47 GMT
The reality in this system are the quantum bits. The sphere packing is a way of devising a quantum error correciton code. Each sphere is in a configuration so it can be independent of adjacent sphere and carry a unique "letter." The E_8 lattice for instance defines a quantum code with Hamming distance 8 in a self dual [8, 4, 4] system. This then preserves quantum information in a channel which can deviate a quantum bit stream by four errors. Yet at the end of this what is physically real are the quantum information bits.

There is more to this for E_8 constructs certain sporadic groups such as E_8xE_8 is the Barnes lattice and three E_8's defines the Leech lattice. I will not for now go into that stuff, though it is fascinating stuff. The automorphism group for the Leech lattice of 196560 root vectors is the Fischer Greis group, or sometimes called the Monster group.

Lawrence B. Crowell

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Georgina Parry wrote on Mar. 5, 2009 @ 08:23 GMT
The set H of all quaternions is a vector space over the real numbers with dimension 4. H can be partitioned in such a way that it looks like an infinite set of complex planes. Each such plane has its own unique version of i, although they all share the same real (scalar) axis. Furthermore, each unique i value corresponds to and is fully defined by a point on the surface of an ordinary unit-radius sphere, thus providing a strong connection between the geometry of ordinary spheres and the far less intuitive four-dimensional properties of H.

The set of quaternions of absolute length (radius) 1 has the form of a 3-sphere or hypersphere, which is also called S³. Within this hypersphere there exists a subset of quaternions with the additional property that their squares are equal to −1. This subset has the geometric form of an ordinary sphere, or 2-sphere (S²).

It can be understood as a three-dimensional "slice" of the larger hypersphere in much the same way that a circle is a two-dimensional "slice"of an ordinary sphere.

This is the mathematical structure that will provide a series of nested universal spheres, which may form a continuum in objective reality or exist as separate structures i.e. a nested series of parallel universes.

That is what the Prime Quaternion model requires. Other mathematics may perhaps also be used to describe this structure.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 5, 2009 @ 09:01 GMT
Georgina,

You're actually starting to talk about the question I haven't asked yet. That is very clever on your part.

Nested 3D spheres (S2), with "I'm guessing here" a square unit vector = -1, you're referring to a dot product of the orientation unit vector, right?

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 5, 2009 @ 09:22 GMT
Lawrence/Georgina,

I need help trying to set up a hypothetical physics problem. I want to know if the Prime Quaternion model or perhaps tesselating octahedractors can help me set up this problem.

I want to take two parallel sheets of (branes perhaps) and slide them over each other. There separation should be some distance d. These two dimensional sheets may belong to extended objects. Outside of these sandwiched sheets, I want to assign the laws of physics as identical to our known laws (Standard model, gravity, etc.). But, I want the two sheets to slide superluninally across each other. Maybe you can guess what I want to do. But I need to know how to set up the octahedractors (if that is the appropriate tool).

I want a description of the branes to fall out, qualities of the bosonic field, and/or something helpful. When I thought about it, I realized the following:

1. c as the space-time speedlimit is taking my energy and converting it into mass; that is a problem.

2. Can I adjust the physics within the sandwich region so that mass cannot be created? All incoming energy must be translated into velocity.

I'm wondering if the Quaternion geometric model can be adjusted to represent adjacent slices with different laws of physics? Or should I be looking at some other part of string theory?

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 5, 2009 @ 10:05 GMT
Georgina,

When you described set H, you said each plane has it's own unique version of i. Does that mean that they scale in some useful way? Can I choose those numbers (real numbers)?

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Lawrence B. Crowell wrote on Mar. 5, 2009 @ 13:57 GMT
Braney physics enters into this picture of tessellations because in a fermionic setting there exists a Fermi surface. The Fermi surface corresponds to quantum bits that under a "target map" are q-bits associated with the sphere packing. In the 10-dimensional superspace there is a Lagrangian of the form sqrt{g}dX^pvdX^{n-p}, where for n = 3 this is a D3-brane in a transversality with a D7-brane. So the overlap of these states on the two branes is determined by

~ a(E/E^*),

where the condition for zero overlap is that E^*-à infinity. Here a is the "alpha} for the string coupling with a ~ G^2. There is also a T-duality involved here. There are some underlying K-theory here, where the fermionic content is determined by a homotopy condition pi_3(X) = Z_2, on the D3-brane. Hence there is an analogue here with the breakdown of a Landau electron fluid on a quantum critical point. There is also a scaling condition here, for in imaginary time t_{im} = hbar/kT, as T à 0, the imaginary time for the quantum uncertainty approaches infinity. In this way the universe is a sort of “frozen” quantum fluctuation, where this condition assures a scale invariance from near zero energy to E_{planck}.

This of course works for near zero energy, which for cosmology and quantum gravity is 10^{-16}E_{pl}. Hence once we reach electroweak “unification recovery” we should get signatures of low energy quantum gravity that scale up to E_{pl}. This scaling principle is induced from a target map from the D3-brane to spacetime, where the appropriate spacetime is AdS. The “great arcs” in a two dimensional reduction AdS_2 are similar to the arcs on the Poincare disk, which scale energy (conformal energy) for particles which leave the boundary at E ~ E_{pl} and return at E à 0.

So the connection to braney physics with the Fermi surface, similar to that in condensed matter physics, and the cohomological/topolgy conditions in K-theory. Some of this topology involves how fermionic states eneter into nontrivial topological configurations and define Skyrmion fields.

I have been working on this stuff for 2-1/2 years, to considerable expense. I am hoping this turns out to have at least some connections to cosmological and quantum gravity foundations!

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Mar. 5, 2009 @ 13:59 GMT
err: the strange E a 0 should read as E rightarrow 0. This editor does not like certain symbols.

L. C.

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georgina Parry wrote on Mar. 5, 2009 @ 19:28 GMT
The set of all quaternions of absolute length form a hypersphere this corresponds to the 4D Megauniverse.

Within H, the set of all quaternions, there is an infinite set of quaternions having a square root of -1These all form a 3D sphere. The square root of a quaternion is −1 if it is a vector (that is, pure imaginary) with norm 1. Such vectors make a sphere by definition.

Thanks for the invitation Jason but it is not something I wish to peruse.

My reasons are firstly that there are no reasons to assume different physical laws in the different parallel universes. The laws arise from variations of dynamic motion within 4D space, continuous motion along the 4th dimension and properties of subatomic particles and energy. Since all are in 4D space and all will be moving along 4th dimension the relevant laws will be the same. All matter and energy is recycled within the 4D Megauniverse so it is most likely that each universe contains the same types of sub atomic particles and energy.

Secondly, to my mind, Bosons are not particles. There will be an area of disturbance where the dynamic interaction occurs interpreted as a Boson. I do not see how identifying a bosonic field helps with the foundational questions. Perhaps that is short sighted of me.

Most important, for me, is getting acceptance of the quaternion structure by demonstrating how it is able to answer the foundational questions, that other structures can not. The details of how "ripples" form in 4D space due to each kind of dynamic interaction and how they can be interpreted mathematically is a much lower priority.

It is very time consuming reading posts,articles and responding. I did not come here to teach physics or maths, or spend my time developing other peoples speculative models. I'm sorry if that sounds selfish but I must prioritise the use of my time. I wish you and Lawrence success in your endeavour.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 5, 2009 @ 21:21 GMT
Lawrence,

I'm going to have to fill in some gaps in my knowledge of mathematics. Fermi surfaces I recognised as zero amplitude points in k-space. I'm getting a sense that these octahedro (sp)are k space expressions. While I'm explaining it badly, I think were on the same page.

I'll post again when I sharpen my Tensor skills, quantum bits understanding, etc.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 6, 2009 @ 07:27 GMT
Georgina,

I totally understand. I know how limited time is. I feel like I got some free physics knowledge out of this. I wish you the best with your piece of the puzzle: the Quaternion Model.

By the way, a fun little fact about bosons. Bosons ten to be force carriers/mediators. Gluons, Higgs particles, Mesons, photons, gravitons are all bosons. One person's particle is another persons disturbance, and so on.

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Lawrence B. Crowell wrote on Mar. 6, 2009 @ 14:05 GMT
I have been a bit glib here. The dodecahedrachoron, or 120-cell tessellates the AdS spacetime. This polytope is a 4-dim extension of the dodecahedra. The dodecahedra has I_m(5); which for m = 3 group structure, which does not tessellate a flat three dimensional space, but will tessellate a hyperbolic space in three dimensions, and for m = 4 a hyperbolic spacetime such as AdS. The four dimensional extension of this is the 120-cell, called the hyperdodecahedron or dodecachoron, which is a polychora with 120 octahedron boundaries, 720 pentagons, 1200 edgelinks and 600 vertices, and Schlafli index {5, 3, 3} . The dual is the 600 cell, with 120 vertices which define a group under quaternionic multiplication. This group is sometimes called the binary icosahedral group, which is a double covering of the icoshahedral group. The symmetry group of the 600-cell is the Weyl group H_4 ~ {3; 3; 5}, a group of order 120^2 = 14400.

So the 120-cell and the 600-cell are dual polytopes. For the 120-cell a tesselation of a 4-d spacetime, the 600-cell is the tessellation of the momentum dual (k-space). In some ways this is similar to Fourier transform logic. Also the 600-cell is the reciprocal space associated with the 120-cell, which defines Brillioun zones of k-vectors.

Lawrence B. Crowell

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 6, 2009 @ 18:20 GMT
Lawrence,

I see the connection between 120 cell space-time tesselation and 600 cell brillouin zone k-space; that fits nicely into descriptions of crystals. But there is one snag. Crystals are spheres. Space-time tesselation with dodecahedrachorons is different from the stacking spheres. Tesselation is a two dimensional stacking of shapes, like building a road with bricks. The bricks tesselate as a flat 2D surface. Sphere stacking is in 3D and leaves interstitial spaces.

I want to make an abstract leap, but the lack of interstitial space in tesselatation is a problem. Please tell me I overlooked something.

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Lawrence B. Crowell wrote on Mar. 6, 2009 @ 18:43 GMT
What plays the role of the "atoms" are Planck units of volume. The planck distance is L_p = sqrt{G hbar/c^3}, which can be found by equating the deBroglie wave length in spacetime of a particle of some mass with the Schwarschild radius r = 2GM/c^2. I leave it as an exercise to compute L_p, it is not hard. This defines the smallest distance we can expect to find physics.

The 24-cell is the minimal sphere packing configuration in flat 4-d space, and the 120-cell for hyperbolic 4-dim space. So for some choice of frame there is a tessellation of spacetime according to Planck units of volume. If you choose another frame there is another tessellation of course. This is one departure from solid state physics. However, since the E_8 roots, which define the polytope of quaternionic quivers, is the group itself this "miracle" makes things more solid state-ish. It means that in any frame the tessellation is by group action equivalent everywhere.

There is a lot of confusion about the Planck length. Some people see it as a discrete structure in spacetime (slice and dice). But really what is means is that there is a Block wave (in lattice QCD a Mantin type of potential) which defines physics on a scale larger than L_p. What is actually real are then the quantum states or q-bits involved and not any real "slicing and dicing" up of geometry.

Lawrence B. Crowell

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 6, 2009 @ 22:19 GMT
I'm thinking about this stuff from a solid state physics approach. let's pretend that the universe really is made of schwartzchilde size spheres. Then, we can compare solid state physics with General Relativity. Let me go point by point and you can tell me where I miss.

1. The quaternion hyperspheres stack in four dimensions. The interstitial space fits another stacking of quaternion hyperspheres of the same size, but in 8 dimensions, it fits nicely

2. The quauternion hyperspheres are the set off all k vectors (k_x,k_y,k_z) that exist for some potential energy scalar at a point.

3. Phonons require two stoms per primitive cell. For atoms of different sizes (Ga and As, etc.) you get optical and logitudinal phonons. But since the quaternion hyperspheres are the same size, all you get are ordinary photons.

4. These spheres stick to each other (fortunately), which should play a role in the stress energy tensor

5. Similar to atoms in crystals, these Schwarzchilde spheres act like oscillators by vibrating back and forth. It is these vibrations that can produce what we observe as wave amplitudes.

6. If phonons are like photons, then electrons (and the holes they leave behind), must be like particles (particle/anti-particle creation/annihilation). Then, particles (complete with all of their conserved quantities like spin, lepton number, quark number, charge, etc.) are coming out of these spheres when we put in the right amount of energy.

7. mass, just like effective mass in crystals, is dependent upon the potential energy distribution due to the schwartzchilde crystal.

With some refinements and choosing the right words, can any of this be a useful way to look at the universe?

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 6, 2009 @ 22:54 GMT
Ok, I admit it needs a lot of work, but I'm trying to test the idea that there really are 4D Quanterion hyperspheres of Schwarzchilde radius that make up space-time.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 7, 2009 @ 00:48 GMT
Lawrence,

If you take two stacks of hyperspheres in 8 dimensions, where one stack is in the interstitial space of the other, then something funny happens.

When you step back by lowering your magnification, it should start to look like hyperspheres stacked in four dimensions with a smaller stack of hyperspheres in the interstitial space. This is a 2 sphere basis in four dimensions.

In the same way that a 3d crystal lattice generates a conduction band in 3 directions, a lattice of hyperspheres in 4D will generate a conduction band that is independent of the k vector orientation (a.k.a) space-time.

Then,

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Lawrence B. Crowell wrote on Mar. 7, 2009 @ 13:01 GMT
The entire root space representation for E_8 is the Grossette polytope in 8 dimensions. The 120 cell and 600 cell, which are duals to each other, exist in 4 dimensions. So the 120-cell of icosian (quivers of quaternions) is 1/2 the E_8 root space. The 120 cell has 120 hexagonal faces, each with 6 vertices. Now suppose that we embed this in 5 dimensions. Further let there be a null condition...

view entire post


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Lawrence B. Crowell wrote on Mar. 7, 2009 @ 13:06 GMT
erratum: Rats, those dreaded carrot signs!

The strange ~ a(E/E^*), should read

(q|*q) ~ a(E/E^*),

for (q| and |*q) the duality between states in 10-dim. As a matter of clarification. the hamming [8,4,4] defines the duality | ) and ( | on the E_8 set of stetes, while the 10 dimensions defines a duality |q) ~ |*q) for states on a p-brane and an (n-p)-brane.

Lawrence B. Crowell

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 14, 2009 @ 20:14 GMT
Lawrence,

These polytopes are geometric shapes that can be stacked without leaving interstitial space. They have 120 or 600 cells (faces, like a 6 sided die has six faces) and are stacked in 8 dimensions (or however many dimensions; two dice are stacked in 3 dimensions (1, 2 or 3dimension)).

The struts and vertices are like edges and pointy parts.

I'm trying to understand the jump to algebra -> polynomials -> roots. I'm going to have to pick up a book on this stuff.

I also want to understand how Lorentz transformation will be satisfied by the 120 dodecahedrachoron? For General Relatiivty to be garanteed, the Lorentz transformation must be invariant.

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Lawrence B. Crowell wrote on Mar. 15, 2009 @ 12:59 GMT
Your observation that the 120 cell would not tessellate spacetime is correct for flat space (spacetime). The 24-cell tessellates flat 4-dim space. The 120-cell tessellates a hyperbolic 4-dim space with Gaussian curvature = -1. The analogue of this is how the octahedron will tessellate a 3-dim hyperboic space. The 4-dim hyperbolic space is the Anti de Sitter (AdS) spacetime, which has its correspondence with the de Sitter (dS) spacetime. The dS models the physical cosmology we actually observe, but under the signature switch [-,+,+,+,+] of the 5-dim embedding space of dS to [-,-,+,+,+] of AdS the essential gauge (like) information carries over. AdS is for a number of reasons more emenable to calculation than dS.

A good source is Conway & Sloane "Sphere Packing. Lattices, and Groups," A Springer publication. This gives a good outline of Golay codes associated with sphere packing.

Lawrence B. Crowell

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 15, 2009 @ 17:25 GMT
Lawrence,

If the 24 cell tesselates flat 4D space, and the 120 cell tesselates hyperbolic 4D space, then doesn't that mean that the geometry of the polytope is dependent upon how much mass/energy I have in the local area? Black holes will change the geometry, and by extention, the properties of the proposed Schwartzschild sphere (solid state point of view)? If we accept Garett Lisi's idea that the geometry of the polytope will describe the particles within that space, then something kind of cool happens. By curving space (as if were that easy), I change the geometric properties of the cell that tesselates it, this in turn (via relationship, not mechanism) changes the properties of the Schwartzschild sphere which, then, changes the kind of particles I can generate. I assume that 24 cell polytopes account for X number of particles, but a 120 cell polytope would account for X + Y particles.

If I'm going to complete my UFO tech blog, I need some way to fiddle around with the particles and the laws of physics. If I didn't misunderstand something important, then I might have something fun and cool to work with. I hope I don't have to carry around singularities and black holes on my hypothetical space crafts.

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Lawrence B. Crowell wrote on Mar. 15, 2009 @ 18:48 GMT
Yes, there is an energy associated with the AdS, with the negative Gaussian curvature. I submitted last month a paper on how this is a "mass-gap" associated with the spontaneous occurrence of AdS_2xS^2 in the extremal condition on an Neissnor-Nordstrom black hole. The two horizonz occur at

r_{+/-} = m +/- sqrt{m^2 - Q^2}

for Q the electric charge (or a BPS gauge charge). In the cas that m^2 - Q^2 = 0 the outer and inner horizons meet and Sean Carroll demonstrated that this spacelike "squashed region" becomes the AdS_2xS^2. I ran with this and demonstrated how this can lead to the quantum tunnelling of a cosmology from the vacuum. The mass-gap is then a fluctuation of mass-energy, which as gotten "frozen out," so to speak, and is the "seed" for the pre-inflationary universe.

Lawrence B. Crowell

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Lawrence B. Crowell wrote on Mar. 15, 2009 @ 18:49 GMT
err: Neissnor should read Reissnor. The really small screen here is hard to read.

L. C.

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Jason Wolfe/wulphstein@gmail.com wrote on Mar. 15, 2009 @ 19:37 GMT
You know, your equations

r_{+/-} = m +/- sqrt{m^2 - Q^2 can be rewritten as

r_{+/-} = m +/- m sqrt (1 - Q^2/m^2) which looks an awful lot like gamma = 1/sqrt (1 - v^2/q^2). If I'm correct (then I'm certain you already know about it), the it means that charge and mass share some special relationship. I assume their units are the same.

So does this mean that Q^2 can never be larger than m^2? It must, I can't imagine defining a complex radius.

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Lawrence B. Crowell wrote on Mar. 15, 2009 @ 20:42 GMT
It is similar to the gamma factor. There is a related condition for rotating black holes, where there is a sqrt{m^2 - J^2}, J = angular momentum. If J^2 = m^2 then just as with the RN metric with Q^2 = m^2, the outer and inner horizons merge and for a pure "eternal" solution the inner singularity is revealed to the world.

For physical black holes that condition can't occur, as it would take an infinite amount of energy to get that added charge q so that Q + q had a magnitude = m. This is the extremal black hole case The same holds for the Kerr metric for rotating black holes. Yet for the quantum vacuum defined over all configurations of possible spacetimes this transition between nonextremal and extremal configurations can occur, though with a small amplitude. This results in the quantum production of a a cosmology.

Lawrence B. Crowell

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Enrique wrote on Dec. 9, 2010 @ 20:03 GMT
There is two kinematic domains:

1-The Classic Domain

2-The Quantum Domain

But this NOT come from the copenhage interpretation. This is a LOGIC consequence from special relativity:

http://www.ingenieria.cl/revista/526b8592e834fcaa
ccec26a22965ea2b6726.pdf

Thanks

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Steve Dufourny wrote on Dec. 10, 2010 @ 08:37 GMT
Interesting the number of x we see the word sphere on this thread .

Very interesting.

Steve ...THE THEORY OF SPHERIZATION .....QUANTUM SPHERES.....COSMOLOGICAL SPHERES...UNIVERSAL SPHERE.

the spheres packing is finite and presise ,the decrease of volume is essential ....the rotations are proportionals withy many things.

ps EUREKA ...

Steve

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