Poincare Invariance from General QFT

  • Thread starter CarlB
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  • #26
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Attempt to unify all science information into mathematical objects

Hi Kea:

and CarlB:
and all others:

I admire your knowledge of bio-mathematics.
I search for the unification with other types of mathematics.
I suspect this will result in a mathematical game of energy exchanges through attractors and dissipators of various gauges.

I prefer your tree branch analogy [of this thread] to your pair of pants analogy [of the Application of topology in nature - auditory energy mapping thread].
https://www.physicsforums.com/showthread.php?t=134962

Such an analogy, may allow physicists [particle, astro, geo, bio, et al], mathematicians, biologists, physicians and engineers of all types, to make translations among disciplines easier, if all science information is translated into mathematical objects.

I am greatly influenced by Nobel Laureate Christian De Duve, most recently.
‘Singularities: Landmarks on the Pathways of Life’ [Cambridge University Press]:
p161 - “ ... be they microbes, plants, fungi, or animals, including humans. It is clear that such similarities can be explained only ...”
p171 - “... Eukaryotes, which may be unicellular (protists) or multicellular (plants, fungi, and animals) ...”
p186 - “,,, eventually, with all plants, fungi and animals; without it we wouldn’t be around ...”
p214 - “... all fungi, and all animals are derived each from a single common ancestor ...”

I only have read the abstract of
“From sphere to torus: A topological view of the metazoan body plan”
Harald Jockusch (Corresponding author)
Email: h.jockusch@uni-bielefeld.de
Pages 57-65
Saturday, June 17, 2006
Journal Bulletin of Mathematical Biology
Publisher Springer New York
ISSN 0092-8240 (Print) 1522-9602 (Online)
Subject Mathematics and Statistics
Issue Volume 65, Number 1 / January, 2003
DOI 10.1006/bulm.2002.0319
Abstract From the viewpoint of mathematical topology, membrane systems in intact living cells can be described as closed and orientable surfaces, i.e., as surfaces with two sides and no boundary lines so that an ‘inside’ and an ‘outside’ can be distinguished. Usually, biomembranes represent topological spheres, often one embedded in another one. Toroidal membranes are occasionally observed, e.g., in specialized structures of plant cells like the prolamellar body. Here, we propose that rules analogous to those that govern the topology of biomembranes hold for the epithelial cell sheets that cover anatomically external as well as internal surfaces of multicellular animals. We suggest to study the emergence of morphological complexity during metazoan development using concepts from mathematical topology, and propose experimental analyses of those topological transitions that appear to be relevant in development and evolution.
Based on a lecture held by H J at the Max Planck-Institute for Physics of Complex Systems, Dresden, 26 April 2001.
http://www.springerlink.com/content/47q7pvkr03882252/

I tend to probably oversimplify [and perhaps confuse] the possible relationships in this effort to demonstrate that evolutionary biology has apparently used experimental mathematics [likely related to the GUT / TOE quest of QM and GR] that we as humans now attempt to understand.

These manifolds from different disciplines probably differ primarily in gauge with similar but not necessarily identical structure and function.

I find that my math ability is like using a foreign language - some understanding with visual aids and a dictionary or reference text - but clearly unable to express thoughts attempting to relate one discipline to another in the language of mathematics [I am trying to improve.

Analogies?:

A tree trunk from the upper most root to the lower most limb can have its tree rings almost perfectly represented by cylindrical coordinate tensor calculus.

Reference diagram - JD Fehribach, Vector & Tensor Calculus, Worcester Polytechnic Institute
http://www.math.wpi.edu/Course_Materials/MA2251C99/images/cylndrcl.gif

The only thing that appears to prevent perfect symmetry is a lack of background independence. Tree ring growth is influenced by magneto, gas, liquid and solid influences - sources of actual perturbations.

Consider the whole tree: roots, cylindrical trunk [with pores?], branches and leaves.

Reference diagram - from VA TECH
http://fwie.fw.vt.edu/rhgiles/trevey/img/TreeBasic2.gif [Broken]

Omitting the leaves for a moment, we appear to have a smooth manifold, bounded but infinite [from the fractal perspective] in surface area with a finite volume.

Add leaves, the surface area may almost be doubled [more than one infinity as per George Cantor] and the volume possibly also doubled but still finite.

For simplicity, again omit the leaves.

Technically this tree manifold may be transformed into a fungus manifold.

Fungi appear to be intermediate to flora and fauna.
Reference diagram - from Sydney [text with links to some pictures]
http://bugs.bio.usyd.edu.au/Mycology/StructureFunction/hyphalStructure.shtml [Broken]

The fungus can be transformed into porifera manifold.
The roots become a holdfast.
The branches [become reduced but tend to reappear in Cnidaria] with inflow / outflow pores as ostia and osculum [or branched oscula].

Cnidaria life cycle more tree-like

Reference diagram - Western Kentucky U
Porifera with Cnidaria life cycle - holdfast demonstrated but not named
http://asm.wku.edu/faculty/Lienesch/225/225lab2.html

Reference diagram - U Miami
Porifera [magnified illustrations] holdfast not demonstrated
http://www.bio.miami.edu/dana/pix/spongeanatomy.jpg

Other body plans omitted for some brevity.

Eventually transformation to sequentially segmented genus-1 toroid manifolds of vertebrate, chordates with respect to the gastrointestinal tract.
Holdfast becomes sphincter.
Genus-3 torus of nares and mouth with lungs more like porifera; oral cavity shared with GI torus.

Reference diagram - Central Middlesex Hospital, London, England
http://www.ibs-research-update.org.uk/ibs/digestion1ie4.html

Nerves and blood vessel are branch-like in providing nutrients and information to various organs and single cells. This symmetry is relatively reversed from flora.

Reference diagram - Netterimages.com
http://www.netterimages.com/images/vpv/000/000/004/4621-0550x0350.jpg [Broken]

These life manifolds can interact with earth [magneto, gas, liquid and solid] manifolds and star [sun] manifolds.

The finest roots and branches [capillaries] appear to serve as gauge interfaces - allowing trans-membrane flow; while coarser branches allow for a generally one way cis-membrane flow [regurgitation may occur, usually in illness].

Most of life might be considered as attractors [contained energy] with a predator v prey [dissipator or uncontained energy] relationship.
 
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  • #27
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Speculative response to question on potential energy

Hi CarlB:

RE:
I've been thinking about how I can justify defining a potential energy that is zero on the scalars, and positive for anything else. Looking at the measurement algebra, this is too general. I can get the same effect if the potential gives zero for both 0 and 1, and then gets large for anything else. Like I mentioned before, I was seeing things in terms of Schwinger's measurement algebra where "1" is a free beam, and "0" is a complete beam stop. Both of these require no fields, more or less. But tonight I realized that another way of justifying it, sort of, is as a generalization of maximization of entropy

Is total energy = potential energy + kinetic energy?
If so, consider:
potential energy = attractor
kinetic energy = dissipator
 
  • #28
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0 or 1 could be a probability range

Hi CarlB:

RE:
... I can get the same effect if the potential gives zero for both 0 and 1, and then gets large for anything else...
Speculative analogy suggests that 0 or 1 may represent the probability limits.

Is the result large for numbers between the interval [0,1]?
 
  • #29
CarlB
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Dcase said:
Speculative analogy suggests that 0 or 1 may represent the probability limits.

I hate to mix probabilities with multivectors. In my view, the multivectors (i.e. what are called "complex numbers" in the usual non geometric version of quantum mechanics) are stresses in spacetime and the particles are dislocations that propagate through spacetime. The probabililty interpretation arises from the dislocations being indeterminate. The idea is that a given chunk of spacetime dislocates with a probability that can be calculated from the stress, hence the probability interpretation. After dislocating, the stresses are relieved, hence the Pauli exclusion principle.

Another way of describing this is that you take the Bohmian interpretation, which combines wave and particle information, and split the information into wave information, which give the stress before the dislocation, and particle information, which gives the actual position and orientation of the resulting dislocation. I should admit that I went to school to study mining engineering, so putting things in terms of crystallography makes sense to me. It's been a hobby for most of a half century. As long as I'm on the subject, here's my crystal drawing program written in Java:
http://brannenworks.com/xtl

Dcase said:
Is the result large for numbers between the interval [0,1]?

The whole idea is that the natural unit for the potential energy is the Planck energy, so it is effectively infinite everywhere where it is not zero. The observed particles are supposed to all have mass zero. The observed masses are due to a splitting of a degeneracy. This is why the observed particles can mix so easily.

An alternative approach is to suppose that the various generations are excitations off the 1st generation. This has the defect of being very difficult to explain why there is, according to very good neutrino data, no 4th generation.

Carl
 
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  • #30
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RECIPROCALS as probabilities and particle generations

Hi CarlB:

1 - I think that I understand your reluctance to “mix probabilities with multivectors”.

There may be an alternative perspective of dealing with this which may even satisfy the hypothesis of David Hestenes in ‘The Kinematic Origin of Complex Wave Functions’: RECIPROCALS!

The 1/R to R relationship suggests as many numbers between the interval [0,1] as between the interval [1,oo].

QM statistical probabilities may be equivalent to reciprocals.

Consider this representation of the real [complex similar?] number line:

[+] Positive --->..........1.....................1..........................n..........................
-----------------------+---------------1-------------------+------------------- +oo
|...............................n....................1...........................1.........................
ZERO (0)
|............................1....................1............................n...........................
---------------------_---------------1--------------------_-------------------- -oo
[-] Negative --->......n.....................1...........................1............................

At some gauge / scale or time it may be possible for +oo to coincide with -oo.

Hyperphysics of GA STATE may even demonstrate the probability relationship with reciprocals in ‘The Correspondence Principle and the Quantum Oscillator’ and ‘Comparison of Classical and Quantum Probabilities for Harmonic Oscillator’.
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hosc6.html

Planck length may be the minimal distance [probably as a radius rather a diameter] of an EM torus, black hole or between any strings or manifolds.

If a black hole is an extreme concept similar to the eye of an hurricane, then the Planck mass may be around but not in the black hole as the winds are around but not in the eye of an hurricane. Yet for the black hole the Planck mass would be centered within the black hole as the hurricane winds are centered within the eye.

2 - Could the “the various generations” be phase transitions?
Could there be a plasma phase?

This is of course a speculative analogy.
 
  • #31
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Physics, ME (fluid dynamics) and attractors

Philip Marcus [UC-Berkeley] is one of the few discussing dissipators as well as attractors.

Researcher predicts global climate change on Jupiter as giant planet's spots disappear [see merger video]
http://www.berkeley.edu/news/media/releases/2004/04/21_jupiter.shtml

or

'Chaos' James Gleick [1987 version]
[last page of color inserts, text preceding page; between p 114-115]

and

Jupiter's Great Red Spot - Temperature Structure of Vortex
http://www.gfdl.noaa.gov/products/vis/gallery/index.html [Broken]

I wonder if Red Jr is related to Shoemaker-Levy-9 collision with Jupiter?
 
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  • #32
CarlB
Science Advisor
Homework Helper
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I've discovered the secret of time travel.

Kea,

I've discovered the secret to time travel, at least one way. You sit down and start writing a book. Days just disappear.

But I've finished the 2nd chapter, even sent the thing through a spell checker:
http://www.brannenworks.com/dmaa.pdf

The planned topic of chapter 3 is "Measurement". Chapter 4 is supposed to be "Potential Energy", but seeing that far into the future is tough. Maybe it would be better to make chapter 4 cover the elementary fermions. Otherwise I would put them into the applications part of chapter 3.

At this time I'm ceasing working on book and preparing lecture for the meeting in Hawaii. They're giving me 25 minutes and I don't want to embarass self by insufficient preparation.

Liquafaction Corporation has kindly allowed me 3 weeks leave with pay to get ready for, and attend, the conference. Thank you, Mark Mollo. Which reminds me, I need to type up an acknowledgements section. And I need some sort of subsection break mark, to indicate when a multiparagarph argument has completed. And I need to type up some sort of exercises for the student at the end of each chapter. And I don't think I have enough marginal notes in the last half of chapter 2. And I haven't proof read the index (which is easily the most boring thing one can imagine doing with ones brief time on earth). And etc., etc., etc.

Carl
 
  • #33
Kea
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CarlB said:
I've discovered the secret to time travel, at least one way. You sit down and start writing a book.

I must try it sometime. But please keep going! :smile:

At this time I'm ... preparing lecture for the meeting in Hawaii.

Great! Please report back on all the gossip. We just love conference blogging.

Good luck. :smile:
 
  • #34
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I am naive!

The Reimann Sphere accomplishes what I was trying to say in my post of 10-11-2006 02:22 PM.

0 at the south pole

oo at the north pole

only reals along the longitude when a=0 for ai

complex along the longitude when a not= o for ai

equator = 1

45 degrees south = 1/2 in interval [0.1]

45 degres north = 2 in interval [1,oo]

Thus any complex number or vector may [?] be mapped to interval [0,1] gainng an insight into the probability of that number or vector whether in [0,1] or [1,oo]
 

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