3 dimensions and their 6 directions
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From: spudnik on 7 May 2010 14:27 you are pretending to define "complex 4-vectors," but "real" 4-vectors are part of the gross and unfinished porgramme of Minkowski, to "spatialize" time, while it is quite obvious that the "time part" is not symmetrical with the spatial coordinates, either in 4-vectors or quaternions. anyway, bi-quaternions would be 8-dimensional or octonions. and, it is all obfuscation, trying to insist that a phase-space tells you what time really is; it's very useful for seeing patterns "in" time though, as in electronics (although, NB, electronics is mostly done in "1-1" complex phase-space, instead of quaternions, as it could be, for some reason .-) maybe, all you and polysignosis need to do, is work the math of quaternions ... that'll take me wome time, as well. (I mean, what is the difference in labeling a coordinate axis with a "different sign" and a different letter, whether or not negatives are even needed?) thus quoth: Actually complex-four-vectors (or bi-quaternions) are not the same numbers as Hamiltons quaternions. The four components have no specific meaning. and: Because it treats time in a geometric way, --Light: A History! http://wlym.com
From: spudnik on 7 May 2010 14:47 how do you know, Lanczos did that, and how'd coordinates geneate fractal patterns, and why would that matter?... if you believe in the Big Bang, then it seems to have had a period, as opposed to "frequency," of 13 billion years, but none of this seems to even be able to be quantized a la "biquaternions;" so, why bother? thus quoth: Lanczos used biquaternions and a couple of others. Interesting is how they generate fractal patterns: Imagine the cosmological scale and the expanding universe. That has a 'frequency' in the range of 13 billion years. Now make the time shorter to -say- a day and we get a sphere, like the surface of the Earth. If this frequency is getting higher we get very small spheres, like atoms and much higher we get subatomic structures. Than we superimpose all of those and find it would look quite like the observed world. thus quoth: you are pretending to define "complex 4-vectors," but "real" 4-vectors are part of the gross and unfinished porgramme of Minkowski, to "spatialize" time, while it is quite obvious that the "time part" is not symmetrical with the spatial coordinates, either in 4-vectors or quaternions. anyway, bi-quaternions would be 8-dimensional or octonions. and, it is all obfuscation, trying to insist that a phase-space tells you what time really is; it's very useful for seeing patterns "in" time though, as in electronics (although, NB, electronics is mostly done in "1-1" complex phase-space, instead of quaternions, as it could be, for some reason .-) maybe, all you and polysignosis need to do, is work the math of quaternions ... that'll take me wome time, as well. (I mean, what is the difference in labeling a coordinate axis with a "different sign" and a different letter, whether or not negatives are even needed?) --Light: A History! http://wlym.com
From: Thomas Heger on 8 May 2010 12:33 spudnik schrieb: > you are pretending to define "complex 4-vectors," > but "real" 4-vectors are part of the gross and > unfinished porgramme of Minkowski, to "spatialize" time, > while it is quite obvious that the "time part" > is not symmetrical with the spatial coordinates, > either in 4-vectors or quaternions. anyway, > bi-quaternions would be 8-dimensional or octonions. > What I did was a bit crude and goes like this: I put 'physics into a shredder and sieved it' and than I looked, what remains in the net. So I tried to count exponents, Pis or sin/cos/exponential functions and tried to reassemble the pieces. In a way complex numbers, arc- and exponential functions and quaternions seem to be the most important. Quaternions with complex entries are bi-quaternions (or the one type of octonions - if you like. The other have eight components as quaternions have four.) Than I have drawn, what you could possible do with those numbers and compared it with observed phenomena. As being not such a good mathematician, I have searched for developed systems of this type and found a few, that look very convincing. The rest is just a bet. Minkowski was right - and all the others, that used such a construct: Hamilton of course, Tait, Tesla (!), Maxwell, Lanczos and a few in recent days like Prof. Rowland or Jonathan Scott. (Bi-quaternions I wanted to model 'internal curvature' as curved spacetime of GR: Imagine an event, described by one quaternion. Than it would require (at least) two, that an event could have some features. So these two act antagonistic and in a general case describe a straight worldline. Because gravity curves worldlines, gravity causes radiation, too. It is more easy to see this phenomenon in the trail of a comet. According to my model the trail is generated as disturbance of the solar wind, that is not radiating. But if those 'elements of spacetime' get disturbed (by a rock flying through), they get tilted and start to radiate. ) > and, it is all obfuscation, trying to insist that > a phase-space tells you what time really is; > it's very useful for seeing patterns "in" time though, > as in electronics (although, NB, > electronics is mostly done in "1-1" complex phase-space, > instead of quaternions, as it could be, > for some reason .-) > I think about programming something, because math is something, I have not enough knowledge about and I don't know, how to cast the model into formulas. This is difficult, even if you know what you want to achieve. Now I have no good idea about how to do that. But I could recommend Peter Rowlands book "Zero to infinity", what is essentially about the same idea. > maybe, all you and polysignosis need to do, > is work the math of quaternions ... Tim is among the very few, that was not rightout hostile to my ideas, but supported me a bit. Maybe his numbers would work even better. I can't tell, but it should possible to find out. > that'll take me wome time, as well. (I mean, > what is the difference in labeling a coordinate axis > with a "different sign" and a different letter, > whether or not negatives are even needed?) > Certainly 'before' could be labeled with a minus. Since a 'now' would require imaginary connections, this minus could be shifted to the 'side' and we could label the imaginary sides with plus and minus, too. The usual Euclidean view would require 'preexisting' curves, but we know, that things evolve and do not just exist as they are. So, even a line in space would be static and we know, this would be our impression, but not a physical entity. Euclidean space is meant timeless and this is not the right picture for physics. What is the right picture than? As said, my bet would be, this bi-quaternion system would work best. Greetings TH
From: Thomas Heger on 8 May 2010 12:52 spudnik schrieb: > how do you know, Lanczos did that, and > how'd coordinates generate fractal patterns, and > why would that matter?... if you believe > in the Big Bang, then it seems to have > had a period, as opposed to "frequency," > of 13 billion years, but none of this seems > to even be able to be quantized > a la "biquaternions;" so, why bother? > Actually I can't tell for sure, that Lanczos used bi-quaternions, but I have found this paper http://arxiv.org/PS_cache/hep-ph/pdf/0112/0112317v1.pdf Fractals are usually build with complex numbers, like the Mandelbrodt set. If we have a generally multiplicative connection within a continuum of such a type, this could have a fractal behavior. That is organized stepwise, like the Szerpinski triangle. We would actually see this behavior in the real world, if we would not insist on assigning different attributes to the entities on the different levels. In the big-bang-theory I don't believe at all. Mainly because it would heavily violate my own ideas and because I think, the idea is contradictive and illogic. But as expansion and contraction are a part of my model, the universe as we see it could be the expanding part of a process with extremely long periodicity. Greetings TH
From: Thomas Heger on 8 May 2010 13:53
Tim Golden BandTech.com schrieb: > On May 6, 1:21 am, Thomas Heger <ttt_...(a)web.de> wrote: >> spudnik schrieb: >> >>> in a paper diagram, >>> the space is one dimensional, so there's no "upwards" available; >>> a mind is a terrible thing to waste on spacetime formalisms! >>> Lanczos used quaternions for "3+1" dimensions, >>> the same as Hamilton's "vector analysis." >>>> imagine a spacetime diagram of a train. Than certainly this train is not >>>> going 'upwards', only this spacetime view is like this. >> The 'real world' is somehow 'volumetric' or things happen in volume and >> not on paper. But this volume or what we usually call space is an > > Hi Thomas. This is some pretty dynamic thinking here. I just want to > point out that the adoption of a 'volumetric' interpretation can > branch away from Euclidean geometry a bit more than some may realize: > > When we take a solid object as the means of observing the freedoms of > space (rather than the Euclidean point) we observe a six dimensional > freedom of space. Even if we accept that the solid is composed of > points, then when we fix the position of one of those points in space > (three coordinates) then the object is still free to rotate about that > fixed point. Choosing another point on the object we witness two more > coordinates are necessary to fix that point in space, and then with > the object rotating on this new axis we see that one more coordinate > completely fixes the object. This is not just a total of six > coordinates. This is a structured form: > x11, x12, x13 > x21, x22 > x33 > This structure we see repeated even within tensor theory where the > antisymmetric tensor becomes important in the expression of > electromagnetism. Eliminate the informational redundancy of that > antisymmetric tensor and you will see this form. This form is exposed > through polysign to provide emergent spacetime, as well as fundamental > algebraic number systems. This is recurrent information and within > information theory this suggests that there is a more compact > expression of theses ideas which can then yield these things, without > redundancy. > > Anyway, I just wanted to amplify what may be going under the radar, > and encourage you on down toward the fundamental, where what we > overlook is what we are after. > Hi Tim (always nice to hear from You. ) I think, we need some kind of blatantly simple 'mechanism', because nature could not be very complex on a fundamental level. Since relativity is regarded as somehow proven, than it would be natural to start we it. This -by the way- would rule out the assumptions of QM as fundamental. So particles would only be a special view on certain structures. E.g. we know from experience, that matter is somehow connected. Why then would we treat these connections different from the particles? Particles could only be a special case of something more fundamental. So something connects these particles and that is spacetime itself, that has 'vortices', what we experience as entities. With this idea we could immediately get rid of a lot of trouble and paradoxes, like 'length-contraction' of SR. The Euclidean view about space would require some kind of static space and an 'absolute' one, too. But if we think relativistic, than space itself has to be relativistic. That isn't such a hard problem, but matter as well should be described relativistic, what is particularly hard to accept. Than we treat time usually uniform and like a steady flow. But this is not an allowed view then. My alternative view would be 'time-domains' of spherical shape, that share the same time (like the surface of the Earth) > - Tim > >> abstraction, too, because it is timeless. If we denote a distance in >> lightyears, than the events in such a distance happened that long ago. >> Now it's somehow illogic to think, that events happened later could >> influence those that happened before. So, what we call space is our >> view, but not 'real'. >> The 'real thing' is than invisible or imaginary (because we could >> imagine, it would exist). In this view timelike and spacelike are >> imaginary directions and the real (described with real numbers) axes of >> space are those, that lie on the light cone. >> If we put the light-cone vertical, than the plane perpendicular is >> actually curved and builds the surface of the Earth. That means, the >> timeline has a geometric meaning and has to be understood locally. >> To achieve this I use a construct called triality, that could be >> arranged to a tetrahedron. From these we need two, that act >> antagonistic. These two tetrahedrons are the two parts of a >> bi-quaternion, what has eight components. >> One is expanding and one contracting and the results are standing waves, >> but only for an axis of time, where those structures are stable and this >> axis could be smoothly curved. This is, what the quaternions are good > > Yeah. This is a pretty construction, but I feel the standing wave > claim is dubious. > This is a problem I see no support for within any wave interpretation > of matter. > The stability of the matter is in direct contradiction to wave > propagation, and so I feel that those theories should address this > conflict head-on. In effect don't we need a basis for the standing > wave rather than just popping it out of thin air? I understand that > there is experimental support for it, but that is not a theory. That > is curve fitting. I guess we're near the stress tensor within > relativity theory. Within pure elastic and compressible spacetime it > is not difficult to picture a droplet of compressed space that would > then push outward, then having stretched itself thin, would contract > again, yet why the effect would not eventually dissipate as > propagation throughout the medium is the problem we face. In effect > you are forced to detatch space, which is no longer a continuum > concept. I guess this is near to a spin foam or some such logic that I > have only thin understanding of. Even within this detatched paradigm > the propagation problem remains until interaction ceases. > Spacefoam is like string-theory a model with preexisting entities (foam, strings). But personally I would prefer a 'nothing concept', meaning 'no things'. Would there be the need of something, than why should that exist and why should it be at the supposed place? This is an relativistic view, too, because of the energy mass relation. Than we would perceive some kind of energy flow with internal structure, that we interpret as matter or radiation, because we have some kind of internal view. Greetings TH |