3 dimensions and their 6 directions
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From: spudnik on 5 May 2010 18:41 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.
From: Thomas Heger on 6 May 2010 01:21 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 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 for, because they enable a smooth transformation of the axes and could 'morph' space into time. But this would also morph matter into radiation (or back), what is a bit counter-intuitive. There are some theories, that model particles with bi-quaternions. This is why assume, that matter is actually a structure within such a 'bi-quaternion field'. Greetings TH
From: spudnik on 6 May 2010 01:43 in other words, you're just BSing me. anyway, just use the quaternions "real, scalar" part to paramaterize the time, and the "pure, imaginary" part as the three orthogonal axes.
From: Thomas Heger on 6 May 2010 08:40 spudnik schrieb: > in other words, > you're just BSing me. anyway, No, I try to describe an idea, that I'm working on. (In case You want to read more, You may look at my 'book': http://docs.google.com/Presentation?id=dd8jz2tx_3gfzvqgd6 ) > just use the quaternions "real, scalar" part > to paramaterize the time, and > the "pure, imaginary" part as the three orthogonal axes. Actually complex-four-vectors (or bi-quaternions) are not the same numbers as Hamiltons quaternions. The four components have no specific meaning. The idea is, that an 'element of spacetime' behaves in a way that is connected to the neighborhood like you would multiply those numbers. This could be interpreted in the same way as complex numbers, like a spinning pointer. But this numbers spin in volume, what is difficult to describe. They whys and hows of this model are not easy to explain, but the model is very simple. The main idea is a 'mechanism' that could be ubiquitous and appear in many different forms and sizes. The rule is, that the spacelike neighbors are twisted in the same direction and that the space is anti-symmetric. Because it treats time in a geometric way, it is quite counter-intuitive, since we usually think about time as a steady flow. But relativity tells us, that time is not, but a phenomenon, that has to be measured locally in a process of counting rhythmic events. Greetings TH
From: Tim Golden BandTech.com on 7 May 2010 08:47
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. - 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. - Tim > for, because they enable a smooth transformation of the axes and could > 'morph' space into time. But this would also morph matter into radiation > (or back), what is a bit counter-intuitive. > There are some theories, that model particles with bi-quaternions. This > is why assume, that matter is actually a structure within such a > 'bi-quaternion field'. > > Greetings > > TH |