3 dimensions and their 6 directions
in [Physics]
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From: spudnik on 5 May 2010 17:01 you can get rid of phase-space ("spacetime") with "movies" (or flip-books), becuase it is totally useless in a non-mathematical-formalist sense, "visualization" e.g. -- death to the lightcones!... and, it gives you an extra spatial dimension to play with. as for the idea of using two quaternions for "in & out," I don't really see, why it'd help, since you can use the same quaternion coordination for both, unless there's some dimensional analysis that needs a pair of them. (see Lanczos' _Variational Mechanics_, Dover Publ., for his treatment of SR -- good luck .-) thus: the second root of one half is just the reciprocal of the second root of two -- often obfuscated as the second root of two, divided by two -- but the rest is indeed totally obscure or ridiculous. since Fermat made no mistakes, at all, including in withdrawing his assertion about the Fermat primes (letter to Frenicle), all -- as I've popsted in this item, plenty -- of the evidence suggests that the "miracle" was just a key to his ne'er-revealed method, and one of his very first proofs. (I wonder, if Gauss was attracted to the problem of constructbility, after reading of the primes.) thus: so, you applied Coriolis' Force to General Relativity, and **** happened? > read more ยป --Light: A History! http://wlym.TAKEtheGOOGOLout.com
From: Thomas Heger on 5 May 2010 18:27 spudnik schrieb: > you can get rid of phase-space ("spacetime") > with "movies" (or flip-books), becuase > it is totally useless in a non-mathematical-formalist sense, > "visualization" e.g. -- death to the lightcones!... and, > it gives you an extra spatial dimension to play with. > imagine a spacetime diagram of a train. Than certainly this train is not going 'upwards', only this spacetime view is like this. This would mean, that our 'now' is actually moving along some line (to keep the train horizontal). If this line would point downwards, than objects would fall. If that 'now' is actually real, but not really visible, than we had to look at a plane perpendicular to our timeline for visible objects. In this picture the sun and the planets perform a real movement perpendicular to the ecliptic and their path' are helical curves. These helical curves could happen on all scales, but with different frequency and superimpose in a fractal way. Light is in this picture an unstable (not timelike) helix, that spirals along a cone, because the spacelike interval equals the timelike (light has no mass). So light denotes the massless type of connections or 'influences', but only for us and our point of view. Because this direction is the lightcone only compared to our timeline. If this timeline is tilted, than this relation is not masslees any more and radiation turns into matter. Since distance in space means age, too, events we see now didn't happen at the same time and could not possibly be the reason to each other (especially not to those happening 'before'). Since we define space over light, we do not address with this term the 'real now', but our impression of the past. If this 'now' would be real, though invisible, than we get some kind of distorted inside view on the 'real world'. > as for the idea of using two quaternions > for "in & out," I don't really see, why it'd help, > since you can use the same quaternion coordination > for both, unless there's some dimensional analysis > that needs a pair of them. (see Lanczos' > _Variational Mechanics_, Dover Publ., > for his treatment of SR -- good luck .-) > 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. Greetings TH
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. |