On May 27, 5:44 pm, zookumar yelubandi <zooku...@yahoo.ca> wrote: > On Wed, 26 May 2010 04:30:39 -0700 (PDT), Tim Golden BandTech.com wrote: > > On May 26, 12:07 am, Thomas Heger <ttt_...@web.de> wrote: > [...] > >> Interesting question would be, what would happen, if that is not seen by > >> us, but with a timeline in an angle - say perpendicular. That is a kind > >> of multiverse picture, where our matter is radiation and our time is a > >> spatial axis. That doesn't need to be far away, but could be 'round the > >> corner'. > > >> Greetings > > >> Thomas > > > I can only half follow what you are describing, but I do see that you > > are exercising a recurrent phenomenon. When you step up to a bi- > > quaternion aren't you now in an 8D work space? > > > As you are thinking in terms or rotation quite a bit, then this is a > > fine area of primitive mathematics to focus on. > > > Can one object have several axes of rotation? Here Euler angles would > > have one thing to say, but can we already accept that even within 3D > > that there are multiple axes? Let's say I spin a top aligned > > vertically here at roughly 43 degrees north latitude. This top may be > > spinning relative to me at, say, 600 rpm. Is it also spinning about > > the earths rotational axis at 6.9E-4 rpm? Experiment and math will > > tell us that it will not. But what about in higher dimension? If we're > > going to worry about the 'axes' of the electrons in the spinning top > > then we'll have to admit that we've caused precessionary forces. What > > about in the atomic nuclei? > > Can there be multiple rotational axes as long as they reside outside the > body of the object? The question of the nuclei wouldn't arise (??? )then > because the group can rotate together about any number of external axes > (but about only one internal axis at any one time). Here, each successive > larger axis of rotation must absorb the entire orbit of rotation about the > preceding smaller axis. In effect, the smaller orbit itself becomes the > object of rotation about the larger axis. Let me get a cup of coffee. > My brain wants to really believe this; but whenever that happens, I know > it's a trap. ;)
Well, I am this way too. A gyroscope's behavior tells us that this 'multiple axes of rotation' will not exist. Even without all that freedom a bike wheel spinning in our hands tells us 'no'. Then coming down to math, what do we have? We can give up mass at this level, and if we want to discuss a solid object and its many possible orientations then we have no problem, but when we attemp to superimpose two simultaneous rotational axes onto one object I believe we witness a noncomuttative property. I may stand to be corrected here, but I'll try to expound on why I think that this is so.
In order to even declare a single rotational axis on an object we will be forced to select two point positions (for a three dimensional object) as forming the axis, and to specify a distict amount of rotation we might take a third point and expose it's traverse.
To declare a second rotation we should repeat the steps of the first selection, but with unique points. These then are two independently defined rotational axes, each acceptable on its own terms.
If we perform the first rotation, then perform the second rotation then we should witness the object's traverse over those discrete rotations.
When we perform the second rotation then the first rotation we witness a new position different from the first commutation of the operation.
I am reasonably comfortable verifying this with a mug with a handle on it here at my desk, performing two 90 degree rotations.
> > Thinking about this longer, doesn't rotation imply restoration? Can > precessionary forces involving multiple axes ever restore a point such that > we can measure its periodicity? > > One question begets another. > > Just thinking out loud ... say you have a solid sphere. Spin it about the > Y-axis. Simultaneously, spin it about the X-axis. Can this be done > without changing the fixed relation of the sphere's composing atoms? > My intuition says no. Which is why I propose that multiple axes of spin > can only be achieved if the axes reside outside the body of the object; > moreover, that successive imparted spins must involve the entire orbit of > the previous imparted spin. It's a tad abstract.
Hmmm. To define the spin on an object from outside carefully would be helpful. Above I've tried it in a way that is coherent to the object. Anyway, these exercises are free aren't they? If you wound up with a coherent model of how that sphere's 'atoms' rearranged themselves you could well wind up with a new theory of atoms. Whether to remain in the physical or recover the physical from a seemingly ambiguos definition... I'd try for the latter, but have a hard time getting away from the former.
> > Then there's the circular saw. You can turn it on its natural axis and > cut yourself a nice piece of lumber, but if you place the next spin axis > anywhere where it intersects any part of the blade's peripheral orbit ... > watch out.
Nice, and we do actually have the ability to control the orientation of that saw with a good amount of freedom, though the forces involved may be a bit trickier than we realize when doing that. It's not as if we're caught in a precession that will not end, cutting aside. Thanks Zook.
> > > > > Somehow I still feel satisfied that there can be many rotational axes, > > and that all of matter can be in such a dizzying rotational flux, and > > that we have no sense of it because all that is around us is in > > similar flux. I've actually had this as an intense sensation before > > and it was memorable. It is a bit chaotic and I don't mean to validate > > it by this means, just trying really to go toward some simple math. > > It is possible to constrain to a purely rotational system, by fixing > > all positions to a unit radius within a 4D Euclidean space. One could > > call this a unified theory from the get go, because of the unity > > distance constraint. What is left is 3D freedom, but no access to the > > origin. All of this 3D freedom is expressible in angular quantities, > > yet there is not necessarily any distinction from standard space, > > except over long distances, where it should be possible to travel in > > one direction and land back at yourself again. Wouldn't it be a grand > > chuckle if all those galaxies were just prior versions of us in a > > kaleidoscopic array? This then would lead us to believe that we are > > existent in a pocket of well behaved space, for the vast open > > territory never populated. This is anathema to Einstein's postulate, > > but I see no problem with it. Space is not the same in all directions. > > I look left and I see a chair. I look right and I see a bucket. This > > is sufficient evidence to observe that space is not the same in all > > directions. > > > Rotation is an awfully pretty concept. That it might be defined in > > terms of translation is just one way to look at things. Translation > > can also be looked at as rotation. We've been programmed to work from > > the Euclidean basis, at least I have, and I wish that I could make > > more sense of the unified rotational approach. Anyway, it's exercise. > > The 'multiple axis problem' is what I see. > > - Tim > > Yes, very interesting stuff. > > Uncle Zook