Re: Structured spacetime

Jonah Thomas schrieb:
Thomas Heger <tt_heg@xxxxxx> wrote:
Jonah Thomas schrieb:

The discussion of the term 'dimension' on the basis of a mathematical construct is somehow fruitless. Since I want to use a method, that has

eight components, this wouldn't make the world eight dimensional.

If the eight components are independent of each other, so that one can
vary without directly affecting the others, then they function as
dimensions by that meaning. But you don't want to use the words that
way. That's OK, just a lot of other people do use the word with that
meaning.


I want to show, that these components are not independent and why and how they are connected.
First the model is about complex numbers. Those you can arrange in a plane and give a geometric meaning to them. In one interpretation they are composed out of a rotation angle and a rotating vector, having a magnitude r.
Take this picture and multiply it by three. That has three angles and three magnitudes.
As I want to use the scalar part for time, we could come to the idea, that a change in space equals to a change in time. So in a given instant we have delta t=0. Meaning that we have three dimensions of space, if we take only the real parts of the three complex planes.
But we could shift the entire picture around an imaginary axis and than things speed up.
Time behaves like an axis, if you think about a rotor in this complex plane. Since there are actually three planes, this generates spherical structures.
So we need four complex number to describe a state, because we could rotate the time axis, too. This is a complex four vector.
Now it is really amazing, that you could do all kinds of physics with those numbers. From classical mechanics over relativity to quantum mechanics. They are even easier to handle, than most other constructs for equivalent purposes (matrices, tensors etc.).
It somehow puzzles me, that they are rarely used.

TH
.

Relevant Pages

  • Re: Meaning, Dylan and his commentators
    ... I once read a book called "The Meaning of Meaning' and my fourth wife, ... what I mean and come up with a common denominator. ... once it gets overly involved in the material dimensions of this world. ... Only Dylan knows what Dylan means by his lyrics. ...
    (rec.music.dylan)
  • Re: Meaning, Dylan and his commentators
    ... I once read a book called "The Meaning of Meaning' and my fourth wife, ... what I mean and come up with a common denominator. ... once it gets overly involved in the material dimensions of this world. ... Only Dylan knows what Dylan means by his lyrics. ...
    (rec.music.dylan)
  • Re: Kants thought experiment : is chirality a dimension?
    ... We talk in clichés, the meaning of "off" in each case ... However, the dimensions of a brick are its width, length and height. ... I have a one-dimensional line and live in a three-dimensional universe. ... Kant was not a mathematician and never programmed a computer. ...
    (sci.physics)
  • Re: Setting constants like hbar to unity
    ... This is physics. ... > dimensions become equal when constants are set to unity. ... They have no 'real' meaning, beyond defining a unit system. ...
    (sci.physics.research)
Quantcast