Page 1 of 3 123 LastLast
Results 1 to 30 of 69

Thread: Complex four-vectors

  1. #1
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771

    Complex four-vectors

    Hi
    there is a mathematical description called complex four-vectors, that I would like to recommend.
    That are ordered four-tupels and behave more like bi-quaternions than like vectors (hence I put them into the family of quaternions, too).
    There reason for chosing this kind of mathematical representation are "aestetical" - meaning categories like simplicity, usability, elegance and power.
    In this meaning I call that model "beautiful" and highly recommend to have a look.

  2. #2
    Join Date
    Aug 2002
    Posts
    9,558
    And what exactly is ATM about this document?
    This gets taught at any good university that is serious about its math and electrodynamics programme.
    But thanks for the doc anyway, it's always nice to have some more references.
    All comments made in red are moderator comments. Please, read the rules of the forum here, the special rules for the ATM section here and conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    Catch me on twitter: @tusenfem
    Catch Rosetta Plasma Consortium on twitter: @Rosetta_RPC

  3. #3
    Join Date
    May 2004
    Posts
    4,135
    thomheg, where are you going with this?

  4. #4
    Join Date
    Oct 2007
    Posts
    5,398
    Quote Originally Posted by thomheg View Post
    Hi
    there is a mathematical description called complex four-vectors, that I would like to recommend.
    That are ordered four-tupels and behave more like bi-quaternions than like vectors (hence I put them into the family of quaternions, too).
    There reason for chosing this kind of mathematical representation are "aestetical" - meaning categories like simplicity, usability, elegance and power.
    In this meaning I call that model "beautiful" and highly recommend to have a look.
    Thank you, this is a very nice book. What is ATM about your claim?

  5. #5
    Join Date
    May 2004
    Posts
    4,135
    thomheg, is this an attempt to say something like, "A lot of respected physicists use addition and find it useful for the formulation of their theories. I also use addition in my theory, therefore my theory must also be plausible"?

  6. #6
    Join Date
    Apr 2005
    Posts
    11,545
    I was under the impression (from one of his "disciples") that David Hestenes' geometric algebra was sorta against the mainstream, but was gaining adherents.

  7. #7
    Join Date
    May 2004
    Posts
    4,135
    Quote Originally Posted by hhEb09'1 View Post
    I was under the impression (from one of his "disciples") that David Hestenes' geometric algebra was sorta against the mainstream, but was gaining adherents.
    That's possibly true, but with thomheg we never get beyond the introduction of some mathematical concept, and then handwaving about how it applies to his theory, but with no real description of how they are really used in his model.

  8. #8
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by adsar View Post
    Thank you, this is a very nice book. What is ATM about your claim?
    I just wanted to hear some comments. As I like the book and the mathematical idea behind, I wanted to get some kind of feedback.
    Actually I'm looking for a mathematical description for an idea I'm working on, that was related to quaternions.
    Since quaternions were nice, but it seems to be a kind of family, I have searched for some better way. This paper remaind in my 'dragnet'.
    If you like to read about my ideas, you should go to the personal info page of BAUT and follow the link to my 'homepage', what is a google.doc presentation, that I utilize as a -public- notebook.

  9. #9
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by adsar View Post
    Thank you, this is a very nice book. What is ATM about your claim?
    Don't know.
    Is this mainstream or not??

  10. #10
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by tusenfem View Post
    And what exactly is ATM about this document?
    Maybe it's better at Q&A.
    The idea I have in mind is, that if quaternions, real four-vectors, complex and real numbers could be treated as a sub-set of those objects, than it would anable a way to modell all branches of physics on the same footing.
    Actually the author mentioned relativity, electrodynamics and quantum-physics.
    Matrices in contrast suffer from various problems. To mention a few: they are very un-intuitive. There have to be negotiations about the meaning of the variables and their connections and the indices make it more difficult to write equations.

    Quote Originally Posted by tusenfem View Post
    This gets taught at any good university that is serious about its math and electrodynamics programme.
    Is it true, that this kind of math is used quite usually?
    Than how does it happen, that apparently all papers are written in the far less intuitive matrix notation?

  11. #11
    Join Date
    Aug 2002
    Posts
    9,558
    Quote Originally Posted by thomheg View Post
    Maybe it's better at Q&A.
    The idea I have in mind is, that if quaternions, real four-vectors, complex and real numbers could be treated as a sub-set of those objects, than it would anable a way to modell all branches of physics on the same footing.
    Actually the author mentioned relativity, electrodynamics and quantum-physics.
    As the OP did not have a question, it has no place in Q&A.
    It was a "Oh look what I found!" message.
    And I am sure you are somehow going to press your old idea again, somehow.

    Quote Originally Posted by thomheg View Post
    Matrices in contrast suffer from various problems. To mention a few: they are very un-intuitive. There have to be negotiations about the meaning of the variables and their connections and the indices make it more difficult to write equations.
    The fact that YOU cannot "intuitively" understand matrices means nothing. In normal physics the matrices are very well defined and understood. The book you linked to starts discussing matrices on page 6. Section 4.2 spinors! (matrices) Table 4.1 vector transformations using matrices. And so on and so on. I am beginning to wonder why on Earth you linked to that book.

    Quote Originally Posted by thomheg View Post
    Is it true, that this kind of math is used quite usually?
    Than how does it happen, that apparently all papers are written in the far less intuitive matrix notation?
    That whole book you linked to is full of matrices! You seem, for some reason or other, infatuated with quaternions. So, instead of the 4 vector (ict, x, y, z) I will use the "quaternion" (ct, ix, iy, iz), so what? (I know I am simplifying it here a bit, but anywhoooooo). It just happens that the "normal" vectors and matrices are much easier to handle. Also, lots of stuff in that book are just ordinary 4 vector stuff, that is why I say it gets taught at any serious university.

    I found this page where there is a word document with the original document of Maxwell. The pfd of that page shows the 20 quaternion equations by Maxwell.

    So, I have no idea what you want, up to now you have not really shown what you want to do, rewrite physics into quaternion notation? Be my guest.
    All comments made in red are moderator comments. Please, read the rules of the forum here, the special rules for the ATM section here and conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    Catch me on twitter: @tusenfem
    Catch Rosetta Plasma Consortium on twitter: @Rosetta_RPC

  12. #12
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by tusenfem View Post

    That whole book you linked to is full of matrices! You seem, for some reason or other, infatuated with quaternions. So, instead of the 4 vector (ict, x, y, z) I will use the "quaternion" (ct, ix, iy, iz), so what? (I know I am simplifying it here a bit, but anywhoooooo). It just happens that the "normal" vectors and matrices are much easier to handle.
    Actually I think, both objects are the same, but multiplied with i.
    Relativity is quite easy to explain, if you think about it as a rotation of one observation into an other. Usually specific matrices are used. 3D-programmers use quaternions for shuffeling their monsters around in space and time and express these rotations over quaternions. They behave better, since they don't suffer from drift or gimbal-look. That's why that system is often hard-wired into grafic-cards. Now, it seem like physicists deal with equivelent problems. Then from time to time someone comes to the idea, that it's less troublesome to deal with these objects than with matrices.
    The reactions about such suggestions are not allways polite. That is kind of puzzeling me: if there is a system, proven to be usefull, than why it isn't used?

    I found this page where there is a word document with the original document of Maxwell. The pfd of that page shows the 20 quaternion equations by Maxwell.
    Thanks a lot for this link. Heard of Tim Bearden before, but not visited his site.

    So, I have no idea what you want, up to now you have not really shown what you want to do, rewrite physics into quaternion notation? Be my guest.
    As former programmer I understand the author better than most of papers in physics. Those software developers deal with problems in a different way. The result counts and not the way: meaning, that you have to develop something that works, but you decide how to make it work. And they want reliable results for moderate effort.
    These principle differ greatly from how physics work. Actually I'm not a physicist and don't need to do anything, but possibly could give some hints.
    In software development there are data objects and programm objects. In physics we have operators acting upon some fields. So that field could be treated as data, and its behaviour associated with programm objects. It turns out, that there is an easy way, if you would treat these four-vectors as objects and their behaviour over the associated algebra. What I want to say is this: that you can describe all (!) kinds of observed systems this way, what would include particles and fields, plus various other phenomena.

  13. #13
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by tusenfem View Post
    So, I have no idea what you want, up to now you have not really shown what you want to do, rewrite physics into quaternion notation? Be my guest.
    Why not? Sometimes I guess modern physics is uncurable in the mess and a complete reformulation would be the best. But certainly not by me, but possibly I could spark the process, since the physicists in the world count in the hundred thousands.
    A few minor corrections to common believes are inevitable and most certainly the task isn't particularly easy.

  14. #14
    Join Date
    Oct 2007
    Posts
    5,398
    Quote Originally Posted by thomheg View Post
    Why not? Sometimes I guess modern physics is uncurable in the mess and a complete reformulation would be the best.
    You are probably unaware but modern physics is:

    1. formulated in terms of 4-vectors
    2. confirmed by experiment

    So, what is your contribution?


    A few minor corrections to common believes are inevitable and most certainly the task isn't particularly easy.
    What corrections? Spell them out.

  15. #15
    Join Date
    Jun 2008
    Posts
    2,779
    Quote Originally Posted by tusenfem View Post

    That whole book you linked to is full of matrices! You seem, for some reason or other, infatuated with quaternions.
    And no one should be surprised that a book on a facet of algebra uses linear algebra.

    The quaternion group is often realized as the subgroup of GL2C (invertible 4x4 matrices with complex entries) generated by the matrices

    | 1 0 | | sqrt (-1) 0 | | 0 -1 | | 0 sqrt(-1) |
    | 0 1 | | 0 -sqrt(-1) | | -1 0 | | sqrt(-1) 0 |

    You can use that as a basis to get the quaternion algebra by allowing sums and scalar multiples.


    The group is also generated by

    | 1 0 | | 1 0 | | 0 1 | | 0 -sqrt(-1) |
    | 0 1 | | 0 -1 | | 1 0 | | sqrt(-1) 0 |

    The last 3 of which physicists may recognize as Pauli spin matrices.


    The point being that quaternions are not particularly a means of avoiding matrices. If you have a vector space, and you have linear transformations, then once you have picked a basis you are rather stuck with matrices.

    This can all be viewed as a small piece of the theory of Clifford algebras. Clifford algebras are not a means of avoiding linear algebra either.

    There is nothing magic about quaternions. In those areas where they offer a genuine simplification (as in the handling of rotations in computer simulations) they are used. But there is no mystery. They have been studied in detail, many years ago. The benefits are known and have been harvested. Where they are not used, it is because they offer no advantage. The astute reader will notice that they are not widely used.

  16. #16
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by adsar View Post
    You are probably unaware but modern physics is:

    1. formulated in terms of 4-vectors
    2. confirmed by experiment

    So, what is your contribution?

    What corrections? Spell them out.
    My plan is -roughly- to do quantum-physics with relativity. That is more or less the opposite approach than quantum-gravity. For this purpose a good representation of spacetime is required. That is - as I assume- this method called complex-valued four-vectors. From this I want to derive things like atoms over multiplicative connections of adjacent points.

  17. #17
    Join Date
    Aug 2002
    Posts
    9,558
    Quote Originally Posted by thomheg View Post
    ...From this I want to derive things like atoms over multiplicative connections of adjacent points.
    My bold
    And what does that actually mean?
    You'd better come with lots of correct math showing this has a meaning, and not just your favourite two equations (the only ones you seem to know).
    All comments made in red are moderator comments. Please, read the rules of the forum here, the special rules for the ATM section here and conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    Catch me on twitter: @tusenfem
    Catch Rosetta Plasma Consortium on twitter: @Rosetta_RPC

  18. #18
    Join Date
    Oct 2007
    Posts
    5,398
    Quote Originally Posted by thomheg View Post
    My plan is -roughly- to do quantum-physics with relativity. That is more or less the opposite approach than quantum-gravity.
    What gives you this bright idea?

    From this I want to derive things like atoms over multiplicative connections of adjacent points.
    I bet that even you don't know what this means

  19. #19
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by tusenfem View Post
    And what does that actually mean?
    Opposite to mathematical space, the observed space is a physical system, hence should 'consist' of some kinds of elements. Those are assumed to exist and to be the foundation of observations.
    From GR we have the requirement of a smooth continuum, hence the elements are pointlike, but nevertheless have features. Since quaternions are able to model the em-field and relativity, I assume, that those 'elements' are connected like a multiplicative connection of quaternions. That could be interpreted as if those points twist each other in a specific way. It's quite counter-intuitive and at least an uncommon way to describe the world. It models the world 'from inside to outside' and allows arbitrary systems to be 'real'. In this picture a particle is a certain structure, like a circle or a knot. Those knots have to be assumed connected. That structure stems from some kind of disturbance, that make those spinning influences of an element concentrate around a certain point.
    This model is related to relativity, but more or less not to QM, since it uses only geometric relations like GR upon a smooth continuum.

    Quote Originally Posted by tusenfem View Post
    You'd better come with lots of correct math showing this has a meaning, and not just your favourite two equations (the only ones you seem to know).
    Actually it's very difficult. Since now I have only some pieces of the puzzle together. Than I want to use this kind of bi-quatrernion system, what is a bit different to Hamillton quaternions. Than I must confess, that this kind of non-linear algebra is nothing, what I'm very familliar with. But possibly you like my illustrations..

  20. #20
    Join Date
    Aug 2002
    Posts
    9,558
    So basically we are back at the starting points of your previoius threads. Please give me one good reason not to close this one, as apparently you will not be able to defend this idea with any solid support. We will just get the same word salat again as before.

    Just because you like the sound of "bi-quaternions" does not immedately mean you know what the are and how they differ from the "normal 4-vectors" etc.

    I liked the sound of "plasma astrophysics" but basically did not know what that implied, and then spend 5 years in college and 4 years in grad school to learn and apply it.

    Before you go anywhere, I would advise you to study algebra and matrices, then you might look at quaternions and then maybe you will be able to rewrite physics in the language of your "muliplicatively connected" points.
    All comments made in red are moderator comments. Please, read the rules of the forum here, the special rules for the ATM section here and conspiracy theories. If you think a post is inappropriate, don't comment on it in thread but report it using the /!\ button in the lower left corner of each message. But most of all, have fun!

    Catch me on twitter: @tusenfem
    Catch Rosetta Plasma Consortium on twitter: @Rosetta_RPC

  21. #21
    Join Date
    Oct 2007
    Posts
    5,398
    Quote Originally Posted by tusenfem View Post
    Before you go anywhere, I would advise you to study algebra and matrices, then you might look at quaternions and then maybe you will be able to rewrite physics in the language of your "muliplicatively connected" points.
    Not in a thousand years

  22. #22
    Join Date
    Jun 2008
    Posts
    2,779
    Quote Originally Posted by thomheg View Post
    My plan is -roughly- to do quantum-physics with relativity.
    You are a little late to the game. That is precisely what quantum field theory is, so long as by "relativity" you mean "special relativity".

    If you mean "general relativity" then that is quantum gravity by another name. You will need more than just 4-vectors.

  23. #23
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by DrRocket View Post
    You are a little late to the game. That is precisely what quantum field theory is, so long as by "relativity" you mean "special relativity".
    If you mean "general relativity" then that is quantum gravity by another name. You will need more than just 4-vectors.
    I refer to GR, but want to use quaternions, because than more observations could be interpreted with the same method. That has been done with the em-field by Maxwell and various other with GR. Most remarkable is, that there are iterpretations of electrons over quaternions.

    My 'method' is to transfer mathematics into grafics and then try to interpret them. So Pi relates to something round and a cross product to something twisting and so forth.
    Now if an event could be characterised by a quaternion, than how to connect events? That could be imagined as a rotation plus a dilation. That generates helical curves in spacetime. It has an outgoing and a returning aspect. If that is squeezed flat, a structure like an atom arises, because there is a core and something electric twisting around.

    Now such a structure could be created out of nothing and I tried to use the example of a comet to explain this. The comet disturbs the solar wind and creates water and radiation.

    Actually I had to modify the interpretation of a spacetime diagram a bit. There are three 'spaces': the past, the present and the future. The present space is the imaginary spacelike region, the observed space the past light cone and the future light cone is where the event could be seen. So spacelike is the 'real thing', but could only be observed in the direct vicinity. That is why a helix has to be squezed flat. The missing dimension is added later, since a circle means actually a sphere.

    That idea I tried to tell about, but people demanded a mathematical description, what is nothing I'm particular talented for.
    It is related to relativity since it is derived from events and their connection and the picture of a light cone. It mimics QM, but uses only events and their connections. For this purpose a two-quaternion system is needed: one for the position and one for the twist. Than this twist could be split off from the position and build moving structures. That isn't a mathematical model, but quite like our world looks like.
    Last edited by thomheg; 2009-Aug-01 at 07:13 AM.

  24. #24
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Possibly this is a hint, for what I have in mind:
    our senses are more or less only able to detect changes. So everything we see or hear is related to a change. If we see an object, that object is assumed to be stable, because it don't change position.
    But obviously we can see it, so something must change. We could interpret this as change happening at a fix position.
    That sounds a bit weird, but if related to thermodynamics it would make some sense:
    if matter isn't order in the sense of thermodynamics, but disorder, we could explain the existence of matter over some kind of age and keep the laws of thermodynamics valid.
    The ordered state would be some kind of ordered energy flow, that we can't detect, because our senses require disorder. If that is disturbed, the 'vortices' of disturbance would be experienced as things.

  25. #25
    Join Date
    Oct 2007
    Posts
    5,398
    Quote Originally Posted by thomheg View Post

    That idea I tried to tell about, but people demanded a mathematical description, what is nothing I'm particular talented for.
    We gathered that. So, in essence, you are finally admitting that your ATM amounts to....nothing.

    It is related to relativity since it is derived from events and their connection and the picture of a light cone.
    It can't be, you have no mathematical formalism. It is obvious that you just started looking at Minkowski diagrams.


    It mimics QM, but uses only events and their connections. For this purpose a two-quaternion system is needed:
    Why? You have no math and you can't establish any connection to any math.

    That isn't a mathematical model, but quite like our world looks like.
    How do you know?

  26. #26
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by adsar View Post

    It can't be, you have no mathematical formalism. It is obvious that you just started looking at Minkowski diagrams.
    Look at this paper called spin and electron structure.
    It's far better, than I could do that, but relates to my own ideas.
    I describes those helices in a more mathematical way.

    Quote Originally Posted by adsar View Post
    Why? You have no math and you can't establish any connection to any math.
    If you want to ride a train you don't necessarily build one, just manage to get a ticket and find the entrance. So I could just give a link and that's it. You may follow, if you like or not if you don't. But I think it's not beneficial to turn a discussion into some kind of sport. Possibly those ideas I have are wrong, but possibly they are not.

  27. #27
    Join Date
    Oct 2007
    Posts
    5,398
    Quote Originally Posted by thomheg View Post
    Look at this paper called spin and electron structure.
    It's far better, than I could do that, but relates to my own ideas.
    I describes those helices in a more mathematical way.
    The point is that your ATM has no mathematical formalism. This makes your ATM unfalsifiable, i.e. worthless.



    If you want to ride a train you don't necessarily build one, just manage to get a ticket and find the entrance. So I could just give a link and that's it. You may follow, if you like or not if you don't. But I think it's not beneficial to turn a discussion into some kind of sport. Possibly those ideas I have are wrong, but possibly they are not.
    You proposed an ATM, according to BAUT rules you need to answer challenges in defending it. You are not doing that.

  28. #28
    Join Date
    May 2008
    Location
    Berlin
    Posts
    771
    Quote Originally Posted by adsar View Post
    The point is that your ATM has no mathematical formalism. This makes your ATM unfalsifiable, i.e. worthless.
    Actually the thread is about complex four vectors, what is a mathematical formalism.
    Then I gave some hints, why I think that this is good formalism. That isn't by itself mathematical, because if you attempt to prove it that way, you get into a vicious circle.
    I usually think about reasoning, that you first make up your mind about a subject, then describe it verbally or with drawings and then try to model it in a quantitative way. The other way round is useless, because you have a result and don't know, what it's good for.

  29. #29
    Join Date
    Jan 2008
    Posts
    99
    you have shown nothing so far, why do you think ATM is the place where others do your homework?
    You are playing the master mind and the math-slaves shall do your work because you have strange feelings about reality.
    This will not happen, neither on the internet nor in real life.

  30. #30
    Join Date
    Oct 2007
    Posts
    5,398
    Quote Originally Posted by worldcruiser View Post
    you have shown nothing so far, why do you think ATM is the place where others do your homework?
    You are playing the master mind and the math-slaves shall do your work because you have strange feelings about reality.
    This will not happen, neither on the internet nor in real life.
    Doesn't seem to stop him :-)

Similar Threads

  1. Complex life in LMC or SMC
    By canopuss in forum Life in Space
    Replies: 4
    Last Post: 2009-Dec-14, 10:15 PM
  2. Vectors of Canopus and Vega
    By Robert Tulip in forum Space/Astronomy Questions and Answers
    Replies: 4
    Last Post: 2009-Jul-05, 04:03 PM
  3. 2012 Vectors
    By Robert Tulip in forum Space/Astronomy Questions and Answers
    Replies: 57
    Last Post: 2008-Dec-13, 02:47 PM
  4. which complex do you think that this is complex
    By suntrack2 in forum Off-Topic Babbling
    Replies: 0
    Last Post: 2007-Jan-08, 05:12 PM
  5. Superbubble Complex N44
    By Fraser in forum Universe Today
    Replies: 0
    Last Post: 2006-Jan-06, 04:33 AM

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •