It must be my Imaginary Imagination

This modification to the unitary twist theory has everything going for it.  Here’s what happened: the twist theory needs a background state for quantization to work–enforcing integer twists means that all twist rotations except for one (the background state) to be unstable.   I originally put this background state  in R3 along with the rest of the twist rotation, but this ran into problems trying to work out charge forces–the requirement for gauge invariance becomes a show stopper.

So, using the fact that EM fields and photons are mathematically described as a complex wave function in C3, I proposed that the background state direction be an imaginary axis.  The twist would reside in a plane defined by one real vector and the single background vector pointing in a direction orthogonal to R3.  Now the photon wave equation immediately falls out, but we still get the quantization and special relativity Lorentz transforms unique to the unitary twist field approach.  The problem with discontinuities vanish now, because the twist never appears in R3, only between R3 and I1–the real and imaginary parts.

Assigning the unitary twist field theory background state to an imaginary direction (note vector arrows are direction only, don't try to assign a physical distance to these arrows!)

What happens to the charge attraction problem?  Can we still do virtual photons, which in this variation of  the theory become partial twists (bends) from the imaginary background state to some basis vector in R3?  I am working out a generalized solution but at first glance the answer is yes.  Two particles near each other will increase the apparent bend of the background state, opposite each other cancel the bend, and 90 degrees apart generate a Sqrt[2] compounding effect, bending to between the two particles–exactly what I would expect.

So, finally, back to the original question.  Can this modification finally make a workable solution to the attraction conservation of momentum problem?  Having the background state be orthogonal to all of R3 makes this a much better problem.  Now there’s no symmetry problem regardless of electron ring orientation.  Unlike before, where the background state was in R3, now the twist moment vector is always in the plane of the ring, which means that regardless of the orientation of the ring, one side of the ring will always experience slightly less background bend than the other.  This delta bend causes a distortion in the ring path travel, making it do a motion to compensate for the shorter return path to the background state versus the other side–causing motion of the overall ring (see figure 1.)  Now there is no momentum problem due to photon energy emission for attraction–the difference in bend from one side to the other simply causes the particle to move.  Now it is easy to see how the field carries the energy.   And most importantly, the solution is symmetric, there is no R3 direction preference, so gauge invariance should hold.

Effect of a remote charge on a local particle ring. Note that regardless of ring orientation in R3 or direction of I0 bend, this drawing will be valid, uplholding rotation and spatial invariance (Lorentz invariance not shown here).

It looks to me that there is no question about it, this has to be the right way to go.

More to come…

Agemoz

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2 Responses to “It must be my Imaginary Imagination”

  1. physicsideas Says:

    Nice post! The use of the complex background vector is very clever. It makes sense conceptually, but why did they need to be necessarily orthogonal in the first place?

    I’ve only read your 5 most recents posts, so bear with me if these questions are all super obvious in the context of the theory.

    In figure 2, the purple ring is the electron, or a representation of the plane? And the blue rings are unitary twists, with the red dotted lines being a field of the background unit arrows.

    So there is only one unitary twist that precesses around or multiple?

    Also, I’m having trouble seeing how the movement is created, and what the “remote charge” arrow is representing.

    I’ve been inspired by your blog to write out some of my own ideas, so take a look sometime if you like. I’m still getting the basics out, but it’s got some content. I would like to see what you think. physicsideas.wordpress.com

    Thanks

    • agemoz Says:

      Hi physicsideas,
      I saw your post about going to school–I would encourage you to continue, don’t give up! Yes, there are problems with peer review and how it’s almost impossible for speculative ideas to go anywhere. Getting grant money has issues of its own. But a physics degree still means that you’ve put a giant effort into your education and mental strength, which is lot more than you can say for most other fields. And I wouldn’t say physicists are stuck–it’s more that the easy problems are long solved and what we have now are incredibly difficult for the human mind to work through. I thought computers would give us a giant step forward, but that payoff hasn’t happened yet. If I were in your shoes, I’d be developing math/computer tools that overcome the abstraction limitations of the human brain. I also think that Dirac didn’t do us all a favor by mathematically deriving the antiparticle, because our mathematics language has become a box that we have trouble thinking outside of. But don’t give up! There is no field that connects to the human search for meaning like physics does!

      Now to address your questions:
      Why orthogonal background vector? Complicated question–the easiest and quickest answer I can say is that a twist that does not lie in a plane has to explain the deviations. If the background vector is not orthogonal (in some frame of reference) then there will be dependencies of motion on the two axes defining the plane of the twist and thus potentially unintended forces. In my theory I try to minimize any unexplained accelerations (because I know my hypothetical Prof Jones will jump all over that, and so would you!).

      Good question on the purple ring, I will fix that document to clarify. It is the electron in this theory, where I posit it makes a single twist around the curve. (There’s a very critical size issue here, I have worked on that in prior posts and will address it again soon. But for now, let’s ignore that). You are correct that the blue rings represent a single field twist as you go around the ring, starting and finishing on the background state vector in red.

      I agree with you about clarity of the movement question–I try to keep the posts moderate length so I can keep track of them, which means I am postponing elaboration of the more detailed description until the next one. Can I prevail on you to wait? Hopefully the next post will address this question.

      Thanks for your interest, I will take a look at your ideas.

      Agemoz

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