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It must be my Imaginary Imagination

April 28, 2012

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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The Quandary of Attraction, part II

April 23, 2012

I mentioned previously that the attraction between two opposite charged particles appears to present a conservation of momentum problem if electrostatic forces are mediated by photon exchanges.  Related to this issue is the question of what makes a photon a carrier of a magnetic field versus an electrostatic field. QFT specifies that this happens because the field (sea of electron-positron pairs/virtual particle terms) absorbs the conservation loss, but as far as I can find, does not try to answer the second question.

Part of the difficulty here is that attempting to apply classical thinking to a QFT problem doesn’t work very often.  Virtual photons in QFT do not meet the same momentum conservation rules we get in classical physics, either in direction or quantity.

But, since I hypothesize an underlying vector field structure, it is interesting to pursue how the Unitary Twist Field theory would deal with these issues.

I ruled out any scheme involving local bending of the background field vector.  This would be an appealing solution, easy to compute, and easy to see how different frames of reference might alter the electrostatic or magnetic nature.  But this doesn’t work because you must assume any possible orientation of the electron ring, and it is easy to show that a local bend would be different for two receiving particles at equal distance but different angles from a source particle.  I worked with this for a while and found there is no way that the attraction due to a delta bend would be consistently the same for all particle orientations.

The only alternative is to assume that the field consists of twists, either full or partial returning back to the background state (photons and virtual photons respectively).  Why does an unmoving electron not move in a magnetic field but is attracted/repelled in an electrostatic field?  QFT answers this simply by assuming that the electrostatic and magnetic components of the field are quantized and meet gauge invariance.   My understanding of QFT is that asking if a single photon is magnetic or electrostatic is not a valid question–the field is quantized in both magnetic and electrostatic components, composed of virtual photon terms that don’t have a classical physical analog.

I suppose the unitary twist field theory is yet another classical attempt.  Nevertheless, it’s an interesting pursuit for me, mostly because of the geometrical E=hv quantization and special relativity built in to the theory.  It seems to me that QFT doesn’t have that connection, and thus is not going to help derive what makes the particle zoo.

This underlying vector field does not have two field components real and imaginary, just one real.  Even if this unitary twist field thing is bogus, it points to an interesting thought.  If  our desired theory (QFT or unitary twist field) wants to distinguish between a magnetic field or an electrostatic field using photons, we only have one degree of freedom available to do the distinction–circular polarization.  What if polarization of photons was what made the field electrostatic or magnetic?

An objection immediately comes to mind that a light polarizer would then be able to create electrostatic or magnetic fields, which we know doesn’t happen.  But I think that’s because fields are made of much lower energy photons.  Fourier decomposition of a field would show the vast majority of frequency components would be far lower even when the field energy is very high–in the radio frequency range.  Polarizing sheets consist of photon absorbing/retransmitting atoms and would be constrained to available band jumps–I’m fairly certain that there is no practical way to construct a polarizer at the very low frequencies required–even the highest orbitals of heavy atoms are still going to be way too fast.

If polarization is the distinguishing factor, then it poses some interesting constructions for the unitary twist field approach.  If it is not, then the magnetic versus electrostatic can only be an aggregate photon array behavior, which seems would have to be wrong–a thought experiment can be constructed that should disprove that idea.  Quantization of a very distant charged particle effect, where the quantized field particle probability rate is slow enough to be measurable, could not show the distinction in any given time interval.

Supposing polarization is the intrinsic distinction in single photons.  Unitary twist fields have two types of linear twist vectors, those lying in the plane common to the background vector and normal to the direction of travel, and those lying in the plane common to the background vector and parallel to the direction of travel.  (There is a degenerate case where the direction of travel is the same as the direction of the background state, but this case still has circular polarization because there are now two twist vectors in the planes with a common background vector and a pair of orthogonal normal vectors).

Since static particles are affected by one twist type (inline or normal) and not the other, and moving particles are affected by the other twist type, one proposal would be that the particle experiences only the effect of one of the twist types relative to the path of motion and the background vector.  For example, if the particle is not moving, only twists normal to the direction of travel will alter the internal field of the receiving particle such that it moves closer or further away (attraction or repulsion).  A problem with this approach is the degenerate case, which must have both and eletrostatic and magnetic response, but both twist vectors will be inline twists, there is no twist normal to the background state that will include the background state vector.

More thinking to come…

Agemoz

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Unitary Twist Field Dreams

April 12, 2012

I’m going to do something a little different in this post.  It’s every amateur’s dream to be taken seriously by the professionals, so I’m going to have a little fun today and pretend that a physics professor looked at this and decided to be nice (he just got a big grant approved for his research and was feeling unusually magnanimous) and go over it with me.  This is not for real–a real professor would almost certainly not give the time of day to an amateur’s ideas–it just is too much work to dig in and be precise about why any set of ideas wont work, nevermind those from someone who hasn’t spent a lifetime dedicated to this field of study.  But, amateurs all get their Walter Mitty dreams, and this is mine–and this is my blog, so I can do what I durn please here!  Actually I don’t care if I’m recognized for anything I come up with, but it’d be cool if some part of it turned out to be right.  Anyway, here goes.

Prof Jones:  Hello, what do you have for me?

Me:  I have this set of ideas about how particles form from a field.

Prof Jones:  You have a theory [suppresses noisy internal bout of indigestion]

Me:  Well, yes.  I think there is a geometrical basis for quantum and special relativistic behavior of particles.

Prof Jones:  We already have that in QFT.  Are you adding or revising existing knowledge?  I’m really not interested in someone telling me Einstein or anybody else was wrong…

Me:  I believe I am adding.  I have tried to take a overall high-level view of what is now known, especially the E=hv relation and the special relativity Lorentz transforms, and see some conclusions that make sense to me

Prof Jones:  Well, I’ve had a lot of ideas thrown at me, and they are a dime-a-dozen.  It’s not the idea that’s important but the logic or experiment that supports it.  A good theory explains something we don’t understand and allows us to successfully predict new things we otherwise would not find.  Is yours a good theory?  Do you have supporting evidence or experiment?  Can you predict something I don’t already know with QFT?  Does it contradict anything I already know?  If you can’t pass this complete criteria, the theory isn’t going anywhere but the round file.

Me:  I don’t have anything that proves it.  I don’t have anything it predicts right now but I see some possibilities.  I don’t think it contradicts anything, but there are some question marks.

Prof Jones:  Urrg…. Well, this is your lucky day.  I happen to be in the mood for shooting down the bright ideas of poor suckers that think Nobel prizes are given out like puppies from a puppy mill to people that haven’t paid their dues in this very, very tough field.  So, let’s start with this question:  What makes you think you are the one that has come up with something new in quantum theory?  After all, you can’t argue that the set of smart-enough people that actually can legitimately call themselves physicists, theoretical or related, have spent cumulative millions of lifetimes trying to break down the data and clues we have to solve the very well-known problem you are looking at.  Don’t you think someone, or many someones, with a much deeper background than you would have long since considered whatever you have and passed it by fairly quickly?

Me:  [meekly] yes.

Me:  But I have thought about this for a very long time, and refined it, and received feedback, and really tried hard to make sure it makes sense.

Prof Jones:  Unfortunately, so has every honest physics PhD, and I’m afraid they are going to have a lot more mental “hardware” than you, having both genuine talent and also having brutally difficult training in abstract mental comprehension and synthesis ability and current knowledge.

Me: OK.  I guess I could quit doing this–I just find it so interesting.

Prof Jones: [softens just slightly, realizing there’s a lot of snarky but not-classy power in putting down those who try, but are so limited in resources or study time].  Well, just so you understand.  You aren’t going anywhere with this.  But let’s see what you got.  Before I dig in, I want to know what you are adding to existing theory, as succinctly as you can communicate.

Me:  Alright.  I thought about the way quantization works on particles and fields, and in both cases the E=hv relation defines very explicitly what must happen.  I spent a lot of time trying to construct a model of a system that is continuous but obeys this relation at the smallest scale.  I came up with three constraints that describe such a system–in fact, it looks to me that the E=hv relation actually specifies a geometrically defined system.  These constraints are:

1: The quantization is enforced by a rotation in a vector field, that is, a twist.

2: To ensure that only single complete rotations can occur, the field must have a local background state that the rotation returns to.

3: To ensure that the energy of the rotation cannot dissipate, the vector field must be unitary.  Every field element must have constant magnitude but can rotate in 3D+T spacetime.

Prof Jones:  I see what you are getting at.  The E=hv relation only allows discrete energy states for a given frequency within an available continuous energy range.  A twist is a modulus operation that works in a continuous 3D field to provide such discrete states provided that there is a default idle state, which would be your background vector orientation.  However, you realize that EM fields do not have limitations on magnitude, nor is there any evidence of a background state.

Me: I understand that.  I am proposing that because QFT shows how EM fields can be derived from quantum particles (photons), my theory would underlie EM fields.  I see a path where EM fields can be constructed from this Unitary Twist Field Theory from sets of quantized twists.  I agree that the background vector direction is a danger because it implies an asymmetry that could prevent gauge invariance–but I suspect that any detector built of particles that are formed from this twist mechanism cannot detect the background state.  The background state direction doesn’t have to be absolute, it can vary, and a unitary vector field has to point somewhere.  Continuity and energy conservation imply that local neighborhoods would point in the same direction.

Prof Jones:  Sets of quantized twists, hunh.  Well, you’ve got a very big problem with that idea, because you cannot construct a twist in a background unitary vector field without introducing discontinuities.  If you have discontinuities, you don’t have a unitary vector field.

Me: Yes, I agree.  However, if the twist moves at speed c, it turns out the discontinuities lie on the light cones of each point in the twist and are stable, each light cone path has a stable unchanging angle.  In a sense, travelling at the speed of light isolates the twist elements from what would be a discontinuity in a static representation.

Prof Jones:  I don’t think I agree with that, I would have to see proof.  But another question comes to mind.  In fact a million objections come to mind but let me ask you this.  You are constructing an EM field from this unitary vector field.  But just how does this single vector field construct the two degrees of freedom in an EM field, namely electrostatic fields and magnetic fields?  Just how are you proposing to construct charge attraction and repulsion and magnetic field velocity effects specified by Maxwell’s relations?  QFT is built on virtual particles, in the EM case, virtual photons.  How are you going to make that work with your theory?  You realize the magnitude, don’t you, of what you are taking on?

Me:  These are questions I have spent a great deal of time with over the last 20 years.  That doesn’t justify a bad theory, I know.  So I’ll just present what I have, and if this dies, it dies.  I’d just like to know if my thinking has any possible connection to the truth, the way things really are.  I realize that we have a perfectly workable theory in QFT that has done amazingly well.  But we also have a lot of particles and a lot of interactions that seem to me to have an underlying basis that QFT or relativity don’t explain, they just happen to work.  Renormalization works, but why?  These are some issues that tell me we can’t stop with QFT.

Prof Jones:  [sotto voce] The hubris is strong in this one.

Me: What

Prof Jones:  Nothing.  Go on.  What is your theory going to do with charge and magnetic behavior?

TO BE CONTINUED, SAME BAT-TIME, SAME BAT-CHANNEL

Agemoz

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Twist Theory and Electrons

April 6, 2012

OK, applying this unitary twist field idea to photons seems pretty workable.  We get real photons and virtual photons, and get a good model for how quantization and circular polarization could work.

There are some big questions, though–the biggest of all is that this method of quantizing a continuous system requires a background vector state.  Now, this isn’t as bad as it would seem, because a unitary vector field has to have some direction, and continuity would imply that local neighborhoods would point in the same direction, and the model does not assume that the backround direction has to be absolute throughout, it can change.  Nevertheless, it would seem that a background direction might somehow be detectable with some variation of a Michelson-Morley experiment.  That’s going to get some attention on my part later, but for now I want to go in another direction.

Let’s talk electron models in the Twist Theory.  This is where real physicists have a heyday killing off new theories like this because the electron is so well studied and measured, there is so much that a theory would have to line up with before even beginning to come up with something new.  Don’t know what to say except it’s fun to see what comes out of such a study.

Let’s start with degrees of freedom, just like I just did with the photon, that could kill off the theory in a hurry–and for a long time I knew there was a problem, here it is:  electrons come in four permutations, spin up electron, spin-down electron, spin-up positron, and spin-down positron.  All of these have the same exact mass, charge (+ or -), spin moment, g ratio, and so on.  I have long felt that the electron is effectively modeled with a single unitary field twist ring.   Here’s a picture of the idea.

Twist ring model of an electron in a unitary field with a background state.

The ring has one point where the twist direction matches the background twist state.  The twist curves, unlike the photon, due to internal effects of the ring twist.  I have done math that shows there is a single such solution that is stable, but only in certain circumstances.  I will come back to the math of twist ring solutions, but right now, let’s just see if the degrees of freedom required would shoot this down even before getting to the math.  Sort of like checking to make sure an equation has consistency of units, otherwise the equation is just nonsense.  As I mentioned, there are four variations of the electron that have to have a unique twist field representation.  Are there four unique solutions for the twist ring?

Twist ring degrees of freedom with no background state. Note that two solutions are just mirror images of the other two, we only have one degree of freedom.

Of course, we have our four cases, and no more.  Ooops–wait, two of the four are just mirror images of the first two–we really only have two unique twist ring solutions!  It took me a while to realize there are actually four–in a unitary twist field there would only be two, but in a unitary twist field with a background state, necessary for quantization to work, there are actually four.

The background state required for quantization also provides a reference that prevents the two mirror cases from being identical to the first two cases. There are now two degrees of freedom.

The background state from which the twist must begin acts as a reference vector that keeps the mirror image twist rings from being identical by rotation.  To see this more clearly, look at the two degrees of freedom as a function of the planes they reside in:

The reference vector along with the ring center defines a plane (green) where two possible twist cases result in a unique degree of freedom. The blue plane that the ring resides in defines ring travel direction and is another unique degree of freedom.

One degree of freedom is establised by the ring rotation within the plane that includes the ring.  There are two possibilities, clockwise or counterclockwise.  The second degree of freedom is defined with the plane that the background vector lies in, as well as the center of the twist ring.  The background vector is the starting point for a rotation about the ring circumference.  It should be clear that the background vector creates a reference that makes the two mirror cases unique.  You could argue that it doesn’t matter if the mirror image rotation doesn’t have the same background state, but actually it does–it determines which way the ring will turn if it is moving in a magnetic field–the spin-up electron will move differently than the spin-down electron due to the opposite direction of its starting point vector.  I’ll keep thinking about this but so far, this appears to be valid.

Agemoz

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