Posts Tagged ‘quantum theory’

Unitary Continuous Fields Cannot be Linear

June 11, 2012

Well, after considerable thought on that surprising revelation of the previous post, I realized that it is true only for unitary fields.  The QFT solution can be both continuous and linear, because the magnitude of an EM field is not constrained.  I thought of the case of a rogue wave on water, and realized that the median plane symmetry problem results from the  ability of the unitary field to block information from passing.  A unitary field that has a stable state over any surface will block information from passing through.  The median plane between two oppositely charged particles, by symmetry, has to consist of background state vectors, but the field that QFT resides in is non-blocking–think of the rogue wave on water analogy.  One wave can ride on top of another because the magnitude is not constrained, and thus is not blocking.  Information from one charged particle will make it through the median plane to the other particle–but NOT in my unitary twist field theory.

This is a show-stopper for unitary twist field theory.  Unitarity (of field magnitude) is necessary to geometrically create quantization.  I see two options:  either my original premise that the field is sparse, or something other than field magnitude is constraining twist magnitude.

Agemoz

Continuous Fields Cannot be Linear

June 10, 2012

A shocking revelation for me, in all my years both as a professional electrical engineer and as an amateur physicist.  I realize I have zero credibility out there with anyone, but at least for myself, I have discovered something fundamental about fields that I did not know.  Perhaps if I were a mathematician I would have worked this out.  Nevertheless, it is quite provable in my mind, and has enormous impact on how I must model the two particle interaction, whether by QFT or unitary twist field theory.

The concept of linear central force fields means that multiple potential sources create the field by means of linear superposition.  If you have two sources of potential, the effect on the field at any point is the sum of the effect due to either one.  There are potential corner cases such as if the potential is infinite at the point source, but in every finite potential situation, the field is the sum of all sources at that point.  Electrostatic fields are supposedly both continuous and linear, but this cannot be at the quantum scale.

I have been discussing in previous posts the concept of a median plane between two charged sources, and particularly enlightening was the attraction case of a positive and negatively charged particle.  Between these two particles will be a median plane whose normal runs through both particles.  This median plane can have no absolute potential (relative to the electrostatic field potential at infinite distance).  This field cannot pass any information, even about the existence of, one charged particle through this median plane.  In fact, it is well known in electrostatics that if you put a metal plane between two particles and ground it, you will get the same charge field distribution as if the second particle wasn’t there–it cannot be determined if the second particle actually exists or not.

The only way a field can pass information across this median plane is if the field is not continuous.  If the field  is created by a spaced array of quantized particles, such that they never, or almost never, interact, then the effect of the field can be made linear.  Indeed, shooting real photons at each other could collide, but that is exceeding rare, and modeling the field by photons, virtual or real, in either QFT or unitary twist field theory,  would produce a linear superposition of fields.  But there is no question now in my mind that if I simulate this, I cannot assume a continuous electrostatic field, such a thing cannot exist.  This field has to be almost entirely empty, with only very sporadic quantized particles, then I can see how linearity would be possible.  Every quantized particle that interacts with a quantized particle from the other source will distort the appearance of linearity, so the fact that deviations from linearity are experimentally unmeasurable strongly points to a extremely sparse field component density.

I had thought that QFT virtual particles could construct a continuous field in a Taylor or Fourier series type of composition, but it is clear that it cannot.  The QFT virtual particles must be exceedingly sparse, just like the twists in unitary twist field theory.  It also suggests that QFT virtual particles would have to clump in some way in order for localized neighborhoods in the field to obey conservation.

Now I see a workable model for twists.  The median plane problem cannot exist if the field is not continous.

Agemoz

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

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