Posts Tagged ‘special relativity’

Special Relativity and Unitary Twist Field Theory–Addendum

February 2, 2017

If you read my last post on the special relativity connection to this unitary twist field idea, you would be forgiven for thinking I’m still stuck in classical physics thinking, a common complaint for beginning physics students. But the importance of this revelation is more than that because it applies to *any* curve in R3–in particular, it shows that the composite paths of QFT (path integral paradigm) will behave this way as long as they are closed loops, and so will wave functions such as found in Schrodinger’s wave equation. In the latter case, even a electron model as a cloud will geometrically derive the Lorentz transforms. I believe that what this simple discovery does show is that anything that obeys special relativity must be a closed loop, even the supposedly point particle electron. Add in the quantized mass/charge of every single electron, and now you have the closed loop field twists to a background state of the unitary field twist theory that attempts to show how the particle zoo could emerge.

Agemoz

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Special Relativity and Unitary Twist Theory

January 30, 2017

I’ve been working diligently on the details of how the quantizing behavior of a unitary twist vector field would form loops and other topological structures underlying a particle zoo. It has been a long time since I’ve talked about its implications for special relativity and the possibilities for deriving gravity, but it was actually the discovery of how the theory geometrically derives the time and space dilation factor that convinced me to push forward in spite of overwhelming hurdles to convincing others about the unitary twist theory approach.

In fact, I wrote to several physicists and journals because to me the special relativity connection was as close as I could come to a proof that the idea was right. But here I discovered just how hard it is to sway the scientific community, and this became my first lesson in becoming a “real” scientist. Speculative new theories occupy a tiny corner in the practical lives of scientists, I think–the reality is much reading and writing, much step-by-step incremental work, and journals are extremely resistant to accept articles that might cause embarrassment such as the cold-fusion fiasco.

Back in my formative days for physics, sci.physics was the junk physics newsgroup and sci.physics.research was the real deal, a moderated newsgroup where you could ask questions and get a number of high level academic and research scientists to respond. Dr. John Baez of UC Riverside was probably one of the more famous participants–he should be for his book “Gauge Fields, Knots and Gravity”, which is one of the more accessible texts on some of the knowledge and thinking leading to thinking about gravity. But on this newsgroup he was the creator of the Crackpot Index, and this more than anything else corrected my happy over-enthusiasm for new speculative thinking. It should be required reading for anyone considering a path in the sciences such as theoretical physics. Physicists 101, if you will–it will introduce you hard and fast to just how difficult it will be to be notable or make a contribution in this field.

I’m not 100% convinced, as I’ve discussed in previous posts, that there isn’t a place for speculative thinking such as mine, but this is where I discovered that a deep humility and skepticism toward any new thinking is required. You *must* assume that speculation is almost certainly never going to get anywhere with journal reviewers or academic people. Nobody is going to take precious time out of their own schedule to investigate poorly thought-out ideas or even good ideas that don’t meet an extremely high standard.

So, I even presented my idea to Dr. Baez, and being the kind and tolerant man he is, he actually took the time review what I was thinking at that time–has to be 20 years ago now! Of all the work I have done, none has been as conclusive to me as the connection to special relativity–but it did not sway him. I was sure that there had to be something to it, but he only said the nature of special relativity is far reaching and he was not surprised that I found some interesting properties of closed loops in a Lorentzian context–but it didn’t prove anything to him. Oh, you can imagine how discouraged I was! I wrote an article for Physical Review Letters, but they were far nastier, and as you can imagine, that’s when my science education really began.

But I want to now to present the special relativity connection to unitary twist theory. It still feels strongly compelling to me and has, even if the theory is forever confined to the dustbin of bad ideas in history, strongly developed my instinct of what a Lorentzian geometry means to our existence.

The geometry connection of unitary twist field theory to special relativity is simple–any closed loop representation of a particle in a Lorentzian systen (ie, a geometry that observes time dilation according to the Lorentz transforms) will geometrically derive the dilation factor beta sqrt(1 – v^2/c^2). All you have to do to make this work is to assume that the loop represention of a particle consists of a twist that is propagating around the loop at speed c, and the “clock” of this particle is regulated by the time it takes to go around the loop. While this generalizes to any topological closed system of loops, knots, and links (you can see why Dr. Baez’s book interested me), let’s just examine the simple ring case. A stationary observer looking at this particle moving at some speed v will not see a ring, but rather a spiral path such that the length of a complete cycle of the spiral will unroll to a right triangle. The hypotenuse of the triangle by the Pythagorean theorem will be proportionate to the square root of v^2 + c^2, and a little simple math will show that the time to complete the cycle will dilate by the beta value defined above.

When I suddenly realized that this would *also* be true in the frame of reference of the particle observing the particles of the original observer, a light came on and I began to work out a bunch of other special relativity connections to the geometry of the unitary twist theory. I was able to prove that the dilation was the same regardless of the spatial orientation of the ring, and that it didn’t matter the shape or topology of the ring. I saw why linear twists (photons) would act differently and that rest mass would emerge from closed loops but not from linear twists. I went even as far as deriving why there has to be a speed of light limit in loops, and was able to derive the Heisenberg uncertainty for location and momentum. I even saw a way that the loop geometry would express a gravitational effect due to acceleration effects on the loop–there will be a slight resistance due to loop deformation as it is accelerated that should translate to inertia.

You can imagine my thinking that I had found a lodestone, a rich vein of ideas of how things might work! But as I tried to share my excitement, I very quickly learned what a dirty word speculation is. Eventually, I gave up trying to win a Nobel (don’t we all eventually do that, and perhaps that’s really the point when we grow up!). Now I just chug away, and if it gives somebody else some good ideas, then science has been done. That’s good enough for me now.

Agemoz

The Arrow of Time and Misuse of Statistics

June 5, 2016

As an amateur physicist I try to avoid disputing established science, but one place I believe science has it wrong is the dimensionality of time.  If you read this blog at all, you’ll see I am trying to create a self-consistent world-view that conforms with peer-reviewed science.  My world-view attempts to add analysis and conclusions on some of the unanswered questions about our universe such as why are there so many elementary particles or how can quantum entanglement work.  I try never to dispute established science and to accept that my world-view is a belief system, not fact that must be forced on others–that is the mark of a crackpot that has just enough knowledge to waste other peoples’ time.

However, one place I break my rules of good behavior is this concept that time is one-dimensional.  For a long time, I’ve recoiled at the notion that the observer’s timeline could physically intersect a particular local spacetime neighborhood of an object event  multiple times.  I discussed this in a previous post, but now I want to discuss this disagreement from another angle–the claim for an existence of an Arrow of Time.

The Arrow of Time is a concept that describes the apparent one way nature of the evolution of a system of objects.  We see a dropped wine glass shatter on the floor,  but we never see a shattered wine glass re-assemble itself and rise up back onto a table.  We record a memory of events in the past, but never see an imprint of the future on our brain memory cells.  This directional evolution of systems is a question mark given that the math unambiguously allows evolution in either direction.  To put it in LaGrange equation of motion terms, the minimum energy path of an object such as a particle or a field element is one dimensional and there are two possible ways to traverse it.  The fundamental question is–why is one way chosen and not the other?

The standard answer is to invoke statistics in the form of the Laws of Thermodynamics, and I have always felt that was not the right answer.  Here is why I have trouble with that–statistics are mathematical derivations for the probability something will happen, and cannot provide a force that makes a particle go one way or the other on a *particular* LaGrangian minimum energy path.  It’s a misuse of statistics to use the thermodynamics laws to define what happens here.  In the case of the shattered wine glass, there are vastly more combinations of paths (and thus far higher probability) for the glass pieces to stay on the floor than there are for the glass shards to reassemble themselves–but that is not why they stay there!

The problem with the Arrow of Time interpretation comes from thinking the math gives us an extra degree of freedom that isn’t really there.  The minimum energy path can truly be traversed in either the time-forward or time-backward path, but it is an illusion to think both are possible.  Any system where information cannot be lost will be mathematically symmetric in time, creating the illusion of an actual path in time if only the observer were in the right place to observe the entirety of that path.  Einstein developed the equations of special relativity that were the epitomy of the path illusion by creating the concept of spacetime.  Does that mean the equations are wrong?  Of course not–but it exemplifies the danger of using the math to create an interpretation.  Just because the math allows it does not mean that the Arrow of Time exists–any relativistic system where information cannot be destroyed will allow the illusion of a directionality of time.

So what really is going on?  I’ll save that for a later post, but in my world-view, time is a property of the objects in the system.  There is only ONE copy of our existence, it is the one we are in right now, and visits to previous existences is simply not possible.  Our system evolves over time and previous existences no longer exist to visit.   Relativity does mean that time between events has to be carefully analyzed, but it does not imply its dimensionality.

Agemoz

Something-From-Nothing, Incompressible Fluids, and Maxwell’s Equations

May 22, 2016

I have made the claim that our universe must have emerged from nothing via the infinity times zero equation, and that we can derive the behavior of our universe from the geometry of a something-from-nothing system.  The something-from-nothing basis (which I’m going to start abbreviating as SFN) suggests an incompressible fluid, and two really cool consequences result from an incompressible fluid–Maxwell’s equations and three dimensions.

The assumption that a SFN system results in an incompressible fluid is a step of negative logic–you cannot have a compressible fluid as the basis of a SFN system because it implies density variation as a fundamental property–an extra rule on top of a nothing existence.  Then the question has to be asked, what is the origin of that rule, how did it come from nothing–and we’ve lost the deductive power of assuming a SFN system.  You can eventually create compressible fluids but you have to start assuming no density variations (incompressible fluid) and show how such a thing could emerge.

Why assume a fluid at all from a SFN?  That’s a much more complex question that I really want to flesh out later.  For now I would like to state that a fluid is just the result of the emergence of movement of elements of a field from an SFN system.  Developing that step is crucial to making a workable SFN theory, but for right now I want to show what results when you take that step.

An incompressible fluid is a really interesting concept that has no equivalent in real life.  Even an idealized steel bar with no internal atomic flexing is compressible by special relativity–apply a force to one end, and relativity dictates that the bar will compress slightly as the effect of the force propagates at the speed of light across the bar.  But an incompressible fluid violates special relativity and cannot exist as an entity with mass in real life.  However as a basis of a SFN system it turns out it can exist–and the very rules of special relativity have to emerge in the form of Maxwell’s Equations and three spatial dimensions.

You can see this when you realize that an infinite volume of an incompressible fluid cannot be pushed in the direction of an applied force.  Not because of infinite mass (mass emerges from an SFN system, but you can’t use it yet else you will engage in circular reasoning) but because an incompressible fluid won’t move without simultaneous displacement of an adjacent region.  Another way to state it is that incompressible fluids require a complete path for movement to happen.  In addition, movement of that path of fluid cannot initiate unless the limit of the size of the region containing the path approaches zero.  You can see that such a requirement eliminates movement in the direction of the force, only a transverse loop is possible.  You cannot have movement in either a one or two dimensional system–both would require movement to occur in the direction of the force in the infinitesimal limit.  You must have three dimensions*.  And, more profoundly, it is easy to see that Maxwell’s field equations are nothing more than the description of the motion of a fluid that rotates around the axis of an applied force (or vice versa).

Wait–I just said the incompressible fluid cant exist in real life, and is limited to an infinitesimal neighborhood?  Doesn’t that sound pretty useless as a basis for the universe?  No, because we use calculus all the time to integrate infinitesimal effects into a macroscale result.  Think Huygen’s principle, or better yet, Feynman path integrals, and the summing of all possible particle paths of LaGrange motion equations and QFT.  Even quantum entanglement has a geometrical explanation in this model–let me save those for a later post, this is about 10 times longer than anybody will read already!

Agemoz

*You must have at least three dimensions, but this analysis does not prove that more aren’t possible.  I’m thinking at this point that since more dimensions aren’t necessary, LaGrange type minimum energy paths eliminate their existence–although at gravitational scales we start to see evidence of spacetime curvature (more dimensions?).  There’s also arguments for more tiny scale dimensions when QFT is merged with relativity–but on an everyday macro scale of our existence, its quite clear that SFN system educes three dimensions.

Relativity and Something From Nothing Dimensions

May 20, 2016

The main guiding principles of the theories proposed in this blog is that this universe we observe have intrinsic principles of geometry that emerged from nothing.  This process of thinking generally leads logically to verifiable conclusions about how the universe works, but also points to some notable exceptions that conflict with currently established peer-reviewed science.  The question of whether a scientist/theoretician should take the time to look at the proposed conflicting theories or just label them as speculative or crackpot is a subject often covered in this blog, but I’m not going to go there today.  Two something-from-nothing conclusions that conflict with established science are the emergence of particles from field twists, and the time-is-a-property concept.  Both conclusions are accepted by no working theoretician, but I have seen reason to consider them and have discussed the former at length in this blog.  I don’t often talk about the relativity/gravity area but have been doing some thinking here lately.

I want to discuss special relativity in the context of the something-from-nothing principle because it leads me to conclude that time and space are not the same concept just observed from different frames of reference.  It will take me a bunch of posts here to flesh out my thinking on this, but in summary, I am suspecting that the interconnectedness of space and time does not mean that time is a dimension in the same way that space is.  In particular, I have come to the conclusion that time is a property of objects in space, and that means that once an object has exhibited a particular time event by an observer, it is not possible to physically revisit that event–by physically revisit, I mean exist in the same arbitrarily small spacetime neighborhood of the event where the observer’s time clock has two different non-local neighborhood times.  In other words, it is not possible for an observer to go back or forward in time to revisit an event he has already observed.  He can certainly observe photons that have traveled from the past or even the future depending on how frames of reference are set up, but not physically revisit as I’ve described here.

Let me elaborate in the next few posts, because knowledgeable relativist theorists will object that there are ways to bend spacetime in pretty extreme ways. The math of special relativity shows a duality between space and time that appears to show that time can be called a dimension.  For this reason, the standard interpretation has been to call time a dimensional quality, which implies that for some observer it is possible to arbitrarily visit any point on the timeline description of events for an object.

I’ve always questioned this.  There has never been a provable instance of actual dimensional behavior of time when defined this way (observer with two different timeline points in the same local spacetime neighborhood of an event).  I suspect that this is not possible for any observer because we are interpreting the math to mean time is a dimensional concept when in fact it is a property of an object that has a direct mathematical coupling to the objects location in space.  Or, to put it another way–they both seem to have dimensional behavior but that is an artifact that both are something-from-nothing concepts.

I’ve discussed the whole something-from-nothing emergence many times in posts on this blog, it essentially means that in a “universe” where there is nothing, it is possible or even certain that certain concepts including the emergence of objects, space, and time must happen–come into existence.  I’ll detail why in future posts (you can go back to previous posts to see discussion there too)–in its simplest form, my thinking is that an infinite emptiness things emerge because the multiplication of zero (nothing) times infinity does not remain zero.   All it takes is a fold, a density change of one of an infinite range of substances, over an infinite distance, over an infinite amount of time–and a contortion of unimaginable size and energy, a big bang could emerge.  Not possible in a finite world, but a nothing by definition, is infinite–no boundary conditions (otherwise you have a something!).  Uggh, you say–what a misappropriation of a mathematical equation!  Maybe so, you might be right–but to me, I see an open door (infinite emptiness) as to how our existence could form without the need for some intelligence of some sort to willfully create it.

I’ve always felt that this has to be true–I think it is a logical starting point to assume that the universe started from nothing.  The problem with assuming anything else, such as a creator, is obvious–what created the creator, and what created the infrastructure that allowed a creator to form.  There really is only one way that does not get into the recursive problem of creation–the formation of something from nothing.   This is the basis, the fundamental rule, of all of my thinking*–I assume the universe evolved from nothing and ask what kinds of physical structures could emerge given that constraint.

What does that say about the philosophical question of is there a God and a purpose or meaning of life?  I think quite a lot, but my focus is much more on what does this mean for the mechanics, the physics, of this existence in the hope of finding a provable and observable confirmation, something new that would prove or disprove my thinking process.

Will I be able to prove this idea?  Will I be able to convince you?  Probably not–I am nothing in the world of theoreticians and thinkers, and do not have the infrastructure access that would allow review and development of these ideas.  Extraordinary ideas require extraordinary proof, and I’m not equipped to provide that.  But I can still present the concepts here and a reader can think for themselves if there’s a possibility here and what to do about it.

More to come

*Note, there actually is a whole realm of beginning-of-universe alternatives I am skipping over due to the fact that I am making a specific set of assumptions about time.  The concept of creation is, of course, intrinsically connected to the interpretation of the observation of time.  There will be a variety of other possibilities of the formation of the universe based on different interpretations of what time means.  So far, I’ve not really investigated those because the something-from-nothing concept appears to be a very solid approach that takes time at face-value and does not require any unintuitive approaches to how time works or things like time as a dimension, which as I said above, does not have experimental confirmation.

Simulation Construction of Twist Theory

December 2, 2014

Back after dealing with some unrelated stuff.  I had started work on a new simulator that would test the Twist Theory idea, and in so doing ran into the realization that the mathematical premise could not be based on any sort of electrostatic field.  To back up a bit, the problem I’m trying to solve is a geometrical basis for quantization of an EM field.  Yeah, old problem, long since dealt with in QFT–but the nice advantage of being an amateur physicist is you can explore alternative ideas, as long as you don’t try to convince anyone else.  That’s where crackpots go bad, and I just want to try some fun ideas and see where they go, not win a Nobel.  I’ll let the university types do the serious work.

OK, back to the problem–can an EM field create a quantized particle?  No.  No messing with a linear system like Maxwell’s equations will yield stable solitons even when constrained by special relativity.  Some rule has to be added, and I looked at the old wave in a loop (de Broglie’s idea) and modified it to be a single EM twist of infinitesimal width in the loop.  This still isn’t enough, it is necessary that there be a background state for a twist where a partial twist is metastable, it either reverts to the background state, or in the case of a loop, continues the twist to the background state.  In this system–now only integer numbers of twists are possible in the EM field and stable particles can exist in this field.  In addition, special relativity allows the twist to be stable in Minkowski space, so linear twists propagating at the speed of light are also stable but cannot stop, a good candidate for photons.

If you have some experience with EM fields, you’ll spot a number of issues which I, as a good working crackpot, have chosen to gloss over.  First, a precise description of a twist involves a field discontinuity along the twist.  I’ve discussed this at length in previous posts, but this remains a major issue for this scheme.  Second, stable particles are going to have a physical dimension that is too big for most physicists to accept.  A single loop, a candidate for the electron/positron particle, has a Compton radius way out of range with current attempts to determine electron size.  I’ve chosen to put this problem aside by saying that the loop asymptotically approaches an oval, or even a line of infinitesimal width as it is accelerated.  Tests that measure the size of an electron generally accelerate it (or bounce-off angle impact particles) to close to light speed.  Note that an infinitely small electron of standard theory has a problem that suggests that a loop of Compton size might be a better answer–Heisenberg’s uncertainty theorem says that the minimum measurable size of the electron is constrained by its momentum, and doing the math gets you to the Compton radius and no smaller.  (Note that the Standard Model gets around this by talking about “naked electrons” surrounded by the constant formation of particle-antiparticle pairs.  The naked electron is tiny but cannot exist without a shell of virtual particles.  You could argue the twist model is the same thing except that only the shell exists, because in this model there is a way for the shell to be stable).

Anyway, if you put aside these objections, then the question becomes why would a continuous field with twists have a stable loop state?  If the loop elements have forces acting to keep the loop twist from dissipating, the loop will be stable.  Let’s zoom in on the twist loop (ignoring the linear twist of photons for now).  I think of the EM twist as a sea of freely rotating balls that have a white side and a black side, thus making them orientable in a background state.  There has to be an imaginary dimension (perhaps the bulk 5th dimension of some current theories).  Twist rotation is in a plane that must include this imaginary dimension.  A twist loop then will have two rotations, one about the loop circumference, and the twist itself, which will rotate about the axis that is tangent to the loop.  The latter can easily be shown to induce a B field that varies as 1/r^3 (formula for far field of a current ring, which in this case follows the width of the twist).  The former case can be computed as the integral of dl/r^2 where dl is a delta chunk of the loop path.  This path has an approximately constant r^2, so the integral will also vary as r^2.  The solution to the sum of 1/r^2 – 1/r^3 yields a soliton in R3, a stable state.  Doing the math yields a Compton radius.  Yes, you are right, another objection to this idea is that quantum theory has a factor of 2, once again I need to put that aside for now.

So, it turns out (see many previous posts on this) that there are many good reasons to use this as a basis for electrons and positrons, two of the best are how special relativity and the speed of light can be geometrically derived from this construct, and also that the various spin states are all there, they emerge from this twist model.  Another great result is how quantum entanglement and resolution of the causality paradox can come from this model–the group wave construction of particles assumes that wave phase and hence interference is instantaneous–non-causal–but moving a particle requires changing the phase of the wave group components, it is sufficient to limit the rate of change of phase to get both relativistic causality and quantum instantaneous interference or coherence without resorting to multiple dimensions or histories.  So lots of good reasons, in my mind, to put aside some of the objections to this approach and see what else can be derived.

What is especially nice about the 1/r^2 – 1/r^3 situation is that many loop combinations are not only quantized but topologically stable, because the 1/r^3 force causes twist sections to repel each other.  Thus links and knots are clearly possible and stable.  This has motivated me to attempt a simulation of the field forces and see if I can get quantitative measurements of loops other than the single ring.  There will be an infinite number of these, and I’m betting the resulting mass measurements will correlate to mass ratios in the particle zoo.  The simulation work is underway and I will post results hopefully soon.

Agemoz

PS: an update, I realized I hadn’t finished the train of thought I started this post with–the discovery that electrostatic forces cannot be used in this model.  The original attempts to construct particle models, back in the early 1900s, such as variations of the DeBroglie wave model of particles, needed forces to confine the particle material.  Attempts using electrostatic and magnetic fields were common back then, but even for photons the problem with electrostatic fields was the knowledge that you can’t bend or confine an EM wave with either electric or magnetic fields.  With the discovery and success of quantum mechanics and then QFT, geometrical solutions fell out of favor–“shut up and calculate”, but I always felt like that line of inquiry closed off too soon, hence my development of the twist theory.  It adds a couple of constraints to Maxwell’s equations (twist field discontinuities and orientability to a background state) to make stable solitons possible in an EM field.

Unfortunately, trying to model twist field particles in a sim has always been hampered by what I call the renormalization problem–at what point do you cut off the evaluation of the field 1/r^n strength to prevent infinities that make evaluation unworkable.  I’ve tried many variations of this sim in the past and always ran into this intractable problem–the definition of the renormalization limit point overpowered the computed behavior of the system.

My breakthrough was realizing that that problem occurs only with electrostatic fields and not magnetic fields, and finding the previously mentioned balancing magnetic forces in the twist loop.  The magnetic fields, like electrostatic fields,  also have an inverse r strength, causing infinities–but it applies force according to the cross-product of the direction of the loop.  This means that no renormalization cutoff point (an arbitrary point where you just decide not to apply the force to the system if it is too close to the source) is needed.  Instead, this force merely constrains the maximum curvature of the twist.  As long as it is less that the 1/r^n of the resulting force, infinities wont happen, and the curve simulation forces will work to enforce that.  At last, I can set up the sim without that hokey arbitrary force cutoff mechanism.

And–this should prove that conceptually there is no clean particle model system (without a renormalization hack) that can be built from an electrostatic field.  A corollary might be–not sure, still thinking about this–that magnetic fields are fundamental and electrostatic fields are a consequence of magnetic fields, not a fundamental entity in its own right.  The interchangability of B and E fields in special relativity frames of reference calls that idea into question, though, so I have to think more about that one!  But anyway, this was a big breakthrough in creating a sim that has some hope of actually representing twist field behavior in particles.

Agemoz

PPS:  Update–getting closer.  I’ve worked out the equations, hopefully correctly, and am in the process of setting them up in Mathematica.  If you want to make your own working sim, the two forces sum to a flux field which can be parametrically integrated around whatever twist paths you create.  Then the goal becomes to try to find equipotential curves for the flux field.  The two forces are first the result of the axial twist, which generates a plane angle theta offset value Bx = 3 k0 sin theta cos theta/r^3, and Bz = k0 ( 3 cos^2 theta -1)/r^3.  The second flux field results from the closed loop as k0 dl/r^2).  These will both get a phase factor, and must be rotated to normalize the plane angle theta (some complicated geometry here, hope I don’t screw it up and create some bogus conclusions).  The resulting sum must be integrated as a cross product of the resulting B vector and the direction of travel around the proposed twist path for every point.

Noncausal solution, Lorentz Geometry, and trying a LaGrangian solution to deriving inertia

December 31, 2012

Happy New Year with wishes for peace and prosperity to all!

I had worked out the group wave concept for explaining non-causal quantum interactions, and realized how logical it seems–we are so used to thinking about the speed of light limit causing causal behavior that it makes the non-causal quantum interactions seem mysterious.  But when thinking of a universe that spontaneously developed from nothing, non-causal (infinite speed) interactions should be the default, what is weird is why particles and fields are restricted to the speed of light.  That’s why I came up with the group wave construct for entities–a Fourier composition of infinite speed waves explains instant quantum interference, but to get an entity such as a particle to move, there is a restriction on how fast the wave can change phase.  Where does that limitation come from?  Don’t know at this point, but with that limitation, the non-causal paradox is resolved.

Another unrelated realization occurred to me when I saw some derivation work that made the common unit setting of c to 1.  This is legal, and simplifies viewing derivations since relativistic interactions now do not have c carried around everywhere.  For example, beta in the Lorentz transforms now becomes Sqrt(1 – v^2) rather than Sqrt(1 – (v^2/c^2)).  As long as the units match, there’s no harm in doing this from a derivation standpoint, you’ll still get right answers–but I realized that doing so will hide the geometry of Lorentz transforms.  Any loop undergoing a relativistic transform to another frame of reference will transform by Sqrt(1 – (v^2/c^2)) by geometry, but a researcher would maybe miss this if they saw the transform as Sqrt(1 – v^2).   You can see the geometry if you assume an electron is a ring with orientation of the ring axis in the direction of travel.  The ring becomes a cylindrical spiral–unroll one cycle of the spiral and the pythagorean relation Sqrt(1 – v^2/c^2)) will appear.  I was able to show this is true for any orientation, and hand-waved my way to generalizing to any closed loop other than a ring.  The Lorentz transforms have a geometrical basis if (and that’s a big if that forms the basis of my unitary twist field theory) particles have a loop structure.

Then I started in on trying to derive general relativity.  Ha Ha, you are all laughing–hey, The Impossible Dream is my theme song!  But anyway, here’s what I am doing–if particles can be represented by loops, then there should be an explanation for the inertial behavior of such loops (totally ignoring the Higgs particle and the Standard Model for right now).  I see a way to derive the inertial behavior of a particle where a potential field has been applied.  A loop will have a path through the potential field that will get distorted.  The energy of the distortion will induce a corrective effect that is likely to be proportional to the momentum of the particle.  If  I can show this to be true, then I will have derived the inertial behavior of the particle from the main principle of the unitary twist field theory.

My first approach was to attempt a Lagrangian mechanics solution.  Lagrange’s equation takes the difference of the kinetic energy from the potential energy and creates a time and space dependent differential equation that can be solved for the time dependent motion of the particle.  It works for single body problems quickly and easily, but this is a multiple body problem with electrostatic and magnetic forces.  My limited computation skills rapidly showed an unworkable equation for solution.  Now I’m chewing on what simplifications could be done that would allow determining the acceleration of the particle from the applied potential.

Agemoz

Vector Field Neighbors

May 28, 2012

I have been thinking a lot about the latest work on twist fields.  It has a lot of good things about it, it appears to successfully add quantization and special relativity to a vector field.  It opens up a possible geometry for the particle zoo.

But if this is really going to be workable or provable, I’m going to have to create a simulation, and that has to start with a mathematical basis.  And that wont come until I understand how the vector field operates on neighbors.  Yes, the unitary twist field has the right configuration to make things work, but the actual quantitative behavior is completely dependent on how the field propagates in space and time.  Up to now, the model looks like a sea of rotating balls, each with a black point spot that normally points in an imaginary direction, but can temporarily point in a real space formed by three real basis vectors orthogonal to the imaginary direction.  (Note that this discrete representation simplifies visualization, but there is no reason that the correct solution can’t be continuous, in fact I suspect it is).  If there is a connection between adjacent ball directions, the necessary quantization, stable particle formation, and special relativity behaviors will result.  However, a quantitative specification of these behaviors is entirely and completely specified by the nature of this neighborhood connection.

How does one ball affect its immediate neighbors?  Can a ball affect nearby balls that are not immediate neighbors?  Can a ball move in 3D or is everything that happens solely a function of ball rotation in place?  I see only two possible connections, one I call gear drive (a twist motion induces an adjacent ball in the twist plane to twist in the same (or opposite) direction) and the other I call vortex drive (a ball twist causes an adjacent ball on the twist axis to turn in the same or opposite direction).  Both of these forces could also induce normal twists, for four possible neighbor connections.  Which, or what set, of these neighbor interactions are valid descriptions of how balls move?  And what mathematically is the exact amount of dispersion of twist to neighbors?  Is the field continuous or can discontinuities occur?

Certainly the requirement for continuity is a powerful constraint, allowing discontinuities from the imaginary to any of the real axes, but prohibiting discontinuities between the real axes or in the imaginary direction.

These are the questions I have been pondering a lot.  I have come up with a nice framework but now I have to work out just how the vector field neighbor connection must happen before I make any further progress.

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

Why Static Twists Cannot Be Stable

March 11, 2012

Some really exciting results from my simulation results of the Twist hypothesis!  I have been simulating this for a while now, to recap:  The twist theory posits (among many other things) that underlying the photon elements of an electromagnetic field is a unitary twist field.  This unitary twist field is a direct (or mapped) result of the E=hv quantization of all particles.  Photons are linear twists of the unitary field, whereas massive particles are self-contained twists, such as a ring for electrons/positrons.  Quarks and other massive particles are posited to be other geometrical constructions.  If this model is studied, one very interesting result is the correct representation of the special relativity space and time Lorentz transforms, where linear twists travel at a maximum, but constant, speed in all frames of reference–but all self-contained structures such as the electron ring must obey time and spatial dilation.  The model correctly derives the beta dilation factor.

As a result of this work, I have put together a simulator to model the twist behavior in the hopes of verifying the existing corollaries to the twist theory, and also to see if more complex geometrical structures could be determined (say for quarks, although it is certain that the strong force would have to be accounted for somehow).

One of the results of the theory seemed to imply that a static linear twist should be possible, yet static photons do not exist in nature.  I’m very excited to have the simulator show its first demonstration of why this happens!  When I set up the simulator to do a static linear twist, I discovered (see previous posts) that the twist always self destructed by dissipation, and it took a lot of work to find out why.  This will be easiest to show with this diagram:

Why the static twist dissipates. Note the narrowing of the twist from the outside in.

The premise of the unitary twist theory is that E=hv particles can only be quantized geometrically in a continuous field system if particles exist in a localized background field direction have a fixed amplitude twist.  The fixed amplitude (different from an EM field that allows any magnitude) prevents the quantized entity from dissipating, and the background direction enforces quantization of the twist–partial twists (virtual particles) are not stable and fall back to the background direction, whereas full twists are topologically stable since the ends are tied down to the background direction such that the twist cannot unwind.  The frequency of the twist is determined by the twist width, shown in the diagram as omega.

Iteration of the linear twist in the simulation showed that, even though the unitary twist magnitude could not dissipate, the twist would vanish (see previous post pictures).  At first, I thought this was an artifact of the lattice form of the simulation, I represented a continuous twist with a stepwise model.  Further sims and analysis showed that the behavior was not a lattice effect (although it definitely interfered with the correct model behavior).  As this diagram shows, I was able to demonstrate that a static twist cannot exist, it is not stable.  What happens is that the twist width cannot be preserved over time because the ends experience normalizing forces to the background.  This process, demonstrated in the simulation, ultimately causes the particle to approach a delta function, at which point the simulation twist model gets a single lattice node and eliminates it.

It would be a valid statement to say that the sim does not correctly model what happens at that final stage, but there’s no question in my mind of the validity of the narrowing of the twist width.  There is only one way that the linear twist can be stable–if the light cones of each twist element are out of range of each other.  This can only happen if the twist elements are moving at speed c.

I was disappointed at first, I didn’t have a working model of the twist field.  But I didn’t see that the sim had handed me my first victory–the explanation of why there are no static photons.

Agemoz