Posts Tagged ‘photon’

Preparing First Collision Sim

June 22, 2017

I’ve been working fairly consistently on the simulation environment for the unitary twist field theory. I’m getting ready to set up a photon/electron collision, modeled by the interaction of a linear twist with a twist around a loop. The twist is represented by e^I(t theta – k x), yes, the same expression that is used for quantum wave functions (I’ve often wondered if we’ve misinterpreted that term as a wave when in fact the math for a twist has been in front of our noses all along).

This is a great first choice for a collision sim because in my mind there’s always been a mystery about photon/particle interactions. If the electron is really a point particle as the Standard Model posits, how can a photon that is many orders of magnitude larger always interact with one and only one electron, even if there are a gazillion electrons within one wavelength of the photon? The standard answer is that I’m asking the wrong or invalid question–a classical question to a quantum situation. To which I think, maybe, but quantum mechanics does not answer it, and I just get this sense that refusing to pursue questions like this denies progress in understanding how things work.

In twist theory there appears to be an elegant geometrical answer that I’m pretty sure the simulation will show–counting my chickens before they are in my hand, to be sure–the downfall of way too many bright-eyed physics enthusiasts. But as I’ve worked out before, the precursor twist field is an incompressible and non-overlapping twist field. If the electron is a closed loop of twists, and within the loop the twists revert back to the I direction (see previous posts for a little more detailed description), then any linear twist propagating through the loop will add a delta twist to some point in the interior of the loop. Since you cannot somehow overlap twists (there’s only one field here, you can’t somehow slide twists through each other. Each point has a specific twist value, unlike EM fields where you linearly combine distinct fields). As a result, the twist of the loop can unwind the linear twist going through it, causing the photon to disappear and the close loop will pick up the resulting linear twist momentum. This isn’t really a great explanation, so here’s a picture of what I think will happen. The key is the fact that the precursor field has one twist value for every point in R3. It’s an incompressible and unitary field–you cant have two twist values (or a linear combination–it’s unitary magnitude at every point!) at a given point, so the photon twists have to affect the twist infrastructure of the loop if it passes through the loop. It really will act a lot like a residue inside a surface, where doing a contour integral will exactly reflect the number of residues inside.

At least that’s what I think will happen–stay tuned. You can see why I chose this interaction as the first sim setup to try.


Geometry of the Twist Sim Math

January 5, 2015
Here is a drawing of the forces on the twist path that the simulator attempts to model.

Here is a drawing of the forces on the twist path that the simulator attempts to model.

I created a picture that hopefully shows the geometry of the simulation math described in the previous post (see in particular the PPS update).  This picture attempts to show a generator twist path about point A in red, with the two force sources F(loop) and F(twist), which are delta 1/r^2 and 1/r^3 flux field generators respectively.  The destination point D path is shown in blue.  The parametric integral must be computed for every source point on each destination point–this will give a potential field.  When the entire set of curves lies on an equipotential path, one of many possible stable solutions has been found (it’s already easy to establish that any topologically unique closed loop solution will not degenerate because the 1/r^3 force will repel twist paths from crossing each other).  There probably is a good LaGrange method for finding stable solutions, but for now I will work iteratively and see if convergence for various linked or knotted loops can be achieved.



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.


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.


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.

Atomic Orbital Correction

July 31, 2013

Oops, an error on the previous post.  I said the strong force is responsible for the repulsion of an atom’s orbital electrons from the nucleus, but of course that’s not right, it’s reponsible for the attraction binding the nucleus particles together.  By quantum mechanics, virtual photons in the EM field provide the electron attraction to the nucleus, and the the electron momentum prevents annhiliation.  In the Twist Theory approach, twists do mediate this interchange, but in the form of linear twist photons–no big surprise, here Twist Field theory does the same thing as quantum theory.  The trouble, though is why is the frequency of the photon what it is?  It would help vindicate the Twist Field theory if there was a plausable twist explanation, but I don’t see it.  As I mentioned in the previous post, the kinetic energy of an orbital is far smaller than the rest energy (and hence wavelength of its twist) of the electron–and the orbital size is correspondingly far larger by 7 or so orders of magnitude.  The twist field could maybe explain the energy of an electron, but right now I don’t see how it could explain the quantization of the orbital energy jumps.  The Rydberg Equation should give a clue with the 1/r^2 factor, but I don’t see a way for this to work geometrically yet.


Gaussian Wave Packets

February 20, 2013

It’s been a little while since I’ve posted, mostly because I have an unrelated big project going on, so I’ve been focusing on trying to get that out the door.  And, I’m working on getting the twist ring inertial math to work, a laborious project since the Lagrangian equation of motion has too many variables for solving.  I’m trying to find ways to simplify.  In addition, I also have an iterative sim of the inertial response ready to go but haven’t had time to set it up and run it.  Hopefully with the other project almost done I’ll get to it this weekend.

One thought I’ve had in the meantime–many  quantum mechanics exercises involve modeling a photon with a wave packet that is described as having the Gaussian integral form.  The most basic variation of this form (Integral[Exp[-x^2]]) is a bell shaped curve with amplitude 1 at zero and asymptotically goes to zero at +/- infinity.  I’ve had lots of lectures where an oscillating squiggle is used to represent the magnitude of the quantized photon wave packet.

A very interesting thought occurred to me is that this integral is a great representation of the unitary twist version of a photon packet.  A one dimensional magnitude projection of a twist from the Unitary Twist Field Theory would be represented exactly by a Gaussian curve, and if we use a complex value r to completely represent the twist function, then the Gaussian integral becomes Integral[Exp[-r^2]] and then this can be interpreted as a working model of twists–and thus support the notion that the twist theory has a well proven basis in the math of quantum mechanics.  Do I buy that, or should my skepticism meter be dinging my thinking process?  Right now, the idea looks pretty workable–it seems pretty clear that the r form clearly would represent a twist as well as a Gaussian envelope packet over a frequency of oscillation of E and B fields–making the twist theory a viable alternative to the magnitude constrained wave packet interpretation.  For the twist theory to be acceptable, there has to be a path to the math of quantum mechanics, and I think I see how this could happen.


Lattice fields and Specular Simulation (latest work)

August 25, 2012

The latest work on the twist model is proceeding.  This work makes the assumptions noted in previous posts–EM interactions are mediated by photons as a quantized linear field twists.  The current work assumes these photons comprise the macroscopic electrostatic and magnetic field,  are unitary, and that they are sparse (do not interact).  It assumes that the twist has a common imaginary axis and three real dimensions on R3, similar but not the same as the QFT EM field, which is a complex value on R3 (t is assumed in both cases).  Electron-photon interactions occur when a twist ring captures a linear twist and absorbs it.  I am assuming that a photon twist is magnetic when the real axis of the twist is normal to the real dimension direction of travel, and is electrostatic when the real axis of the twist is tangent to the direction of travel (note how relativistic motion will alter the apparent axis direction, causing the expected shift of photons from electrostatic to magnetic or vice versa).

This set of assumptions creates a model where the linear twist of the photon will affect a twist ring electron in different ways depending on the photon twist axis direction.  Yes, this is a rather classical approach that ignores the fact that quantum interactions are probability distributions, among other things.  My approach is to create a model simulation environment to test the hypothesis that quantization can accurately be represented by field twists, the foundation of the unitary twist field theory.  It does not currently include entanglement, which I represent as the assumption that field twist phase information is instantaneous but that particles (twists) are group wave assemblies that propagate no faster than the speed of light.

These assumptions require that I make changes to my current simulator, which is a lattice approximation of a continuous vector field twist.  I was able to show in that simulator that a continuous twist solution could not work due to the unitary field blocking effect.  From that (and from QFT), I concluded that the twist field must be sparse and specular, where interactions are mediated by linear twist photons that do not interact.  I cannot use my existing simulator for this model but must make a new version, which is underway.  It will take a while so my posts will become less frequent until I get this working.

However, since I am now going away from a lattice simulator to a sparse model simulator, it did make me think about lattices as a representation of existence, and I concluded that that cannot be.  I have often seen theories that our universe is a quantum scale lattice of Planck length.  This supposedly would explain quantization, but I don’t think it works–the devil is in the details.  If the lattice is periodic, such as an array of cube vertexes or tetrahedral vertices, then there should be angles that propagate photons differently than others.  If our existence is spinning on a periodic lattice, we should see harmonics of that spin as background noise.  Within the range of our ability to detect such “radiation” from space, neither are happening.

So, suppose the lattice is not periodic but is a random clustering of vertexes, which solves the problem of periodicity causing background frequencies.  In that case, I would expect that photon propagation would have velocity variation as it propagated through varying spacing of vertexes.  There would have to be an upper bound to the density of vertexes to ensure apparent constant speed, and I struggle to think what would enforce that bound.  This is probably the most workable of the lattice ideas, but due to the necessity of a vertex spacing constraint, there would have to be an upper limit to the allowable energy of a photon, something we have no evidence for.  At this point, I think there is no likelihood that existence can be described as a lattice.  That hypothesis is attractive because we can easily imagine a creator God could build a computer that could most easily create a model of existence using a lattice of some form.  But even though the Planck length lattice is far too small for us to detect directly, I don’t think the evidence points that way.  (Side note:  it’s so interesting to look at early literature to see the historical evolution of what people thought formed the underlying basis for our existence–early on, God creating and controlling a mechanical model, then universe models were complex automated assemblies of gears and pullies, then the steam-engine or steam-punk type of machine, then mechanical computing engines, and now computer program driven machines simulating a lattice…  What is next? !)

Back to the lack of evidence for an underlying lattice to our existence.  This is a more important  realization than it might appear, especially from a philosophical standpoint.  If there was evidence that the universe was built on a lattice, that would strongly imply creation by a being, because a lattice is an underlying structure and constraint.  Evidence that there is no lattice, which is what I think I am seeing, would imply that there is no higher being because it is hard for me to imagine constructing a world without a lattice.  Of course, it would only be a mild implication, because my ability to imagine how a universe could be constructed without a lattice is limited.  Nevertheless, it is a pointer in the direction of existence coming from nothing rather than being constructed by a God.

Pretty interesting stuff!  More to come as the new simulator work gets underway.

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…


Conservation of Twist Energy

April 2, 2012

 I worked for a while with the 1/r^2 – 1/r^3 solution set and quickly discovered that this is just a lucky subset of the twist field solutions–every solved solution is unstable.  I can’t even find the solution that works in the ring case that appears stable, although I quit working on this because I realized that the twist field would yield a lot of cases that dont go into the 1/r^2 – 1/r^3 subset of solutions.

So, I went back to the generalized twist field, and  realized I had set up my simulations wrong.  The twist, as explained in a much earlier post (“Turning Bicycle Wheel”), has to be in-line with the direction of travel in order for the circular polarization degree of freedom of a photon to exist.  But even so, simulations show that the width, and hence the energy of the photon, has to be conserved but is not if the twist is not moving at the speed of light.  Even when moving at the speed of light, it was not clear why the width would be constant–but it has to be, else conservation of energy wont happen.  How can I make a simulation which observes both the quantization and conservation of energy of the twists in the vector field?

I thought for a while about this, and attempted to draw a Minkowski diagram (3D + T) representation of the twist.

Picture of field twist in Minkowski spacetime

This got really interesting really fast.  After a few mis-draws (my mind isn’t very well wired to view things in 4D), I realized that in Minkowski space, there is no twisting of the photon along the light cone path–in fact, in the one case of a twist moving at speed c, there is no acceleration at all–no forces needed to explain the twist structure!  Each light cone path has a twist angle that does not change over time, thus showing how twist width is conserved and thus how a photon holds its energy quantum without dissipation.  It’s hard to see, but I attempted a diagram–note that along the red light-cone paths, there is no change of the field angle.  A narrowing of the twist width either timewise or space wise would require a merging or deviation of angle paths not possible without some force source.

This should provide a basis for how to simulate the twists in a way that conserves energy.