Agemoz's Physics Blog

I had mentioned Dr. John Bell having done groundbreaking work on entangled states in my review of some of the pivotal work discovering how the quantum world works. Let me lay some groundwork here, and here you will find my primary interest in talking about unitary field twists. Let’s start with the two-slit experiment–the start of it all when it comes to my thinking about twists. The two slit experiment demonstrates the quantum mechanical property that a particle will exhibit when it strikes a barrier with two slits in it. The particle will either be absorbed, reflected, or go through one or the other but not both, slits. The quantum oddity of the two-slit experiment is that the particle will hit the target as if it had gone through both slits and perform a wave-like interference with itself–this is observed by where the particle lands on the target. Here’s where it gets very weird–if both slits are open, there are certain areas on the target where the particle will not go due to wave-like interference of the particle with itself. But if one of the slits is covered up, this target area will get struck by the particle, an apparent logical impossibility. This is why we say that quantum mechanics requires that every particle have wave-like properties.

But wait–there’s more. If the particle is acting wavelike, then detectors placed at both slits should somehow detect the particle going through both slits. They never do–they always detect the particle like property of always going through one or the other. So what is it–a particle, or a wave? Conventional physics says it depends–if you don’t try to detect the particle, it will act as a wave and go through both. If you put detectors there, it will act as a particle and only go through one. You can put the detectors far behind the barrier with slits (so that the detector itself cannot affect the slit traversal outcome by proximity) and still get the same result.

The trouble with the “depends” answer is this doesn’t match anything we can observe at the macroscopic level, and even at the mathematical level this creates a paradox that has been argued to no end (see posts earlier on this blog for various thoughts on this). Reference the EPR decoherence and many histories and all kinds of other philosophical efforts to make sense out of it. Reference the “shut up and calculate” mindset of working the math to excellent accuracy in spite of not understanding what we are seeing in this experiment.

What this experiment really forces us to make sense of is what it means for something to move. Say what? What’s that got to do with anything? Think about it for a second. There’s two ways to think about what it means to move from point A to B. Either there is some object like a baseball that some how picks itself up and physically extricates itself from spot A and lands in spot B with all of the components now in the new location, or: there is an image, in some sense of the word, of a baseball in spot A, and through some kind of image copy the image disappears and reappears in spot B. No actual objects moved, but the image movement was effected by in-place alteration of field vector direction, say. Our macroscopic view of things would say that the first was a particle, and the second was a wave. For example, a circular ripple on a pond is a wave–there’s no net movement of water, yet the ripple can exert forces, tides, and so on–it is a real object that moves, even though there’s no underlying net movement of the field elements that compose the wave.

The problem that the two-slit experiment presents is conventional physics says that the detectors become a boundary condition for the form of the object, wave or particle. Physicists have worked through all the logic to have this come out correctly, but there is some level of debate about the right way to interpret what we see–I don’t think any physicist really claims they completely understand this. Just what is it that passes through those slits? If something passes through both slits to affect the direction of the something, but the something can never be detected in both slits, we can’t be talking about a wave or a particle. If it were only a wave, it should be detectable as such (in both slits). If it were a particle, the second slit can’t affect the path it takes. A third possibility, called the many-histories solution (initiated by Everett and advocated by Dr. Hawking) says that all possible paths and outcomes exist at once, undetectable by observers, and combine to produce what we see when the particle is detected. I don’t like this because it doesn’t really explain why a wave can’t be detected at both slits (and certainly has no observable analog or evidence in the macroscopic world–we never see anything but one outcome–who picked that outcome for us to see!). Note, though–the math, Feynman path integrals, is correct and does say that all possible paths (“histories”) have to be applied to get the correct solution, but I am debating that this can be interpreted to mean that all outcomes occurred. A fourth solution, called the Pilot Wave solution, suggests that particles have a wave-like shroud that somehow influences the path that the particle takes. I like this because it is a geometrical alternative to thinking of a quantum object as either a particle or a wave. And, it suits my pet theory of twists. Unitary field twists are quantized by the need for the twist to return to the background field state after turning, but the turn can be slightly abbreviated or extended if the background field is distorted (turned a bit). I can readily imagine this turning resulting from residual effects pouring through the second slit–the wave effect over all possible paths altered due to the presence of the two-slit barrier. And the twist has particle behavior as well, since the twist itself will only go through one slit–the field twist region is one dimensional along the axis of travel. Finally, getting back to what it means to move–the twist is represented by a unitary vector field whose components do not actually physically move, but turn and twist to create the image of an object that moves and interacts. Previous pilot wave approaches were hampered (more accurately, eliminated as possible models) because EM waves do not form solitons, or wave assemblies that are stable in time. Unitary field twists are stable topologically since the ends of the twist must match the background vector state, and thus have stable linear, ring, and other geometrical configurations.

Alright, I thinks! We have our answer! Uh, well, not so sure about that, and for the reason why we need to look at what Dr. Bell concluded and the Aspect experiment confirmed. Let’s save that for another post.

Agemoz

One thing to note in the previous post: You may have read where I describe Schroedingers Wave Equation solution for the free electron, and wondered… Uhh, why is this nut saying twist rings describe electrons when we already have a provably correct quantum solution for electrons? Oh, that is a brilliant question, but the answer is that we don’t have a provably correct quantum solution for electrons or even photons. Remember that the Schroedinger wave equation gives us a probability distribution for where the particle is and what the states of the particle are when it interacts with something. It cannot and does not describe the particle internals. Field twists are my attempt to resolve what is actually going on internally in the particle, and must first correctly give the observation outcomes specified by Schroedinger’s wave equations and all of the rest of quantum and relativity theory. Only if verified in this way can we then draw additional conclusions from the theory based on twist geometry.

Now this brings up another question, which is due to the brilliant work by John Bell (who should have received a Nobel Prize for his work but died first–Nobels cannot be awarded post-humously). He proved that entangled particles cannot have substructure as a means for explaining the non-causal propagation of state resolution. Yow, I’ll bet that was a mouthful to absorb–but it has implications for my attempt to describe photons and electrons as a field twist. We’ll go there another day.

I added a glossary with brief descriptions of terms I use a lot here, I hope you find that helpful (and accurate) in reading my stuff.

Agemoz

[note: updated, fixed a few errors in the writing of this post]

I’ve had some wonderful insights this week about why quantum theory has not come up with the twist solutions that seem to be such good solutions to things like photons and electrons. There’s always the distinct possibility that the twist ideas are just dumb crackpot ideas, and I’d kind of like to know if that’s what a physicist would think if he were to sit and really look at them. To do that, I need to try and think like a physicist, and that means having a better understanding of the equations that drive quantum theory. This will tax my ability to write a coherent post, so I will try especially hard to make this readable. I’m going to experiment with changing the blog format to include a glossary on the side, but for now I’ll just create this post and see what happens. This is going to be simplified to the point that my feeble mind can understand it–let’s review the ground-breaking equations that form the basis for quantum theory.

OK, let’s start with the simplest form that Einstein discovered from the photomultiplier experiment–the equation E=hv. This says that for any frequency v (that should be the greek letter Nu) there is a fixed energy E related as Planck’s constant h. In other words, only one possible energy is possible for a given frequency and vice-versa; energy of a particle is quantized. You cannot change the energy of a particle without somehow changing its frequency.

Next comes the Heisenberg uncertainty relation x * p >= h. This means that at the quantum scale we have to work with probability distributions, not the actual x or p of a particle. I’ve more or less been ignoring this in my thinking but its always in the back of my mind that I cannot come up with equations that explicitly specify field vectors that are observable.

Now, look at the Schroedinger (non-relativistic) wave equation. This really is just a potential energy central force solution combined with E=hv. Potential energy central force solutions are only relevant in two (or more) body problems such as electrons about a massive center (proton-neutron nucleus of atoms, for example). In 3D, you get an interesting array of solutions that will give the orbital electron energies that can be thought of as waves that circle around the center–DeBroglie thought that quantization resulted from the fact that waves have to “fit” (phase of multiple go-arounds have to match). I always doubted that–it might be true if the uncertainty relation didn’t exist, but with a probability distribution, or electron cloud, it’s not clear to me why anything would have to phase match. In any event, it doesn’t explain the quantization of particles that don’t go around in an orbit, such as a free electron or a photon. There is a free particle version of the Schroedinger that sets the potential to zero, this yields wave solutions F = A e^i*Pi(kx -vt). But this doesn’t quantize the particle or where the particle is! All of these equations only describe probability distributions of where the particle is or what state it is in (actually, the related solution of probability density). Boundary conditions (information about the system outside of the particle) are necessary to set the constants here.

Now, suppose we want to add special relativity to the mix. What does that mean? Special relativity means that spatial and time dimensions are linearly altered according to the velocity and direction of the observer’s frame of reference. This means the solutions will have to obey the Lorentz transformations as you change the frame of reference. I thought this would be very hard to do mathematically, but in reading about how this was done, I realized how clever these guys were–instead of somehow trying to incorporate the Sqrt[1-beta^2] factors into the Schroedinger wave equation, they said–lets make the Schroedinger equation solutions invariant to frame of reference changes. This is what led to the Klein-Gordon equation–they did this by forcing the solution to be equivalent if there is a spatial or time-like displacement or rotation, using a matrix that is unitary in 3D + T. Expressing the wave solution in a form where it is valid whether or not there is a displacement or rotation in 3D + T constrains the solution set to work relativistically–meaning, if the particles involved are moving close to the speed of light.

It turns out that this approach does not take into account the electron spin property, so in some cases, the wrong energies are computed for electron orbital energies, so Dirac came up with an operator-based methodology that solves this problem. Schroedinger eventually fixed this with his wave equation but Klein-Gordon got there first and got their name on the solution. I’m not going to go there today.

The point of this exercise in reviewing these equations is to understand how something as simple as field twists could have been overlooked. Note that this history shows how these discoveries were atom-based. You really cannot detect an electron until it hits an atom, and observe the energies of, say, emitted photons that result. We see quantization based on these observations, and then it becomes logical why we have Schroedinger, Klein-Gordon, and Dirac equations. But, they don’t really work for free electrons and photons! The free electron solution in an unbounded box is just a wave solution–it could be valid, it says it will be analytic, but has no explanation for why its energy is quantized. It needs boundary conditions to provide definition for its solutions for location or state (electron in a box quantum mechanics).

DeBroglie was on a path to explain the quantization with his fitting waves around an orbit, but that begs the question of why phase has to match on each orbit. Since each orbit spatial starting point is time-wise separated, I see no reason why matching phases at this point would yield a lower energy state than if they weren’t matching.

However, twists in a background field have the appealing geometric property of a lowest energy state when the twists are quantized. Twists have lots of other appealing properties, such as deriving the Lorentz special relativity transforms and deriving the correct energy of an electron based on the energy connection between electrostatic and magnetic properties, explaining the polarization of photons, and lots of other things I’ve documented on this blog ad-nauseum. That’s what keeps me going on this–the current science hasn’t developed in a way where experiments and the resulting math could observe or deduce the twists.

Agemoz

I’m doing several lines of thought at once. I’ll just try to summarize here and flesh each out in later posts. First–I said no discontinuities, but this keeps nagging me, and I began to see some reasons why that approach is still on the island. Any discontinuity clearly cannot have a spatial dimension, even if that dimension lies on one spatial slice of a light cone–there will always be some frame of reference where some portion does not lie on a light cone, and thus violate analytic behavior of a field. I said that a twist has a wavelength and thus has a spatial dimension, and thus cannot be a valid solution for that reason. However, a wavelength can have a “length” and lie on the light cone. It would have a spatial distance representing the particle’s wavelength, but only a point at any given point in time–that is, the point of twisting expresses wavelength by twisting in time. It would lie on the light cone, so would be at a boundary for a possible discontinuity–in every frame of reference except its own. This should still be workable and I think I gave up on it too soon. I have to decide whether this is more likely to be correct or whether the analytic solution with the magnetic field sheath has fewer flaws. I also have come to a point where I need to understand what it means to move and what momentum really means. Are the field components in a photon actually moving, or just staying in place but spinning in such a way that adjacent field vectors are somehow influenced by its neighbors, this influence travelling at speed c. If the field components of a photon are actually moving, then the vector field going magnetic because its moving in the pointing direction makes sense (the dimension in relativistic travel goes to zero), but if it’s just a wave passing through spinning elements, then I don’t see how a magnetic interpretation could be formed (nothing is actually moving at c). In either scenario, what is it that is actually propagating in a twist and why does it continue to move (that is, why does the twist continue around in a circle rather than being pulled back or stopping). In fact, it’s not even clear that this is a question that can be asked. Quantum mechanics defines momentum in a way that doesn’t really have a classical geometrical interpretation. Yet another area of questioning is this–in order to make E=hv quantization to work, there has to be a local neighborhood where the field vector has a lowest energy state (the background direction). A twist is stable because both ends are tied down to this background direction, even though the middle of the twist is not in the lowest energy state. But what is the property of a field vector that gives it this potential energy state? Electric field elements do not interact. What keeps the twist from dissipating? Finally, I want to know what it means to have a point (dimensionless) twist in a field. This seems problematic to me.

Yeah, everything I think about grows questions like rabbits, and the ability to test possible answers has no experimental method that isnt too small for me to execute. So should I quit asking, or is there a path somewhere in here?

Agemoz

Every college student majoring in science and engineering goes through the EM physics course that teaches about the behavior of electrostatic fields and Maxwell’s field equations. Curl(E)=0, Div(E)=0 unless there’s a charged particle in there. So why do I argue for a twist in the field? Am I not going to get shot down immediately by an eager beaver freshman physics major? Twists, particularly the analytic solution that I propose that encloses it with a magnetic field sheath, are going to have curl non-zero. Why do I persist with this nonsense?

Well, I should have made it clear in previous posts–quantization of a field cannot happen with Maxwell’s field equations. The particle portion is an empirical addition to the field equations but create a magical black box on the particle itself. We know from QFT that the field has to be quantized. What rule do we break, and what do we hold to make this work? Right now, all we have for particles such as photons and electrons is a black box with very precisely defined aggregate or macroscopic behavior.

I have looked at what quantization means geometrically and have concluded that quantization has to result from field twists, and that a degree of freedom is given when we go from macroscopic EM field behavior to the quantum behavior of fields. To enforce quantization, I’ve come up with a modified vector field element that in aggregate will show the macroscopic behavior we observe such as inverse force law, spin and so on. This modified vector field is unitary in order to achieve E=hv quantization (otherwise there is a degree of freedom in field magnitude that will enable the quantization to dissipate), and generates aggregate E and B fields as collections of photons. I form photons from linear twists of this vector field, and electrons from rings of these twists. Doing all this readily derives Planck’s uncertainty relation and the special relativity Lorentz transforms.

But, getting back to the original question–what about div(E), curl(E)? How do we get there from twists?

That is a valid question, and any hypothesis about twists is going to have to answer that. But first, I have to come up with a mathematical model for the twist that doesn’t break some obvious constraint, and all my cavorting and groaning and blogging for the last few years has been to try to come up with something that will hold up. Not there yet, working on it–so far have found a whole bunch of ideas that won’t work, and chewing on one right now that might work. One thought I am having, though–I would expect *any* system that is granular (composed of quantized components) to exhibit macroscopic div(F) = 0, curl(F) = 0 behavior, regardless of the internals of the components–if the granular components don’t interact with each other. Maybe that’s what makes my twists work at the macroscopic scale…

Agemoz

One question that has come to me–if the twist is such a great solution, surely a zillion people before me would have followed this path–why haven’t they? It’s either because it doesn’t work, or because no one has seen it yet as a valid solution. Unfortunately, the odds are rather good that lots of people a whole lot smarter than me have already looked at it and said it doesn’t work. If that’s true, then I’m wasting my time, and anyone’s time who is reading this. But I actually think there’s a small possibility that a field twist as a quantum solution hasn’t been followed through enough. I’ve already posted a lot that shows why it maybe should be taken seriously, but am finding it taxes my abilities and IQ to prove that it is the correct solution to things like photons and electrons. The most important reason that I think it has validity is the clean way it provides a geometric basis for quantization. All particles, whether force-exchange particles like photons or stable particles like electrons, must be quantized as E=hv. And all fields must consist of quantized exchange particles (see QFT). So–this says that the energy of the quantized entity comes in integer multiples, and fields have to be built out of these. The only geometrical transform for this is a modulo function, which can be modeled as, and only as, a rotation that returns to a starting point. In other words, a twist.

So why hasn’t this popped out of all the math of quantum field theory? Why hasn’t there been studies of twists as a logical outcome of the experimental evidence. It’s a relatively simple construct, there’s absolutely no question that every physics researcher and mathematician would have thought of this as a quantum solution. Why do they abandon it? Well, one possibility is that it just plain doesn’t work, and they find it trivial to see why. Science history spends no time or documentation of failed theories.

But I think there’s a possibility there’s another reason why. The history of science is full of cases where the right solution was not seen for a long time because a conceptual bias about the problem blinded researchers to the actual solution. In the case of quantum mechanics, the math is elegant when working with waves. Everything works well, and any solutions that aren’t geometrically obvious from compositions of waves can be derived because linear combinations of waves (Fourier) can produce any analytical, and hence physical, solution. The problem is that many physical solutions require an infinite number of waves to produce, and both quantized particles and twists fall into that category. Waves are infinitely repeating cycles, but quantized particles and twists are localized. A delta function is one of the closest analogs and requires an infinite Fourier composition to produce. Twists are significantly worse–I wouldn’t be surprised if analytical solutions based on waves provide a significant barrier to understanding their value as a solution. But look at the Schroedinger wave equation and Klein-Gordon! Differential equations don’t readily lend themselves to non wave-based solutions, and thus other valid solutions can be extremely difficult to find. Sure, second order equations such as 3D Schroedinger can yield provably limited base vector sets of solutions–but it doesn’t restrict any combination of waves, so all we can say is that whatever solution results must be analytic–a rather large subset in solution space!

All I’m saying here is, I think quantized field twists are an “out of the box (waves) possibility” and deserve a lot of study. There’s a lot of potential for using them to form a basis for the field and particle behavior we see in reality, and the math of QFT is ill suited to working with them.

Agemoz

In the previous post, I talked about how special relativity might allow a twist to exist without creating a causally connected discontinuity–indeed, it may be possible for a point discontinuity to exist if it is moving at speed c because a discontinuity can form between the time and spatial regions of a light cone loci from a point. But continuing to think about this, I don’t think this is the answer for twists. First, a twist must exist over a length that is the wavelength of the particle, not a point–and thus appears to require a discontinuity that is at least a line and I think actually has to be a surface. Second–any discontinuity that satisfies a light cone boundary in one frame of reference will be time-like in another, a no-no. If the light-cone boundary is what enables the discontinuity, then it must be valid in every frame of reference, an intersection of all light-cone boundaries available within the time-like region of the particle–a geometric impossibility, that forms the null set. When I added special relativity to the twist problem, I did not end up with a solution due to light-cone boundaries permitting discontinuities.

However, after thrashing this out, I suddenly realized that special relativity does allow one of my old solutions to work–the sheathed twist. Recall that there is a solution for an E field twist if the sheath around a twist points radially. I discarded this previously because I could show that a static solution dissipates–but special relativity does some interesting things here. This solution surrounds the twist (bicycle wheel or radial) with orthogonal field vectors, pointing along the axis of the twist. Statically, this just dissipates–but when the whole twist plus sheath assembly is moving at c along the axis, the sheath becomes a field vector pointing in the direction of velocity c, and special relativity will make the vector go to zero–effectively removing any discontinuity boundary yet maintaining the unitary characteristic required for a twist to be quantized. The vector doesn’t vanish, though–it’s still there but invisible in any frame of reference except that which is moving at c along with the particle. I have hypothesized that field elements pointing in the direction of travel become a B field. Such a system clearly could exist–does special relativity keep this system from dissipating?

More thinking and analysis to come..

Agemoz

I see it now. Reviewing the field structure of an electron moving close to the speed of light, which has a field discontinuity, showed the way (my quandary about how a field discontinuity has to exist for E field twists to be possible, but I couldn’t resolve that with the quantizing behavior of a unitary field. I worked for quite a while trying to find a way that static discontinuities could exist, but finally came to the point that they couldn’t, hence no static twists are possible. Then I guessed that special relativity would provide a context where twists would be stable, but didn’t see a viable way until now.

In special relativity, there is the concept of light cones defined for every point in spacetime. For each point in R3+T, there are two 4D conic shaped regions that define other time-separated points and other space-separated points. The time-forward looking cone defines those points which could interact with the originating point, and the time-backwards-looking cone defines those points that could affect the behavior of the originating point. The key is this–no spatially separated point can influence or be influenced by the originating point. The light cone itself defines a boundary where no connection can be made, and thus is a perfect candidate for defining (for that point) a permissible field discontinuity. The trouble is, the discontinuity must be permissible for all points at a given time, which means a static point of discontinuity isn’t possible, nor is any point moving on any timelike trajectory (spacelike trajectories would be faster than the speed of light and can’t happen). Only a point moving along a world line path on the light cone can provide a valid solution. A world line on the cone means that the point is moving at the speed of light. A discontinuity can only exist if it moves with this point! But–a twist isn’t just a point, it has to have a length defined by the wavelength of the photon? No problem, as long as this “length” only lies on a path on the light cone. A string of worldline points, (lying on a single world line on a light cone) can all sustain a twisting field discontinuity somewhere on the light cone for each of the points. The twist field vector never has to match the default background field vector until the discontinuity vanishes (matches the background field vector) which can only happen with integral rotations–our quantization of a twist in a background field vector direction.

Thus, the photon cannot have a spherical shell (or topological equivalent) for its discontinuity–the sheath of the twist mentioned several posts prior. The discontinuity in its entirety for a particular set of points must lie on the 3D light cone of every point where a discontinuity exists. As time passes, the location of the possible loci of the discontinuity will move–but if the discontinuity is more than a point at a given point in time, then the allowable region of the future (and past) discontinuity loci must be the intersection of lightcones from all points–a severe constraint on the discontinuity. A point discontinuity can exist as a path on a light cone and could sustain a twist. A (spacelike) line or volume discontinuity, straight or not, moving at c cannot work because no light cone points at one end of the line/volume will lie on light cone points at the other end of the line, and thus we will have a reachable discontinuity in space–already shown to be an impossibility. Only a point moving at c (in 3D+T this will be a line on the light cone) will sustain a discontinuity, and thus cannot enclose a region, and thus a photon cannot have a finite volume radius.

But what I think does work is a twist about a point moving at speed c. This twist of a point, or rather, in our field case, a field vector at that point, can do whatever it wants as long as it moves at speed c–if any slower, the discontinuity becomes spacelike and we get a contradiction–a spatial discontinuity in the field, that cannot work. Note that the point twist does not have to move at c in a straight line, but, for example, could move at speed c in a circle or other path (a spiral in 3D + T, this is legal because the light cone moves as the point moves. It can be generalized that any path will work as long as the point’s speed is c). A twist ring still seems to be a workable solution and is a soliton that has the characteristics (mass/energy) of an electron.

More to come…

Agemoz

I’ve done a lot of thinking about the relativistic twist idea and photons, and realized that if this approach is correct, I should be able to find a twist solution to the relativistic quantized wave equation (Klein-Gordon equation). This wave equation was originally an attempt to give the electron states of an atom, but doesn’t work on electrons (my own theory would say that as well since I model electrons not as a relativistic quantized wave but as a twist ring). However, the equation should work for photons. The basic wave equation is purely linear, which is why my attempts to find a quantized twist solution failed–but further thinking resulted in the realization that quantization and special relativity together should permit such a solution, and it seems to me that starting with the Klein-Gordon equation would be logical.

Agemoz