In this paper https://agemozphysics.com/wp-content/uploads/2020/12/group_wave_constant_speed-1.pdf, I show how a classical (Newtonian) system that forms point particles as a Fourier sum of waves (a group wave composite) will obey the constant speed postulate of special relativity. In such a system, an observer with any relative velocity to the group wave particle will observe Doppler shifted waves that will cancel out his relative velocity, leaving only the constant velocity of the particle. Thus, the observed speed will appear to be independent of the observer’s frame of reference and we have a clean explanation of why we see the relativistic behavior of particles in our existence.
Digging deeper, however, exposes a showstopper to this hypothesis that all particles are group wave constructs. If there are two observers, spaced equidistant from the particle but positioned orthogonally from each other to form 90 degrees of separation, both must see constant speed of the particle independent of their own frame of reference. However, it is easy to construct this system such that one of the observers will not see any Doppler shifting and thus will not see the expected constant speed of the particle. The observation of constant speed must hold for all frame of reference angles simultaneously, and this is not possible with a group composite of linear plane waves.
The emergence of the special relativity constant speed postulate in a classical system has long convinced me I was on the right track, but with a lot of recent thinking, it became clear I wasn’t there yet. In a serendipitous Aha moment, I realized that plane waves were not the only possible wave solution that would Doppler shift. Any valid wave solution has to have a constant fundamental frequency in order to Doppler shift in the required way, and linear plane waves are not the only solution. Bessel functions also meet this requirement–in all directions.
Bessel functions are a class of solutions to partial differential equations with polar (radial) boundary conditions. The most famous example is the radial vibration of a drum surface–drum surface vibrations form standing waves that look like (but not identical to) a radial sinc function (sin(x)/x). The observed periodicity of the Bessel function will Doppler shift depending on the observer’s frame of reference regardless of his relative positioning to the particle, making it a much better solution than plane waves.
Fig. 1 Example of a radial Bessel function. Note the constant oscillation frequency required for Doppler shifting to give rise to the special relativity constant speed postulate.
This is a much cleaner hypothesis than group wave formation of particles. I will go forward with this to see what new insights come from this line of thinking.
This paper, https://agemozphysics.com/wp-content/uploads/2020/12/group_wave_constant_speed-1.pdf, is in my opinion the most profoundly groundbreaking thing I’ve ever written. Even with all the work I’ve done on the Activation Layer and Dual-Spin particles, this paper, more than anything else, redefines for me how elementary particles must exist. Let’s take a look and see why I think this.
To summarize, the paper does a mathematical proof of how particles formed as a composite group wave will always obey one of Einstein’s fundamental postulates that gives us special relativity–all observers see light particles moving at a constant speed, regardless of the observer’s frame of reference velocity. Along with this, it answers the dilemma of the violation of causality of entangled particles and the instantaneous energy-free affects of quantum interference in the Stern-Gerlach and two-slit experiments. We don’t have to resort to weird things like Everett’s Many Worlds, multiple rolled up dimensions, or Bohm’s pilot waves. The funny thing is, at least for me, is how historically we have assumed all field and particles must be causal (limited by a constant speed c), but I’m always surprised that everything by default doesn’t move at infinite speed–what limits all particles and field motions to this arbitrary constant speed? This paper cleanly explains how this works, and that is why I have such high regard for it.
A big part of why the group wave construct is so interesting is how it denies the traditional understanding of what an elementary particle is. As the paper shows, the group wave assumption cannot just be a mathematical equivalent to a point particle, that is, a Fourier expansion of a delta function. Suppose the correct physical explanation for an elementary particle is just an existence as a point in R3 space, and the math for the particle’s properties happens to be easier by creating a Fourier representation. A rotating point particle giving off quantum waves will not Doppler shift and will not show the constant speed of special relativity!
No, to observe the constant speed postulate of special relativity, the group wave concept is fundamental to reality. For it to work, that is, show the constant speed c over time, the particle’s existence must come from a composite of waves that have a linear component in the direction of motion that will Doppler shift. This is such a revolutionary way to think of our existence. One consequence appears to be that every particle in our brain, for example, is a stable “rogue wave” confined by the boundaries defined by the Activation Layer thickness and the particle’s light cone. The stability comes from these boundaries, there is no way the particle can vanish except via an annihilation of an oppositely phased anti-particle (or some equivalent such as a pair of photons).
There is something very profound about realizing how completely dominant waves are in this existence, that far from being a wave-particle duality, it is all waves! Particles (and us!) are just a consequence of various ways waves interact.
I have often discussed the Activation Layer theory on this physics site. To summarize, this theory claims we exist in a slice of 4D spacetime, a 3D hypersurface I call the Activation Layer, that moves in the time direction and confines all particles, fields, and interaction forces. This approach claims that while the layer must curve according to the stress-energy tensor of general relativity, no portion of 4D spacetime outside of this hypersurface is necessary for our existence. I have discovered a number of fascinating properties that result from assuming the real-life validity of this time slice. It gives us dual-spin point particles and quantizes them (see https://wordpress.com/post/agemozphysics.com/1917) and shows how particle annihilation is just the exchange of momentum energy from linear to angular momentum states and computes a valid quantized angular momentum (see https://wordpress.com/post/agemozphysics.com/1839 ). Both Special Relativity and General Relativity operate correctly even when limiting our existence to this Activation Layer portion of 4D spacetime, and even shows how the Lorentz beta value must emerge–see https://agemozphysics.com/2024/12/01/special-relativity-and-the-3d-hypersurface-activation-layer/ and https://agemozphysics.com/2025/02/13/general-relativity-and-the-3d-hypersurface-activation-layer/. Even making allowances for confirmation bias, that’s a big block of supporting evidence, and now I have found a new one.
A really interesting question arises when I ask the question–how thick is this Activation Layer? Is it zero, asymptotically small, does it vary over the range of the hypersurface? If it is not zero, could it support resonances that define specific particle masses over the entire universe?
It really doesn’t take much of an inference to think that the Heisenberg Uncertainty Relation points to an answer. There are several related non-commutative parameters in the Standard Model, one of which is an object’s position and momentum. The Uncertainty Principle states that the product of the standard deviation of both properties must be equal to or greater than Planck’s constant.
If the Activation Layer has a fixed thickness and is moving in the time dimension direction, you can immediately see that any massive particle will automatically conform to the Uncertainty principle, because the only thing missing from the product of the Activation Layer’s width and velocity is the particle’s mass. This is perfect, because the only thing not constrained by the Uncertainty Relation is the mass used to compute momentum (this is true for all of the non-commuting relations). Confining a particle to the Activation Layer means that you cannot establish (detect) a particle’s position and momentum any more accurately than the volume of a region within the Activation Layer–both the detector and the object are limited by the Activation Layer properties of width and motion (see the figure).
I’m actually very surprised that when the Heisenberg Uncertainty principle was shown to be true experimentally, researchers didn’t immediately conclude that some variation of the Activation Layer had to be true–that is, if our existence used the entirety of 4D spacetime, it would have to violate this principle.
Do we have enough data to determine the Activation Layer thickness and velocity? I believe the answer is yes for the velocity–a static particle will have no velocity in any direction within the hypersurface Activation Layer, so the layer velocity has to be related to the velocity of photons along the light cone, and thus will be c/sqrt(2), assuming we can treat the time direction scaling as equivalent to the spatial direction scaling in R3. However, the width still has an unconstrained variable (the mass of the particle). My thinking is that resonances within the Activation Layer width, along with allowable dual-spin multiples in the particle, will specify allowable masses and hence provide insight into the Activation Layer width, but that is pure speculation at this point and I do not yet see an unambiguous answer…
Dr. Hossenfelder states that our universe includes all of 4D spacetime (what she calls the “Block Universe”), rather than just the 3D hypersurface we exist in and can observe. She uses the observer dependent event timing of special relativity and the overall spacetime curvature math of general relativity to make her case, and this view appears to be shared by physicists in general, including Dr. Thorne, the science adviser for the movie Interstellar. I disagree, and in previous posts I’ve detailed my claims and the evidence backing the Activation Layer concept (that is, that we exist in a single curved 3D slice, or hypersurface, within 4D spacetime that moves in the time direction). To be able to substantiate my claim, I must look at how special and general relativity would exist in within this Activation layer without requiring connections to other hypersurfaces or anything else in 4D spacetime.
In my previous post, “Special Relativity and the 3D Hypersurface Activation Layer” (https://wordpress.com/post/agemozphysics.com/1989), I show how special relativity is an observation effect that results because the observer’s frame of reference affects event simultaneity only for that observer–his frame of reference does not affect any event behavior that other observers see (unless they are observing that first observer). In that post I show how the wavelike construction of elementary particles results in the observation effects seen in special relativity, and how nothing outside of our 3D Activation Layer hypersurface existence is needed to explain special relativity.
General relativity is different in that all observers will see spacetime curvature, it affects all objects and fields within our universe. In this post, I will show how general relativity can exist solely within our hypersurface.
General relativity does not need anything outside of our Activation Layer hypersurface (although it is clear that the hypersurface must curve according to Einstein’s stress-energy tensor equation). You can see this if you look at how stress-energy tensors are defined as 4 dimensional entities, such as a t,x,y,z functional matrix. All contributions to the stress-energy tensor at a given point must either be local or propagate causally through the Activation Layer. This tensor then sets up spacetime curvature via a 4 dimensional metric, that when multiplied by a translation or rotation operator defines how that translation or rotation occurs within that curved spacetime–but within the Activation Layer hypersurface. We can then use LaGrangian equations of motion or other tools to find the path (e.g, a planetary orbit) taken in our potentially curved hypersurface.
Note, I’m only going to talk about what general relativity requires within standard 4D spacetime–hypothetical extradimensional theories will create exceptions, and yes, spacetime curvature can be affected by masses in other hypersurfaces–but general relativity does not require those. It can wholly exist and operate within our existence as a 3D hypersurface moving in the time dimension within 4D spacetime. If we could show the existence of stress-energy tensors that required sums over multiple times (multiple hypersurface x,y,z points) that didn’t just propagate their effect through our Activation Layer, then the Block Universe concept would have to be true, but my research shows no such entity has been proven to exist. To reiterate–nothing from outside our hypersurface existence is required for general relativity to hold.
Dr. Hossenfelder believes that our past is left behind in an accessible set of successive hypersurfaces, sort of like the tesseract we see in the movie Interstellar, and should be accessible. I claim that the mass and resulting curvature induced by such an enormous object as the tesseract makes such a conclusion impossible. Within the limits of what we have observed in the cosmos, no such masses exist outside of our Activation Layer hypersurface. These copies of the past are not necessary for any aspect of either special or general relativity, thus, the Activation Layer is necessary and is also sufficient for our existence.
In the last bunch of posts, I’ve explored the Activation Layer, my name for the 3D hypersurface within 4D spacetime that we exist in. It holds all particles and fields, and all forces and laws such as special relativity and quantum field theory. I discussed how even the observable effects of general relativity is confined within this hypersurface, although the principles of general relativity must deform the hypersurface within 4D spacetime. While my main interest has been discussing how this activation layer constrains elementary particles and their interactions, in the last post I explored what this idea means for our cosmos. In particular, I believe the Big Bang would look different–it would look like a surface shell rather than what scientists say about a spherical expansion from a core Big Bang point. I believe there should be a variety of ways to test this with astronomical observations (see this link: https://agemozphysics.com/2024/10/22/our-hyperspace-within-4d-spacetime-does-not-violate-special-relativity-part-ii/). We already have observations that appear to point to the hypersurface model–in this post, I want to examine why scientists still think these observations point to the spherical expansion model of the Big Bang.
Observations of the cosmic microwave background radiation (CMB) shows a uniform distribution and velocity in every direction. I made the point that this would verify that the activation layer hypersurface is the correct representation rather than the spherical volume expansion of the Big Bang that is currently the accepted thinking. The CMB is almost perfectly isotropic everywhere, and not only that, the James Webb telescope is not seeing significant variation for the maturity of galaxies in all directions. As I posted in the above link, both of these are direct consequences of a hypersurface activation layer Big Bang, and should be further confirmation that the Big Bang is not spherical.
However, it appears that scientists explain the cosmic isotropy as present even in the initial moments of the Big Bang, and that the observable expansion both of the spacetime dimensions and its contents would retain their isotropy to the present day. The claim is that this isotropy is why there is no detectable direction pointing to the original Big Bang region from our point of view on earth and why instead the Big Bang remnants show up as the CMB. As I mentioned in my previous post, I don’t see how this could be true–if there is an expansion from a Big Bang point, 4D spacetime will have an outflow of galaxies from that point and in a Euclidian representation of 4D spacetime, there is no question that outflow direction would be detectable. Of course, the universe expansion is not Euclidian; instead, by general relativity, the dimensions of the universe will curve dramatically. The accepted argument is that this curvature will compensate for the outflow from the Big Bang point to make it appear isotropic and radiation will appear to be omnidirectional. To me, the problem with this approach is that photons from observation sources also are affected by this dimensional curvature, and thus dimensional curvature will not affect what is observed! If there is an outflow source, that will look the same as if the observer saw the Big Bang in Euclidian space!
Of course, general relativity does make a mess of this line of thinking, since not only is there a dimensional curvature, but there is also a substantial effect on the motion of the galaxies within the expansion. Nevertheless, I can see no way at all that observations of the early universe, a few hundred million years after the Big Bang, would not reveal the direction of galaxy outflow. If the isotropic spherical expansion is the correct model, we should see the direction of the Big Bang core. Perhaps we currently cannot go back far enough in time to see this core, but there will be a region of space with fewer deep red-shifted galaxies–a consequence of those galaxies having a smaller velocity relative to our observer’s position on earth. I also just simply do not see how the CMB can be nearly perfectly homogenous and isotropic in a spherical Big Bang. No matter what kind of Big Bang expansion curvature we have, the CMB should be globally anisotropic in a spherical expansion. It is not, and that result is exactly predicted by the hypersurface model of the cosmos.
Agemoz
Big Bang Spherical Expansion versus the Hypersurface Activation Layer Expansion. Note that technically the Hypersurface version should be represented by spherical shells, but the discussed conclusions are the same for the depicted rings and is easier to visualize.
EDIT: If a physicist were to read this, I’m pretty sure he/she would say that the hypersurface activation layer concept, where our existence and all interactions are confined to a 3D time slice of 4D spacetime is incompatible with the principles of special relativity. Rest assured that I have considered this objection in depth. Special relativity denies the idea of simultaneous events for all observer frames of reference, among other things, and also proves the interchangeability of space and time in observations for a given frame of reference. This would seem to contradict the idea that we exist in a single 3D time slice activation layer of spacetime. Currently, I don’t think it does, because the observation process (receipt of particles) in different frames of reference is complicated. There will be variations of a given observation in relativistic frames of reference due to things like Doppler shifting and the corresponding shift in detection times of source particles. Observers in different frames of reference have to observe (receive source particles) events at different times, but this outcome does not then imply the existence of multiple active hyperspaces or connections between them. There is no question that this subject deserves my full attention and I will dedicate a post to analyzing this–hopefully objectively!
I have been investigating Emergent Fields, which are fields that have the creation/annihilation concept built in, in order to come up with a way to solve quantum field theory problems analytically. In current research, we do interaction computations by separating particles and virtual particles from the fields they exist in. This forces us to compute perturbative solutions–and thus significantly limits the type of interactions we can realistically compute, both for complexity and convergence reasons. By specifying stable particles as a particular manifestation of wave behavior, emergent fields should not only enable analytic solutions for more complex interactions, but yield new insights into our physical reality. For example, this work shows an elegant basis for elementary particle quantization. If you read through this, I think you will be convinced that our existence requires that all elementary particles have to be quantized.
One such wave proposal I came up with for an emergent field is a 4D vector field that can have spins pointing in both the three physical dimensions as well as the time dimension. This type of field has a number of interesting properties such as giving point particles independent dual spins (for example, one in the X-Y plane and one in the Z-T plane, see https://wordpress.com/post/agemozphysics.com/1839). By constraining this field with the fact that we exist in a 3D hypersurface of 4D spacetime, I found some elegant insights. One of the most beautiful results I see is how it enforces quantization of particles such as photons.
Einstein was able to prove that photon energy had to be quantized for a given wavelength, and from that the entire quantum theory infrastructure (quantum mechanics, quantum electrodynamics, quantum chromodynamics) was built and verified beyond a shadow of doubt. What scientists didn’t discover is why this quantization occurs, and I have found that an emergent field constrained by our 3D hypersurface existence within 4D spacetime gives us a beautiful answer.
As I discussed in these posts (https://wordpress.com/post/agemozphysics.com/1891 and https://wordpress.com/post/agemozphysics.com/1910), we exist in a 3D hypersurface of 4D spacetime I call the activation layer, and there is good reason to believe that other hypersurfaces adjacent to ours cannot exist or interact with the 3D hypersurface activation layer that we live in. This is a common portrayal of particle interactions in Minkowski spacetime:
An incorrect view of an e-/p+ annihilation depicted in 4D spacetime
As discussed in this post https://wordpress.com/post/agemozphysics.com/1910, this cannot be correct, the 3D activation layer hypersurface view of the same interaction must actually look like this:
A more accurate view of an e-/p+ annihilation depicted in 4D spacetime
Constraining the emergent field particle view with this activation layer behavior will help define the required formula for the generalized emergent field. As I mentioned in the previous post, I didn’t like one of the specifications of the emergent field example I use–particles are defined as quantized twists such that there is a lowest energy spin state pointing in the time dimension direction. Why is there a lowest energy state for a particular spin rotation, there is no evidence of such a thing? I’m sure any of you that read that post were thinking, no, that can’t be right.
I had a wonderful insight, I realized we don’t need that lowest energy concept. The activation layer does it for us, and is why experimenters in Einstein’s time were finding good experimental evidence for particle quantization.
Many research papers have been written that attempted to compute the shape and length of a photon.The underlying basis for quantization and the quantum theories we have comes from extensively verified experimental evidence of particle quantization, and researchers have tried to visualize or mathematically describe what drives this quantization. It’s really dangerous–and usually completely wrong–in quantum physics to try to ascribe classical attributes such as “looks like” to quantum particles. We don’t have an answer why quantization exists, we just know it is there. Here is a typical textbook drawing of a “quantized” photon, shown with a gaussian envelope that fits the uncertainty principle constraint.
However, my annihilation diagram above gives some great insight on the why this is a bad depiction. Let’s modify the annihilation diagram above by moving our activation layer hypersurface to the photon output of the collision, it will look like this:
That gaussian picture of a photon, or any other similar depiction, has to be wrong! We exist in an activation layer, a 3D hypersurface slice in 4D spacetime–so the photon has to be nothing more than a single vector direction, rotating as time passes and the activation layer hypersurface moves forward. The confining of all particles to our existence in the 3D slice, our activation layer, is what quantizes particles!
You can increase the radiation intensity by adding more nearby rotation vectors, but this still is a quantized step. You might say, well, just increase the magnitude of the vectors, but we know we can’t do that because the photon energy is only a linear function of its frequency, E=hv. There is no magnitude degree of freedom. This isn’t just for photons–every single elementary particle has to be quantized via a single vector within our 3D slice of 4D spacetime. We don’t need the (questionable) lowest energy rotation state idea for quantization or a bogus gaussian packet description, our 3D hypersurface activation layer does the quantization for us!
Agemoz
PS: An exciting corollary is how emergent field quantized vector fields leads to why probability amplitudes add and sometimes subtract (actually, add with negative amplitudes). We’ll cover that in another post!
An Emergent Field is a term that refers to a field with quantum creation/annihilation behavior embedded within the field description, and a careful study of our hypersurface within R3 + T spacetime further refines its form.
We need emergent field mathematics (see these posts: https://wordpress.com/post/agemozphysics.com/1860 and https://wordpress.com/post/agemozphysics.com/1873 ) because current perturbative methods separate out the fields and particles used in quantum field theories and are limited in ability to solve most interaction LaGrangian equations of motion. By forming particles from field elements, emergent fields should allow analytic solutions, and I found one such field that contains 4D (R3 + T spacetime) vector twists. In such a field, quantization to a background state, for example a vector rotation to and from the time direction, will force the spins to be integer multiples, which I state will be stable particles if the background state is a lowest energy state. Partial twists have to fall back to the background state and thus can behave as virtual particles, influencing LaGrangian equations of motion without a net mass (off shell to use physicist terminology). Now we have an infrastructure for quantum field theories which does not require the use of separate fields and particles currently used in perturbative quantum field calculations.
However, I’ve never liked this “lower energy state” idea. It does conceptually work, but I have never thought of any workable real-existence reason why a point particle spin pointing in the time direction would have lower energy and thus a tendency to move to that orientation. Since we are constantly moving forward in time, I thought there would be some kind of drag on the spin orientation, perhaps pointing backwards from the time direction like a wind–but to me, this seemed very hand-wavy hokey. We do get a similar kind of drag effect from the Higgs field that gives inertial mass to particles in R3, but mass isn’t spin, and it is a bridge too far for me to think that is what quantizes spin.
A Minkowski space diagram showing every moment in time with particle components–this cannot be a correct depiction of real life
The Interstellar movie is the most recent famous example of this assumption–claiming that there is some point of view within a 4D or higher tesseract where we can see, move, and interact with various points in time and space. I claim that if we actually did travel back along the time dimension via a wormhole, we wouldn’t see anything there. Real life does not keep a copy of every moment like a reel of film, and thinking in terms of emergent fields and quantum field theory reinforces this.
A better depiction of particles interacting, all moments in time except for our current hypersurface time have nothing in them
There can be no doubt that we live in a single slice, a 3D hypersurface layer within R3 + T spacetime, at a specific but moving moment in time I like to call the activation layer of 4D spacetime. We clearly have no direct way of interacting with other hypersurfaces, even when severely contorting the shape of the hypersurfaces near black holes. We see no photons escaping other hypersurfaces even near a black hole, only those that can be found to be emitted from within our own hypersurface. Folding spacetime does not cause particles to leak into other hypersurfaces. Wormholes theoretically could connect us to other hypersurfaces, but there will be nothing there.
EDIT addition: There are Feynman path combinations that include reverse-time particles that Feynman himself claimed would show the existence of particles moving in the reverse time direction. However, there are two ways to use time to describe a particle–its movement in the time dimension, and its internal time clock. These are not the same thing, and if a particle were truly moving in the negative time direction (a tachyon), it would only show up as a momentary blip in our activation layer hypersurface. Feynman reversed-time particles actually have a reversed internal clock but move along in the forward time direction, and are just going to be another variation of particle (for example, anti-particles) traveling with us in our hypersurface. They are not going to be particles from another spacetime hypersurface.
In addition, I believe that all particle interactions have to be confined to within our hypersurface. Each particle (lepton or boson) has a wave phase that must be different for every unique hypersurface time, which means that if interactions were the weighted sum of phase contributions from each hypersurface, the LaGrangian solutions of motion would be vastly different than those computed from only within our hypersurface. There is nothing there. Life does not appear to record every moment, contrary to popular sentiment, so wormhole travel will not reveal what we all think it will. And more importantly for my study, removing the Minkowski spacetime path assumption for fields and particles provides significant guidance on how emergent fields must work.
This was a major insight for me, let me describe what I see in my next post.
In my last post, I described how quantum field theories use perturbative methods to evaluate particle interactions, and posited that a better way will come from using the emergent field concept. Emergent fields are a type of field that has the creation/annihilation operator properties built in, and in the last post I began to describe what such a field would look like as well as the impact it would have on existing thinking about the standard model. This immediately opened a line of thinking where I think I see a better way to construct quantum field theories that doesn’t depend on particles. I still question whether this is right–but it seems to work, it is consistent with existing physics, and I think this might be a step forward.
One of the principle properties resulting from an emergent field is the embedding of the particle definition within the field as a group composition of waves rather than the standard model way of assuming particles among fields. In my last post (https://wordpress.com/post/agemozphysics.com/1860) I gave an example of a spin twist in a vector field that has rotations quantized to a lowest energy background direction such as toward the time dimension. In this light, when you look at quantum field theories, a lot of really interesting ideas pop out–I think the most important is that separating out particles (virtual or real) from fields is a mistake. Yes, you can calculate with incredible accuracy this way, but it is a big hurdle to really understanding what is going on.
Let’s look at the very simplest quantum field case, the electron emitting and absorbing a virtual photon, one of the components of the electron’s self energy that resists its motion.
In the standard model, we compute electron equations of motion (LaGrangian minimum energy paths for the electron’s probability distribution) by assuming a random emission of a virtual photon particle, and then add in the contribution due to its re-absorption. There is an electron momentum change at emission and re-absorption, and all the possibilities of when and where and how much effect are all summed in as probability amplitudes. Not surprisingly, we can get infinite values in some cases, so we sum everything up anyway, cancel out what infinities we can, and then renormalize the probability distribution to get back finite answers (I’m glossing over a lot of the complexity of this, but that’s the idea). We also have to add in the smaller possibility of electron/positron pair formation, even the possibility of quark/gluon formation for whatever level of accuracy we are aiming for. This perturbative approach to particle interaction computations is extremely effective and works for both leptons and quarks, but this way of thinking where we separate out the field and particle aspects of such systems shuts down any further thinking about the underlying analytic form of quantum field theories.
If we imagine an emergent field like the dual-spin method I described earlier, things look very different and appear to lead to a more precise way of understanding quantum field effects. In the emergent field approach, there are only waves, no mysterious random appearance of particles. Note that in the electron self energy case shown above, the only time there is an effect on the electron’s momentum is at emission and re-absorption.
The rest of the time, we can assume the virtual particle doesn’t exist, which means that quantum field effects can be entirely described as momentum change pairs of equal magnitude. In the standard model, this doesn’t help you, you might as well call the whole path a virtual photon particle. That’s all she wrote. We don’t currently have a picture in the standard model and current quantum field theories of what is happening at the virtual particle level, we just know the math comes out.
In the emergent field methodology, these points are “spin-off”waves from the electron wave construct. These waves will interfere with the group wave electron construct, and cause a momentum change. Just like the sum of particle paths in the standard model, you can sum all of the potential momentum changes, but something different happens if the electron is moving. Since the emergent field approach now treats the quantum field effect as waves rather than particles, the doppler shift effect comes into play along the direction of electron motion. Emissions still occur in all directions and will have identical effects on the electron (resulting in a net zero effect on its momentum), but the resulting re-absorption momentums will be different depending on direction because now we are dealing with waves that doppler shift. There will be no net effect normal to the direction of electron travel, but forward re-absorptions will be stronger and reverse re-absorptions will be weaker due to doppler shifting, and the electron will slow down. The quantum field behavior will have a net effect on the electron’s momentum, and we don’t need virtual particles to describe it.
There is a lot more to come. Let’s see if this holds up.
Edit: Looking at the LaGrangian (equation of motion) for the strong force, which has been developed and refined over decades, I kind of noped out on the dual-spin idea for quark/gluon interactions. I did get a good sense of what chromodynamic color is–it’s not a property of quarks or gluons, but a mathematical device that ensures which particles can interact with each other. One way to determine this is the fact that all color quarks interfere, and all color pair gluons interfere. I thought the coupling number tensor field adds a crazy degree of complexity that something simple like the 4D dual-spin point concept cannot begin to cover. It’s worth it to study the LaGrangian and SU(3) in more detail, but all this really does throw a monkey-wrench in the works for dual-spin point particles.
Edit #2: Added note that shows that the 4D dual-spin point particle concept not only shows a clean explanation (conversion of angular to linear momentum) for annihilation products of electron or quark particle/antiparticle collisions, but it also shows why those are the only direct products of the collision.
In the last post (https://agemozphysics.com/2024/05/12/spin-wave-functions-in-the-e-p-dual-spin-annihilation/), I showed how the analysis of 4D dual-spin point particle/anti-particle annihilation gives an elegant picture where annihilation is the process where one of the dual spins’ angular momentum components gets converted to the linear momentum of, for example, the resulting photons. This analysis then shows how to derive the quantized angular momentum /h (reduced Planck’s constant) of the source particles.
While this derivation was shown for the electron/positron annihilation case, there is nothing in the formula that limits to the electron/positron annihilation case. In fact, some beautiful results occur when you apply the same work to quarks. Unfortunately, there is a rather stinky fly in the ointment to this line of thinking.
Unlike lepton/antilepton annihilation, which can only annihilate to two photons, quarks can annihilate directly to either a pair of photons or a pair of gluons. Like photons, gluons have a transverse polarization angle, and like photons, they have no rest mass and thus move on the lightcone at the speed of light. Quarks have charge magnitude of either 1/3 or 2/3, and in the dual-spin point particle representation, this means that one of the two spins has a 1/3 ratio to the other.
The beautiful thing about this representation is that in quark annihilation, you can annihilate (convert to linear momentum) either the 1/3 spin, giving a photon pair result, or the 1 spin, giving a gluon pair result. Thus, the 4D dual spin point particle concept makes a case for covering all three annihilation cases, the lepton and both of two quark particle/antiparticle annihilation cases. Since the lepton case only involves 1/1 ratios, you never get a 1/3 spin result and hence never see annihilation into two gluons.
Edit: Note that a quark-antiquark annihilation has no other direct result products–all other collision products require intermediate particles within the collision neighborhood. That is a nice affirmation of the validity of the 4D dual-spin point particle concept–it not only shows an elegant and simple way to get the observed collision products for both electron and quark annihilation, but it also shows why those are the only results.
e-/p+ annihilation into two photonsq+/q- annihilation into two photonsq+/q- annihilation into two gluons
Unfortunately, the quark situation is actually not this simple–this does not show why we have chromodynamic color constraints on quark interactions.
In the Standard Model, we represent reality by two overlapping fields, the electromagnetic field covered by U(1), and the strong force field, covered by SU(3). The strong force field can be represented by a unitary constrained 8 dimensional real-valued adjoint (diagonally antisymmetric) matrix with eight orthogonal eigenvectors. The EM and strong force fields are clearly not completely independent, or else we could not have particles that stay in the same place on both fields when either electromagnetic or strong forces are applied. As a consequence, unification of the EM and strong force fields seems to imply there should be a single field representation, and with these annihilation analysis results, I had thought the 4D dual spin point particle concept would get us there.
However, I currently see no way that the 4 dimensional dual-spin point particle representation could be sufficient to constrain chromodynamic quark/gluon interaction characteristics. I’ve studied this for a while and think something has to be added to make the 4D dual-spin point particle concept fully work for quarks and gluons.
In summary, I do think that the four-dimensional dual-spin vector field is a good starting point for unifying the electromagnetic and strong forces–it certainly seems to provide an elegant view of several fermion/antifermion annihilations and pointing to how to get the quantized moments–but as is, it is not sufficient to cover quark/gluon chromodynamic color constraints.
[edit: NOTE: dual-spin of 4D point particles is not superposed states on a single spin–see addendum below]
Four dimensional point particles in R3 + T spacetime have unique properties, in particular, the ability to have two independent spins, that appear to make them good candidates for a deeper understanding of what happens when a particle and anti-particle annihilate. I detailed this in the previous post (agemozphysics.com/2024/04/19/creation-annihilation-of-dual-spin-point-particles/).
I’ve made some additional progress, in particular, I see a fairly simple way to show the quantized angular moment of the electron from the details of the collision. I started by putting on my skeptic’s hat (actually, I try to make sure that stays on at all times), and posed a couple of questions:
Why do we need 4D point particles when the current Standard Model works fine with 3D spin wave functions for particles?
There is no measurable radius in a point particle such as an electron, so how are you going to compute an expected angular moment for the electron?
Let me do a quick summary from the previous post to start off: We have substantial experimental evidence that elementary particles such as the electron and quarks are point particles. From a idealized geometric point of view, point particles in three dimensional space are relatively uninteresting with only one possible spin axis and no internal structure. However, we also have significant experimental evidence of four dimensions including curvature in the time dimension, so it is very reasonable to assume that spin angles can point in that direction. In fact, point particles in four dimensions can have two independent spin planes, one in the X-T plane and one in the Y-Z plane, for example. When you examine the e-/p+ collision shown in the figure, we see a better view how the two point particles annihilate into two photons, where the mass and charge of the point particles vanish.
We know that quantum wave interference is present at the same wavelength in both the before and after cases, and the only way for a point particle to produce a wave is to oscillate in some way, which for a point particle can only be induced by some kind of spin. Therefore, the fact that mass and charge disappear after the collision cannot be due to that spin disappearing. But there is nothing else that can be added to a 3D point particle without giving it a radius of some sort–but 4D point particles can have two independent spins, and this is why I saw a door opening as to how the collision transformation would work. The second orthogonal spin encodes the mass and charge effects without changing the geometrical point particle concept. The collision can be explained simply as the transformation of the point particle Y-Z spin angular momentum entirely into the photons’ X momentum (and vice-versa for the e-/p+ pair creation). We get interesting insights when we set the dual-spin point particle angular momentum at some radius re to the linear momentum of the resulting annihilation photons.
However, point particles have no measurable radius, which fails to reasonably explain the actual measured angular moment of the electron. You would have to have an infinite mass to get a finite moment. How did I think this was going to work?
Quantum theory comes to our rescue here–we can’t think classically when working with elementary particles. I bet every good quantum scientist would immediately see the obvious solution–the electron is a point particle, but its location is always defined as a probability distribution–a wave function with a constant normalized magnitude radius, just like an electron orbiting a hydrogen nucleus. Now you can do a simple computation from the annihilation that looks like this:
Ee = h freq = p c (one of the pair of photons)
so then pphoton = h freq / c
In the dual spin situation, the Y-Z angular moment of the point particles must equal the photon moment at quantum radius re, so for one particle transformation:
me omega re = h freq /c
Let’s assume equal dual spins for the electron, where omega = freq * 2 Pi
so then me c re = (h / 2 Pi)
This is a nice way of saying the angular moment of the electron probability distribution is quantized to the quantum angular moment /h of the electron. Thus, the properties of a 4D dual spin point particle lead directly to the quantization of the electron moment.
Agemoz
Addendum: I realized that the dual-spin property of 4D point particles could be misconstrued as some variation of superposed states on a single spin property of a particle. In the Standard Model, quantum spin of elementary particles have two states such as +1 and -1. Until the spin of a particle is detected, the spin will generally be a superposition of these two states, and the orientation of the detector will determine the probability of decohering into one or the other state. Dual-spin point particles refers to something completely different, that is, the presence of two spin properties in a particle–either one of which could have superposed spin states.
I'm an amateur physicist. I've studied physics and philosophy for a very long time, and have investigated some of the unanswered questions in physics with an intent of finding some possible explanations or theories on how they might work. Two of the most interesting questions for me are whether there is a geometrical basis for quantization and special relativity, and why there is a particle zoo (that is, is there an underlying structure that results in the particle zoo). I'm well aware of the danger of crackpot theories (usually characterized by just enough knowledge to get things wrong or silly), but allow myself to pursue ideas anyway as long as I'm clear about their speculative nature. I don't pretend that I have any significant discoveries to report, but thoroughly enjoy pursuing various ideas about how the universe works. To faciliate this study, I've created a lattice simulator that allows me to test a variety of ideas.
Archives
Unitary Twist Field Theory
A long description and justification for the thinking that has led to the Unitary Twist Field Theory. Note, IANAP (I am not a Physicist). This is long and describes the historical evolution of the Unitary Rotation Vector Field. The latest work has changed several parts, I am in the process of updating this.
Summary: A unitary rotation vector field is investigated as an underlying field that gives rise to the particles and fields of the Standard Model. The underlying field is single-valued, waves cannot pass through other waves. This is the means by which quantum interference redirects particle paths. The simulation work has revealed a new principle:
Quantum interference is responsible for redirecting particles along wave interference peaks–and also for creating those particles.
Long description: This effort to work out the details of this unitary twist field is based on the underlying assumption that our existence can emerge from nothing, and posits a reductionist approach to explaining the particle zoo. The theory basically says that there is a continuous rotation field in R3 + I that can produce stable solitons. Here is a list of the steps I have taken to arrive at this theory:
a: If existence does not require an intellect to form, the existence must arise from nothing, both space and time.
b: If existence does require an intellect (e.g, God) then further investigation isn’t really necessary because the rules for existence are set in a place we do not have access to.
c: One way to determine if the creating intellect exists would be to determine if the existence could not come into being without at least two rules, and such rules would have to come into existence from a creator. Saying that existence formed with one and only one rule is equivalent to saying that existence could arise from nothing and God is not required.
d: Finding God seems to be pretty much unanswerable without clear direct communication from God, whereas coming up with a way that existence could form from nothing seems to be an alternative possible approach for a human mind to answer the question about the existence of God.
e: Such an approach could start with the limits of current human knowledge, the known existence of the particle zoo. If a reductionist approach could be taken as to why the particles exist, we may be a step closer to saying that an intellect is not needed to create this existence. Conversely, if we can show with reasonable probability that it’s impossible to form particles from some continuous field, that’s an argument in favor of the necessity of an intellect in creating our existence.
f: I am assuming that a continuous field that can create stable particles is a reductionary step–that is, a step in the direction of finding a single rule defining this existence.
g: Now I start applying known physics to this field to determine what it must look like. I am assuming that this field is opaque, that is, there aren’t any parallel overlapping fields. This is clear because multiple rules are necessary to form two fields.
h: I assume that this field has elements that can only rotate. No displacement or magnitude can be applied to any field element. This assumption comes from the E = hv relation for particles, which basically says that particles are described only by frequency, there is no field degree of freedom equivalent to field magnitude.
i: when objects move, the field elements pass rotations via three types of momentum to adjacent elements. In this theory, no field element ever “moves”, instead particles move because field rotations pass as momentum from one field element to the next.
j: In order for E = hv to work, there has to be a means of ensuring that no partial or multiple count of rotations can exist. This is a form of field quantization, and I have proposed a background lowest energy state. In such a system, field rotations called twists start and stop at the background state rotation angle.
k: To ensure that R3 does not have an observable resonance (which would be experimentally discernable) that would undermine gauge theory symmetries, this background states points to an imaginary dimension. It is not possible to have the background state point to a basis vector in R3.
l: If the field has a crossproduct momentum transfer as well as the more standard linear translation of angular momentum of field rotation elements, this becomes a necessary and sufficient condition for forming stable linear particles of arbitrary frequency. UPDATE: simulation work shows that quantum interference is responsible for particle formation.
m: the crossproduct rule for momentum displacement allow a particle to start a single twist, and allows the particle to end the twist after one full rotation.
n: The crossproduct rule also allows the formation of twists that move along a curve. This is possible due to the vector combination of the crossproduct that is normal to the current element rotation orientation and speed. UPDATE: simulation work shows that quantum interference is responsible for path curvature.
o: If twists can curve, there are some twists that will form stable closed loops. There are many possible stable curve solutions, which I am proposing is the basis for the particle zoo.
p: A single free linear twist models a photon of some energy and length defined by the frequency of twist rotation.
q: Since the twist moves from +I background state to an R3 direction and continuing to rotate through to the +I direction, polarization of this twist arises as a linear combination of the two R3 vectors normal to the direction of twist travel. UPDATE: new simulation data suggests that quantum interference and momentum provide a basis for polarization, this will be revised.
r: The crossproduct momentum translation is necessary to allow a twist to start and to stop, otherwise field symmetry would propagate in both directions simultaneously at every point in the twist, and stable particles could not form (they would dissipate). In other words, the quantization of the field is ensured with the background state, and the ability to start and stop a twist arises from the crossproduct momentum translation. Thus it can be stated that to form stable particles from a field, it is necessary that a field capable of forming stable particles must have a handedness that can only come from a crossproduct momentum property. UPDATE: simulation results show this and following sections needs to be revised.
s: This handedness thus must be ingrained in any field solution that produces stable particles. This handedness of the field will show up in some cases as a chirality violation.
t: In order for the twist propagation to be stable, the only possible momentum transfer via crossproduct relation is at the speed of light, where the leading and trailing edge of the twist cannot be affected or connected to neighboring element rotations.
u: Any closed loop rotation sequence thus will be limited to the speed of light. If one were to unravel the cylindrical spiral path this loop takes in Minkowski space, a single quantized twist will form a right triangle where the hypotenuse is the speed of light times the time of one rotation of the twist, one side is the particle travel distance, and the other side of the triangle is the radius of the loop. This right triangle enforces a relation between the loop travel speed and the speed of light. This relation computes to the beta factor of special relativity and is the means by which special relativity geometrically arises from the twist theory.
v: A corollary to u: above is that time dilation for every particle results from the constrained stretching of the spiral helix in Minkowski space as the particle increases speed proportionate to the speed of light. In other words, each particle’s relativistic clock is implied by the time to complete a single twist. Observing from different frames of reference will alter the apparent time to complete a twist and thus affect the relative passage of time between particle and observer.
w: A single closed loop models the electron of one type of spin. The twist direction relative to direction of travel defines a spin-up or spin-down electron, whereas the loop curvature relative to the handedness of the field defines the particle vs the antiparticle version of the electron. Note that a linear twist does not have these degrees of freedom, so there is no antiparticle to the linear twist photon.
x: Quarks are posited to be linked twist loops, the up quarks have a single link going through its center and the down quark has two. The strong force results when linked twist loops are pulled apart such that twist momentums approach each other with an asymptotic direction conflict. The passage of a twist through the center of a loop affects the rotation of the loop by increasing the crossproduct momentum of the loop. Note that since electrons are modeled by a loop with no central twist going through it, electrons (and positrons) cannot combine with quarks.
z: This modeling of quarks seems to correlate to the masses of the up and down quarks–the twist going through the center of a up quark loop acts with a central force that causes the loop radius to reduce by half. The doubling of the resultant normal (to direction of twist travel) acceleration results in a loop that is 1/4 the size of the electron loop model. Similarly, a down quark has two twists going through its center, doubling again the normal acceleration of twist travel and causing that loop to be 1/8 in size. The rest masses of the electron, up quark and down quark correlate to this geometric analysis of particle loops. Electrons have a .511MeV mass, up quarks are 2.3MeV, and down quarks are 4.8MeV. Admittedly this may all be numerology, but I was surprised to find this mass correlation to loop length.
y: A possible model for the weak force results because there is a small chance for linked twist loops to tunnel through each other. If the rotation of one twist loop matches the rotation of a linked loop right at the point where linked loops are being pulled apart, the loops can separate. This is proposed as particle decay and would model the randomizing effect of the weak force.
Glossary
3D + T: the three spatial and 1 time-wise dimensions of our existence. Equations usually are set up for solutions in this space.
Causal: Causality: The property where a particle or field changes according to special relativity, that is, changes cannot propagate faster than the speed of light.
Dirac Equation: Relativistic equations using operators that effectively describes electron behavior in an atom and relativistic interactions of particles
Electron, Positron: charged fundamental quantum particles with spin (no known substructure with a fixed rest mass)
EM: EM Field: Electromagnetic Field.
Entangled Particles: A property of a system of particles where resolving a state of one of the particles instantly (non-causally) affects the remaining particles
Frame of Reference: Used in Special Relativity, refers to the observer's position relative to a system being observed. Special Relativity describes how a system (for example, a set of particles) will appear to the observer that is dependent on how fast and in what direction the observer is moving in relation to the system.
General Relativity: Einstein's theory describing the stress-energy tensor, which details the equivalence of acceleration and gravity and describes how dimensions distort and forces apply when objects are accelerated, especially as speeds approach the speed of light. For example, it describes how a particle's mass increases as it is accelerated.
Interference: Quantum interference: The property at small (quantum) scale where the probability of a particle state or location varies according to wave superposition, the trait of waves interfering with each other
Lorentz Transform: equations that describe how dimensions of time and space distort in different frames of reference (special relativity)
QFT: Quantum Field Theory: theory of how fields, such as the electromagnetic field, are quantized.
Quantum, Quanta: property where fields or particles have a property that can only have a particular value from a set (the set of real or complex numbers, for example)
Quantum Mechanics: the equations that describe the wave-like behavior of particles in various systems, such as a particle in a box.
Photon: quantum of light. Only one possible value of energy, depending on frequency.
Planck's Constant: The lower bound for simultaneous measurement of two orthogonal properties such as a particle's position and momentum.
Relativistic: Usually refers to particles or interactions of particles with velocities that approach the speed of light
Rest mass: Since any particle with mass will have that mass increase as it is accelerated, rest mass is defined as an intrinsic property of a particle that is not moving
Schroedinger Equation: Wave Equation: second order differential equation that describes the probability distribution of (for example) an electron around an atom
Special Relativity: Einstein's theory that describes how dimensions (space and time) interconnect and vary according to an observer's frame of reference. It specifies causality of all particles or field components, and that the speed of light is the same constant in every frame of reference.
Twist: Field Twist: Author's idea of how photons and electrons (twist rings) substructure could be described
Uncertainty relation: Heisenberg uncertainty principle: the lower bound (planck's constant) for resolving two orthogonal properties of a system.
Unitary: in transforms, the property that preserves magnitude (such transforms can cause rotation or displacement, but cannot change the size or shape of objects). In vector spaces (such as fields), unitarity implies that all vectors have a constant magnitude, only direction varies.
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