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.
One of the current big controversies in cosmological physics is why there is stronger gravitational attraction in our universe than can be explained by the presence of observable mass. This is most readily seen by the observation of galaxy size and rotation rates. I’ve seen a lot of discussion how to explain this, but most researchers seem to accept that there has to be some kind of new but undetectable “dark” matter. as a consequence, there has been a lot of effort toward detecting new particles not covered by the Standard Model, such as WIMPs, axions, and other more exotic things. There has even speculation that the equations of gravity start to break down at galactic scales, but all of these ideas have met their demise so far–the LHC appears to have ruled out reasonable WIMP masses, the experimental evidence for gravitational corrections is non-existent, and the experimental existence for axions and other conceptual particles is currently non-existent as well. So far we have no evidence of any new physics or particles that might explain the additional gravitational force we observe. Could the observations somehow be wrong? Right now, no researcher appears to think that–it appears incontrovertible that observational measurements show that something is going on that we don’t understand.
The interesting thing about the dark matter controversy is how the gravitational anomaly shows up at galactic scales, but local gravitational measurements as well as orbital variations and even gravitational lensing measurements show no detectable error or variation in Einstein’s general relativity equations. The explanation has to come from the vast scales present at galactic scale but not at planetary or smaller scales. For this reason, physicists have determined that there must be some mass (a lot of it!) that is undetectable–we can’t see it, it doesn’t interact with (for example) photons headed toward our observatories.
I think there is another explanation that I have not seen anyone consider.
I think it would also have to alter the observable gravitational effects on a galactic scale.
There is a critical difference between the traditional 4D spacetime perspective of the Big Bang and the Activation Layer theory that I am proposing. In that previously mentioned post about Activation Layer cosmological implications, I show the difference, and you can see it in the figure:
Fig 1: Traditional and Activation Layer views of the universe. Note that I show the Activation Layer as expanding rings, but a more accurate picture (but hard to view) would be an expanding R3 sphere in 4D spacetime.
The difference requires a creative imagination to see it: in the traditional spherical Big Bang, there is no curvature unless there is nearby mass (mass/energy tensor is not zero). But the Activation Layer Big Bang will have curvature even when there is no mass present, because the hypersurface is a spherical surface in 4D spacetime expanding about the initial singularity point. This curvature will cause the appearance of gravitational effects even where no mass is present! (It should be noted that while gravitation takes effect within the Activation Layer, the math of general relativity allows for the effect of masses outside of it–see https://agemozphysics.com/2025/02/13/general-relativity-and-the-3d-hypersurface-activation-layer/). It will show up at galactic scales, but will scale down to presumably undetectable levels at local distances. Is the Activation Layer Big Bang curvature sufficient to explain the extra gravitation we observe? I will attempt some analysis here. But there’s no question that the Activation Layer curvature is going to have some effect not directly explained by general relativity.
Maybe we are looking in the wrong place for the cause of the extra gravitational effects we see. The Activation Layer view of the universe provides a geometrical explanation that does not require the alteration of the laws of gravity or the presence of exotic particles for which we have yet to see any evidence.
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.
EDIT: I added the math behind my claim that the 3D hypersurface activation layer is sufficient to contain the laws of special relativity, see about 4 paragraphs down. Also, fixed missing constant c in solution.
One of many aspects of the idea that all of our existence must be confined to a 3D hypersurface (the “Activation Layer”) within 4D spacetime is the principle that special relativity does not need anything outside of the hypersurface. However, I think most scientists are likely to reject the Activation Layer concept because special relativity has a number of characteristics and consequences that appear to require a true 4D spacetime existence, rather than a single 3D surface that moves through time.
Anytime someone tries to assign a single point in time for all of our existence is going to instantly run afoul of the way special relativity has observers seeing different event times and spatial or time intervals depending on an observer’s relative velocity. Even my own immediate reaction to the activation layer idea is “no way, that can’t work”. However, a lot of study and thinking has convinced me that the activation layer must be true and that special relativity does not deny its validity. I spent a lot of time thinking and studying special relativity to see how the two concepts could both be true, and this meant taking each of the special relativity cases in depth.
For example, let’s look at an obvious case: one detector receiving photons from two source events. Let’s set the geometry of the three components (detector, two sources, see figure), and assume photons are point particles. Classically, it does not matter whether the detector is moving or not (that is, if you vary the detector’s frame of reference)–if the photons arrive at the same time when the detector has no velocity, giving the detector any velocity will not change the simultaneous detection of the two event photons. But special relativity says that this cannot be true–detection will no longer be simultaneous, and a quantitative analysis will show that the apparent times of the two source events will vary depending on the detector’s frame of reference velocity and direction. This would appear to defeat the activation layer idea, which has both events emitting photons and being detected within a single 3D hypersurface, moving along the time dimension, of 4D spacetime. (A side note–general relativity also does not appear to require more than a single 3D hypersurface, but the hypersurface will contort according to the stress-energy tensor. I’ll discuss that in another post).
But in a quantum existence, the foundation of the activation layer theory, it’s actually a lot more complicated than that. I was able to show that when assuming a quantized 3D hypersurface, observing different event times does not defeat the activation layer concept, in fact, the activation layer predicts it. The quantized activation layer assumes that all particles are quantum group wave constructs. Neither photons nor detectors are point particles, but are spread out in some sort of Gaussian shape–they have a width both in space and time, and this changes the detection process analysis dramatically. I think you will readily see this in a qualitative way if we go back to the classical case but replace the three components with spatially distributed equivalents. Now study how different detector frame of reference velocities affects the apparent detection times. As before, a static detector will detect both photons simultaneously, but if the detector is moving, notice how the detection absorption time will vary and the events will no longer appear to be simultaneous. We don’t need to assume special relativity to see that the quantum behavior of the activation layer concept will exhibit the same type of time varying event behavior of special relativity.
Fig 1. In the Activation Layer case, photons and the detector are quantized size, and the time to be absorbed is a function of the detector frame of reference. As a result, the two photons may arrive at the detector at the same time, but detection times will be dependent on the detector velocity and will always be different for different detector frames of reference.
UPDATE: Here’s a bit of math to support this claim. This is dependent on the constant speed of the photons and on the quantum property that both the photons and the detector are group waves that Doppler shift (see this paper: https://agemozphysics.com/wp-content/uploads/2020/12/group_wave_constant_speed-1.pdf). The derivation goes like this (sorry, Latex doesn’t work on this blog):
Refer to figure 2, a simplified view of the velocities of the moving detector and one of the event emitters. The time for the detector to capture the photon, where td is the detection time, vp is the photon velocity, vd is the detector frame of reference velocity, and d is the detector capture region length:
td = d / Sqrt[vp^2 – vd^2]
which converts to:
td = d / (vp Sqrt[1 – vd^2 / vp^2])
But, since the photon is assumed to be a quantum group wave assembly, it will Doppler shift in such a way that its velocity is not dependent on the observer’s (detector’s) velocity–see the above-mentioned paper for this calculation. The constant photon speed is arbitrary in this analysis, but to match reality we will choose the speed of light c. Thus, the detection time occurrence will only vary as a function of the detector’s frame of reference:
td = d / (c Sqrt[1 – vd^2 / c^2]) = (d / c) * beta
Here we have the Lorentz Beta factor describing the time dilation of photon event detection. There are many other cases to examine, but it should be clear that special relativity doesn’t need other hypersurfaces, or for that matter, any of the rest of 4D spacetime, to correctly describe our existence.
Figure 2. This computation shows how a photon detection time varies as the detector frame of reference velocity.
This is just one case, and it doesn’t prove the activation layer concept, it just shows that special relativity does not deny its potential validity. You might object that at the quantum scale the time differences will be tiny and thus irrelevant, but this is not the case–significant detector frame of reference variations will cause dramatic differences in observable photon absorption times.
If the activation layer can be shown to be true, there are a lot of implications both at the quantum and cosmological level that I would hope would advance our understanding of many fields of science. It’s a significant constraint on the definition of our existence for which I keep seeing good evidence. While at first the 3D activation layer hypersurface appears to prevent the known properties of special relativity, a deeper investigation has led me to the discovery that the two theories can coexist.
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: This post describes how special relativity still holds in a subset of 4D spacetime, the 3D hypersurface slice (Activation Layer) that confines the fields, particles, and interactions of our existence. After posting this, I realized that cosmologically, this should be testable. This figure shows a 2D version (“Flatland”) view of the Big Bang expansion and compares the cosmos appearance for a 3D spherical Big Bang expansion with a 3D Hypersurface Big Bang expansion. You can see how the expansion of galaxies differs–in the spherical Big Bang, we will see Doppler red shifting away from a central point core, but this doesn’t happen in a 3D Hypersurface Big Bang (assuming we can’t directly observe the core, the spherical Big Bang will have a region of space with fewer deep red-shifted galaxies; this will pinpoint the direction of the core due to galaxies streaming out from it). If we are able to, looking deeper into the spherical space should ultimately show the core remnants and eventually, back in time far enough, the core itself.
In the hypersurface expansion, the core will never be visible, it will only show up as massively red-shifted cosmic radiation in all directions.
Another possible test: if we were able to look deep enough into space, the hypersurface expansion should reveal copies of any subset of galaxies from any direction we choose. This assumes we can look back far enough, and we have to account for the fact that the perspective will change. We would have to choose equal distance views–otherwise the time evolution for the different views will likely make the subset change too much to be comparable). The spherical Big Bang will not show any galaxy copies.
By far the most compelling case for the 3D Hypersurface Activation Layer Big Bang approach comes from the James Webb telescope images of deep infrared galaxies. These galaxies are measured only a few hundred million years after the Big Bang, but are observed to be too mature–the spherical expansion means not enough time has passed to form mature galaxies. Scientists are working to revise galaxy formation theories based on this data, but this is an expected outcome for the hypersurface activation layer Big Bang theory. You can easily see from the figure that the hyperspace Big Bang will never show visible early proto-galaxies from the observer’s point of view, the photon path lengths will be far longer than the spherical Big Bang path lengths. All visible galaxies in any direction and any observable distance back in time from the observer will be fully mature.
These are just a few of the potential ways we can test the validity of the hypersurface activation layer concept. As far as I know, researchers have never identified a central point core direction for our universe from galaxy redshift measurements, thus giving credence to the hypersurface activation layer form of the Big Bang.
ORIGINAL POST: In my previous post, I describe how our existence and all particle and field interactions must lie within a 3D slice of 4D spacetime, a hypersurface I call the Activation Layer. This property defines a bound on the effective neighborhood of particles, so when this is combined with the wave properties of all elementary particles, it causes the particle properties to be quantized (see https://wordpress.com/post/agemozphysics.com/1947 for the details of my thinking here). Assuming the existence of the activation layer hypersurface results in a mathematical description of what I call an Emergent Field, one that does not separate out fields from particles. The goal is to simplify the current standard model process that requires complex perturbative solving solutions to the LaGrange equations of motion for particles–and additionally should give new insights into how our existence works.
However, I can see that physicists would balk at confining our existence to a single hypersurface, especially because special relativity shows how observers in different frames of reference will observe events at different times. In that previous post I described how the activation layer does not invalidate special relativity since the equations will hold within a single hypersurface; special relativity does not force either the observers or the observed events to be in different hypersurfaces. Let me go into a little more detail here.
There is no question that if different observers see events occurring at non-matching intervals based on observer velocities, and especially if they observe spatial components morphing into time separation and vice versa, that it would appear that the entire 4D spacetime set of dimensions is necessary to make this work. But careful inspection shows this not to be necessary–that a timewise moving 3D hypersurface is sufficient to contain the observed variations in event times.
As I mentioned in the previous post, the Lorentz operators of special relativity can be described as a form of a first order (linear) tensor transform, an operator that transforms the working spacetime dimensions to a function of the observer’s velocity. The same thing is true of general relativity, except now the tensor operator is second order and is a function of gravity as well as the observer’s acceleration. We need to examine these two transforms to see if they truly can lie within a 3D hypersurface or if they force our existence to occupy multiple hypersurfaces.
For special relativity, it is clear that the Lorentz operator must be observational, whether or not multiple hypersurfaces are necessary. Unlike the stress-energy tensor, an observer’s velocity cannot alter 4D spacetime for other observers or events. The Lorentz operator describes what an observer sees, not what is actually happening (a concept that Einstein showed doesn’t exist, there is no such thing as a frame of reference that describes “what is actually happening”). And what an observer sees is a really tricky concept involving the exchange of wavelike particles such as photons. I suspect that physicists would object to the proposal that our existence being confined to the single activation layer hypersurface (moving forward in the time dimension) because having observers see different event times based on their position and velocity would seem to require all of 4D spacetime. But it doesn’t.
All particles have wavelike behavior that are confined via group wave constructs (for example, the Fourier decomposition of a delta function describes a point particle). All such group waves will Doppler shift, regardless of whether observers move at classical or relativistic speeds, and there are many interesting properties of Doppler shifted group waves. For example, see this paper (https://agemozphysics.com/wp-content/uploads/2020/12/group_wave_constant_speed-1.pdf ) which shows how any object described as a group wave construct will appear to be moving at a constant speed, regardless of the observer’s velocity. The same type of thing happens for comparing event times for different observer frames of reference–entirely within a single hypersurface. The event, composed of wave-like particles, will appear Doppler shifted depending on the observer’s velocity, and the photon group wave will thus coalesce at the observer’s detector at different times as a function of his velocity. It should be clear to everyone that the detection times have to vary, and this has nothing to do with anything happening outside of our activation layer hypersurface.
General relativity transforms are different. While the Lorentz operator cannot change spacetime transforms for other observers, the stress-energy tensor does. An observer’s acceleration will change what other observers see due to the presence of increased effective mass or energy, and this will distort the spacetime manifold for all observers and events.
Note carefully–neither operator requires more than a single hypersurface! One 3D activation layer slice of 4D spacetime is sufficient to contain both special and general relativity, although the stress-energy tensor will clearly deform it.
So, now the ultimate question becomes, if we acknowledge that all existence is confined to a single hypersurface slice of 4D spacetime and this does not violate special relativity, then… why? Why do we not have any evidence or even reason to exist in more than one hypersurface slice of 4D spacetime?
My current thought is that the Big Bang is responsible. I apologize for pure speculation at this point, but I think the Big Bang produced a single expanding surface of existence in both space and time dimensions, like a balloon, and all particles and interactions have nowhere to operate except within this surface. The thickness of the layer defines Planck’s constant and constrains the commutativity of things like position and momentum.
Think of blowing soap bubbles where the surface has beautiful colored patterns, that is our existence!
We live in a slice of 4D spacetime, a 3D hypersurface I call the Activation Layer, that confines all particles, fields, and interaction forces. 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 ).
However, I am sure that physicists would not accept this idea that we live entirely within a single hypersurface slice of spacetime. I suspect they would point to how special relativity enables the exchange of space and time elements depending on an observer’s frame of reference, and thus would invalidate the activation layer concept. I have found that a closer look at special relativity will defeat this argument.
One of the main tenets of special relativity states that observed event distances and times are dependent on the observers velocity magnitude and direction. The Lorentz transforms are a type of tensor operator, based on the first derivative of position in time (velocity or momentum) within 4D spacetime and thus could be called a first order tensor operator on spacetime. Gravity, on the other hand, is based on the second derivative of position in time (acceleration or gravity) and is described by the stress-energy tensor and the Riemann curvature tensor, and could be called a second order tensor operator on spacetime.
Both of these tensor operators can bend spacetime, including the activation layer hypersurface. The Lorentz transforms produce a linear (flat angle) bend of the observer-object dimensional axes, where the axes approach the light cone angle depending on observer velocity. The stress-energy tensor induces spacetime curvature that has a central force (second order polynomial) behavior. Note that passing a given 3D hypersurface through either of these linear operators will not split, break, or join the hypersurface to or from another hypersurface, there will be a one-to-one mapping to another transformed hypersurface. Just because these tensor operators can bend our hypersurface to extreme degrees, such as near a black hole, doesn’t mean that our existence will somehow leak out of it or get transferred to another hypersurface. We are locked in, imprisoned if you like, to this hypersurface activation layer no matter how it is contorted, and as a result, you cannot use these two tensor operators to say that the activation layer cannot be real.
Another critically important way to think about this is that two spatially separated observers can both occupy the same hypersurface, yet still observe each other or outside events as special relativity demands. You cannot create a situation where either of the observers or the events must be in some other hypersurface.
Note that even though there are theoretical ways to get to another hypersurface via, for example, the oft-repeated idea of wormhole bridges or other mathematical permutations of the 4D spacetime manifold, we cannot get there. Many physicists have showed that such 4D spacetime constructs are mathematically possible, but each case requires a pre-existing spacetime discontinuity. It’s the same topological constraint of trying to make a torus out of a disk. If you don’t have a discontinuity to begin with, these linear tensor operators aren’t going to create one for you.
You can’t get there from here without a discontinuity, and right now the only possible place for such a discontinuity might be within a black hole. Right now, there is zero evidence that black holes have such a discontinuity inside–we have no way to look inside and see what’s there. It is possible, maybe, but absolutely no evidence for it. I suspect we will eventually find that quantum theory will prevent a true discontinuity there, but for the time being I have a lot of evidence that validates the activation layer hypersurface concept along with a lot of valid consequences of it, but zero evidence, particularly from special relativity, that can be used to invalidate it.
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!
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.
Agemoz's Physics Blog 