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!
Agemoz
Tags: general relativity, general-relativity, quantum, science, special relativity, special-relativity
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