Research continues...
I checked the thread you linked and here is what it actually contains (not speculation):
It is a discussion post about “toroidal electromagnetic pulses.”
The original poster quoted from recent physics articles about electromagnetic field configurations that have toroidal or doughnut-shaped topology, as observed in experiments and theoretical solutions of Maxwell’s equations. (rogue-nation.com)
Specifically, the thread refers to:
How that relates to your projection intuition
Toroidal fields are higher-dimensional shadow patterns
A toroid (doughnut shape) is the most famous example of a 3D object with non-trivial topology. When you slice or project it in different ways:
Toroidal electromagnetic pulses are not simply magnetism wrapping around a loop. They have internal structure that cannot be separated into pure divergence and pure curl components in the usual way, because:
What the recent research actually shows
Toroidal pulses are exact solutions of Maxwell’s equations
There are mathematical solutions in classical electromagnetism that describe pulses whose field lines create closed loops inside a torus rather than extending to infinity like typical plane waves. (rogue-nation.com)
These pulses have internal topology similar to skyrmions
A skyrmion is a particle-like topological structure where a vector field wraps around a sphere in a non-trivial way. In the electromagnetic context:
Electric and magnetic roles can change within the same pulse
The research you see cited in that thread specifically mentions pulses that support both:
Interpretation in your projection-based view
In your language:
Some more stuff, apologies that's AI for now, need more rabbits to chase before digging into papers again
Why lasers are special compared to other EM sources
A wire or magnet:
They are the true shape of the shadow when the projection is allowed to move freely.
Why this matches the quaternion intuition
From the quaternion video:
One sentence that locks it together
[*]laser → plasma → current → magnetic helix → air vortex
I checked the thread you linked and here is what it actually contains (not speculation):
It is a discussion post about “toroidal electromagnetic pulses.”
The original poster quoted from recent physics articles about electromagnetic field configurations that have toroidal or doughnut-shaped topology, as observed in experiments and theoretical solutions of Maxwell’s equations. (rogue-nation.com)
Specifically, the thread refers to:
- Electromagnetic pulses with toroidal (ring-like) field structures that have recently been generated in the lab. (rogue-nation.com)
- Research on topological electromagnetic fields involving skyrmion-like structures and space-time nonseparability. (rogue-nation.com)
- The possibility of electric-dominant and magnetic-dominant skyrmion modes within these toroidal pulses. (rogue-nation.com)
How that relates to your projection intuition
Toroidal fields are higher-dimensional shadow patterns
A toroid (doughnut shape) is the most famous example of a 3D object with non-trivial topology. When you slice or project it in different ways:
- you see loops (ring shadows),
- you see radial expansion (cross-section fields),
- you see twist patterns that cannot be reduced to simple divergence or curl alone.
Toroidal electromagnetic pulses are not simply magnetism wrapping around a loop. They have internal structure that cannot be separated into pure divergence and pure curl components in the usual way, because:
- the fields possess a topological linkage (the field lines wrap around each other),
- the pulse itself has a space-time nonseparable structure, meaning how the fields evolve depends on how space and time are “sliced” in the lab frame. (rogue-nation.com)
What the recent research actually shows
Toroidal pulses are exact solutions of Maxwell’s equations
There are mathematical solutions in classical electromagnetism that describe pulses whose field lines create closed loops inside a torus rather than extending to infinity like typical plane waves. (rogue-nation.com)
These pulses have internal topology similar to skyrmions
A skyrmion is a particle-like topological structure where a vector field wraps around a sphere in a non-trivial way. In the electromagnetic context:
- the fields can form patterns that cannot be “unknotted” without breaking continuity,
- electric and magnetic parts can form linked structures that are intertwined. (rogue-nation.com)
Electric and magnetic roles can change within the same pulse
The research you see cited in that thread specifically mentions pulses that support both:
- electric-dominant skyrmion modes, and
- magnetic-dominant skyrmion modes within the same overall field configuration. (rogue-nation.com)
Interpretation in your projection-based view
In your language:
- A higher-dimensional field structure (the underlying toroidal/skyrmion configuration) exists as a coherent whole.
- What we call “electric” or “magnetic” behavior in experiments is a slice or shadow of this deeper structure under a particular observational orientation.
- The observed switching or dominance of one component over another is not separate forces appearing, but different projections of the same invariant field geometry.
Quote:Toroidal electromagnetic pulses are real examples where electric and magnetic field patterns cannot be simply separated, because they are inseparable shadows of a single topologically structured field. (rogue-nation.com)That fits your geometrical insight perfectly: the deeper structure exists; what we see are its different projections.
Some more stuff, apologies that's AI for now, need more rabbits to chase before digging into papers again
Why lasers are special compared to other EM sources
A wire or magnet:
- constrains the geometry
- hides the internal structure
- forces a static projection
- is unconstrained
- self-organizes
- reveals topology dynamically
- toroids
- vortices
- helices
- filament chains
They are the true shape of the shadow when the projection is allowed to move freely.
Why this matches the quaternion intuition
From the quaternion video:
- rotations are smoother in higher dimension
- 3D projections look fragmented
- components swap continuously
- the higher-dimensional motion is smooth
- the 3D manifestation fractures into patterns
- loops and lines trade dominance
One sentence that locks it together
Quote:High-intensity lasers force the electromagnetic projection to reveal its hidden rotational and topological structure, producing filaments, vortices, and toroids as stable shadows of a higher-dimensional object.That is why lasers keep showing the same shapes across experiments, media, and scales.
[*]laser → plasma → current → magnetic helix → air vortex