Strings, disks, blobs, toruses, and higher-dimension objects {brane} can vibrate.
Rather than strings, fundamental elements can be membranes {supermembrane} {2-brane} {3-brane} {p-brane}|, of dimension 2, 3, or any natural number p. Minimum length is Planck length. Branes vibrate and have high-energy waves. Branes require ten space dimensions (three infinite and seven curled up) and one time dimension.
Open-string endpoints can stay fixed at one point (Dirichlet boundary condition) (zero-dimension brane), which maintains vacuum gauge invariance. Endpoints can move along straight or curved lines (Neumann boundary condition) (one-dimension brane), which fixes particles. Endpoints can move around surfaces (two-dimension brane) or higher branes.
Membranes {Dirichlet-brane} {D-brane} can contain string ends. Black holes have many D-branes, and black-hole temperature is number of possible D-brane arrangements.
Curled-up dimensions have curved cylindrical handles {handle, string}, which have branes wrapped around them.
Curled-up dimensions have spikes {throat, string}, which have branes at tips.
Perhaps, three-dimensional space {braneworld} is a brane.
Triangles {2-simplex} have two dimensions and three lines/sides. Tetrahedrons {3-simplex} have three dimensions and four triangles/faces. Simplexes {4-simplex} can have four dimensions and five tetrahedrons/faces. 4-simplex connections dynamically determine number of space-time dimensions.
Space can be tiny causally-connected (over time) 4-simplexes {causal dynamical triangulation} (CDT). CDT allows only causally possibly configurations. CDT results in three large-scale spatial dimensions and one Planck-scale spatial dimension, making four space dimensions. CDT can account for all forces and particles.
If dynamical triangulation can be causal or non-causal, space has infinite dimensions or two dimensions.
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Date Modified: 2022.0225