The geometry of space itself may play a far more central role in physics than previously thought. Instead of serving only as the backdrop where forces act, spacetime may be responsible for the forces and particles that make up the universe.
New theoretical work suggests that the fundamental behavior of nature could arise directly from the structure of spacetime, pointing to geometry as the common origin of physical interactions.
In a paper published in Nuclear Physics B, physicist Richard Pincak and collaborators examine whether the properties of matter and forces can emerge from the geometry of unseen dimensions beyond everyday space.
Their research proposes that the universe includes additional dimensions that are not directly observable. These dimensions may be compact and folded into complex seven-dimensional shapes called G2-manifolds. Until now, such geometric structures were typically treated as fixed and unchanging. The new study instead explores what happens when these shapes are allowed to evolve over time through a mathematical process known as the G2-Ricci flow, which gradually alters their internal geometry.
"As in organic systems, such as the twisting of DNA or the handedness of amino acids, these extra-dimensional structures can possess torsion, a kind of intrinsic twist," explains Pincak. This torsion introduces a built-in rotation within the geometry itself.
When the researchers modeled how these twisted shapes change over time, they found that the geometry can naturally settle into stable patterns called solitons. "When we let them evolve in time, we find that they can settle into stable configurations called solitons. These solitons could provide a purely geometric explanation of phenomena such as spontaneous symmetry breaking."
In the Standard Model of particle physics, mass arises through interactions with the Higgs field, which gives weight to particles such as the W and Z bosons. The new theory suggests a different possibility. Instead of relying on a separate field, mass may result from torsion within extra-dimensional geometry itself.
"In our picture," Pincak says, "matter emerges from the resistance of geometry itself, not from an external field." In this view, mass reflects how spacetime responds to its own internal structure rather than the influence of an added physical ingredient.
The researchers also connect geometric torsion to the curvature of spacetime on large scales. This relationship could help explain the positive cosmological constant associated with the accelerating expansion of the universe.
Beyond these cosmological implications, the team speculates about the existence of a previously unknown particle linked to torsion, which they call the "Torstone." If real, it could potentially be detected in future experiments.
Extending Einstein's Geometric Vision
The broader ambition of the work is to push Einstein's idea further. If gravity arises from geometry, the authors ask whether all fundamental forces might share the same origin. As Pincak puts it, "Nature often prefers simple solutions. Perhaps the masses of the W and Z bosons come not from the famous Higgs field, but directly from the geometry of seven-dimensional space."
The article published in the journal Nuclear Physics B.
The research was supported by R3 project No.09I03-03-V04-00356.
Curated by Dr. Amara Okafor
