Frontier physics
M-theory and dualities
See how M-theory's 11th dimension «opens up» as the coupling g_s grows, illustrating the duality between strongly coupled type-IIA strings and 11-dimensional theory. Relate to the extra radius .
Equipment
- 3D model of the extra dimension expanding with coupling
- Coupling g_s slider
- Pause button
Procedure
Weak coupling: the string description
Set g_s low (~0.2): the 11th dimension shrinks invisibly and the effective world is IIA superstrings in 10 dimensions with weak-coupling perturbation — the regime computable by string Feynman diagrams.
Raise g_s: the extra dimension opens
Drag «Coupling g_s» gradually to 1.0: the new dimension visibly «inflates». Check the idea — the 11th circle's radius is proportional to g_s; strong coupling is no longer described by strings but by an 11-dimensional theory.
Duality: two faces of one theory
Observe that the «same» system looks like 10-dimensional strings at small g_s and like an 11-dimensional theory at large g_s — that is the essence of duality: two different mathematical descriptions of one physics. Similarly, T-duality swaps small ↔ large radius, S-duality swaps weak ↔ strong coupling.
Predict the limits
Predict the scene as g_s → 0 («free» strings, the 11th dimension collapsing to a point) and as g_s → ∞ (the full 11-dimensional theory — M-theory — with 2-dimensional M2-branes instead of strings). Set the values and check visually; note M-theory still lacks a complete microscopic definition — known only through dual limits.