Within complex six-dimensional shapes called Calabi-Yau shapes, the extra dimensions required for string theory can be curled up, making them consistent with current theory. Calabi-Yau shapes hypothetically determine the vibrational patterns of strings through their precise geometry and the number and arrangement of holes in the dimensions, thus giving rise to the physical properties of the universe. Theorists including Greene have demonstrated the ways that Calabi-Yau shapes can be changed through flop transitions, topology-changing transitions, and conifold transitions to enable different surprising effects (like tears in the fabric of spacetime).

The four forces are gravitation, electromagnetism, weak force, and strong force. Each force has a particle associated with the smallest possible “packet” of that force. Each known matter particle has a kind of charge (negative or positive) that relates to each kind of force. Each force has a corresponding particle: strong force and gluon; electromagnetic force and photon; weak force and weak gauge boson; gravity and graviton. (See Table 1.2 on page 11 of the book.)

Einstein’s theory of gravity, general relativity shows that the gravitational force is communicated through the curvature of spacetime by objects with mass. In addition, general relativity posits the symmetry of all viewpoints, regardless of their accelerated motion, if observations include a suitable gravitational force.