Exploring the deepest mysteries of physics: from quantum mechanics to general relativity, from string theory to loop quantum gravity. The ultimate goal: a Theory of Everything.
Our two most successful theories of physics are fundamentally incompatible:
Spacetime curvature describes gravity
$$R_{\mu\nu} - \frac{1}{2}Rg_{\mu\nu} + \Lambda g_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu}$$
Einstein Field Equations
Wave functions and uncertainty
$$i\hbar\frac{\partial}{\partial t}\Psi = \hat{H}\Psi$$
Schrödinger Equation
At the Planck scale, both theories must apply but they break down:
$$l_P = \sqrt{\frac{\hbar G}{c^3}}$$
≈ 1.616 × 10⁻³⁵ m
Planck Length
$$t_P = \sqrt{\frac{\hbar G}{c^5}}$$
≈ 5.391 × 10⁻⁴⁴ s
Planck Time
$$E_P = \sqrt{\frac{\hbar c^5}{G}}$$
≈ 1.221 × 10¹⁹ GeV
Planck Energy
An attempt to quantize gravity, but it leads to the "problem of time":
$$\hat{H}\Psi[g_{ij}] = 0$$
No time evolution in quantum gravity