Quantum Gravity and the 'No Boundary' Proposal

Key Insight

Classical general relativity predicts that the universe began at a big bang singularity, a point of infinite density and curvature where all known laws of science break down, rendering the universe's origin inexplicable and necessitating an arbitrary initial state. To resolve this, a quantum theory of gravity is required, which could allow scientific laws to apply universally, including at the universe's beginning, thereby eliminating singularities. A key feature of such a unified theory is expected to be Feynman's 'sum over histories' approach, where a particle follows all possible paths through space-time. To address the severe technical difficulties in these calculations, 'imaginary time,' a well-defined mathematical concept, is introduced. This transforms real space-time into a 'Euclidean' space-time, where the distinction between time and space directions vanishes, making them geometrically equivalent.

When Feynman's sum over histories is applied to Einstein's theory of gravity, the history of the entire universe is represented by a complete curved Euclidean space-time. In this quantum gravity framework, a novel possibility emerges: space-time can be finite in extent without possessing any singularities or boundaries, analogous to the surface of the Earth, which is finite but has no edge. This concept, known as the 'no boundary' proposal, suggests that the universe has no requirement for boundary conditions, meaning there is no point in time or space where scientific laws cease to apply, and no need to invoke an external creator to initiate the universe. The universe, under this proposal, would be entirely self-contained, neither created nor destroyed, simply existing as 'BE.' This idea, while initially based on aesthetic or metaphysical considerations, must ultimately be validated by predictions that align with observation.

Under the 'no boundary' proposal, calculations suggest that while many possible universe histories exist, only a particular family of histories is highly probable. These histories can be visualized as a sphere, where imaginary time is distance from the North Pole, and the universe's spatial size is represented by circles of latitude. Starting as a point at the North Pole, the universe expands in imaginary time to a maximum size at the equator and then contracts to a point at the South Pole. These 'poles' are not singularities, and scientific laws remain valid there. In real time, this history would correspond to a universe expanding from a minimum size (10 to 20 billion years ago) akin to the chaotic inflationary model, eventually re-collapsing. The 'no boundary' condition predicts that the universe is highly likely to be expanding uniformly in all directions at its current density, which is consistent with observations of the microwave background radiation's uniform intensity. It also predicts that the universe began with the minimum possible non-uniformity allowed by the uncertainty principle, which were then amplified during inflation to form galaxies and stars. The COBE satellite's 1992 detection of slight variations in the microwave background, consistent with these predictions, reinforces the 'no boundary' proposal as a strong scientific theory.