This blog flows like a river. Posts are waterfalls where words get caught upstream while others go over. The best way to conceive expansion of the Universe, Julian Barbour writes, is subtle. His use of the term “subtle” echoes Wing Tsit-Chan’s translated words, that non-being defines the subtlety of all things and being is the outcome. Nothing is neither space, time, nor matter. It precedes and vanishes. Its number is zero, a circle that dives into eternity, a well that plunges into infinity, the daily exercise of Ensō.
Which of zero or one pertains to unity? Zero is nothingness, and one is wholeness. Both could imply unity, but the former, concealed, is unity in darkness; the latter is unity brought to light. Within one system, one Universe, there occurs a unitary evolution. Unity refers to an invariant variational upon which “energy is conserved because time is uniform; momentum is conserved because space is the same everywhere — it is homogeneous; angular momentum is conserved because space looks the same in every direction — it is isotropic.”It isn’t the stars rustling that I hear but the muffled sound of nothingness.
There appear to be conceptual objects too subtle to differentiate, subtleties that call for candid recognition. One is the gate of all subtleties. In our pursuit of nothingness, we find ourselves at the Janus point where no direction is distinguished. Stephen Hawking is quoted to have said that asking what came before the Big Bang is meaningless. It is like asking, “what lies south of the South Pole?”. It would be like sliding down the celestial Sphere from the imaginary point of the celestial South Pole beyond the dark clouds of the Chamaeleon complex and the South Pole Wall. Is it where lies the elusive birth of time?
If we could go back in time to near the presumed start of the Universe, Barbour writes, we would find that indeed time becomes space. “Since a beginning of the Universe presupposes time, this would mean the Universe did not in fact have any singular beginning.” It would imply that time may not have preceded everything else, that it is space from which all things emerge. Could a timeless quantum-size geometrical object, suspended by itself like a lost memory, be the origin of everything? Is that all what time is about: something added to space?
Space-time picture of the causal relationship between the events (Nima Arkani-Hamed, Paolo Benincasa, Alexander Postnikov)
Determining the geometry of the Universe implies measuring spatial correlations between cosmological structures. In their attempt to trace the cosmic web, cosmologists chase discreet geometrical patterns in the sky, one cosmological polytope at a time. They infer angles from not readily seen tetrahedrons, double square pyramids, and amplituhedron, hoping for all the lines to be drawn, the pieces to fit into a larger geometry so that the puzzle of the Universe is complete. Over time because of scattering amplitudes contained within, spatial correlations grow and expand, giving a history of time itself. Faces of polytopes speak a more familiar language as if they originate from a distant memory. Geometrical figures are symbols used in the conversation between the Universe and Consciousness. They project a big picture on the universal screen, an overview of a process that takes us from nothingness through the quantum state into a classical view of the observable Universe.
The bootstrap method is different—instead of asking “what is the answer for the correlator?” it asks, “what is the question to which the correlator is the unique answer?”
In Thoughtland, there are mathematical spaces — deSitter Space, Swampland, and String Landscape. Sean Carroll, for his part, proposes that the fundamental ontology of the world consists of a vector in Hilbert space evolving according to the Schrödinger equation. The phase space is a space in which the set of all possible states is represented. Julian Barbour poetically describes it as a “prison in which a Nietzschean eternal-recurrence nightmare gives sleepers no respite.” His words echo those engraved in my memory of Baudelaire’s immense trails of rain spreading like the bars of a vast prison. But the girl in sandals, Barbour adds, can “walk in an infinite sandpit, and streams need not, like the River Jordan, end in the Dead Sea. They can and often do reach ‘great Neptune’s ocean.”
Take Hilbert space, a realm of infinite dimensions swarming with arrow-shaped abstractions called vectors. Pondering Hilbert space makes me feel like a lump of dumb, decrepit flesh trapped in a squalid, 3-D prison.
Chamaeleon II molecular cloud viewed by Herschel and Planck (ESA/Herschel/Planck; J. D. Soler, MPIA)
While the thermodynamic arrow coincides with time direction, shapes of the Universe hold inconspicuous clues about the nature of time. Is it the causal structure of spacetime that provides a rationale for having intersections of lines in the sky? Or will the true shape of the Universe be revealed once the scale falls from one’s inner eye? The Universe is moving along a path chosen out of all possibles that appear to have been otherwise available from the initial state, pulled by unknown attractors. Barbour sees that path not only devoid of scale but apart from time itself. “Everything that is essential is kept; everything that is not is eliminated. That included not only scale but also time”. The philosopher Mariam Thalos depicts in her book on the Scale Freedom of the Universe a figure of reductionist ontology that brings me back to the collapsing circles of concepts.
Cosmology is a historical science that knows neither its end nor its beginning. How can the endgame be without a scale if attractors lead us to it? How can an expanding universe be a finite one? It is hard to fathom a finite universe with a closed geometry that appears out of nowhere. In order to discuss the initial state, spacetime needs to be quantized. The main idea is to find an underlying first-principle mathematical structure which the wavefunction of the Universe arises from. As we struggle to spell out how nothing creates something, it is replaced by something akin to a quantum tunneling effect. The wavefunction of the Universe represents a probability distribution that presupposes the necessary condition of our existence. While probabilities are said to be an operational concept, they unveil shadowy figures and hidden patterns that silently wait for their turn before taking a particular path among all possibles. Is the whole Universe a lark mirror, made up of looking glass that sparkles in the light for our eyes only and causes us to build bottomless castles on the sandy shores of our dreams?
The iconic representation of a no-boundary saddle point in the absence of matter other than a cosmological constant. The geometry is regular and Euclidean near the south pole and evolves across a matching surface into an expanding de Sitter universe (J. J. Halliwell, J. B. Hartle, and T. Hertog)