This spin foam is a 3+1-dimensional structure, where the 1 represents the direction along which the changes between spin networks occur. What is remarkable about spin foams is that although they seem to be purely spatial, a phenomenon that we recognize as time emerges from the successive changes in these networks.
The justification for interpreting this axis of change as time has to do with one of the most important features of relativity, called causality. This principle holds that effects must come after their causes in space-time, which allows us to connect events together in a logical timeline.
Think about a drawing of your family tree. The lines you draw between your grandparents, your parents, and yourself are meant to be indications of cause and effect, not physical lines in space. But they do form a very crude timeline. Similarly, causality lets us assign changes in a spin foam to sequences that we interpret as space unfolding over time.
Embedded in each spin network is a small collection of nodes and links that can serve as a clock for that network — like a timestamp in a photograph. But just as a timestamp does not exist outside of a photograph, the concept of time can only exist within the spin networks.
The emergence of time
This idea that time is an emergent phenomenon from within our space-time and not present outside of it was proposed in 1983 by physicists Don Page of the University of Alberta in Edmonton and William Wootters of Williams College in Williamstown, Massachusetts. It was a dramatic solution to the origin of time, placing its source in a phenomenon called quantum entanglement.
In quantum mechanics, two particles are entangled if they interact with each other in such a way that their quantum states can no longer be described independently: That is, if you measure the quantum state of one particle, causing its fuzzy cloud of possible states to collapse to one single state, you can immediately deduce the quantum state of its partner particle. The wave function of the partner particle also collapses instantly, even if it has since zipped off to the other side of the universe. Einstein hated this because it violates the principle of causality in relativity — another way in which quantum mechanics and relativity don’t mix.
But Page and Wootters suggested that an entangled system could give rise to the phenomenon of time — and recently, scientists have begun to test this hypothesis in the lab. In 2013, experiments led by physicist Ekaterina Moreva at the Istituto Nazionale di Ricerca Metrologica in Torino, Italy, showed that the emergence of time occurs in a system of two entangled photons. If an observer uses one photon as a reference clock — or timestamp — to observe its entangled partner, the system appears to evolve in time. But to an observer comparing the entangled photons to the rest of the universe, the system remains static. This means time only emerges for observers within the universe — there can be no “outside the universe” clock where time exists.
Related to this idea of quantum entanglement is the no-boundary proposal for the origin of the Big Bang, developed by James Hartle at the University of California, Santa Barbara, and the late Stephen Hawking, as well as independently by Alexander Vilenkin at Tufts University. In 1983, they proposed that one of the universe’s four spacelike dimensions underwent quantum mechanical tunneling into a timelike dimension at the Big Bang. This triggered what Vilenkin calls “eternal inflation.” Although the universe initially was made of pure space in many dimensions, once one dimension emerged as the direction of a past-to-future succession of states, the Big Bang occurred. This triggered the progression of the universe in the direction of increasing entropy, defining the arrow of time — a critical transition. According to Smolin, without it there could be no coherent 3+1 space-time, but simply a random collection of 4D spacelike spin foams that do not lead to our physical space-time.
The bottom line
Our experience of time may be subjective and limited to a sense of now, but on the cosmic scale, time seems to be a feature of entangled relationships between objects and not a feature from outside our universe. The arrow of time is a consequence of the increasing entropy of an expanding universe since the Big Bang. It appears this precludes us from remembering the future. But at least we have our memories, courtesy of the steady march of entropy, which allows us to recover past events and stitch them into a consistent story. Lucky for us, our universe seems to have a consistent story to tell in the first place!