The arrow of time is often explained in terms of entropy. The seemingly irreversibility of time is the result of our universe moving from a state of lower to higher entropy. This is easy enough to grasp. We are more likely to see the falling glass shatter into pieces than the shattered pieces coming together to form the glass.

I wonder, though, if time and entropy may have a deeper connection than this simplified version of our standard theory suggests. It’s a muddled picture in my mind, made less clear by a lack of mathematics. More like fragments of random observations. The simplistic image goes something like this: assume four dimensionless points (I refrain from describing these points as particles as that can lead to conceptual problems). Why only four? I wish to draw a square to make the geometry more straightforward, that’s all. These points don’t exist in spacetime. They do not fill anything or take up space. They have no connection to each other. They do not self-interact.

What do these points consist of then? A number, that is to say, they have an intrinsic or spin angular momentum. Because there is no connection, these isolated points have no inertia (Mach’s principle). There is no space between them because there is no connection field. So where do these points exist? They are not embedded in spacetime for the point of the exercise is to predict the very existence of spacetime emerging as a connecting field takes hold.

For simplicity sake, let us say that these points (and here, let us begin calling them Q-bits to liberate these points from our common association with particles) exist within a complex topological boundary where spacetime is unable to exist within the regime of a non-inertial connection. Space isn’t expanding “into” anything. Space remains fixed to its initial boundary conditions while the formation of a connection field gives rise to inertial forces that “project” or map out the space of a concrete geometry (in this case a square). The boundary conditions can be described through a scalar field mapped onto the complex space (the stress-energy tensor of general relativity). Conceptually, these connecting fields are identified through their so-called duality frames.

A complete muddle. So what drives these four Q-bits to converge and form a connecting field? What is the combination? Is it like a slot machine where a lever comes up with a random pattern – heart, diamond, cherry, lucky7 – no jackpot, no connecting field? Another random pull yields a new kind of pattern – say all four lucky7s – jackpot! A connecting field emerges. Why and how did this symmetry break? Perhaps the laws of quantum mechanics do not allow four Q-bits to share the same spin. Thus, a connection field entangles the Q-bits in order to conserve angular momentum through a more complex geometry of spacetime. No information transfer is needed across each point. Entanglement ensures the eternity of spacetime.

Time, in this sense, is flattened, pancaked, localized space. Time is a rebounding effect or echo as a state moves from lower to higher entropy and space itself expands. Space is non-localized time. Entropy is the well curve for any defined “closed” system along the world line/sheet/volume.

Speculation without an equation.

Entropy in such a picture would emerge from an intrinsic conservation of angular momentum. The state goes from simple order (lower entropy state) of four independent points to a more complex organization (higher entropy state) with a connecting field representing a value in each point of space.

But this is all a muddle, and being an amateur theoretical physicist in one’s spare time is not conducive to real discoveries. As a Philosopher, I enjoy the muddle. Somehow, in ways that are not always clear, a rogue suggestion or an obvious error can lead others to great breakthroughs. And we all share in some small way in these victories.