Maybe someone can help me wrap my head around this. Let's say you have a box of gas in a low entropy state: all the particles are on one side of the box. A moment later, the particles will have spread to the other side of the box, so the entropy is lower. But to say "a moment later", we're assuming a quantity called time. I'm confused how you can see this in reverse: "because the particles spread to the other side of the box, a moment passes".
The perspective is kinda like this:
All moments are equally real, like the movie frames on a film roll. The laws of physics say how a point on one frame relates to the same point on the neighboring frame, just like they say how a point relates to a neighboring point on the same frame. You can cut out all the frames from the film roll and stack them on top of each other, resulting in a “block” of points in space-time.
Einstein’s relativity implies that there isn’t a unique way to slice that block into same-moment-in-time frames; instead there are many different ways. Nevertheless, the laws of physics specify how the points within the block relate to each other (e.g. in terms of electro-magnetic field strength and orientation at each point, and all the other physical fields), independent of the particular slicing.
It happens that these physical relations give rise to a structure/flow/weaving that is different along one direction than along other directions. It also happens that along that particular direction the structure implies an increase in entropy, if entropy is calculated on slices perpendicular to that direction (= the increase is from one slice to the next). And that is what has us perceive that direction as time.
But all that really exists is the four-dimensional space with a-priori no distinguished direction, just physical laws describing how points in that space relate to each other. The laws happen no imply that the points will generally be in a pattern in which some direction looks different from the others, and will have a structure that results in us perceiving that direction as time. But there is no externally flowing time, it’s just a pattern within that immutable block of physical reality.
Note: The currently accepted laws of physics do have time as an a-priori dimension. But the idea is that we will come up with laws that don’t have that presumption, and which instead will have time as an emergent property, connected to directions of entropy increase.
You mean, higher?