It is time, once again, for me to write another blog post‒though, actually, for you reading this, that time has already passed; for you, it is time to read another blog post. That temporal disjunction is mildly interesting, and I have probably long since dwelt on it beyond the level of anyone’s but my own interest.
Still, it does illustrate some of the weird directionality of time, for while the time between when I write and when you read can be, in principle, limitless, it is always and only in one direction. You will never read one of my blog posts so much as a single Planck time before I write it.
This is the character of causality, and its speed is the real speed limit that we narrowly think of as “the speed of light”. It is actually the speed limit of causal influence, and that’s a fundamental part of the restrictions entailed in special relativity.
There is, though, the longstanding question of why time is not merely one-dimensional but unidirectional, since at local scales, the laws of physics don’t appear to have an inherent directionality but are time-symmetric.
Spatial dimensions don’t work that way. You can go up or down, back or forth, left or right, however you please, with equal ease (don’t be a tease). At least…you can do all that provided there are no strong influences nearby.
One such influence might be, for instance, a planet. I just happen to have such a planet, right here. It’s called Earth, and it is quite dense and so produces quite significant curvature of spacetime (time more than space, interestingly enough) in its vicinity.
This has the effect of making space asymmetric locally.
So, near a strongly gravitating object, space acquires directionality. That directionality is actually spherical, so it’s not a simple kind of one-dimensional directionality, but in local regions it looks linearly directional. Wherever you may be on Earth, odds are you can move any combination of left-right and forward-backward with equal ease (more or less). But the difference between up and down is quite another matter.
That difference would be even more pronounced near a much stronger gravitational source. If you were near the surface of a neutron star, your capacity to go any direction but down (i.e. toward the surface of the neutron star) would be more or less nonexistent. Space would have a profound and irresistible directionality. Things seem to become even more inevitably directional beneath the event horizon of a black hole.
And, analogously, when one is not far from a highly energetic, very low-entropy region of spacetime, like our Big Bang, time is forcibly constrained to be directional, since change can only really happen in the direction of lower entropy in such a region, as dictated by sheer mathematics, if nothing else.
I’ve written about this before, about how, in principle time could have more than one dimension, like space, but be so forcibly constrained by the very strong local effects of the Big Bang to be pseudo-linear, just as space is pseudo-planar at the surface of the Earth or a neutron star, with free movement in only two of its three dimensions.
I won’t get into it too much now; I think there are posts both here and on Iterations of Zero that address it. I will just quickly point out that, in the distant future‒much like when one is much farther from the surface of a gravitating body‒as entropy approaches local maxima, time will lose its directionality and forward and backward will be identical.
The fact that it takes so long for that to happen may point toward the geometry of time being less than three dimensional. Three dimensional influences fall off as the square of the distance. So, twice as far from a source, the influence is one quarter as strong, and ten times as far away, it is one one hundredth as strong.
The directionality of time doesn’t seem to be falling off at any notable rate since the Big Bang*. It doesn’t even seem to be falling off linearly, as would be the case for a two-dimensional process (the circumference of a circle increases linearly with the radius, whereas a sphere’s surface area increases as the square of the radius). Based on a fairly straightforward interpretation of this, it does seem to point to time being one-dimensional.
But we don’t know the scale of the thing. We may be, compared to the scope of any higher dimensionality of time, vanishingly close to the Big Bang, still. We may be like tiny, tiny mites on Earth’s surface (or that of a neutron star), unable to sense or travel a significant height to be able to detect even the local curvature of the planet, let alone the drop-off in the directionality of space (i.e., gravity).
Maybe the nature of time is similar. Maybe we are too small, moving through time too slowly, too close to its local source of directionality, to be able to discern that it has more dimensions. Certainly, spacetime around us appears “flat” as best we can measure. But we recognize that, at much bigger scales, it may be curved. And time, at those scales, may have more than one dimension.
Or maybe:

Maybe if we can wait long enough, it will be obvious. Or maybe not.
Have a good bit of time over these next 24 hours if you can, please.
*Though there is the current significant question of the nature of the “Hubble tension”. Maybe it’s a subtle change in the strength of the directionality of time itself that leads to the seeming disparity in the Hubble “constant” when measured by CMB as opposed to by supernova data. Hmmm.


