Can an abstract measuring system and a mass noun have a direction? This then depends on what ‘direction’ means, but it does infer a predetermination. It is borrowed from the spatial dimension abstract as already mentioned, and hence comes pre-loaded with connotations and expectations.
As has been stated, time is either an abstract measuring/calibration framework (how can that have a direction); or it’s a mass noun. Perhaps a mass noun can have a direction, but surely it’s the underlying components of the set that the mass noun refers to (in this case a set of events/change) who’s ‘direction’ we are fundamentally concerned with?
Time doesn’t have a ‘direction’, though irreversible change can make it appear so. Irreversible change happens, not necessarily to a simple change element, but in composite entities the complexity of multiple interacting change streams will prevent symmetric reversal of all change streams together in synchronisation.
So you can’t get back to exactly how it was before (unless you are dealing with simple, isolated systems). In other words, change happens (and is ‘directionless’ too unless you consider trillions and trillions of particles all doing their own, sometimes random, thing a ‘direction’) – but there’s no going back.
But irreversible change (e.g. scrambling an egg) may cause change to seem like a direction. That’s more about treating the composite egg as if it were a single change object – it’s not, its millions of individual (component) change elements each with their own change streams. The change in the egg from whole to scrambled isn’t reversible, but the change of any single simple component particle or element might be.
Perhaps it’s change that has the direction, not time.
The “Arrow of Time”
The Arrow of Time is a notion supposedly invoked to help explain time (Carroll, S (2010, all From Eternity to Here). It is based on the tendency for successive events to behave in a particular (i.e. non-random) manner.
It may be that the second law of thermodynamics makes successive events tend toward higher entropy. But what has that got to do with explaining time? It doesn’t give time a ‘direction’ it gives event outcomes a ‘direction’. Time just gives relative measurement or calibration to the events. How can either an abstract framework or a mass noun have a direction?
[Not only that, but to make the assertion that time has an ‘arrow’ would imply a complete understanding of the nature of time. If that understanding of the nature of time doesn’t exist (and it doesn’t else why is this intended as a part explanation of time – this is kind of circular), then how can one assert that time has a direction?]
I suggest this notion should more accurately be called the “Arrow of Event Outcomes”, not the “Arrow of Time”.