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- to tend toward higher entropy.
Professor Carrol never actually demonstrates how this observation therefore explains the nature of time. Time merely seems to measure the impact of entropy. [A basic observation, he makes the assertion that time has an ‘arrow’; making this assertion implies he has a complete understanding of the nature of time. But his understanding of the nature of time doesn’t exist (else why is this intended as a part explanation of time – this is kind of circular), then how can he assert that time has a direction?]
A dimension can’t have a direction – it is abstract, it merely calibrates and indexes. So Professor Carroll must be referring to the ‘flow’ of time (not that he differentiates). Surely a ‘flow’ can have a direction – rivers flow downstream for example.
But are we talking about the ‘flow’ of time or the flow of change? Isn’t time just the collective noun? It is change, the underlying objective reality, that ‘flows’. Is it change that has the direction, the arrow?
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. And compound change (as opposed to quantum change) is sequentially dependent.
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, energy is dissipated – and 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.
Really, it’s change that has the direction, not time.
Change may have a direction, but change (unlike Time the mass noun) is event or reference-frame specific. ‘Arrow of time’ implies a universal time objective; Time might be a universal calibration, but that’s abstract; the underlying reality of change, is reference-frame or quantum specific.
I suggest this notion should more accurately be called the “Arrow of Change”, not the “Arrow of Time”. There are zillions and zillions of individual of ‘Arrows of Change’.
Units of time or units of change?
From the framework of the earth’s motion, we have constructed units of time; years, hours, days, minutes seconds and so on.
It’s worth bearing in mind that in fact these units of time are actually units of change; they are based upon regular event-series – the constant stream that is the earth’s continual motion..