Doctor Whom and That Stubborn Arrow of Time

Currently, there is a trend among popularizers of scientific method to mistreat Time as a discrete "stuff," even when it isn't explicitly articulated that way. Many thinkers believe that they are giving you a clear understanding of Time when they explain Time in terms of entropic physics, or the known general tendency of well-ordered material systems to be subject to a high probability of becoming more and more chaotic or disordered over the course of Time. Of course, this is a demonstrable fact, such as when you break an egg. Stuff gets messy, and in such a way that it becomes nearly impossible to simply "reverse" the matter by some act of the will. As Adam Becker points out, it is almost always easier to just wash up than unbreak an egg.

Time's arrow does seem to always point "one way" (though what "one way" means here isn't exactly a unified spatial direction for all local events), even if all the known physical laws, described pristinely through the language of mathematics, does not prevent us from articulating a reversal of the equations of nature. According to these theorists, the act of Time reversal appears entirely possible, if only almost infinitely improbable. Now, it should be evident to many that there is something of an unsatisfying itch in this explanation. If the mathematics of nature truly allows for such a reversal, why then does it remain so utterly problematic to engineer a mechanical device that would allow us at least to reverse even a small portion of the space-time framework?

This question leads us to keep in mind a central fact: physics does not operate in an existential vacuum. In order to further clarify this fact, let us engage in a thought experiment: Let us suppose that there is a theoretical physicist whose sole aim is to engineer a technologically advanced device which will allow for some small region of three-dimensional space, however infinitesimal, to transcend the usual arrow[s] of Time, and kick it[/them] into reverse. Let's call him "Dr. Whom".

Dr. Whom is as ingenious a fellow as we might hope to allow for, and he is as well-funded as Batman.  But he still has fundamental physical problems to overcome. From the outset, in order to isolate this teensy-wheensy little bit of Space from the rest of the flow of spacetime, so as to bring about this reversal, he will have to dissociate this space-stuff from the fact that every single dimension of space is entirely pervaded by, and quite plausibly even entirely constituted by, the prior arrow[s] of Time. That is, he will have to live in a world in which space and time are not unified.

This should give us pause to consider what it is we are asking for when we ask how to enable a device to reverse the Time stream. Are we asking for Time to lose its vector altogether? (and would not a putative Time which at the same time lacked a vector be, to all evidence, without any Spatial character?) Are we asking for the reversal of a Time that is the unity of all times? Or for the reversal of a separable Time (or set of times) which is isolatable from other Times? Or are we simply stuck with thinking in Kantian-Newtonian terms, in which Time might be regarded as a purely conceptual force, a non-reality which exists only as a convenient fiction?

One thing is for sure, Time can only be entirely differentiated from Space if we can divide Space and Time into discrete "things". And it is not at all obvious that we can do this. Indeed, if Einstein's theories of special and general relativity are entirely correct—so that there is not a basic three-dimensional space plus a one-dimensional time, but only a four dimensional spacetime—then such a separation is wholly impossible, without exception.

We can get greater clarity on this problem by considering what our Dr. Whom has been forced to reckon with. This little, itty bitty piece of spacetime which he is trying to reverse necessarily has no means of differentiation from the spacetime around it. That is, spacetime is a fully continuous, fully unified phenomenon (the metrical differentiation is a conceptual artifice, a symbolic distinction, indicating two functions of spacetime, but not two things as such). What device then could succeed in separating this little "space" from the spacetime around it?! The device itself would of necessity be constructed with spatiotemporally constituted matter and energy, and this would suggest that in order to isolate this little "island of space", the good Doctor would need to reverse the space it was directly contiguous with, and this contiguity would hold "all the way up", from the smallest spatiotemporal scales to the greatest cosmic scales; in other words, the only way Dr. Whom could reverse this little piece of spacetime would be to reverse all spacetime, everywhere. And this would necessarily require an infinite amount of energy.

"Why?" you ask? Well, think of it this way: If Dr Whom was feeling a little more ambitious, and wanted to reverse the orbit of the Earth, he would need also to reverse the Galactic orbit of the Sun, because of the way that rotational inertia works. And likewise, if he wanted to reverse the Galactic orbit of the Sun, he would necessarily need to reverse the vector of the whole friggin' Milky Way! In fact, if he wanted to reverse the vector of the whole Milky Way, it is likely that he would have to reverse the universal phenomenon of inflation (I think you can see where this is going by now). So, while in extreme abstraction, the mathematics of physics seems to allow for this reversal, the omnipotent fiat existential fact of a prior arrow of Time, the one that already exists everywhere and everywhen, has an infinitely overwhelming advantage in predetermining the general direction of the flow of causal events.

Now, it may be possible that there are some fundamental laws which can be described regarding the function of inflation, so that in time it may become possible to shortcut the reversal method I have imagined above, but until then, I must remain something of a teapot skeptic toward the hope for a functional theory of Time reversal. Pending that much, Time still leads the way for my common-sense intuitions about causation and the fatal force of that enduring arrow.