Here's a topic that's always mystified me. Go back to the late 17th century. Newton and Leibniz had both independently developed calculus, and, when they weren't bickering over who deserved credit, they were disagreeing about the metaphysical nature of time. Newton believed that space and time were real and independent from each other. No, countered Leibniz, time and space are just two interrelated ways of ordering objects: "For space denotes, in terms of possibility, an order to things which exist at the same time, considered as existing together." Clever. But most physicists ended up siding with Newton—our basic intuition is that space and time both exist, and are separate from each other.

But then things got tricky. Once general relativity was formulated, we suddenly had this notion of space-time as a continuous fabric. In Einstein's universe, how time flows depends on one's location. In places where gravity is weaker, time runs faster. Technically, you age slightly more rapidly living in a penthouse than you would living down on the street level—think of it as a small dose of cosmic income redistribution. So that's one troubling little chink in Newton's theory.

Then we get even bigger problems burrowing down into the quantum universe, where it's not clear that time is even a relevant concept. How would you measure it? There are experiments to nail down all sorts of qualities about particles—their position, their momentum, their spin—but not how they mark time, or how long they'll stay in a certain place. Or, rather, there are plenty of ways to try to measure that, but all result in wildly different answers. Not only that, but electrons and photons don't even appear to be bound by the arrow of time; their quantum states can evolve both forward and backward. An observation of certain particles in the present can affect their past natures, and so on.

So how are we supposed to reconcile all this? Some scientists now seem to think that maybe Leibniz was right all along, and we should reconsider his argument more carefully. In a recent issue of New Scientist, Michael Brooks interviewed Carlo Rovelli, a theoretical physicist at the University of the Mediterranean, who argues that the simplest approach to time is to stop talking about how things change over time and, instead, just talk about how things relate to each other: "Rather than thinking that a pendulum oscillates with time and the hand of a clock moves in time, we would do better to consider the relationship between the position of a pendulum and the position of the hand." The notion of time is only a meaningful metaphor when dealing with, say, human experience. It's useless, Rovelli argues, for most of the universe.

That's a bit wild, and maybe we don't want to abandon Newton just yet. So one potential way to preserve time as a really-existing entity has been offered up by Lee Smolin, who argues that the reason scientists haven't been able to reconcile quantum physics and relativity—and bring the laws of the universe under one tidy grand theory—is that they aren't accounting for the fact that the laws of physics can evolve over time. In the early moments of the universe, after all, we know that the electromagnetic and weak forces were rolled up together. So why can't we see other such evolutions? Time is fundamental—it's just the laws of physics that change. (And, fair enough: There's no logical reason why the laws of physics have to be eternally true—they've only really applied for less than 14 billion years.)

Then there's the weird fact that the arrow of time always seems to move forward, as encapsulated by the second law of thermodynamics, which holds that the entropy or disorder in the universe is always increasing. That explains why cream mixes with your coffee over time—technically, it would be possible for me to dump in some cream, mix it around, and then have the two liquids sort themselves out: milk on top, coffee on bottom. But this is staggeringly unlikely from a statistical perspective, and the most probable states are some sort of mixture. Time moving in reverse—i.e., the milk and coffee "unmixing"—is very, very, very, very, unlikely. (Very.) So unlikely from a statistical perspective, in fact, that it basically doesn't happen.

But that raises at least one squirm-inducing question: How did the universe, then, start out at a low-entropy, extremely orderly state (which has been getting messier ever since) in the first place? Sean Carroll wrote a whole article in Scientific American earlier this year about this and outlined one possible (and possibly wacky) solution:

This scenario, proposed in 2004 by Jennifer Chen of the University of Chicago and me, provides a provocative solution to the origin of time asymmetry in our observable universe: we see only a tiny patch of the big picture, and this larger arena is fully time-symmetric. Entropy can increase without limit through the creation of new baby universes.

Best of all, this story can be told backward and forward in time. Imagine that we start with empty space at some particular moment and watch it evolve into the future and into the past. (It goes both ways because we are not presuming a unidirectional arrow of time.) Baby universes fluctuate into existence in both directions of time, eventually emptying out and giving birth to babies of their own. On ultralarge scales, such a multiverse would look statistically symmetric with respect to time—both the past and the future would feature new universes fluctuating into life and proliferating without bound. Each of them would experience an arrow of time, but half would have an arrow that was reversed with respect to that in the others.

The idea of a universe with a backward arrow of time might seem alarming. If we met someone from such a universe, would they remember the future? Happily, there is no danger of such a rendezvous. In the scenario we are describing, the only places where time seems to run backward are enormously far back in our past—long before our big bang. In between is a broad expanse of universe in which time does not seem to run at all; almost no matter exists, and entropy does not evolve. Any beings who lived in one of these time-reversed regions would not be born old and die young—or anything else out of the ordinary. To them, time would flow in a completely conventional fashion. It is only when comparing their universe to ours that anything seems out of the ordinary—our past is their future, and vice versa. But such a comparison is purely hypothetical, as we cannot get there and they cannot come here.

Hm. These are things I don't really understand at all (feel free to drive that point home in comments!) and wonder if it's even worth the effort to try. Probably not. The other maddening fact about time is that there's not, alas, ever enough of it.