“You’re thinking about time all wrong, according to our best physical theories. In Einstein’s general theory of relativity, there’s no conceptual distinction between the past and the future, let alone an objective line of “now.” There’s also no sense in which time “flows”; instead, all of space and time is just there in some four-dimensional structure. What’s more, all the fundamental laws of physics work essentially the same both forward and backward.”
“None of these facts are easy to accept, because they’re in direct conflict with our subjective experience of time. But don’t feel too bad: They’re hard even for physicists to accept, an ongoing tension that places physics in conflict not just with common sense but also with itself. As much as physicists talk about time symmetry, they do not allow themselves to invoke the future, only the past, when seeking to explain occurrences in the world.”
“When formulating explanations, most of us tend to think in terms laid down by Isaac Newton over 300 years ago. This “Newtonian Schema” takes the past as primary and uses it to solve for the future, explaining our universe one time-step at a time.”
“Some researchers even go so far as to think of the universe as the output of a forward-running computer program, a picture that is a natural extension of this schema. Even though our view of time has changed dramatically in the last century, the Newtonian Schema has somehow endured as our most popular physics framework.”
“But imposing old Newtonian Schema thinking on new quantum-scale phenomena has landed us in situations with no good explanations whatsoever. If these phenomena seem inexplicable, we may just be thinking about them in the wrong way. Much better explanations become available if we are willing to take the future into account as well as the past. But Newtonian-style thinking is inherently incapable of such time-neutral explanations.”
“Computer programs run in only one direction, and trying to combine two programs running in opposite directions leads to the paradoxical morass of poorly plotted time-travel movies. In order to treat the future as seriously as we treat the past, we clearly need an alternative to the Newtonian Schema.”
“And we have one. Most physicists are well aware of a different framework, an alternative where space and time are analyzed in an even-handed manner. This so-called Lagrangian Schema also has old roots and has become an essential tool in every field of fundamental physics. But even physicists who regularly use this approach have resisted the last obvious step: thinking of the Lagrangian Schema not just as a mathematical trick, but as a way to explain the world. Perhaps we haven’t been taking our own theories seriously enough.”
“The Lagrangian Schema doesn’t just allow future-based explanations. It demands them. By treating the future and the past on the same footing, this framework avoids paradoxes and makes new explanatory opportunities available. And it just might be the viewpoint that physics needs for the next major breakthrough.”
“The first step toward understanding the Lagrangian Schema is to fully set aside the temporal “flow” of Newtonian thinking. This can best be done by treating spacetime regions holistically: considering the full duration all at once, rather than as sequential frames of a movie. We can picture regions of spacetime as bounded four-dimensional structures, with not just spatial boundaries, but also temporal boundaries—the initial and final bookends of the region.”
“All of classical physics, from electricity to black holes, can be expressed via the simple Lagrangian-based principle of “least-action.” To use it on a spacetime region, you first describe how physical parameters are constrained over the entire boundary. Then, for each set of possible events inside that boundary, you calculate a quantity called the “action.” The set of events with the lowest value of the action is the one that will actually occur, given the original boundary constraints and a few other technical caveats.”
“For instance, when a ray of light travels from point A to point B, the action corresponds to the amount of travel time. The actual path is the fastest route, given the intermediate obstacles. By this way of thinking, a light ray bends at a glass interface simply because it minimizes the overall travel time. The Lagrangian Schema works a bit differently in quantum physics and yields probabilities rather than decisive predictions, but the basics are the same: Spacetime boundary constraints are still imposed all at once.”
“By Newtonian logic, this sounds quite strange. The light ray at A seems to possess foreknowledge (about point B and future obstacles), vast computational ability (to survey the different paths), and agency (to choose the fastest one). But this strangeness is merely evidence that Newtonian and Lagrangian thinking don’t mesh—and that we probably shouldn’t anthropomorphize light rays.”
“Instead of explaining events via only the past, the Lagrangian Schema starts with the entire boundary constraint—including, crucially, the final boundary. If you don’t impose a final constraint—for light rays, the location of point B—this approach fails to give the proper answer. But if used properly, the success of the mathematics indicates a clear logical priority of the boundary constraint: The boundary of any spacetime region explains the interior.”
“The Lagrangian approach provides the most elegant and flexible account of known physics, and physicists often prefer it. Still, despite the wide applicability of Lagrangian-based principles, even the physicists who use them don’t take them literally. It is hard to accept that events might be explained by what goes on in the future. After all, there are obvious distinctions between past and future. Given that we see such an evident arrow of time, how could future boundaries possibly matter just as much as past ones?”
“But there’s a way to reconcile the Lagrangian Schema with our causal experience. We just have to think sufficiently big, without losing sight of the details.”
“One lesson here is that satisfying explanations account for complicated events in terms of simple givens. They take a single fact, with just a few relevant parameters, to explain a plurality of events. This should be evident no matter which schema one is using.”
“But this asymmetry of A and B is not a rebuttal to the Lagrangian perspective, which merely says that A and B together can best explain the details of what happens in between. Even in the Lagrangian Schema, A and B are not independent of each other. To see how they’re related, we need to think bigger. According to the boundary framework of the Lagrangian Schema, explanations don’t chain. They nest. In other words, we don’t picture event A leading to event B leading to event C. Instead, we treat a small spacetime region in its entirety; then we treat this region as part of a larger region (in both space and time). Applying the same Lagrangian logic, the larger boundaries should now explain everything in their interior, including the original boundaries.”
“Running this procedure for the statue example, we find the same asymmetry of bulb and illumination writ larger. That is, we find a satisfying explanation for the camera flash in its past, but we don’t explain the illumination of the statue by looking to its future. Then we can enclose that larger system in an even bigger one, and so on, until we have gone all the way out to the cosmological boundary—the external constraints on our entire universe. To the best of our knowledge, we see the same asymmetry at that scale: an unusual, smooth distribution of matter near the big bang, and greater disorder in the future.”
“Looking at ordinary spacetime regions from a Lagrangian perspective, the fact that initial boundaries (light rays diverging from flashbulbs) are simpler than final boundaries (lit statues) is strong evidence that our closest cosmological boundary lies to our past. The consistency of this ordering implies there is no corresponding cosmological boundary in the comparable future. So given the big bang as our best explanation of the obvious features of our universe, the evident direction of time is essentially no different from the spatial temperature gradient you feel when standing next to a cold window. In neither case is space or time asymmetric; it’s just a matter of where you are located relative to the nearest boundary constraint.”
“On the classical scales that we typically observe, we don’t get any new information from the future boundary that we didn’t already have in the past. If this held true at all scales, the Lagrangian Schema would be in trouble, because the future boundary wouldn’t really matter at all. But in fact it isn’t true when we get down to the level of quantum uncertainty: Microscopic future details cannot be deduced from only the past. And the quantum scale is where the real power of the Lagrangian Schema becomes evident.”
“Addressing such questions might not just help physics; it might also inform how we see ourselves as part of our four-dimensional universe. For example, according to the Lagrangian Schema, microscopic details in any region are not entirely constrained by the past boundary. On the level of the atoms in your brain, there are relevant but unknown constraints in the future. Perhaps this line of thinking could even help to explain our sense of free will, by providing a new sense in which the future is not purely determined by what has come before. Certainly it would require us to rethink the idea that there is a neat and objective difference between a fixed past and an open future.”