Benjamin Franklin once quipped in a letter to a friend that “in this world nothing can be said to be certain, except death and taxes.” Perhaps taxes are timeless but death is not so. Rather, it is intimately linked to the direction time flows — the arrow of time. If time flowed backward, I would say that nothing is certain except birth and taxes. (Or maybe “sexat dna htrib”.)
Most people talk about the arrow of time in the context of the 2nd law of thermodynamics, the law that entropy always increases with time. But this “law” is statistical, and it is a classical law based on classical assumptions about physics that we know, in the context of quantum physics, to be false.
People also talk about how all dynamics in the universe are time reversible. That means that if you watch a video run forwards or backwards the path of each and every particle in that video obeys the same laws of physics. It is only the aggregate paths of those particles that gives you an idea of which direction is forward.
But all dynamics in the universe may not be time reversible if this one quantum law is not correct. This is called the law of unitary evolution.
Unitary evolution is at the heart of all questions about time reversibility including the black hole information paradox (the death of which has been greatly exaggerated.) If unitary evolution is true, then time really is reversible and the arrow of time is a mystery. If it is false, then time reversibility is likewise false and the arrow is built into the true laws of physics — we just got ours wrong.
To understand what unitary evolution is, you have to know a little quantum physics. Rather than get into the mathematics of Schrödinger’s equation (where it pops out), I am going to explain it from the perspective of the quantum measurement paradox.
The quantum measurement paradox is best explained by the double slit experiment. In this experiment, a laser is trained on a barrier containing two closely spaced, narrow slits. On the opposite side of the barrier is a screen where the light from the laser is recorded. The laser is tunable so that it can emit only individual light particles. We can see these particles show up as individual dots on the screen.
When we send a lot of light through the barriers at once, they form a pattern of light and dark bars from the waves passing through the two slits and interfering with one another.
If we fire individual light packets, called photons, at the barrier, they show up as dots on the screen but also obey the same interference pattern.
The interference pattern suggests that the photon is somehow traveling through both slits, despite being a single particle. If you put detectors in front of each slit, however, you find that you only ever detect the photon going through one slit at a time. Never both. Sometimes called wave-particle duality, it tells us that photons are waves and particles at the same time.
The reason the photon appears to go through both slits at once is intimately connected to unitary evolution. Before you detect it, the photon’s position appears smeared out across space, including going through both slits. So the path through the left slit and the right slit are in what is called superposition with one another. You can think of superposition as the photon being in more than one place at a time. When you detect the photon, however, it only shows up in one place. No one has ever observed a superposition state directly.
Yet, it is only when superposition states are maintained in the wavefunction that the wavefunction’s evolution can be said to be unitary — meaning that all probabilities of paths add up to one. As soon as part of the superposition disappears, all probabilities no longer add up to one, and the wavefunction has evolved into a non-unitary state.
This isn’t just a problem of being uncertain about the photon’s position since the interference pattern shows up even for individual photons. If you were only uncertain, the photon would have nothing to interfere with. It also is not the case that the photon is actually smeared out since it shows up as individual dots and not smears of light.
The transition from superposition of positions to a single position is sometimes called wavefunction collapse. The wavefunction is a representation of the photon before it is detected. We don’t know what the wavefunction is or even if it represents a real thing. What we do know is that out of the many choices of positions of the photon that appear in our equations that it seems to occupy, only one ever appears in a measurement.
If wavefunction collapse is real, then unitary evolution is false and if unitary evolution is false then time has an arrow. This is because wavefunction collapse is far more likely than wavefunction uncollapse in the forward time direction. (Uncollapse is possible but rare.) Just as the possibility of the photon being in multiple places exists simultaneously and then vanishes, the march of time then is overall collapse of all possible realities into one. If on the other hand wavefunction collapse is a mirage, then unitary evolution may be true.
This has implications far beyond the arrow of time. One of the nice features of unitary evolution is that it is information preserving. With unitary evolution, information is never lost nor gained in the universe. The same cannot be said even about energy. Despite being enshrined in the 1st law of thermodynamics, the theory of gravity, general relativity, does not conserve energy. It can create and destroy energy at will and may have for the Big Bang to have occurred out of nothing.
Philosophically, anything that is, by its own nature, eternal can guarantee the existence of other things. If nothing is eternal, however, then it is infinitely more likely that nothing would exist. The reason is because in infinite time all finite things have the opportunity to cease to exist. Thus, if nothing is eternal, then it is likely that all things would cease to exist at some point. If nothing exists, then nothing can cause anything else to exist, so non-existence would be the ultimate fate of all things. This is the basis for the Cosmological argument for the existence of God — God is a necessary eternal being for anything to exist at all. If information is eternal, however, then information, through unitary evolution, would guarantee the continued existence of the universe.
By accepting unitary evolution, we lose the arrow of time (at least derived from wavefunction collapse) but we gain so much more. Unitary evolution not only guarantees information preservation and therefore an argument for existence, it also guarantees basic laws of physics like conservation of energy laws (not counting that lost or gained because of general relativity). If unitary evolution is fundamental, it also suggests that general relativity may need modification in order to account for it — solutions to information paradox notwithstanding.
If unitary evolution is false, we need to modify the equations of quantum physics to model the reduction of the wavefunction upon measurement. That turns out to be extremely difficult because we can’t say what constitutes an actual measurement. Quantum interpretation pioneer John Bell pointed this out in the 1960s. You can’t draw the line between microscopic particles and macroscopic instruments. In fact, any theory that depends on an explicit definition of measurement, unitary or not is doomed to fail for this reason. All you can say is that quantum effects are small in some places and large in others. So some have turned to nonlinear, stochastic (stochastic=theory with random noise) evolution theories that give the appearance of wavefunction collapse but don’t explicitly model measurement. These dynamic reduction theories are inherently non-unitary since they are nonlinear, and they do not preserve information.
If these theories are true, they may also explicitly model information loss in black holes. The nonlinear evolution of particles would constantly shed information. This might be a good thing for some interpretations of physics because it is never a good thing to have big exceptions in a theory. Black holes may be such an exception to information preservation, but current research suggests that they are not.
If unitary evolution is true, however, then what is going on with the photons?
That gets into quantum interpretation theory. If the wavefunction does not collapse it can mean that (1) the wavefunction is not a real thing, (2) there is some underlying reality that, added to the wavefunction, creates what we measure, or (3) we just aren’t seeing the whole wavefunction because of something about either us or the wavefunction’s nature. It could also be a combination.
If the wavefunction is not a real thing, then it means that the equations of quantum physics are more like probability theory. The wavefunction is actually a measure of uncertainty or a measure of deviations from classical reality. Certain interpretations of quantum physics that propose a universe that always has a single classical state from the Big Bang on, like consistent histories and superdeterminism, take this view. They model the particle as having a definite state all along that is simply hidden from us.
The second option assumes that we are measuring something other than the wavefunction. Created in the 1950s by David Bohm, Bohmian mechanics says the wavefunction is a real thing, called the guiding function. The guiding function, however, is not the entire, complete state of the photon. Rather, the guiding function guides the particle to form an interference pattern. You can think of the guiding function as being like the harddrive for the particle. It preserves all information about the particle including all possible states, positions, and so on about it. Assuming unitary evolution, everything would have a guiding function, even human beings, that contains all possible lives we could have lived (or more correctly that the particles in us could have experienced). The guiding function, from this perspective, is like the ghost of what might have been, following us around forever and occasionally nudging us in one way or another as it does the photon.
The third option would be that the whole wavefunction is somehow present and we just aren’t seeing it. There are quite a few ways to interpret the wavefunction this way. You can either say that the whole wavefunction is there but we can’t observe all of it because some aspects are suppressed such as with superselection. Or that it only has one “real” property and the rest is invisible but somehow there like the modal interpretation. Or you can say the issue is us. This last one gets into Everettian Many Worlds (Multiverse) interpretations and its cousin the Many Minds interpretation. In that case, the ghostly guiding function is actually a real set of copies of either you physically or your conscious mind.
There are more interpretations that combine different aspects of these. Yet all of them preserve unitary evolution in one way or another.
If information is eternal in the universe (however you want to interpret that given general relativity and the Big Bang), then as information theoretic beings, humans may exist forever. Once you exist, you never cease to exist because you are part of the information content of the universe. The information in our minds and in our pasts is always reconstructable, just scrambled.
If on the other hand, wavefunction collapse occurs through some nonlinear, stochastic process, that process can simply reduce you out of existence. You wouldn’t be scrambled. You would be erased. Why the universe exists at all in that case is a complete mystery.
Reichenbach, Bruce, “Cosmological Argument”, The Stanford Encyclopedia of Philosophy (Spring 2021 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/spr2021/entries/cosmological-argument/>.
Giddings, Steven B. “Black holes, quantum information, and unitary evolution.” Physical Review D 85.12 (2012): 124063.
Okon, Elias, and Daniel Sudarsky. “The black hole information paradox and the collapse of the wave function.” Foundations of Physics 45.4 (2015): 461–470.
Bassi, Angelo, and GianCarlo Ghirardi. “Dynamical reduction models.” Physics Reports 379.5–6 (2003): 257–426.