Stir a drop of ink into a glass of water and the drop is gone. Not gone. Count the molecules and every one of them is still in the glass. What happened to the ink is that it got spread out, shared evenly with everything around it, until the local concentration dropped below anything you could see. That is mixing, and mixing is a different thing from deletion.
Physics has no delete key. It only has a stirrer.
I want to push that as far as it goes, because it goes further than most people find comfortable, and because the place it ends up is stranger than the place it starts.
Two kinds of loss
There is a kind of loss that costs something. Erasing a bit of information dissipates at least kT ln 2 of energy as heat, which Rolf Landauer worked out in 1961 and which people have since measured in the laboratory with real devices. Irreversibility and heat generation in the computing process, and the experimental check is Bérut and colleagues in Nature in 2012. So deletion exists, it is physical, and it has a bill attached to it.
Then there is a kind of loss that costs nothing at all. Nobody has to do work for ink to spread through water. It spreads on its own, immediately, and no amount of care stops it. This is the loss the second law of thermodynamics is actually about.
We use one word for both, and I think that is the source of the surprise. Erasure is rare, deliberate, and expensive. Mixing is constant, free, and the default behaviour of anything left alone. Almost everything we experience as loss is the second kind, and the second kind does not destroy anything.
The equations have no delete key
Start with the classical picture. A system of particles evolving under ordinary mechanics preserves the volume of its phase space, which is Liouville’s theorem, and the flow is invertible. Run the equations backward and you get the earlier state, exactly. Nothing in the dynamics throws anything away.
The quantum version is stricter. Evolution is unitary, so two distinct states stay distinct forever, and the no-hiding theorem that Braunstein and Pati proved in 2007 makes the point sharper still: quantum information cannot be destroyed, and it cannot even be hidden away in correlations, because if it leaves one subsystem it has to show up somewhere in the rest of the universe. Quantum information cannot be completely hidden in correlations.
This was not obvious, and it was not accepted for a long time. Loschmidt pointed out in 1876 that every irreversible process has a reversed movie that satisfies the same laws, so the laws cannot be the reason the movie only runs one way. Zermelo followed with a recurrence argument that seemed to make the second law impossible. Boltzmann’s answer is the one that survived: the second law is not a prohibition, it is a statement about counting. There are overwhelmingly more ways for a system to be scrambled than ways for it to be ordered, so a system is not forbidden from returning to its past, only outvoted. Lebowitz’s version of that argument is the one I keep going back to. Boltzmann’s entropy and time’s arrow.
So the past is not destroyed. It is outnumbered.
Why it still looks gone
Two things do the work, and neither of them is deletion.
The first is chaos. Reversing the dynamics is formally allowed and practically hopeless, because the inverse map is unstable. Any error in your knowledge of the current state grows exponentially, so the precision you would need to run the equations backward to a specific Tuesday doubles on a short timescale and keeps doubling. The information is intact and the recovery is not merely hard, it is unstable in the technical sense. A near miss does not give you a near answer.
The second is decoherence. When a quantum system interacts with its surroundings, the information about it does not vanish. It leaks into the correlations between the system and everything it touched, which is what Zurek’s work on einselection is about. Decoherence, einselection, and the quantum origins of the classical. To read what happened you would have to measure the environment, which means essentially all of it. The information is not gone, only distributed, and distributed turns out to be worse than gone.
This is why the second law gets described as a statement about knowledge. Jaynes made the case in 1957 that entropy is a measure of what you do not know given the constraints you have, rather than a substance that accumulates. Information theory and statistical mechanics. I should flag that this reading is not the only one and not universally accepted. Some physicists argue irreversibility is a physical fact about the world rather than a fact about our ignorance, and the disagreement is live. But for the question of whether the past still exists, the two sides agree. Nobody thinks it was deleted.
Even black holes only stir
The best test case is the one that looked like it might break the rule.
Hawking’s calculation in the 1970s implied that a black hole radiates, shrinks, and disappears, taking whatever fell in with it. If that were right, information would be destroyed, unitarity would fail, and the whole picture above would be wrong. The argument ran for about forty years.
Don Page had already worked out in 1993 what unitarity would require. The entanglement entropy of the outgoing radiation should rise for a while and then fall back to zero, a shape now called the Page curve, and the falling half cannot happen unless information is coming back out. Information in black hole radiation. Then in 2019 and 2020, several groups computed the entropy of the radiation directly from gravity using the island formula and replica wormholes, and the Page curve came out. Penington and Almheiri and colleagues are the papers I would start with.
The reading I take from it is that even the most destructive object we know of turns out to be a very good mixer. It scrambles what falls in beyond any hope of reading and then radiates it back out into the universe, which is what the stirrer does to the ink.
I want to be careful here, because this is quantum gravity adjacent and it is built on assumptions rather than on a measurement. The statement I am confident in is that the current best description of black holes is unitary. The statement that information provably survives a black hole is a claim about a theory that is not finished.
The part nobody has explained
If everything is reversible, there is an obvious question nobody has answered. Why was the universe ever ordered in the first place?
Reversibility explains why you cannot recover the past, and it says nothing about why the past was worth losing. The equations are time-symmetric, so a universe that starts scrambled stays scrambled, and a universe that starts ordered gets scrambled, and both of those are equally consistent with the dynamics. The reason we have a past to mourn at all is that our universe started in an extraordinarily low-entropy state, and that assumption, usually called the past hypothesis, is an assumption. It is doing enormous work in every argument about the arrow of time, and it is the one piece that nobody has derived from anything else.
The second thing to be honest about is that “recoverable in principle” is nearly empty. It is a claim about an observer who can see the whole universe, has unlimited precision, and is not part of the thing being observed. No such observer exists, and the interesting physics is about observers who are inside. For anything inside the room, the mixing is total, and the phrase in principle is doing no work at all.
So the honest version of the wild claim is this. Nothing is deleted, and that does not help you, because deletion was never the problem.
What follows, if it is true
Preservation is a fight against mixing, not against destruction, and mixing runs on a clock. Once you see it that way, storage stops being an engineering preference and becomes a question about a substrate.
What is the mixing time of the thing holding your data? A magnetic domain on a hard drive is metastable, and it relaxes slowly, and that slow relaxation is what we call bit rot. Bit rot is not decay into nothing. The stored pattern gradually loses its distinction from the noise around it. Paper kept dry and dark is a remarkably low-mixing substrate, which is why archives on paper keep outliving the formats that replaced them. Flash memory traps charge in a way that slowly leaks, and the leak is mixing.
Only two levers exist. You can isolate the thing from the environment that would stir it, or you can copy it faster than the stirring happens. Every storage strategy ever devised is one of those two or a combination, and the rest is decoration.
Which gives a colder way to state the second law than the one in the textbooks. Operationally, it is the reason your files cannot be recovered. Not because they were destroyed. Because they were shared with the room.
What I take from it
The past is not gone. It is entropied. Everything that has ever been lost is still in the room, spread across every particle in it, entangled with everything that touched it, and the reason it cannot be handed back to you is not that it stopped existing.
The universe keeps everything. It just stops telling you where.