Is “Information” Eternally Conserved?

Conservation of information implies that the universe records every thought you’ve ever had. Just in case, I record my thoughts in journals. On the page above, which I wrote June 16, 2020, I record my reaction to encountering “conservation of information” on page 9 of Leonard Susskind’s Theoretical Minimum book on classical mechanics.

Hoboken, March 29, 2024. I’m a compulsive journal-scribbler. This habit, which goes back to my teens, has proved useful to my career; my books and articles invariably start as journal entries. But my motivation is not merely professional. If I don’t record my thoughts, I won’t remember them, and they won’t matter, or so I fear. This feeling has grown as I’ve aged.

Compounding my concern is the possibility—no, probability—that someday humanity and its artifacts will vanish. Everything we have thought and done will be for naught. If nothing about us endures, if nothing is remembered, we might as well never have existed.

No wonder so many of us, even in this materialistic age, still believe in God, an immortal, omniscient being who watches over each of us, and not just celebrities. He/she/they/it remembers us after we’re gone, like a cosmic backup device with infinite storage capacity. Supposedly. If this divine entity does not exist, and someday all traces of us disappear forever, in what sense do our lives matter?

Scientists are not immune to such anxieties. Existential angst, I suspect, accounts for physicists’ belief in conservation of information. I first heard about this proposition decades ago, but I only gave it serious consideration during my recent attempt to learn quantum mechanics.

Two of my primary texts were Theoretical Minimum books on classical and quantum mechanics by physicist Leonard Susskind (and co-authors), which impart “what you need to know to start doing physics.” One thing we need to know, according to Susskind, is that “information is never lost.” This law, Susskind asserts, “underlies everything else.”

Conservation of information is more fundamental, Susskind says, than Newton’s first law (motion is conserved); the first law of thermodynamics (energy is conserved); and what is sometimes called the zeroth law of thermodynamics (if systems A and B are in equilibrium with C, then A and B are in equilibrium with each other). Hence Susskind calls conservation of information the “minus-first law.”

The minus-first law encompasses the principle of determinism, which holds that if you know the current state of a system, you know its entire past and future. Susskind insists that quantum mechanics, although not deterministic in the same way as classical mechanics, still conforms to the minus-first law.

In the 1980s Stephen Hawking challenged the minus-first law when he proposed that black holes destroy information. Susskind rebutted Hawking in papers and a popular book, The Black Hole War: My Battle with Stephen Hawking to Make the World Safe for Quantum Mechanics. In a 2008 interview, Susskind says the minus-first law “underpins everything, including classical physics, thermodynamics, quantum mechanics, energy conservation, that physicists have believed for hundreds of years.”

That’s the back story. Now I’ll tease out implications of Susskind’s remarkable claim that “information is never lost.”

First, the concept of information--as defined by mathematician Claude Shannon, founder of information theory [see Postscript], as well as by physicists like John Wheeler--requires minds to be informed. Hence information assumes the existence of consciousness. If information is conserved, so is consciousness; if consciousness exists now, it must always exist. Or so the minus-first law implies.

And in fact many scientists and philosophers have proposed that consciousness is as fundamental as matter, or even more fundamental. I’ve lumped these speculations together under the label neo-geocentrism, because they resurrect the ancient, narcissistic notion that everything revolves around us. Neo-geocentric theories represent attempts to sneak a consoling religious assumption—this universe is all about us—back into science, and so does conservation of information.

If I had to rank laws of physics, I’d go with the second law of thermodynamics, which holds that  entropy always increases; our expanding cosmos is headed toward heat death, a state of terminal blandness in which nothing ever happens. The second law of thermodynamics trumps the minus-first law. I see evidence for the second law whenever I look in the mirror or read the news. Things fall apart, the center cannot hold.

Actually, I’m suspicious of all “laws” of physics, which strike me as manifestations of scientific hubris. Scientists take an assumption that applies under certain very tightly controlled conditions and exalt it as a cosmic principle applying to all things at all times in all places. I’m especially skeptical of the minus-first law. Never mind Hawking’s conjecture that black holes destroy information, I’m worried about more mundane processes.

My father recently died. He persists, sort of, in the fragmentary, fading recollections of those who loved him, like his wife, children and grandchildren. Polymath Douglas Hofstadter coined the heartbreaking phrase “soular coronas” to describe these memories of those eclipsed by death. But soular coronas inevitably dim and vanish.

The minus-first law implies that the universe will bear the imprint of my father’s life forever. Long after our sun and even the entire Milky Way have flickered out, our clever cyborg descendants could in principle (that handy, all-purpose hedge) reconstruct the lives of my father and every other person who has ever lived.

That’s a nice thought (which inspired the 1996 book The Physics of Immortality by physicist Frank Tipler.) But I don’t buy conservation of information any more than I buy reincarnation or heaven—or a god who cherishes us. These propositions, scientific and religious, represent understandable but finally unpersuasive attempts at consolation.

And so, as my end looms, I keep frantically filling up notebooks.

Postscript: Saturday, April 6, I am participating in a “celebration” of Claude Shannon’s work at Stevens Institute of Technology. For more information, see “From Bits to Qubits: A Celebration of Claude Shannon, Father of the Information Age.”

Further Reading:

Although I don’t buy conservation of information, I’m rather fond of a related idea, which I explain in Conservation of Ignorance: A New Law of Nature.

For more on death and conservation of information, see also Chapter Three of my book My Quantum Experiment.

Self-plagiarism alert: This is an enormously improved version of a paywalled Scientific American column.