Physicists talk about conservation of information. It is a fundamental law of classical physics—information cannot be lost or destroyed. Stanford physicist Leonard Susskind calls it the zero-minus law because it comes before all other laws—before the first laws and even before the zeroth laws.[1]
It means that each moment in time includes information about the state of the universe in that moment and every moment leading up to that moment. The location and momentum of every microscopic particle in a system, together with the forces and fields interacting with those particles, comprise the complete specification of the system in that moment. From that complete information, it is possible to determine exactly the state of the system in the immediately prior moment. And with that information comes the information about the state of the system prior to that. The entire prior history of a system, including the universe, is time reversible from the information contained in any one moment.
The result is that information about every prior moment is never lost. It cannot be lost. It exists in the full specification of every subsequent moment and the operation of the laws of physics on the particles, forces, and fields interacting in the system.
Not just the “important” information, but all information
The information in that moment includes everything about the system that could possibly be known. It is not limited to information that we have the practical means of discovering or knowing, but includes all the information, whether we know it or not. Theoretically, the complete specification of the system includes information about every element of physical existence in the universe at that moment.[2] That means the state of every planet, star, and galaxy, every molecule, atom and subatomic particle, and every entity of any kind. That includes information about all of biological existence, every cell and neuron in the brain of every entity. Even our thoughts and desires, which at some level arise from our physical existence, are included in the record of that moment.[3]
Are the past and the future as real as the present?
Einstein believed in what is called a “block universe”. He believed that conservation of information and the principle of relativity demonstrate that the flow of time is an illusion created by our perceptions. In the reality beneath our perceptions, time is not absolute, and the past and the future are as real as the present. If that view is correct, then the record kept by the universe may reflect more than a trail of time-reversible moments; it may reveal a universe in which every moment lives forever, in which moments actually do not die. We may exist even after we seem to die, as do those who came before us, and those that come after. We all exist because all moments exist at once in the block universe.
Is the record kept forever?
Physicists debate what forever really means. Black holes exist throughout the universe, and nothing, not even light, escapes a black hole. Stephen Hawking posited the possibility of radiation escaping from the event horizon of black holes as they dissipate over time. But we do not know if the physical information in so-called “Hawking radiation” is time-reversible in any meaningful way. If not, then the information about any particle that falls into a black hole is not conserved, but lost forever.
There is also the possibility that the universe will end its existence in a state of maximum entropy or “heat death”, with all information seeped away in a great expanse of dissipated nothingness. If that is the future universe, then all memory of our existence may be lost in that final state of maximum entropy, without any possibility of time-reversible recreation of the moments leading up to that state. But physicists have also theorized that our universe is one in a cycle of universes, that our universe will not die in a state of information-free nothingness, but rather will evolve to an end-state which could serve as the foundation of a new universe. Information about our universe could influence the wave function of the next universe, which then could influence another, on and on.[4]
Is conservation of information only a hopeful dream?
It is a comforting thought to imagine that we and all our loved ones exist forever in a physically possible block universe. But is it wishful thinking? Do physicists theorize about information recovery simply as a form of consolation?[5] Do we imagine that the universe will remember us to feel better about the inevitable loss of all that we and other humans are? Will Shakespeare and all his creations—and everything ever thought or created by any human—cease to exist without any record whatsoever? We want to believe that the universe keeps a record of our existence that cannot be erased, that exists for all time.
But time may not be what Einstein believed it to be. Time may pass. And not come back.
The block universe requires one arrow in and one arrow out
Conservation of information is based on the premise that both the past and the future can be calculated from the present. There must be one arrow in from the past and one arrow out to the future.[6] But quantum mechanics tells us that the arrow in may not tell the full story of the past and the arrow out may be only one of many possible futures. Conservation of information may not be absolute.
The future is probabilistic, but random
Evolution of particles and waves in the subatomic quantum world is governed by the quantum wave function described in the Schrödinger equation. Continuous evolution under the Schrodinger equation is time symmetric, even time-reversible, meaning the equations can be solved backward or forward, predicting the future or describing the past. The wave function produces weighted amplitudes that predict with great accuracy the evolving probabilities of a range of outcomes in the future. But the Schrödinger equation predicts only probabilities; it cannot predict the specific outcome of any one event. Specific outcomes are governed by a second phase of the quantum wave function, called quantum state reduction, in which the continuous evolution of the wave function devolves or reduces into discontinuous evolution and the probabilities resolve themselves into specific unique occurrences in the macroscopic world. Effectively, the dice are thrown, and the range of probabilities described by the equation is replaced by a single outcome—a unique event in time. There is no way to know in advance what that unique event will be. The equations predict the likelihoods of different events, but the actual unique outcome in each instance is a random result that occurs somewhere within the range of probabilities.
That means there is more than one possible arrow out to the future. The block universe may be less settled (or blockish) than we once thought.
The unrealized possibilities of the past are not recoverable
Perhaps even more significantly, the arrow in from the past cannot be reconstructed in its complete form based on information about the present. After the second phase of the wave function results in a specific random outcome, it is not possible to determine the shape of the wave function that preceded it. The weighted amplitudes of the Schrödinger equation, as well as the probabilities predicted by those amplitudes, cannot be recalculated from the outcome of the quantum reduction process. We can observe the result of the process, but we can no longer calculate the range of probabilities that produced that result. One possibility occurs, and all others are forgotten.
An imperfect record
We are left with a situation in which the future is probabilistic in general, but unpredictable in a specific instance; the future always has an element of randomness. The past also cannot be recreated fully from the present. We can find the specific event that preceded the present moment and track the string of present moments that resulted from the evolution of the wave function, but we cannot recreate the range of possibilities and probabilities that generated that string of moments. The logical conclusion is that the future is never completely known, and the possibilities of the past are lost forever.
So yes, there is a record kept. But the record is incomplete and likely impermanent. Moments are created in time, and time may not be eternal. Even if it were, time records only moments that actually occur in the macrocosmic world. Time is not a record of the manifold possibilities inherent in the microcosmic quantum world. In that world, there may be no record at all. Moments as we know them may not exist in that world. Moments come into being when the dice are thrown, when a unique outcome results from the second phase in the evolution of the wave function. It is that moment that is recorded in the temporal history of the universe. All other possible moments are lost to the macrocosmic world. They continue to exist, if at all, only in the great lake of quantum interaction from which all possibilities spring.
[1] “We could call it the first law, but unfortunately there are already two first laws—Newton’s and the first law of thermodynamics. There is even a zeroth law of thermodynamics. So we have to go back to a minus first law to gain priority for what is undoubtedly the most fundamental of all physical laws—the conservation of information.” Susskind (2013), p. 9 (emphasis in original).
[2] “[C]onservation of information implies that each moment contains precisely the right amount of information to determine every other moment.” Carroll (2016), p. 34. Information is here defined as “the ‘microscopic’ information: the complete specification of the state of the system, everything you could possibly know about it. When speaking of information being conserved, we mean literally all of it.” P. 34.
[3] “[T]he universe keeps a faithful record of the information about all you have ever said, thought, and done.” Hossenfelder (2022), p.14.
[4] Penrose (2010).
[5] Horgan (2020).
[6] “The conservation of information is simply the rule that every state has one arrow in and one arrow out.” Susskind (2013), pp. 9-10.
