Schrödinger’s Bitcoin

The Center Cannot Hold: 9

“I always go to sea as a sailor, because they make a point of paying me for my trouble, whereas they never pay passengers a single penny that I ever heard of. On the contrary, passengers themselves must pay. And there is all the difference in the world between paying and being paid. The act of paying is perhaps the most uncomfortable infliction that the two orchard thieves entailed upon us. But BEING PAID,–what will compare with it? The urbane activity with which a man receives money is really marvellous, considering that we so earnestly believe money to be the root of all earthly ills, and that on no account can a monied man enter heaven. Ah! how cheerfully we consign ourselves to perdition!” – Moby Dick

Schrödinger’s cat is a thought experiment in quantum mechanics that demonstrates a paradox of quantum superposition.

Quantum superposition states that any two or more quantum states can be added together to form a valid quantum state, while at the same time, every quantum state can be represented as the sum of two or more distinct states.

In terms of fungibility, Bitcoin is in a quantum state. Bitcoin is both fungible and not. All Bitcoin share all of their attribute set with the rest, but many unspent transactions do not trace the same path through time. (Legacy addresses may be spent in near future blocks, so they too are fungible and have a unique transaction history.) Bitcoin are fungible to the extent that each is interchangeable, meaning 1,000 satoshis of mine and 1,000 satoshis of yours share all the same set of Bitcoin characteristics, and all can be spent. Whether or not humans have access to their private keys, Bitcoin do not lose their protocol. Though the probability that lost private keys will be discovered can reach near zero, it is not zero, even though functionally, socially or economically, we can behave as though lost coins are off the table without consequence.

The ledger history of each unspent transaction is unique. Virgin coins from the same block sent to the same address are one and the same. But at the same time every unspent Bitcoin is primed to take on several and collective histories in later blocks. In this way Bitcoin exist in a quantum superposition of states: unspent/spent. One cannot in good conscience say any coins will never move, even if it is exceedingly unlikely that lost keys will be discovered, even if some coins have never moved.

There will be Bitcoin offered at a premium or a discount based on their history. There is already a premium on some non-know-your-customer Bitcoin, or newly minted Bitcoin. Many would for example certainly pay a bit of a premium for coins moving for the first time directly from a wallet of Satoshi. However, this is more of a premium on a service, a premium on novelty, an over valuing, a premium on privacy, a handling fee of Bitcoin rather than a premium expressed by the Bitcoin proper.

Much of what a Bitcoin is is dormant. A generous total transaction value of 150,000 BTC per day is .714286% of the terminal 21,000,0000 BTC on the network that are moving each day. You could say your Bitcoin are built to be hodled.

There are of course coins that have never moved. Most have not moved for varying lengths of time. Some percentage of those 150,000 BTC worth of daily transactions are the same coins extending their history across the ledger several times within 24 hours. So on one hand you have Bitcoin that evidence life with their activity and transaction history, and on the other you observe a dormant network. A superposition of activity and inactivity.

In quantum superposition, a quantum system such as an atom or photon can exist as a combination of multiple states, corresponding with different possible outcomes. In the Schrödinger’s cat experiment, a hypothetical cat can be considered both alive and dead at the same time as a result of subatomic events that may or may not occur. The experiment was a result of a conversation Erwin Schrödinger had with Albert Einstein in 1935.

In some ways, our Bitcoin exist as a combination of multiple states, collapsing into either spent or unspent when we check the ledger.

What does it mean to consign our Bitcoin to cold storage? It means that we have a rational or irrational conviction that our private keys will remain private or at the very least, that our Bitcoin will remain orphaned and dormant.

There are many clever solutions to provide us with greater conviction that our Bitcoin may remain unspent. This does nothing, however, to negate the innate ability Bitcoin have to be consigned a new place in the ledger. In this way Bitcoin are fungible, primed for transaction, yet many are idle, existing solely as stores of value across space and time.

In another way, Bitcoin exists as both particle and wave. Bitcoin blocks become more stable, more consigned to dormancy over time. In this metaphor, they would be particles. But the time chain is ever growing. It is a dynamic wave. We often envision and talk about Bitcoin as a token, a particle virtually and in some cases even physically instantiated, yet Bitcoin is also merely the state of a ledger which is expanding.

There is a related theory, from which the Schrödinger’s cat experiment arose. That theory is called the Copenhagen Interpretation, which states that until a quantum system interacts with, or is observed by the external world, it remains in superposition. When the system is observed, it collapses into one or another of the possible wave particle states. Schrödinger, in his correspondence with Einstein about his experiment, acknowledged it was useful in illustrating the absurdity of quantum mechanics. Many physicist’s today however, take the experiment as a quite literal example of quantum mechanic’s complex nature.

Take again the generous estimate that .714286% of the terminal Bitcoin supply is moving on any given day, those Bitcoin are the ones that are being interacted with. Those transactions are at some moment validated or invalidated, but in all cases energy is being expended to measure them and allot them or cast them from blocks. Those are the coins we, the network, have interacted with on some level for some amount of time. Thus, they have collapsed from superposition to either and both spent or unspent. The question is whether and to what extent the rest of the chain is in superposition.

Although we can replicate information about unspent Bitcoin without changing them, and validate that they are indeed not presently being spent or allotted to a block in the mempool, that is not the same thing as interacting with them. So the question remains, are unspent Bitcoin, and the vast majority of the time chain at any given moment, in a state of superposition?

In Schrödinger’s own words: “One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.”

Replace the living and dead cat in a box with a Bitcoin signing device and a node. The signing device and node will broadcast a transaction for 100 sats (including a relatively high fee) immediately upon being connected to the internet. Whether or not it does this is dependent upon the following: In a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay flips a switch which brings the node online

Schrödinger’s continues, “It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naïvely accepting as valid a “blurred model” for representing reality. In itself, it would not embody anything unclear or contradictory.”

“There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks,” he wrote.

One interpretation of this experiment is that while the box is closed, the system exists in a superposition of the states undecayed nucleus / unspent Bitcoin, and decayed nucleus / spent Bitcoin, simultaneously. In the original experiment, only once the box is opened and an observation is made does the wave function collapse into one state or the other.

In our distributed Bitcoin network, the point of observation is legion, and geographically independent. Schrödinger’s experiment poses the question: ”when does a quantum system stop existing as a superposition of states and become one or the other?” It also demonstrates how these microscopic quantum states dictate the larger scope of our observable universe.

Our human experience would suggest that we can not be in an alive and dead or other state at once, though the experiment would suggest one can and is. Does the state of the Bitcoin ledger require an external observer at all?

In response to Schrödinger’s absurd experiment, Einstein wrote: “You are the only contemporary physicist, besides Laue, who sees that one cannot get around the assumption of reality, if only one is honest. Most of them simply do not see what sort of risky game they are playing with reality—reality as something independent of what is experimentally established. [. . .] Nobody really doubts that the presence or absence of the cat is something independent of the act of observation.”

In the many-worlds interpretation of quantum mechanics, observation is not a special process. Rather, both the spent and unspent coins would persist after the experiment, though they are in decoherent states from one another. That would mean, there is a universe in which an observer finds their wallet continues to have 100 unspent satoshis, and also one in which an observer finds their wallet empty, their Bitcoin spent. Although, these universes have no communication or effective interaction with each other. Through opening the box, an observer’s state becomes entangled with and corresponds to that of the cat, or in our case the state of the time chain.

These mechanisms of quantum decoherence are the same that produce what is known as consistent histories. Decoherence prevents us from observing the other state. For example, in this theory, your car may have started this morning, but in another state, in another universe, it also did not, though you have no way to communicate with the state of yourself whose car wouldn’t start.

Such split realities and superimposed states have been achieved with photons when cooled to near absolute zero. A beryllium ion has also been trapped in a superimposed state. Experiments of this nature have been proposed for the flu virus and bacterium. In quantum computing, several qubits achieve a superimposed state of both 0 and 1 simultaneously.

The many-worlds interpretation of Bitcoin would have it that multiple time chain histories exist, but do not to affect each other, for if they did, they would become entangled, and merge to form a single history. Once you experience Bitcoin you become entangled. We have in one way or other agreed upon this single history.

Decoherence prevents us from viewing that other world, the one where Bitcoin failed, or we failed to find it.

17 October 2021

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