Where has Bitcoin gone, and how far can it go?

This article originally appeared in Bitcoin Magazine’s „Moon Issue.“ To get a copy, visit our store.

Bitcoin’s potential reach among the world population is unlimited in terms of memetic knowledge dissemination. In part due to its increasing adoption, Bitcoin is widely considered a technology that has or will alter the course of humanity.

But in terms of physical reach, where has Bitcoin been? Where could it go? In this essay I intend to demonstrate how Bitcoin pioneers into the cosmos, literally, and how we will use it as we migrate as a species from the Earth. 

REACH 

Let us define reach as the physical distance of a funded key pair, a piece of bitcoin, a UTXO, from Earth.

Most bitcoin transmitted via hobbyist radio waves into space are garbled and reflected off the Earth’s ionosphere. Like all electromagnetic waves, radio waves in a vacuum travel at the speed of light, and through the Earth’s atmosphere at a close but lower speed. Those broadcasts that make it through the ionosphere travel at the speed of light.

If the furthest radio transmitted bitcoin made it through the ionosphere intact, and we optimistically presume they passed the ionosphere in 2012, they will have enjoyed a travel of just about 10 light years by this time. That’s 58.8 trillion miles or 94.6 trillion kilometers.

Bitcoin sent as radio waves, despite being massless, are subject to the laws of thermodynamics, however, which means they are subject to entropy as anything else. While it is tempting to imagine the furthest bitcoin from Earth are still traveling, the data representing these far-flung radio bitcoin weaken with distance and time.

As a radio signal distances itself from its transmitter, the field strength of the radio waves decreases as the inverse square of the distance traveled because the energy of the transmitted wave diffuses across space. This means the signal of the furthest radio-broadcasted bitcoin is at most one-fourth as strong as those just half that distance. This means that no bitcoin broadcast into the universe will maintain its dominant position, distance wise. Bitcoin’s reach expands and contracts as newer and stronger signals surpass the reach of the older and faded.

The furthest Bitcoin signal will probably be, if it has not already been, broadcast via laser, but without a receiver or amplification relay in space or on another planet, these laser bitcoin are also subject to degradation over distance in time.

The law of conservation of mass and energy states that the amount of energy can neither be created nor destroyed. The total energy of our Bitcoin radio waves is conserved, though scattered across space. By the time most radio signals reach 100 light years (588 trillion miles or 946 trillion kilometers) away, they become so attenuated and weak as to be basically undetectable. Private keys transmitted as radio waves will eventually devolve into noise, gradually, then suddenly cease to be.

SUPERPOSITION 

The furthest bitcoin has likely already been broadcast via radio into the cosmos. The question is, are its private keys known or orphaned?

The most distant private key can be known or unknown to anyone. Bitcoin is agnostic to our knowledge about it.

The most distant bitcoin UTXO with a known private key could be spent. In which case it would cease to be the most distant bitcoin. If its private key is unknown, it could still be spent, but the likelihood is considerably smaller that this would happen.

If we assume that the data describing the key pair of the bitcoin furthest from us hasn’t yet been reproduced anywhere on Earth, then we could call those bitcoin orphaned, and next to unspendable.

Data is by definition copyable. The probability that these far-flung Bitcoin private keys could be spontaneously replicated is next to zero.

But it isn’t zero. In mathematics, the pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must hold more than one item. The pigeonhole principle applies to Bitcoin private keys as well.

At the greatest estimate, there are 10^82 atoms in this universe.

Though difficult to imagine, the realm of possible Bitcoin private keys is both finite and considerably smaller than the number of atoms in this universe. There are just under 2^256 possible Bitcoin private keys out there and the same number of public keys. While one can recover a public key with a private key, it is impossible to derive a private key using only the public key. Take n here to mean the number of Bitcoin private keys in existence. 

There are 2^160 possible Bitcoin addresses out there. Take m to mean the number of Bitcoin addresses in existence: 

It is unlikely two addresses for the same private key will be realized by us, but there is a considerable non-zero probability this could happen. Each Bitcoin address corresponds to roughly 2^(256-160) = 2^96 private keys, as n > m

There are 2^96 private keys for any given Bitcoin address, meaning all Bitcoin addresses could in theory be spent by multiple parties. The likelihood, however, of discovering one, let alone two private keys that can sign for an occupied Bitcoin address is so astronomical, that all the world’s current and near future computing power would be better spent simply mining bitcoin instead.

The bitcoin now furthest in distance from Earth could in theory be cracked and spent, thereby losing its dominant distance to the second furthest. Though in actuality, this is so improbable as to be negligible. Even if it became feasible to crack Bitcoin’s current encryption, the chain would be incentivized to fork, upgrade and resolve itself.

So, if we assume that at least some of the private keys corresponding to 2012-era UTXOs were lost, these can safely be considered the farthest bitcoin in space — up until the point where their radio waves devolve into noise.

TIME CONSTRAINT 

Now let’s move from the present to the future. How far could the furthest actual Bitcoin users be? There will always be opportunities to expand Bitcoin’s reach. Let us assume Bitcoin mining will be (near-)Earth bound for the foreseeable future. One of the consequences of the second law of thermodynamics is that a certain amount of energy is necessary to represent any data, including that of Bitcoin private keys. Once energy has been expended to make and represent a private key, corresponding public keys, and Bitcoin addresses, their individual maintenance costs are insignificant, unlike the maintenance cost of the network as a whole.

Thermodynamically sound data can travel no faster than light in a vacuum, which means data representing bitcoin will incur a minimum time penalty when sent anywhere in any form, though this penalty is trivial for Earth-bound routes on human time scales. For example, if you sent your bitcoin via light wave on a perfect course around the equator, it could circle the globe approximately 7.5 times in one second.

Radio waves take 1.28 light seconds to travel the average 238,900 miles to the moon. Thus, future moon dwellers’ copy of the Bitcoin ledger will be a minimum 1.28 seconds out of date. Their batched final settlement transactions will also take at least 1.28 seconds to be received on Earth. This is a showstopper neither for making nor receiving payments.

This time delay will also not inhibit Bitcoin mining on the moon, though moon message propagation to and from the Earth will always incur a minimum time penalty of about 2.56 seconds. This is not great but can perhaps be compensated for with increased solar-powered energy efficiency on the moon.

Using bitcoin becomes more complicated on an interplanetary scale, because there is considerable time dilation between the planets. An interplanetary internet could be built on a cosmic computer network. The network would be made of nodes, the nodes consisting of planetary satellites and ground-dwelling lander robots and stations. A laser-powered telecommunications network of amplifiers, relays and receivers would populate the solar system, trading bandwidth over time and distance for Bitcoin. Technology and protocols that are tolerant to large delays and errors will be developed for the internet and for bitcoin to function economically across planets.

Mining bitcoin from, say, Mars would be uncompetitive, however, barring Bitcoin’s hash rate moving much closer to the red planet itself. A hash rate migration would signal an extreme change for life on Earth. In order for this to occur, great portions of the global hash rate would have to leave the planet.

The further the distance from the majority of hash power, the fewer blocks a mining pool can win due to the minimum communication time penalty incurred. A Bitcoin mining pool may be competitive even hundreds of thousands of miles away, but as its distance from Earth increases, the pool can only win fewer blocks due to the minimum communication time penalty incurred. At some distance the spacefaring mining pool will cross a horizon after which it will no longer win any blocks at all.

For any Bitcoin signal, there will be a distance at which it becomes indistinguishable from the background noise of the universe. Entropy would have it that all signals fade in time. The distance our broadcasted bitcoin can be received intact depends on the initial strength of the transmission, assuming the waves are not running into other celestial bodies or being warped as they pass by supermassive objects. Inevitably some do encounter these cosmic fates, preventing them from moving smoothly through the vast vacuum of space.

Remember, sound doesn’t travel at all through the vacuum of space. Most of the universe is silent. In order to be heard, your radio bitcoin must first be received or else the waves diffuse slowly, faintly through the universe and faintly diffusing, like the ascent of their last end, upon all the matter and the void.

HOME BASE 

Although Bitcoin is a relatively decentralized technology on a human scale, in the grand cosmic scheme of things its production will probably always be centered on or near Earth, the moon, and perhaps space stations orbiting the Earth, although its reach extends far beyond. 

Increasing time penalties due to the speed of light barrier on data transportation will make moving the majority of Bitcoin’s hash rate very far from Earth impractical under most circumstances. The exception to this would be events that put Earth’s population, and, therefore, its Bitcoin economy and large percentages of its mining pools at risk. Internal, external, anthropogenic or non-anthropogenic risks could all play a factor in whether bitcoin will always be mined on Earth.

However, Bitcoin will remain useful both on and off Earth. Outside of cosmic Bitcoin broadcasts, communities of offworld beings can transact and develop their economies using Bitcoin’s second layers such as the Lightning Network. They can even achieve batched final settlement, though in that future, the price of final settlement will be high and additional security measures will be necessary to protect transactions en route to the most up-to-date copy of the Bitcoin ledger.

This means future offworld dwellers will use and transact in bitcoin and its emergent layers. They will also run their own (time lagged) nodes, however, they will be dependent on their laser or radio broadcast bitcoin being received on Earth, and just as dependent upon Earth’s transmission of good ledger data back to them. One would think this would drastically and irrevocably tip the scales of power toward the Earth, however, bitcoin is a power as well as a token. It is the ability to send energy regardless of geographical location, provided there are means of transmission and reception. Outside of holding bitcoin, offworlds will transact, and Earth’s economy will remain highly incentivized to receive their bitcoin.

The question becomes what value will offworlds provide in exchange for bitcoin? Entertainment via novel data? Cosmic VR experiences perhaps? Maybe stake in the real estate of foreign planets.

In the event the space dwellers find themselves ostracized or at a political and economic disadvantage, or should Earth be destroyed or come under threat of destruction, they may choose to abandon Bitcoin altogether in favor of their own blockchain whose hash rate they can control. In this way, the offworlds will be able to determine the lengths of their dependence, the limits of their endurance, their own fate. Overcoming interplanetary time-lag and hash rate complications is perhaps the only practical use case for blockchains outside of Bitcoin.

Although Bitcoin is a revolutionary technology for humans, a consideration of the grander scheme reveals that it is not a fundamental force in the universe. Rather, the evolution of technology, Bitcoin’s longevity, is beholden to entropy and the passage of time. Bitcoin are but rejoinders to the cosmic storm. It is our engineering of cosmic receivers and transmitters, the expansion of our nodes, that will make bitcoin the first native currency of space.

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