OrbitalHub

 

 

Abstract

This post explores what happens to proof-of-work cryptocurrency protocols once the network stretches across the solar system and beyond. Cryptocurrencies are here to stay, and it is plausible that future colonists will prefer a decentralized currency over a fiat currency issued by a distant central authority. Ubiquitous access, independence from exchange-rate and interest-rate policy set on another planet, and freedom from financial institutions serving foreign interests are strong arguments in an emerging exo-economy.

It is tempting to assume that relativistic time dilation would be the main threat to an interplanetary proof-of-work network. Running the numbers says otherwise: inside the solar system, time dilation is a rounding error, and the real enemy is the finite speed of light. This post works through both effects and sketches designs that could hold up.

Motivation

Today, information broadcast by a node reaches nearly every other node within a few seconds. The Internet spans the Earth’s surface and low Earth orbit, so the worst-case path is a fraction of a light-second long.

That stops being true the moment the network leaves Earth’s neighborhood. Approximate one-way light delays:

Link, One-way delay
Earth to LEO satellite: a few milliseconds
Earth to Moon: about 1.3 seconds
Earth to Mars: about 3 to 22 minutes, depending on orbital positions
Earth to Jupiter: about 33 to 53 minutes
Earth to TRAPPIST-1: about 40 years

Once delays approach the block interval, the network starts to suffer: more communication failures, more frequent and longer blockchain forks, and eventually segregation into local sub-networks (let us call them topological forks). For deep-space links, the plumbing is not TCP/IP either. NASA and others use Delay/Disruption-Tolerant Networking (the Bundle Protocol), which stores and forwards data across links that are slow and intermittently available.

Nullius in verba, as they say. Let’s go into the details and figure out what a truly interplanetary cryptocurrency would need.

Cryptocurrency 101

Think of a cryptocurrency as a digital money ecosystem. It combines decades of research in cryptography and distributed systems: a decentralized network of computers, a public transaction ledger (the blockchain), a set of transaction validation rules, and a decentralized consensus mechanism [ANTO].

The network. Computing power and data are spread across many nodes. Every full node keeps a copy of the ledger, so the network survives disruption, including physical damage to individual nodes.

The blockchain. A public, distributed ledger of every transaction the network has accepted. Each block holds as many transactions as fit within the network’s block size or weight limit. Transactions name the sender, the receiver and the amount or asset changing hands. Each block contains the cryptographic hash of the previous one, a backward link that runs all the way to the chain’s Genesis block. Tampering with any old block changes its hash and breaks every link after it.

Validation rules. Every node checks every transaction. The most common fraud attempt is double spending, so nodes verify that each transaction’s inputs exist and have not already been spent. Invalid transactions are rejected and never reach the chain.

Consensus. The consensus mechanism lets all nodes agree on which transactions go into the next block. It replaces the authority of a central clearing house with a network of nodes that do not trust each other, and do not need to, because the protocol enforces the trust.

The Proof-of-Work

Satoshi Nakamoto proposed proof-of-work consensus in 2008 [NAKA]. A proof-of-work is a piece of data that is costly and slow to produce but trivial to verify. Think of a semester project: it takes you a whole semester to finish, and your supervisor an hour to grade.

To add a block, a miner must find a nonce that makes the block’s hash fall below a target. The only way to find one is brute-force guessing, so a miner’s chance of winning the next block is proportional to its share of the network’s total hash rate. The network retunes the target so that blocks arrive at a fixed average interval. For Bitcoin that is 10 minutes, with difficulty recalculated every 2,016 blocks (about two weeks).

When two miners find blocks at nearly the same moment, the chain forks briefly. Nodes resolve it by following the chain with the most accumulated work. This is how Nakamoto consensus reaches agreement without a trusted authority.

Then and now. For years, proof-of-work was the de facto consensus mechanism. That is no longer true. Ethereum switched to proof-of-stake in September 2022 (“the Merge”), and most newer networks use proof-of-stake or other Byzantine-fault-tolerant designs. Bitcoin, the largest network by value, remains proof-of-work, and it is the reference case for the rest of this post.

Why latency breaks it. The longest-chain rule quietly assumes that a new block reaches everyone much faster than the block interval. If a block takes d seconds to reach the bulk of the hash rate, and blocks arrive every T seconds on average, the chance that a competing block appears in the meantime is roughly:

$$
P_{text{stale}} approx 1 – e^{-d/T}
$$

On Earth, d is a few seconds and T is 600 seconds, so stale blocks are rare. For a miner on Mars, d is 3 to 22 minutes, giving a stale probability of roughly 26% to 89%. Mars miners would also spend those minutes hashing on top of a block that Earth has already buried. Their effective reward collapses, they have no reason to stay honest participants, and the network segregates. That is the topological fork from the motivation, and it happens long before relativity enters the picture.

Enter the Ansible

We have no technology that communicates quickly and reliably across interplanetary, let alone interstellar, distances. Consider a mining corporation in the TRAPPIST-1 system, about 40 light-years away in the constellation Aquarius, paying a planetary engineering firm in the Sol system. The payment would take about 81 years for the round trip, plus the block confirmation time.

Science fiction already offers a fix. Readers of Rocannon’s World [LEGU], where Ursula K. Le Guin coined the word in 1966, and of Ender’s Game [CARD] will know the ansible: a device that sends and receives messages over any distance with no delay.

One honest caveat before we lean on it. Special relativity says there is no universal “now”. Two events that are simultaneous for one observer are not simultaneous for another moving relative to the first. An instantaneous link is therefore instantaneous only in some chosen frame, and combining such links with moving observers can deliver a message before it was sent. The ansible is not just beyond our engineering; it is in tension with the physics the rest of this post relies on. We will use it anyway, because it isolates a cleaner question: if latency vanished, would relativity still hurt proof-of-work?

The Special Theory of Relativity

Before upgrading the protocol, we need the physics of how time and distance depend on the observer’s frame of reference.

Einstein received the 1921 Nobel Prize in Physics, awarded in 1922, “for his services to Theoretical Physics, and especially for his discovery of the law of the photoelectric effect.” Relativity was famous by then but still controversial, and the committee chose not to cite it.

Einstein set out to reconcile two principles: the principle of relativity, and the constancy of the speed of light. His well-known thought experiment uses a train [EINS]. A passenger walks toward the front at speed w relative to the train, while the train moves at speed v relative to the embankment. Classical mechanics says an observer on the embankment measures the passenger’s speed as W = v + w. Replace the passenger with a beam of light and the same rule gives v + c, contradicting the principle that light travels at c in every inertial frame. Einstein resolved the contradiction by giving up absolute time.

The Lorentz transformation. Before relativity, time was absolute, independent of the observer’s motion. After it, every inertial frame has its own time, and a statement about time must say which frame it refers to. Requiring that light moves at c in every inertial frame leads to the Lorentz transformation between a frame K and a frame K′ moving at velocity v along the x axis:

$$
x’ = gamma,(x – v t), quad y’ = y, quad z’ = z, quad t’ = gammaleft(t – frac{v x}{c^{2}}right), qquad gamma = frac{1}{sqrt{1 – v^{2}/c^{2}}}
$$

Here γ is the Lorentz factor. Letting c go to infinity makes γ equal 1 and recovers the Galilean transformation of classical mechanics (x′ = x − vt, t′ = t), where both distance and time are absolute.

Time dilation. The corollary that matters here: a clock moving at speed v relative to an observer runs slow as measured by that observer. If Δτ is the interval between two ticks in the clock’s own rest frame (its proper time), the observer measures:

$$
Delta t = gamma,Deltatau
$$

Since γ ≥ 1, the observer always measures the longer interval.

Real frames are not inertial. A clock on Earth’s surface rides a rotating planet orbiting the Sun, so strictly it is not in an inertial frame. For most purposes the approximation works, but precise timekeeping must also account for gravity. General relativity adds gravitational time dilation: clocks deeper in a gravitational well tick slower. GPS is the everyday proof [ASHB]. Satellite clocks run about 7 microseconds per day slow because of their orbital speed, and about 45 microseconds per day fast because they sit higher in Earth’s gravity well. Without the net correction of roughly 38 microseconds per day, GPS positions would drift by kilometers within a day.

Relativistic Effects on Proof-of-Work

The twin paradox is the classic illustration of time dilation. One twin travels on a relativistic spaceship and returns home to find the other twin has aged far more. Fly fast enough or long enough, and several generations pass on Earth during the trip. Orson Scott Card used exactly this in Ender’s Game [CARD]: Mazer Rackham, the pilot who ended the Second Formic Invasion, is sent on a relativistic round trip so that, decades later, he can train the next commander while having aged only a few years.

Now put a mining sub-network on a fast-moving ship, connected to the rest of the network by an ansible. Measured in Earth’s frame, the ship’s hardware runs slow by the factor γ, so it computes fewer hashes per Earth-second.

The tempting fix. One could treat this as a fairness problem: lower the proof-of-work difficulty on the ship by the Lorentz factor, so relativistic miners solve an easier puzzle, and shorten their block confirmation time.

Why that does not work. Proof-of-work is not a race against the clock; it is a measure of computation. Chain weight is accumulated work, and the protocol never asks how long a miner took. A time-dilated miner is, to everyone else, simply a slower machine, exactly like an older ASIC on Earth. Bitcoin does not lower difficulty for slow hardware, and it should not lower it for fast-moving hardware either. A lower difficulty on the ship means cheaper blocks, which means either the ship’s blocks count for less chain weight (so the discount cancels out) or they count the same (so the ship can out-produce Earth at a fraction of the cost). Worse, the discount is triggered by a claim that nobody else can verify: any node that can fake a slower beacon gets cheaper blocks. Fairness in proof-of-work is measured in hashes, and the network should keep a single global difficulty.

How big is the effect, anyway? For realistic solar-system traffic, it is negligible:

Scenario, Clock rate difference vs Earth, Effect on hash rate
Mars miner (orbital speeds up to tens of km/s, plus gravity difference): on the order of 1 part in 100 million: about a millisecond per day
Ship at 0.5c: γ ≈ 1.15: about 13% fewer hashes per Earth-second
Ship at 0.87c: γ ≈ 2: half the hashes per Earth-second

Compare the first row with the 26% to 89% stale-block penalty that light delay imposes on the same Mars miner. Inside the solar system, latency is the whole problem and relativity is a footnote. Relativity only matters for ships moving at a large fraction of c, and even there the right response is to accept the lower effective hash rate, not to discount the difficulty.

Where clocks do matter: timestamps. Proof-of-work protocols do care about clocks in one place. Block timestamps must fall within a tolerance of network time, and difficulty retargeting is computed from them. A node whose local clock is dilated, or sits in a different gravity well, will drift away from everyone else’s notion of time. The fix is the one astronomers already use: define a single coordinate time for the network (for the solar system, something like Barycentric Coordinate Time, TCB) and have every node convert its local clock to it. A simple beacon does the job. If an Earth-side ansible broadcasts a tick every fixed interval of network time, a node that counts its own seconds between ticks learns its clock rate relative to the network and can correct its timestamps. (With ordinary light-speed beacons instead of an ansible, the measured interval would be dominated by the Doppler shift from the node’s motion, not by γ alone, and would need to be separated out.)

A More Down-to-Earth Solution

Let’s fork the storyline (pun intended) back at Enter the Ansible and drop the faster-than-light link. Light delay is now the constraint, and there are several ways to live with it.

1. Peripheral nodes relay, Earth mines. Mining stays on and around Earth, and nodes on Mars or elsewhere only relay transactions and verify blocks. A Martian payment confirms after roughly twice the one-way light delay plus the confirmation time: on the order of an hour or more. Its weakness is an eclipse attack. A local miner can feed Martian nodes a fabricated chain until the real one arrives minutes later. Martian merchants therefore cannot trust anything that has not been confirmed by blocks that demonstrably came from Earth’s hash rate, so local commerce waits on interplanetary round trips.

2. One currency, local settlement layers. Keep a single base chain for interplanetary settlement, and run fast local systems on each world: a Mars-side payment channel network, a sidechain, or a rollup that periodically anchors its state to the base chain. Everyday payments on Mars clear in seconds; only the net balances cross the gap. The catch is that today’s channel designs rely on time-locked dispute windows, which would need to be far longer than any interplanetary round trip.

3. Separate local chains, trustless exchange. Each world runs its own chain, with a block interval and consensus tuned to its own network. Value moves between them through atomic swaps or bridges. This accepts the topological fork as a feature rather than fighting it. It mirrors how separate economies already trade, but bridges have been among the most frequently exploited components in crypto, so this layer needs the most scrutiny.

4. Consensus with finality. Proof-of-stake and other Byzantine-fault-tolerant protocols finalize blocks once a supermajority of validators agrees. They avoid probabilistic forks, but each round of voting is bounded by the slowest validator, so an interplanetary validator set would finalize at the pace of light delay. A local validator set per world, with periodic cross-world checkpoints, is the more practical variant.

Whichever design wins, one incentive rule still holds: for every node, the reward for staying honest on the shared network must outweigh anything it could gain by cheating locally.

Concluding Remarks

The ansible is fiction; the rest is not. Running the numbers gives a clear answer: inside the solar system, the speed of light breaks proof-of-work long before time dilation does. Relativity’s real lesson for an interplanetary protocol is about clocks, not difficulty: pick one coordinate time and convert everything to it.

Thank you for working through this exercise with us. Cryptocurrencies have kept reshaping finance in recent years, and as a species we will go far beyond low Earth orbit. History suggests that decentralization is key to resilience and prosperity. The protocols that follow us out there will have to be designed for the delays of space from day one. Let us make that future happen together.

Image: A futuristic city on Mars, built under a vast geodesic glass dome around lakes and parks, with tower blocks at its centre and smaller domes scattered across the red terrain beyond. Credit: DALL-E 3, released into the public domain, via Wikimedia Commons.

References

• [ANTO] Antonopoulos, Andreas M., Mastering Bitcoin, Second Edition, O’Reilly Media, 2017.
• [ASHB] Ashby, Neil, “Relativity in the Global Positioning System,” Living Reviews in Relativity 6, 2003.
• [CARD] Card, Orson Scott, Ender’s Game, Tor Teen, 2014 (first published 1985).
• [EINS] Einstein, Albert, Relativity: The Special and the General Theory, Princeton University Press, 2015.
• [LEGU] Le Guin, Ursula K., Rocannon’s World, Harper & Row, 1977 (first published 1966).
• [NAKA] Nakamoto, Satoshi, Bitcoin: A Peer-to-Peer Electronic Cash System, 2008.