OrbitalHub

In a basement lab at Ben-Gurion University of the Negev, a cloud of about 20,000 rubidium atoms has just answered a question physicists have been asking for nearly a century. Cooled to a few nanokelvin above absolute zero and held still by microscopic wires on a fingernail-sized chip, the atoms were nudged into a quantum superposition in which one half of the cloud rose a few micrometres and fell back under gravity while the other half stayed put. When the two halves were brought back together, the interference pattern between them showed a clean phase shift, and that phase shift matched Einstein's prediction to within 2.5 percent.

The result, published in Science Advances on 2 September 2026 by Dobkowski, Folman, Penrose, Vedral, Schleich and a dozen other collaborators, is the first direct measurement of the quantum phase accumulated by a freely falling particle. It is also a fresh check on Einstein's equivalence principle, the assumption that gravity disappears for an observer in free fall. The principle works fine for billiard balls and spacecraft. Until now, no one had checked whether it still works when the falling object is in a quantum superposition of two places at once, which is what the Ben-Gurion group, along with partners at Oxford and Ulm, set out to do. That the check matters at all is because general relativity and quantum mechanics describe the universe with completely different mathematical machinery, and they have resisted every attempt to combine them for almost a century. Most attempts to unify the two assume, implicitly, that the equivalence principle still applies at quantum scales, and this result is the first empirical reason to believe that assumption is correct.

Building the right kind of interferometer took the Folman group years. Ordinary atom interferometers, which have existed since the early 1990s, can compare two paths that both involve motion, one slightly higher than the other or one slightly accelerated with respect to the other. What they cannot do is compare a path that is genuinely free of forces against a path that is held artificially still, which is exactly the situation an equivalence-principle test requires, as Ars Technica reported on 11 September 2026. The team called the new device the Quantum Galileo Interferometer, or QGI, in honour of Galileo's original observations of free fall, and the underlying method is laid out in detail on arXiv.

Inside a glass cell held under vacuum, a few micrograms of rubidium-87 gas is cooled into a Bose-Einstein condensate, a quantum state in which all the atoms share a single wave function. The condensate floats about 113 micrometres beneath an atom chip, a flat substrate etched with microscopic current-carrying wires that paint the surrounding space with carefully shaped magnetic fields. The chip itself is mounted upside down, with the wires facing the atoms, so the magnetic gradient can levitate the condensate in place. The whole apparatus is small enough to fit on a desk, which is part of why a single lab group could afford to spend years getting it to work, but the measurement it produces has implications for the largest questions in fundamental physics.

The reason it took so long is that interference, the property the experiment depends on, is fragile. Interference only appears when there is no way, even in principle, to tell which path a particle took; any measurement that distinguishes the two paths destroys the quantum superposition and forces the particle to behave like a localised classical object. Wave packets that have fallen under gravity are moving fast, while stationary wave packets are not, and that difference in speed is itself information about the path, so a naive setup would never produce an interference pattern at all. Folman and his colleagues had to design a sequence of pulses that cancels the path information without cancelling the phase information they actually wanted to measure.

Once the atoms are ready, the experiment unfolds in four microwave and magnetic pulses, summarised in Figure 1 of the arXiv preprint. The first pulse puts every atom into a superposition of two spin states: one that feels the magnetic field and one that does not. A magnetic pulse then kicks the magnetically sensitive state upward, launching it on a ballistic arc, while the insensitive state stays put. A second microwave pulse swaps the roles: the rising atom becomes magnetically insensitive and falls freely under gravity, while the stationary atom becomes magnetically sensitive and is held hovering by a field tuned to exactly cancel its weight. A final magnetic pulse acts as a parachute, gently braking the falling atom so it lands back where it started, where the two halves of each atom can interfere. At their farthest apart, the two trajectories were about 7.5 micrometres apart and the longest free-fall time was about two milliseconds. The interference pattern at the end of each run depends on the phase that the falling path accumulated during its trip. The longer the fall, the more phase, and the chirp in those oscillations is the signature the theory predicts. As the team lengthened the fall duration, the measured phase grew in proportion to gT squared, exactly as general relativity predicts for a classical trajectory and as the equivalence principle predicts for a quantum one.

The interpretation is the part that makes the result satisfying rather than just technical. From the perspective of the falling atom, there is no gravity at all: it is in free fall, the way an astronaut is in orbit, and its wave should pick up no extra phase. From the perspective of the laboratory, the same atom is being pulled downward at 9.81 metres per second squared, and its wave should accumulate a phase proportional to gT squared. The two views should agree, and Einstein's equivalence principle says they do. The QGI measures the lab-frame phase directly and shows that, to within the experiment's precision, the falling quantum wave accumulates exactly the phase that gravity predicts. As The Brighter Side reported, the measurement is a checkpoint on the boundary between two theories that physicists are still trying to merge. The result does not say which, if either, will eventually have to give way, but it sets a baseline that future versions of the experiment will sharpen.

A first upgrade is already under construction at Ben-Gurion. The next-generation QGI is being designed to put nanodiamonds, particles roughly ten orders of magnitude heavier than rubidium atoms, into the same kind of superposition. Nanodiamonds sit in a mass range where several competing quantum-gravity models and collapse theories make different, falsifiable predictions, and putting a nanodiamond in superposition for any usable time has not yet been achieved. Folman told Ars Technica that his lab is already working on a design that he hopes will let the heavier experiment run within the next four or five years, though he was clear that it is "a very, very challenging project." If it works, the team would have a direct laboratory test of the boundary between quantum mechanics and gravity in a regime where competing theories actually disagree.

In the meantime, the September result establishes something that has been assumed but not shown. When an atom falls, the quantum phase it picks up is the phase that gravity, applied classically, would predict. The equivalence principle, written down by Einstein in 1907 and tested for classical masses by Galileo, Newton, Bessel and Eötvös, has now been demonstrated, in a single careful experiment, for a particle that is in two places at once. The result does not resolve the long-standing tension between general relativity and quantum mechanics, but it removes one of the most reasonable doubts about how the two might eventually be unified: that the equivalence principle, which is foundational to general relativity, might quietly break at quantum scales. It does not appear to.

Abstract

The blogpost explores relativistic effects on proof-of-work based cryptocurrency protocols. Cryptocurrencies are here to stay and it is quite plausible that future human colonists spread across the solar system and beyond will use a decentralized cryptocurrency as opposed to a fiat currency issued by a central authority. The low transaction fees, the ubiquitous access, not being bound by exchange rates or interest rates, not being controlled by financial institutions who are serving foreign interests -- these are some of the advantages cryptocurrencies will enjoy in the thriving exo-economy.

Motivation

At present, on a cryptocurrency network, the information exchanged by the nodes in the network reaches each node almost instantaneously. The speed at which the TCP/IP packets travel on the network and the fact that the Internet spans only the Earth and the LEO makes this possible. However, once the region the network is spread across will reach certain boundaries, the network size would have negative impact on the network: increasing communication failures due to network delays, more frequent and longer blockchain forks as part of the proof-of-work protocol, network segregation into local sub-networks (let us call them topological forks), just to name a few.

Nullius in verba... as they say. Let's go deeper into details and figure out a feasible solution for a truly interplanetary cryptocurrency.

Cryptocurrency 101

You can think of a cryptocurrency as a digital money ecosystem. Plain and simple. A collection of technologies are part of this ecosystem, all of them the result of years of research in the cryptography and distributed systems fields: a decentralized network of computers, a public transaction ledger -- also known as a blockchain, a protocol that consists of a set of rules for transaction validation, a decentralized consensus mechanism. [ANTO]

A decentralized network of computers ensures the resilience of the network. We can think of both computing power and data storage capabilities. As the computing power is distributed across the network, any disruption can be successfully handled by the network. Transaction data resides on all nodes of the network. This implies that even physical damage done to network nodes will not take out the network.

The blockchain is a public distributed ledger which stores all transactions handled by the network. As the name suggests, the blockchain is a list of data blocks. Each of these blocks contains a set of transactions, as many as can fit in the block, given the maximum size of the block (a characteristic of the network). Transactions contain sender and receiver info, and the amount/asset that is changing ownership, and they are broadcasted and added to blocks by network nodes. Blocks are linked to the previous block in the chain by a cryptographic hash (the hash of the previous block becomes part of the current block). This backward link leads all the way to the first block in the chain, the Genesis block. Each cryptocurrency blockchain has one. The cryptographic hashes have an important role in protecting the blockchain from tampering attempts.

The transaction validation rules enforced by the nodes in the network ensure that the content of each block in the blockchain is valid. By far, the most frequent form of fraud is double spending. The validation process makes sure that the inputs on the transactions exist and that they have not been already spent. The transactions marked as invalid are rejected by the network and do not make it on the blockchain.

The consensus mechanism is designed so that all the nodes in the network can agree on the set of transactions to be included in the current block. It shifts the authority and the credibility required by a central clearing house to a network of nodes. Important to mention here that, inherently, the nodes do not trust each other, and they do not have to because the trust is enforced by the consensus mechanism itself.

The Proof-of-Work

We mentioned above that one of the key innovations that make cryptocurrencies possible is the decentralized consensus mechanism. Currently, the de facto consensus mechanism is the proof-of-work.

The proof-of-work consensus mechanism was proposed by Satoshi Nakamoto in 2008 [NAKA]. In general, a proof-of-work is a piece of data that requires costly and time consuming computational effort, but it is very easy to verify. A very good analogy is one of your semester projects in college... it takes you a whole semester to finalize it, but it takes very little time and effort for your supervisor to evaluate and grade it. Similarly, proof-of-work is used by cryptocurrencies for block generation. For the network to accept the block, nodes must complete a proof-of-work which also guarantees the integrity of the transactions included in the block. The difficulty of the proof-of-work is adjusted by the network so that a new block can be generated every fixed time interval. This fixed time interval is characteristic to every cryptocurrency. Most notably, for Bitcoin this time interval is set to 10 minutes.

Satoshi Nakamoto's solution, emobodied by the proof-of-work algorithm above, achieves consensus on the network without a central trusted authority (hence the name decentralized consensus mechanism).

Enter the Ansible

For the astute reader, it is quite obvious at this point that communication delays between the network nodes have a direct effect on the protocol described above. An important assumption made when the protocol was designed is that these delays are small, and this is why they can be handled by the network when the nodes choose to follow and validate the blocks on the longest blockchain fork. Also, this is the reason why all the nodes in the network can have a say in the network consensus. They all can find a solution for the current block, and they all can be rewarded when they find the solution. The communication delays witnessed by the peripheral nodes will cripple their ability to find solutions and these nodes will not be incentivized to remain in the network. Hence, the segregation of the network effect mentioned earlier.

Unfortunately, given the current technological level of our civilization, we do not have at our disposal a technology that allows us to communicate fast and reliable over the large expanse of space. It would take a hell of a wait time to proces a payment made by a mining corporation in the TRAPPIST-1 system, 12 parsecs within the constellation of Aquarius, to a planetary engineering corporation located in the Sol system... twice 39 years plus the block confirmation time.

Fortunately, the Sci-Fi literature already offers a solution for our problem. For those of you, Sci-Fi nerds like myself, that have already read Rocannon's World [LEGU] and Ender's Game [CARD], the Ansible device must sound very familiar. The ansible is a fictional device capable of faster-than-light communication. To word this differently, an operator of such device can send and receive messages to and from another device over any distance with no delay.

Hence, even if only in the realm of science fiction, we will be able to devise a solution for the problem that the future cryptocurrency enthusiasts, living in the outer space colonies, will eventually face.

The Special Relativity Theorem

Before elaborating more on a required upgrade of the network protocol, we have to discuss the special relativity theorem and its implications on how time and distance are perceived in reference systems.

Albert Einstein was awarded the Nobel Prize in Physics in 1921. He received it for his contributions to the understanding of the photoelectric effect, after publishing a paper on it in 1905. At that point his contributions to the understanding of gravity through his theory of relativity were well known, but the new perspective on gravity offered by Einstein's theory was so controversial that the Nobel Prize Committee members chose to protect their reputation. They decided that it was appropriate to award Einstein the Nobel Prize for "his services to theoretical Physics, and especially for his discovery of the law of the photoelectric effect."

During his research Einstein attempted to reconcile the principle of relativity with the principle of the constancy of the velocity of light. This attempt led Einstein to the discovery of the special relativity theorem. Einstein's Gedankenexperiment (thought experiment) with a test subject travelling by train is very well known in the scientific community. If our human subject is walking towards the front of the train with velocity w with respect to the train, and the train is moving with velocity v with respect to the embankment, then an observer on the embankment will measure as W = v + w the velocity of our subject on the train. If instead of our traveller, we consider a beam of light propagating with velocity c, the velocity measured by the observer on the embarkment would be v + c. However, this violates the principle that the velocity of light is constant in any inertial reference system and equal with c. Einstein found a solution for this problem and thus resolved the incompatibility.

One direct consequence of the special relativity theorem is the Lorentz transformation.

Before the relativity theorem, time in physics had an absolute significance, independent of the state of motion of the reference system. However, every inertial reference system has its own particular time. We always have to be told which inertial reference system the statement of time refers to. If you look at your watch, the time you read is the time as measured in the Earth inertial reference system. By the way, the Earth circles the Sun on an almost circular orbit, which means that any body maintaining a constant position in the Earth reference system should experience some centripetal force. However, this centripetal component is negligible compared to the gravitational pull of the Earth. Hence, engineers use this aproximation when calculating satellite orbits.

Back to our original trail of thoughts... the axiom that lays the foundation for the Lorentz transformation states that every ray of light possesses the velocity of transmission c relative to any inertial reference system. That is the velocity of transmission in vacuo (in a vacuum).

If following Einstein's thought experiments [EINS], the above-mentioned axiom leads to a set of four equations that explain the relation between dimensional and temporal coordinates in two inertial reference systems:

  x' = (x - vt)/sqr(1 - v²/c²)
  y' = y
  z' = z
  t' = (t - x*v/c²)/sqr(1 - v²/c²)

where:

 x, y, z, t coordinates in inertial reference system K,
 x', y', z' , t' coordinates in inertial reference system K',
 v the relative velocity between inertial reference systems;

also, the expression 1//sqr(1 - v²/c²) is known as the Lorentz factor.

The Lorentz transformation equations are a more general case of the Galilean transformation:

  x' = x - vt
  y' = y
  z' = z
  t' = t

which is the basis of the assumptions of the classical mechanics as to the absolute character of both dimensional and temporal coordinates. The above are the result of replacing velocity c with ∞ in the Lorentz transformation equations.

The Lorentz transformation has a few corollaries which have an impact on time dilation, length contraction, relativistic mass, relativistic momentum, and relativistic kinetic energy. The one that concerns us is the time dilation corollary:

 Δt = γΔt'
 
where γ is defined by

 α = 1/γ = sqr(1 - v²/c²)

Assuming a clock at rest in inertial reference system K, and moving with the velocity v in the inertial reference system K', the time Δt' between two ticks as measured in the frame K' is longer than the time Δt between the same ticks as measured in the rest frame of the clock, K.

Relativistic Effects on Proof-of-Work

To better understand the relativistic effects on how relative time is perceived in two inertial reference systems (or Galilean reference systems [EINS]) we have to mention the twin paradox. The twin paradox is a thought experiment that involves two identical twins. One of the twins makes a journey into space onboard a relativistic spaceship, and upon his return to Earth discovers that his twin has aged much more than he did. Depending on how fast the spaceship moves through space and/or how long the journey was, our traveller could return to Earth and realize that several generations have passed meanwhile.

As a direct application of the twin paradox, we have Mazer Rackham, International Fleet Admiral and Ender Wiggin's mentor, as portrayed by Orson Scott Card [CARD]. The fighter pilot who destroyed the Formic Fleet Flagship, killed the Hive Queen, and ended the Second Formic Invasion, Mazer Rackham is sent on a journey on a relativistic spaceship and returns to Earth 100 years later in order to assist the International Fleet. Upon his return he has barely aged a few years.

Similarly, if a subnetwork is moving relative to the rest of the network, the nodes in the subnetwork would experience time dilation as predicted by the special relativity theorem. Hence, they are at a disadvantage compared to the rest of the nodes because they have less time available to find a solution for the proof-of-work problem. In order to make thing square for all the nodes in the network, the difficulty of the problem should be adjusted in each subnetwork using the Lorentz factor: in order to compensate for time dilation, the relativistic nodes should have to solve a simpler problem. Also, their block confirmation time should decrease as well.

One element is missing still... how do ansibles synchronize? What value has the Lorentz factor for each one of them? One simple solution for this problem is having one of the ansibles (let us say the Earth-bound one) broadcasting a beacon every fixed number of seconds. The ansibles interfacing to subnetworks would pick up the broadcast, and by measuring the time interval between the beacons, infer the Lorentz factor. Once the Lorentz factor is determined, the nodes mining on the subnetworks will have their proof-of-work difficulty and the block confirmation time adjusted accordingly.

A more Down-to-Earth Solution for the Problem

We will fork the storyline (pun intended) at Enter the Ansible paragraph, and suggest a more down-to-earth solution for the problem. The peripheral nodes are not to participate in the consensus. Their function would be just to relay messages (a.k.a. payment information) across the network. In our multi-planetary scenario, the nodes working on the proof-of-work would reside on/around the Earth, and the network nodes on Mars or any other region in the Sol system would have to wait 2x (network packets travel time) + (block confirmation time) in order to confirm a payment. However, such a solution would have an Achilles heel very hard to defend... if starting its mining engine, any peripheral node could take over the local network and force a topological fork of the network. For a node, the incentive of staying honest on the current network must be stronger than any reward obtained by cheating.

Concluding remarks

While the blogpost contains some elements of fiction, it accurately describes the cryptocurrency ecosystem, the special relativity theorem, the Lorentz transformation and its corollaries. We would like to thank the readers that went through this exercise with us. Undeniably, cryptocurrencies are disrupting the global economy and they are here to stay. Undeniably, we -- as a species -- will explore and migrate farther than the LEO. History has taught us that decentralization is the key to survival and prosperity. Let us together make the future happen.

References

[ANTO] Antonopoulos, Andreas M., Mastering Bitcoin, Second Edition, O'Reilly Media, Inc., June 2017;
[CARD] Card, Orson Scott, Ender's Game, A Tor Teen Book, 2014;
[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;
[NAKA] Nakamoto, Satoshi, Bitcoin - A Peer-to-Peer Electronic Cash System, www.bitcoin.org, 2008;