OrbitalHub

For a brief window about 2.1 billion years after the Big Bang, a hyperluminous quasar at the centre of a still-forming galaxy cluster puffed out a halo of X-ray-bright plasma at roughly 20 million kelvin, a temperature the local universe reserves for the intracluster medium that fills mature clusters today. A 634-kilosecond (about 176 hours) Chandra observation of the protocluster MQN01, reported by Andrea Travascio, Sebastiano Cantalupo and collaborators in the second paper of their X-ray series, has now caught that halo in the act of forming. After subtracting the bright point-spread function of the central quasar, the team is left with about 66 net X-ray counts in the soft 0.5 to 2 kiloelectronvolt band, an 8-sigma detection of extended plasma reaching out to at least 30 kiloparsecs, roughly 100,000 light-years, around quasar CTS G18.01.

Mature galaxy clusters hold most of their baryons not in galaxies but in a diffuse, X-ray-glowing plasma called the intracluster medium (ICM). That plasma is what makes clusters visible to X-ray observatories and what gives cluster cores their characteristic pressures, entropies and cooling times. The unanswered question has been when, exactly, that gas first becomes hot. At redshifts above about 3, almost every extended X-ray feature that telescopes have managed to pick out around a forming cluster has come from a radio-loud galaxy, where relativistic jets launder cosmic microwave background photons into X-rays through inverse Compton scattering. The thermal hot-gas component, the one that will become the future ICM, has been the part hiding.

MQN01 is the first clean case where the hot component shows up on its own. The central quasar is radio-quiet, so there is no jet to blame. Photoionization by the quasar cannot account for the morphology or spectrum. After a long checklist of alternatives, the only model that fits is thermal emission from a hot, optically thin plasma in collisional ionisation equilibrium. The detection therefore pins down a stage of cluster evolution that theorists have been modelling but have never before measured directly: cold gas pouring into the deep potential well of a forming halo and being shock-heated to X-ray temperatures as it falls.

The MQN01 field has been on Cantalupo's target list for almost a decade. It hosts one of the brightest Lyman-alpha nebulae known at high redshift, mapped first by Borisova et al. in 2016 and now extended across more than two arcminutes by deeper VLT/MUSE adaptive-optics pointings. The same field also contains the largest galaxy overdensity seen at z > 3 and the highest concentration of rapidly accreting supermassive black holes of any surveyed protocluster, with six X-ray-detected active galactic nuclei inside a comoving volume of about 16 square megaparsecs (paper I, arXiv 2410.03933).

To follow up on the AGN census, Cantalupo's Cosmic Web group at the University of Milan-Bicocca obtained 634 kiloseconds of Cycle 23 Chandra ACIS-I time on the field. Paper II, published in Astronomy and Astrophysics on 27 July 2026 and distributed as arXiv 2508.20074, focuses not on the point sources but on what is left when you subtract them. The team built a careful point-spread-function model for each observation, using simulated Chandra PSFs that account for the instrument response and spectral shape of quasar CTS G18.01, and subtracted it from the merged soft-band image.

What emerged is a soft, isotropic glow that follows a classical beta-model surface density profile with a steep inner slope (beta approximately 2.1) and a core radius near 36 kiloparsecs. Joint spatial and spectral fitting pins the gas temperature at kT about 1.8 plus or minus 0.4 kiloelectronvolts, which is about 20 million kelvin. The implied virial halo mass is about 3 plus or minus 1 times 10 to the 13 solar masses, and the hot gas inside the virial radius carries about 2.6 times 10 to the 12 solar masses, roughly 56 percent of the cosmological baryon budget expected for a halo of that mass.

The INAF press release of 27 July 2026 and a German-language scinexx write-up on 20 August 2026 popularised the work as the first clear image of a forming cluster atmosphere. A Space.com piece by Robert Lea on 29 July 2026 highlighted the temperature comparison: at 36 million degrees Fahrenheit the gas is hotter in absolute terms than anything in today's nearby clusters, while being at an earlier point in its cooling life.

The detection method is the conceptual heart of the paper. Quasar CTS G18.01 dumps most of its 0.5 to 2 keV photons into a single pixel region, but a few percent leak into the surrounding 2- to 4-arcsecond annulus, which at z = 3.25 corresponds to about 15 to 30 kiloparsecs in projected distance. The team's approach is borrowed from studies of local Seyfert galaxies: build a high-fidelity PSF from CIAO's simulate_psf tool, weighted by the per-observation exposure and spectral shape, subtract it from the data, and look at what is left. The annulus holds 172 total counts in the 0.5 to 10 keV band and 96 in the soft band. After PSF subtraction, about 66 net counts remain, a significance near 8 sigma.

The spectral and spatial fits are performed jointly with an MCMC walk using emcee. The thermal component is modelled with xsmekal, a plasma code that includes bremsstrahlung, recombination continuum and line emission for highly ionised species in collisional ionisation equilibrium. Metallicity and temperature are tied across four concentric radial bins, while the normalisations scale with the surface density of a beta-model profile. The best fit yields kT approximately 1.8 plus or minus 0.4 keV and a hot gas mass fraction inside the virial radius of about 8 percent of the dynamical mass, or 56 percent of the available cosmological baryon budget.

The pressures and densities implied by that fit are one to two orders of magnitude above today's clusters. Cooling times in the inner 15 to 30 kiloparsecs sit between 1 and 10 times the local free-fall time, which means the gas would be locally unstable if there were no heating source. The team argues that gravitational shocking, cool gas dropping into the halo's deep potential well and being heated by the accretion shock, is enough to do the work. Quasar feedback cannot be ruled out, but the soft X-ray spectrum and the lack of any excess in the hard band make a feedback-dominated scenario hard to sustain.

The same field carries a 200-kiloparsec Lyman-alpha nebula mapped by Borisova et al. 2016 and recently extended with MUSE AO mosaics. The soft X-ray emission sits inside the inner 6 times 10 to the minus 18 erg per second per square centimetre per square arcsecond contour of that nebula, suggesting that the hot phase coexists with the cold phase rather than displacing it. The thermal pressure of the X-ray-emitting plasma is high enough to confine the cold clumps that produce the Lyman-alpha emission, which is one of the better pieces of evidence yet that the multiphase circumgalactic medium at cosmic noon can be pressure-confined rather than radiation-confined.

The combined view pairs the wide-field F150W2 mosaic of the protocluster with a zoom panel in which the Lyman-alpha nebula mapped by Borisova et al. 2016 appears in blue and the new soft-X-ray halo appears in red. The black disc in the zoom masks the quasar itself.

A radio-quiet quasar 11 billion light-years away has given astronomers the first direct look at hot, X-ray-bright plasma in the act of becoming the intracluster medium. The Chandra data show about 100,000 light-years of 20-million-kelvin gas around the quasar, with the pressure and density expected for a halo that is still accreting cool gas through gravitational shocks. Whether MQN01 is a typical waypoint for protoclusters or an unusually bright outlier is the open question; the team is working through archival X-ray data on hundreds of additional high-redshift quasars and has Atacama Large Millimeter/submillimeter Array time queued to test the gas conditions independently. If the picture holds up across a larger sample, the textbook story of how cluster atmospheres form will finally have a measurement at the epoch where it begins.

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;