Bits travel, atoms do not

Leans on Entropy is missing information.

Why send a mind instead of a ship?

The seed that founded the Vigil weighed one tonne. It spent 297 years on the way, and it needed a laser array to launch it and a fusion stage, with 17,206 kg of propellant, to stop it. The push alone gave the launch 1.0 × 10¹⁹ joules of motion.

In the story, a mind is represented by a pattern of stored bits that can be copied to a computer elsewhere. frontier The destination supplies the hardware; a light signal carries the data. Entropy is missing information explains how physical systems represent bits.

The Vigil receives minds over a laser link. Sending is the easy half: a modest transmitter can send a small survey home slowly. Receiving a mind in seconds takes a large mirror at the far end, and the seed spent years building one. It sent its survey in 2454, after a year of work, and the survey reached Saturn in 2482. A year later Saturn sent the first minds blind, aimed at a receiver it knew was planned but had not heard was finished. The seed had finished it in 2481, a pair of mirrors 1,000 metres wide. Its ready signal reached Saturn in 2509, long after the minds had left. A laser beam can be varied far faster than any radio signal, and every change carries bits. The model assigns 1 × 10¹⁷ bits to a mind, based on estimates of brain storage. The amount of data needed to represent a mind is unknown. frontier

Someone had to be waiting at the far end to build the receiver and the computers. The seed carried a bootstrap mind, a machine intelligence of the 2150s, built after the first general AI. frontier It could survey the system up close (a fast flyby had already mapped it roughly), send the survey home, build the receiver and stockpile raw material. It was not sent to settle the system. The minds it prepared for were more than three centuries newer than it and had studied its survey before they were sent, so it avoided decisions that could not be undone and saved scarce feedstock such as chips. In 2511 the first of those minds arrived, the First Waking, and the rapid building began (Doubling).

Light takes 28 years to cross this distance, which sets the propagation delay. What the laser controls is the second delay: how long it takes to pour the whole mind into the beam. That takes 9.5 seconds at the capacity calculated for this beam. The beam carries so much light that, counting photons alone, a mind would fit through in 0.023 seconds. Bandwidth imposes the tighter limit: it sets how many independent modes the beam can carry each second. Either way, it is seconds against 297 years.

The transmission also uses much less energy than the seed launch. The laser spends 9.5 × 10¹² joules sending one mind, and the launch stack carries 1.1 × 10⁶ times more energy in motion alone. The burst's energy has a mass equivalent of 0.11 grams.

Guess first A friend suggests a stronger laser to shorten the trip. Does the mind arrive sooner?

The propagation delay stays the same. The light needs 28 years whatever the laser does. A stronger laser barely shortens even the few seconds of sending, because the beam already carries more light than its pulses can use.

The sender can retain its copy of the data, so sending does not end the mind running at Saturn. Whether the mind that wakes at the far end is the person who was sent, or a second person with the same memories, is a question philosophers still argue about frontier; the last fold takes it up.

How much of the beam arrives?

Light spreads. Even a perfect laser, shining from a mirror of width D, fans out by about

θ ≈ λ / D

where λ is the wavelength. Here λ is 1 micrometre (near infrared) and D is 1,000 metres, so the beam widens by 1 × 10⁻⁹ of a radian. Over 28 light-years it grows into a spot 2.6 × 10⁸ metres across, about 2.6 × 10⁵ times the width of the mirror that is trying to catch it.

The catching mirror, a disc of the same width, collects only the sliver of the beam that falls on it:

fraction caught ≈ (area of mirror × area of mirror) ÷ (λ × distance)²

For the Vigil's link that is 8.8 × 10⁻¹². The laser sends 1 × 10¹² watts, so 8.8 watts arrive. At this wavelength every photon carries only 2.0 × 10⁻¹⁹ joules, so those watts are 4.4 × 10¹⁹ photons a second.

Quantity	Value
Beam spread	1 × 10⁻⁹ radians
Footprint at the receiver	2.6 × 10⁸ m
Fraction caught	8.8 × 10⁻¹²
Power received	8.8 W
Photons received	4.4 × 10¹⁹ per second

Most of the beam misses the receiver. The received photon flux still exceeds what the assumed bandwidth can use at the photon budget below.

A beam spreads by diffraction, so almost none of it lands on the receiver. Illustrative: not to scale, with the spread greatly exaggerated.

How fast can a mind be read out?

The data rate is constrained by both the received photon flux and the available bandwidth.

The first is photons. Say each bit costs 10 photons as an assumed budget. Then 4.4 × 10¹⁹ photons a second carry 4.4 × 10¹⁸ bits a second, and a mind of 1 × 10¹⁷ bits takes 0.023 seconds.

The second is pulses. A beam cannot change faster than the width of its band of frequencies allows, and that band cannot be much wider than the light's own frequency, 3.0 × 10¹⁴ hertz. With two polarisations, that gives the beam 6.0 × 10¹⁴ pulses a second to write on. Each pulse then holds 7.4 × 10⁴ photons, and the capacity grows logarithmically with photon count: ten times more photons in a pulse add only about three bits to it. Each pulse here carries 17.6 bits, so the beam carries 1.1 × 10¹⁶ bits a second.

	Photons alone	Pulses alone
Bits a second	4.4 × 10¹⁸	1.1 × 10¹⁶
Photons spent per bit	10	4,200
Time for a mind	0.023 s	9.5 s

The bandwidth-limited rate is lower by a factor of 419, so a mind takes 9.5 seconds. The beam has light to spare: a laser a hundred times weaker would slow the mind by a factor of only 1.6.

For scale, the deep-space laser link NASA flew in 2023 ran at 2.67 × 10⁸ bits a second. At that rate a single mind would take 12 years. The Vigil's link is 4.0 × 10⁷ times faster, over a distance 8.5 × 10⁶ times longer.

With JavaScript on, this is a calculator: slide the mirror width, the laser power and the distance, and it shows the footprint, the power received and the time for a mind under each limit. The Vigil's link gives a footprint of 2.6 × 10⁸ m, 8.8 W received, and 9.5 seconds for a mind.

Preparing the receiving memory also has a thermodynamic cost: erasing 1 × 10¹⁷ bits at room temperature costs at least 2.9 × 10⁻⁴ joules (The cost of forgetting).

Open everything

Where do the beam and the numbers come from?Gaussian beams, the link budget and the capacity of light

A beam spreads by diffraction

For a Gaussian laser beam, diffraction prevents the field from remaining narrow: squeezing it into a width $w_0$ at the mirror (the waist) forces its directions to spread, and the tighter the squeeze, the wider the spread. Solving the wave equation for such a beam (Kogelnik and Li, 1966) gives a half-angle

$\theta = \frac{\lambda}{\pi w_0}$

and a distance $z_R = \pi w_0^2/\lambda$ , the Rayleigh range, beyond which the beam spreads in a straight cone. For a mirror of width $D$ , $w_0$ is of the order $D/2$ , which is where the rule of thumb $\theta \approx \lambda/D$ comes from. The Vigil's link is 3.4 × 10⁵ Rayleigh ranges long, so the far-field approximation applies: at distance $z$ the beam radius is $w(z) \approx \theta z$ .

The link budget

On the axis, a beam of power $P$ and radius $w$ has intensity $I = 2P/(\pi w^2)$ . A receiver of area $A_r$ small compared with the beam catches

$f = \frac{2 A_r}{\pi \theta^2 z^2} = \frac{2 A_t A_r}{(\lambda z)^2}, \qquad A_t = \pi w_0^2 .$

A uniformly lit mirror of area $A_t$ gives the same expression without the 2, and that is the form the Vigil's numbers use:

$f = \frac{A_t A_r}{(\lambda z)^2}.$

Engineers write it as a product of three factors, the antenna gain $G_t = 4\pi A_t/\lambda^2$ , the spreading loss $1/(4\pi z^2)$ and the collecting area:

$P_{rx} = P\, G_t\, \frac{1}{4\pi z^2}\, A_r .$

Mirror area counts twice, once for sending and once for catching, so doubling both mirror widths multiplies the received power by 16. Halving the wavelength gives a factor 4. Doubling the distance costs 4. Mirror size and wavelength are design variables; the distance is fixed by the destination.

The link also has to point. A beam this narrow must be aimed where the receiver will be when the light arrives, not where it is seen. The light by which the sender sees the receiver left it $z/c$ ago, and the beam needs another $z/c$ to cross, so the aim must lead the seen position by about $2v/c$ , where $v$ is the receiver's sideways speed. The receiving mirrors orbit Ember near Kindling. Their sideways speed is at most Ember's own speed around the pair's centre, 82 km/s, plus their orbital speed around Ember, 88 km/s, which is 170 km/s in the worst case; how the two systems drift against each other would add to it. That gives 1.1 × 10⁻³ radians, or 1.1 × 10⁶ beam widths. A node at the inner edge of zone C, circling Vesper at 326 km/s, would need 2.2 × 10⁻³ radians. The aim has to be computed from the orbit, decades ahead.

What one pulse of light can carry

Treat each pulse of the beam as one mode of the light field, with mean received photon number $x = \eta N$ : $N$ photons sent, a fraction $\eta$ surviving the trip. Send coherent states (the quantum state of laser light) with a Gaussian spread of amplitudes. A coherent state that loses light is still a coherent state, so each output state is pure and has zero entropy, while the average over all of them is a thermal state with entropy

$g(x) = (1+x)\log_2(1+x) - x\log_2 x \quad\text{bits.}$

Holevo's theorem says an ensemble carries at most the entropy of its average output minus the average entropy of its outputs, and long codes reach that, so $g(\eta N)$ bits per mode can be sent. In 2004 Giovannetti and colleagues proved that nothing does better: $g(\eta N)$ is exactly the capacity of a channel that only loses light.

The dependence of $g$ on photon count explains the bandwidth limit. For many photons per mode, $g(x) \approx \log_2(e x)$ : ten times more light adds only $\log_2 10 \approx 3.3$ bits. For few photons per mode, $g(x) \approx x \log_2(e/x)$ , and the information per photon is

$\frac{g(x)}{x} \approx \log_2\frac{e}{x}.$

At a hundredth of a photon per mode that is 8.1 bits per photon, and it grows without bound as the light gets sparser. This requires more modes. A pulse-position code, for instance, places one photon in one of $M$ time slots and gets $\log_2 M$ bits from it, spending $M$ slots. Higher information per photon therefore requires more bandwidth.

Why the photon budget loses

Bandwidth is finite. A band of width $B$ carries $B$ independent modes a second in each of the two polarisations, and a band centred on the carrier cannot be much wider than the carrier frequency $\nu = c/\lambda$ itself: frequencies cannot go below zero, and the low ones would spread far wider on the way. With $B = \nu$ , a generous upper end, the rate is at most

$R = 2\nu\; g\!\left(\frac{\Phi}{2\nu}\right),$

with $\Phi$ the photon rate arriving. For the Vigil's link $\Phi/2\nu$ is 7.4 × 10⁴, deep in the crowded regime where each mode carries 17.6 bits, so $R$ is 1.1 × 10¹⁶ bits a second and a mind takes 9.5 seconds.

The photon budget of one bit per 10 photons would need $g(x)/x$ to rise to a tenth, which happens near 77 photons per mode. Spreading the same light that thinly takes a band 956 times the carrier frequency. That exceeds the assumed available bandwidth, so the photon-limited figure serves only as a comparison. And because $R$ grows only as the logarithm of the light, additional laser power gives diminishing returns, while additional bandwidth would increase the rate more directly.

Could the link write on several beam shapes at once, as some fibre links do? The number of shapes two mirrors can pass between them almost without loss is about the Fresnel number product, $A_t A_r/(\lambda z)^2$ , the same expression as the fraction caught. When it is large there are about that many nearly lossless channels side by side. When it is far below one, as here at 8.8 × 10⁻¹², a single shape gets through, with transmission equal to that fraction, and every other shape arrives weaker still. The link has one spatial mode in two polarisations, and that is what the rate above assumes.

Has anyone done this, and what is not known?Laser links to deep space, the limits of the photon channel, and identity

The first deep-space laser link

In 2023 NASA flew Deep Space Optical Communications (DSOC) on the Psyche spacecraft. A flight transceiver with a 0.22 metre telescope sent infrared light to the 5.1 metre Hale Telescope at Palomar, where a superconducting nanowire detector counted single photons. In December 2023 it streamed video from 3.1 × 10⁷ kilometres away at its top rate of 2.67 × 10⁸ bits a second, about as fast as a good home broadband line. The Vigil's link is 8.5 × 10⁶ times longer and 4.0 × 10⁷ times faster. DSOC is the proof that the method works: pointing, tracking and counting single photons across millions of kilometres.

How close to the limit can real hardware come?

It depends on how crowded the light is. In the Vigil's regime, with many photons per pulse, an ordinary heterodyne receiver, which measures the amplitude and phase of every pulse, gets $\log_2(1+x)$ bits per pulse, within $\log_2 e \approx 1.44$ bits of $g(x)$ . The hard case is the opposite one, sparse light, where reaching capacity takes a measurement made jointly on many pulses at once. Receivers that count photons pulse by pulse fall short there, and closing the gap, with codes and quantum measurements designed together, is a research problem in 2026.

The calculation above also leaves out noise: starlight, scattered light and detector dark counts. A channel that adds noise as well as losing light needed one more piece of proof, that the vacuum gives the least output entropy of any input. Giovannetti, García-Patrón, Cerf and Holevo supplied it in 2014, and with it the capacity of noisy Gaussian channels. Noise lowers the rate below the clean figure on this page, so the Vigil's 9.5 seconds is a best case.

Copies, and the question of who arrives frontier

The link is classical. A bit string can be read any number of times without being disturbed, so the sender never has to lose its copy, and the receiver can write the same pattern into many memories. Nothing in the physics stops two minds from being built from one message.

The no-cloning theorem (Wootters and Zurek, 1982) says an unknown quantum state cannot be copied. Its relevance to mind transmission depends on how the mind is represented. It applies only if what makes a mind is a quantum state that cannot be read off as classical bits, and whether anything like that matters is an open question. The 1 × 10¹⁷-bit mind size is therefore an illustrative assumption.

The link calculation establishes the capacity to transmit a classical pattern. Whether the mind that wakes at the Vigil is the one that was sent, or a second one with the same history, is a question about identity. Derek Parfit's Reasons and Persons made it sharp with a teleporter that scans you, builds you elsewhere and, in one version, leaves the original standing: exactly the case of a mind sent by light. The communication physics does not resolve personal identity; Copy, merge, choose your clock discusses that question.