Coder Legion - Recent posts tagged physics

Distance and Speed from a Radar Echo: Two Equations, and What the Module Datasheets Publish

Tue, 27 Oct 2026 23:24:14 +0000

Distance and Speed from a Radar Echo: Two Equations, and What the Module Datasheets Publish

A radar echo carries two kinematic quantities: range — how far away the reflecting target is — and radial velocity, the component of the target's motion along the line between the radar and the target. Both are recovered from the same received signal, by two different routes. Range comes from timing, expressed through frequency. Velocity comes from the Doppler effect, expressed through frequency shift.

This article sets out the two equations, derives the quantities that follow from them for the two bands we ship — 24 GHz and 61–62.5 GHz — and states which parameters the module datasheets publish and which they do not.

The conceptual overview, without arithmetic, is in How mmWave Radar Works: From FMCW to Breathing Detection.

Range

The underlying idea: round-trip time

The radar transmits, the wave travels to the target, part of the energy returns, and the receiver sees it. Electromagnetic waves propagate at c ≈ 3×10⁸ m/s, and the wave covers the distance twice, so the round-trip time t gives the range:

d = c · t / 2

The division by two accounts for the outbound and return legs.

Why the time is not measured directly

For a target at 1 m the round trip is 2 m, which takes about 6.7 ns. Measuring delay at nanosecond resolution directly is not practical in a module of this cost and size.

How it is done instead: FMCW

The modules use FMCW (frequency-modulated continuous wave). The transmit frequency sweeps linearly with time, so the echo received at any instant is a delayed copy of an earlier transmit frequency. Mixing the received signal with the current transmit signal produces a beat frequency proportional to that delay, and therefore to range.

The published radar type confirms this: the fall module and the sleep module are both specified as 60 GHz FMCW, and the fall module as 1T3R (one transmit, three receive channels).

The round-trip-time equation remains the correct way to understand where range comes from. The beat frequency is the engineering route to the same number.

What sets how finely two targets can be separated

Range resolution is set by the swept bandwidth B, not by the carrier frequency:

Δ d = c / 2B

Where a datasheet publishes the transmit frequency band, a figure follows. The fall module publishes a transmit frequency of 61–62.5 GHz, a span of 1.5 GHz:

Δd = c / (2B) = 3x10^8 / (2 x 1.5x10^9) = 0.10 m

So about 10 cm, on the assumption that the published operating band is also the swept span. Two notes on that figure:

It is the separation at which two targets appear as two. The accuracy on a single target is finer, because a single return is localised by interpolation and by phase, not by which resolution cell it lands in.
The 24 GHz datasheet we supply does not publish a swept bandwidth, so no equivalent figure is stated here.

This explains the distinction that is often blurred: a resolution cell of roughly 10 cm, and the detection of chest-wall displacements below 1 mm, are not the same measurement. The second comes from phase within a cell, covered below.

Velocity

The Doppler effect

When target and radar move relative to each other, the echo returns at a frequency offset from the transmitted one. Approaching shifts it upward, receding shifts it downward, and the sign gives the direction.

The equation

With wavelength λ and Doppler shift Δf:

v = Δ f · λ / 2, Δ f = 2v / λ

The factor of two again comes from the two-way path.

Wavelength from the published frequency

Wavelength follows from the carrier: λ = c / f.

Module	Published band	Wavelength
R24AVD1	24 GHz	12.5 mm
R60ABD1, R60AFD1-V, R60ABD2-H	61–62.5 GHz	4.80–4.92 mm

For every 1 m/s of radial velocity, the shift is therefore:

24 GHz: 2 / 0.0125 ≈ 160 Hz per m/s
61–62.5 GHz: ≈ 410 Hz per m/s

Shift magnitudes in practice

Target	Radial velocity	Δf at 24 GHz	Δf at 61–62.5 GHz
Chest wall during breathing	≈ 0.0075 m/s	≈ 1.2 Hz	≈ 3 Hz
Walking	1.5 m/s	≈ 240 Hz	≈ 610 Hz
Running	5 m/s	≈ 800 Hz	≈ 2.0 kHz

The shifts fall in the hertz to kilohertz range. They are small fractions of the carrier, and they are recovered by coherent processing rather than by comparing nominal frequencies.

Where sub-millimetre sensitivity comes from

Phase is the more sensitive quantity. A displacement Δx produces a round-trip phase change of:

Δ φ = 4\pi · Δ x / λ

For a 1 mm displacement this is about 58° at 24 GHz and about 144° at 61–62.5 GHz. The shorter wavelength gives roughly 2.5 times more phase per millimetre, which is the quantitative form of the statement made in How mmWave Radar Works — that 60 GHz is the band to use when breathing or heart rate is required.

Three parameters that set precision and span

Each of the following is a sampling constraint, so each is a trade rather than a setting that can be widened independently.

Range resolution follows the swept bandwidth, Δd = c / 2B. More span gives finer separation.

Velocity resolution follows the observation time T_obs over which the phase history is collected:

Δv = λ / (2 · T_obs)

For a one-second observation this gives about 6.3 mm/s at 24 GHz and about 2.4 mm/s at 61–62.5 GHz. Longer observation gives finer velocity resolution, which is why slow periodic motion — breathing — is measured over intervals rather than from single frames.

Unambiguous velocity follows the chirp repetition interval T_c:

v_max = λ / 4 · T_c

This is the one quantity where the shorter wavelength works in the opposite direction. At the same chirp interval, the 61–62.5 GHz band reaches a smaller unambiguous velocity than 24 GHz. A radar tuned to resolve sub-millimetre chest motion and a radar built to measure vehicle speed are therefore sampling the same physics with incompatible timing.

Not published: the modules' internal chirp timing and coherent processing interval do not appear in the datasheets, so no T_c or T_obs value is given here, and the worked figures above are labelled as illustrations of the equations.

Published output cadences

Separate from the radio parameters above are the intervals at which results are reported. These are published, and they are output cadences, not integration times:

Report	R24AVD1 (24 GHz)	60 GHz finished units
Occupied → unoccupied	40 s	about 40 s
Unoccupied → occupied	< 0.5 s	—
Static / active change	< 0.5 s	—
Approach / leave / no lateral movement	2 s	—
Body-movement amplitude 0–100	5 s	1 s
Breathing rate, heart rate	—	about 3 s

The asymmetry — under half a second to declare a room occupied, about 40 seconds to declare it empty — is a deliberate stability choice, described in Three mmWave Radar Specs That Are Almost Always Exaggerated.

Distance and position are reported by the finished units in centimetres and as x/y/z, both about every 2 s, and both documented as non-critical functions with limited accuracy. They are useful while commissioning, as set out in Using Distance and Position Output to Debug a Radar Installation, and are not a basis for a product feature.

The body-movement amplitude is a dimensionless index from 0 to 100 with defined bands, not a velocity. It is not converted to metres per second.

The two bands side by side

Quantity	24 GHz	61–62.5 GHz
Wavelength	12.5 mm	4.80–4.92 mm
Doppler shift per 1 m/s	≈ 160 Hz	≈ 410 Hz
Phase change per 1 mm displacement	≈ 58°	≈ 144°
Phase change per 1 mm, relative	1×	≈ 2.5×
Velocity resolution at 1 s observation	≈ 6.3 mm/s	≈ 2.4 mm/s
Unambiguous velocity at equal chirp interval	larger	smaller
Swept bandwidth published	no	61–62.5 GHz (1.5 GHz span)
Derived range resolution	not stated	≈ 10 cm

What this accounts for

Respiration and heart rate use 60 GHz. Displacement sensitivity scales inversely with wavelength, so the shorter band returns about 2.5 times more phase per millimetre.
Presence over a wide area uses 24 GHz. The longer wavelength and the wider beam cover a larger volume; the published beam for R24AVD1 is 90° horizontal by 60° vertical.
A posture radar is not a speed instrument. The unambiguous velocity limit moves against the higher band, and the same processing budget is spent on deciding what the target is doing. The practical figure for a home posture radar is around 3 m/s, with the reasoning in Three mmWave Radar Specs That Are Almost Always Exaggerated.

Summary

Range comes from round-trip time, recovered in practice from an FMCW beat frequency, and its resolution follows the swept bandwidth. Velocity comes from the Doppler shift, and its resolution and span follow observation time and chirp interval respectively.

The two bands differ by a factor of about 2.5 in wavelength, and that one ratio propagates through every sensitivity figure — phase per millimetre, Doppler shift per metre per second, velocity resolution — while moving the unambiguous velocity limit in the opposite direction.

Where a datasheet publishes a value, that value is used here. Where it does not, the equation is given and the absence is stated.

Where to go next

The conceptual version without arithmetic: How mmWave Radar Works
Practical limits on angle, distance and speed: Three mmWave Radar Specs That Are Almost Always Exaggerated
Module specifications in full: 60 GHz & 24 GHz Radar Modules for OEM Integration
Using distance and position while commissioning: Using Distance and Position Output to Debug a Radar Installation

Full documentation: https://249263431.github.io/60GHz-Radar-SDK/

Modules and finished units: https://www.tindie.com/stores/fuxinsuo/

The Physics Under The Protocols: A Developer's Tour Of Electromagnetism

Fri, 04 Sep 2026 14:25:09 +0000

Most of us debug things that ride on electromagnetic waves all day without ever looking at the physics underneath. This is the short version, written for developers, of why radio, WiFi and visible light are literally the same phenomenon.

One Force, Not Two

Until 1820 electricity and magnetism were treated as unrelated curiosities. Then Hans Christian Oersted noticed a compass needle deflect when current ran through a nearby wire. That was the entire experiment, and it meant the two could not be independent.

Andre-Marie Ampere had the mathematics for the force between current carrying wires within months. In the 1830s Michael Faraday showed the reverse, that a changing magnetic field induces a current in a nearby wire.

In the 1860s James Clerk Maxwell turned all of it into four equations. They predicted a self sustaining wave travelling at roughly 3 x 10^8 meters per second, a number already known from optics as the speed of light. Maxwell had derived light from equations written about wires and magnets. Heinrich Hertz generated and detected radio waves in 1887 and confirmed it.

Why The Spectrum Is Continuous

Radio, microwave, infrared, visible light, ultraviolet, X-rays and gamma rays are one phenomenon sliced by frequency. Nothing physical changes at the boundaries between them, only the wavelength and what that wavelength happens to interact with.

Once that clicks, a lot of separate networking facts collapse into one. Antenna length tracking wavelength, why 2.4 GHz passes through a wall better than 5 GHz, why interference shows up where two links share a band. Same equations, different numbers.

Induction Is The Part You Touch Every Day

A changing magnetic field induces a current in any nearby conductor. That is the transformer inside your power brick and the wireless charging pad on your desk.

It is also crosstalk. A fast switching signal trace induces current in the trace beside it whether you wanted that or not, which is Faraday's law showing up as a bug rather than a feature. Ground planes and spacing rules exist because of a discovery from the 1830s.

Ohm's Law Is Still The Fastest Debugging Tool

V = IR. Voltage is the potential difference pushing charge, current is the rate that charge flows, resistance is what opposes it. Measure any two and the third follows.

For hardware faults that is often quicker than reaching for a logic analyzer. A multimeter tells you whether the rail is at voltage, whether current is being drawn, and whether something in the path has gone open or short, and that narrows most problems before you ever look at a waveform.

What Makes This Worth Reading Twice

The pattern is worth borrowing beyond physics. Two domains looked separate, one experiment linked them, and a single mathematical description then covered both. That description went on to predict something nobody had put into it, and the prediction turned out to be a number already measured in a different field.

A description reorganizes what you already know. A model tells you something you did not.

The full walkthrough, covering charge and current, electric and magnetic fields, the four equations, the spectrum, induction and circuits, is in this guide to how electromagnetism works.

Quantum Mechanics For Developers: The Physics Under The Hardware You Ship

Wed, 26 Aug 2026 22:45:18 +0000

Most of us here write code that runs on transistors, and almost none of us ever had a reason to ask why a transistor works at all. This is a short tour of the physics that answers that question, written for developers rather than for physicists.

Quantum mechanics has a reputation problem among people who write software. It arrives as cats in boxes and particles in two places at once, which makes it sound like philosophy rather than engineering. It is neither. It is the most experimentally verified theory in physics, its predictions have never once failed, and it is the reason semiconductors, lasers and MRI machines exist at all.

The Principles That Do The Work

Five ideas carry almost all of the weight.

Quantization. Energy comes in discrete packets. An electron in an atom is restricted to specific energy levels, like a staircase with no ramp between the steps. Planck found this in 1900 while working out why hot objects glow the colors they do.

Wave-particle duality. Send electrons through a crystal and they produce an interference pattern like water waves through two openings. Detect those same electrons on a screen and each one arrives as a single point. Neither description is complete on its own.

Superposition. A system can sit in a combination of states until a measurement forces one outcome. This is not a statement about our ignorance of some hidden value. No theory that assigns pre-existing definite values to every property can reproduce all the quantum predictions.

Entanglement. Two particles become correlated such that neither has a state you can describe independently, at any separation. Einstein called it spooky action at a distance and believed it showed the theory was incomplete.

Tunneling. A particle crosses an energy barrier it classically cannot cross, because the wave function decays through the barrier rather than stopping at it, and still has a nonzero value on the far side.

The Experiments That Forced It

The double-slit experiment is the center of all of it. Particles sent one at a time build an interference pattern, which is wave behavior. Add a detector that records which slit each particle went through and the pattern disappears. Feynman said this single experiment contains the only mystery in quantum mechanics, because everything else is a variation of the same puzzle.

The photoelectric effect settled the question of whether light is quantized. Shine light on a metal and electrons are ejected, but only above a threshold frequency, no matter how intense the light is. Einstein explained it in 1905 with photons carrying energy proportional to frequency, and it earned him the Nobel Prize in 1921.

Stern-Gerlach in 1922 sent silver atoms through a non-uniform magnetic field and got two distinct beams instead of a continuous spread, which is the first direct evidence of quantum spin.

Bell test experiments, from Alain Aspect in 1982 through the loophole-free versions in 2015, ruled out local hidden variable explanations for entanglement. That is about as close as physics gets to closing an argument.

Where It Shows Up In Your Stack

Semiconductors are quantum band structure applied at industrial scale, which means every transistor you have ever run code on is a quantum device. Flash memory writes and erases by tunneling electrons through an oxide layer. Lasers depend on quantized energy levels and stimulated emission. Scanning tunneling microscopes image individual atoms using tunneling current as the signal.

And quantum computing treats superposition and entanglement as a computational resource rather than a curiosity, which is why the field cares so much about coherence times. If you want the computing angle specifically, the quantum computing guide covers qubits, gates and error correction without the marketing.

The Takeaway

You do not need the mathematics to get value out of the intuition. Knowing that energy is quantized, that measurement is not passive, and that tunneling is a real transport mechanism changes how you read hardware documentation and how much sense device physics makes. The full walkthrough of the principles, the experiments and the applications is in the quantum mechanics guide, and it is written for people coming in without a physics background.

The End of Time: What It’s Really Like to Fall Into a Black Hole

Fri, 21 Aug 2026 08:03:22 +0000

Imagine drifting through the silent expanse of space when, suddenly, the stars begin to warp. You’re being drawn toward a dark abyss where the familiar rules of physics start to unravel. You aren’t just falling into a void you’re entering a mathematical enigma where space and time themselves begin to twist.

Drawing on explanations popularized by physicists like Brian Cox, the reality of falling into a black hole turns out to be far stranger and more unsettling than science fiction ever suggested.

What Exactly Is a Black Hole?
At its simplest, a black hole is an object so massive and so densely compressed that its gravity becomes inescapable. If you were to take our Sun and crush it down until its radius was just 3 kilometers, you would form a black hole. At that point, the speed required to escape — known as the escape velocity exceeds the speed of light. Since nothing can travel faster than light, not even light itself can escape.

We detect black holes indirectly by observing their accretion disks whirling rings of gas and dust orbiting at extreme speeds. Friction heats this material until it glows brilliantly. Because black holes warp spacetime, they also bend light, allowing photons from the back of the disk to curve around to the front, creating a distorted halo that looks almost unreal.

The Two Journeys: A Matter of Perspective
One of the strangest aspects of falling into a black hole is that there isn’t a single, objective experience. Gravity distorts spacetime, meaning what happens depends entirely on where you’re observing from.

The Outside Observer: To a distant observer watching through a telescope, your clock appears to tick slower and slower as you approach the event horizon. You never quite cross it. Instead, you seem to freeze in place, fading into deep red as your light is stretched to longer and longer wavelengths.

Your Perspective: For you, nothing dramatic happens at the horizon. You’re in free fall, which initially feels like floating similar to astronauts aboard the International Space Station. Space behaves like a river flowing inward; at the event horizon, that flow reaches the speed of light. Once inside, escape becomes as impossible as swimming upstream faster than light itself.

Spaghettification and the Singularity
As you fall deeper, gravity pulls much harder on your feet than on your head. This difference creates a violent stretching force known as spaghettification, elongating and compressing your body until molecules, atoms, and even protons are torn apart.

What remains is drawn toward the singularity. In classical Einsteinian physics, this isn’t merely a point in space it represents a breakdown of time itself. Inside a black hole, moving toward the singularity is as unavoidable as moving toward tomorrow. There is no path around it.

The Information Paradox: Do You Really Die?
For decades, physicists believed that anything falling into a black hole was lost forever. That view changed when Stephen Hawking showed that black holes emit a faint glow known as Hawking radiation. Over unimaginably long timescales, this radiation causes black holes to evaporate completely.
This raises a profound question: what happens to the information describing everything that fell in? According to quantum physics, information cannot be destroyed.

Research from recent years suggests a startling possibility: the information may be encoded in the radiation itself, returning to the universe in an extremely scrambled form. Some speculative theories even propose that tiny wormhole-like connections could link the interior and exterior, offering a mathematical route for information to escape.

A Universe of Wonder
Black holes are more than cosmic traps. They are natural laboratories for probing the deep structure of reality, where gravity, quantum mechanics, and information collide. Some physicists now suspect the universe itself may function less like a machine and more like a vast network of information, not unlike a quantum computer.

As Cox has often emphasized, understanding these ideas doesn’t diminish the awe of the universe it deepens it. The night sky becomes more mysterious, not less.
The closer we look at black holes, the clearer it becomes that they are not just places where matter disappears but where our understanding of time, space, and reality is pushed to its absolute limits.

Unjammable by Physics, Not by Architecture: A VLF Channel from Orbit

Mon, 10 Aug 2026 12:56:50 +0000

Subtitle: Resistance to counter-jamming built into the nature of the band, not into the number of nodes. Slow. Physical. Hopeless for video.

This is the second post in the series. The first one covered the tooling; this one is about what a VLF channel from orbit can do at all, where its limits are, what it depends on, and what that costs.

A fair warning, so nobody builds false expectations: below there will be plenty of talk about "fundamental" and "unjammable", but precisely as much as justified, and not a bit more. We will stop at the honest boundaries of the idea, including the ones behind which our optimism ends.

Why all modern communication is hostage to architecture

Let us start with what happens to fast communication in the moment things turn bad.

Every modern terminal depends on a chain where breaking one link is enough: a repeater, a cable, a beam, an allocated band, a physical object. That is exactly what an adversary with modern electronic-warfare tools does: it does not have to destroy the network wholesale — one careful strike at the right point is enough. At night, at dawn, at the least convenient moment — and the city goes silent, the continent goes silent, the terminal goes silent.

The familiar counter-measure to this disease is to multiply channels. The concept of a dense constellation, where each terminal works with many vehicles at once and losing one node does not kill the link, is not new: this principle, a network of many independent carriers, was originally developed in the Soviet Union back in the 1970s, and today it underlies systems such as Starlink. When people say "unjammable satellite internet", they mean exactly this.

But look closely at the nature of that survivability. It is architectural. It relies on quantity: while there are many components, the network survives; when the enemy removes a sufficient share, it degrades into weak isolated segments, and each becomes a target again. Survivability here is built on duplication, not on the property of the physical channel itself. Many copies make the network blind to one jammer; the essence does not change.

The watershed: architecture today, physics tomorrow

Why now? Because over recent decades electronic warfare has become cheap and mass-produced: a portable jammer can be worth more than an entire network built as a collection of duplicates. The more duplicates, the higher their running cost, and quantity stops helping — for example when many vehicles all work within the same narrow focused beams. A lot of targets does not save you when all targets are cut from the same yarn.

An idea that rests on the nature of the band

My approach is different: a bet on a band where resilience against suppression is baked in at the physics level, not at the level of quantity. Meaning not "add a thousand more nodes", but "the wave carrier itself is arranged so that jamming it means jamming the medium, not the equipment".

This is the key difference: the jammer targets the channel, not a transceiver. In the first case it fights numbers; in the second it would have to rewrite the law of propagation.

Meet VLF. The key numbers are simple: a few kilohertz at the top, wavelengths in the kilometers range — radio waves comparable in size to the terrain they travel along.

Here physics works in favor of communication:

the extreme wavelength does not let the wave hide behind relief or below the horizon — the planet guides it, in the waveguide between the conductive Earth and the lower ionosphere, thousands of kilometers with zero repeaters;
reception does not require line of sight — the wave hugs the surface;
the receiver already sits inside the signal, because the wave embraces the surface.

The main consequence: to jam a VLF, a jammer does not need to aim at one point. Interference travels in the same waveguide as the useful wave, and to choke the path, one must cover the whole territory with noise at once — a huge footprint, or nothing.

Suppression stalls not because there are many nodes. It stalls because the wave has no single point of application that one jammer can "eat".

Where honesty begins: what the channel still depends on

I will not turn the desirable into the actual and promise "vacuum independence". That would be precisely the kind of marketing promise we criticize today.

The channel does not exist on its own. The wave that feeds it is produced by powerful ground transmitters — of which there are a handful in the world. If those stations are down, nothing is transmitted: the source remains ground infrastructure, and it is just as fragile as any critical point.

What is physically protected from jamming is the receiving side and the wave itself inside the channel path. For the waveguide the concept of "switching off a node" does not hold: there is no "server" to attack, the wave is carried by the medium. Survivability belongs to the receiver and the path, not to the source.

So the lower bound of the estimate is precise: the physics of the channel cannot be bent by jamming, but the source remains a risk area. The advantage is real, direct, but bounded.

The speed, worth stating openly

Now for the thing VLF is traditionally laughed at for, and justifiably.

Speed is bits per second, at best kilobits. For a terminal used to megabits and video, this looks like a mockery from a past millennium. No video. No stream. A page takes hours.

But it is a trade-off, not a hole. On such a speed lives exactly what a catastrophe needs to deliver: a short command, an emergency word, a reserve call. Not a permanent stream, but the one key message that has to arrive when the rest of the communication is already silent.

If you need megabits, this channel is not for you, and I will not argue. If you need the last chance itself — here the math is different.

What would be the use, and in what configuration

If the hypothesis clears the run, the channel takes its place not where the bit is cheap, but where nothing else would be left:

a short command at the moment when habitual channels go silent;
a couple of emergency words from a site where a continuous network is no longer guaranteed;
a reserve thread "to survive", until the infrastructure gets back on its feet.

The common ground: they do not need bandwidth, they need the bare possibility. And that possibility has to fit on a platform of dozens of kilograms — an engineering question which, 40 years ago, would have required a station the size of a house. Today compact high-voltage hardware and dense power electronics make the "funny" solvable.

Status: as it is

Everything said so far is a hypothesis.

There is not a single experiment confirming that such a channel works in the real world. The numbers live in calculations, and calculations may give zero. If the idea turns out infeasible, I will publish an accurate negative result and show why: a story of "does not work" is legitimate physics, no less interesting than "works", if it is reproducible.

Instead of a conclusion

The essence is one formula: to build resilience not by repeating copies, but by the property of the wave itself. This transition, from architecture to physics, is what I consider significant — and even if this project never happens, the question is worth asking: can we build a channel for which "jamming" is poorly defined for a fundamental reason?

If you have a comment about the weakest point of this logic, write it — that is why I publish. At the bottom of the spectrum the community is small, but that way I can claim to know every nick.

It Isn't Computing That Costs Energy, It's Forgetting

Thu, 30 Jul 2026 02:48:38 +0000

Physics sets no minimum energy for computation, only for erasing information. That fact is true, beautiful, and ten orders of magnitude below your actual datacenter bill. The real lesson is the argument this essay has with its own headline.

In 2012, in a lab in Lyon, a team of physicists watched a single glass bead forget one bit of information, and measured the heat it gave off while doing it.

The setup, published by Bérut and colleagues in Nature that March, was “a single colloidal particle trapped in a modulated double-well potential”: a microscopic bead sitting in one of two laser-made energy valleys, left valley or right valley, a physical one-or-zero. Erasing the bit means forcing the bead into one designated valley regardless of where it started, destroying the record of where it had been. Fifty-one years earlier, an IBM physicist named Rolf Landauer had predicted exactly what that destruction must cost: any logically irreversible operation, any step that throws information away, must dissipate at least kT ln 2 of heat per erased bit. At room temperature that is about 2.9 zeptojoules, a 21-digits-of-zeros fraction of a joule. The Lyon experiment confirmed it: “the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles.”

Here is why that bead belongs in an essay for people who think about datacenters. Landauer's 1961 principle, and a companion result by his IBM colleague Charles Bennett in 1973, together say something genuinely strange about where the energy cost of computing lives. Bennett showed that a logically reversible computation, one that never discards information, has no known thermodynamic floor at all; there is no law of physics that sets a positive minimum on its energy. The floor attaches only to erasure. Physics does not charge you for computing. It charges you for forgetting.

That is the title of this essay, and as a statement about fundamental limits it is true. The intuition behind every AI-energy headline, that arithmetic itself is what burns the megawatts, has the physics upside down. So you might expect the practical lesson to be: make your chips forget less, and the energy problem melts away.

It is not, and the reason it is not turns out to be a better lesson than the one the title promises. Stay with me, because this essay is going to argue with its own headline, and the argument is where the value is.

What a chip actually pays for

Take the Landauer floor seriously as a unit and price a modern machine against it.

Erasing one bit at room temperature: about 2.9 zeptojoules, 2.9 × 10⁻²¹ joules. Erasing all 64 bits of a doubleword: about 1.8 × 10⁻¹⁹ joules. Hold that number.

Now the engineering side. The canonical accounting of what operations cost on real silicon is Mark Horowitz's 2014 analysis, still the reference point the architecture community argues from (and the gaps have widened, not narrowed, since). In round figures from that dataset: a 64-bit floating-point operation costs 0.4 to 3.7 picojoules. An on-chip register access, around 6 picojoules. A cache access, 10 to 100 picojoules depending on size. And an off-chip DRAM access: 1,300 to 2,600 picojoules.

Set those against the floor, and label this arithmetic as mine, derived from the cited figures. The 64-bit floating-point operation runs a factor of a few million to a few tens of millions above the Landauer cost of erasing 64 bits. And the DRAM fetch, at roughly two nanojoules against a 64-bit erasure floor of 1.8 × 10⁻¹⁹ joules, runs about ten billion times the thermodynamic price of destroying the same data outright.

Ten billion. Ten orders of magnitude. Whatever your intuition just did with that number, follow it one more step: in any real machine, the thermodynamic cost of forgetting is a rounding error on a rounding error. The physics floor is set by erasure, but the bill is set by something else entirely: charging and discharging the capacitance of wires to shuttle bits across physical distance. A CMOS gate dissipates energy whether or not the operation it performs destroys information; the destruction is incidental. Moving a bit from DRAM to the register file costs vastly more than moving it from existence to nonexistence.

This is also exactly why the economics of AI inference are what they are. Serving a large model is memory-bandwidth-bound, not arithmetic-bound; the industry's architectural energy goes into data locality, high-bandwidth memory stacked millimeters from the compute, keeping weights resident, batching to amortize fetches. Nobody optimizes erasure, because erasure was never on the bill. The developer takeaway from the actual numbers is nearly the inverse of this essay's title: energy efficiency in computing is, in practice, the art of moving less. Keep data close. Distance is the enemy. The kilowatt-hours in an AI-energy headline are overwhelmingly spent hauling bits around, and secondarily on the cooling that hauls the resulting heat away.

A law that is true and does not bind

So what is Landauer's principle worth to a working technologist, if it sits ten orders of magnitude below the bill?

This is where the essay earns its keep, because learning to classify physical laws by whether they bind is a transferable skill, and this lane has now seen both kinds.

A while back this blog argued that softmax is the Boltzmann distribution: the “temperature” in your sampling code is not a metaphor for 1870s thermodynamics but the same equation, and the physics transfers for free, today, as working intuition. That is one kind of physics result: an identity. It binds immediately.

Landauer is the other kind: a bound that does not currently bind. It is real, experimentally confirmed, and it constrains nothing you will ship this decade, because the constraint that actually operates on your systems is capacitance, distance, and cooling, all of it engineering, none of it fundamental. A recent analysis of CMOS limits (arXiv:2312.08595) estimates the ceiling for conventional silicon at around 4.7 × 10¹⁵ four-bit operations per joule, roughly two hundred times more efficient than current microprocessors. Two hundred-fold is the real, harvestable headroom on the table, and it comes from better engineering of the same physics, not from approaching Landauer. The floor is so far down it plays no role in the game. A law can be perfectly true and operationally irrelevant, and knowing which kind of law you are holding, an identity that transfers, a bound that binds, or a bound that waits, is worth more than either law alone.

But “waits” is the right word, and the waiting has teeth. Because there is one research program for which Landauer is not a curiosity but the entire prize, and its troubles are the most instructive part of this story.

Why the headroom can't be cashed

If erasure is the only thing physics charges for, then a computer that never erases, a reversible computer, could in principle run at arbitrarily low energy. Bennett proved the logic in 1973. People have been trying to build it ever since, and three barriers keep standing, each verified, each illuminating.

First, you pay in time. Adiabatic switching, the practical route toward reversibility, saves energy exactly in proportion to how slowly you switch; dissipation approaches zero only as switching time approaches infinity. Even the Lyon bead only touched the Landauer bound “in the limit of long erasure cycles”; erase fast and you dissipate extra. Reversible computing does not eliminate the energy cost so much as convert it into a time cost, and for a latency-priced workload like inference, time is often the more expensive currency.

Second, you pay in memory, and the bill is literally incomputable. A reversible computation must retain its intermediate results, the so-called garbage bits, to stay invertible. Discard the garbage and you pay Landauer after all; keep it and it accumulates. Worse, the theory community has shown there is in general no upper bound on the extra storage required, and computing the minimum garbage for a given computation is an undecidable problem. Energy traded for memory, with no algorithm even to tell you the exchange rate.

Third, and sharpest: the devices themselves foreclose it. A paper in Scientific Reports on adiabatic superconducting logic states the obstacle in one sentence: “The bit energy of conventional logic devices, including CMOS and energy-efficient superconductor logics, is at least larger than ~1,000 kBT, which is too large to permit their use as reversible logic gates.” Sit with the irony. The gap between today's devices and the Landauer floor is the headroom the whole program wants to harvest, and it is precisely that gap that makes the harvesting impossible: a gate that dissipates a thousand kT per operation swamps the fraction of kT you were trying to save. You cannot climb down to the floor on a ladder made of the thing keeping you off it. The demonstrations that have genuinely operated below the threshold live in exotic superconducting circuits at four kelvin, and the assessments in venues like Communications of the ACM are blunt: they have not scaled, and remain no more practical than the refrigerated alternatives. (The four-kelvin detail hides one more honest wrinkle: the Landauer floor scales with temperature, so cryogenic logic lowers the floor itself, which is one reason superconducting computing keeps being reinvented despite everything.)

None of this makes reversible computing foolish. It makes it a physics program rather than an engineering roadmap: a real claim on a real prize, currently unreachable by any device we know how to build at scale. The three orders of magnitude of “headroom” between a good transistor and the floor are not an efficiency budget waiting to be spent. They are, for now, the moat.

What to take home

Three things, in descending order of daily usefulness.

Optimize movement, not arithmetic. The bill for your workload lives in data motion: DRAM fetches at a thousand times the cost of the FLOP they feed, network hops above that, cooling on top of everything. When you profile for energy, or reason about why inference pricing looks the way it does, or evaluate the next accelerator's claims, the question is always locality: how far do the bits travel? A model that fits in on-chip memory is not slightly cheaper than one that spills to DRAM; it is categorically cheaper, and the categorical difference is measured in those Horowitz ratios. This is the lens the actual physics of computing hands you, and it is the opposite of the folk version where the multiplications are what cost.

Classify your limits before budgeting against them. Landauer is a hard law ten orders of magnitude below your problem; the CMOS ceiling is an engineering limit a mere factor of a few hundred away; your cooling budget binds this quarter. Treating a distant fundamental limit as if it constrained this decade's roadmap (or citing it to claim efficiency is nearly exhausted) is a category error in both optimistic and pessimistic directions. The habit generalizes far beyond chips: for any “fundamental limit” invoked in a technical argument, ask what actually binds at the current operating point. It is usually something much more boring and much more fixable.

And keep the bead in mind, because the floor is patient. Every doubling of efficiency closes the gap by one factor of two, and the trend that has run since the 1960s (Koomey's law, the efficiency sibling of Moore's) points at the zeptojoule scale on a horizon measured in decades, not centuries. If computing keeps improving, there is exactly one wall at the bottom, it is made of thermodynamics rather than silicon, and the only door through it is learning to compute without forgetting, with all three barriers above waiting at the door. The title of this essay is false about your datacenter bill and true about the end of the road. Physics does not charge for computing. It charges for forgetting. It is just that, for a few more decades, the delivery fees dwarf the price of everything on the menu.

Sources

Landauer, R. (1961). “Irreversibility and heat generation in the computing process.” IBM Journal of Research and Development, 5(3), 183–191. (The kT ln 2 erasure bound; ≈2.9 zeptojoules at 300 K, arithmetic from the constant.)
Bennett, C. H. (1973). “Logical reversibility of computation.” IBM Journal of Research and Development, 17(6), 525–532. (No thermodynamic floor for logically reversible computation.)
Bérut, A., Arakelyan, A., Petrosyan, A., Ciliberto, S., Dillenschneider, R., & Lutz, E. (2012). “Experimental verification of Landauer's principle linking information and thermodynamics.” Nature, 483, 187–190. (“A single colloidal particle trapped in a modulated double-well potential”; “the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles.”)
Horowitz, M. (2014). “Computing's energy problem (and what we can do about it).” ISSCC keynote dataset: 64-bit FLOP 0.4–3.7 pJ; register ~6 pJ; cache 10–100 pJ; off-chip DRAM 1,300–2,600 pJ (figures as reported in Communications of the ACM and SemiEngineering's coverage). Ratios to the Landauer floor in this essay are derived from these figures.
Ho, A., et al. (2023). “Limits to the Energy Efficiency of CMOS Microprocessors” (arXiv:2312.08595): maximum CMOS efficiency ≈4.7 × 10¹⁵ FP4/J, “roughly two hundred-fold more efficient than current microprocessors.”
“Reversible logic gate using adiabatic superconducting devices.” Scientific Reports 4:6354. (“The bit energy of conventional logic devices, including CMOS and energy-efficient superconductor logics, is at least larger than ~1,000 kBT, which is too large to permit their use as reversible logic gates.”)
Hänninen, I., Lent, C., Snider, G., & Blair, E. (2014). “Reversible and Adiabatic Computing: Energy-Efficiency Maximized” (Notre Dame).
Thomsen, M. K. (2023). “Design of Reversible Computing Systems” (arXiv:2309.11832): garbage-bit retention and the undecidability of minimum garbage.
Markov, I. L. (2014). “Limits on Fundamental Limits to Computation” (arXiv:1408.3821).
CACM, “The Future is Reversible.” The time cost of adiabatic switching; scaling assessments.
On foundations: “Physical Foundations of Landauer's Principle” (arXiv:1901.10327): the derivation remains philosophically debated; this essay says “experimentally confirmed,” not “settled.”
This blog, “Softmax Is the Boltzmann Distribution”: the companion case of physics that transfers as an identity, referenced for the contrast.

For any “fundamental limit” invoked in a technical argument, ask what actually binds at the current operating point.

That discipline, the cost lives where you are not looking, not where the impressive-sounding number points, is the one agent trust needs too. What binds whether you can trust an agent's output is not the model's fluency or a headline benchmark; it is whether you can verify what the agent actually did. The Agent Trust Stack is the harness for measuring that real thing rather than the apparent one: durable identity, a provenance record of what the agent did, a rating that survives adversarial checking, and an audit trail that holds when the model has a confident bad day.

Read the Theory of Agent Trust · See Hosted Chain of Consciousness

pip install agent-trust-stack · npm install agent-trust-stack

Or a layer at a time: pip install chain-of-consciousness / npm install chain-of-consciousness · pip install agent-rating-protocol / npm install agent-rating-protocol

Originally published at vibeagentmaking.com.

Physics might be entering its own “LLM moment.”

Fri, 01 May 2026 05:32:49 +0000

What if one AI model could simulate all fluids, from ocean currents to plasma in space?

The problem:

Simulating liquids and gases has always been slow and expensive.

And that's the reason current AI models are limited to one specific use case.

Buthat’s starting to change.

Here comes Walrus, a transformer model that can simulate liquids, gases, and plasmas in a general way.

It’s even open-source.

What’s different?

Instead of focusing on one system, Walrus learns how physics behaves broadly.

It predicts the next state of a system from past states , similar to how models like ChatGPT predict the next word.

The key idea: “jittering”

Simulations break down over time because small errors keep adding up.

Walrus fixes this with a simple trick:

Slightly shift the data at every step

In simple language:

Imagine you’re trying to walk straight ahead with your eyes closed.

Each step you take is slightly off, maybe a tiny bit to the right.

At first, it’s barely noticeable.

But after 100 steps, you have drifted far off course.

That’s exactly what happens in simulations:

tiny errors -> keep adding -> completely wrong result

Now add “jittering”

Instead of always stepping straight (and slightly right), you:

Randomly adjust your direction a tiny bit each step, left, right, forward

Now:

Your errors don’t keep pushing you in one direction

They cancel each other out over time

This is actually a good move toward general-purpose physics models.

What do you think?

DevLog 20250722: (Special Project) Correct Physics Handling

Tue, 22 Jul 2025 23:45:02 +0000

Overview

This little project deals with very simple (2D) right body physics. I will not spoil all the fun - essentially we control a 2D rocket. It would be fun to visualize data processing in such a fashion on a node canvas - kind of matches our Divooka visual programming scheme.

The hypothesis is that at least for 2-dimensional cruise control, a simple PID should be able to do something useful, and it's with that gut I am set to experiment a bit to verify my idea.

I've done some experiments in July last year but ended up not going far due to technical challenges.

Challenge

The challenge was to get it working properly with physics setup. Per RigidBody2D doc:

So is it relative or global? Without being able to visualize the force, it's a bit hard to tell also whether to use a force, or to use impulse.

It's been a while and I almost gave up - never really have time to create our own physics engine. But Godot got a new physics kernel and I thought maybe give it a try.

Some Inspiration

I've been doing some analytics and talking with ChatGPT on a new airship design that puts the air vessel at the bottom of the ship instead of hanging overhead - that inspired me maybe there are two things with current setup that's not working:

After fixing a few API calls related to GraphEdit get_children() change. I was looking at the force application code once again:

func _physics_process(delta):
# Remark: We are not using to_global directly because of issues with viewport transform
var left_anchor = %LeftThrusterCenterOfAction.position
var right_anchor = %RightThrusterCenterOfAction.position

# Remark: applied force is RELATIVE to the body (aka. current object)
apply_force(Vector2(0, -1).rotated(rotation + _left_engine_angle_degrees / 180.0 * PI) * _left_engine_thrust, left_anchor)
apply_force(Vector2(0, -1).rotated(rotation + _right_engine_angle_degrees / 180.0 * PI) * _right_engine_thrust, right_anchor)

Again, it's really simple once we figure out what's the right way to do things.

References

Video and intro: YouTube