Infinite Loop · Physics of Computation

Are We Reaching the Limits of Moore’s Law — or the Limits of Computation?

Everyone knows computers get faster. Almost nobody knows why that progress is now slowing — and whether the wall ahead is built by engineers or by the universe.

The Core QuestionAre today’s hardware limits engineering problems we can out-clever — or fundamental laws of physics we cannot?

The Short AnswerBoth. One wall is made of heat and money. A second, deeper wall is written into thermodynamics itself.

Dr. Henry Caldwell — Principal Research Scientist | Varg Research Lab

Stage 1 · The Abstract

What this article shows

For sixty years, the number of transistors on a chip doubled at a steady rate — a pattern called Moore’s Law. That doubling has slowed. This article reconstructs why. We separate two very different kinds of limit: the engineering limits (heat, electrical leakage, the cost of printing ever-tinier patterns) and a single physical limit set by the laws of thermodynamics. We will define every term as we go, derive the physical floor of computation from first principles with arithmetic you can check by hand, and then ask the honest question: when computers stop getting faster, which wall did we hit?

Background

How the doubling began, and why it held for so long

In 1965 the integrated circuit — the “chip” — was only six years old. Gordon Moore, then director of research at Fairchild Semiconductor, was asked to predict the next decade of the industry for a trade magazine. He plotted the number of components on the best chips of each year, drew a line through the points, and extrapolated.

His article, Cramming More Components onto Integrated Circuits, appeared in Electronics on April 19, 1965. In it he observed that the component count had been doubling roughly every year, and predicted the trend would continue. Ten years later, in 1975, he revised the rate to a doubling about every two years. The forecast proved astonishingly accurate: for 1975 he had projected around 65,000 components, and a memory chip released that year held 65,536 — within one percent.

I just did a wild extrapolation. — Gordon Moore, reflecting on the 1965 article (2015 interview)

It is worth being precise about what Moore’s Law is. It is not a law of nature. It was an observation about an economic and engineering trend — one that became, as the Caltech engineer Carver Mead (who coined the name “Moore’s Law” around 1970) and others noted, a self-fulfilling prophecy. The industry treated the doubling as a target and organized billions of dollars of research around hitting it.

For decades, two trends advanced together. Moore’s Law described how many transistors fit on a chip. A second, quieter rule explained why those extra transistors also ran faster without melting. That rule was formulated by IBM researcher Robert Dennard and his colleagues in 1974, and it is the key to the whole story.

Dennard scaling: the engine behind the magic

Dennard scaling says that as you shrink a transistor, its power consumption shrinks in proportion to its area. Make every dimension smaller, lower the voltage to match, and the power density — the heat produced per square millimetre — stays constant. So each new generation could pack in twice the transistors, run them faster, and still dissipate about the same total heat. Smaller, faster, and cooler, all at once.

This is the deep reason the early decades felt like free progress. Engineers were not fighting physics; physics was cooperating. Then, around 2005 to 2007, it stopped.

Both curves once rose together. After ~2005, transistor counts kept doubling but clock speeds stalled near 4 GHz. Hover or tap to enlarge. Schematic; vertical axis is a logarithmic illustration, not to scale.

What this establishes Moore’s Law is an observation, not a physical law, and it rode on a second trend — Dennard scaling — that kept shrinking chips cool. To understand why progress slowed, we must look at why Dennard scaling broke. That requires a few precise definitions.

Definitions

The vocabulary, defined before we use it

Let us define each term precisely. Nothing below this point will use a word that has not first been pinned down here.

Transistor: A microscopic electrical switch. It turns a tiny current on or off. A modern chip contains tens of billions of them; switching them in patterns is what “computing” physically is.
Integrated circuit (chip): A single sliver of silicon carrying many transistors and the wiring that connects them.
Process node (“2 nm”): The name of a manufacturing generation — e.g. “3 nm” or “2 nm”. Crucially, since about 1997 these numbers are marketing labels, not real measurements. Nothing on a “2 nm” chip is actually 2 nanometres wide.
Power density: The amount of heat produced per unit of chip area. When it climbs too high, the chip cannot be cooled fast enough and fails.
Leakage current: Electricity that trickles through a transistor even when it is supposed to be “off.” In very small transistors this waste becomes large.
Thermodynamics: The branch of physics describing heat, energy, and the direction in which processes naturally run.
Entropy: A measure of disorder, or of how many microscopic arrangements a system could be in. The second law of thermodynamics says total entropy never decreases.
Bit: The smallest unit of information: a single yes/no, on/off, 1/0.
Boltzmann constant (k): A fixed number of nature linking temperature to energy: 1.380649 × 10⁻²³ joules per kelvin (J/K).
Kelvin (K): The scientific temperature scale. Room temperature is about 300 K (≈ 27 °C).
Landauer’s Principle: The rule that erasing one bit of information must release a minimum amount of heat. This is the deep physical limit at the centre of this article.
Quantum tunnelling: A quantum effect where a particle (like an electron) passes through a barrier it classically shouldn’t be able to cross. It grows worse as barriers get thinner.
Reversible computing: A computer design that avoids erasing information, and so could — in principle — sidestep Landauer’s heat cost.

Stage 2 · The Deconstruction

Why progress is slowing: four walls, taken apart

The slowdown is not one problem but several, layered on top of one another. Three of them are engineering walls — hard, but human-made. The fourth is the one written into physics. We take them in order.

The Power Wall (heat)

When Dennard scaling broke around 2005–2007, engineers could no longer keep lowering the voltage as transistors shrank. Pack twice as many switches in and you now produce roughly twice the heat in the same space. Push the clock speed up and the chip cooks itself. This is why everyday processor clock speeds have hovered near 4 gigahertz for nearly two decades, and why the industry pivoted to multi-core chips — several slower processors side by side — instead of one ever-faster one.
The Leakage Wall

Dennard’s simple rule ignored leakage current and a floor called the threshold voltage. In large transistors that waste was negligible. As transistors shrank below roughly 65 nanometres, leakage grew exponentially: the “off” switch was no longer fully off. More leakage means more heat, which feeds straight back into the Power Wall.
The Lithography & Cost Wall

Chips are “printed” with light. To draw finer features you need shorter-wavelength light and extraordinarily complex, expensive machines (extreme-ultraviolet lithography). Each new generation costs more, takes longer, and yields fewer perfect chips. Progress did not stop — but it became slower and far more expensive, which is itself a kind of limit.
The Atomic / Quantum Wall

Here is the fact the marketing hides. A silicon atom is about 0.2 nanometres across. The smallest real features on today’s “2 nm” and “3 nm” chips are not 2 or 3 nanometres — they are closer to 12–20 nanometres, only a few dozen atoms wide. As insulating barriers thin toward a handful of atoms, quantum tunnelling lets electrons slip through where they shouldn’t, and the switch becomes unreliable. You cannot build a transistor smaller than the atoms it is made of.

The node name is a generation label, not a length. The real shrink has nearly reached the size of individual atoms. Hover or tap to enlarge.

What this establishes Three of the four walls — power, leakage, cost — are engineering problems. They are being attacked with new transistor shapes (gate-all-around nanosheets), 3-D stacking, and new materials. The fourth wall, atomic size, is closer to a physical limit. But none of these is the fundamental limit of computation. For that, we must leave silicon entirely and ask a stranger question: does information itself cost energy?

The Deep Limit

Information is physical: thermodynamics enters the chip

In 1961, an IBM physicist named Rolf Landauer asked a question that sounds like philosophy but turned out to be physics: does it cost energy to forget?

His answer reshaped how we think about computers. Landauer argued that information is not an abstract, weightless thing. A bit is always stored in a physical system — a charge, a magnet, the position of a particle. And there is a fundamental asymmetry in nature: you can copy information for free, in principle, but whenever you erase a bit, you must dump a minimum amount of heat into the surroundings.

Information is physical. — Rolf Landauer, IBM (the principle, in two words)

Why must erasing cost something? Think about entropy — the count of possible arrangements. Before erasure, a bit could be either 0 or 1: two possibilities. After you force it to a definite 0, there is only one. You have reduced the disorder of that little system. The second law of thermodynamics forbids destroying entropy outright, so the lost disorder must reappear as heat flowing out into the environment. Erasing information and producing heat are, at bottom, the same event seen from two sides.

This is Landauer’s Principle, and it sets a hard floor: a minimum energy per erased bit that no engineering trick can beat, no matter how clever, as long as the computer erases information the ordinary way. For decades it was theory. Then in 2012, a team led by researchers in Lyon, publishing in Nature, built a one-bit memory from a single microscopic bead trapped by lasers in a double-welled trap, erased it, and measured the heat. The dissipated heat settled right at Landauer’s predicted floor. The principle is now experimentally confirmed.

What this establishes There exists a true, physics-imposed minimum energy to erase a bit — independent of silicon, transistors, or any technology. It is small, but it is not zero. In the next stage we calculate exactly how small, using nothing more than multiplication.

Stage 3 · The Derivation

A worked example: the cheapest possible thought

Let us compute the Landauer limit for erasing a single bit at room temperature. Every number here is one you can verify on a calculator. The result is the absolute floor price of one elementary act of forgetting.

The Landauer Bound

Landauer’s Principle states that the minimum heat E released when one bit is erased is the product of three things: the Boltzmann constant k, the absolute temperature T, and the natural logarithm of 2.

E_min = k · T · ln 2

The “ln 2” appears because a bit has exactly two possible states; erasing collapses two into one. Let us put in the numbers.

Write down the constants. The Boltzmann constant is k = 1.380649 × 10⁻²³ J/K. Use room temperature, T = 300 K. And ln 2 ≈ 0.6931.
Multiply k by T first. 1.380649 × 10⁻²³ × 300 = 4.142 × 10⁻²¹. [units: (J/K) × K = J ✓ — the kelvins cancel, leaving joules, exactly what energy should be]
Multiply that result by ln 2. 4.142 × 10⁻²¹ × 0.6931 = 2.87 × 10⁻²¹ J.
State the result. It follows that erasing one bit at room temperature must release at least about 2.9 × 10⁻²¹ joules — equivalently, about 0.018 electron-volts of energy.

That number is almost unimaginably small. A joule is roughly the energy to lift a small apple one metre; this is a few billion-trillionths of one. If a computer could erase bits exactly at this floor, it could do an enormous amount of computing on the energy in a single breath.

Why a bit “wants” to release heat — the double well

Picture the bit as a ball that can rest in one of two valleys: the left valley means 0, the right means 1. To erase the bit — to force it to read 0 no matter what it was — you must smooth away the right valley and push any ball over to the left. Squeezing two possible starting positions into one guaranteed ending position is exactly the loss of disorder we described. The energy you spend doing the squeezing leaves as heat.

Two possible states are forced into one. That collapse of possibility is paid for in heat — at minimum, kT ln 2. Hover or tap to enlarge.

What this establishes We now have the exact physical floor: about 2.9 × 10⁻²¹ joules per erased bit at room temperature. The next question is the decisive one for our title — how far above this floor do real computers actually operate?

Stage 4 · The Real-World Anchor

The gap, the grid, and the energy bill of thinking

Here is where the abstract floor meets the electricity meter. Today’s transistors do not erase bits anywhere near the Landauer limit. Each switching event in a real chip wastes somewhere on the order of tens of thousands to a million times the theoretical minimum. The classic statement, often quoted, is that around 2012 a typical computer used roughly a billion times the Landauer minimum per logic operation — and estimates vary, but the message is consistent: we operate far, far above the floor.

That gap is, in one sense, good news: it means physics is not what’s stopping us today. Most of the waste is engineering — leakage, wiring losses, the overhead of moving data. There is enormous headroom in principle. But in another sense the gap is the entire crisis, because we run so many operations that even a tiny per-bit waste, multiplied by astronomical scale, becomes a civilisation-sized energy demand.

Figures are International Energy Agency estimates and scenarios — projections under stated assumptions, not a single measured line. By 2026 the high-growth case approaches the electricity use of Japan. Hover or tap to enlarge.

Data centres consumed roughly 460 terawatt-hours of electricity in 2022 — about 2% of the world’s total. The International Energy Agency projects that figure could reach around 1,000 terawatt-hours by 2026 under high-growth scenarios, comparable to the entire electricity consumption of Japan, and roughly 945 terawatt-hours by 2030 in its central forecast — close to 3% of global demand. The single biggest driver is artificial intelligence, whose specialised processors are extraordinarily power-hungry.

This is the real-world face of the Landauer gap. As long as each operation wastes far more than the physical minimum, scaling up the number of operations scales up the heat and the power bill in lockstep. The pressure to compute more is now colliding with the pressure to compute efficiently — and the second law of thermodynamics is the referee.

What this establishes The limit we are hitting right now is overwhelmingly an engineering and energy limit, not the fundamental physical floor — but the floor is the reason efficiency cannot improve forever along the current path. So what lies beyond silicon?

Beyond Silicon

Two escape routes: quantum and reversible computing

When people hear “the end of Moore’s Law,” they often reach for quantum computing as the rescue. It is a profound technology — but it is widely misunderstood, and it is not a faster version of the laptop on your desk.

Quantum computing: a different tool, not a bigger hammer

A quantum computer exploits superposition and entanglement to explore certain problems in ways a classical machine cannot. For a narrow class of tasks — simulating molecules, some optimisation and cryptography-related problems — it offers dramatic speedups. For ordinary computing — spreadsheets, web pages, most software — it offers essentially nothing. It is a specialised instrument.

The field has advanced strikingly. In late 2024 Google’s Willow chip, with 105 qubits, demonstrated “below-threshold” error correction — meaning that as the system grew, errors fell rather than multiplying, a milestone many thought might be impossible. Through 2025 and into 2026, IBM, Google, and others reported further error-correction and “quantum advantage” results on specially chosen problems. Yet the overhead remains enormous: it can take hundreds of fragile physical qubits to build one reliable logical qubit, and practical machines may need tens of thousands to millions of qubits. Quantum computing extends what is computable in reasonable time for special problems; it does not repeal Landauer’s Principle for everyday computing.

Reversible computing: the only known way under the floor

Here is the subtle and beautiful escape route. Landauer’s heat cost is triggered specifically by erasing information. The physicist Charles Bennett, building on Landauer’s work at IBM, showed that if a computer never throws information away — if every step can in principle be run backwards — then it need not pay the kT ln 2 toll at all.

This is reversible computing. A reversible logic gate keeps enough information to reconstruct its inputs from its outputs, so no possibilities are collapsed and no entropy is forced out as heat. In theory, such a machine can compute arbitrarily close to — even effectively below — the Landauer limit. The catch is engineering, not physics: reversible designs are slower, more complex, and demand near-perfect components. But they represent the one known path to keep improving efficiency after conventional shrinking ends.

What this establishes Neither route abolishes thermodynamics. Quantum computing changes which problems are tractable; reversible computing changes how close to the floor we can run. Both confirm the same lesson: the ultimate limit of computation is not silicon — it is energy and information themselves.

Stage 5 · The Open Problem

So which wall are we hitting?

Return to the core question: are today’s limits engineering problems or fundamental laws of physics? The honest answer, reconstructed from the chain above, is that they are both — but at different distances.

The walls we are pressed against today — heat, leakage, lithography cost, the atom-scale floor of silicon — are engineering walls. They are slowing Moore’s Law and have already ended the easy “free speed” of Dennard scaling, but they are being actively pushed back with new transistor architectures, 3-D stacking, new materials, and smarter chip design. Moore’s Law as originally stated is fading; progress in computing per watt continues, more slowly and more expensively.

Beneath all of it sits the one limit no engineering can repeal: Landauer’s Principle. We are still many orders of magnitude above that floor, so it is not what stops us this decade. But it is the reason there is a floor at all, and it converts the question “how fast can we compute?” into the deeper question “how cheaply can we compute?”

The Open Problem How close to the Landauer limit can a practical machine be built before noise and error overwhelm it? Can reversible or quantum architectures be engineered at scale, or will they remain laboratory curiosities? And as global computing demand keeps climbing, will efficiency improve fast enough to keep the energy cost of thinking from outrunning the power grids that feed it? Moore’s Law was always a promise about engineering. The limit of computation is a promise from physics. The work of the coming decades is the distance between the two — and that work is not finished.

References

Sources

Ten high-level sources, with working links where available. Figures and dates were cross-checked against these.

Computer History Museum — 1965: “Moore’s Law” Predicts the Future of Integrated Circuits (Moore’s original 1965 paper and 1975 revision). computerhistory.org
Intel — Moore’s Law (history and the 1975 accuracy of the prediction). intel.com
Rambus — Understanding Dennard Scaling (the 1974 Dennard paper and its breakdown ~2005–2007). rambus.com
Wikipedia — Moore’s law (end of Dennard scaling, leakage, the multi-core pivot). en.wikipedia.org
Wikipedia — 5 nm process & 22 nm process (node names as marketing terms since ~1997; real gate lengths). en.wikipedia.org
Wikipedia — Landauer’s principle (the kT ln 2 bound; ≈0.018 eV at room temperature; comparison to real computers). en.wikipedia.org
Bérut, A., et al. (2012). Experimental verification of Landauer’s principle linking information and thermodynamics. Nature 483, 187–189. doi.org/10.1038/nature10872
International Energy Agency — Energy and AI: Energy demand from AI (data-centre electricity projections to 2030). iea.org
Brookings — Global energy demands within the AI regulatory landscape (2026; ~460 TWh in 2022, ~1,050 TWh by 2026). brookings.edu
Riverlane — Quantum Error Correction: 2025 trends and 2026 predictions (Google Willow below-threshold error correction; qubit overhead). riverlane.com

Constants used in the worked example: Boltzmann constant k = 1.380649 × 10⁻²³ J/K; room temperature taken as 300 K; ln 2 ≈ 0.6931. Result: E_min ≈ 2.9 × 10⁻²¹ J ≈ 0.018 eV per erased bit.