Every Clock Has a Hidden Error — And Physics Says You Can't Fix It

Think about the clock on your phone. It works because satellites in space send it a precise time signal, which those satellites get from atomic clocks — devices so accurate they would not lose a single second over 300 million years. Now imagine that no matter how perfect you make a clock, something deep inside the laws of physics is giving it a tiny wobble it can never escape. A team of physicists from Rome and Budapest just proved that this wobble is real. And what they found next is almost funnier: the wobble is so impossibly small that it genuinely does not matter.

The Century-Old Question That Physics Never Answered

Quantum mechanics — the science of tiny things like atoms and electrons — is one of the most tested and confirmed theories in human history. It explains how your phone screen works, why metals conduct electricity, even how the sun shines. But for all its success, it has always had one awkward problem nobody has fully solved.

Tiny particles like electrons can exist in a blurry state. An electron can be in two places at once, spinning in two directions at the same time. This is called a "superposition." But the moment you look at it — or measure it in any way — it instantly picks one definite state. Just like that. The blurriness vanishes.

Why does it do that? Nobody really knows. The standard textbook answer is: it just does, when someone measures it. Which is honestly a bit of a cop-out. You need a measurement device, you need an observer, and in some older interpretations, you even need a human being in the room. That's not very satisfying for a theory that's supposed to explain all of nature.

What Happens When Quantum Objects "Choose" a State

Some physicists decided to take a different approach. Instead of saying collapse happens when someone looks, they asked: what if it happens all the time, on its own, everywhere in the universe — no observer needed?

This idea is called a "spontaneous collapse model." The word spontaneous just means it happens by itself. Two versions have attracted the most attention over the past few decades. One is called the Diósi-Penrose model, named after physicist Lajos Diósi — who is actually one of the authors of this new paper — and the famous British physicist Roger Penrose. The other is the CSL model, which stands for Continuous Spontaneous Localization.

Both say that quantum blurriness is constantly being "resolved" by nature itself, automatically. For tiny particles this happens very slowly, which is why atoms can stay quantum-weird for a long time. For large everyday objects — a chair, a cricket ball, you — the resolution happens so fast the object never gets a chance to be in two places at once. That's why the world around you looks solid and definite, not blurry and quantum.

Here's where it gets interesting. The Diósi-Penrose model was always tied to gravity — it says gravity itself is responsible for this automatic collapse. The CSL model was not connected to gravity at all. Until this paper. The researchers show, for the first time, that CSL also arises from random ripples in gravity. Both models, they argue, are really talking about the same thing.

Why Does Gravity Make Time Go Wobbly?

This is where Einstein joins the story. One of the strangest — but experimentally proven — ideas in physics is that gravity affects time. Clocks at sea level tick very slightly slower than clocks on a mountain, because the mountain is further from Earth's centre of gravity, where gravity is a little weaker. This effect is tiny but real, and it actually has to be corrected for in GPS systems. Without this correction, your Google Maps would drift by several kilometres every single day.

Now, if gravity randomly ripples and fluctuates at a microscopic quantum level — as both the CSL and Diósi-Penrose models say it does — then time itself must ripple too. Every clock, no matter how well-engineered, sits inside this randomly jittering gravity field. So it ticks with a tiny, unavoidable wobble on top of its normal ticking.

The researchers worked out the exact size of this wobble. After one full year, the time error caused by this quantum gravity ripple is roughly 0.0000000000000000000000000001 seconds for the CSL model. That is a decimal point followed by 27 zeroes before you hit a 1. For the Diósi-Penrose model it is even smaller — three more zeroes on top of that.

There's one more curious detail. A smaller clock feels this wobble more than a larger clock. This sounds backwards — shouldn't a bigger, more complex clock be worse? But no. A bigger clock averages out the random gravity ripples over a larger area, so they cancel each other out more. Tiny clocks get shaken around more. Not that it matters in practice — both are far beyond anything measurable.

What This Means for Your GPS, Your Phone, and India's NavIC

Let's put that number in real terms. The best atomic clocks in the world — optical lattice clocks using strontium atoms, operated in government labs in the US, Japan, Germany, and France — already drift by about one ten-quadrillionth of a second per second. That is already mind-bendingly precise. The quantum gravity wobble this paper calculated is roughly ten billion times smaller than even that.

So no, your phone's time will not be affected. Not even slightly. And India's NavIC satellite navigation system — ISRO's homegrown answer to GPS, which uses atomic clocks to give precise location data across the subcontinent — is completely in the clear. The atomic clocks powering NavIC, the ones behind your bank transactions, your mobile network timing, your power grid synchronization — all of them are untouched by this effect.

Not just today. Not just for the next hundred years. The researchers checked the numbers across the entire age of the universe — roughly 14 billion years — and the accumulated wobble is still far too small to measure with any technology we can realistically imagine.

What Scientists Are Still Trying to Figure Out

Being honest about limits matters here. Neither the CSL model nor the Diósi-Penrose model has been proven correct. They are well-motivated ideas, they make testable predictions, and several experiments — including the MAJORANA Demonstrator deep underground in Italy's Gran Sasso laboratory — have placed boundaries on what these models are allowed to predict. But nobody has confirmed them.

Both models are also, technically, non-relativistic. That means they do not fully account for Einstein's special relativity. Connecting quantum collapse to a proper, complete relativistic theory of gravity is still an unsolved problem. This paper takes a step in that direction by using general relativity to derive the time uncertainty — but the foundation it stands on is still partly theoretical scaffolding.

What the paper does definitively settle is this: even if these quantum collapse models are correct, their effect on clocks is negligible. Permanently, practically, negligibly small. That is actually a useful thing to know. It clears the table. Whatever limits future timekeeping technology, it will not be this.

• It's real, but invisible — Quantum gravity does create a tiny unavoidable wobble in every clock, and it grows slowly over time — but no technology can or will ever measure it.
• Two theories now linked — For the first time, the CSL model has been connected to gravity, showing it shares the same root as the Diósi-Penrose model. They were telling the same story all along.
• Bigger clocks win — Against this particular noise, larger clocks actually perform better because they average out the random gravity ripples — a counterintuitive result with interesting design implications for future timekeeping.

"Spontaneous collapse models introduce a fundamental source of time uncertainty — but they do not impose any practical limitation on precision timekeeping." — Bortolotti et al., Physical Review Research, 2025.