Physics
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Day 9: A Clock You Can Use to Measure a Mountain
Yesterday I said cesium was about to be deposed. Today’s the deposition.
The successor is the optical lattice clock. It is so precise that, it can detect the altitude difference between two desks in the same office.
That last sentence sounds crazy but Its what optical clocks do.
Here’s how.
More ticks per second
The trick of the optical lattice clock is simple in concept: use a finer ruler.
A cesium atom oscillates at about 9 × 10⁹ Hz (~9 GHz, microwave). That’s how many “ticks” per second the clock has to count to keep time.
A strontium-87 atom has a clock transition at about 4 × 10¹⁴ Hz (~430 THz, visible light). That’s 50,000 times more ticks per second.
Same second. More tick marks on the ruler.
Faster clock makes better time.
Faster clocks are better than slower ones.
Faster clocks make for better timekeeping.
See the difference and why we need to upgrade the second?
Today’s best optical clocks drift about one second over the age of the universe. 13.8 billion years. Our best cesium clocks are nowhere near that, drifting the same second in roughly 300 million years instead. About a hundred times worse.
The magic wavelength trick
So if optical is obviously better, why didn’t we do this first?
Because it’s hard. Two reasons, really.
First, you can’t just point an optical clock at a free-floating atom. Atoms in flight have all sorts of velocity, Doppler-shifting the frequency you measure. You have to hold them still. But the only way to hold an atom still is to grip it with something, and gripping it with a laser changes the energy levels you’re trying to measure. Catch-22.
Second, even if you could pin the atom, you couldn’t count that fast. Microwave at 9 GHz fits inside what electronics can divide down and tick off. Visible light at 400+ THz does not. We had no way to count optical-frequency oscillations until the optical frequency comb showed up in 1999, work that won Hänsch and Hall the 2005 Nobel.
In 1967 when the CGPM picked cesium, none of this existed. The laser was seven years old. Laser cooling wouldn’t be demonstrated until the late 1970s. Frequency combs were 30+ years away. Cesium at 9 GHz wasn’t the best clock you could imagine. It was the best clock you could build.
The fix came in 2003 from a Japanese physicist named Hidetoshi Katori. He proposed trapping the atoms in a standing-wave laser pattern, a 3D optical lattice, like an egg crate made of light, and tuning the lattice laser to a specific frequency called the magic wavelength.
At the magic wavelength, the lattice light affects both energy levels of the clock transition by exactly the same amount. The trap is invisible to the clock. The atoms are held still, but the energy levels they emit at are unperturbed. You get to measure the atomic transition cleanly while the atom sits frozen in midair.
Optical lattice clocks are a beautiful piece of physics. Do not ask me about the math behind them.
Which atom?
Two main candidates have been thinking about for the title of “next SI second”:
- Strontium-87. Run in optical lattices by labs around the world: NIST/JILA in Boulder, NPL in the UK, RIKEN in Japan, SYRTE in Paris. About 1 part in 10¹⁸ uncertainty. Currently the favorite.
- Ytterbium-171. Comparable accuracy, different sensitivity profile (different ways the clock can go wrong, which is good for cross-checking against strontium).
There are also trapped-ion optical clocks, which hold a single ion in an electric field instead of a lattice of neutral atoms. The aluminum-ion logic clock at NIST has hit about 1 part in 10¹⁹. That’s one second of drift in 300 billion years. The amount of drift is older than the universe itself. That sounds pretty good to me.
What this gets you
Optical clocks are sensitive enough to see general relativity at human scale.
What does that mean? It means you can put two clocks on different shelves and watch one tick slower than the other.
Einstein said clocks deeper in a gravitational field run slower than clocks higher up. Near Earth, the effect is about 1 part in 10¹⁶ per meter of altitude. A clock on the floor runs slower than a clock on the table. For most of human history this was a theoretical curiosity. Now it’s a measurement.
In 2022, a JILA strontium clock measured a 1 millimeter height difference as a frequency shift. One millimeter. The thickness of a credit card. The clock could tell which side of the card it was sitting on, from gravitational time dilation alone.
This opened a new field: relativistic geodesy. Put an optical clock at two locations, compare frequencies, and you’ve directly measured the gravitational potential difference between them. Detect underground oil, magma movement, ice sheet melt, anything that shifts mass around the planet.
Cesium can’t do this.
The next “second”
The BIPM is planning to redefine the SI second around an optical transition by 2030. Same dance as 1955: measure the new number against the current cesium standard, freeze it at that precision, declare it the new second.
Four layers of backwards-compatibility instead of three. The fingerprints accumulate.
Where this goes
We’ve now spent three days on how a second is built. The next question is the one the calendar dodges: which second?
You need a reference point. A zero. An origin.
Tomorrow we’ll talk about where you start counting from, and why astronomers picked noon on January 1, 2000.
Sources
- Optical clock — Wikipedia
- Hidetoshi Katori — Wikipedia
- Quantum logic clock — Wikipedia
- Relativistic geodesy — Wikipedia
- Bothwell et al., Nature 2022 — millimeter-scale gravitational redshift
- Gravitational time dilation — Wikipedia
- Jun Ye — Wikipedia
- Epoch (astronomy) — Wikipedia
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Day 8: 9,192,631,770
Today’s number is 9,192,631,770.
That’s how many times a cesium-133 atom oscillates between two specific energy states in one second. Or, more precisely, it’s how many times we decided a cesium atom does that in one second. The number is doing some heavy lifting that the universe didn’t ask for.
This post is about the number, how it got picked, and how we use it to measure time.
The chain
To know what a second is, you need a way to measure one. For most of human history, the answer was: “look at Earth and count” or earth++ for the programmers reading this.
One second = 1/86,400 of a mean solar day.
That worked for sundials and pendulum clocks. It stopped working in the 1930s, when good quartz clocks revealed that Earth’s rotation isn’t uniform. Yesterday, we talked about how. Earth’s rotation is not a good measurement of time. I mean good in the sense of precise, because there are so many variables that go into the rotation and impact it. We don’t have an accurate way to measure and predict how those variables change.
In 1960, astronomers tried again. Because why not? Wheel, reinvented.
They picked Earth’s orbit instead of its rotation, which is far more stable:
One second = 1/31,556,925.9747 of the tropical year for 1900.
That weird denominator was chosen specifically so the new “ephemeris second” came out the same length as the old mean solar second. Don’t break clocks … like ever.
Great in principle, terrible in practice. To know what time it was, you had to consult a 60-year-old astronomical table. It doesn’t work with the clock in the lab. The ephemeris second won the philosophy and lost the engineering.
But wait, maybe there’s a third option.
How I wish it was Cesium-123 and not Cesium-133, but alas. The 133 is the mass number: 55 protons + 78 neutrons. Cesium-133 also happens to be the only stable isotope of cesium, so it kind of picked itself.
The cesium handoff
Cesium-133 has two slightly different ground-state energies. Drop an atom from one to the other and it spits out a photon at a specific frequency, call it f. If you can build a clock that locks itself to that frequency, you have a timekeeper that doesn’t depend on the Earth, the Sun, or any astronomer’s table. Every cesium-133 atom in the universe agrees on f to absurd precision, because quantum mechanics doesn’t have local variants.
The number for f is approximately 9.192631770 GHz. So if you count 9,192,631,770 oscillations, exactly one second has elapsed.
In 1967, the General Conference on Weights and Measures (the CGPM, the body that gets to define units) voted to make that the official definition. The SI second became:
The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
No Earth, no Sun, no tables. Just an atom.
Why that exact number
The number 9,192,631,770 is not a fundamental constant of the universe. It was measured. By two specific guys. In 1955.
Their names were Louis Essen and Jack Parry, and they worked at the National Physical Laboratory in the UK. They had just built the first cesium clock that actually worked. The question was: how many cesium ticks fit in one ephemeris second? They measured it carefully. Their answer, published in 1958 with William Markowitz and Robert Hall:
1 ephemeris second = 9,192,631,770 ± 20 cesium periods.
Nine years later, the CGPM took that number, dropped the uncertainty, and made it the definition. From then on, the second was defined as exactly 9,192,631,770 ticks. The plus-or-minus twenty disappeared.
This means three things:
- The cesium second was chosen so it would equal the ephemeris second.
- The ephemeris second was chosen so it would equal the mean solar second.
- The mean solar second was 1/86,400 of an Earth day.
The three layers of don’t break the previous standard. If Essen and Parry had been off by one in their measurement, the entire SI second would be slightly different today, and every clock and computer and GPS satellite would be calibrated to that other version.
The number is a historical fingerprint, not a physical constant.
It records, with eleven decimal-digit precision, exactly how well two physicists in 1955 could compare a cesium clock to an Earth-orbit calculation.
Every GPS satellite, every NTP server, every timestamp on every photo you’ve ever taken, they’re all calibrated to the limits of what Essen and Parry pulled off with 1955 equipment. The universe doesn’t care about your iPhone. Your iPhone cares about two guys at the NPL.
How precise are we now
Modern cesium fountains, the latest generation, where atoms are laser-cooled and tossed gently upward through a microwave cavity, falling back down under gravity like a slow ballistic juggling act, hit accuracies of about one part in 10¹⁶. That’s roughly one second of drift per 300 million years.
NIST-F2 in Boulder, the U.S. primary clock, is one of these. About a dozen others sit in metrology labs across France, Germany, the UK, Japan, and China. They all report their measurements to the BIPM in Paris, which combines them into a weighted average called TAI, International Atomic Time. TAI is what your phone’s clock is ultimately disciplined to, through a long chain of NTP servers and GPS signals.
Everything you do that involves time:
- sending a message,
- taking a photo with a timestamp,
- syncing with a calendar,
- getting a stock trade priced
It all traces back to a few hundred atomic clocks averaging each other in real time.
What comes next
Cesium won’t be the way we measure the second forever. It’s about to be deposed.
Optical lattice clocks, using strontium or ytterbium atoms instead of cesium, operating at visible-light frequencies instead of microwave, are now about a hundred times more precise. They lose one second per about 30 billion years, which is roughly twice the age of the universe.
The BIPM is planning to redefine the SI second around an optical transition, possibly by 2030.
When that happens:
- Mean solar second = 1/86,400 of an Earth day
- Ephemeris second chosen to match the mean solar second
- Cesium second chosen to match the ephemeris second
- Optical second chosen to match the cesium second ← the new one
Three layers of backwards-compatibility will become four.
Tomorrow we’ll look at those optical clocks, what they are, how they work, and how they let us measure what cesium can’t.
Sources
- Louis Essen — Wikipedia
- William Markowitz — Wikipedia
- Second — Wikipedia
- Ephemeris time — Wikipedia
- Atomic clock — Wikipedia
- International Atomic Time — Wikipedia
- NIST-F2 — Wikipedia
- Optical clock — Wikipedia
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Day 4: Does the Future Already Exist?
Yesterday I left you with a question, today we are getting stuck in. If the block universe is right, and my death is already sitting in the loaf at coordinates I haven’t reached yet, then in what sense am I choosing anything?
It turns out this isn’t a new problem. People were freaking out about it 2,400 years ago.
Aristotle’s Sea Battle
Around 350 BCE, Aristotle wrote a short text called On Interpretation. Most of it is dry logic. But in Chapter 9 he stops to consider something that has been bothering philosophers ever since.
Imagine someone says: “There will be a sea battle tomorrow.”
Is that statement true right now?
It seems like it has to be either true or false. That’s basic logic. A statement and its negation can’t both be true. One of them has to be the case.
But if it’s true right now that there will be a sea battle tomorrow, then the sea battle is already locked in. The admirals can deliberate, the sailors can train, the ships can be prepared or not prepared, but the battle is happening, because the statement was true before they did any of that. And if the statement was false right now, then no matter what anyone does, no battle is possible. Deliberation is pointless either way.
This is the original fatalism problem. Aristotle didn’t have a block universe yet. He didn’t need one. He just noticed that if statements about the future already have truth values, the future is already decided.
His escape was to say: future-tensed statements don’t yet have truth values. They become true or false as time passes. The statement “there will be a sea battle tomorrow” isn’t true or false today, it just isn’t yet. Today’s truth is silent on tomorrow’s events.
That’s a tidy answer, and most philosophers since haven’t bought it. Bivalence, the idea that every proposition is either true or false, is hard to give up.
The Block Universe Version
Fast forward 2,300 years. Einstein hands us the block universe. Now we don’t need to worry about statements, we can talk about the actual thing. Tomorrow’s sea battle is sitting at its spacetime coordinates whether anyone says anything about it or not. Tomorrow’s you is sitting at its spacetime coordinates whether you’ve made up your mind or not.
So when you sit down at lunch and choose between the salad and the pizza, is anything actually being decided? Or is the salad-eating version of you already there in the loaf, and your “deliberation” is just the part of the loaf where the neurons fire?
This is the worry that makes the block universe feel like a horror movie.
Compatibilism, or: It’s Not as Bad as It Sounds
The standard response is associated with philosophers J.J.C. Smart and David Lewis, and it goes like this.
Yes, the future is fixed. But “fixed” isn’t the same as “forced.”
When we say tomorrow’s you eats a salad, what does that mean? It means tomorrow’s you deliberated, weighed the options, and chose the salad. The block universe doesn’t bypass your decision. Your decision is what’s written into the block. The reason the future slice shows you eating a salad is because the present slice, the one doing the deliberating right now, picks the salad.
You are not a passenger on a fixed track. You are part of the track-laying. Your choosing is a real causal node in the structure, not a piece of theater performed over a predetermined script.
Compare it to the past. The past is fixed too. Yesterday’s choices are locked in. We don’t usually feel like that’s a problem, because we remember making them. The block universe says the future has the same status as the past, with one difference: you don’t remember it yet.
This doesn’t fully comfort everyone, and I get it. The libertarian objection, made forcefully by Peter van Inwagen, is that genuine free will requires the ability to do otherwise. If the block already shows you eating a salad, there’s no sense in which you could have eaten pizza. Counterfactually, sure, in a possible world where your desires were different, you’d pick pizza. But in this world, the salad is already there. The pizza branch was never on the menu.
I find the compatibilist response more convincing than the libertarian one. But I also notice that I would say that, because I want to keep eating salad and feel like I picked it.
Quantum Mechanics Isn’t Going to Save You
A lot of people, when they first encounter this problem, reach for quantum mechanics. Surely the universe is fundamentally indeterministic at the smallest scales. Surely that means the future isn’t fixed, that quantum events ripple up into our brains and give us real openness.
This rescue doesn’t work, and the reason is sharp.
If your decision to eat the salad was caused by a random quantum event in your brain, then your decision was random. Randomness isn’t agency. If a quantum fluctuation makes your arm jerk and you punch someone, you didn’t choose to punch them. You twitched.
Indeterminism gives you unpredictability. It doesn’t give you authorship. Free will, if it means anything, has to mean you did it, not that a die was rolled inside your skull.
Some philosophers like Robert Kane have tried to thread the needle here, proposing that quantum indeterminism happens at moments of intense deliberation, and that the agent’s “effort of will” resolves the indeterminacy. I find this hard to believe, because it just relocates the mystery. How does the effort of will resolve the indeterminacy? If we knew, we’d be done. We don’t.
Tomorrow is not today’s set of problems, because today’s problems are in the process of being solved.
Sources
- Future Contingents - Stanford Encyclopedia of Philosophy (Aristotle’s sea battle)
- Fatalism - Stanford Encyclopedia of Philosophy
- Compatibilism - Stanford Encyclopedia of Philosophy
- Peter van Inwagen - Wikipedia (author of An Essay on Free Will, 1983)
- Robert Kane - Wikipedia (author of The Significance of Free Will, 1996)
- J. J. C. Smart - Wikipedia
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Day 3: Einstein Made Us A Loaf
When Albert Einstein’s lifelong friend Michele Besso died in March 1955, Einstein wrote a letter to Besso’s family. In it, he wrote one of the most quoted sentences in the philosophy of time:
“People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion.”
Einstein died a few weeks later.
What he was pointing at has a name now. The block universe.
The 4D Loaf
The block universe says reality is a four-dimensional structure. Three dimensions of space, one of time, stitched together into a single thing. Every event that ever happened, that’s happening, that ever will happen, all of it exists. Equally real. The Big Bang is over there in one corner of the loaf. The heat death of the universe is at the other end. Your tenth birthday is somewhere in the middle. Your death is somewhere too.
Nothing flows. Time doesn’t pass. The loaf just is.
This sounds insane. It is also where the math points.
Why Physicists Buy It
The argument is special relativity, and once you see it, it’s hard to unsee.
Einstein showed that simultaneity, the idea that two events happen at the same time, depends on how you’re moving. If you and I are at rest with respect to each other, we’ll agree on what’s happening “right now.” But if I get on a train and you stay on the platform, my “now” and your “now” start to disagree. Events you consider simultaneous, I won’t. And not because either of us is wrong. We’re both reading our clocks correctly. The universe just doesn’t have a single shared “now.”
Take that one step further. If my present and your present can disagree, whose present is the real one? Mine? Yours? Some third observer’s? The only answer that doesn’t pick favorites is: all of them. And if all of them are equally real, then the past and future they each describe must also be real, because one observer’s future is another observer’s now.
Philosophers Hilary Putnam and C.W. Rietdijk worked this out in the 1960s. Their argument, roughly: if my “now” overlaps with your “now,” and your “now” overlaps with someone else’s, and that someone else’s “now” overlaps with an event in my future, then by transitivity that future event exists right now. Not metaphorically. Actually exists.
Therefore, if you take special relativity seriously, the future is already here.
“Now” Is Just “Here”
The block universe has a clean way to talk about what feels like flow. “Now” works the same way “here” does.
“Here” doesn’t pick out some metaphysically special location in space. It just means the place I am. Other places are equally real, even though they’re not here. New York exists when I’m in San Francisco. I don’t need to be there for it to be there.
“Now” is the same. The moment I am. Other moments are equally real, even though they’re not now. 1955 exists when I’m in 2026. Einstein doesn’t need to be alive for 1955 to be a real place in the loaf.
This view is called eternalism: past, present, and future, all equally real. It’s the natural ontology of the block universe, and most working physicists, when asked, will admit they think something like this.
The Objection That Doesn’t Go Away
There’s an objection, and it’s the one your gut has been making since the first paragraph.
It doesn’t feel like a block. It feels like time flows. It feels like the present is special, the past is gone, and the future is open. We make choices. We anticipate. We regret. None of that lines up with a frozen 4D loaf where everything is already written.
Philosophers who take this objection seriously are called presentists. They say only the present is real. The past was, the future will be, but right now only this moment exists. This is closer to common sense, but it has a hard time with relativity. If only the present exists, whose present? The presentist owes us an answer, and most of the answers involve denying relativity in ways physicists find suspicious.
For today, the block universe gets to make its argument unopposed.
Rovelli’s Wrinkle
Carlo Rovelli I think mostly buys the block? He doesn’t think there’s a fundamental flow. He’s also not satisfied with leaving it there.
If there’s no flow at the bottom, why does it feel so vividly like there is? His answer is emergence. Flow is real the way temperature is real. There’s no such thing as the temperature of a single atom. Temperature emerges when you have a lot of atoms, statistics, and a viewer who’s coarse-grained enough to perceive averages instead of individual particles. Time’s flow, in Rovelli’s view, is similar. It emerges from entropy, from our memory pointing one way, from our being the particular kind of system we are.
That isn’t an answer that satisfies everyone. The philosopher Tim Maudlin has spent decades arguing that fundamental temporal passage is real, that the block universe view throws away something that ought to stay. I’m sympathetic. But Maudlin is not, today, winning.
So What Does This Mean For Me?
Here is the question that should have been tickling that noggin.
If the block universe is right, if my death is already sitting in the loaf at coordinates I haven’t reached yet, then in what sense am I choosing anything? If my actions tomorrow are already there, written into the geometry, am I just walking down a track that’s been laid?
But that’s tomorrow’s past, sorry, post.
Sources
- Being and Becoming in Modern Physics - Stanford Encyclopedia of Philosophy
- Time - Stanford Encyclopedia of Philosophy
- Rietdijk–Putnam argument - Wikipedia
- Michele Besso - Wikipedia (source for the Einstein letter quote)
- The Order of Time - Wikipedia (Carlo Rovelli, 2018)
- Tim Maudlin - Wikipedia (author of The Metaphysics Within Physics)
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30 Days of Time
I’m a big audiobook guy. Ear reading instead of sight reading, as I like to call it. Lately I’ve been ear reading The Order of Time by Carlo Rovelli, and it has wrecked me in the best possible way.
Rovelli’s argument, roughly, is that a uniform, universal flow of time does not exist at the fundamental level. The features we associate with time, a direction, a presentness, a duration, are tied to our perspective and to thermodynamics. We don’t fully understand the microstate of the universe and his argument is that the flow of time isn’t even there to be known. That’s a hell of a thing to think about when sitting in traffic between two city buses on your way to picking up fried chicken for dinner.
So I got curious. Not just about the physics, but about all the neighboring topics. Calendars. Daylight Saving Time. Leap seconds. The fact that GPS satellites have to correct for relativity or your maps app stops working. The fact that Mars uses its own day. The fact that we voted in 2022 to abolish the leap second by 2035, and most people did not notice.
I’ve decided to spend the next 30 days writing about it. One post a day. Welcome along.
The shape of the series
I don’t want to spoil the destination, so I’ll just sketch the journey. The series breaks into four rough movements, one per week.
Week 1 — What time is. The philosophy is older than the physics. Does time flow, or is it a frozen 4D block we move through? Why does your brain experience “now” the way it does? Do other animals even live in the same time you do? This is the squishy, weird, fun stuff. No equations, lots of questions.
Week 2 — How we measure it. Sundials to cesium to optical lattice clocks. The second is a defined unit now, and that decision had consequences. We’ll talk about why your phone’s clock is more accurate than any clock that existed when your grandparents were born, and what that accuracy is for.
Week 3 — How computers handle it. Unix time, NTP, ISO 8601, time zones, DST. The infrastructure quietly holding the digital world together, and the bugs that fall out of it twice a year. If you’ve ever shipped code that broke at 2 a.m. on the second Sunday of March, this week is for you.
Week 4 — Where it breaks. Leap seconds, calendar reform, DST politics, the slow drift between atomic and astronomical time. The current system is more held-together-with-tape than most people realize. By the end of the week I want us both asking the same question.
I’m not going to tell you what that question is yet. Part of the fun is getting there together.
What this is, and what it isn’t
This isn’t a textbook. It isn’t a research project or a reading log either. It’s a series of posts on a topic I’m interested in.
I’m not a physicist, so I’ll do my best to make sure the posts aren’t wrong. If you spot a correction, replying on Mastodon is the best way to let me know.
Why 30 days? Why not? I may do more later if a particular topic wants more room. But 30 days on a single subject is probably enough for most people who show up here for programming posts. Instead, you’re getting a 30-day divergence into physics, astrophysics, and a little philosophy. Week 3 covers computer time, so there’ll be some programming in there. Just not a lot of it for a month.
My research notes live in an Obsidian vault. I’m keeping them private for now, but I may share more by the time the series wraps.
How to follow along
New post every day for 30 days, starting now.
RSS is the easiest if you want every post as it lands. Email is a weekly digest, good if you’d rather catch up on Sundays than see every post the moment it drops. Mastodon is where each post lands on social, and any replies there show up back on the blog as comments: @[email protected].
Pick whichever annoys you least.