Spacetime Metric — Season 1 — 01-what-is-a-metric

Transcript

Cold open (≈ 110 seconds)

A man stood at a workbench in the lecture you just heard, and he said this. "Pons and Fleischmann, they did a simple garage experiment."

That is Ashton Forbes — the curator of the source corpus that motivated this series, not a credentialed physicist. The lecture series is taking him seriously, in this way. Not because the sentence is, by itself, a piece of physics — it is not. But because that sentence is the editorial frame against which we are going to test twelve lectures of carefully cited, peer-reviewed material. The frame is: the principle, where it is understood, has historically been within reach of motivated experimenters at small scale.

The next twelve lectures examine, claim by claim, whether the principle is understood, whether the principle is correctly described, and whether the engineering distributes the way the historical pattern would predict.

The series begins here. On a dark hillside, somewhere far from a city, looking up. Pick two stars. Any two. Now ask one question, the simplest question anyone has ever asked of the sky.

How far apart are they?

Not how far each star is from you. How far apart are they, from each other.

You'll notice, almost immediately, that the question is harder than it sounds. The stars are at different distances. The light from one of them left its source two hundred years ago; the light from the other left fifty thousand years ago. The space between them is not flat. The space between them is not even fixed. So before you can answer "how far apart," you have to answer a deeper question first.

You have to pick a rule for what distance means in that part of the universe.

That rule has a name.

It is called a metric. And the question of whether that rule is something we are merely permitted to describe — or something we might one day learn to engineer — is the question this entire lecture series is built around. The question the man at the workbench pointed at. The question the next forty minutes begins to give you the vocabulary to ask carefully.

This is Lecture One.

The question (≈ 2.5 minutes)

The word distance is one of those words that feels obvious until you try to write down a definition of it. Two points on a kitchen table — sure, you can measure between them with a ruler. Two cities on a globe — that's harder. The ruler doesn't lie flat anymore; you have to follow the curve of the surface, and you have to decide whether you're measuring along the surface or through the body of the planet. Two galaxies separated by ten billion light-years of expanding space — that's a research paper. The space between them is not the same space it was when the light started traveling.

The distance you measured yesterday is not the distance you measure today, because the geometry has changed in between.

So let's start with the easy case and build outward. That's what this lecture is going to do, twice. First on a flat sheet, then on a sphere, then we'll generalize — and at the end of the generalization, we'll have what physicists call the metric tensor, and we'll have it in a form that does not require you to have taken a course in calculus.

If you've ever seen the symbol g_{munu} — pronounced "gee-mu-nu" — in a physics video or in a popular-science book and quietly skipped past it, this lecture is the one where it stops being a symbol you skip past and starts being a thing you can actually read.

If you take a flat sheet of paper and you put two dots on it, you have one obvious way to measure how far apart they are. You draw a straight line between them and you measure the line. Everybody learns this in school. Everybody also learns the trick for computing it without bothering to draw the line — you measure how far apart they are sideways, you measure how far apart they are up-and-down, you square both numbers, you add the squares together, and you take the square root. That's the Pythagorean theorem. It's been around for about twenty-five centuries.

Here is the thing about the Pythagorean theorem that nobody told you in school: it is not just a clever shortcut. It is a rule. It is a rule that says, "on this kind of sheet of paper, here is how distance works." And the rule is so deeply baked into how we think about geometry that it took two thousand years for mathematicians to even notice that they were making an assumption about the paper.

The assumption is: the paper is flat.

If the paper is not flat — if it has any curvature at all — the rule for distance changes. The Pythagorean theorem becomes an approximation, accurate for small triangles, less accurate for large ones. And the way in which it becomes inaccurate tells you something specific about how the paper is curved. The same triangle, drawn the same way, gives you a different answer for the squared distance depending on whether you drew it on a flat sheet, on a sphere, or on a saddle. The number depends on the geometry. The geometry depends on the surface.

And the surface, as we will see in Lecture 3, depends on what's pressing on it.

What happens if it isn't flat?

The metric on a flat plane (≈ 6 minutes)

Let's get specific. Let's actually look at the Pythagorean rule, slowly, and see what it's really doing — because every word we say after this depends on it.

You have two points. Call them point A and point B. To get from A to B, you have to move some amount sideways — call that amount the change in x, written Delta x. The Greek capital delta is a physicist's shorthand for "the change in." Then you have to move some amount up or down — call that the change in y, written Delta y. Same idea: delta means change in.

So your trip from A to B has a horizontal piece, Delta x, and a vertical piece, Delta y. These are the two legs of a right triangle. The straight-line distance — the hypotenuse — we'll call Delta s. The s stands for "separation," but you can also think of it as "the actual distance you walked if you went straight." Pythagoras says:

$Delta s^2 = Delta x^2 + Delta y^2$

Read that out loud: the square of the distance equals the square of the horizontal step plus the square of the vertical step.

Three questions worth asking about this rule. First: why do we square everything? Two reasons. One — squaring a number kills the sign. A step backward and a step forward are the same distance; you don't want your distance formula to depend on which way you chose to walk. Two — when you square, you get a quantity that adds up cleanly across right angles. The horizontal and vertical directions are perpendicular, and Pythagoras is, at heart, the statement that for perpendicular directions, the squared distances add.

Second question: why "delta" — why the change in x rather than just x? Because distance is between two points. It's not about where either point is on its own. It's about the difference. You could slide the whole triangle anywhere on the page; the distance between its two endpoints does not change. Distance is translation-invariant. The metric only cares about the gap.

Third question — and this is the one that is going to matter for the rest of the lecture series — why a small delta? Why don't we measure the whole trip in one giant step?

The answer is that on a flat sheet, the rule is the same everywhere, so you can measure the whole trip in one giant step. But the moment the paper starts to bend — even slightly — the rule changes from one place on the paper to the next. So if you want a rule that survives on a curved sheet, you have to write it for an infinitesimally small step. Tiny enough that the curve hasn't started yet. That's why physicists write the rule with lowercase d's instead of uppercase deltas:

$ds^2 = dx^2 + dy^2$

Each lowercase d is the same physicist's shorthand: it means "an infinitely small change in." So the equation reads: the square of an infinitely small distance equals the square of an infinitely small horizontal step, plus the square of an infinitely small vertical step.

That is the metric on a flat plane. That is the entire rule. And on a flat plane, that rule is the same on every single patch of the paper.

Now we change the paper.

The metric on a sphere (≈ 6 minutes)

Take that flat sheet and curl it into a sphere. Same two points, A and B — but now they live on a curved surface. The grid lines that used to be horizontal and vertical are now lines of latitude (the horizontal-ish ones, running parallel to the equator) and lines of longitude (the vertical ones, running from pole to pole).

Try to measure the distance from A to B with the old Pythagorean rule. It doesn't work. The reason it doesn't work is the same reason a road map of a small town works fine but a road map of a continent has weird stretching at the edges. The flat rule assumes the paper is flat, and the sphere is not.

So here is the first hard idea of the lecture. The rule for distance has to depend on where you are.

On a sphere, a step of one degree of longitude doesn't cover the same physical distance everywhere. One degree of longitude at the equator is about a hundred and eleven kilometers. One degree of longitude near the north pole is about a meter. The longitude step is the same step in coordinate units — same one degree on the map — but it covers wildly different physical distance depending on where on the sphere you take it.

So the rule that converts coordinate steps into actual physical distance has to know where on the sphere you are. The rule, in other words, has to vary from place to place.

Let's write it down. On a sphere of radius one, the standard coordinates physicists use are theta — the angle from the north pole, like a co-latitude — and phi — the angle around the equator, like a longitude. A small step in theta is a small change in how far down from the pole you are. A small step in phi is a small change in which way around you've rotated.

The rule for the squared distance on the sphere is:

$ds^2 = dtheta^2 + sin^2theta, dphi^2$

Three things to notice.

First, there are still two terms, just like on the flat sheet. One term for each direction of step. That part is unchanged.

Second, the first term is just dtheta^2 — a clean, plain squared step in theta, no extra factor in front of it. That's because steps in theta — steps from the pole toward the equator — do cover the same physical distance no matter where on the sphere you take them. They're like the latitude lines being evenly spaced.

Third — and this is where the geometry of the sphere lives — there is a factor of sine-squared-theta in front of the dphi^2 term. That factor is the entire point. Sine of theta is zero at the north pole. Sine of theta is one at the equator. So the longitude term gets multiplied by a number that depends on where on the sphere you are. Near the pole, a step in phi barely contributes any distance at all — sine is near zero, so the whole term is near zero. At the equator, a step in phi contributes the most — sine is one.

That little sin^2theta is the sphere's geometry encoded into the metric.

A straight line on a sphere — meaning, the shortest distance between two points — is not a straight line in the Pythagorean sense. It's a great circle. If you fly from New York to Tokyo, you don't fly in a straight line on the map. You fly an arc that bulges north, over Alaska. That arc is the great-circle path. On a sphere, that's what "straight" means. The metric tells you which paths are "straight" and which aren't, because the metric tells you how distance works locally, and the shortest path is the one that minimizes the total distance traveled, summed up step by tiny step along the way.

The technical word for this kind of "straightest possible path" on a curved surface is a geodesic. We'll use that word a lot in this series. For now, just remember: geodesic equals straight-as-the-curvature-permits.

There's one more thing worth pausing on, because it's going to come back in Lecture 4. Imagine you're standing at the equator and you decide to walk what feels, locally, like a perfectly straight line. You don't turn the wheel. You keep your feet pointing exactly forward. Step by step, you check that you have not, locally, deviated. After a few thousand kilometers, you look up — and you are no longer where Euclid's geometry said you would be. You have, in some real sense, been turned by the geometry of the surface itself. You didn't turn. The surface turned you. That is what curvature does.

The metric is the rule that encodes how a surface will turn you when you try to walk straight on it.

Here is the lesson of the sphere. The Pythagorean rule on a flat sheet is one specific case of a much broader idea. The broader idea is: at every patch of any surface, there is a rule for distance. On a flat sheet, the rule happens to be simple — same rule everywhere. On a sphere, the rule depends on where you are. On a saddle, on a balloon, on a sheet that's been bent by something pressing on it — the rule is going to depend on where you are and on what's pressing.

That rule, in its full general form, is what physicists call the metric.

Generalizing — $g_{\mu\nu}$ as the metric (≈ 6 minutes)

Here is the generalization. Imagine any smooth surface, in any number of dimensions, possibly bent however nature wants to bend it. At every point on that surface, there is a local rule — a rule that takes two infinitesimally small coordinate steps and tells you what the actual physical squared-distance is, between the start of the step and the end of the step.

That rule is the metric. And in its full general form, physicists write it like this:

$ds^2 = g_{munu}, dx^mu, dx^nu$

Let's slow that down, because the equation looks intimidating until you've named every piece, and then it isn't intimidating at all.

The thing on the left, ds^2 — that's the same little squared-distance we've already met. Square of an infinitely small physical step. Same idea.

The pieces dx^mu and dx^nu — those are infinitely small coordinate steps. The Greek letters mu and nu are labels. They are labels for which direction. On a flat plane, mu might be x and nu might be y. On a sphere, mu might be theta and nu might be phi. In four-dimensional spacetime — which is where we're heading in Lecture 2 — there are four directions: three of space, one of time, so mu and nu each run over four possible values. The Greek letters are just bookkeeping for "which direction of step."

And the middle piece, g_{munu} — that is the metric. That's the rule itself. It's a table of numbers. One number for each pair of directions. On a flat plane in two dimensions, the table has four entries: one for x-and-x, one for x-and-y, one for y-and-x, one for y-and-y. On a sphere, same four entries, different numbers. In four-dimensional spacetime, the table has sixteen entries.

Most of the time most of those numbers are zero, and the equation collapses into something simple. For the flat plane, g{munu} is the identity — a one when mu and nu point in the same direction, a zero otherwise — and the line element reduces to the Pythagorean rule we started with. For the sphere, g{munu} has a one in the theta slot, a sin^2theta in the phi slot, and zeroes off the diagonal — and the line element reduces to the sphere formula we just wrote down. The full g_{munu} notation is not introducing a new physical idea.

It's introducing a bookkeeping device that handles all possible metrics at once.

The clever part — and this is something Einstein adopted around 1916 — is that when you see two of the same Greek letters appearing once "up" and once "down" in the same expression, you understand that you're meant to sum over all the values that letter could take. So when you see g_{munu}, dx^mu, dx^nu, with mu appearing once up and once down, and nu appearing once up and once down, you sum over all four values of mu and all four values of nu. That's the Einstein summation convention. It is, again, bookkeeping. It saves writing.

Here is the part that matters for the rest of this series. If you change the surface — if you deform it, push on it, bend it — the numbers in the metric change. That is the whole game. The metric is not a fixed background. The metric is the thing that tells you what the geometry is, locally, at every point. When something — mass, energy, momentum, vacuum structure — changes the local geometry, what physically changes is the metric.

One subtle but important consequence. Because the metric varies from place to place, two listeners standing at two different points on the surface can both follow what looks, locally, like a straight line — and end up moving toward each other, or away from each other, even though neither one is steering. The geometry does the steering. Apples fall to the ground not because some mysterious force is pulling on them, but because near the Earth, the metric of spacetime is such that the "straightest possible path" of an apple in four-dimensional spacetime intersects the surface of the planet. That is not a metaphor.

That is the content of general relativity as Einstein wrote it down. Gravity, in his framework, is what the metric does.

So here is the one-sentence definition this lecture has been aiming at. Write it down somewhere if you're the kind of listener who writes things down. A metric is the local rule for converting coordinate steps into physical distances, and the metric can vary from point to point on the same space.

That definition is going to do a lot of work in this series. It is the definition Einstein needed when he wrote down general relativity in 1915 and 1916. It is the definition Alcubierre needed when he wrote down his 1994 warp-drive solution. It is the definition Morris and Thorne needed when they wrote down the traversable-wormhole geometry in 1988. And it is the definition Hal Puthoff has built a four-decade research program on top of — the research program from which the phrase metric engineering derives.

Which brings us to the handoff.

From describing the metric to engineering it — the Puthoff handoff (≈ 4 minutes)

For about a hundred years, the working assumption of relativistic physics has been: the metric is a thing you describe. You measure where the masses and energies are. You solve Einstein's equations. You read off what the local metric is. The metric is the output of the physical situation. The geometry, in this picture, is whatever the universe hands you. Your job, as a physicist, is to figure out what was handed to you.

In the late 1980s and early 1990s, a separate question started to be asked — quietly, in a smaller body of literature, in journals like Physical Review A and Foundations of Physics. The question was: what if the metric is also something you can act on? If the local rule for distance depends on what's happening in the local quantum vacuum, and the local quantum vacuum is something you can — in principle, with the right boundary conditions — change — then the metric might be a thing you can engineer, not just a thing you can describe.

The geometry, in this alternative picture, might be partly an input, not only an output.

The physicist most associated with this framing is Harold Puthoff. He earned his PhD in electrical engineering at Stanford in 1967 — his dissertation, with advisor Richard Pantell, was on the stimulated Raman effect and its application to tunable lasers, and his Wiley textbook with Pantell, Fundamentals of Quantum Electronics, came out in 1969. Since 1985 he has directed the Institute for Advanced Studies at Austin. Since 1991 he has been President and CEO of EarthTech International. His publication stream on quantum-vacuum physics in Physical Review A and Physical Review E extends from 1989 to the present.

In 2002, in the journal Foundations of Physics, Puthoff published the paper that formalized the program. The paper is titled "Polarizable-Vacuum (PV) Approach to General Relativity," and it appears in volume 32, pages 927 through 943. Let me bring him in directly to state the program in his own published voice.

The viewpoint I want to put forward is this. A theoretical approach to gravity is to consider the spacetime metric to be a derived quantity — derived from the underlying behavior of the quantum vacuum. Where mass and energy are present, the vacuum is polarized; its permittivity and permeability change; light slows, clocks run slower, rulers shrink. The geometric effects we call gravity, in this approach, are refractive effects of a vacuum whose properties vary from place to place. Under this approach, gravitation is not a curvature imposed on a fixed background.

It is a manifestation of a vacuum that has its own structure, and that structure can in principle be acted upon. That is the research-program question. Whether the metric is purely descriptive — a label we hang on a geometry that nature delivers to us — or whether the metric is, at some level we have not yet learned to access, an engineerable property of the vacuum.

The framing matters. Puthoff is not claiming, in that paper, that anyone has engineered the vacuum. He is claiming that there is a research program — open, well-defined, formally published in a peer-reviewed journal — that asks whether such engineering is possible. The polarizable-vacuum reformulation of general relativity is the mathematical scaffolding for that program. In subsequent lectures we'll see what that scaffolding has been used to attempt, what has been claimed, what has been measured, and what has not.

But "the research program exists in the published literature" is one claim. "The research program will succeed" is a very different claim. And here we need the other voice in this lecture.

The skeptic intervenes — Hossenfelder's caution (≈ 4 minutes)

There is a discipline in physics — a discipline this entire lecture series will try to honor — of separating two questions that often get blurred. The first question is does the math admit a solution? The second question is does the universe permit you to build it? The math admitting a solution and the universe permitting an implementation are different questions, and conflating them is the single most common error in popular physics writing.

The physicist who has articulated this distinction most cleanly, in the context of warp drives and metric-engineering proposals specifically, is Sabine Hossenfelder. PhD in theoretical physics, Goethe University Frankfurt. Research fellow at Perimeter Institute, Nordita, and the Frankfurt Institute for Advanced Studies. Author of Lost in Math (Basic Books, 2018) and Existential Physics (Viking, 2022). On her Backreaction blog, in a post titled "Warp Drive News. Seriously!", published November 21, 2020, she wrote — and this is the exact quotation, word for word, from the published post:

Any space-time will solve the equations of General Relativity, provided you assume suitable mass and energy distributions. The real question is whether required distributions are physically reasonable.

Read that sentence again, slowly. Any space-time will solve the equations of General Relativity, provided you assume suitable mass and energy distributions. In other words: if you are willing to write down whatever stress-energy you want on the right-hand side of Einstein's field equations, you can produce essentially any geometry you want on the left-hand side. Warp drives. Wormholes. Time machines. All of them are solutions of general relativity — given the right inputs.

The catch is in the inputs. The catch is that the required mass-and-energy distributions, for most of those exotic geometries, are not anything we know how to source. They require what physicists call negative energy density, at macroscopic scales, in configurations the quantum vacuum has never been observed to deliver. Hossenfelder's discipline is to say: yes, the math admits a solution. Now show me the source.

This is the cleanest articulation of the mainstream-physics critique of every metric-engineering proposal, including all the proposals this series is going to engage. It applies, in equal measure, to the Alcubierre warp metric we'll meet in Lecture 4 — to the Morris-Thorne wormhole geometry we'll meet in Lecture 5 — to the engineering proposals we'll meet in Block D. And it should apply, in equal measure, to the lecture you're listening to right now.

The discipline of this series is this. When a credentialed physicist publishes a research program in Foundations of Physics, we will tell you what they published, accurately, with the citation. When the skeptical mainstream-physics response also exists in the published record — also in journals or on long-form on-record blogs by named theoretical physicists with verifiable credentials — we will tell you about that too, with that citation. We will not collapse the two. We will not pretend the research program is settled when it isn't, and we will not pretend the critique disposes of the research program when it doesn't. We will hold both.

Here is the rule we will hold throughout these lectures. A solution of the equations is not yet a piece of physics. A piece of physics is a solution of the equations that the universe has been independently observed to permit.

That distinction is going to do a lot of work for us. Hold it.

What this lecture buys you (≈ 4 minutes)

Let me tell you what this lecture has just bought you. Because the next eleven lectures all rest on it.

You can now read the central object of general relativity. You can look at an expression like ds^2 = g_{munu}, dx^mu, dx^nu and say what each piece carries. That is going to matter in Lecture 2, when we meet Hermann Minkowski's four-dimensional spacetime and the Lorentz transformations that preserve its metric. It is going to matter in Lecture 3, when we meet Einstein's field equations, which are the rule that tells you what the metric has to be, given a particular distribution of mass and energy.

It is going to matter especially in Lecture 4. In 1994, a numerical-relativist named Miguel Alcubierre — at the time at the University of Wales College of Cardiff under advisor Bernard Schutz, now Director of the Institute for Nuclear Sciences at UNAM in Mexico — published a paper in Classical and Quantum Gravity with a deceptively simple title: "The warp drive: hyper-fast travel within general relativity." Alcubierre wrote down a specific metric — a specific choice of g_{munu} as a function of position — that solves Einstein's equations and that describes a localized region of spacetime moving through the surrounding spacetime faster than light.

The trick of the construction is that the local metric ahead of the bubble is contracted and the local metric behind the bubble is expanded; the bubble itself doesn't have to move through space faster than light, because space itself is doing the moving. The metric is real. The paper is in Classical and Quantum Gravity. The mathematical object exists. The engineering question — can the required stress-energy distribution be physically constructed — is exactly the question Hossenfelder just raised.

It is going to matter in Lecture 5, when we meet the Morris-Thorne wormhole — Kip Thorne, who is the 2017 Nobel laureate in physics and the Feynman Professor of Theoretical Physics Emeritus at Caltech, and his graduate student Michael Morris, in American Journal of Physics volume 56, page 395, in 1988. Same situation. The metric exists. The geometry exists.

Morris and Thorne wrote down the line element for a spherically symmetric throat connecting two otherwise separated regions of spacetime, the wormhole "flare-out" condition that the geometry has to satisfy if anything is going to traverse it, and the precise stress-energy distribution at the throat that would be required to hold it open. The engineering requirement — negative energy density at the wormhole throat — does not yet have a demonstrated source at the scales required.

It is going to matter in Lecture 7, when we meet the quantum vacuum — the only known place in nature where negative energy densities have been experimentally measured on macroscopic scales. The Casimir effect, predicted by Hendrik Casimir in 1948 and measured by Steve Lamoreaux at Yale in 1997 in Physical Review Letters, is the cleanest entry point into the question of whether the vacuum is something you can act on.

Two parallel uncharged metal plates in vacuum attract each other, with a force that depends only on the geometry of the gap and on Planck's constant and the speed of light — the signature of a quantum-mechanical effect of the vacuum mode structure itself.

The dynamic version — predicted by Gerald Moore in 1970 and measured by Chris Wilson and collaborators at Chalmers University in Nature in 2011, then independently confirmed by Pasi Lähteenmäki and colleagues at Aalto and VTT in PNAS in 2013, and again by Schneider et al. at Chalmers in Physical Review Letters in 2020 with the quantum-statistical entanglement signature that pins down the vacuum origin of the radiation — is the cleanest operational demonstration that the structure of the quantum vacuum is manipulable. Modulate a boundary fast enough and you pull real photons out of the vacuum.

It is going to matter in Lecture 10, when we meet the patent series filed by Salvatore Pais, formerly Chief Engineer at the Naval Air Warfare Center Aircraft Division — patents granted by the United States Patent and Trademark Office, with the Secretary of the Navy as assignee, claiming the manipulation of the local metric via high-energy electromagnetic boundary conditions. We will read those patents as the engineering specifications they claim to be. We will read the published peer-reviewed paper in IEEE Transactions on Plasma Science that accompanies the plasma-compression-fusion-device application.

We will read the public record of the Sheehy attestation — the Naval Aviation Enterprise's Chief Technology Officer writing to USPTO that the inventions were operable, which is part of how some of these patents were granted at all. And we will read the public record of the Navy's own internal evaluation, costing approximately five hundred thousand dollars over three years, which reportedly could not demonstrate the central effect. We will hold the distinction the entire way through. Patent filed and attested is not the same as effect demonstrated and replicated.

The discipline of holding that line is exactly the discipline of Hossenfelder's distinction — mathematical solution versus physically realized — applied to the engineering register.

The vocabulary you now have is the vocabulary that lets every one of those subsequent conversations make sense. You can tell a metric from a stress-energy. You can tell a mathematical solution from a physically realized one. You can ask, of any claim, what does the geometry require, and has the required physical input been independently sourced. That is the question every Block-B lecture and every Block-D lecture in this series is going to come back to. The metric is the language. The discipline is the editorial spine. Both were named in this lecture.

Closing (≈ 90 seconds)

Go back to the hillside. Same listener. Same star field. The two stars are still there. The light from one of them still left two hundred years ago. The light from the other still left fifty thousand years ago. The space between them is still not flat and not fixed.

But the question you can now ask is sharper than the question you started with.

Not just how far apart are they — but what is the metric on the region of spacetime between them, and what local sources of mass and energy and vacuum structure determine that metric. Those are the questions general relativity will let you ask, when we get to it in two lectures. And whether any of that local structure is something we can one day act on — whether the metric is something that can be engineered, not just described — that is the question this entire series is built around.

Lecture 2 picks up where this one stops. Special relativity. Four-vectors. Minkowski's spacetime. The metric that turns three dimensions of space and one of time into a single geometric object, and the transformations that leave that metric invariant.

Same listener. Same stars. New tools.