Aug 18, 2026 · 36 min · 11 segments
The Navier-Stokes equations are enormously successful at predicting how fluids flow and swirl. But they fail to account for the microscopic bits that make up matter. But now math based on symmetries…
And there was a big paradigm shift in physics in the mid to late 1900s, and I think of it like the old-school style of doing physics was what you see is what you get.
You see pendulums, you see light, you see whirlpools, and you write down equations that match those, and once you've tested them, you're done.
There's atoms and there's electrons and molecules, and those are all ripples in quantum fields, and those all give way to who knows what.
And so these days, physicists start from a place of ignorance, where they know that they don't and may never know what's happening at those fundamental scales.
And even if they did, it's probably too hard to calculate what that means for, like, an apple or a magnet for us.
And so our equations now, we should think of them as capturing just the biggest, most obvious parts in the world, and that's why they're so simple.
We should think of every theory from Einstein's theory of gravity to the Navier-Stokes equations as having a hidden kind of dot, dot, dot at the end with more terms to come that will tell us more about the complications that arise as you zoom further and further.
They're observing something in the world, they see the mathematical relationships in the way that a pendulum or a river behave, and they came up with equations that describe that exactly.
But we know now that there's a whole bunch of uncertainty and different ways that things operate at subatomic levels, so implied in all of these great equations that we have that describe the physical world is something else, [laughs] something more that we might not see the obvious effects of.
Now we know that reality has this kind of telescoping structure, right? The more you zoom in, the more things change, and the more complicated they get, and the original way of formulating the laws of physics sort of leaves that aside and just describes our level.
And so now we have this effective field theory philosophy, which I'm sure we're gonna get to.
Well, a field theory is a theory that describes a substance spread out in space, and then an effective field theory is an approximate field theory, one where you make peace with the fact that you don't know what's happening at more microscopic levels of reality, and you're just gonna develop a theory that works for one specific level.
Right, our level, for example, although you can take this philosophy and apply it at any level.
You know what's happening at that one level where you apply it, and you rigorously prove that that's the correct and justified thing to do at that level, even though you don't know exactly what's happening below.
And there was a big paradigm shift in physics in the mid to late 1900s, and I think of it like the old-school style of doing physics was what you see is what you get.
You see pendulums, you see light, you see whirlpools, and you write down equations that match those, and once you've tested them, you're done.
There's atoms and there's electrons and molecules, and those are all ripples in quantum fields, and those all give way to who knows what.
And so these days, physicists start from a place of ignorance, where they know that they don't and may never know what's happening at those fundamental scales.
And even if they did, it's probably too hard to calculate what that means for, like, an apple or a magnet for us.
And so our equations now, we should think of them as capturing just the biggest, most obvious parts in the world, and that's why they're so simple.
We should think of every theory from Einstein's theory of gravity to the Navier-Stokes equations as having a hidden kind of dot, dot, dot at the end with more terms to come that will tell us more about the complications that arise as you zoom further and further.
They're observing something in the world, they see the mathematical relationships in the way that a pendulum or a river behave, and they came up with equations that describe that exactly.
But we know now that there's a whole bunch of uncertainty and different ways that things operate at subatomic levels, so implied in all of these great equations that we have that describe the physical world is something else, [laughs] something more that we might not see the obvious effects of.
Now we know that reality has this kind of telescoping structure, right? The more you zoom in, the more things change, and the more complicated they get, and the original way of formulating the laws of physics sort of leaves that aside and just describes our level.
And so now we have this effective field theory philosophy, which I'm sure we're gonna get to.
Well, a field theory is a theory that describes a substance spread out in space, and then an effective field theory is an approximate field theory, one where you make peace with the fact that you don't know what's happening at more microscopic levels of reality, and you're just gonna develop a theory that works for one specific level.
Right, our level, for example, although you can take this philosophy and apply it at any level.
You know what's happening at that one level where you apply it, and you rigorously prove that that's the correct and justified thing to do at that level, even though you don't know exactly what's happening below.
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3 of 9
Fluids Join Fundamental Physics
Fluids finally fit into physics' grand framework
Black Holes Explain Motor Oil
Black holes may explain ordinary fluids better
The Two-Fluid Trick
Physicists doubled fluids to capture disappearing energy
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