Speaker 1: Welcome to the core side. Quantum Physics podcast, an exploration
Speaker 1: of the fundamental structure of reality, where quantum laws govern matter, energy,
Speaker 1: and information. Here, uncertainty is a feature, not a flaw,
Speaker 1: and understanding begins at the smallest scales.
Speaker 2: Imagine for a second the absolute ultimate divide in our
Speaker 2: understanding of reality.
Speaker 3: Oh yeah, the classic split.
Speaker 2: Right on one side, you have the classical universe. This
Speaker 2: is the world of the intuitive, the visible, predictable stuff.
Speaker 3: The everyday world exactly.
Speaker 2: It's where gravity pulls an apple from a tree, or
Speaker 2: where a baseball follows this perfect predictable mathematical arc. And
Speaker 2: massive planets they just orbit stars with absolute clockwork precision.
Speaker 2: The rules here, they just make sense to us.
Speaker 3: Well, yeah, because the the physics of everyday reality are
Speaker 3: built on this foundation of certainty. I mean, we can
Speaker 3: measure a macroscopic object, figure out its speed, and predict
Speaker 3: exactly where it will be an hour or a day
Speaker 3: or a century from now.
Speaker 2: Right, It's totally deterministic. But then, and this is where
Speaker 2: it always gets wild. You cross this threshold. You zoom
Speaker 2: in close enough down to the level of individual electrons
Speaker 2: and photons, and you enter the quantum realm, and all.
Speaker 3: Those comforting rules just completely evaporate.
Speaker 2: They really do. Suddenly, particles seem to just like teleport
Speaker 2: or they exist in this fuzzy cloud of probability, potentially
Speaker 2: being in multiple places at once until someone actually looks.
Speaker 3: At them, which is deeply unintuitive.
Speaker 2: Highly unintuitive, And for nearly a century, the consensus has
Speaker 2: been that these two realms are just fundamentally incompatible. Yeah,
Speaker 2: we've been told essentially that the universe speaks two completely
Speaker 2: different languages.
Speaker 3: Right, classical mechanics for the big stuff and quantum mechanics
Speaker 3: for the tiny stuff.
Speaker 2: Yeah, and having two totally disparate rule books for the
Speaker 2: exact same universe, depending entirely on how closely you're squinting
Speaker 2: at it. That's always been an uncomfortable compromise.
Speaker 3: Hast uncomfortable as an understatement, I mean that philosophical and
Speaker 3: mathematical factor has pretty much defined modern science.
Speaker 2: Well, that compromise might actually be over because in April
Speaker 2: of twenty twenty six, researchers at MIT published this paper,
Speaker 2: which is in the Proceedings of the Royal Society A,
Speaker 2: and it fundamentally shatters this separation.
Speaker 3: It really does. It's a massive paradigm shift.
Speaker 2: It is they mathematically proved that the most iconic, the
Speaker 2: most bizarre quantum behaviors can actually be perfectly reproduced using
Speaker 2: purely classical physics concepts.
Speaker 3: And we should clarify there are no approximations here, no
Speaker 3: semi classical half measures were only kind of work right, No.
Speaker 2: Close enough. It is an exact mathematical bridge between the
Speaker 2: macro and the micro, which is just its mind blowing.
Speaker 3: The implications really cannot be overstated by showing that a
Speaker 3: separate quantum rule book isn't strictly necessary to get quantum results.
Speaker 3: I mean, Jean Jacques Lautine and Winfrey low Miller from
Speaker 3: MIT's Nonlinear Systems Lab. They've really changed the game here.
Speaker 2: So today we are going to unpack the mechanics of
Speaker 2: how these scientists actually prove this. We're going to look
Speaker 2: at the math, the physical models, and this wild reality
Speaker 2: that the classical universe and the quantum universe might just
Speaker 2: be the exact same thing, view through different lenses.
Speaker 3: It's a lot to wrap your head around, it is.
Speaker 2: So to really understand this breakthrough, we need to ground
Speaker 2: ourselves in the original rule book. First, Let's look at
Speaker 2: the classical world, specifically something called the principle of least action.
Speaker 3: Right, So, the principle of least action is essentially the
Speaker 3: beating heart of classical mechanics, and it's intimately tied to
Speaker 3: this mathematical framework known as the Hamilton Jacoby equation.
Speaker 2: Okay, Hamilton Jacoby, what does that mean in plain English?
Speaker 3: In simple terms, this principle basically states that when a
Speaker 3: physical system evolves, like say, a rock tumbling down a mountain,
Speaker 3: it will always always take the path that minimizes a
Speaker 3: specific quantity, and that quantity is called action.
Speaker 2: An action just to clarify for everyone, is the mathematical
Speaker 2: difference between kinetic energy, so the energy of the rock's
Speaker 2: actual motion, and potential energy, which is its stored energy
Speaker 2: based on where it is tracked over time.
Speaker 3: Exactly nature is. Well, it's incredibly a canonmical Macroscopic objects
Speaker 3: inherently seek out the absolute most mathematically efficient route to
Speaker 3: get from point A to point B, just based on
Speaker 3: the forces acting on them.
Speaker 2: A good way I like to visualize this and tell
Speaker 2: me if this tracks is to think of the classical
Speaker 2: universe as this perfectly efficient delivery driver using the ultimate
Speaker 2: GPS system.
Speaker 3: Oh, I like that.
Speaker 2: Yeah, right, So if you throw a ball across a field,
Speaker 2: the universe instantly calculates the absolute laziest, most efficient trajectory
Speaker 2: for that ball to take.
Speaker 3: It factors in gravity, wind, resistance, starting velocity, all of
Speaker 3: it exactly.
Speaker 2: And it plots one single hyper efficient path. The ball
Speaker 2: doesn't wander around the field exploring. It just follows that
Speaker 2: one eye optimal route. It's totally deterministic.
Speaker 3: One starting point, one optimal path, one destination. That is
Speaker 3: classical physics in a nutshell, right. But the contrast comes
Speaker 3: in when we try to apply that exact same logic
Speaker 3: to the quantum realm, because there we run headfirst into
Speaker 3: the Schrodinger equation.
Speaker 2: The famous Shrodinger equation, Right.
Speaker 3: It's the central pillar of non relativistic quantum mechanics. It
Speaker 3: governs everything from electron orbitals to the behavior of light.
Speaker 3: And the Schrodinger equation explicitly rejects the concept of a
Speaker 3: single defined path.
Speaker 2: So the single delivery driver's just gone.
Speaker 3: Replaced by an infinite swarm. According to the foundational models
Speaker 3: of quantum mechanics, like Richard Feynman's path integral formulation, a
Speaker 3: particle doesn't pick one efficient route.
Speaker 2: It explores like an infinite number of paths simultaneously.
Speaker 3: Right, Yes, it takes a direct route, sure, but it
Speaker 3: also mathematically takes a route that loops around the moon
Speaker 3: and a route that zigzags through the floorboards. Every conceivable
Speaker 3: path through the universe is calculated and some together, which.
Speaker 2: Sounds completely absurd when you say it out loud.
Speaker 3: It does. But mathematically, all those infinite paths interfere with
Speaker 3: each other. They create constructive and destructive interference, and that
Speaker 3: results in a wave function.
Speaker 2: So instead of knowing exactly where a particle is, the
Speaker 2: Schrodinger equation just gives us a mathematical description of the
Speaker 2: probability of finding it somewhere exactly.
Speaker 3: We're just left with these clouds of possibility.
Speaker 2: Okay, so this is where I'm struggling. We have a
Speaker 2: single hyper efficient delivery driver taking the most logical route
Speaker 2: on one hand, and on the other, an infinite swarm
Speaker 2: of drivers taking literally every conceivable path in the entire
Speaker 2: universe at the same time.
Speaker 3: The ultimate contradiction.
Speaker 2: Right, So, how could anyone possibly claim that these two
Speaker 2: mathematical models are identical? It sounds impossible on its face.
Speaker 3: Well, that was the genius of Slotein and low Miller.
Speaker 3: They looked at the classical Hamilton Jacobe equation the math
Speaker 3: for our single efficient driver and realized it actually had
Speaker 3: the inherent capability to handle messy quantum scenarios all along.
Speaker 2: Wait, really, the classical math already had it.
Speaker 3: It did it simply lapped two very specific ingredients to
Speaker 3: bridge that gap, and the first ingredient they introduced is
Speaker 3: something called multipaths.
Speaker 2: Multipaths Okay, let me guess instead of one single lease
Speaker 2: action path, we just upgrade the system to an infinite
Speaker 2: number of classical paths.
Speaker 3: H No, actually, because that would just be reinventing Feinman's
Speaker 3: complex path integrals all over again. We want to avoid infinity.
Speaker 2: Oh right, fair point. So what do they do?
Speaker 3: The MIT team expanded the classical framework to consider a
Speaker 3: select few highly efficient leased action paths simultaneously, so the
Speaker 3: math is allowed to evaluate multiple optimal routes at once,
Speaker 3: rather than forcing just one deterministic outcome.
Speaker 2: Okay, so, going back to our analogy, we have a
Speaker 2: handful of really good delivery drivers taking the top three
Speaker 2: or four best routes rather than an infinite swarm covering
Speaker 2: the whole earth.
Speaker 3: Exactly. It's a multi valued, classical action.
Speaker 2: That makes mathematical sense. It's cleaner. But and here's where
Speaker 2: I get stuck. A few efficient routes still don't explain
Speaker 2: the fuzzy cloudlike nature of a quantum particle, right.
Speaker 3: Because a particle isn't just a fleet of trucks.
Speaker 2: Yeah, So how do we get the cloud?
Speaker 3: This is where the second absolutely crucial ingreding comes into play.
Speaker 3: Density density like mass, not quite. The researchers use the
Speaker 3: Greek letter row to represent a classical concept borrowed directly
Speaker 3: from hydrodynamics. You know, the study of fluid motion.
Speaker 2: Okay, fluid dynamics, right, And.
Speaker 3: Fluid dynamics density describes how a substance flows, how it clusters,
Speaker 3: and how it interacts with its environment. They essentially grafted
Speaker 3: this classical notion of fluid density onto those multipaths we
Speaker 3: just talked about.
Speaker 2: Wait, hold on, I need to push back here. Particles
Speaker 2: like electrons, they are discrete, indivisible points of matter. They
Speaker 2: aren't liquids. So if we are tracking a single electron,
Speaker 2: treating it like a continuous flowing fluid seems like a
Speaker 2: huge fundamental contradiction. How does a single microscopic billiard ball
Speaker 2: suddenly behave like a river.
Speaker 3: It's a great question. The density here doesn't mean the
Speaker 3: physical mass of the electron is smearing out like spilled
Speaker 3: milk across the room.
Speaker 2: Okay, good, that would be messy.
Speaker 3: Very no. It represents a fluid of probability, and it's
Speaker 3: tied strictly to those multiple classical paths. Think about like
Speaker 3: traffic density.
Speaker 2: Traffic density.
Speaker 3: Yeah, even if you are only tracking one specific car,
Speaker 3: the mathematical probability of where that car might end up
Speaker 3: on its journey behaves a lot like a fluid. It
Speaker 3: clusters around bottlenecks, it spreads out over open highways.
Speaker 2: Oh I see.
Speaker 3: So by combining a multi valued classical action those multiple
Speaker 3: efficient paths with an analytically computed density flowing along those
Speaker 3: exact paths, the system starts to behave completely differently than
Speaker 3: just a single deterministic particle.
Speaker 2: The friction and the crowding of the paths dictate the behavior.
Speaker 2: So by calculating how this probability fluid flows and bunch
Speaker 2: of up along a few highly efficient routes, they built
Speaker 2: a mathematical replica of a quantum system.
Speaker 3: Actually, they went much further than just a replica. What
Speaker 3: do you mean when they integrated multiple classical paths with
Speaker 3: that fluid density, The resulting math produced the exact quantum
Speaker 3: wave function predicted by the Scherdinger equation. Wait, exactly exactly.
Speaker 3: The equations become literally identical once that classical density is
Speaker 3: properly accounted for in the math. Slow Teine even pointed
Speaker 3: out that they didn't have to invent any new quantum
Speaker 3: physics at all. They literally just applied classical fluidynamics to
Speaker 3: classical action principles.
Speaker 2: That is a massive claim because normally, you know, attempts
Speaker 2: to bridge the macro and the micro rely on those
Speaker 2: semi classical theories we mentioned, right.
Speaker 3: The ones that kind of work for large molecules but
Speaker 3: completely fall apart the second you try to model a
Speaker 3: single solitary electron exactly.
Speaker 2: But claiming an exact rigorous bridge means this theory has
Speaker 2: to survive like the ultimate boss battles of quantum mechanics.
Speaker 2: It has to explain the stuff that is historically defied
Speaker 2: classical logic entirely, and it does well. Let's test that.
Speaker 2: Let's start with the most famous one, the double slit experiment.
Speaker 3: Oh, the quintessential demonstration of quantum weirdness.
Speaker 2: Right, so we all know the basic setup. You have
Speaker 2: a barrier with two vertical slits in it and a
Speaker 2: blank screen behind it.
Speaker 3: Simple enough.
Speaker 2: But if you fire quantum particles like individual electrons through
Speaker 2: the slits one at a time, they don't just form
Speaker 2: two simple bands on the back wall like you'd expect.
Speaker 2: Over time, these single electrons build up an interference pattern,
Speaker 2: a really complex series of alternating light in dark stripes.
Speaker 3: Which looks exactly like the ripples created when two distinct
Speaker 3: waves crash into each other in a pond.
Speaker 2: Yes, but because you are firing the electrons strictly one
Speaker 2: at a time, the implication is that a single electron
Speaker 2: is somehow traveling through both slits, simultaneously interfering with the
Speaker 2: self and deciding where to land based purely on probability.
Speaker 3: Which is why the traditional quantum explanation requires calculating the
Speaker 3: complex phases for infinite and so many possible meandering routes
Speaker 3: the electron could take through space just to figure out
Speaker 3: where that constructive and destructive interference will happen on the screen.
Speaker 2: It is incredibly heavy, incredibly unintuitive math extremely so if
Speaker 2: the mit team is throwing out the infinite paths, how
Speaker 2: on earth do they get the alternating stripes? Because if
Speaker 2: you only have two classical multipaths, like one highly efficient
Speaker 2: route going through the left slit and one going through
Speaker 2: the right slit, that shouldn't create a complex ripple.
Speaker 3: No, two simple paths should just give you two solid
Speaker 3: stripes on the back wall exactly.
Speaker 2: So where does the wave pattern come from?
Speaker 3: Classically, it emerges entirely from the physical constraints of the
Speaker 3: slits themselves, acting upon that second ingredient we discussed the
Speaker 3: fluid density.
Speaker 2: The physical constraints.
Speaker 3: Yeah, the researchers mathematically modeled the physical barrier with the
Speaker 3: slits as a space with highly constrained choke points. So
Speaker 3: as the probability fluid travels along those two optimal paths,
Speaker 3: it is quite literally forced to squeeze through the narrow openings.
Speaker 2: Okay, So the physical boundaries of the slits are acting
Speaker 2: as literal constraints on the probability fluid exactly.
Speaker 3: The boundaries force the paths to bend, and they force
Speaker 3: the fluid density to ripple outward. The mathematical term involves
Speaker 3: constraint forces, specifically non Lipschitz forces altering the momentum of
Speaker 3: the classical density.
Speaker 2: Oh wow.
Speaker 3: Yeah, So when the fluid density from the left path
Speaker 3: interacts with the fluid density from the right path after
Speaker 3: squeezing through those constraints, they naturally create interference.
Speaker 2: That is wild.
Speaker 3: The alternating stripes of the famous wave function emerge entirely
Speaker 3: naturally from the friction and pressure of classical fluid dynamics
Speaker 3: interacting with a physical boundary.
Speaker 2: So no particle being in two places at once, no
Speaker 2: infinite paths taking detours through the Andromeda galaxy. Just a
Speaker 2: probability fluid naturally rippling as it squeezes through two tight
Speaker 2: classical paths.
Speaker 3: That's it. No quantum magic required.
Speaker 2: That actually makes a terrifying amount of sense. It really does.
Speaker 2: But let's push this even further. What about quantum tunneling?
Speaker 3: Ah another great boss battle right.
Speaker 2: This is the phenomenon where a particle simply passes straight
Speaker 2: through a solid energy barrier, like walking through a wall.
Speaker 3: Which in a purely classical framework is totally forbidden. I mean,
Speaker 3: if you roll a ball up a hill, but it
Speaker 3: lacks the kinetic energy to reach the crest, the ball
Speaker 3: just rolls back down.
Speaker 2: It can't magically cross over to the other side exactly.
Speaker 3: Yet in the quantum world, electrons routinely appear on the
Speaker 3: other side of barriers they mathematically shouldn't have the energy
Speaker 3: to cross, and.
Speaker 2: The traditional quantum explanation is always that the particle is
Speaker 2: a wave of probability, and a tiny piece of that
Speaker 2: wave is basically leaks through the barrier. It's always described
Speaker 2: like a ghost walking through a brick wall. So how
Speaker 2: does a classical lazy delivery driver model explain walking through walls.
Speaker 3: By analyzing how fluid pressure and density naturally behave when
Speaker 3: confronted with an obstacle. The MIT team just applied their framework,
Speaker 3: relying again on those same multipaths and density evolution.
Speaker 2: Okay, so how does a fluid act differently than a bowl?
Speaker 3: Well, while a single solid particle obviously lacks the energy
Speaker 3: to surmount the barrier, a fluid distributed over a multiple
Speaker 3: paths behaves very differently. The formulation inherently allows for what
Speaker 3: they term transmission through forbidden.
Speaker 2: Regions, transmission meaning it seeps through.
Speaker 3: Precisely because the density represents a distribution of probability, the
Speaker 3: mathematical pressure of that fluid along the classical multipaths just
Speaker 3: finds efficient routes that seep through the barrier's constraints.
Speaker 2: Wow.
Speaker 3: And the most amazing part the classical calculation, they did
Speaker 3: perfectly match the exact Shreddinger predictions for the tunneling probability.
Speaker 2: So the fluid density is just finding mathematically valid, highly
Speaker 2: efficient microscopic routes through the barrier that a single classical
Speaker 2: trajectory would just completely ignore. That completely reframes how we
Speaker 2: visualize the micro world. And it's my understanding they didn't
Speaker 2: just stop at the double slater tunnel link, right. They
Speaker 2: applied this classical framework to a massive roster of textbook
Speaker 2: quantum mysteries.
Speaker 3: Oh, they systematically proved the framework against numerous foundational problems.
Speaker 3: I mean, they modeled the harmonic oscillator, which is essentially
Speaker 3: a particle trapped in a quadratic potential, and they tackled
Speaker 3: a particle in a box.
Speaker 2: What did they find with the box?
Speaker 3: In that scenario? They demonstrated how a single particle bouncing
Speaker 3: back and forth off the walls naturally generates the very
Speaker 3: multipaths we've been discussing, which builds up a complex internal
Speaker 3: density all on its own.
Speaker 2: I want to dive deep into one of their specific successes,
Speaker 2: because just listing phenomena kind of doesn't do the underlying
Speaker 2: mechanics justice. Let's talk about the hydrogen atom.
Speaker 3: The kulum potential problem.
Speaker 2: Right, because applying classical physics to the orbit of an
Speaker 2: electron around a nucleus usually ends in total disaster, which
Speaker 2: is basically why quantum mechanics had to be invented in
Speaker 2: the first place.
Speaker 3: Right. Yes, classical physics says an orbiting electron should instantly
Speaker 3: radiate away all of its energy and just crash into
Speaker 3: the nucleus. It shouldn't be stable.
Speaker 2: So how did multipaths and fluid densities solve the hydrogen atom.
Speaker 3: By mathematically linking classical kepler orbits directly to quantum wave functions.
Speaker 2: Kepler orbits like planetary orbits.
Speaker 3: Exactly the same. Kepler orbits are the mathematical principles that
Speaker 3: describe how massive planets orbit the Sun. They are elliptical, predictable,
Speaker 3: deterministic paths dictated by gravity. Okay, the MIT team took
Speaker 3: the electrical attraction between the electron and the nucleus the
Speaker 3: coulum potential, and applied their classical fluid framework.
Speaker 2: But They didn't just treat the electron like a tiny planet,
Speaker 2: did they.
Speaker 1: No?
Speaker 3: No, they treated it as a fluid density distributed over
Speaker 3: multiple classical Kepler like orbits simultaneously. Oh yeah, and by
Speaker 3: mapping how the probability density flows along these elliptical paths,
Speaker 3: the classical math natally produced the exact complex, three dimensional
Speaker 3: shapes of elect orbitals.
Speaker 2: Wait, you mean the SP and D shells, the things
Speaker 2: that basically define all of chemistry, The.
Speaker 3: Very same the stationary states of an atom emerge simply
Speaker 3: because the fluid density falls into a stable repeating pattern
Speaker 3: along those classical orbital paths.
Speaker 2: So the shapes of chemistry are literally just stable fluid
Speaker 2: patterns built on top of planetary orbits. That is beautiful.
Speaker 2: But if that's true, how does this framework handle what
Speaker 2: I think is the most mystical part of quantum physics
Speaker 2: rock wave function collapse?
Speaker 3: Ah? Yes, the measurement problem.
Speaker 2: Right, the idea that a fuzzy cloud of probability instantly
Speaker 2: snaps into a single, definite point of reality the very
Speaker 2: moment a scientists looks at it or measures it. Does
Speaker 2: classical fluid density explain why observation actually changes reality.
Speaker 3: It demystifies it completely because in the traditional quantum view,
Speaker 3: measurement triggers this magical, instantaneous collapse of the wave function
Speaker 3: that completely defies classical explanation.
Speaker 2: Right, it's always felt a bit like magic.
Speaker 3: But in the MIT work, measurement is simply treated as
Speaker 3: a classical update of information.
Speaker 2: Like updating a statistical model when new data comes in.
Speaker 3: Precisely in that vein, if you have a fluid density
Speaker 3: of probability spread across several paths, and you place a
Speaker 3: detector along one of those paths, you are imposing a
Speaker 3: new physical constraint on the entire system because.
Speaker 2: The detector is a physical object interacting with the fluid.
Speaker 3: Exactly the moment the detector interacts with the fluid, the
Speaker 3: density distribution mathematically must update to reflect the new boundary conditions. Oh,
Speaker 3: the fluid doesn't mysteriously collapse due to human consciousness or
Speaker 3: anything spooky. The density simply redistributes itself instantly according to
Speaker 3: classical statistical mechanics, purely because the physical parameters of the
Speaker 3: environment changed.
Speaker 2: Wow. That removes the mysticism entirely, it really does. It
Speaker 2: just translates the spookiest quantum behaviors into rigorous classical statistics
Speaker 2: and fluid dynamics. I mean, didn't they even manage to
Speaker 2: map quantum entanglement with this?
Speaker 3: They did. They mapped entanglement, which Einstein called spooky action
Speaker 3: at a distance to complex classical mathematical structures called tensor
Speaker 3: products of spiners.
Speaker 2: It is a total rewrite of how we model the universe.
Speaker 3: It really is.
Speaker 2: But you know, if I'm listening to this, I'm probably wondering,
Speaker 2: does bridging this math actually change anything in the real
Speaker 2: world or is it just like the ultimate flex for
Speaker 2: theoretical physicists. Does this have practical applications in a laboratory today?
Speaker 3: Oh, the practical applications are immense, particularly when you look
Speaker 3: at the limits of modern computation. How so well, think
Speaker 3: back to Feinneman's pass integrals we discussed earlier the infinite
Speaker 3: swarm of paths. If you are a material scientist trying
Speaker 3: to simulate a complex molecule to invent, say a more
Speaker 3: efficient solar panel or a room temperature superconductor, the quantum
Speaker 3: math using Feinnemann's method becomes impossibly complex.
Speaker 2: Because asking a computer to calculate infinity or even just
Speaker 2: a close approximation of infinity across hundreds of interacting particles
Speaker 2: is going to choke even the most advanced supercomputers on Earth.
Speaker 3: The computational overhead scales exponentially. It hits a wall very fast.
Speaker 3: But this new classical approach relies on a tiny, minimal
Speaker 3: subset of highly constrained multipaths and a fluid density.
Speaker 2: You're replacing an infinite sum of probabilities with a defined
Speaker 2: system of fluid.
Speaker 3: Dynamics exactly, which drastically reduces the computational burden. It could
Speaker 3: massively massively speed up simulations in quantum chemistry and material science.
Speaker 3: It allows us to model complex molecular interactions that are
Speaker 3: currently just completely impossible to compute.
Speaker 2: It changes the fundamental algorithm of how we simulate reality.
Speaker 3: And it unlocks an entirely new tool set because the
Speaker 3: classical paths utilized in this framework are mathematically differentiable.
Speaker 2: Differentialbal meaning you can take the derivative of them.
Speaker 3: Yes, and in computer science, differentiability is the absolute core
Speaker 3: requirement for training neural networks and machine learning algorithms.
Speaker 2: Oh because gradient descent, which is how AI actually learns,
Speaker 2: relies on taking smooth mathematical derivatives to find the most
Speaker 2: efficient path to a solution.
Speaker 3: Right, and infinite quantum path integrals are notoriously difficult to differentiate.
Speaker 3: They basically block machine learning from effectively tackling quantum problems.
Speaker 2: But by translating the quantum system into a differentiable, classical
Speaker 2: fluid dynamics system, scientists.
Speaker 3: Can now bring the full unbridled force of modern artificial
Speaker 3: intelligence to bear on quantum simulations. We can train neural
Speaker 3: networks to solve quantum problems because the underlying mathematics finally
Speaker 3: speak the exact same language as the algorithms.
Speaker 2: That is a huge technological bottleneck just being completely removed revolutionary,
Speaker 2: But okay, to maintain our scientific rigor here, we do
Speaker 2: have to look at the boundaries of this breakthrough, because
Speaker 2: they haven't solved literally every single problem in physics overnight.
Speaker 2: Right Where does this new classical bridge currently fall short?
Speaker 3: That's a fair question. The foundation is incredibly solid, but
Speaker 3: it is currently proved for specific, solvable, non relativistic cases.
Speaker 3: The textbook mysteries we explored the double slit tunneling hydrogen atoms,
Speaker 3: those have all been definitively conquered. However, the researchers are
Speaker 3: actively working to extend this mathematics to interacting many body
Speaker 3: quantum systems, any.
Speaker 2: Body systems, which is when you have what thousands or
Speaker 2: millions of particles all interacting with each other simultaneously.
Speaker 3: Exactly heavily entangled, sharing complex potentials. The math required to
Speaker 3: track the multi paths and density evolution of thousands of
Speaker 3: heavily interacting particles introduces immense complexity. I can imagine they
Speaker 3: are currently developing complex actions for broader, general nonlinear potentials.
Speaker 3: They're pushing the framework beyond isolated textbook examples into the
Speaker 3: messy reality of macroscopic quantum materials.
Speaker 2: So it is an ongoing effort, but the structural integrity
Speaker 2: of the bridge they've built is basically undeniable at.
Speaker 3: This point, absolutely undeniable.
Speaker 2: It's amazing to think about. For nearly a century, the
Speaker 2: impassable casm between the predictable macro world and the probabilistic
Speaker 2: microworld just forced us to accept a fractured reality. We
Speaker 2: literally assumed the universe had a split personality.
Speaker 3: We did. But what the nonlinear System's laboratory demonstrated is
Speaker 3: that the laws of physics are far more elegant and
Speaker 3: far more deeply interconnected than our previous models ever suggested
Speaker 3: the strain seemingly magical behaviors of the quantum realm, the
Speaker 3: interference patterns, the tunneling, the orbital shapes. They emerge entirely
Speaker 3: naturally when we just allow classical paths to multiply and
Speaker 3: treat probability as a flowing physical density.
Speaker 2: Which leaves us with a truly mind bending question as
Speaker 2: we reflect on all of this. We started by comparing
Speaker 2: classical physics to a single delivery driver and quantum physics
Speaker 2: to an infinite swarm, And the solution wasn't a swarm
Speaker 2: at all. It was a fluid network of highly efficient
Speaker 2: classical roots acting under physical constraints. So if everything that
Speaker 2: makes the quantum world weird can emerge purely from the friction, pressure,
Speaker 2: and density of classical mathematics.
Speaker 3: It really makes you wonder does.
Speaker 2: The weird quantum world even exist as a fundamentally separate reality,
Speaker 2: or have we just been looking at a deeply classical
Speaker 2: universe through the wrong mathematical glasses this entire time, mistaking
Speaker 2: the complex flow of a fluid from magic.
Speaker 3: It's a fascinating thought to leave on