The Planck Length - Where Space Itself Stops Making Sense

Tonight we're going to explore something extraordinary. The smallest possible distance in the universe. Not just tiny, but fundamentally the smallest length that can exist. Below this scale, our understanding of physics collapses. Space and time as we know them cease [music] to make sense.

This is the plank length, and understanding it changes how you see reality. Most people have never heard of the plank length. It doesn't come up when you're measuring ingredients or checking your height, but it might be the most important distance [music] in all of physics. It marks the boundary where our two greatest theories clash head on. And by the end of this journey, you'll understand why physicists consider it fundamental to the nature of existence itself. If you enjoy exploring the deepest questions in science, a quick like or subscribe [music] helps the channel grow. Now, let's begin.

Let me give you a sense of scale. The plank [music] length is roughly 1.6 * 10 to the -35 m. To write that out, you'd need a decimal point followed by 34 zeros before reaching the actual digits. It's about 20 orders of magnitude smaller than a proton. And a proton is already so small, you'd need a 100 million of them to span the width of an atom. Here's a comparison that might help. If you could scale up a plank length to the size of a grain of sand, a proton would be about as large as the observable universe. That's not an exaggeration. The gap between the plank length and everyday scales is so vast that normal comparisons fail.

To appreciate this properly, we need to start with distances we understand and work our way down. This journey will take us through centuries of scientific discovery from the first microscopes to modern particle accelerators until we reach the absolute limit.

You're probably between 1.5 and 2 [music] m tall, about 5 to 6 1/2 ft. That's the scale at which you experience life. Your eyes can see objects maybe a tenth of a millimeter across if you look carefully. That's roughly the width of a human hair, about 70 to 100 micrometers or 3 to 4,000 of an inch. Below that, things become invisible without help. [music]

The microscope changed everything in the late 1600s. Anton Van Lovenhook built some of the first powerful microscopes [music] and discovered bacteria single-sellled organisms about one micrometer across. That's 1 millionth of a meter, a thousand times smaller than a hair's width. At this scale, an entirely new world appeared. Leven Hook examined pond water and saw it teeming with creatures swimming and moving. He looked at plaque from his teeth and found microorganisms never seen before. This wasn't just a technical achievement. It revealed that reality had hidden layers of complexity.

If life [music] existed at scales a thousand times smaller than visible, what else might exist at even tinier scales? This question drove science [music] for the next few centuries. Each improvement revealed new structures. Scientists discovered that living things are made of cells. Cells contain [music] smaller structures with specific functions. Heredity is controlled by molecules [music] inside the nucleus. Each layer suggested more layers beneath.

As microscopes improved through the 1800s and early 1900s, researchers saw smaller structures, cells, [music] nuclei, chromosomes. But there was a limit. Light itself has a wavelength and you can't use light to see things smaller than that wavelength. Visible light ranges from about 400 to 700 nanome. A nanometer is 1 billionth of a meter. This meant optical microscopes could only go so far.

The electron microscope developed in the 1930s solved this problem. Electrons behave like waves with much shorter wavelengths than visible light. This allowed scientists to see structures down to about 1 nanometer. At this scale, [music] you can see large molecules and viruses which typically measure 20 to 300 nanome across. You're approaching the molecular scale where chemistry happens. But let's go smaller still.

Everything around you, [music] everything you touch, everything you are consists of atoms. Atoms are the basic building blocks of matter, the smallest units of chemical elements. A typical atom measures about 1/10enth of a nanometer across. That's one angstrom, a unit scientists use at atomic scales. If you lined up 10 billion atoms, they'd stretch about 1 meter or 3 ft.

For most of human history, atoms were purely theoretical. Democrus, an ancient Greek philosopher, proposed around 400 BC that matter must be made of indivisible particles. He called them atoms from the Greek word atomos meaning uncutable. Democrus imagined cutting a piece of gold repeatedly until you reached a piece so small it couldn't be cut anymore. That would be the atom. But Aristotle rejected this idea. He believed matter was continuous, infinitely divisible. You could always cut smaller. For nearly 2,000 years, Aristotle's view dominated Western thought. Atomism was considered interesting speculation. without proof.

The 1800s changed this. Chemists studying how elements combined noticed something peculiar. When hydrogen and oxygen formed water, they always combined in the same ratio by mass. 8 g of oxygen always combined with 1 g of hydrogen. When carbon and oxygen formed carbon dioxide, they combined in fixed ratios. This pattern held for every chemical reaction. This made sense if matter consisted of atoms with specific masses. If a water molecule contains two hydrogen atoms and one oxygen atom, and oxygen atoms are 16 times heavier than hydrogen atoms, you'd always need 8 times more oxygen by mass than hydrogen. The fixed ratios were evidence for discrete units of matter, but it was indirect. Nobody had seen an atom.

The first real evidence came in the early 1900s. In 1905, Albert Einstein published a paper explaining Brownian motion, [music] the random jittery movement of small particles in fluid. He showed this motion resulted from atoms and molecules constantly bombarding the particles. His equations allowed scientists [music] to calculate atomic size and mass.

Around the same time, JJ Thompson and Ernest Rutherford began revealing atomic structure. Thompson discovered the electron in [music] 1897, showing that atoms contained smaller, negatively charged particles. This was revolutionary. Atoms weren't indivisible after all.

Then in 1911, Rutherford performed his famous gold foil experiment. He fired alpha particles, helium nuclei at thin gold foil. These particles moved at high speed with significant energy. [music] If Thompson's model was correct, they should pass through with slight deflection. But that's not what happened. Most particles passed straight through as expected, but occasionally an alpha particle bounced back at a large angle. Some bounced nearly straight backward. Rutherford was astonished. He later said it was like firing a cannonball at tissue paper and having it bounce back. This made no sense unless all the positive charge and most of the mass were concentrated in a tiny region at the center. This was the nucleus.

The atom, [music] already incredibly small, was mostly empty space. All the mass and positive charge were packed into a nucleus 10,000 times smaller than the atom itself. Lightweight electrons orbited this dense nucleus at relatively large distances. An atom was almost entirely empty with a tiny dense core and electrons buzzing around far [music] away.

The nucleus itself measures about 1 phentometer across. That's one quadrillionth of a meter. If you scaled an atom to the size of a football stadium, the nucleus would be about the size of a P at the center. Everything else is just empty space with electrons zipping around.

But the nucleus has structure. It contains protons and neutrons, collectively called nucleons. Protons carry positive charge. Neutrons have no charge. And both have roughly the same mass. The number of protons determines which [music] element an atom is. Hydrogen has one. Helium has two, carbon [music] has six, and so on.

For a while, scientists thought protons and neutrons were fundamental. But experiments at particle accelerators in the 1960s and 70s [music] revealed something surprising. Protons and neutrons are themselves made of smaller particles called quarks. Each proton contains two up quarks and one down quark. Each neutron contains one up quark and two down quarks. Quarks are held together by particles called gluons that carry the strong nuclear force.

Quarks are extremely small. They don't have a well- definfined size in the classical sense because they're quantum objects. But experiments suggest they're smaller than about 10 to the9 m. That's less than 1,000th the size of a proton. We're now at scales where everyday understanding of size starts breaking down. Quantum mechanics dominates here and particles don't behave like tiny billiard balls. They're more like fuzzy probability clouds existing in multiple states until measured. As far as we know from particle accelerators like the large hadron collider, quarks and [music] electrons appear to be point particles. They have no internal structure we can [music] detect. They might truly be fundamental with no size at all. Or they might have structure at scales we can't probe yet. Some theories like string theory suggest what we think of as point particles are actually tiny vibrating strings or loops. But we're getting ahead of ourselves.

There's a fundamental problem when trying to probe smaller distances. [snorts] It's not technological. It's [music] built into the laws of physics. This problem is the Heisenberg uncertainty principle and it sets absolute limits on what we can know.

Verer Heisenberg formulated this principle [music] in 1927 while developing quantum mechanics. He was studying electron behavior in atoms and realized something profound. In Newtonian physics, a particle has a definite position and momentum at every moment. If you know where something is and how fast it's moving, you can predict exactly where it will be. The universe is deterministic. But Heisenberg showed this isn't true at the quantum level.

The uncertainty principle states that pairs of properties cannot both be known precisely simultaneously. The most famous example is position and momentum. The more precisely you know where a particle is, the less precisely you can know its momentum and vice versa. This isn't about measurement limitations. You might think we just need better instruments. But that's not the issue. These properties literally don't have definite values simultaneously. The particle doesn't have both a precise position and a precise momentum. That's simply not how quantum mechanics works. Nature itself is uncertain at this level.

Here's an analogy. Imagine photographing a fastmoving object in a dark room. With a very fast shutter speed, you capture exactly where the object is. The position is sharp, but the motion is blurred because the shutter was open so briefly. [music] You can't tell if it was moving fast or slow. With a slow shutter speed, you see the motion clearly as a streak, but you can't tell where the object was at any particular instant. This resembles the uncertainty principle, except it's not about shutter speeds. It's about the fundamental nature [music] of quantum particles. They exist in a fuzzy state where both properties are somewhat undefined until you measure one.

Mathematically, the uncertainty in position times the uncertainty in momentum must be greater than or equal to a certain value related to plank's constant, a fundamental constant of nature. There's a fundamental trade-off. To measure position more precisely, you need shorter wavelength probes with higher energy. But higher energy probes [music] disturb momentum more. You can't avoid this trade-off.

This has profound implications for probing smaller distances. To see something small, you need a probe with a wavelength smaller than what you're observing. This is why electron microscopes [music] see smaller things than optical microscopes. Electrons have shorter wavelengths than visible light. To probe smaller distances [music] requires even shorter wavelengths, meaning higher energies.

Einstein showed in 1905 that energy and mass are equivalent. His famous equation E= MC² tells us energy can convert into mass and vice versa. When you concentrate enough energy in a small region, you can create particle antiparticle pairs from pure energy. This happens constantly in particle accelerators. High energy collisions create showers of new particles. So when you try probing very small distances using high energy particles, strange things happen. The energy you're using can create new particles in the region you're studying. You're not just observing, you're fundamentally changing what's there. The [music] measurement creates the very particles you're trying to study.

But it gets worse. General relativity [music] tells us energy curves spaceime. Mass and energy are equivalent and both create gravitational fields. The more you concentrate in a region, the more that region curves spacetime. At extreme [music] densities, spacetime curves so much it forms a black hole where gravity is so strong not even light can escape. There's a distance scale where your probe's wavelength equals the Schwarz shield radius of a black hole with the same energy below this scale. Trying to measure distance creates a black hole larger than the distance you're measuring. [music] You cannot probe smaller because the measurement itself creates black holes that obscure what you're trying to see.

This fundamental distance is the plank length. It's approximately 1.6 * 10 -35 m. The plank length [music] represents fundamental granularity to space itself. Below this [music] scale, concepts of distance and space as we understand them might not make sense. Spacetime might not be smooth and continuous. It might be quantized with the plank length as the smallest meaningful unit. Just as matter is made of atoms, space itself might be made of plank scale units.

So where does this number come from? The answer lies in combining three fundamental constants. three numbers that appear repeatedly in nature's laws and seem built into the universe's structure. These are the speed of light, the gravitational constant, and plank's constant.

The speed of light in vacuum denoted C is approximately 299,792 km/s or 186,000 [music] m/s. This is the ultimate speed limit. Nothing can travel faster. This isn't practical. It's built into space-time structure. Einstein's special relativity published in 1905 showed that light speed is constant [music] for all observers regardless of their motion. Light speed appears in all sorts of physics equations. It relates [music] space and time, energy and mass, electricity and magnetism. [music] It's one of nature's most fundamental numbers.

The gravitational constant denoted [music] g is approximately 6.67 * 10 [music] to the 11 m/ kg/s squared. The units are complicated, but essentially g tells you how strong gravity is. It appears in Newton's law of universal gravitation and Einstein's field equations of general relativity. The larger G is, the stronger gravity would be. Gravity is the weakest fundamental force by far. The electromagnetic force, making magnets stick to your refrigerator, is about 10 36 times stronger. You can easily overcome Earth's entire gravitational pull by jumping. Your legs can push you up against a whole planet's gravity. That's how weak gravity is. It dominates at large scales only because it's always attractive and adds up.

Planck's constant denoted h or often h bar which is h / 2 pi is approximately 6.6 3 * 10 to the -34 seconds. This constant is quantum mechanics signature. It sets the scale for quantum effects. It appears in Heisenberg's uncertainty principle, in the equation for photon energy, in Schrodinger's equation, in angular momentum quantization. Whenever something is quantized coming in discrete chunks rather than continuous values, plank's constant is involved. Max plank introduced this constant in 1900 while solving a problem called the ultraviolet catastrophe. Classical physics predicted that hot objects should emit infinite high energy radiation which obviously doesn't happen. Plank showed that if you assume energy comes in discrete packets called quanta with each quantum's energy proportional to its frequency, the math works correctly. The proportionality constant [music] was H plank's constant. This birthed quantum mechanics.

These three constants have different [music] units. Light speed has units of meters/s. The gravitational constant has units of me cubed per kilogram/s squared. Plank's constant has units of jewel seconds, which is kilogram m squared/s. All different. But through dimensional analysis, you can combine them. So the units work out to give a length. If you take plank's constant h bar, multiply by the gravitational constant gide by light speed cubed, then [music] take the square root, you get a length. This is the plank length. Mathematically, it's the square roo of h bar * g / c cubed. When you plug in these constants [music] values, you get approximately 1.6 6 * 10 to the -35 m.

This isn't random. It's the only combination of these three fundamental constants that gives a length. If you're building a theory involving gravity, quantum mechanics, and relativity, this length naturally emerges. It tells you something deep about reality's structure. When you combine our best theory of gravity with our best small scale theory and account for the cosmic speed limit, you inevitably arrive at this length scale.

Similarly, you can combine these constants to get other plank units. The plank time is the time light takes to travel one plank length approximately 5.4 * 10 to the - 44 seconds. This is the shortest meaningful time interval. The plank mass [music] is about 2.2 * 10 to the -8 kg roughly a flea egg's [music] mass. This sounds small but is enormous by particle physics standards. The plank energy is the plank mass's energy equivalent about 1.96 * 10^ the 9 jew roughly the energy in 50 L of gasoline. The plank temperature is about 1.4 * 10 32 Kelvin. The temperature where quantum gravity effects become important.

These are all extreme values. The plank scale represents the regime where quantum gravity becomes essential. Below the plank length and time, our current theories break down. General relativity doesn't include quantum mechanics. It treats spacetime as a smooth continuous fabric curved by mass and energy. Quantum mechanics doesn't include gravity meaningfully. It treats spacetime as a fixed flat background on which quantum fields fluctuate. Both theories are spectacularly successful in their domains. General relativity describes large scale universe structure, black holes, gravitational waves, and space expansion. Quantum mechanics describes atoms, molecules, nuclear physics, and particle physics. But they can't both be right at the plank scale.

This is one of physics unsolved problems. How do you merge our quantum picture of reality with Einstein's curved spaceime? For nearly a century, physicists have worked on this. Despite enormous effort by thousands of researchers, we still don't have a complete answer. We have candidate theories, [music] frameworks showing promise, but we don't have a final theory, and we [music] certainly don't have experimental evidence to guide us.

In quantum mechanics, fields fluctuate. Even in empty space, in a perfect vacuum, quantum fields constantly fluctuate [music] due to the uncertainty principle. Virtual particles pop in and out of existence, borrowing energy from the vacuum briefly before disappearing. These quantum fluctuations are real. [music] We've measured their effects. They cause the Casemir effect and lamb shift subtle energy level changes that have [music] been precisely measured.

In quantum field theory, these fluctuations become more violent at smaller scales and higher energies. If you look at a small enough region for a short enough time, the uncertainty principle [music] allows enormous energy fluctuations. At the plank scale, [music] energy fluctuations are so large that according to general relativity, they should curve spacetime dramatically. They should curve it so much that spaceime becomes violently turbulent, frothing with tiny black holes and wormholes constantly forming and dissolving. This is sometimes called space-time foam or quantum foam, a term John Archerold Wheeler coined in the 1950s.

But here's the problem. In general relativity, spacetime is smooth and well defined. It has geometry. You can discuss distances and times and space curvature. But if spacetime is foaming and fluctuating at the plank scale, these concepts don't make sense. What does measuring distance mean when space itself fluctuates wildly? What does space geometry mean when that geometry changes faster than you can measure it?

There's another way to see the problem. In quantum field theory, when you calculate the probabilities of processes involving gravity, you get infinities. The calculations blow up. The mathematical tools that work perfectly for the other three fundamental forces fail for gravity. Physicists develop techniques called reormalization to handle infinities in quantum field theories. These work beautifully for the other forces, but for gravity they fail. Gravity is nonreormalizable. No matter how hard you try, you can't eliminate the infinities. This tells us general relativity in its current form cannot completely describe gravity at all scales. It works magnificently at large scales from millimeters to galaxy clusters and beyond. But it must be an approximation, an effective theory emerging from some deeper underlying structure. At the plank scale, that deeper structure becomes important. And we need a new theory that incorporates both quantum mechanics and gravity consistently. This is quantum gravity.

Finding a quantum gravity theory is arguably theoretical physics holy grail. >> [music] >> It would unify our understanding of nature. It would tell us what really happens inside black holes where general relativity predicts singularities, infinite density points, where the laws of physics [music] break down. It would tell us what happened at the universe's beginning in the first moments after the Big Bang [music] when the entire observable universe was smaller than a plank length. It would [music] tell us whether spacetime is fundamentally smooth or made of discrete building blocks. It would answer questions we can't even formulate properly without quantum gravity.

So what are the leading quantum gravity candidates? What frameworks are physicists exploring? Several approaches exist, each with its own philosophy and mathematical structure. The two most developed are string theory [music] and loop quantum gravity.

There's another way to see the problem. In quantum field theory, when you calculate the probabilities of processes involving gravity, you get infinities. The calculations blow up. The mathematical tools that work perfectly for the other three fundamental forces fail for gravity. Physicists [music] develop techniques called renormalization to handle infinities in quantum field theories. These work beautifully for the other forces. But for gravity, they fail. Gravity is nonreormalizable. No matter how hard you try, you can't eliminate the [music] infinities. This tells us general relativity in its current form cannot completely describe gravity at all scales. It works magnificently at large scales from millimeters to galaxy clusters and beyond. But it must be an approximation, an effective [music] theory emerging from some deeper underlying structure. At the plank scale, that deeper structure becomes important and we need a new theory that incorporates both quantum mechanics and gravity consistently. This is quantum gravity. Finding a quantum gravity theory is arguably theoretical [music] physics holy grail. It would unify our understanding of nature. It would tell us what really happens inside black holes, where general relativity predicts singularities, infinite density points, where the laws of physics break down. It would tell us what happened at the universe's beginning in the first moments after the big bang [music] when the entire observable universe was smaller than a plank length. It would tell us whether spaceime is fundamentally smooth or made of discrete building blocks. It would answer questions we can't even formulate properly without quantum gravity.

So what are the leading quantum gravity candidates? What frameworks are physicists exploring? Several approaches exist, each with its own philosophy and mathematical structure. The two most developed are string theory and loop quantum gravity.

String theory proposes that the universe's fundamental building blocks are not point particles but tiny one-dimensional strings. These strings vibrate in different patterns like guitar or violin strings. Different vibration patterns correspond to different particles. An electron is a string vibrating one way, a quark another way, a photon yet another way. All the diverse particles we see are just [music] different vibrations of the same underlying strings.

Think about a guitar string briefly. When you pluck it, [music] it vibrates and produces a note. The exact note depends on how the string vibrates, which depends on where you pluck it, how hard, and the string's tension and length. The same physical string produces different notes by vibrating in different patterns. String theory proposes something similar. [music] There's one fundamental string type, but it can vibrate in many patterns and each pattern corresponds to a different particle type with different properties. The strings are about a plank length long. This is why we haven't detected them directly. Our particle accelerators can't probe scales that small. To us, strings look like point particles because we can't resolve their internal structure. It's like viewing a rope from far away. The rope has thickness and structure. But from a distance, it looks like a line. From our perspective, strings look like points. Even the Large Hadron Collider can't reach the energies needed to see string structure.

String theory naturally incorporates gravity. One string vibration pattern corresponds to the graviton, the hypothetical particle that carries the gravitational force, just as photons carry the electromagnetic force. In string theory, gravity isn't added as an afterthought. It emerges naturally from the mathematics. When physicists first developed string theory in the 1960s and '7s, they weren't trying to create a quantum gravity theory. They were trying to describe the strong nuclear force. But they kept finding that the theory predicted a massless spin 2 particle, exactly what a gravitton should be. At first, this seemed problematic. They didn't want gravity in their strong force theory. But eventually they realized this was string theory's greatest strength. It was naturally a quantum gravity theory. This is one of string theory's great achievements. General relativity and quantum field theory are notoriously difficult to combine. When you try quantizing gravity using standard techniques, you get infinities that can't be removed. calculations break down. But string theory solves this. The extended nature of strings their length rather than being points smears out interactions in a way that eliminates the infinities. String theory is a mathematically consistent quantum theory that includes gravity from the start.

But string theory has unusual features. To be mathematically consistent, strings can't vibrate in just the three space dimensions we experience. They need extra dimensions. Depending on the string theory version, you need 10 or 11 total dimensions. That's 9 or 10 [music] space dimensions plus one time dimension. Where are these extra dimensions? We experience three spatial dimensions. up, down, left, right, forward, backward. We don't experience six or seven additional directions. So where are they? String theorists propose that the extra dimensions are compactified, [music] curled into tiny shapes, so small we can't detect them directly. Imagine a garden hose. From far away, it looks one-dimensional. You can move along it forward or backward only. But if you were an ant on the surface, you'd discover another direction. You can also walk around the hos's circumference. This is a second dimension curled so small that from a distance you don't notice it. [music] String theory proposes something similar, but with more dimensions. At every point in our three-dimensional space, six or seven extra tiny dimensions curl into complex geometric structures called calabaya manifolds. These are mathematical objects with specific geometric properties that ensure certain symmetries string theory requires. The manifolds might be at the plank [music] scale. So at every point, if you could zoom in far enough, you'd discover this extra geometric structure. These additional dimensions curled so small we can't detect them with current technology.

The geometry of these hidden dimensions isn't arbitrary. Different shapes correspond to different physics. Think of it [music] like musical instruments. A trumpet, violin, and drum all vibrate air to produce sound. But their shapes determine which notes they can play and what those notes sound like. Similarly, the shape of the extra dimensions determines which particles exist in our universe and what their properties are. This is [music] both exciting and frustrating. It's exciting because it [music] means string theory might explain why we have the particles and forces we do. The electrons mass, the strength of electromagnetism, the number of quark flavors. All these might be determined by the hidden dimensions geometry. Properties we think of as fundamental might actually [music] be consequences of geometry at the plank scale. It's frustrating because there are an enormous number of possible calabaya manifolds. Mathematicians have cataloged thousands of them and there might be many more. Each gives a different version of physics. This is the landscape problem. Estimates suggest roughly [music] 10 to the 500 different possible string theory vacua each corresponding to a universe with different properties. Which one describes our universe? We don't know. And we might not figure it out without plank scale experiments. Some string theorists have suggested [music] our universe might just be one possibility among many in a vast multiverse with different regions having different extradimension geometries and thus different laws of physics. This is controversial. Critics argue that if a theory predicts everything, it predicts nothing. Proponents argue the landscape might be testable through cosmological observations.

The other major approach is loop quantum gravity. This is a very different philosophy. Instead of replacing particles with strings, loop quantum gravity tries to quantize spacetime itself. It treats space as something that comes in discrete chunks, quantized like energy comes in photons and [music] matter comes in atoms. The basic building blocks are tiny loops or loop networks forming what's called a spin network. These loops represent quantum [music] states of the gravitational field. Space emerges from how these loops connect and interact.

In loop quantum gravity, [music] the plank length sets the scale for these quantized space units. Area is quantized in units proportional to plank length squared. Volume is quantized in units proportional to plank length cubed. There's a smallest possible area and volume. Space is grainy at the plank scale, not smooth. If you could zoom in far enough, you'd see space has a discrete structure like pixels on a screen or atoms in solid material. Imagine fabric. From a distance, it looks smooth and continuous, but examining it closely, you see individual threads woven together. The threads are discreet. You can count them, but from a normal viewing distance, the individual threads blend and the fabric appears continuous. Loop quantum gravity proposes space is similar. At large scales, it appears smooth as Einstein described in general relativity, but at the plank scale, it's made of discrete quantum units woven together. The loops themselves are about a plank length in size. They're not sitting in space. They are space. There's no background spaceime in which the loops exist. The loops and their connections are all there is at the fundamental level. Space as we experience it, the three-dimensional arena where things happen, emerges from these loop networks, quantum states. It's like how your TV screen's image emerges from millions of individual pixels, each displaying a single color. No individual pixel looks like the image. But with enough pixels arranged properly, an image appears.

The mathematics of loop quantum gravity is based on spin networks introduced by Roger Penrose in 1971 for different reasons. A spin network [music] is a graph with labeled edges and vertices. The edges represent quantum states of area and the vertices represent [music] quantum states of volume. Different configurations of spin networks [music] correspond to different geometries. As time evolves, spin networks change. They can split, merge, and create new connections. The evolution follows specific rules derived from the quantum version of general relativity. This produces what's called a spin foam, which is to spin networks what spacetime [music] is to space. Spin foam is the four-dimensional history of how three-dimensional space evolves.

Loop quantum gravity doesn't require extra dimensions. It works in the three space dimensions and one time dimension we experience. This is appealing because it doesn't introduce anything we haven't observed. You don't have to explain [music] where the extra dimensions are hiding or why we can't detect them. The theory takes the dimension count we see [music] and quantizes the geometry directly. But it also doesn't naturally include the other forces. String theory tries unifying all forces into one framework. Loop quantum gravity focuses [music] specifically on gravity and space-time structure. To describe the other forces, you need to add matter fields on top of the quantum geometry. This is possible, but it's not as unified as string theory's approach where everything emerges from string vibrations.

Loop quantum gravity's mathematics is quite different from string theory. It's based on a formulation of general relativity developed by Abhear in 1986 that makes the theory [music] easier to quantize. The theory describes space geometry using loops of gravitational field lines, similar to how you might describe [music] electromagnetic fields using field lines. When you apply quantum mechanics to these loops, they can only take certain discrete values like energy levels in an atom.

One exciting prediction of loop quantum gravity concerns black holes in the early universe. In general relativity, when matter collapses to form a black hole, it creates a singularity at the center, an infinite density point where the laws of physics break down. Similarly, extrapolating the big bang backward, general relativity predicts a singularity at the beginning where all matter and energy compress to infinite density. Loop quantum gravity [music] suggests that quantum effects resolve these singularities. Instead of infinite density, matter reaches plank scale densities about 10 the 96 kg per cubic meter and then quantum geometry effects create a repulsive pressure. This pressure [music] has no classical analog. It appears only at extreme densities near the plank scale. It's not thermal pressure from particle motion or degeneracy pressure from quantum statistics. It's geometric pressure from space-time's quantum structure, but it also doesn't naturally include the other forces. String theory tries unifying all forces into one framework. Loop quantum gravity focuses specifically on gravity and space-time structure. To describe the other forces, you need to add matter fields on top of the quantum geometry. This is possible, but it's not as unified as string theory's approach where everything emerges from [music] string vibrations. Loop quantum gravity's mathematics is quite different from string theory. It's based on a formulation of general relativity developed by Abbe Ashtikar in [music] 1986 that makes the theory easier to quantize. The theory describes space geometry using [music] loops of gravitational field lines similar to how you might describe electromagnetic fields using field lines. When you apply quantum mechanics to these loops, they can only take certain discrete values like energy levels in an atom.

One exciting prediction of loop quantum gravity concerns black holes and the early universe. In general relativity, [music] when matter collapses to form a black hole, it creates a singularity at the center, an infinite density point where the laws of physics break [music] down. Similarly, extrapolating the big bang backward, general relativity predicts a singularity at the beginning where all matter and energy compress to infinite density. Loop quantum gravity suggests that quantum effects resolve these singularities. Instead of infinite density, matter reaches plank scale densities about 10 to the 96 kg per cubic meter and then quantum geometry effects create a repulsive pressure. This pressure has no classical analog. It appears only at extreme densities near the plank scale. It's not thermal pressure from particle motion or degeneracy pressure from quantum statistics. It's geometric pressure from spaceime's quantum structure. In black holes, the center might not be a point, but rather a region of highly curved but finite density space. When matter collapses, it bounces at plank density. Some calculations suggest this might create a white hole, a time reverse black hole that expels matter, possibly in another region of spaceime or even another universe. These are speculative ideas, but they show how quantum geometry might resolve singularities.

In cosmology, the big bang might not be a singularity, but a bounce. The universe might have contracted from a previous phase, reached plank density, then bounced into the current expansion. This is called loop quantum cosmology. Quantum effects at the plank scale prevent the universe from collapsing all the way to a singularity. Instead, it reaches plank scale densities and then bounces. The repulsive force comes from quantum pressure. If correct, [music] the big bang might not be the beginning but just a transition from a previous contracting phase to the current expanding phase. There was a universe before ours. It was expanding at first, then started contracting. It contracted for billions or trillions of years until reaching plank scale densities. Then quantum gravity effects took over and caused the bounce. The contraction stopped and expansion began. We're in the expansion phase now. This resolves some conceptual problems with traditional [music] big bang cosmology. Where did the universe come from in the bounce scenario? It didn't come from anywhere. It always existed going through cycles. What happened before the big bang? There was a [music] previous contracting phase. Time didn't begin at the big bang. It's eternal. But bounce cosmology also raises questions. If the universe is eternal and [music] cyclical, does it repeat exactly each cycle or does each cycle have different properties? Does entropy increase across cycles or does it reset somehow? These questions are being actively researched.

Both string theory and loop quantum gravity face challenges. Neither has made predictions we can test with current experiments. Both involve mathematics at the cutting edge of our understanding. Both have passionate advocates and critics and both might be wrong. There might be a completely different approach we haven't thought of yet. Other approaches [music] exist too. Asytoic safety pioneered by Steven Weineberg proposes gravity might be renormalizable after all if you handle high energies carefully. The idea is that gravity's effective strength might approach a fixed value at high energies rather than growing without bound. If true, this would solve the infinity problem without needing strings or loops. Causal set theory developed by Rafael Sin and others suggests spacetime is fundamentally a discrete set of events with causal relationships between them. Instead of smooth continuous spacetime, there's a network of events where some events can influence others and some cannot. Spac-time geometry emerges from this causal structure. Emergent gravity theories propose spacetime and gravity aren't fundamental but emerge from something more basic like temperature emerges from molecular motion. Eric Valinde has proposed gravity might be an entropic force [music] arising from information theory considerations rather than being a fundamental interaction. These ideas are controversial but represent different [music] ways of thinking about the problem. Causal dynamical triangulations developed by Renate Lol and others takes yet another approach. It approximates smooth spaceime by gluing together simple building blocks called simplices which are higher dimensional analoges of triangles. By summing over all possible ways to glue these blocks together, accounting for quantum fluctuations, a picture of quantum spacetime emerges. Computer simulations using this method have produced intriguing results showing how four-dimensional spaceime might emerge from quantum geometry. [music]

Each approach has merits and challenges. What they share is recognition that something fundamental happens at the plank scale where quantum mechanics and gravity [music] must both apply.

What would it actually be like at the plank scale? What happens there? We're entering speculation territory because we lack a complete theory. [music] But we can make educated guesses based on what we know. [music] And the picture is bizarre.

John Wheeler, one of the 20th century's great physicists, described the plank scale as space-time foam. Imagine viewing the ocean from an airplane. The surface looks smooth and continuous. A flat blue expanse to the horizon. From high altitude, the ocean appears calm, uniform, almost glassy. Now imagine getting closer, [music] flying lower. You start seeing waves, ripples, structure. The smooth surface breaks into patterns. Get closer [music] still, and you see turbulent churning. waves breaking into white caps, foam and spray. The smooth surface breaks [music] into chaotic motion. Up close, the ocean is violent and complex, nothing like the calm blue sheet it appeared from altitude. Wheeler suggested something similar happens with spacetime at the plank scale.

At large scales, spacetime looks like a smooth continuous fabric curving gently around masses. When you watch a planet orbit a star, spacetime behaves, as Einstein described, a geometric structure that curves but remains smooth and well- definfined. You can draw space-time maps, calculate geodeics, and predict object motion. Everything is orderly and predictable. But as you zoom to smaller scales, quantum fluctuations become important. Just as the ocean surface looking smooth from far away becomes turbulent up close, spacetime looking smooth at large scales becomes chaotic at small scales. At the plank scale, these fluctuations are so violent that spacetime is no longer smooth. It's foaming and churning. Geometry itself fluctuates wildly. Distances aren't well defined. Angles aren't well defined. The very concepts we use to describe geometry concepts like distance and curvature and connectivity start breaking down.

Tiny black holes might spontaneously form and evaporate in fractions of a plank time. According to quantum mechanics, energy can fluctuate. For brief moments, large amounts of energy can appear from nowhere, borrowed from the vacuum, as long as they disappear quickly enough [music] that the uncertainty principle is satisfied. At the plank scale, these energy fluctuations are so large they [music] might create tiny black holes. These quantum black holes would be about a plank length across, exist for about a plank time, then evaporate via Hawking radiation. >> [music] >> They'd pop into existence and vanish so quickly they'd barely exist. The formation and evaporation of these quantum black holes would be extraordinary. Unlike [music] stellar black holes that form from collapsing stars and persist for eons, quantum black holes would be transient quantum fluctuations. They wouldn't have [music] time to swallow anything or grow. They'd appear and disappear faster than light could cross them. >> [music] >> They'd be more like violent quantum hiccups in spaceime than the black holes we observe in space.

Wormholes might appear and disappear. A wormhole is a tunnel through spaceime [music] connecting distant points. In classical general relativity, wormholes are solutions to Einstein's equations, but they require exotic matter with negative energy to stay open. They're mathematically possible, but probably don't exist in our universe at macroscopic scales. But at the plank scale, quantum fluctuations might create tiny wormholes connecting different regions of space. These wormholes would be incredibly tiny, about a plank length across existing for incredibly brief times, about a plank time. They'd connect two points for an instant, then disappear. Quantum foam would be riddled with these temporary connections. These quantum wormholes would change spacetime's topology. Topology describes space's overall shape and connectivity. Normally, we think of space as having a fixed topology [music] like a flat sheet or curved sphere. But at the plank scale, topology might fluctuate. Wormholes appearing and disappearing would constantly change how space is connected. One moment, two regions are separate. The next moment, a wormhole bridges them, then it closes and they're separate again.

Space geometry might fluctuate wildly. One moment, two points might be separated by a certain distance. The next moment the distance might be completely different because the geometry fluctuated. The very concept of a well-defined distance or time interval might break down. It's not just that distances [music] are small. It's that the concept of distance itself becomes fuzzy [music] and illdefined. You can't say two points are exactly this far apart because the distance constantly fluctuates due to quantum effects. This has profound implications. In quantum mechanics, we're used to particles having uncertain positions and uncertain momentum. But we still think of space itself as a fixed background on which this uncertainty plays out. At the plank scale, even that background fluctuates. Space itself is uncertain. The stage on which physics plays out is itself a quantum object with its own uncertainty. This isn't just speculation. The uncertainty principle guarantees there must be energy fluctuations in any quantum field and gravity responds to energy. So spacetime must fluctuate at small scales. The question is how much and what the fluctuation structure looks like. Without a complete quantum gravity theory, we can't calculate precisely. But we know it [music] must happen. The laws of quantum mechanics demand it.

Here's another strange implication. At the plank scale, black holes behave very differently than at large scales. A black hole with mass equal to the plank mass would have a size equal to the plank length. Its schwarz chilled radius, the event horizon size would be one plank length. Such black holes are [music] called plank scale or quantum black holes. They'd be incredibly hot, radiating energy through Hawking radiation so intensely they'd evaporate almost instantly [music] in about one plank time.

Steven Hawking showed in 1974 that black holes aren't completely black. They emit radiation due to quantum effects near the event horizon. The mechanism involves virtual particle pairs appearing near the horizon. Normally these pairs annihilate quickly but near the horizon one particle can fall in while the other escapes. The escaping particle becomes real radiation. The infalling particle has negative energy from an outside perspective, reducing the black hole's mass. Smaller black holes are hotter and evaporate faster. The relationship is inverse. A black hole twice as massive is half as hot and evaporates eight times slower. Large black holes like those we observe in space are very cold and evaporate incredibly slowly. A solar mass black hole would have a temperature about 110 millionth of a degree above absolute zero. It's colder than the cosmic microwave background radiation filling space. Such a black hole actually absorbs more energy than it emits. It's growing, not shrinking. But smaller black holes are much hotter. A black hole with the mass of Mount Everest would have a temperature about 100° C water's boiling point. A black hole with the mass of a large ship would glow white hot with a temperature of thousands of degrees. And plank mass black holes would have a temperature around the plank temperature about 10 32 Kelvin. That's incomprehensibly hot, far hotter than anything in the current universe. At this temperature, a plank mass black hole would evaporate in about 10 -44 seconds, one plank time. It would exist for the shortest possible time interval and then explode in a burst of radiation carrying all its energy. The radiation would be incredibly energetic with photons at plank energy.

This led some physicists to propose that at the plank scale there might not be a sharp distinction between particles and black holes. What we call a particle might just be a quantum black hole in certain circumstances. The boundary between matter and space-time geometry might blur. We're used to thinking of matter and space as different things. Matter exists in space, but at the plank scale, this distinction might not hold. Space, time, matter, and energy might all be aspects of the same underlying quantum gravitational structure. Think about it this way. A particle is a localized concentration of energy. A black hole is also a localized concentration of energy. Both have mass. Both [music] create gravitational fields. The only difference is a black hole has an event horizon. But at the plank scale, this distinction becomes meaningless. The Compton wavelength of a particle, the quantum mechanical size associated with its wave nature equals the Schwarz shield radius at plank mass. Quantum mechanics and gravity effects become equally important. Some physicists speculate all particles might be micro black holes when viewed correctly. Electrons, quarks, photons, all might be quantum black holes at the plank scale, but ones where quantum effects completely dominate. So they don't behave like classical black holes. This is speculative, but it shows how radically our concepts might need to change at the plank scale.

There's also the question of what exists beyond the plank length. Can you go smaller or is the plank length truly the minimum possible length? This touches on the nature of space itself. Is space continuous infinitely divisible so you can always zoom in further or is [music] it quantized made of discrete chunks with the plank length as the smallest unit? In classical physics, space is assumed continuous. Between [music] any two points are infinitely many other points. You can always find a point halfway [music] between two others. Space can be divided infinitely. This is the continuum model. It's mathematically elegant and

has worked well for hundreds of years. Calculus, the mathematical language of physics, is built on continuous functions, but it might not [music] be correct at the deepest level.

If space is quantized, there's a smallest possible distance. You can't have half a plank length. It doesn't make sense. It's like asking what's half an atom in chemistry. Atoms are the smallest units of chemical elements. You can break atoms into protons, neutrons, and electrons. But then you're no longer doing chemistry. You're doing nuclear physics.

Similarly, if space is quantized, the plank length is the smallest unit. Below that, the concept of distance might not apply. You're not doing geometry anymore. You're doing something [music] else, something we don't have good language for yet.

This has profound implications. If space is quantized, [music] so is time. There'd be a smallest unit of time, the plank time. Time would flow in discrete ticks like movie frames. The universe would be fundamentally digital rather than analog instead of smooth continuous change. Everything would happen in quantum jumps.

This raises questions. How do motion and change work if time is [music] discrete? In continuous time, objects move smoothly from one point to the next, passing through all intermediate points. In discrete time, do they jump or is there some quantum superp osition of being in multiple places that resolves to a definite location when measured?

How do particles move through space [music] if space is made of pixels? If an electron moves from one plank cell to the next, does it disappear from one and appear in the other instantaneously? That would violate relativity's spirit, which says there's no such thing as instantaneous anything. Or does the electron exist in superp osition, spread across multiple cells with measurement collapsing it to one cell? Quantum mechanics suggests particles don't have definite positions anyway, existing instead as probability clouds. So maybe asking exactly where an electron is in discrete space doesn't make sense. The electron's wave function would be defined on a discrete latis rather than continuous space.

This is technically possible. You can do quantum mechanics on a latis. Latis quantum chromodnamics used to study quarks and gluons does exactly this. Some theories, particularly loop quantum gravity, explicitly predict spaces quantized. Area and volume can only take discrete values quantized in units of plank length squared and cubed. Other theories like some versions of string theory suggest space might still be continuous even though the fundamental objects are planksized strings. We don't know for sure. We'd need experiments at the plank scale to tell and such experiments seem impossible with current or foreseeable technology.

Ancient Greeks thought about these questions. Zeno of Ilia around 450 BC proposed paradoxes challenging the idea of continuous space and time. His most famous paradox, the dichotomy paradox, goes like this. To walk from point A to point B, you first need to cover half the distance. But before covering the entire half, you need to cover half of that, a quarter of the total distance. and before that half of a quarter, an eighth and so on infinitely. If space is infinitely divisible, you need to complete infinitely many steps to go [music] any distance. But how can you complete infinitely many steps in finite time? Therefore, motion is impossible.

Obviously, [music] motion is possible because we see it constantly. But the paradox reveals a deep puzzle about the nature of space and time. For over 2,000 years, philosophers and mathematicians wrestled with Zeno's paradoxes. The development of calculus in the 17th century by Newton and Linets provided mathematical tools to handle infinite sums of infinitely small quantities. You can add infinitely many infinite decimally small distances and get a finite result. Problem solved, right? [music] Not quite. Calculus works brilliantly for physics, but it doesn't address the deeper question of whether space is actually [music] continuous or discrete. Calculus assumes continuity. It's a mathematical framework, not a statement about physical reality.

If space is quantized with a minimum length, Zeno's paradox is resolved differently. You don't need infinitely many steps because you can't subdivide space infinitely. There's a smallest step, the plank length. Motion proceeds in discrete [music] jumps from one plank-sized region to the next. You don't pass through infinitely many intermediate points because there aren't infinitely many intermediate points. Space has a granular structure and you cross a finite number of pixels to get from A to B.

But this raises other questions. If space is made of pixels, [music] what shape are they? Little cubes? That seems arbitrary. Why cubes rather than spheres or octahedrons? [music] And cubes don't tile four-dimensional spaceime nicely. You'd need more complex shapes, perhaps simplices, the higher dimensional generalization of triangles. Do they form a regular grid like a crystal latice? [music] that would break relativity's symmetries. In special relativity, space looks the same in all directions and from all reference frames. A regular latis has preferred directions axes along which the latis is aligned. This would violate isotropy, the property that space has no preferred directions. Loop quantum gravity deals with this by having an irregular network. The spin networks aren't arranged in a regular grid. They're more like a tangled web with no preferred directions. Different observers moving at different velocities would describe the same spin network differently, but the underlying quantum state would be the same. This preserves relativity's spirit while having a discrete structure.

Or is the structure more dynamic? Perhaps space-time geometry fluctuates so rapidly at the plunk scale that no fixed latis structure exists. What appears from a distance as smooth space is actually roing quantum foam with constantly changing geometry. Discrete quantum states of geometry exist, but they're in superposition all possibilities coexisting [music] until measurement collapses the wave function.

And how do objects move through discrete space? Classical motion assumes continuity. An object is at position A at time t1, position b at time t2, and at all intermediate positions at intermediate [music] times. But if space and time are discrete, intermediate positions and times might not exist. One possibility is teleportation. An object disappears from one pixel and appears in an adjacent pixel without existing [music] anywhere in between. But this seems to violate energy and momentum conservation. If an object teleports, it has no velocity during the transition. How does momentum get transferred?

Another possibility is an analog of quantum tunneling. In quantum mechanics, particles can tunnel through barriers. They're on one side, then the other side, without [music] ever being detected in the middle. The probability of detection in the middle is zero. Yet, they get through. Perhaps motion through discrete space is similar. An object has a probability amplitude to be in one pixel, a probability amplitude to be in an adjacent pixel, and motion is the quantum transition between these states.

A third possibility is that our concepts of motion are simply wrong at the plank scale. We think of objects as things that move through space. But perhaps at the fundamental level, there are no objects and no motion. There are just quantum states of geometry that change according to quantum rules. What we perceive as objects moving through space is an emergent phenomenon appearing only when we zoom out from the plank scale.

This connects to philosophical questions about the nature of reality. Are particles fundamental or is space fundamental? Do particles move through space or does space itself give rise to particles? At the plank scale, these distinctions might dissolve. Everything might be different aspects of the same underlying quantum gravitational entity.

The idea of discrete space also challenges the notion of symmetry. Physics laws as we know them are symmetric under continuous translations and rotations. You can shift your coordinate system by any distance or rotate by any angle and the laws of physics remain the same. This is continuous symmetry and it's crucial to modern physics. Noithther's theorem connects symmetries to conservation laws. Time translation symmetry gives energy conservation. Space translation symmetry gives momentum conservation. Rotation symmetry gives angular momentum conservation.

But if space is discrete, these continuous symmetries must be approximate emerging at large scales from some underlying discrete structure. At the plank scale, you can't translate by an arbitrary distance because distances come in discrete units. You can't rotate by an arbitrary angle because angles might be quantized. The fundamental theory might have a different kind of symmetry, perhaps discrete symmetry like crystals have. Loop quantum gravity deals with this by having discrete [music] quantum states of geometry that superpose creating effectively continuous spaceime at large scales. At the plank scale the states are discrete but there are so many of them and they mix so [music] completely that at larger scales continuous symmetries emerge. It's like how water made of discrete molecules appears as a continuous fluid at human scales.

String theory maintains continuous space with strings themselves providing the plank scale cutoff. Strings vibrate in continuous spacetime. [music] But being plank length sized, they can't probe distances smaller than themselves. So effectively there's a minimum distance even though space itself is continuous different approaches different philosophies but both take seriously the idea that something fundamentally new happens at the plank scale where quantum and gravitational effects meet.

Let's discuss the early universe and the role of plank scale physics. The Big Bang is the moment when the universe began roughly 13.8 billion years ago. But what does it mean for the universe to begin? What happened at time zero? And what, if anything, existed before? These are [music] questions that have puzzled philosophers and scientists for millennia.

General relativity combined with observations of the expanding universe suggests that extrapolating backward in time, the universe becomes smaller and denser [music] and hotter. Galaxies move closer together. Temperature rises. Eventually, you reach an [music] epoch when the universe was hot enough that atoms couldn't exist. Electrons and nuclei were separate plasma. Going back further, nuclei themselves break apart into protons and neutrons. Further still, protons and neutrons dissolve into quark gluon plasma. Keep going backward and you eventually reach a point where all the matter and energy in the observable universe was compressed into a region smaller than an atom, smaller than a nucleus, smaller than a plank length.

At this point, roughly one plank time after the universe began, conditions [music] are so extreme that quantum gravity effects dominate. General relativity alone cannot describe what happens. You need [music] quantum mechanics as well. This is the plank epoch lasting from time 0 to about 10 to the -43 seconds. During this brief moment, the universe was smaller than a plank length across and hotter than the plank temperature. All forces were unified. There was no distinction between gravity, electromagnetism, the strong force and the weak force. There were no particles as we know them. Space and time themselves might not have existed in familiar form.

What happened during the plank epoch? We honestly don't know. We lack the tools to calculate. We don't have a complete quantum gravity theory. We can speculate based on candidate theories, but we can't be confident. It's like asking people in the 1800s to describe nuclear physics. They didn't have the framework. We're in a similar position regarding the plank epoch.

Different quantum gravity theories give different answers. Some propose the big bang singularity is resolved by quantum effects. In classical general relativity, extrapolating to time zero gives [music] infinite density, infinite temperature, infinite curvature. All physics [music] breaks down. But quantum effects might prevent these infinities.

Keep going backward and you eventually reach a point where all the matter and energy in the observable universe was compressed [music] into a region smaller than an atom, smaller than a nucleus, smaller than a plank length. At this point, roughly one plank time after the universe began, conditions are so extreme that quantum gravity effects dominate. General relativity alone cannot describe what happens. You need quantum mechanics as well. This is the plank epoch lasting from time zero to about 10 -43 seconds. During this brief moment, the universe was smaller than a plank length across and hotter than the plank temperature. All forces were unified. There was no distinction between gravity, electromagnetism, the strong force, and the weak force. There were no particles as we know them. Space and time themselves might not have existed in familiar form.

What happened during the plank epoch? We honestly don't know. We lack the tools to calculate. We don't have a complete quantum gravity theory. We can speculate based on candidate theories, but we can't be confident. It's like asking people in the 1800s to describe nuclear physics. They didn't have the framework. We're in a similar position regarding the plank epoch.

Different quantum gravity theories give different answers. Some propose the big bang singularity is resolved by quantum effects. In classical general relativity, extrapolating to time zero gives infinite density, infinite temperature, infinite curvature. All physics breaks down. But quantum effects might prevent these infinities.

Think about the bore model of the atom. In classical physics, an electron orbiting a nucleus should spiral inward radiating energy and crash into the nucleus in a tiny fraction of a second. Atoms should be unstable. But quantum mechanics [music] prevents this. The electron can't spiral below a certain energy level. There's a ground state it can't go below. Quantum mechanics saves atoms from classical collapse. Similarly, quantum effects might prevent the universe from collapsing to a singularity. There might be a minimum size, a minimum density related to the plank scale. The universe can't compress smaller than a plank length or denser than plank density.

What happens instead? That depends on the theory. One possibility is spacetime [music] itself emerges from a quantum state that doesn't have the usual concepts of space and time. Before the plank epoch, asking what happened doesn't make sense because time didn't exist. Time is a property that emerges when the universe reaches a certain size or state. Below that, there's just a quantum superposition of geometries without a well-defined time coordinate.

Think about temperature again. Temperature [music] is the average kinetic energy of particles in a system. It's a statistical property of collections. A single particle doesn't have temperature. Temperature is an emergent concept requiring many particles. Similarly, time might be an emergent property requiring certain minimal complexity or scale to make sense.

This is what the Hartleh Hawking no boundary proposal suggests. James Hartle and Steven Hawking proposed in the 1980s that going back to the big bang, time becomes space-like. Near the big bang, the distinction between space [music] and time blurs. You can't ask what happened before the Big Bang any more than you can ask what's north of the North Pole. The question doesn't make sense because the time direction ends or becomes a space-like direction. In the Hartleal Hawking model, the universe doesn't have a boundary in time. It's finite but unbounded. Like Earth's surface is finite but has no edge. You can walk anywhere on Earth without falling off an edge. Similarly, you can go back in time to the big bang, but there's no moment before it. Time itself begins there, emerging from a quantum gravitational state. Mathematically, the Hartleyhawking model uses ukidian quantum gravity. Instead of a real time coordinate, they use imaginary time, which behaves like a space dimension. The universe's quantum state is calculated by summing over all possible fourdimensional geometries with certain boundary conditions. The result is the wave function of the universe, a quantum state describing all possible geometries [music] and their probabilities. This is controversial and speculative. The mathematics is difficult and involves approximations, but it shows one way quantum gravity might resolve the big bang singularity. Time might not extend infinitely into the past. It might begin at the big bang, emerging from a quantum gravitational state without time.

Other proposals suggest the big bang might be a bounce. This is a prediction of loop quantum cosmology. In this scenario, the universe didn't begin at the big bang. [music] It existed before in a contracting phase. It contracted for perhaps billions or trillions of years, getting smaller and denser. But instead of collapsing to a singularity when density reached the plank scale, quantum effects kicked in. In loop quantum gravity, quantum geometry creates a repulsive effect at plank densities. This isn't like normal pressure from gas or radiation. It's a geometric effect from the quantized space structure. When space is [music] compressed to the plank scale, quantum geometry prevents further compression. Instead, it creates a bounce, reversing the contraction into expansion. The bounce happened roughly 14 billion years ago, which we call the big [music] bang. But it wasn't the beginning. It was a transition from a contracting phase to an expanding phase.

Before the bounce, the universe was large, perhaps infinite. It was old, having existed [music] for an indefinite time. Then it started contracting. Gravity pulled everything together. The universe got smaller and hotter until reaching the plank scale. Then the quantum bounce occurred and expansion began.

If correct, this resolves many cosmological puzzles. Where did the universe come from? It didn't come from anywhere. It always existed. What happened before the big bang, a previous contracting phase? Why was the early universe so smooth and uniform? Because the contracting phase compressed everything, smoothing out irregularities.

But bounce cosmology raises questions too. What caused the initial contraction? Why did the expansion phase before the contraction end? Will the current expansion eventually reverse into a new contraction leading to an endless cycle? If so, how many cycles have there been? Is there a first cycle or has the universe been bouncing eternally? These questions are being actively researched. Some models suggest the universe undergoes infinite cycles of expansion and contraction. Each cycle lasts perhaps hundreds of billions of years. Big crunch becomes big bounce becomes new big bang. An eternal cycling universe, neither beginning nor ending.

Other models suggest the cycles might not be identical. Each bounce might create a universe with slightly different properties. different constants, different particles, different forces. The multiverse might exist not in space but in time with different epochs having different physics.

Still other ideas propose our universe is part of a larger multiverse where many universes exist simultaneously each potentially having different laws of physics. In the eternal inflation scenario, rapid expansion called inflation never completely stops everywhere. Instead, different regions stop inflating at different times. Each region that stops becomes a separate universe with its own properties. Our observable universe. Everything we can see with telescopes is just one bubble in an infinite [music] foam of universes. Each bubble might have different values for the fundamental constants. Some might have stronger gravity, [music] others weaker. Some might have different particle types. Most might be sterile, unable to form stars or galaxies or life. We exist in a bubble with properties that allow life because only such bubbles have observers. This is anthropic reasoning controversial in physics. Critics argue that if you allow arbitrary variation of constants, [music] the theory loses predictive power. You can explain anything by saying, "We happen to live in a universe where it's true." Proponents argue [music] anthropic reasoning might be legitimate if combined with testable predictions about what's probable given the requirement for observers.

Some suggest the universe is cyclical in a different way. Paul Steinhart and Neil Turk proposed a cyclic model where our three-dimensional universe is a brain, a three-dimensional surface embedded in higher dimensional space. String theory allows such brains. There's another brain parallel to ours, and the two brains collide periodically. Each collision is a big bang, resetting our universe and starting a new cycle. Between collisions, [music] the brains drift apart. During this phase, each brain evolves quietly. Dark energy, the mysterious force [music] accelerating expansion might be due to brain separation. Eventually, the brains reach maximum separation and start approaching again. They collide, producing tremendous energy that becomes matter and radiation in a new big bang. Then the cycle repeats. This model addresses several cosmological problems while making some testable predictions. [snorts] But it requires extra dimensions and brains structures not yet observed. It's an elegant possibility but currently speculative.

All these ideas, Hartle Hawking, no boundary, loop, quantum cosmology, bounce, eternal inflation, multiverse, cyclic brain collisions involve [music] plank scale physics. Understanding the universe's origin requires understanding what happens when quantum mechanics and gravity meet at extreme energies and tiny [music] distances. The plank length and plank time mark the boundary between known physics and fundamental mystery.

Inflation, a period of rapid expansion thought to have occurred shortly after the Big Bang, also connects to the plank scale. Alan Guth proposed inflation in 1980 to solve several cosmological problems. The standard Big Bang theory had puzzles it couldn't explain. One was the horizon problem. Different regions of the universe visible today were never in causal contact in the standard Big Bang model. Light hasn't had time to travel between them since the Big Bang. Yet they all have the same temperature, the same properties. How did they coordinate if they couldn't communicate? Inflation solves this by proposing all these regions were once close together in thermal equilibrium [music] before inflation. Then a brief period of [music] exponential expansion lasting perhaps 10 the -30 seconds stretched a tiny region to a size larger than the currently observable universe. Regions now far apart and causally disconnected were once close together and thermalized.

Another puzzle was the flatness problem. The universe appears almost exactly flat geometrically. [music] It's not curved like a sphere or saddle, at least not detectably. But in the standard Big Bang, the universe should evolve away from flatness. To be as flat as we observe, the early universe must have been fine-tuned to flatness [music] with incredible precision like balancing a pencil on its point. Why? Inflation solves this by stretching space so much that any initial curvature gets smoothed out. It's like inflating a balloon. A small region of the balloon's surface is curved. But inflate it to an enormous size and any small patch looks flat. Similarly, inflation stretched the universe so much that the observable region appears flat even if the overall universe is curved.

Inflation also explains the origin of structure, how galaxies and stars formed. In the very early universe, quantum fluctuations created tiny density variations. Some regions were slightly denser than average, others slightly less dense. These variations were minuscule about one part in a 100,000. During inflation, these quantum fluctuations got stretched to macroscopic scales. Fluctuations that started at the plank scale due to quantum uncertainty in the inflaton field driving inflation were expanded to scales larger than the observable universe. After inflation ended, the denser regions gradually collapsed under gravity over millions of years, forming galaxies and stars. This is stunning. The galaxy distribution across billions of light years traces its origin to quantum fluctuations at the plank scale. The universe's largest structures arose from the smallest quantum fluctuations. This connects the plank length to cosmic scales in an observable, testable way. [music]

We've measured these density variations by observing the cosmic microwave background radiation, light from 380,000 years after the big bang when the universe first became transparent. The pattern of hot and cold spots in this radiation corresponds to density variations in the early universe. It matches inflation predictions remarkably well. Different inflation models make different predictions about these patterns. By measuring the cosmic microwave background precisely, we test inflation theories and learn about the physics during inflation. Since inflation occurred at very high energies close to the plank [music] scale, we're indirectly probing the quantum gravity regime through cosmological observations.

One key test [music] involves primordial gravitational waves. Inflation should produce gravitational waves, ripples in spaceime from quantum fluctuations in geometry itself. These waves would leave a specific signature in the cosmic microwave backgrounds polarization called Bodes. Detecting Bodes would confirm inflation and tell us the energy scale when it occurred. If the inflation energy scale was near plank energy, it means quantum gravity was [music] important during inflation, we'd have observational evidence for physics at [music] nearly the plank scale. Multiple experiments are searching for B modes. So far, they haven't been detected, which constrains inflation models. But the search continues with ever more sensitive instruments.

There are also transplankian problems with inflation. During exponential expansion, [music] scales smaller than the plank length were stretched to observable sizes. Wavelengths that started subplank became super plank. Does this make sense? Can we trust calculations involving physics below the plank length? This is a thorny issue. On one hand, we don't know what happens below the plank [music] length. our theories break down. On the other hand, if we can't discuss subplankian physics, how can we trust inflation predictions? Different quantum gravity approaches give [music] different answers about whether transplankian modes affect observable predictions. Resolving this requires better understanding of plank scale physics.

Now let me discuss modern experimental and theoretical approaches that might give [music] us indirect windows into plank scale physics. While we can't build a plank scale accelerator, physicists have developed clever ways to test quantum gravity predictions at accessible scales.

One promising avenue involves studying how spacetime might be discrete rather than continuous. If space is made of plank scale [music] pixels, this could affect particle propagation at very high energies. Imagine a car driving on a perfectly smooth road versus a cobblestone street. On a smooth road, the car glides effortlessly. On cobblestones, there's vibration. The road's granular structure affects motion. Similarly, [music] if spacetime has a granular structure at the plank scale, this might affect particle propagation, especially at very high energies where wavelengths approach the plank scale. This could show up as tiny violations of Lorent's invariance. The principle that the laws of physics are the same for all observers moving at constant velocity. Einstein's special relativity is built on Lawrence [music] invariance. Light speed is constant for all observers. Time dilation and length contraction ensure the laws of physics have the same form in all inertial reference frames.

But some quantum gravity theories predict tiny Lorent violations at extreme energies. For example, light speed might depend slightly on photon energy. In standard physics, all photons travel at exactly the same speed in vacuum regardless of energy. Red light, blue light, gamma rays, all travel at light speed. But if spaceime is discrete at the plank scale, higher energy photons might interact differently with the discrete structure [music] than lower energy photons. They might travel slightly faster or slower. The effect [music] would be incredibly tiny. We're talking about differences of maybe one part in 10 to the 30 or smaller. The difference between speeds would be less than a meter/s. Completely unmeasurable in a laboratory.

But here's where cleverness comes in. We can observe photons that have been traveling for billions of years from distant astronomical sources. Even tiny speed differences accumulate over these enormous distances and times. Gammaray bursts are particularly useful. These are some of the most energetic events in the universe, possibly from colliding neutron stars or collapsing massive stars. They produce photons with energies millions of times higher than visible light, up to hundreds of billions of electron volts. When a gammaray burst occurs billions of light years away, it emits photons of many different energies simultaneously in a brief flash. If light speed depends on energy, higher energy photons and lower energy photons would arrive at Earth at slightly different times, separated by milliseconds or seconds. despite being emitted simultaneously. This is a time delay we could measure.

Sensitive detectors on satellites and on the ground continuously watch for gammaray bursts and measure the arrival times of photons at different energies. Astronomers have carefully studied dozens of gammaray bursts looking for such energy dependent time delays. So far no consistent energy dependent speed of light has been detected. All photons from gammaray bursts regardless of energy arrive at the same time within measurement precision which is very good better than a millisecond for some bursts. This puts very tight constraints on quantum gravity theories. Any theory predicting energy dependent light speed above a certain threshold is ruled out. This is remarkable. We're using observations of distant astrophysical events to constrain physics at the plank scale. That scales 35 orders of magnitude smaller than an atom. Of course, the absence of an effect doesn't prove space is continuous. It could be discreet in a way that doesn't produce measurable Lorent violations or effects might be smaller than current sensitivity, [music] but it rules out certain models and guides theory development.

Another experimental approach involves ultrarecise measurements in particle physics. The standard model describes all known particles and three of the four fundamental forces. It's been tested to incredible precision over decades, but the standard model doesn't include gravity. It's an effective theory valid up to some energy scale, probably well below plank energy. At very high energies, quantum gravity effects might modify standard model predictions slightly. The modifications would be tiny, but modern experiments are incredibly precise. The Large Hadron Collider measures certain quantities to better than 1% precision. Future colliders might do even better. If quantum gravity predicts specific modifications at accessible energies, we could test those predictions. This requires detailed calculations from quantum gravity theories, which is challenging since we don't have a [music] complete theory. But physicists are working on it, computing predictions from candidate theories and comparing them with experimental data. For example, extra dimensions predicted by string theory might [music] affect particle interactions at LHC energies. If the dimensions are larger than originally thought, if extra dimensions exist and are accessible, particles could escape into them, showing up as missing energy in collisions. Or virtual particles could propagate through extra dimensions, slightly modifying forces [music] between known particles. The LHC has looked for such effects. None have been found which constrains extra dimension sizes. They must be smaller than a certain threshold or not exist at all. Again, the absence of an effect is informative. It narrows down possibilities and guides theory.

The laser interpherometer space antenna or lizer scheduled for launch in the 2030s will be a space-based gravitational wave detector. Unlike LIGO which sits on Earth's surface detecting [music] high frequency gravitational waves, LISA will [music] detect much lower frequency waves. It will consist of three spacecraft flying in triangular formation separated by millions of kilome. This enormous baseline lets LIZA detect gravitational [music] waves with periods of minutes to hours versus LIGO's milliseconds. Different sources produce different frequency waves. LIGO detects waves from stellar mass black hole mergers and neutron star collisions. Liza will detect waves from super massive black hole merges in distant galaxies and potentially primordial gravitational waves from the very early universe. Primordial gravitational waves would [music] carry information about physics at energy scales approaching plank energy. If inflation occurred, it should produce gravitational waves from [music] quantum fluctuations in spaceime itself. These waves would propagate through the entire history of the universe, getting stretched and redshifted as the universe expands. By now, they'd have very long wavelengths, perfect for LIZA to detect. If LIZA succeeds, [music] we'd have direct observational data about conditions when quantum gravity was important. Different inflation models predict different amplitudes and spectra for primordial waves. By measuring them, we could distinguish between models and constrained quantum gravity theories. The challenge is sensitivity. Primordial gravitational waves, if they exist, would be incredibly weak by now. They've been traveling almost 14 billion years, diluted by universe expansion. Detecting them requires eliminating all other sources of noise. Liza's design includes sophisticated systems to isolate [music] the spacecraft from vibrations, solar wind, thermal fluctuations, anything [music] that might mask the gravitational wave signal. The spacecraft will be in solar orbit trailing Earth. The three spacecraft form a triangle with 5 million km sides. Laser beams pass between spacecraft and a gravitational wave passing through distorts spaceime slightly changing the distances. Intererometry measures these tiny [music] distance changes sensitive to variations smaller than the width of an atom across a million km baseline.

On the ground, next generation particle colliders are being proposed. >> [snorts] >> The future circular collider or FCC would be a ring 100 km in circumference four times larger than the LHC. It would collide particles at energies up to 100 trillion electron volts about seven times higher than the LHC. These energies are still nowhere near plank energy which is about 10 to the 28 electron volts. The FCC would reach 10 to the 14 electron volts, 14 orders of magnitude short. But quantum gravity effects might appear as subtle modifications even at accessible energies. The FCC could measure standard model parameters with unprecedented precision. Any deviations could hint at new physics. The China Electron Positron Collider takes a different approach, focusing on precision measurements at moderate energies rather than pushing to the highest energies. Sometimes subtle effects are easier to detect through precision than brute force. By measuring certain processes with extreme accuracy, you can see tiny quantum gravity corrections that would be invisible at higher energies where processes are more violent.

In cosmology, the Simon's Observatory in Chile is constructing telescopes specifically designed to measure cosmic microwave background polarization. The polarization pattern carries information about primordial gravitational waves. Previous experiments like bicep set upper limits but haven't detected [music] B modes. The Simons Observatory aims to be sensitive enough to finally see them if they're there at levels predicted by many inflation models. The CNBS4 project will be even more sensitive. It will deploy thousands of detectors at the South Pole in Chile, observing the sky for several years. The goal is to map cosmic microwave background polarization across a large fraction of the sky with unprecedented detail, potentially [music] detecting B modes and thus providing evidence for inflation and information about the energy scale when it occurred.

Why is cosmic microwave background polarization so important? When light scatters off electrons, it becomes polarized. The cosmic microwave background we observe was scattered by electrons in the early universe when atoms first formed. The pattern of polarization depends on what disturbances were present [music] when the scattering occurred. Density perturbations which became galaxies create an emode polarization pattern. This has been detected [music] and measured precisely. It matches inflation predictions well, but gravitational waves create a different pattern called B modes. These haven't been detected yet, but they're the smoking gun for primordial gravitational waves and thus [music] for inflation. If B modes are detected and measured, we'll learn the energy scale of inflation. If the energy scale is close to plank energy, it means quantum gravity was important during inflation. We'd have observational evidence for physics at nearly plank scale energies. This would be an extraordinary breakthrough connecting [music] the plank length to observable cosmology.

In particle physics, experiments at lower energies continue searching for anomalies. The moon G2 experiment at Fermy Lab measures [music] the magnetic moment of the moon with incredible precision. Recent results show a small discrepancy between the measured value and the standard model prediction. This could be a statistical fluctuation or a hint of new physics. Could it be quantum gravity? Probably not [music] directly. The effect is more likely from an unknown particle or force that the standard model doesn't include. But any new physics beyond the standard model is interesting because it shows the standard model is incomplete. And we know the standard model must be incomplete because it doesn't include gravity. Finding cracks in the standard model helps us understand what a complete theory [music] including gravity might look like.

The deep underground nutrino experiment or dune will shoot a neutrino beam from firmy lab in Illinois to detectors in South Dakota 1300 km away by observing how nutrinos oscillate between flavors over this distance. Dune will measure neutrino properties with unprecedented precision. Some quantum gravity theories [music] predict tiny violations of special relativity at very high energies. These violations might affect [music] neutrino oscillations. The effects would be tiny, but Dune's sensitivity might [music] be enough to detect them. Even if Dune doesn't see anything unusual, the measurements will constrain quantum gravity theories.

Dark matter experiments also provide potential windows. We know dark matter exists from gravitational effects, but we don't know what particles it's made of. The leading candidates are wimps, weakly interacting [music] massive particles, but decades of searching haven't found them. Space geometry might fluctuate wildly. One moment, two points might be separated by a certain distance. Next moment [music] distance might be completely different because geometry fluctuated. The very concept of well-defined distance or time interval might break down. It's not just that distances are small. It's that distance concept itself becomes fuzzy and illdefined. You can't say two points are exactly this far apart because distance constantly fluctuates due to quantum effects. This has profound implications. In quantum mechanics, we're used to particles having uncertain positions and uncertain momentum. But we still think of space itself as fixed background on which this uncertainty plays out. At plank scale, even that background fluctuates. Space itself is uncertain. The stage on which physics plays out is itself a quantum object with its own uncertainty. This isn't just speculation. Uncertainty principle guarantees there must be energy fluctuations in any quantum field and gravity responds to energy. So spacetime must fluctuate at small scales. The question is how much and what fluctuation structure looks like. Without complete quantum gravity theory, we can't calculate precisely. But we know it must happen. Quantum mechanics laws demand it.

Here's another strange implication. At plank scale, black holes behave very differently than at large scales. A black hole with mass equal to plank mass would have size equal to plank length. Its schwarz chilled radius event horizon size would be one plank length. Such black holes are called plank scale or quantum black holes. They'd be incredibly hot, radiating energy through Hawking radiation so intensely they'd evaporate almost instantly in about one plank time. Some theorists propose dark matter might connect to quantum gravity. Perhaps dark matter particles are relics from the plank epoch, primordial black holes formed in the early universe, or manifestations of extra dimensions. [music] Finding dark matter and understanding its properties might teach us about quantum gravity. The Lux Zeppelin [music] experiment uses 7 tons of liquid xenon to search for dark matter. When a dark matter particle passes through, it might occasionally collide with a xenon nucleus, producing a tiny flash of light. [music] The detector is sensitive enough to see individual collisions. So far, no dark matter has been detected, but the experiment continues each year of data improving sensitivity.

On the theoretical side, researchers use supercomputers to simulate quantum gravity effects. These aren't simulations of real quantum gravity since we don't have a complete theory, but they're simulations of toy models that capture some features while being simple enough to compute. Researchers simulate causal set theory by generating random networks of events [music] and seeing what geometric structures emerge. Others simulate ads divided by CTF correspondence computing black hole properties by doing calculations in the dual quantum field theory without gravity. These simulations develop intuition about how quantum gravity might work. Quantum computers are increasingly used for these simulations. Unlike classical computers that process bits representing [music] zero or one, quantum computers use cubits in superposition of both states. This lets them efficiently simulate quantum systems classical computers struggle with. Researchers have used quantum computers to simulate simple quantum gravity models and space-time emergence. These are toy models, far simpler than the real universe, but they help test ideas. As quantum computers improve, they'll simulate more complex models, potentially giving insights classical calculations can't provide.

There's also growing interest in tabletop experiments that might probe quantum gravity. These don't reach plank energy but might detect subtle quantum gravity effects through clever designs. One approach involves putting massive objects [music] in quantum superp osition. Quantum mechanics usually deals with tiny particles but in principle it applies to objects of any size. Can you put something visible in quantum superp osition where it's in two places at once? Several groups are working [music] toward this. The challenge is isolating a massive object from the environment well enough that it maintains quantum behavior. Every interaction with the environment tends to destroy superposition through decoherence. But recent experiments have achieved quantum superposition with increasingly massive objects from molecules to microscopic particles. Why is this relevant to quantum gravity? Because if you could put a massive object in superp osition, its gravitational field would also be in superp osition. This creates a unique situation where gravity and quantum mechanics interact measurably. Some quantum gravity theories predict specific effects in this regime. Observing these effects would teach us about quantum gravity.

Another tabletop approach involves ultrarecise gravity measurements at small [music] scales. Gravity is the hardest force to measure at laboratory scales because it's so weak. But experiments have measured gravitational force down to distances of about 50 micrometers, roughly the width of a human hair. Some quantum gravity theories [music] predict gravity modifications at small scales. Extra dimensions might make gravity stronger at small distances. Other theories predict new forces appearing by measuring gravity precisely at the [music] smallest accessible distances. These experiments constrain theories. So far, gravity behaves exactly as Newton and Einstein predicted down to the smallest scales measured. This rules out certain quantum gravity models and constrains others. As experimental techniques improve, we'll push to smaller scales and tighter constraints.

Atomic clocks have reached extraordinary precision, becoming useful for fundamental physics tests. The best atomic clocks today are accurate to about one part in 10 the 18. They'd be off by less than 1 second in 15 billion years, longer than the universe's age. At this precision, atomic clocks are sensitive to general relativity effects over height changes of a few cm. Take two atomic clocks, put one slightly higher than the other, and the higher clock runs measurably faster due to time dilation from the gravitational field. Could atomic clocks detect quantum gravity effects? Possibly. Some theories predict tiny violations of general relativity detectable with sufficiently precise clocks. Researchers are exploring this possibility, comparing clocks at different locations and looking for anomalies that might indicate new physics.

There's fascinating work on quantum entanglement and space-time structure. Recent developments suggest deep connections between quantum entanglement and space geometry. This comes from studying the holographic principle and ads divided by CTF correspondence. The idea is that when quantum fields in different regions are entangled, this entanglement literally creates a spatial connection between those regions. More entanglement means shorter distance. If you could somehow disentangle the fields, the distance between regions would increase. Take entanglement to the extreme and regions become completely disconnected. This is profound. It suggests [music] space itself isn't fundamental. Space emerges from quantum entanglement patterns in a more fundamental quantum system. Distance [music] isn't a basic property of reality. It's a derived quantity, a consequence of how quantum information is distributed [music] and correlated.

Physicists are exploring this using quantum computers and quantum simulators. They're creating simple quantum systems with controllable entanglement and studying how spatial structure emerges from entanglement patterns. These are toy models, far simpler than real spaceime, but they might teach fundamental lessons about how space works. Imagine a collection of quantum bits, cubits, the building blocks of quantum computers. Each cubit can be in state zero, state one or a quantum superposition of both. Now imagine entangling these cubits in specific patterns. The pattern defines a network. Some cubits are strongly entangled, some weakly, some not at all. You can assign distance to pairs of cubits [music] based on their entanglement. Strongly entangled cubits are close together. Weekly entangled cubits are far apart. Completely unentangled cubits aren't part of the same space. From this entanglement network, you can derive a geometric structure, a space with distance relationships. This is a toy model of emergent space. Real spac-time emergence is much more complicated, involving quantum fields rather than simple cubits and including time as well as space. But the basic idea is the same. Space might not be fundamental. It might emerge from quantum information theory.

If correct, this has implications for plank scale physics. The discrete nature of quantum information might explain why space appears discrete [music] at the plank scale. Quantum systems have discrete energy levels, discrete states. If space emerges from quantum systems, it might inherit discrete structure. This also provides a possible resolution to the black hole information paradox. Information falling into a black hole doesn't disappear. It gets encoded in the entanglement structure between quantum fields inside and outside the black hole. As the black hole evaporates via Hawking radiation, information gradually leaks out in subtle correlations in the radiation. Information is preserved, just highly scrambled.

There's also active research on analog systems that might mimic quantum gravity effects. These are condensed matter or fluid dynamics systems with mathematical structure similar to quantum gravity. Even though they're describing different physical situations, sound waves in certain fluids behave remarkably similar to light in curved spaceime. Fluid flow creates an effective geometry that sound waves propagate through. If the fluid has the right properties, this geometry can even include an analog black hole horizon beyond which sound waves can't escape. These are called analog black holes or dumb holes. And physicists have created them in laboratories. They're not real black holes. They don't involve gravity. They're just fluid flows carefully arranged so sound waves behave like light [music] near a black hole. But by studying analog systems, we might learn about quantum effects near real black hole horizons. One prediction is that analog [music] black holes should emit analog Hawking radiation. A thermal spectrum of sound waves created by quantum fluctuations near the analog horizon. This would be experimental verification of the Hawking radiation mechanism [music] even though it's in a completely different physical system. Researchers have claimed to observe this effect [music] though results are still debated. The point is we can learn about quantum gravity by studying systems we can actually build and control in a laboratory. systems that share some mathematical features [music] with real quantum gravity but operate at accessible scales.

There's also work on quantum corrections to classical gravity. Even if we can't reach the plank scale, quantum effects might produce small corrections to classical general relativity predictions at lower energies. The corrections would be tiny but might be measurable with extremely precise [music] experiments. Gravitational wave observations provide one avenue. LIGO and other detectors have opened a new window on the universe. Current detectors measure gravitational wave properties quite precisely. Future detectors will be even more sensitive. Quantum gravity might [music] predict subtle modifications to gravitational wave propagation. Waves might travel at slightly different speeds depending on frequency. Waves might lose energy differently than classical theory predicts. Waves might have additional polarization states beyond what classical gravity allows. None of these effects have been seen yet. Observations match classical general relativity perfectly. But as detectors improve and we observe more events, we might detect quantum gravity corrections. This would give us an experimental handle on quantum gravity without needing plank scale energies. Precision tests of gravity at small scales also provide constraints. Experiments measure gravitational force precisely at the smallest accessible distances. Some quantum gravity theories predict modifications. Extra dimensions might make gravity stronger at small distances. Other theories predict new forces. So far, gravity behaves as Newton and Einstein predicted. This rules out certain models and constrains others. As techniques improve, we'll push to smaller scales and tighter constraints, gradually narrowing down what quantum gravity can be.

One of the most beautiful aspects of plank [music] scale physics is how it represents the ultimate unification. Throughout physics history, we've repeatedly discovered that apparently different phenomena are actually [music] related. Electricity and magnetism unified into electromagnetism. Space and time unified into spaceime. Mass and energy proven equivalent. The weak force and electromagnetism unified into the electroeak force at high energies. At the plank scale, this pattern continues but becomes complete. All fundamental constants converge. All fundamental forces reach comparable [music] strength. The distinction between particles and space-time geometry blurs. Everything that

looks separate at low energies merges into a single framework. This suggests deep unity to the laws of physics. At the most fundamental level, there might not be separate forces or separate matter types. There might be one unified structure, one mathematical framework describing everything. As you move away from the plank scale to lower energies, the unified structure breaks apart into the separate pieces we call different forces and particles. But fundamentally, it's all one thing.

This is what physicists mean by theory of everything. Not a theory explaining literally everything, including biology, sociology, and art, but a theory unifying all fundamental physics into a single framework. A theory starting from one principle at the plank scale and showing how all observed physics emerges at lower energies.

We don't have that theory yet, but we have candidates. String theory and M theory attempt such unification. Loop quantum gravity is more modest, focusing specifically on quantum gravity, but even it suggests deep connections between space, time, and matter. The quest continues.

What drives physicists to pursue this? Why spend careers working on a theory that might not have practical applications? The answer is simple. Curiosity, the desire to understand. Humans are curious creatures. We want to know how things work. We want to understand our place in the cosmos. We want to answer fundamental questions about existence.

The plank scale represents the deepest level of those questions. It's as fundamental as you can get. Understanding it means understanding reality at its root. That's a compelling goal worth dedicating careers to, worth building international collaborations around, worth investing resources in. And there's an aesthetic component. Physics at its best is beautiful. Elegant equations describe complex phenomena. Deep symmetries connect apparently different things. Simple principles have far-reaching consequences. This mathematical beauty attracts people to theoretical physics.

The equations describing physics at the plank scale when we finally discover them will almost certainly be elegant. Not because the universe owes us elegance, but because elegant mathematical structures tend to be the deepest ones. Simple symmetries and principles when worked out fully produce complex emergent behavior. That's the pattern throughout physics history.

Looking forward, the next decade will be crucial. New gravitational wave detectors will come online with sensitivity orders of magnitude better than LIGO. The next generation of particle colliders is being planned. Quantum computers are advancing rapidly, potentially giving us tools to simulate quantum gravity effects we can't access experimentally.

Most exciting missions are planned to detect primordial gravitational waves from inflation. If successful, these would give us a direct observational window into physics at energy scales approaching plank energy. We'd have experimental data about the quantum gravity regime for the first time in human history.

Theoretically, progress continues. String theorists are developing new mathematical tools and discovering surprising connections between their theory and other areas. Loop quantum gravity researchers are making predictions about black hole entropy and the early universe that might be testable. New approaches to quantum gravity emerge periodically, offering fresh perspectives.

The international physics community is more connected than ever. Researchers collaborate across continents. Ideas spread rapidly. When a breakthrough comes, whether theoretical or experimental, it will be built on contributions from thousands of physicists worldwide working toward a common goal.

What we learn about the plank scale will reshape our understanding of reality. It will tell us whether space and time are fundamental or emergent. Whether the universe has a beginning or is eternal, whether there are other universes beyond ours. These aren't idle speculations. They're questions with answers. And we're developing the tools to find those answers.

We've come from measuring distances with our hands and feet to grasping distances 35 orders of magnitude smaller than anything we can see. We've connected the incredibly small to the incomprehensibly vast. The plank length reminds us there are limits to knowledge, but also that we can transcend those limits through reason. We can understand things we cannot see.

We are beings made of plank scale quantum stuff evolved to understand the universe that created us. The plank length is reality's pixel size. It's the fundamental building block from which everything is constructed. You, me, Earth, the stars, galaxies. We're all structures built from plank scale quantum degrees of freedom. We're all patterns in quantum information. We're all temporary configurations of something deeper we're only beginning to understand.

And that's what makes physics so compelling. We don't have all the answers. We don't have a complete quantum gravity theory, but we're working on it. Thousands of physicists worldwide are developing theories, performing calculations, making observations, slowly building toward complete understanding. Each year, we know a little more. Each decade brings new insights.

Thank you for joining me on this journey to the smallest scale. If you found this exploration valuable, a like or subscribe helps keep these deep dives into physics going.

Every moment of your existence happens in a universe built from plank scale quantum gravitational degrees of freedom. You are a macroscopic pattern in quantum information evolved to understand the universe that created you. And that's something worth appreciating.