The video explores the profound complexities surrounding the Planck length, a region considered the smallest scale in the universe and a frontier where the known laws of physics break down. By challenging traditional conceptions of space and time, the video examines historical breakthroughs, including contributions from René Descartes, Isaac Newton, and Albert Einstein, that have shaped our understanding of reality. The discussion delves into Einstein's general theory of relativity, explaining how it shifts under the forces of gravity and presents fundamental challenges, especially in singularities where equations lose their meaning.

The narrative questions the very fabric of reality, as traditional physics encounters its limitations in explaining quantum phenomena at tiny scales. It introduces quantum mechanics and the peculiar nature of amplitudes, probabilities, and entanglements and how these concepts revolutionize our understanding of matter and energy. The video further discusses quantum field theory and the monumental challenge of harmonizing it with gravity, positing a picture of reality where space-time could emerge from a deeper, quantum realm.

Main takeaways from the video:

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Key Vocabularies and Common Phrases:

1. Planck length [plæŋk lɛŋθ] - (n.) A theoretical scale in physics representing the smallest measurable length, beyond which the laws of physics break down.

All of this happens at the Planck length, because here, gravity is quantum.

2. Manifold [ˈmænɪˌfoʊld] - (n.) A mathematical space that on a small scale resembles Euclidean space but can have different shapes.

Einstein's big revelation in his general theory of relativity is that space time is a Manifold that bends and curves in the presence of matter or energy.

3. Entanglement [ɪnˈtæŋɡəlmənt] - (n.) A quantum phenomenon where particles become interconnected such that the state of one instantaneously influences the state of the other.

The idea is that if two things are entangled in one description, they become physically connected in the other.

4. Singularity [ˌsɪŋɡjəˈlærɪti] - (n.) A point in space-time where gravitational forces cause matter to have infinite density and zero volume.

In places called singularities, such as at the moment of the big Bang and at the center of black holes, matter becomes so dense that it squeezes infinitely.

5. Quantum Mechanics [ˈkwɒntəm mɪˈkænɪks] - (n.) The branch of physics that deals with phenomena at nanoscopic scales, where action is on the order of the Planck constant.

Ever since physicists realized that quantum mechanics is the underlying language of the universe, we've been trying to fit everything we know about nature into its strange laws.

6. Holographic principle [ˌhoʊləˈɡræfɪk ˈprɪnsəpəl] - (n.) A theory in quantum gravity suggesting that the entire universe can be seen as a two-dimensional information structure "painted" on the cosmological horizon.

In the 1990s, these questions coalesced into a compelling idea called the Holographic principle.

7. Amplitude [ˈæmplɪˌtud] - (n.) In quantum mechanics, a description of the state of a system's wave function.

Instead, they have amplitudes. Amplitudes are like probabilities, but unlike probabilities, they can be complex numbers.

8. General Relativity [ˈdʒɛnərəl ˌrɛləˈtɪvɪti] - (n.) Einstein's theory describing gravitation as a property of the geometry of space and time, or space-time.

This is the Einstein tensor, which describes the curvature of spacetime. It's a function of the Metric our ruler for 4d space time.

9. Cosmological Constant [ˌkɒzməˈlɒdʒɪkəl ˈkɒnstənt] - (n.) A value representing the energy density of the vacuum of space, influencing the universe's expansion rate.

This next part accounts for the cosmological constant, which is the energy intrinsic in space.

10. Quantum Field Theory [ˈkwɑːntəm fiːld ˈθɪəri] - (n.) A theoretical framework for constructing quantum mechanical models of subatomic particles in particle physics and quantum field physics.

The result of these efforts is quantum field theory, a more sophisticated version of quantum mechanics.

Decoding The Mysteries Of Space Time: Holography And Quantum Gravity

This is the Planck length. It's a trillion, trillion times smaller than an atom. It's also the biggest problem in physics, because when we try to ponder what's happening near ten to the -33 laws of nature break down the stage of our universe, space time seems to dissolve, and we can't make sense of the awful chaos underneath.

Decades of investigations have Converged on a haunting conclusion. Our best descriptions of nature, quantum mechanics, and general relativity are failing us. To dig into the deepest layers of reality, we're going to need new physics. In this video, we'll build a stage of space time from the ground up, and then we'll see that we have no choice but to tear it all down again. And in the wreckage will look for clues to paths forward towards a quantum theory of gravity.

During our journey, we'll be forced to challenge our basic assumptions. Is space time real or just a large scale illusion? At the fundamental level of nature? Do questions like where and when even have answers? In 1637, the French mathematician Rene Descartes imagined a hidden mathematical framework for space. He invented the Cartesian grid, which labels points in space using x, y, and z coordinates. He thought of this grid as the backdrop of our stage of reality.

A few decades later, Isaac Newton described time in a similar way, as an absolute and rigid part of the stage. But for Descartes and Newton, space and time existed independently of each other. Then, in 1905, Albert Einstein entered the scene with his theory of special relativity. Einstein's first revelation was that time is relative.

An observer's measurement of the time between events depends on their motion in space. This was a clue that we should think of space and time as a single entity, the physical fabric of our universe, with three dimensions of space and a fourth of time. With this picture of space time as a unified Continuum, Einstein began to wonder about its shape. To get a sense for the mathematical model of space time, let's begin with one flat grid.

Now let's take another one. And another. And another. When we stitch them together, we create a mathematical object called a Manifold. Let's imagine we're a cat walking on the surface of this Manifold. Locally, the grid looks flat with straight line coordinate axes everywhere.

But if we zoom out, the Manifold turns out to be made up of curved coordinate axes. Einstein's big revelation in his general theory of relativity is that space time is a Manifold that bends and curves in the presence of matter or energy. The effects of this curvature produce what we experience as gravity.

To measure this curvature, let's return to our flat space. Thanks to Pythagoras we know that if you have a triangle with sides x and y and diagonal s, then s squared equals x squared plus y squared. Now, suppose you make the triangle really small and call the displacements in the x and y directions along the two sides of dx and dy. Then the diagonal ds satisfies this formula.

But this is also simply the distance between the endpoints of the diagonal. So we can think of this formula as giving us a ruler for 2d space. What happens when we put these coordinates on a rubber sheet and stretch it? They are still separated by the same number of grid spacings, but their physical distances have changed. Now we need a new ruler that tells us how much stretching and skewing is happening on our Manifold.

This is the Metric, our modified ruler for curved 2d spacetime. Einstein expanded on this ruler, creating a Metric for how spacetime curves in a 4d universe like ours. To describe the geometry of space time, you have to calculate where and by how much matter tells our Manifold to curve, producing the effects of gravity. That brings us to the crown jewel of general relativity, Einstein's field equation for how the distribution of matter and energy curves spacetime.

This is the Einstein tensor, which describes the curvature of spacetime. It's a function of the Metric our ruler for 4d space time. This next part accounts for the cosmological constant, which is the energy intrinsic in space. This part is the stress energy tensor. It describes the energy density, momentum density, and pressures of matter and energy at each location in space.

In other words, it tells us where stuff is and how much there is of it. You can think of this equation as matter and energy telling spacetime how to bend. In a simpler world, this would be the end of physics, an elegant theory of distances in space and time described geometrically by the Manifold. But buried in Einstein's blueprints are places where the theory describes its own demise.

In places called singularities, such as at the moment of the big Bang and at the center of black holes, matter becomes so dense that it squeezes infinitely, forcing space time to curve infinitely, too. In physics, when you encounter infinities in your equations, it's a signal they've broken down. So we have to conclude that general relativity fails to describe physics at these singularities.

Einstein's theory is also ignorant of physics at the subatomic level, where the particles are too light to noticeably curve space time, and physics is quantum mechanical. To investigate space time at the fundamental level, to really ask questions about what it's made of, we have to take a quantum point of view, this is the quantum stage.

In this probabilistic universe, subatomic particles don't have fixed positions in space. Instead, they have amplitudes. Amplitudes are like probabilities, but unlike probabilities, they can be complex numbers, which means that amplitudes can cancel each other out. Quantum mechanics says that to go from here to there, a particle can take many different paths, each with an amplitude. These amplitudes must be summed up to find the total amplitude of that transition.

So, on our quantum stage physics is not described by saying where things are and how they move, but rather how amplitudes for different possibilities change over time. This evolution is described by the famous Schrödinger equation. And then there's Quantum entanglement. When two particles are entangled, their amplitudes become contingent.

If you measure either particle, the outcome is uncertain. But if you measure one, it appears to collapse the state of the other, so that the outcome of the second measurement is suddenly, completely determined. Ever since physicists realized that quantum mechanics is the underlying language of the universe, we've been trying to fit everything we know about nature into its strange laws.

The result of these efforts is quantum field theory, a more sophisticated version of quantum mechanics. It's the framework that allows us to apply quantum principles, or quantize all the matter and force fields of the universe, except one, gravity. That's because in all quantum field theories, the matter and force fields are described as lying on top of a smooth, fixed, continuous grid of spacetime, the special relativity stage.

But to describe gravity, we have to quantize the space time stage itself. How are we supposed to do this without a stage to stand on? This is the problem of quantum gravity. It brings us to the edge of our understanding of physical reality, to the end of space time as we know it.

Let's see what happens when we apply quantum mechanics directly to our Manifold. Just like particles, the Manifold should behave quantumly. This means it can't be fixed. It must have a probability of being in many different states. There is even some probability for space time to start shredding itself, resulting in an awful soup of quantum uncertainty, where bits of spacetime pop in and out of existence.

All of this happens at the Planck length, because here, gravity is quantum. At these short distances, the notions of here and there become murky. If we try to place coordinates on our Manifold, they quickly lose meaning. Our Metric dissolves into the chaos of quantum uncertainty.

In the quest to understand what happens at very small distances, experimental physicists have built powerful particle accelerators. Today, the large hadron collider at CERN can probe physics at ten to the -17 cm. But to see what's happening at the Planck length, you'd need a particle collider a thousand trillion times more powerful, one, about as big as our entire Milky Way galaxy.

And even if we could build one, the collisions it would produce would put so much energy into such a tiny region of space that the region would collapse into a black hole. There's simply no operational way of probing space time below this length.

That suggests that spacetime below the Planck length doesn't have meaning. Something deeper is happening here. We might be tempted to ask, what if spacetime isn't the base layer of reality? What if there's a more fundamental description of physics which produces something that looks like spacetime?

In the 1970s, Jacob Bekenstein and Stephen Hawking stumbled on a compelling clue about the nature of quantum gravity. To appreciate the profound implications of what they discovered, we need to first review the laws of thermodynamics and their origin in statistical physics. Suppose you have a system with large numbers of atoms or molecules and macroscopic properties like temperature.

The Entropy of such a system measures the number of different possible molecular arrangements, or micro states, that produce a macroscopic system at this temperature. While using the equations of general relativity to explore black holes, Bekenstein and Hawking discovered that black holes act as if they have an Entropy and that quantum mechanics causes them to radiate particles in a particular way that gives them a temperature.

But black holes, like everything else, need to comply with the laws of thermodynamics. So if black holes have an Entropy, they must be made of more primitive parts, quantum microstates that can be thought of as the atoms of space time. Usually, the Entropy of a system is related to its volume, because it depends on how many ways you can arrange all the microstates inside.

But Bekenstein and Hawking showed a that with black holes, something surprising happens. A black hole's Entropy is proportional to its area, more specifically, the area of its event horizon, or boundary. It's as if we can know all of the possible microstates of a black hole's interior structure just by counting the ways of arranging things on its surface.

But how could a surface know everything about an interior volume? This strange finding is the best clue we have about the quantum nature of space time. If a 3d object like a black hole is best understood using only two dimensions, could the same be true for the entire universe?

In the 1990s, these questions coalesced into a compelling idea called the Holographic principle. The Holographic principle says that spacetime is like a hologram projected from the information available on some lower dimensional surface, like the boundary of the universe. On the holographic stage, the fabric of our reality, spacetime and gravity, actually emerges from a quantum description in a lower dimension.

If the Holographic principle is true, the math describing gravity and the geometry of space time should be equivalent to the math of quantum physics in a space time of one fewer dimension. In the last few decades, physicists have searched for these mathematical equivalences with the goal of creating a dictionary of physics that bridges the dual descriptions.

The best example so far is something called the ads CFT duality. This is a well understood quantum theory known as a conformal field theory, or CFT. It has no gravity in it. Let's consider CFT in two spatial dimensions and, of course, time. This is a kind of space time permitted in general relativity, known as anti de sitter space, or ads.

It has gravity. Let's consider an ads space with three spatial dimensions and time. The Ads CFT duality is a dictionary that relates the math of the two theories. You can use it to calculate anything in one theory in the language of the other.

We might describe this situation by saying that the ads spacetime is emergent from the CFT because some of its dimensions appear out of the dynamics of the lower dimensional CFT. But if spacetime is emergent, what are the quantum processes that produce it? Here, ads CFT gives us a compelling hint. The ads spacetime geometry, along with Einstein's equations of general relativity, emerge from entanglement, a sort of quantum inseparability between the states of the particles of the CFT.

The idea is that if two things are entangled in one description, they become physically connected in the other. So at the deepest level of reality, it's possible that Quantum entanglement is knitting space time together, giving rise to the geometry of the space time Manifold and our universe. If space time is emergent in this way, entanglement doesn't happen in space time.

Entanglement creates spacetime below the Planck length. It's entirely possible that the Quantum entanglement knitting spacetime fluctuates wildly. Things are connecting and disconnecting all the time in such a way that distances as we understand it may cease to exist.

Maybe this is why we can't measure distances below the Planck lengthen. The Holographic principle is one place where we've made lots of progress towards a quantum theory of gravity. There's a catch, though. The ads universe has a different space time geometry than our own.

So while the ads CFT duality is remarkable in its own right, it's not proof that we live on a holographic stage. Instead, you can think of it as a toy model for how space, time and geometry can emerge from entanglement. To make further progress, we have to find a way to extend these ideas to a model describing our universe with its particular geometry, particles and peculiarities like dark energy.

Ideally, we should also find a way to test the Holographic principle experimentally. That's going to take lots of creative new ideas. To me, space and time are two of the most fundamental concepts in all of science. The very language we use to describe nature depends on them.

So if space and time are emergent in some sense not really there, we have to figure out what replaces these concepts. This is the exciting quest for the next generation. There's hardly anything deeper or more inspiring to work on than that.

Science, Technology, Physics, Quantum Gravity, Cosmology, Einstein