Video Transcript
Whatever number we're about to be shown as the maximum energy to break spacetime is not the real number. That number can be manipulated. We can bring that number down by increasing the frequency of our gravitational wave. Here we go. How much elastic energy would be stored inside a single planksiz cube of space just as it reaches the point of fracture? To answer that, we begin with the elastic energy density. Earlier we showed that the energy stored per unit volume of an elastic material is equal to half sigma x* epsilon. And then if we use the definition of young's modulus we can rewrite the energy density as sigma^ 2 / 2 y. The volume of our tiny planksiz cube is equal to the plank length cubed. And so we now have an expression for the okay. So what are we doing here? We are trying to figure out how much energy we can pack into an energon cube. chat. You guys understand transformers? They have transformers in your dimension. Transformers, they drink Energon cubes. I don't know how it works. No one asks. No one ever says they just need the energon cubes for something. Anyway, how much energy can we fit in an energon cube before the energon cube explodes? That's what we're trying to figure out here. Yes, the all spark. Thank you. Appreciate you, Phoenix. Energy density and an expression for the volume. And therefore the total elastic energy stored in the cube will be equal to the energy density multiplied by the volume. And if we sub in our two previous expressions we find the following result. Now we're interested in the instant just before fracture begins. And that means the stress has reached the critical stress value. And so we can write that sigma is equal to sigma subscript c. And so our expression then takes the following form. And if you recall, the Griffith criteria stated that sigma c^ 2 scaled like y * gamma / d. And since we're assuming the smallest possible crack length equal to the plank length, we can write this as y * gamma / l sub. >> Okay, chat. Now, this is a lot of math, but you're about to watch something really magical happen. If you've totally zoned out and you're just thinking about Transformers and Megan Fox, I don't even blame you. I don't blame you. It doesn't even matter. You don't even have to pay attention. Get ready because here comes the answers. P. And then if we substitute this into the elastic energy expression, we find the following result. We now notice that something rather elegant happens. The Young's modulus completely cancels and we end up with half gamma* a blank length square. Look, things are happening. Chat variables things are canceling out. This is my favorite. When when your physics is legit and you'll know because things start canceling out. You're like, "Wait a minute. Things are canceling out. things are getting simple. That's because you just figured something out from first principles. And then since we're only interested in order of magnitude, we can write the elastic energy as roughly equal to gamma* the plank length squ. Now this is a remarkably simple result. It says that the elastic energy stored in a planksiz cube of space at the onset of fracture is simply the hypothetical surface energy per unit area multiplied by the area of one face of the cube. Notice something else. The Young's modulus has disappeared entirely. At first, that might seem surprising. After all, we've spent most of the video calculating the effective stiffness of spaceime, but it actually makes physical sense. You see, for the same strain, a stiffer material stores more elastic energy. However, that same stiffness also raises the stress required to make a crack grow. So, I might have to repeat. So, a more stiff material holds more energy. But if it has more energy, it requires more energy for a crack to grow. This explains why there's this relationship between the frequency and the stiffness of this. And here we look at this. He says this equation is actually really simple. We're just saying take the amount of energy in one imaginary cube and multiply by the total number of cubes and that's the total number of energy. Yeah, that's simple. That's actually not even complicated at all. And those two effects exactly compensate one another. So the elastic energy at the onset of fracture no longer depends explicitly on the stiffness. Everything and so what it's saying is the stiffness of the material no longer even matters. And you're like wait what? Well, why is that the case? Because the more energy you put in there, the stiffer it gets or the less stiff it gets. You get the point is then these things cancel each other out. And so therefore, the stiffness doesn't even matter anymore. Has now been reduced to a single unknown quantity gamma subscript S. But our equation alone cannot tell us its value. However, we can turn the problem around and ask what is the greatest amount of energy that could plausibly be concentrated inside a plank-sized region of spaceime. Well, the natural scale is the plank energy. If too much energy is squeezed into too small a region, its gravitational field becomes so strong that a horizon can form. Well, well, well, that looks quite interesting. If you squeeze too much energy into a cube, a horizon can form and you can see this deformation of spaceime. I mean, this is the exact visual that they're doing to the plane. We don't see it, but this is the exact bending that you would see of the plane getting stretched out to its new location. And when the size of that region approaches the plank length, the corresponding gravitational collapse energy is of order the plank energy. Now, one way of reaching this scale is by considering the concept of power. Power, as you probably know, is simply energy transferred per unit time, which and what did Gary Stevenson say? What did Annie just tell us? power scales to the to the fourth power I believe. So power scales exponentially as well which we can write as P= E overt. Now suppose there exists some fundamental maximum power allowed by nature. So if we can estimate the greatest physically meaningful power and determine how much energy it could deliver over the natural time scale of a planksiz region, we obtain an estimate of the maximum energy available on that scale. So, can we estimate this maximum power? Well, the answer is yes. And for those interested, I've made an entire video explaining how to do this. The link should be at the top of the screen. But for the purposes of this video, we will simply motivate the result by using dimensional analysis along with the speed of >> Okay. Well, we're going to skip ahead a little bit. So, he's we're going to skip ahead to the answer. It's like a few minutes in here instead of watching all this. It's somewhere right around here. Oh, yeah. Okay. We're going to watch this part right here. Perfect units on the left hand side. The units of surface energy are jewels per square meter and the units of plank length are clearly meters. And okay, so you guys love your math. Here you go. We're going to have to do some conversions here. Now, the problem we find when we're trying to equate these two things to figure out where is the energy level by which spacetime will break is that we find out the units of measure aren't the same. Units of measure aren't the same. So, we got to do a little bit of math. Here you go. The units of the entire left hand side are jewels per meter which we recognize as being equivalent to newtons which are the units of force. So the left hand side is a force. More specifically it is the characteristic force associated with breaking a planksized patch of spaceime if spacetime had something like a surface energy. And the so [clears throat] we're now getting to the numbers. The left side here says this is the amount of force that's going to be required to break spaceime. The answer to that is it's going to be less than C to the power / big G. But we have to make a modification first. Inequality says that this tearing force cannot be larger than C to the^ 4 / G. But this combination of constants already has a name. It is the plank force. Numerically it has a value of around 10 44 Newtons. The plank force is closely related to an idea in general relativity called the maximum force conjecture or the maximum tension principle. The idea is that classical general relativity may not allow arbitrarily large forces or tensions. One, so it turns out when you look at this is already the plank force. So it already says, wait a minute, but we're saying the force then has to be less than the plank force, which is essentially the maximum force that physics has already calculated. There's already a conjecture about this force. Now, I haven't double checked, but I'm going to go ahead and guess this is exactly the Schwinger limit. This is exactly how we derive the Schwinger limit and determine the maximum energy density by which spaceime breaks down. Motivation is that attempts to concentrate too much energy into too small a region can instead lead to horizon formation and black hole creation essentially. And there it is right there. Why do I say that? Because it says if you try to put too much energy in there, it can lead to black hole formation, event horizon formation, is that if you go higher than that, now you're manipulating spaceime, you're creating a black hole by which light can no longer escape. Now, this is what we want. And I think that what we found out from the MH370 videos is if you trap light, if you trap light in a mirror and give it nowhere to go except for internally, it finds a new path. It creates a new path. It creates space. This is how the wormhole works. This is how the phase inversion works. When you make your bubble, your mirror, all the light is trapped inside the bubble and it has to go this way. It can't go out. There's nowhere for it to escape. And when it can't escape, it finds a new direction. It creates a new spaceime. It creates a bridge. And that's why it comes out in a different location. And that's where the plane comes out, too. They're just using physics in an intelligent way to trap light. And that's what the wormhole is. And so a lot of people say, Ashton, you've given me all these different interpretations, these theoretical conceptual views of a wormhole. Which one's right? I'd say they all are. It is a macroscopic quantum tunneling event. It depends on if you're looking at it from a quantum perspective or if you're looking at it from a macroscopic perspective. And the bridge between those two theories is er equals epr. Einstein roen bridge macroscopic wormhole is equivalent to Einstein powski roen quantum entanglement quantum tunneling. They're the same phenomenon. Okay, let's go back to it. The geometry of spacetime itself intervenes. So the plank force is sometimes discussed as a fundamental limiting scale in general relativity. A bit like the speed of light is a fundamental limiting speed in special relativity. And so our inequality can be read as follows. If we define gamma times the plank length as the characteristic force scale associated with tearing a planksiz region of spaceime, then that force must not exceed the plank force scale. If fracture is to be energetically possible, but notice what this does and does not tell us. It gives us an upper bound, but it does not tell us the actual tearing force of spaceime or how far below the plank force it might be. It could be close to this limit or it could be many orders of magnitude smaller. So this is what's crazy to me. I think the conclusion here is that this doesn't tell us where the limit is. But it kind of does. It tells us there is not one specific limit. The limit is based on the frequency. If you manipulate the frequency, you're going to lower the swinger limit. You're going to lower the critical limit. You're going to lower the stiffness. But this is what's so surprising about it. If this is true, then how come the orbs aren't spinning around the plane at hypersonic speeds? Why aren't the orbs like like why can we even see them? Why they look like they're moving at a speed which wall fast is still something I can see with my naked eye even on a six. What is it? Six frames per second video. We can still see them spinning around. That's my only question is something must work out with the math by which these things don't have to be spinning around at hypersonic speeds. They found a way where it's like they've hit some kind of resonant condition. Yeah. Yeah. And then JK Phillip says, "Maybe it's because of parametric oscillations where there's a ramping up." Like this is the reason why theoretically that it doesn't just instantly teleport. There's this like ramping up effect. It may be that there's these oscillations that are scaling up higher and higher and higher and then cracking through. There you go. Good input from JK Philly Fan. Okay. I forget. Uh I think there's only one. >> We can nevertheless consider the most extreme case in which the bound is saturated. In other words, we can consider when gamma * blank length is roughly equal to c ^ 4 / g. If we then rearrange for the surface energy, we find the following result. And if we then sub in the values, we obtain a value of approximately 10^ 79 jw per meter squ. This number is almost impossible to comprehend. For reference, >> yeah, this number is crazy. So, this is not really the level to break the swinger limit. I think what is the shringer limit like 10 to the 25? Well, let me let me look up. The Schwinger limit is 10^ the 18 volts per meter cubed or meter. No, 18 moles per uh volts per meter, not cubed, just volts per meter. Uh how does that compare to jewels per meter squared? I don't know. Whatever. We'll find >> the surface energy of glass is only a few jewels per square meter. And for most metals, it is also roughly of order 1 to 10 jewels per meter squared. So what we're seeing here is an extreme upper limit scale for the surface energy of spaceime that is almost 80 orders of magnitude larger than the corresponding values for ordinary materials. But it's important to remember what this means. The argument does not tell us how resistant spacetime actually is to fracture. What it tells us is that the natural upper scale for any such tearing force is essentially the plank force. if the fracture. >> So it tells you right there is it says [clears throat] it may not be meaningful for us to understand where spaceime is going to break but it tells us where the upper limit is and the upper limit makes so much sense. It is the plank force the plank scale. Clearly the plank scale is a very meaningful size scale and this is where we are must be seeing general relativity fall apart where quantum mechanics begins to take over that that really is some kind of limit where if we get to this limit suddenly magic begins to happen suddenly physics as we know it no longer works anymore. And this is the secret to gravity. We say there's something missing. What is it that we're missing? Well, what did I just teach you right here? I taught you that spacetime is really stiff. And this is the reason why we can't manipulate it very easily. But if we increase the frequency, the stiffness comes down by many orders of magnitude. 18 orders of magnitude according to Gary Stevenson. Just by increasing our frequency going up to I think it's gigahertz frequencies. So by changing the frequency going up from LIGO, we significantly change the stiffness of spaceime. We significantly bring down the Schwinger limit. Let's skip ahead to the last clip, 43 minutes. Other words, if we take the effective Young's modulus and multiply by the plank length, we obtain a comparable energy per area scale. And we can then ask at what frequency this becomes comparable with the surface energy scale. Now, if you recall, we found earlier that the effective Young's modulus takes the following form. So, let's now sub this into our new relation. And then when we do this, we find the following expression. So, here we go. We got our Young's modulus, our stiffness of spacetime. There's our equation with our frequency guy in here. And now on the right, uh I don't know, we took some other Young's modulus. And now we're going to calculate it and we're going to figure out, okay, what does this mean? So, now we can finally ask our question. What is the frequency at which the two scales become comparable? To answer this question, we simply rearrange for frequency and we find that it scales as the square root of gamma * G / C^ 2 L. And then if we take the expression for the surface energy that we derived earlier and sub this in, we get the following expression. And then if we simplify, we end up with C / LP. Now, if you recall, the plank time was equal to LP / C. And so we see that the frequency that naturally emerges is equal to one over the plank time, which is none other than the plank frequency. Okay, we're going to need to pull Annie in here. I don't know what just happened, but all the numbers just simplified. All the numbers simplified and the plank frequency came out. And he said the cutff point is the plank frequency by which these two scales the surface energy and the stiffness of spaceime correlate to one another which is of order 10 ^ 43 hertz. So if we ask when the young's modulus scale from gravitational waves oh so this is when the two scales change. So when we get our frequency up high enough when the frequency gets tough to 10 to the 43 that's where everything breaks down or something like that something like that we'll pull Annie in in a second chat is comparable with the surface energy scale from fracture mechanics the answer is only when the disturbance frequency is comparable to the plank frequency ordinary gravitational waves such as those detected by LIGO are nowhere close to this scale. So >> okay yes so that is what it means. So it means what I just said, which is that normal gravitational waves 100 hertz are nowhere near near the scales where you're going to see space-time manipulation. Where are you going to see spacetime manipulation? He's saying you're not going to see it till you start to get to these really really high frequencies. Now obviously we know there's other methods to bring it down even more than that. But this is also like what JK Philly fan saying in the chat. This is what Salvador Pis has been saying over and over and over again. He says, "Look at the equations. They show a scaling with frequency." Look at that. That's the whole reason why we're doing the live stream tonight. I'm just going to grind this into your head. The stiffness of spaceime goes down as frequency goes up. So maybe we should be messing around with high frequency electromagnetic waves.