 So, I'm watching a drop fall into the water in my sink, and I notice it produces a circular wave that expands symmetrically outward from the point where the drop hit the water. Wanting to see this phenomenon on a larger scale, I go to the shore of a large body of water and throw in a rock. And I watch as the circular wave expands cementi- Eh? Huh? Wait a minute. It's not symmetric. It's expanding faster to the right and to the left. Why, the wave isn't even centered on the point where the rock entered the water. Aha! Of course. Yes, Sherlock. The body of water must be moving to the right. Indeed, if I wanted to see a symmetric wave, then I should have followed the current along the shore. And from that point of view, the ground would appear to move, but the water would appear to be at rest. In that case, the wave would have expanded symmetrically from a fixed point of entry. That is the unique frame of reference from which to quote-unquote properly view a water wave. Okay. So what does that have to do with the theory of relativity? Well, just about everything. There's a curious ambiguity in classical mechanics. Although in daily life we generally consider how things move relative to Earth, the laws of mechanics don't define any ultimate frame of reference. In fact, let's consider the following mechanical interaction between, oh, I don't know, say, a ping-pong ball and paddle when viewed from three different cameras, or we'll call them reference frames. Case one, collision viewed by a camera that's stationary with respect to the paddle. The ball's speed before and after the collision is the same, hence the kinetic energies of the two objects don't change, and there's no kinetic energy transfer. Case two, the collision is viewed by a camera that's moving to the right relative to the paddle. The paddle appears to give the ball a whack and cause it to move faster after the collision than before, and so in this reference frame it appears that kinetic energy has been transferred from the paddle to the ball. In case three, the collision is viewed by a camera moving to the left relative to the paddle. From this point of view, it appears to be the ball that's doing the whacking with the result that the ball's speed after the collision is less, and hence it appears kinetic energy has been transferred from the ball to the paddle. So it's obvious which camera recorded the real event, right? I mean, you can't have energy being transferred from the ball to the paddle, and from the paddle to the ball, and at the same time, no energy being transferred at all, right? I mean, obviously, physics should tell us what really happened, right? Nope, this is an example of Galilean relativity, first described by, well, Galileo in 1632. If the laws of physics work in one reference frame, then they also work in any other frame that's moving uniformly in a straight line relative to the first frame. The fact that different observers can have different interpretations of the same physical event doesn't mean one's right and one's wrong, just right in their own particular frame of reference. There's no single correct interpretation. If you're flying at near the speed of sound, you are quite correct to say that your cup of water is, quote, at rest. True, it's blazing across the sky, according to people on the ground, but it stays put on your fold-down tray, just fine. It's at rest relative to your perfectly valid frame of reference. Einsteinian relativity builds on the Galilean version, so let's get this one under our belt first. We typically take this piece of the puzzle for granted, since we have day-to-day experience with it, it seems intuitive, but if it seems bizarre that Einstein showed that the interpretation of time depends on your frame of reference, keep in mind that Galileo had already showed us that the interpretation of energy transfer and a collision also depends on your frame of reference. Suppose you and your fellow Latins place a frame of reference at rest in space, which allows you to determine the respectable Latin coordinates x and y of any given point, and let's say you also have a clock that tells you the time t. Along come some troublesome Greeks with their own coordinate system moving to the right along your x-axis with velocity v and labeled with the quite tacky Greek letters xi and eta, and they even have their own clock and they call the time tau. You find that t and tau agree and y and eta agree, but their xi coordinate is a mess. You explain that they need to add the velocity of their reference frame times the time to their xi values to get the true at rest x values. You even make a plot of space versus time, a space-time diagram to illustrate the Greeks problem. If an object is at rest at position three at time zero, then at, let's say, time four, it'll of course still need to be at position three. It's at rest after all. But the Greek frame is moving, so constant xi values, the red lines here, actually correspond to moving points. It's not at rest. You explain that if at time zero an object was at x equals three and xi equals three, then at time four to have remained at xi equals three would need to be moving with a velocity v, along with the Greek reference frame, but a truly at rest object, which at time four was still at x equals three, would actually have a xi coordinate less than three. This is very clear. Imagine you're surprised when the Greeks explain that, excuse us, but we are the ones at rest and you upstart Latins are actually moving to the left with velocity v. It's your x coordinate that's messed up. To get the proper at rest xi value, you obviously need to subtract off your frame's velocity v times the time. You're particularly shocked when they show you a space-time diagram that shows your Latin coordinates as the moving frame. You argue back and forth about who is really at rest, but every mechanical experiment you cite, the Greeks can turn around and interpret it to show that they're the ones at rest. It eventually dawns on all of you that there's no way to demonstrate that you're at rest in space because space is not a thing. You can't measure velocity with respect to a non-thing. No. Velocity, including zero velocity or at rest, is a relativistic concept that has no absolute meaning. But then a light goes on in your head. Well, not that kind. Yeah, no, that's better. And you recall your rock in the water experience. Wave phenomena do define the unique reference frame, the one that's at rest with respect to the oscillating medium. And since it's the late 1800s, and there's abundant experimental and theoretical evidence that light is a wave phenomenon, you propose to use an optical version of the rock in the water experiment to establish the one, the only, universally at rest reference frame. Now, there is something that gives you pause. In a water wave, you know that water is the stuff oscillating, and in a sound wave, air is the stuff oscillating. But in a light wave, what exactly is the stuff that oscillates? Unlike sound waves, light waves obviously propagate through, quote, empty space. So the oscillating stuff can't be any known material. But you say, even if we don't yet know what it is, there's got to be something doing that, quote, waving, right? I mean, that's just common sense logic and reason. So let's just call it the luminiferous ether and try to find the reference frame at rest with respect to it. So you call up your respected colleagues, Michelson and Morley, and you ask them to devise an experiment to measure velocity relative to this luminiferous ether. Their elegant solution, the so-called Michelson interferometer, sends a light wave out from a central point, the magenta dot here, like the rock hitting the water. And this wave is reflected from two mirrors that are at the same distance, but in different directions. If the apparatus is at rest relative to the ether, the waves will be symmetric, and the two reflected waves will strike the central point at the same time. However, if the apparatus is moving relative to the ether, the waves will not be symmetric just as in the water experiment we saw before, and the reflected waves will strike the central point at different times. By measuring the difference in times of these reflected waves through a process called interferometry, this apparatus can therefore definitively measure velocity through this luminiferous ether. And we know that at least sometimes the earth has to be moving relative to the ether, because it orbits the sun. So whichever way it's moving today, it'll be moving the opposite direction in six months. Anyway, Michelson and Morley set up a practical implementation of this interferometer, and they make measurements over an extended period, and the results, published in November 1887, failed to detect any motion of the earth relative to the supposed luminiferous ether. Fast forward to the 21st century, where supersized Michelson interferometers operate 24-7 as the laser interferometer gravitational wave observatory. And although they were built for another purpose, a byproduct is that they run continuous 24-7 Michelson-Morley experiments with mind-boggling precision, and we still haven't seen any evidence for a moving ether. If we had, it would have meant that the speed of light would have been different in different directions and in different reference frames. But the negative result of the Michelson-Morley experiment instead suggests that the speed of light is the same in all directions and in all inertial reference frames. And there is no evidence that light is the oscillation of some medium that would define a unique reference frame quote at absolute rest. This experimental fact just put our quote common sense logic and reason in the trash. Consider our two coordinate systems from before, and imagine we send out a flash of light at time zero when their origins coincide. If the speed of light is the same in both frames and in all directions, it means that as time goes on, the objects perceive their origin to be the center of the same expanding wave, even though those two origins are moving apart. How can two different circles be the same physical object? Or how can one circle have two different centers? Based on our day-to-day intuitive ideas of space and time, these concepts are totally absurd, and yet the Michelson-Morley experiment tells us that in some sense, this is just how things are. In the next video, we'll see how through this bizarre turn of events, a young Albert Einstein perceived a fundamental property of nature, the principle of relativity. The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations and mechanics hold good. While in first glance, this may not seem to say much, the theoretical implications forced a profound change in humanity's understanding of space and time and energy and mass. That is a basic physical reality.