 Hello, and welcome again to my backyard, where we'll begin our video book How Fast Is It. We started here in the first video book How Far Away Is It, where we went from my backyard to the furthest reaches of the visible universe. We started here again when we did How Small Is It, which took us down to the smallest things that exist. In this video book, we'll start with the things in our backyard, snails, people, birds, and move on to faster and faster things, all the way to and including the speed of light. Along the way, we'll cover how we measure things like the speed of sound, the speed of light. We'll start with the lowly snail. Here we see a snail making good time across the tile. We can measure the distance traveled and the amount of time it took. We define speed as the distance divided by the time. Here we have 14 centimeters traveled in 35 seconds, that's 0.4 centimeters per second. If we plot this on the time versus distance graph, with time in seconds for the vertical axis and distance in meters for the horizontal axis, we see that slow is a very steep slope. Standing still would be straight up. Here's a wild tiger angelfish. They have been seen to move at around 1.3 meters per second. Of course, people can move a lot faster than this. The fastest man alive is Jamaican Usan Bolt, who ran the 200 meters in 19.19 seconds, or 10.4 meters per second, but that's slow compared to cheetahs. They're the fastest mammal, topping 27.8 meters per second, that's 100 kilometers per hour. But the peregrine falcon puts that to shame. They are the fastest animal on the planet, soaring up to 389 kilometers per hour. That's 25,000 times faster than the snail. Graphing these speeds against the snail's almost vertical line shows how horizontal lines can get at faster velocities. Of course, we have cars that can travel faster than any of these animals. Arthur McDonald was one of the first to capture the land speed record at Daytona Beach in a nap year, back in 1905. It set the record with 168.4 kilometers per hour. Malcolm Campbell took the record in 1935 in his bluebird. It recorded a top speed of 484.6 kilometers per hour. Craig Bridlove streaked his jet-powered spirit of America across the western Utah desert flats, October 13, 1964, to set a whirl land speed record of 754.3 kilometers per hour. Gary Gabelik smashed the record at Bonneville Salt Flats with the blue flame, reaching the record speed of 1066 kilometers per hour. And in 1997, Andy Green drove the thrust SSC through the sound barrier to 1,228 kilometers per hour. This is the current world record for ground speed. Let's listen to what breaking the sound barrier sounds like. To graph these speeds, we recalibrate the x-axis intervals from 1 meter per mark to 100 meters per mark. Now that we're talking about the speed of sound, let's take a closer look at just what sound is and how fast it travels. An elastic substance is one that returns to its original shape after having been disturbed, like this ball. And any elastic medium doesn't, like this pizza dough. A disturbance in an elastic medium will propagate through the medium. Air is an elastic medium, and sound is a disturbance that moves through it. Sound waves are compression waves. These are waves where the disturbance moves along the line that the wave moves. In this animation, each dot represents an air molecule. As the surface on the left moves in, the nearest molecules are compressed. When it moves back, the compression area becomes rarefied. The compression, followed by a rarefaction cycle, moves to the right. How fast the wave moves depends on the characteristics of the medium. In particular, the higher the resistance to compression, its compressibility, the faster the movement. And the closer the molecules are to each other, its density, the slower the movement. In dry air at 20 degrees centigrade, that's 68 degrees Fahrenheit, the speed of sound is 1,236 kilometers per hour. Chuck Yeager was the first to break the sound barrier in the X1. In October 1947, he reached 1,100 kilometers per hour. We use Mach numbers to signify the multiple of the speed of sound a vehicle travels. This was Mach 1.06. The Lockheed SR-71A Blackbird set the current world's record for jet aircraft at 3,530 kilometers per hour in 1976. That's Mach 3.3. The fastest rocket-powered manned aircraft was the X-15. It set the record at 7,258 kilometers per hour in 1967. That's Mach 6.7. To graph the speeds these cars and aircraft have achieved, we'll need to adjust the units on the X-axis again. This time, we'll make each interval on the X-axis equal to the distance sound travels in air in one second. That's 341 meters. The line at 45 degrees that divides the area in half is the line that represents the speed of sound in air. We're now getting close to as fast as humans and machines can move. The last three we'll cover are all spacecraft. Apollo 10 reached 39,896 kilometers per hour in 1969 as it paved the way for manned spacecraft landing on the moon. I remember watching this launch. The New Horizons spacecraft was launched in 2006, headed for Pluto. It is traveling at 58,536 kilometers per hour. The record for unmanned spaceflight as measured relative to the Earth. It started sending back never-before-seen pictures of Pluto in July 2015. Helios A and Helios B are a pair of probes launched into orbit around the Sun in order to study solar processes. Launched on December 10, 1974, on January 15, 1976, the probes were notable for having set a maximum speed record for spacecraft at 252,792 kilometers per hour. But this speed is measured relative to the Sun, not the Earth. At these speeds, we have to increase the distance intervals again. We'll set them at 10,000 meters per mark. Helios is moving 204 times faster than the speed of sound in air and 17.5 million times faster than the snail in my backyard. All our speeds so far, except for the last one, was relative to the surface of the Earth. In the time before we knew the Earth was spinning on its axis once a day and rotating around the Sun once a year, everyone thought that the universe had a preferred frame of reference against which all other speeds could be measured. That preferred frame was the Earth, the center of the universe. But once Galileo spotted the moons around Jupiter, another approach was needed. We'll use a train example. Let's measure the speed of the person walking on the train. We'll use the same measuring technique we used for the snail. The person on the train sets his clock to zero, marks his starting spot, walks down the car, stops the clock, and marks the second point. Now he just measures the length of the line and divides by the time. In this example, he went 3 meters in 5 seconds, for a speed of 0.6 meters per second. Now picture the train car moving slowly to the right at 2 kilometers per hour, or 0.56 meters per second. This is the speed as measured by a person on the ground. We then repeat the measurement for the observer on the ground who is watching the train go by. He sets his clock to zero, at the same time the rider on the train does. He marks the rider's starting spot. He watches the rider move down the moving car. He stops the clock when the rider does, and marks the second point. Now using the same process, he just measures the length of the line and divides by the time. In this example, the rider went 5.8 meters in the same 5 seconds, for a speed of 1.16 meters per second. Who was correct? Is he moving at 0.6 meters per second, or almost double that speed, at 1.16 meters per second? In the old system before Galileo, you could argue that the observer on the ground was correct. But in the actual world of equal reference frames, both are correct. In fact, we could have done it from the point of view of the train instead of the person on the ground. In that case, it is the person on the ground that is moving at 0.56 meters per second to the left, instead of the train moving to the right. If we put this on our space time graph, we see the train moving as the inertial frame velocity v' and the person walking with the velocity 1.1 meters per second. Now just rotate the velocity lines to make the train standing still. This turns it into the space time graph, the train's frame of reference. Here we see that the ground is moving backwards, at 0.56 meters per second, and the person on the train is moving at 0.6 meters per second. With this in mind, to be completely accurate, the statement needs to be worded as the person on the train is moving at 0.6 meters per second with respect to the train. The person on the train is moving at 1.16 meters per second with respect to the ground. You can see that we are simply adding the speed of the train to the speed of the person with respect to the train. This is the Galilean transformation, between two reference frames moving at constant speed with respect to each other. These are called inertial frames because they are not experiencing any acceleration. In this model, time flows at the same rate in all inertial reference frames, and all motion is relative. The Galilean transformations give us the equations for converting from one frame to another. Let's look at another example. Here the train is moving faster at 25 meters per second. The person on the train kicks a ball in the direction of the train movement and measures its speed at 10 meters per second. The person on the ground would add this to the speed of the train and gets 35 meters per second. Now if the person kicks the ball in the opposite direction, the person on the ground would subtract the speed of the ball from the speed of the train. He would see it moving at 15 meters per second. Here's another example that illustrates that it doesn't matter what is moving. Suppose the person on the train kicks a water container, initiating a sound wave in the water moving in the direction of the train. He would measure the speed of sound in water as being the same when he kicks it forward and when he kicks it backward. The speed of sound in water is around 1,484 meters per second. The person on the ground would measure the forward moving wave at 25 meters per second faster than that, and he would measure the backward moving wave at 25 meters per second slower than that. It followed that if it were a light bulb that the person on the train turned on, he would see the light moving in the direction of the train and the light moving in the opposite direction of the train to be the same speed of light. But the person on the ground would measure the light moving with the train at 25 meters per second faster than that and the speed of light traveling against the movement of the train at 25 meters per second slower than that. This view stood the test of time from Galileo until the mid-1800s because no one could measure the speed of light and no one had instruments sensitive enough to measure the small differences in the speed of light. Then, in 1849, a French physicist named Antonio-Louise Friseux did measure the speed of light. He repeated an unsuccessful experiment conducted by Galileo in the 1630s. Galileo's method was quite simple. He and an assistant each had lamps which could be covered and uncovered at will. They climbed to the tops of hills around 1.5 kilometers apart. Galileo would uncover his lamp and as soon as his assistant saw the light he would uncover his. By measuring the elapsed time until Galileo saw his assistant's light, factoring in reaction times calculated earlier and knowing how far apart the lamps were, Galileo reasoned he should be able to determine the speed of light. Given how fast light is, we know that the time interval Galileo was trying to measure was around five microseconds. The clocks available to him at that time could not measure that tiny a time interval. His conclusion was that light was very fast, if not instantaneous. As Galileo had done, Fitzhugh chose two high points, but in his case they were a good deal further apart at just over eight and a half kilometers. In place of covering and uncovering lanterns, he used shining light through the edge of a toothed wheel. Whether the light beam got through the edge of the wheel depended on the wheel's position. If one of the gaps was in front of the light beam, it got through. If one of the teeth was in front of the light beam, it was blocked. To avoid the problem of human reaction time, Fitzhugh placed a mirror on the far hill instead of a person. He also added a partially reflected mirror to guide returning light to his eye. When Fitzhugh set the wheel spinning at slow speed, a flash of light that shot through one of the gaps would travel to the mirror on the distant hilltop, get reflected and travel back to Fitzhugh so fast that the gap was still in place. The wheel had not had time to move a tooth in the way of the beam of light to block its return. Fitzhugh then increased the speed of the wheel until the light moving through each gap of the mirror and back encountered a tooth instead of the gap on its return. This blocked the light from getting to his eye. Fitzhugh continued to make the wheel spin faster until eventually the light would shoot through a gap and by the time it traveled to the mirror and back, the tooth had moved completely across the line of sight, the beam of light returned just in time to move through the next gap and he could see it again. In super slow motion, it would look like this. Knowing the number of teeth and the rotation rate, Fitzhugh could calculate the time it took for one tooth to move out of the way of the returning light. Dividing the distance by the time gave him the speed of light at 313 million meters per second. He was only off by 4%. Today we beam laser light through a vacuum and measure the timing with atomic clocks. Here is the current number. Wheel round to 300 million meters per second. In 1881, a physicist named Albert Michelson found a way to measure extremely small differences in the speed of light. This is precisely what we need to verify the Galilean transformation for light. This basic idea revolved around light interference patterns. For example, if we combine two waves that are in sync with each other, they reinforce the output wave. As we shift one of the input waves, we see the output deviate from the maximum reinforcement. As we reach one half of a wavelength out of sync, we get total destructive interference. The waves in effect cancel each other out. If we keep going, we move back into complete constructive interference as we reach one full wavelength. What Michelson did was to leverage this light interference behavior in what we now call an interferometer. Here's one from the MIT physics lab. A light source shines light into the interferometer where it is split and reconstructed using mirrors. The reconstructed light shows up on a screen. The bright lines indicate areas of constructive wave interference, and the darker lines indicate areas of destructive wave interference. Moving the mirror changes the position at which the light constructively and destructively interferes. Here's how the light flows through the apparatus. The incoming light source is split into two by a partially reflecting mirror. These two beams then reflect off of mirrors and recombine at the splitting point. If the distances traveled are exactly equal, they will be in sync when they recombine. This produces the maximum constructive interference. The main fringe has been marked with tape to help keep track of any shifting. If we move one of the mirrors by one quarter of a wavelength, that wave will have traveled one half of a wavelength less distance than the other one. This produces the maximum destructive interference. You can see the shift in the fringes from the bright to the dark. As we continue to shorten the wave to the point that it travels one whole wavelength less than the other one, we return to being in sync and get back to maximum constructive interference. The fringe pattern has now shifted one full fringe, producing a pattern just like the one we started with. As we continue to shorten the path for the split wave, we can count the number of fringe shifts. In our experiment, we shortened the wave by 65 micrometers and produced 10 fringe shifts. A simple division gives us the wavelength. So knowing the distance and counting the shifts gives us the wavelength. But as we'll see shortly, the important thing for us to note is that knowing the wavelength and counting the shifts gives us the distance the split wave was shortened. In 1887, Michelson teamed up with Edward Morley and published the results of their experiment that used an interferometer to measure the differences in the speed of light from platforms moving in motion with respect to each other. We'll spend a little time here going over how they did it. Since 1801, when Young proved that light traveled as a wave and throughout most of the 19th century, it had been assumed that space was filled with a substance called the ether to support light propagation, just like air supports sound wave propagation. The ether represented the universal frame of reference against which all other motion could be measured. The question at the time was, how fast is the ether moving? Or more precisely, how fast is the earth moving through the ether? Michelson and Morley were trying to answer this question with their experiment. A good way to see what's happening is to picture a river that measures d across and is flowing to the right with a speed V. Now we put two boats in the river, each moving with a speed lowercase v. One boat will move across the river to a point on the other bank directly opposite the starting point and then return. The other boat will travel downstream the distance d and then return to its starting point. We'll calculate the time required for each round trip. Let's take a look at the boat going across the river. If the boat headed directly to the destination point, the current would take it downstream and it would miss its target. To compensate, the upstream component of its velocity would have to match the flow velocity of the river. This would give us a right triangle, where V' would be the net speed across the river. We can calculate V' by using the Pythagorean theorem. The same analysis works for the trip back, so the time for the round trip can be calculated as twice the time for one way. That's two times the distance divided by V'. Substituting the value for V', we get the final equation. Now let's take a look at the boat traveling down the river and back. The time it takes to go the distance d is simply d divided by the speed of the boat plus the speed of the river. The trip back takes d divided by the speed of the boat minus the speed of the river. Using the common denominator to add these two times gives us the time it takes to make this round trip. Let me take a quick aside here, because this is a good equation for illustrating how we use math and physics. Notice that if the speed of the river is greater than the speed of the boat, time goes negative. If we took the equation to be a general statement about time, one would conclude that time can flow backwards. But if we stick with the situation that we use to develop the equation, we see that a negative time simply means that the poor slow boat can never get back to its starting point. The river will simply continue to carry it downstream. Now back to our example. If we take a look at the ratio of the cross river time, p sub a, to the down river time, t sub b, we see that it creates an equation that can be solved for the velocity of the river. For example, if the boat speeds are 25 kilometers per hour, and we carefully measure the time of the two round trips to be 10 minutes for the cross river round trip, and 15 minutes for the down river round trip, then we can find the river flow. In this example, it's 8.68 kilometers per hour. Michelson and Morley understood that the earth is moving through the ether in different directions at different seasons. In our segment on the solar system, we found that the earth is revolving around the sun at 30 kilometers per second. What Michelson and Morley did was to measure the ratios for light traveling with the ether and across the ether to determine the speed of the ether, just like we did for the boats in the river. Here's the apparatus they used. It worked like the one from MIT. Only it's mounted on a stone slab and floating in a pool of mercury to allow for slowly rotating the interferometer. Here's the actual interference pattern they saw. As the interferometer is rotated, the light flowing perpendicular to the direction of the ether would take time t sub a, and the light flowing with and against the ether would take time t sub b. Rotating the interferometer would change the ratio from t sub a over t sub b to t sub b over t sub a, and the interference pattern would shift. Using the speed of the earth through the ether, they estimated that the shift in the pattern would be just under one half of a fringe, but there was no shift. When the experiment was performed at different seasons and at different locations, the results were the same. No shift. Initially, the fact that there was no shift was viewed as a failure by Michelson and Morley to measure the velocity of the ether. And on reflection, scientists started asking some very fundamental questions. Is there an ether? How can we add the velocity of light and the velocity of the platform and come out with the velocity of light? Are the Galilean transformations wrong? And for us, in this video book, a big question was, does the fact that the speed of light is a constant mean that it is also a speed limit, and nothing can go faster than that? These are the questions we'll address with Einstein's theory of special relativity in the next segment.