Okay, lets begin a little thought experiment. Lets suppose i take a baseball. We have a baseball playing game and i throw a baseball to you. No, i dont throw it to you. I have a Little Machine that throws a baseball. You ever see those things . And that machine can only throw the baseball at 30 meters per second. Thats how fast. 30 meters per second. Its all regulated to throw that fast. Now, its gonna throw a ball to you. You got your catchers mitt. Hit, boom, you catch. How fast do you catch it . 30 meters per second, right . Thats because the machine is at relative rest to you. Theres no motion between you and the machine. So youre gonna catch it at 30 meters per second. Now, lets suppose you are in a truck and the truck is going that way at 10 meters per second. 10, get that . I throw the ball just like before. You catch it. How fast its going . Well, check your neighbor. Youre going away. Youre moving away from it. Faster or slower, gang . Slower. In fact, whats the answer . 20. Youre gonna catch it at 20, 20 minutes per second, right . Aboutish . Lets suppose you turn the truck around and you come toward the ballthrowing machine and the ballthrowing machine throws just like before to 30, but youre now moving this way at 10 meters per second. When you catch the ball, that balls gonna hit your glove at what speed . 40. We can do that, right . And if you got outside and you did that and you found out that when you traveled away, it hits slower and when you travel to it, it hits faster, you would not be surprised. You would expect that and there might be some quibbling, does that really come out to be exactly 30, exactly 40. But you know, if theres a speed how about if we did this really and no matter how you moved, every time you caught the ball, you still caught it at 30 meters per second . Whether youre racing toward the machine still, or racing away from the machine. And you know that machine can only throw at 30 and every time you catch it, you catch it at the 30, how about it . Would that be a little wild, huh . Well, that would really be wild. That can shake you up a little bit. You start to say, wait a minute. Am i dreaming . Something wrong here, right . Well, let me tell you a similar thing happened, gang. A similar thing happened just before the turn of the century, 1800s. It turned out they found out that light has the same speed for all observers, whether the light source is coming to you, away, or whether youre moving away, make no difference. Every time the speed of light was measured has the same value 300,000 kilometers per second. And every measurement showed it to be the same. When the earth is racing toward the sun or toward a star or something, the same speed six months later when its racing away, same speed all the time. This had a lot of people upset. The Physics Community was starting to shake a little bit. And about this time, there was a fellow who was going through school. At the age of four, he could hardly talk. In grade school, he did not really stand out too much, but he plugged away. An uncle gave this fellow a compass on his ninth birthday or Something Like that. He says, how come the compass always point north . And the uncle says, well, thatsit always points north. The young fellow says, well . And the uncle says, i wont be knowing such thing. I mean theres probably no reason for that. Compass is just pointing north, okay . Im making this up a little bit, yeah . But it turns outwho are we talking about now . Albert einstein. Albert einstein. And Albert Einstein went through school. Oh, he took algebra in high school and flunked. Hey, dont knock it. Some people pass, some people flunk. I mean hes just one of the ones that flunked, okay . Dont make a deal of it. And some people get a High School Diploma and some people dont, right . Some can hack it, some cant. Right . Well, einstein couldnt hack it. Thats all right. You know, you can still make it. No High School Diploma, gang. And hes out there and it turned out that he met a young lady who influenced him to go back to school. So he tried going back to school. Took the entrance exams and flunked. And he flunked the exam. Hey, i mean he cannot not everybody passes everything, huh . And then he studied hard and he took the entrance exams again and passed. Turned out he had trouble with the french language. You know, in europe they speak all these languages. He couldnt do the french so well. Anyway, Albert Einstein went through school and he did go all the way and got his ph. D. Got his ph. D. In physics. And about this time, he had a hard time getting a job. His thinking was a little bit well, for one thing, he didnt have a high regard for many of the ideas at the time. You know, we always name the streets after military heroes, you know, and if someone really butchers millions of people, man, they put a big monument up for him, right . Einstein thought that was kind of upside down. That we werent choosing our heroes very properly. You know, he had kind of funny ideas. Anyway, he wasnt too popular and had some trouble getting a job. But he did get a job with the help of his lady friend again. And he get on at the patent office, i guess, in switzerland, going over patents that were being submitted. And heres a guy with his ph. D. In physics and all that. Anyway, he was interested also in light. He asked a teacher one time, what would a light beam look like as it goes by . Teacher was, well, its going too fast, you cant see it. You know, what if you go along with it and take a look . What do you mean, what if you go along with it and take a look . Well, how would it look . Will it be a little squiggly wave . What it would look like . Hes all the time asking questions like that, never getting any answers. And he was wondering about the bit with light light having the same speed for all observers. Its a matter of some history whether he knew about the experiments by michelson and morley you read about that that told that light speed was the same for all observers. Its even questionable as to whether he knew about that experiment. But the more he thought about light, the more he realized that if you did travel with light, it would look just as if you were at rest and everyone ought to see the speed of light traveling the same, regardless of their motion. And heres some of the reasoning that kind of went into that. Lets look at what speed is, by definition. What is speed . See, the speed of lights the same for everyone that measures it. Whats speed . Its a distance compared to time. Distance through what . Space. Okay. So, its really space compared to time, see . We measure it kilometers per hour, okay, meters per second, okay, space per time. And einstein realized that the reason the speed of light is constant in some instance perhaps maybe more space should traveling, in which you travel through, then corresponding that more time will be taken. And if something happens where maybe he puts only a small bit of space, because of motion, then the time will be smaller in turn. Einstein realized that the ratio of space to time for light would be constant, like the ratio of the circumference of a circle to the diameter. For a big circle. A little circle, boom. That ratio is a constant. And einstein felt that these two were related. Who would think that what time it is on your clock would be related to like space, as we know it . Space and time. Einstein said that if you travel through space, youll also travel through time. How . Such that the ratio of space to time for light will be constant. So, we do know the speed of light is a constant and thats one of the postulates of einsteins special theory of relativity. Everyone who measures the speed of light will get the same value. Now, that has some interesting consequences. Lets try a little thought experiment here. Im gonna throw this piece of chalk up in the air. Now, were all observing whats happening here. Lets suppose we made measurements as to the speed of the chalk. In this case, it varies, because its going quickly here, slow, slow, slow, and its accelerating, okay . So, we just kind of fudge it up a little bit. Lets talk about the average speed. We would get the average speed by taking the distance divided by the time. That would give us the average speed. And lets suppose every one of us makes careful measurements and we all get the same average speed, okay . But heres the postulate, that no matter how i move, we will still all get the same average speed. Well, right here, this is not controversial. You see it go up, you see it go down. You see it go through that particular space and you measure on your watches that particular time. I measured the same thing. I measured the same space, i measure the same time. We all get the same value. Im gonna repeat. This time, im gonna move. Im gonna look at it and you look at it. I see the same thing as before. I saw the same thing as before, okay . I saw it go straight up and straight down. Get into an airplane and flip a coin. Whats the path . Straight up and down, right . Now, get outside the airplane and look at the path. Whoosh, whoosh. Okay . You guys saw this. Watch again. You guys saw it go like this. Now, if you get the same speed, you dont, you really saw it moving faster. But if you got the same speed, if you did, if the speed is the same and the space is admittedly bigger, then the only way you can get the same speed, gang, is if you get a longer what, beginning with a t . Time. And so your witnessing of that event, your timing of the event and my timing of the event, would be different. A lot or a little, begins with a l . Lot. No. A little bit different. A little bit different, okay . But i exaggerate the figures. Ratios the same. Einstein could see that somethings funny going on with light too. Because take this example, einstein at one time is sitting in a cable car, hes gonna cable car through the streets and looks up and sees the village clock. And every village always has a big tower and a big clock in there, okay . And the clock says and the clock says 8 00. Okay, that means the little hands on the 8 00 and the big hands on the 12 00. Did you hear me . Okay . Now, einstein is sitting there. He says, what does it mean to say the clock reads 8 00 . What it means is that light is bouncing off the clock and coming down and giving me information, 8 00. If its midnight and theres no lights around and the moon is out, hes not gonna see anything. But its in the daytime, in the morning, yeah . So he sees 8 00. Einstein wonders, wow, 8 00, boom, hit me like that. What happen. I move my head . Wont the 8 00 keep going . Now, the 8 00 had pssh. Meeting some guy way, way down there, who later on, boom, says, its 8 00. Now, its 8 00 when it passed me. But how about some guy way, way down there . Uhhuh . How about some guy in some planet way, way out there . It takes time for that 8 00 information to move. Isnt that true . When light leaves the sun, you know how long it takes to get to us . Eight minutes. The sun is eight light minutes away, gang. Eight minutes away, you see. Okay . So, anyway, einstein what if that 8 00 information keeps going . Now, what if this cable car started to try going on with it . And what if this cable car went as fast as light goes and the cable car keeps going out, occupants in the cable car would look at the clock and theyd see what, gang . How would they see the clock . What would the clock say . Eight, eight, eight, eight, eight, eight, eight. He would see time frozen, at least the clock. Is that understandable . You see . So hed see the time completely frozen. So einstein realized if he stays still, he can watch that clock do its thing, at the rate that we call 24 hours per day. 12 hours it makes it comes all the way around one time, yeah . But einstein realized if he moves as fast as light, then he sees it frozen. Now, often times, when youre thinking about ideas, its nice to look at the extremes. Hes looking at the extremes there. One extreme is zero speed, what do we see . The ultimate speed, what do we see . And theyre quite different. Now, whats in between . Whats in between zero and the speed of light . Do we see the clock slowing down . Do we see the clock running a little slower . How about it, gang . Check your neighbor. If you went like near the speed of light, but not quite the speed of light, would you see the clock running just as fast, if you stayed still . Think about that and discuss it. How about it, gang . How many say, yeah, i think it would go slower . I think we would see it going slower anyway. From our frame of reference, we would see the time slower. Yeah. Thats right. I wanna talk to you about the twin drip, which is discussed in the book, but i wanna preface something. I wanna preface that trip with a little hardcore physics. Pay attention, gang. Lets suppose someones standing on a planet here and they have a flashlight and they shine a flashlight off to a distant planet over here. And people on this distant planet are gonna have a telescope all lined up here and theyre gonna stand right here and theyre gonna watch the flashes of light. And lets suppose a person here emits a flash of light every three minutes. This little flash, flash. I got a question for you. If theres no relative motion between the two planets, its gonna take some time for that first flash to get up here. But under zero gravity here, boom, sees a flash. How long theyre gonna have to wait for another one . Three. And the next one . Three. And the next one . Three. Theyll come at regularly spaced intervals, all right . Now, lets suppose i have a rocket ship thats traveling at a very, very high speed between the two planets. Now, this rocket ship is traveling away from the planet, the source of light. Will that rocket ship see the flashes as often as three minutes apart or more compressed to more often than three minutes apart or kind of stretched out . Check your neighbor. See, the rocket ship catches this flash. If the rocket ship waits here, this flash will come by in three minutes. But the rocket ship doesnt wait there. The rocket ship travels up here. So that threeminute flash is gonna be stretched out a little bit. Do you see that . So the flashes will be seen less frequently, same speed, but less frequently. Difference now, okay . Lets pretend that the rocket ship travels so fast that the rocket ship sees the flashes six minutes apart. Can we see that that could be the case . Okay, so the rocket ship sees them six minutes apart. Its like when youre listening to sound neeeh. Now you travel away from it, neaaaah. That kind of goes down, right . The pitch goes down. Heres sort of that pitch is going down, the frequency at which you see those flashes goes down if you move away. This is called the doppler effect, okay . So this person sees them every six minutes. Now were gonna invoke einsteins first postulate that all light is seen to travel at the same speed by all observers. What the ship does is every time it receives a flash, its got its own little beacon here and it emits a flash and it directs those flashes to this observer. Now, these flashes are gonna be emitted every six minutes on the rocket ship. But wont the flashes keep right up with the flashes by the earth types . So let me ask you a question. These six minutes flashes, six minutes apart flashes are gonna be seen by this observer to be how many minutes apart . Three. So when a rocketeer gets up here, hes gonna say to his friend, hey, howd you like my flashes, six minutes apart . The friends gonna say, with all due respect, those flashes, honey, were three minutes apart. No, they were six. He says, i saw em at three. Could be . Yes. So, six minute flashes by a moving source can be seen over here to be three minutes apart. Lets put that information over here. A person seeing that ship approach will see six minute flashes, six minutes apart, every three minutes. Okay . Now, lets come back here and look. Every three minutes, they are blipped off, sees them at six. Im gonna ask you a question, use your reasoning. Lets suppose instead the sender over here sends em every six minutes, you know, half as many flashes. If they were sent every six and nothing changed, how often would they be seen here . 12 every 12. Now, heres einsteins second postulate all the laws of physics will be seen to be the same in uniformly moving reference frames. This is moving uniformly with respect to this. In fact, einstein said, it makes no difference whether this is at rest and this is moving or this is at rest and this is moving away. Motion really is relative. Its a relative motion between the planet and the ship. So, let me ask you a question. These six minute flashes that the ship really is sending really is sending the six, we agreed on that before these six minute flashes are gonna be seen how long apart by that person back here, whos now looking, who puts the telescope up and takes a look . Check your neighbor. Whats the answer, gang . 12. 12. You see that. I mean if 6 is seen as 12, then 6 will be seen as 12. So we can complete this diagram up here and say this. We have another planet here. A person watching these flashes, okay . What happens . Really the flashes are like this, okay . Theyre all scrunched up in here and all dragged out here. And so, six minutes will be seen three for approach, but for a recession, 12 minutes. Do you kind of see that . Now, these flashes act as a clock. A clock is anything thats periodic. You could say that clock usually is a pendulum swinging back and forth, right . Or vibrations in a crystal lattice, okay . In this particular case, the clock is regularly spaced flashes of light and one can keep track of time by counting up the flashes of light. So far so good . Lets see what happens if we apply this to space travel. Heres the earth, our cradle, gang. Thats our cradle, the cradle of humankind. What do we do with cradles, by the way, even if theyre comfortable . We outgrow. We outgrow them, thats right. And we see that starting to happen now, dont we . The spaceships going out. Were talking about space platforms, okay . Anyway, this is our cradle right here and here comes our rocket ship, same one, streaming by. And were gonna say at this point, boom. Both times are 12 00 noon. 12 00 on the ship, 12 00 on the earth and the ship continues. Now, what the ship is gonna do . Its gonna take a onehour trip out and its gonna turn around very quickly. So quickly that the time is negligible in comparison to the hour trip. So ship is going out, turn around and come back. Its gonna take one hour going out and one hour coming back with negligible turnaround time. And were gonna see how time compares for people on the ship who are moving relative to the earth and how time compares on earth relative to the ship. Now, 100 years ago, the answer would be ss samesame, but we find out nature is not that way. Nature is more interesting, because watch what happens, gang. Our ships gonna go out for 60 minutes. Onboard the ship, were gonna emit a flash of light every six minutes. Okay . Every six minutes, were gonna emit a flash. And the people on the earth are gonna count the flashes. Then, were gonna turn around and were gonna continue to emit a flash every six minutes. Six minutes, mmm, precisely. Off goes a flash, got it . Question time during the outgo of the ship, that 60 minutes, how many flashes will the ship get off . 10. 10 is 6 minutes apart and you get 60 minutes. Try it. 10. 10 flashes. So while the ship is going away, its gonna emit 10 flashes. Those flashes will get to the earth. The first ones right away. The flashes will ultimately get to the earth. So the earth types gonna set up a telescope and theyre gonna start counting flashes. Okay, 10 flashes going away. Then it gotta turn. When it comes back in, how many flashes are gonna be emitted by the ship coming back in . 10. How many minutes apart . Six, okay . So lets look at that. Ship point of view, ship frame of reference. Going out 10 flashes, 6 minutes apart 60 minutes. Coming back in 10 flashes, 6 minutes apart 60 minutes. The total time, gang . 120 minutes. Convert that to hours. Can you do it . How many hours . Two hours. Now, i got a question for you. When that ship as soon as it passes the earth, what is the time on a ship . Whats it gonna be, gang . Its gonna be 2 00 and itll be 2 00 on the ship when the ship gets back. Do you believe that . Any funny business here . Straightforward stuff. 2 00 on the ship thats been gone for 2 hours. Lets see what the earth types think about that. The earth types, how many flashes theyre gonna see for the ship going out, beginning with a t . 10. Okay . How often are these flashes gonna be seen when a ship going away . 12. 12 minutes apiece, honey. 12. Its up here, huh . Going away this 6minute flash is gonna be seen at 12minute intervals. Lets look. Whats 12 times 10 . 120 minutes, right there. Shouldnt you label that, the ships point of view . Oh, i now wanna label this here earth. Thank you very much. Saved again, saved by lee. All right, lee. From the earths frame of reference, 10 flashes would be seen in 120 minutes altogether. Gang, when the earth type is looking at a telescope and sees that 10th flash, thats when the ship turns around. Hes got the 10th flash, then he looks down or she looks down, looks at the watch. What does their watch say . 2 00 the ships still out there. Somethings going on. See why people got excited about relativity . Now the ship coming back in, how many flashes coming back in . 10. How often theyre gonna be seen . Three. Whats ten 3s . 30. Even i can do that. Add those up. 150. Whats 150 in hours, gang . 2 1 2. Can you see, its 2 1 2 . 120 will be two when you get there. Huh, huh, okay. So its 2 1 2 hours. How much time has gone by on the earth during this ships twohour trip . 2 1 2 hours, gang. And when that ship comes back, what is the time on the earth . On the ship, its gonna be 2 00. So its taken a trip that long, but on the earth its gonna be 2 30. So what will seem to take 2 hours for the ship will take 2 1 2 hours for the earth. So the traveling person doesnt age as much as the person who stays at home. Adventure ga, get out there and keep jogging. You know, so i walk back and forth all the time, uh, all right . Yeah. Questions on that, lee . The point of view of the person in the ship, if we ignore the turnaround, which we gave negligible time, why did it seem like the earth went away at the speed and then came back at that same speed . Yes, yes. This is whats been called the twin paradox. Why couldnt it as well be the same for the other observer . Why cant it be that maybe the spaceship is at rest and the earth moves away . Okay . Well, heres the hitch. Its not a symmetrical situation, because if that happened, the earth moves away, then the earth if it keeps moving away, well never know. But its gotta turn around and come back. And so, one switches from one realm id like to put it like this, switching spacetime realms. You know, we all live in some particular space, dont we . It happens to be in this particular room, right now, right . On the earth, duhduhduh, right . How about time . Do we all share the same time . Yes, we do. According to relativity theory, were all at rest relative to one another. We will all agree with how fast clocks move and were all sharing the same realm of time. But as soon as i now im moving. Now im in a different time than you guys are in. My clock is moving differently than yours. A lot or a little . Even without the hand, what is it . A little. Thats right, because im moving how . A little. How about if i move fast . How about if i move like this fast . Then, little turns into a lot. So its a matter of degree. So when you move, youre in a different realm and you know youre traveling different space. Hey, youre in a different realm of time and that is kinda wild. So what happens . Its the ship thats in one realm of time, coming out and in another realm of time, coming back. How about people on the earth . One realm. And one way to check that is to bring a cup of coffee with you thats brim filled. If the cup of coffee stays brim filled, stays right there, then thats an indicator that youre not changing realms of time. But when you accelerate, the coffee spills. That acceleration marks the change from one realm of time to another. So, theyre on different realms. So, it doesnt come back. They can meet again at the same space, but at the expense of time. But when the rocket is going at a steady speed, the earth seemed to be slowed down compared to it . Yes, yes, yes. If flashes are being emitted by the earth, then the ship sees those slowed down too. Would you like to see that . Can we get into that . How many of youll say, no, information overload. Ive got too much to digest already. Can we switch frames of reference and see if it still works . Lets try it. Lets suppose instead of the fellow over here with the telescope, we put a person over here shining a light, okay . A light beams gonna go off and now the ship observes, all right . Now, the person on earth is gonna flash a light every six minutes. Okay . Now, the ships going out. Now, the ship is gonna watch those flashes. How long apart will those flashes appear to people on the ship . Do you see its 12 . Theyre gonna go out for 60 of their minutes. How many flashes will they see 12 minutes apart in their 60 minutes . All of you can figure that out. Five. Good. So, going out, the ship types are gonna see five flashes. From the ship point of view, the ships going out, its gonna see five flashes, 12 minutes apart, thats gonna be 60 minutes, okay . Now, coming back in, the ships gonna see flashes, how many minutes apart . Oh, you dont remember that. Three, okay . So, the ship is gonna see those flashes three minutes apart, okay . How many flashes is the ship gonna get in its one hour, three minutes apart . Youve gotta figure out how many 3s will go into 60 . 20. 20. So, the ship is gonna see 20 flashes coming back in, yeah . Re flashes coming back in than going out. I mean when the rains coming down like this, you get fewer drops hitting you per minute, this way. But when you turn around and bababababam, okay, same type thing here. Now, we get 20 flashes coming in, 3 minutes apart, twenty 3s is 60. Okay . So what time is it on the ship . 120 minutes. Two hours. What time is it on the earth . How many flashes have been emitted on the earth during this trip . 25 so, from the earth. 25 x 6 is what, gang . Mmm eee now, let me ask you a question. You know, when you see these guys, they got the green pea and they got the three jars and they go like this, like that, all right. Which ones it under . And you always guess wrong. But you know, theres a catch, because theyre pulling theyre very, very skilled, and theyre pulling something over on you, right . And you always or a card trick, right . Dahdahdahdahdah, right . Wheres the catch . Ive got a friend that does the card tricks. How do you even suspect . This guy is so good ive even suspected him of really being magic and pretending he has skill. You know what i mean . Hes so good, okay. But anyway, theres always a trick. Wheres the trick here, gang . Where did i trick you into thinking that 2 hours on one frame of reference would be seen 2 1 2 hours on does that make sense . What did einstein say common sense was . That layer of prejudices laid down usually by the age of 18. This does not make sense to you, because you know why . Its not part of your background. Its not part of your experience. This is off your experience. Maybe jet planes wouldnt make sense to a caveman and this stuff is just starting to make sense to us, yeah. Ill tell you what, gang . Theres no catch, as we understand it, nature is this way. Many, many experiments to see if theres something wrong about this and all these experiments have only gone into confirming that einstein was right. Let me say a neat thing about science too. In a lot of fields, therell be some sort of hero like einsteins our hero, here. We all love einstein. Most of us do, yeah. So, einsteins our hero, and you tend to think, well, if hes a hero, you dont wanna take shots at him. But in science, its different. In science, say heroschmero. Everybody is trying to crack that hero and find something wrong. Everyones attacking to see if they can find something wrong. And so science doesnt rest upon the reputation of some hero. Science rests upon everyone else trying to find a crack in that theory. And all attempts, so far, have only gone on to substantiate this time really is different when youre moving. But ill tell you what . Were gonna talk more about these ideas next time and you know what i wanna do for you now . I wanna share with you a film that a friend of mine made way back in 1976. When i was teaching these ideas in the early 70s, i discovered this kind of treatment at the class board. Thats one thing about teaching, you learn at the class board. You know, you guys arent the only ones learning. I learn too. And what i did at that time was to be able to see the ship at different positions. I made a whole lot of drawings, cartoons, and i took photographs and made slides. And i would get at the back of the room and id show this slides in quick succession. Id have a carousel, id hold the things, ill go click, click, click, click, show the slides, so you guys could see the ship at different positions. And about that time, my First Edition of the book was out and i went to a party over in berkeley and there was a fellow there who had just graduated from San Francisco state, who was showing some of his movies. He was into moviemaking, cartoons. I really liked his cartoons. They had a warmth to them. I really liked him steve smith. I said, steve, you know, ive got this little thing i do with these little slides. I wonder maybe you could make up a little cartoon movie. We could make a movie of this and share it with more people. And at that time, he was working as a dishwasher down on telegraph avenue. And i said, steve, quit the dishwashing. Ill grubstake you. Ill get you groceries. Ill feed you and ill grubstake me. Maybe city college will let you use some of their equipment and well make a little animated movie. And he made an animated movie on everything that we would you like to see it . Okay. Roll it, lionel. Well see it right here, gang. Right here. Where did the time go . Does anybody, does anybody know . When did the day break . Did someone drop it, was it a mistake . La, la, la, la la, la, la. Did you know that times different when you move at different speeds, that when you move through space, you change the rate at which you move into the future . Well, you cant really notice these differences for everyday speeds, but for really high speeds like for rockets traveling about half the speed of light, these ti differences can be noticed. Lets take a look at the socalled twin paradox. Well, bye. I dont know if ill see you again. And while the traveling twin experiees weeks. The stayathome twin experiences years. You know, i think ill just sit here and do nothing. That sounds like yeah, ill do that. Now, what . What . What is going on out there . Ah, my goodness. Hey. I dont believe this. Look at you. Good to see you. I must relax. I cant relax. Im too old to relax. Look at the size of this one, will you . Could a situation like this be true . You bet it can. This is time dilation. We can see time dilation by comparing clocks from different frames of reference. Say, from the earth and from a highspeed rocket ship. Now, a clock can be anything that measures periodic intervals of time. To simplify, were gonna let the ticks of our clock be periodic flashes of light. Look at the light flashes emitted by the stationary rocket ship. Now, some time goes by before they reach the disnt plat. But since thereno relative motion involved, successive flashes get to the planet at regularlyspaced intervals. Thats to say, both the sender and the receiver will agree on the time intervals between thflashes. Now, theres nothing unusual about this. But suppose the rocket ship moves. Look at the doppler effect. An observer sees thelashes at shorter intervals. Suppose the ship moves fast enough so an observer sees the flashes at intervals twice as short as the ship sends them. Then if the ship moves away, just as fast now, an observers gonna see intervals twice as long. Like if the rocket sends a flash every six minutes, they will be seen every 12 minutes by the observer when the rocket moves away, but every three minutes when the rockets approaching. Now, lets apply this to time dilation. If the ship passes by the earth and moves away at the same high speed for one hour and quickly turns around and then returns in one hour, rocket ship time, this 2hour trip is seen by the earth as taking place not in 2 hours, but in 2 1 2 hours. And this is because the ship and the earth have been in completely different realms of time. Lets look at this in greater detail. Suppose that when the ship goes by the earth, that clocks on earth and on the ship are synchronized to 12 00 noon. Then, as the rocket leaves the earth, a flash of light is emitted by the ship every six minutes. Thats six minutes rocket time. Then the ship emits 10 of the 6minute flashes while going away from the earth. The 10th flash is gonna be emitted 60 minutes after leaving the earth. Then the ships clock is gonna read 1 00, just when this 10th flash is emitted. Now, suppose this is the moment that the ship turns around. Our earth observers dont see the turnaround until they see the 10th flash. Now, here it comes. Its gonna take some time for it to get to them. Closer, closer, closer. And there it is 10 flashes, 12 minutes apart. Thats 120 minutes. Two hours. So that means its 2 00 now on earth. Now, the 10 flashes the ship emits when approaching the earth, they are gonna be seen three minutes apart or all 10 in 30 minutes. The first is three minutes after 2 00, earth me, the next is three minutes later and so on, until the last flash is emitted just as the ship whizzes past the earth. And thats gonna be 2 30, earth time. So a clock aboard the rocket ship reads 2 00, while a clock on the earth reads 2 30. This checks out. Check the figures. Now, lets go through this once again. Watch carefully and compare the clocks. Well get the same results if we switch frames of reference. The earth will send flashes now at sixminute intervals and the rocket ship will observe them, while again, departing and returning on, what for the ship is, a twohour journey. One hour out and one hour back. While going away, the ships gonna see flashes 12 minutes apart. That means its gonna see a total of five flashe during this hour, going away. See that . Now, while returning, the ship sees flashes 3 minutes apart. Theyre gonna see a total of 20 during the hour of return. For the round trip then, the earth emits a total of 25 flashes at 6minute interval, thats 150 minutes or 2 1 2 hours. Same results as before. So, from either frame of reference, a person on earth ages more than a person in a highspeed rocket ship. Its not so much a question of whos moving and who isnt, but rather the different spacetime experienced. The person on earth remas in one spacetime throughout the experiment whereas the person in the rocket ship is in a completely different realm of time while traversing space going away from the earth and in still another realm of time while traversing space and coming back to the earth. Thats two spacetimes, two spacetimes separated by the acceleration of the ship and turning around. Now that acceleration is interesting in its own right. Get to that in general relativity, but we see that the details of that acceleration arent really essential in this case. The principal significance of that acceleration is that it marks the changing from one spacetime to another. Now, our twins have been in differentpacetimes and they can meet again at the same place in space, but only at the expense of time. Isnt that great . Thats time dilation. Peace. Where did the time go . Does anybody, does anybody know . When did the day break . Did someone drop it, was it a mistake . Ive got a notion, circular motion im finding out in the ocean, out in the ocean of time