![]() Now, you’ve got to say, it is very surprising, people cannot agree on length difference between two events. People cannot agree that they were simultaneous. ![]() Something here, something there, separated by distance. So, I don’t want to deal with such cosmological objects right now. “Your momma” jokes your momma is so big she can have a kid in New York. So, I started with unfortunate example of twins born in Los Angeles and New York, and you guys were pointing out that no normal woman could do that, except the one from “your momma” jokes. Now, the important result I showed you was a lack of simultaneity. So, l will be L 0 times–if you bring the square root to the other side, L will be L 0√ whereas Δt’ would be some Δτ under this frame, divided by the square root. The spatial difference between them will be simply the length of the rod in your frame of reference. And one thing occurs at one end, another thing occurs at the other end. And as long as you’re moving with the rod, the rod has got two points which are separated by the length L 0. The distance between them is what I call the length of the rod. So, you make sure the two measurements are done at the same time, so Δt = 0. You’ve got to measure both ends at the same time. That’s the meaning of the length of a moving rod. Then, I showed you how when you wanted to measure the length of a stick which is traveling past you, you get your assistants on the–who are all lined up on the x axis to measure the two ends of the rod, or any particular time they like. The clock that you think is set best with respect to you will look slow to me. And it’s easy to see, from the same equations, that if you replace the′ and unprimed ones, simply change u to -u, nothing changes. Therefore, you will say my clocks are running slow. So you will say, hey, the time your clock ticked one second, I really claimed two seconds have passed. ![]() So for you, Δt’ = 1 s/√ which is more than one second. The space difference is zero because the clock is not going anywhere for me. So for me, the time difference between the two ticks will be, let’s say, one second. And let’s say it goes tick and it goes tick one more time. Or let’s take a clock that I’m carrying with me and let’s see how it looks to you. ![]() You remember that? For example, I said, take a clock that you are carrying with you. This isn’t generally, if you’ve got two events, not necessarily at the origin, then there’s spatial separation and time separation are connected in this fashion. Even this one you can think of as a formula for a difference, except one of the coordinates, or the origin. But I will write it anyway, because I will use it sometimes one way and sometimes the other way. So, differences are related the same way that coordinates themselves are. In other words, if two events are separated in space by Δx for one person and Δx’ for another person and likewise in time, then you get similar formula for differences. From this, by taking differences of two events, you can get similar equations for coordinate differences. But I remind you that if you’ve got an event that occurs at x,t for one person, and to a person moving to the right, at velocity u, the same event will have coordinates x’ = x - ut/√ and t ’ = (t - ux/C 2)/√. I won’t go over how we derive them, because I’ve done it more than once. And you guys should be really on top of those two marvelous equations, because all the stuff we are doing is a consequence of that. Professor Ramamurti Shankar: Let me remind you that everything I did so far in class came from analyzing the Lorentz transformations. Fundamentals of Physics I PHYS 200 - Lecture 14 - Introduction to the Four-VectorĬhapter 1: Recap-Consequences of the Lorentz Transformations ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |