36. Special Relativity

Consequences of Relativity

# Proper Frames and Measurements

Patrick Ford

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Hey, guys, Before moving on to the next topic, I want to spend just a little bit more time talking about proper frames versus non proper frames. Okay, just to clear up any sort of inconsistencies that we have in those definitions. Okay, it's really, really, really important to know exactly what your proper frame is for the particular measurement that you're making and what the non proper frame is for the measurement that you're making. We typically deal with lab frames and moving frames, and sometimes the proper frame will be the lab frame. And sometimes the proper frame will be the moving frame. It just depends on what you're trying to measure now. Ah, proper frame is always, ah, frame that is at rest with respect to I'm just gonna right here something important now that seems extremely vague. And the reason that's so is because it's extremely vague. Um, proper distance. Proper length is very, very easy. When you have an object, the proper length of that object is always gonna be measured at rest with respect to that object. Okay, so if you're talking about, you know, a spaceship, which is the most popular um, example to use in special relativity because spaceships you can make go extremely fast. Then whenever you're measuring the length of that ship at rest with respect to that ship, that's going to be a proper length. Let's say there was a person going very, very, very fast. If you wanted to know how the height of that person would change based on their speed, you would need to know. You would say that the proper height for that person, right that proper length was measured when that person wasn't moving. Okay, so if we look at this example right here, ah shit passes Sally, who's standing on the earth's surface watching this ship fly pastor, right? If Sally measures the length of the ship to be 100 m, is this the proper length or the contracted length? Now, in some problems, they will give you both lengths, and they'll ask you to find this speed. We saw a problem with a triangle where that was true. We were given both lengths and asked to find the speed. That's very easy, because the contracted length is gonna be the shorter length. The proper length is gonna be the longer length But in problems like this, where you are only given one length, you need to know which is the proper length, which is the contracted length. In this case, this 100 m is the contracted length. Okay, here's Sally and the ship is passing her at some speed. And when that ship passes her, she sees a length of m. That ship is moving with respect to Sally. So it's absolutely not the proper length that she is measuring the proper length. This, by the way, we would call s the lab frame. The proper length would be measured in a moving frame as prime and specifically a frame that moves with the ship. So the ship is at rest in this particular moving frame as prime and this length, whatever that would be, that would be the proper length. Okay, so it's really easy to understand. For objects, it gets a little bit harder for times. Okay. For time dilation, it's oftentimes mawr tricky to establish, which is the proper time in which is the, um, dilated time. Now, like I had said, the proper frame is always going to be the frame where the thing that you're interested in is at rest. So the proper frame is going to be the one at rest. With respect to the clock you care about ran a little bit out of space here. Okay, In, um, problems with time dilation, you're basically going to be comparing two clocks. That's always the scenario. When we saw a problem with the Milan, we said that the Mulan took 2.2 microseconds to decay. And it's rest frame. How long is it gonna take to decay in the lab frame? So that was essentially comparing two clocks, one clock moved with them yuan and measured 2.2 microseconds. One clock was stationary while the muon flew past it and measured a different time. The clock that we were interested in the clock measuring the event that we cared about was the clock moving with the mu on. So that was the proper time. And the lab frame time was the dilated time. If we look at this problem right here on astronaut is leaving home on a long trip. But before he goes, he synchronizes the watch with his brother. These were very popular problems, by the way, allowing them to compare the amount of time that passes when he returns during the astronauts trip, He measures himself to be five years older while his brother measures a different amount of time passing. Which of the two is measuring the proper time? Okay, now one guy is stationed on Earth as the other astronaut or as the other brother, the astronaut is flying very, very far away. The time that the astronaut measured was five years. Oftentimes, the way that these problems were phrased are going to specifically, um, give some sort of preference to one of the two people. In this case, the preferred person is the astronaut, right? The guy on earth we're saying is just stationary. The ash not is flying away very, very fast from that guy. All of this implies that the thing that we're interested in is the aging of the astronaut. And then the brother on earth is going to compare his age to the astronauts age. So this would be the proper time, right that time measured by the astronauts and then the guy on Earth would measure the dilated time so that when astronaut came back, he would be younger than his brother who stayed behind. Okay, so this is sort of how you want to approach these problems. Thio figure out which is the proper time, which is the dilated time, which is the proper length, which is the contracted length. Like I said, for length contraction, it's very, very easy for time violation. It can be a little bit more difficult, but you wanna look at the problem and figure out what is the event that you care about, which is the clock that you care about. If it's talking about something like a particle decaying like for them yuan, it's very, very easy, because that's the thing that you're interested in the decay of them yuan. For something like this, it could be a little more difficult and a little bit more ambiguous. But you want to figure out what is the event that's actually happening that you care about. And in this event, that is the astronaut aging. So that's gonna be the proper time. The brother is going to compare his time to the astronaut when he gets back, and the brother at rest on Earth is going to measure the dilated time. Okay, Alright, guys, that wraps up this concept this little last bit about time dilation and link contraction that we needed to talk about. Alright, Thank you guys. So much for watching.

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