hippopviolin said:Hello, everyone
I am learning special relativity in high school.. I understand the time dilation thing...but i have trouble to understand the length contration..
I am getting confused why
Lm=ts*V and Ls=tm*V
Please help..thank you
hippopviolin said:Thanks to Diazona and Feynman respond to my question
Ls is the proper length, and Ts is the proper time
now, I think I understand the formula..
however, i still don't really get one concept..
My textbook says,
when you look at the length of the spaceship as proper length, then the distance between Planet A and Planet B will shrink.
If you look at the distance between Planet A and Planet B as proper length, then the length of the spaceship will shrink..
I understand the first idea, and I don't get the second one
Thank you for helping
When you write Lm=ts*V and Ls=tm*V, what are Lm, tm and V?hippopviolin said:Thanks to Diazona and Feynman respond to my question
Ls is the proper length, and Ts is the proper time
Probably the first means that in the rest frame of the spaceship, the distance from planet A to planet B is less than it is in the planet's own rest frame, and likewise the second would mean that in the rest frame of the planets, the length of the spaceship would be less than it is in the ship's own rest frame.hippopviolin said:when you look at the length of the spaceship as proper length, then the distance between Planet A and Planet B will shrink.
If you look at the distance between Planet A and Planet B as proper length, then the length of the spaceship will shrink..
I understand the first idea, and I don't get the second one
The proper length Ls isn't related to time in the formulas I posted, it's related to Lv, the length in the frame where the object is moving at speed v. Why would you think length is calculated using time? Does it say that in your textbook?hippopviolin said:What I confused about the formula is why Ls is calculated by Tv instead of Ts..
why should we use the moving time to calculate the proper length
But that's just a step in a longer derivation, right? Without seeing the context of what assumptions they're making in the derivation I can't really make sense of that...what's the name of the textbook? Maybe we can find the page on google books.hippopviolin said:Yeah..My textbook use the time dilation relationship to derive the length contraction formula.
They mutiply both sides by v, which is the speed of the spaceship..
then V*Ts becomes Lv, and V*Tv becomes Ls
Excellent, turns out I could actually download that section from http://access.mmhs.ca/docs/Science/MMHS%20Web%20folder/physics12/Physics%20CD/physics12/a40.html . The key is that Lm = v*ts is not meant to be a general relationship that would hold in any situation, but only in the case of the specific situation they describe on p. 573, where a ship is traveling between two planets, and in the ship's frame the distance between the planets is Lm, while the time between passing each planet as measured by the ship's clock is ts. So naturally in this frame if the second planet is a distance Lm away at the moment the ship is next to the first planet, and the ship remains at rest while the second planet rushes towards it, reaching the stationary ship a time ts later, then since that planet covered a distance of Lm in a time of ts the planet's speed must be v = Lm/ts, just based on the fact that in any frame speed is defined as distance/time (in terms of that frame's coordinates). Likewise, in the frame of the planets it takes the ship a time of tm to get from one planet to the other, and the distance between the planets is Ls in this frame, so the speed of the ship in this frame must be v = Ls/tm. And obviously if you take this equation and multiply both sides by tm you get Ls = v*tm, likewise the first equation can be rearranged to give Lm = v*ts.hippopviolin said:haha thank you for helping me
It is Thomson Nelson Physics 12. By Hirsch, Martindale, Sewart and Barry
It is in page 574
If you have to ask this kind of question, that means you know the math equation but you do not understant its physical meaning. I guess you must know the so-called Lorentz transformation by now. He had similar question about time, since there are two "time" in the his equations. One is "time", one is "tau". He did not understand it, so he called one "time" and the other "local time". Lorentz think local time is just a mathematical trick that greatly eased the computational burden of finding new solutions of Maxwell's equations. Einstein cleared things up in one stroke. We now call one the "coordinate time' and the other "proper time", or (Eigen-Zeit) in German, it means its own time.hippopviolin said:Thank YOu Jesse M, i think I get it now.
but..ah..I am not sure how do you know which one is suppose to be the proper length.
In this scenario, is it true that the captain finds the distance separating the two events to be Lm is because of she thinks the planets are moving, and she is stationary?
No, it is "shorten" if you measure it with ruler, Not just "seem to be shorten" to the observers who are stationary.hippopviolin said:If that is true, so basically the objects that are moving will seem to be shorten to the observers who are stationary?
Proper length is the distance between the two endpoints of an object (or two separate objects with space between them like the planets) in the frame where the endpoints are at rest.hippopviolin said:Thank YOu Jesse M, i think I get it now.
but..ah..I am not sure how do you know which one is suppose to be the proper length.
Right.hippopviolin said:In this scenario, is it true that the captain finds the distance separating the two events to be Lm is because of she thinks the planets are moving, and she is stationary?
Well, there's no absolute truth about who's "moving" and who's "stationary" since all speeds are relative, but objects that are moving relative to a given frame of reference will shorten to observers who are stationary relative to that same frame. This explains why if your ship is moving relative to my ship, and both ships have the same proper length, then in my rest frame your ship will shorten relative to mine, while in your rest frame my ship will shorten relative to yours.hippopviolin said:If that is true, so basically the objects that are moving will seem to be shorten to the observers who are stationary?
Special relativity is a theory in physics that explains the relationship between space and time. It was developed by Albert Einstein in the early 20th century and is based on two main principles: the laws of physics are the same for all observers in uniform motion, and the speed of light is constant for all observers in any inertial frame of reference.
Special relativity deals with the behavior of objects in a non-accelerating frame of reference, while general relativity takes into account the effects of gravity and acceleration on objects. Special relativity is a more limited theory, while general relativity is a more comprehensive one.
Special relativity has been applied in many areas of modern technology, such as GPS systems, particle accelerators, and nuclear power plants. It also plays a crucial role in our understanding of the universe, including the behavior of stars and galaxies.
Special relativity has been extensively tested and verified through experiments and observations. One of the most famous tests is the Michelson-Morley experiment, which showed that the speed of light is the same in all inertial frames of reference. Therefore, special relativity is considered a well-established and proven theory.
One common misconception is that special relativity only applies to objects moving at near the speed of light. In reality, it applies to all objects in motion, regardless of their speed. Another misconception is that it only applies to large-scale objects, when in fact it also applies to subatomic particles. Additionally, it is often mistakenly believed that special relativity contradicts common sense, when in fact it is supported by extensive evidence and mathematical equations.