For example 2, the main thing to notice is that they are asking us to find the *distance from the origin of S’ to where the lightening struck* ....... NOT the length of the rod. If you have a 1cm pencil and you place it between x=7 and x=8 on some coordinate system, it’s length is still 1cm. However, the distance between the origin and the end of the pencil is 7cm. It’s really subtle but the question is asking for the distance from O’ to lightening bolt, not the length of a related rod in S’. If this makes sense, the professor’s explanation will make sense to you fully :) Best wishes, friends
Yashi Jainj in last example of this lecture, in s' frame event happened before than in s frame, sir says that after some time both origin coincide at t=0 but condition to coincide both origin is that X and t both should be 0 but here t=0 but x=20
It is correct that according to an observer sitting at the origin of S', lightening would occur earlier than her reaching the origin of S. That is why the time of the event of lightning striking earth is negative in S' frame. It is also true that when the observer in S' reaches origin of S, time in her watch would be zero and even the watch of observer in S would show zero at that time. It is also true that x co-ordinates of the event of two origins coinciding would be zero in both frames. However the event of lightening occurred in S at x= 20 km at time t=0. For this event t' would not be zero in S'. Basically if any event occurs at x=0 at t=0 in S, only then this event would appear to occur at t'=0 and x'=0 in S'.
I want a answer for this question How fast must a spacecraft travel relative to earth for each day on the spacecraft to correspond to 3 day on the earth? Question no 7 from athur bieser I hav done little change
3 года назад
What actual measurement has already been made of the length contraction?
sir in 21:44 we said that t2^' is not equal to t1^1 but suppose when we are in train we can measure the length of the rod at same time then how we can say that t1^1 is not equal to t2^' bcoz we can measure at any time it may be at same time thank u
Sir in discussing length measurements you took an unnecessarily long and in a way inaccurate approach. 1) When measuring a stationary or non moving rod in one's own frame you MUST emphasize at the very OUTSET that the time coordinates at the 2 ends of the rod are ALWAYS the same whether or not one takes a tea break. Only the length or X coordinates differ. This is why one can use a tape measure to get the difference in the two X coordinates and get the proper or maximal length. Taking a tea break as you say is irrelevant as long as the time coordinates at the 2 ends remain identical. 2) Due to the failure of simultaneity (FOS) the moving rod CANNOT have the same time coordinates at the 2 ends. The leading end always appears delayed. It is precisely because the front and back time coordinates are ALWAYS different in a moving rod, one cannot just measure the difference between two X' coordinates to get the moving length. You are inaccurate when you suggest that the time interval is unimportant when measuring length of a stationary rod or that the front and back time coordinates of the stationary rod can somehow vary BETWEEN themselves if you take a tea break etc. The front and back X coordinates must have the same time coordinates at ALL times, tea break or no tea break, because there is no FOS. So please stop giving misleading examples of tea breaks and FOCUS on the UNITY of time coordinates throughout a stationary rod.
Sorry but It is you who appear confused. My post is absolutely accurate. Of course the FOS between the ends of a moving rod is as seen by the stationary observer only. The observer moving WITH the rod will not see it. For THAT observer the time coordinates at the 2 ends of the rod will be the same as the rod will be stationary for him/her. The way one measures time coordinates at the 2 ends of a rod is to keep accurate clocks at EACH end and see if they do or do not show the same time. I cannot be any clearer so if you still do not get it then...TOUGH!
