- #1
NoahsArk
Gold Member
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There are a few fundamental questions I wanted to ask about related to special relativity:
1) Firstly, is there an intuitive explanation for length contraction and why lengths are relative? For example, the fact motion is relative is intuitive. E.g. someone sitting inside a train moving 60 miles per hour bouncing a ping pong ball up and down on a table will see the ball moving zero distance in the X direction, whereas someone on the ground will have seen it move in the X direction at 60mph. With length contraction, however, the person on the train measures objects themselves which are outside the train as smaller lengthwise than a person on the ground would measure the same objects. Is there any kind of physical or visual explanation of this like in the case of the ping pong ball? The only explanation that I read which makes sense is a mathematical one: that is, for the observer on the ground velocity = distance/time (v=d/t), and for the one in the train v = d1/t1. Since we know t and t1 are different, we can conclude that d and d1 are different.
Another question is, since time dilation and length contraction are two sides of the same coin, is it possible to say which one is "causing" the other?
2) Regarding the Lorentz transformations the formula for converting distance in one frame to distance in another frame makes much more sense to me (even without doing the lengthy derivation) than the formula for converting time. The formula for distance is X = γX1 + γVT1. That makes sense because to get the distance of an event in a stationary frame from a distance in a moving frame, like a rocket frame, we'd need to know how far the rocket traveled plus how far the event is from the rocket (and multiply both sides of the "+" sign by γ. The formula for converting time, T = γV/C2X1 + γT1, is confusing for me. If an event happened inside the rocket, the X distance would be zero and the formula for converting time would just be T = γT1. Is there an intuitive explanation behind the γV/C2X1 part? If the person in the rocket measures the time of some event happening outside of the rocket, say on a second rocket moving faster than him and even faster than the person on earth, wouldn't the Lorentz transformation for time need to take into consideration how fast the second rocket is moving with respect to the first?
Thanks
1) Firstly, is there an intuitive explanation for length contraction and why lengths are relative? For example, the fact motion is relative is intuitive. E.g. someone sitting inside a train moving 60 miles per hour bouncing a ping pong ball up and down on a table will see the ball moving zero distance in the X direction, whereas someone on the ground will have seen it move in the X direction at 60mph. With length contraction, however, the person on the train measures objects themselves which are outside the train as smaller lengthwise than a person on the ground would measure the same objects. Is there any kind of physical or visual explanation of this like in the case of the ping pong ball? The only explanation that I read which makes sense is a mathematical one: that is, for the observer on the ground velocity = distance/time (v=d/t), and for the one in the train v = d1/t1. Since we know t and t1 are different, we can conclude that d and d1 are different.
Another question is, since time dilation and length contraction are two sides of the same coin, is it possible to say which one is "causing" the other?
2) Regarding the Lorentz transformations the formula for converting distance in one frame to distance in another frame makes much more sense to me (even without doing the lengthy derivation) than the formula for converting time. The formula for distance is X = γX1 + γVT1. That makes sense because to get the distance of an event in a stationary frame from a distance in a moving frame, like a rocket frame, we'd need to know how far the rocket traveled plus how far the event is from the rocket (and multiply both sides of the "+" sign by γ. The formula for converting time, T = γV/C2X1 + γT1, is confusing for me. If an event happened inside the rocket, the X distance would be zero and the formula for converting time would just be T = γT1. Is there an intuitive explanation behind the γV/C2X1 part? If the person in the rocket measures the time of some event happening outside of the rocket, say on a second rocket moving faster than him and even faster than the person on earth, wouldn't the Lorentz transformation for time need to take into consideration how fast the second rocket is moving with respect to the first?
Thanks