x*****8 发帖数: 10683 | 1 Today my student asked me: If A travels from left to right with light speed
c (relative to earth), B also travels from left to right with light speed c
(relative to earth), what should be the relative speed between A and B?
I applied the formula:
relative speed = (u-v)/(1-u*v/c^2) = (c-c)/(1-c*c/c^2) = 0/0
That is undefined!
Now I'm not very sure if I did right.
Please help me!
Thank you! |
p*********r 发帖数: 7944 | |
p*********r 发帖数: 7944 | 3 (u-v)/(1-u*v/c^2) = (c+c)/(1+c*c/c^2) = c |
g****5 发帖数: 1639 | 4 你可以这么想:如果v=2c怎么办?
在用狭义相对论的公式之前,应该搞清楚每个量的取值范围。对于v也就是两个参考系
之间的相对速度,取值范围是[0, c)。
这么一来,就不存在问题了。如果u在一个参考系中是c,在另一个里面也必然是c。 |
p*********r 发帖数: 7944 | 5 就是同方向走,相当速度也是c:
(u-v)/(1-u*v/c^2) = (c-v)/(c(c-v))/c^2 = c
where u is replaced by c。 |
g****5 发帖数: 1639 | 6 这个解法有问题。
你做的是:lim_{v->c}lim_{u->c}(u-v)/(1-u*v/c^2)。
如果算含多个变量的极限问题,沿着什么路径取极限很重要。你不妨试试先让v->c,然
后再让u->c。结果就成-c了。
【在 p*********r 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 就是同方向走,相当速度也是c: : (u-v)/(1-u*v/c^2) = (c-v)/(c(c-v))/c^2 = c : where u is replaced by c。
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p*********r 发帖数: 7944 | 7 只要有一个速度是c,另外一个速度无所谓。
正负号表示观察者交换了位置。
【在 g****5 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 这个解法有问题。 : 你做的是:lim_{v->c}lim_{u->c}(u-v)/(1-u*v/c^2)。 : 如果算含多个变量的极限问题,沿着什么路径取极限很重要。你不妨试试先让v->c,然 : 后再让u->c。结果就成-c了。
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n*******r 发帖数: 2010 | 8 我发现崇拜相对论的都是在办公室里捣鼓纯数学公式的人, 任何一个东西, 纸上一算
就好, 都不带出门走走做做实验做做观测的。 完全忘了老祖宗伽利略开普勒牛顿的教
诲。
另外一批崇拜相对论的就是大妈和少女这个人群。
speed
c
【在 x*****8 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Today my student asked me: If A travels from left to right with light speed : c (relative to earth), B also travels from left to right with light speed c : (relative to earth), what should be the relative speed between A and B? : I applied the formula: : relative speed = (u-v)/(1-u*v/c^2) = (c-c)/(1-c*c/c^2) = 0/0 : That is undefined! : Now I'm not very sure if I did right. : Please help me! : Thank you!
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g****5 发帖数: 1639 | 9 这个理解不对。符号当然重要。
仔细想想吧~
【在 p*********r 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 只要有一个速度是c,另外一个速度无所谓。 : 正负号表示观察者交换了位置。
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g****5 发帖数: 1639 | 10 你说的那帮人有个统一的名称叫:民科
【在 n*******r 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 我发现崇拜相对论的都是在办公室里捣鼓纯数学公式的人, 任何一个东西, 纸上一算 : 就好, 都不带出门走走做做实验做做观测的。 完全忘了老祖宗伽利略开普勒牛顿的教 : 诲。 : 另外一批崇拜相对论的就是大妈和少女这个人群。 : : speed : c
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a***e 发帖数: 27968 | 11 It could be any value.
speed
c
★ 发自iPhone App: ChineseWeb 8.7
【在 x*****8 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Today my student asked me: If A travels from left to right with light speed : c (relative to earth), B also travels from left to right with light speed c : (relative to earth), what should be the relative speed between A and B? : I applied the formula: : relative speed = (u-v)/(1-u*v/c^2) = (c-c)/(1-c*c/c^2) = 0/0 : That is undefined! : Now I'm not very sure if I did right. : Please help me! : Thank you!
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l******t 发帖数: 55733 | |
x*****8 发帖数: 10683 | 13 Thank you very much!
You're right!
【在 a***e 的大作中提到】![](/moin_static193/solenoid/img/up.png) : It could be any value. : : speed : c : ★ 发自iPhone App: ChineseWeb 8.7
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x*****8 发帖数: 10683 | 14 我方向是正确的。
【在 p*********r 的大作中提到】![](/moin_static193/solenoid/img/up.png) : 方向搞错了。
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s*i 发帖数: 5025 | 15 Depends on the observer?
If the observer is on earth, 0.
For both A and B, they all see others traveling at c?
speed
c
[发表自未名空间手机版 - m.mitbbs.com]
【在 x*****8 的大作中提到】![](/moin_static193/solenoid/img/up.png) : Today my student asked me: If A travels from left to right with light speed : c (relative to earth), B also travels from left to right with light speed c : (relative to earth), what should be the relative speed between A and B? : I applied the formula: : relative speed = (u-v)/(1-u*v/c^2) = (c-c)/(1-c*c/c^2) = 0/0 : That is undefined! : Now I'm not very sure if I did right. : Please help me! : Thank you!
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