GR9277 #94



Alternate Solutions 
ramparts 20090816 17:32:18  Make it one step simpler  they're kind enough to give you natural units (c=1), so the Lorentz transformations for x and t are exactly the same  just switch your x's and t's (primes left intact). Equation 3 looks like that. Great!
Just like the official solution, but no need to factor anything out.
Calculating spacetime intervals seems.... a bit much for this test.   student2008 20081016 13:54:16  LOL! The simplest way here is to calculate the interval , it should be equal to . This can't be true for (A) & (B), and in (D) . But, it is correct for (C).
In general situation (i.e. when y's and z's also change) this is the only practical method. You would get stuck using the general form of transformations.  

Comments 
nyuko 20091030 22:32:21  I did this problem by:
(1) x and t transform in the same way (c=1)
(2) has to be greater than 1
then the answer is (C)
However, now I look back at the choices; there is a choice (E) so we need to check if and are corresponding to the same relative velocity of frame...and then I guess ETS does not want us to check the math but just to know (1) and (2) I stated above?   ramparts 20090816 17:32:18  Make it one step simpler  they're kind enough to give you natural units (c=1), so the Lorentz transformations for x and t are exactly the same  just switch your x's and t's (primes left intact). Equation 3 looks like that. Great!
Just like the official solution, but no need to factor anything out.
Calculating spacetime intervals seems.... a bit much for this test.   ramparts 20090816 17:32:02  Make it one step simpler  they're kind enough to give you natural units (c=1), so the Lorentz transformations for x and t are exactly the same  just switch your x's and t's (primes left intact). Equation 3 looks like that. Great!
Just like the official solution, but no need to factor anything out.
Calculating spacetime intervals seems.... a bit much for this test.   CaspianXI 20090319 15:59:11  If you're low on time, here's an easy way to solve this problem.
Thus, the first terms in both x' and t' must be the same. And the coefficients of the second terms for both x' and t' must be the same. (C) is the only one which satisfies this, so you're done.
CaspianXI 20090320 20:55:39 
Oops... typo. I *meant* to list the equations as:
The rest of the logic still applies.
WARNING: in general. This is only true because we've been given that we're using some funky units where c = 1.

ramparts 20090806 23:20:57 
They're not funky units, they're natural! ;) Thank God for natural units, too. The c's are so unseemly.

  tinytoon 20081107 02:18:56  I think Yosun's solution is valid, but the easiest way to do it is to recognize that Lorentz transformations are the following:
and
In units of c = 1, which the problem kindly gives us, the second transformation becomes:
Now we can clearly see that the 's and the 's are symmetrical in the two transformations and out pops (C).   student2008 20081016 13:54:16  LOL! The simplest way here is to calculate the interval , it should be equal to . This can't be true for (A) & (B), and in (D) . But, it is correct for (C).
In general situation (i.e. when y's and z's also change) this is the only practical method. You would get stuck using the general form of transformations.
neon37 20081029 01:52:17 
Note: ds=0 for light.
spacelike
null
timelike

  FortranMan 20081012 08:58:48  you can eliminate D by remembering that must be greater than 1. To absolutely eliminate E, note that here , then double check .   evanb 20080626 19:37:47  Actually, that's not enough to satisfy that it's a Lorentz transformation.
Consider:
x' = 10x  1t
t' = 10t  x
According to the official solution, this would be a Lorentz transformation with and , but we can check that such a transformation is unphysical: and are not independent, and because
$\frac{1}{\sqrt{1\beta^2}} = \frac{1}{\sqrt{10.1^2}} = \frac{1}{\sqrt{0.99}} << 10 = \gamma$, this is not a legit Lorentz transform.
However, since the numbers here happen to be 5/4 and 3/4, we're in the clear.
Maxwells_Demon 20080921 17:12:38 
Wait, how are we in the clear??????? If gamma really is 5/4 then beta should be 3/5. Beta is clearly 3/4 = 0.75
So how is it a valid transformation?

 

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