- #1

JDoolin

Gold Member

- 723

- 9

Hi. I am trying to make my way through

http://www.mathpages.com/rr/s8-09/8-09.htm

one step at a time if I have too.

I already got stuck once, where it says:

The paper makes it sound like these two variables are constant, but the way it should be defined is

That way neither of the variables is a constant, and it makes sense to do impliciti differentiation.

Now I am stuck at another step, where it says:

When I solved equation (1) for t2 when t1=0, I got:

[tex]t_2 = \frac{2 c}{a} \pm \frac{c}{a}\sqrt{\left ( 2 - \frac{4 a L}{c^2} \right )}[/tex]

and I can't see how

[tex]\frac{1-\frac{a}{c}t_1}{1-\frac{a}{c}t_2}[/tex]

evaluates to

[tex]\frac{1}{\sqrt{1-\frac{2 a L}{c^2}}}[/tex]

http://www.mathpages.com/rr/s8-09/8-09.htm

one step at a time if I have too.

I already got stuck once, where it says:

If a pulse of light is emitted from the bottom of the elevator at time t1 and absorbed at the top of the elevator at time t2, we have the relation

The paper makes it sound like these two variables are constant, but the way it should be defined is

*"Let t1 be the time at the bottom of the elevator. Let t2 be the time at which a photon emitted from the bottom of the elevator at time t1 arrives at the top of the elevator."*That way neither of the variables is a constant, and it makes sense to do impliciti differentiation.

Now I am stuck at another step, where it says:

Solving equation (1) for t2 at the time t1 = 0, and inserting into this equation for that same instant, we get

When I solved equation (1) for t2 when t1=0, I got:

[tex]t_2 = \frac{2 c}{a} \pm \frac{c}{a}\sqrt{\left ( 2 - \frac{4 a L}{c^2} \right )}[/tex]

and I can't see how

[tex]\frac{1-\frac{a}{c}t_1}{1-\frac{a}{c}t_2}[/tex]

evaluates to

[tex]\frac{1}{\sqrt{1-\frac{2 a L}{c^2}}}[/tex]

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