Re: Challenging exercises in relativity theory


Spoonfed wrote:
Ben Rudiak-Gould wrote:
Spoonfed wrote:
My concept is that the original angle is 90 degrees because that is the
way we set up the problem. I chose .866c because the Lorentz Factor is
2, then I thought of the plane that contains earth and RocketShipB as a
receding flat perpendicular surface, on which, due to time dilation,
everything goes at half the speed. So the plane is receding at .866c
and the rocketship is moving along the plane at .433c from
RocketShipA's perspective. This forms a 30 degree angle, and if
correct, it would be another 30 degrees at RocketShipB's perspective.

You'd need to use the redshift formula rather than the time dilation formula
for that. I don't recommend this approach. I think it would be hard to get
right.


I'm now quite certain it is 150 degrees.

If you're going to make a mistake, make it loud. That's what my
marching band director used to say.

Consider the idea of a larger
spacecraft going by at .866c. On this spacecraft, there is a design
that appears to have a line oriented straight toward you, and another
oriented forty-five degrees. As the spacecraft goes by, I can imagine
the spacecraft grabbing one of the rocketships, and the other
rocketship moving straight along the forty-five degree stripe. The
rocket that was grabbed would now see the ship in all of its
UN-contracted form. What was a forty-five degree angle becomes a 30
degree angle. 90+30+30=150.


When the UN-contracted form comes out, you have the y-coordinate stay
the same, while the x-coordinate doubles. So you go from an angle
whereTan(theta)= 1 to where Tan[theta]=2. I was calculating
ArcCos[1/2] instead of ArcTan[1/2].

I'll have to work my way through what you did and see any place where
our assumptions differ.

Nope, no difference in assumptions.

Good job, Ben.

.

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