Relativity interstellar travel question

[Phymath]

well the textbook question is (transfer me over to hmwk help its ok)

2 Civilizations are evolving on oppposite sides of our galaxy (d = 10^5 ly) at time t = 0 in the galaxy frame of reference, civilization A launches its first intersteller spacecraft , 50,000 years later, measured in the galaxy frame, civilization B lunches its first spacecraft . a being from a more advanced civilization, C, is traveling through the galaxy at .99c on a line from A to B. Which civilaztion does C judge to have first achieved interstellar travel, and how much in advance of the other?

the book given answer is as follows but how?
C judge B 1st by 350,000 years

well I assumed anyways that C would observe B because the light from B is going to get to him before the light from A gets to him seeing how it has to travel 10^5 ly s so how do i calc this?

 

[Fredrik]

well I assumed anyways that C would observe B because the light from B is going to get to him before the light from A gets to him seeing how it has to travel 10^5 ly s so how do i calc this?

That's a mistake. It has nothing to do with what light reaches C first. Suppose e.g. that observer C is right next to A when they launch. Then he will definitely see the light from A first, but B will still have launched 350000 years earlier in C's frame.

I won't do the calculation for you, but I'll try to tell you how I like to visualize these things.

First, think of space as a 2-dimensional plane (instead of 3-dimensional). Now you can think of spacetime as a one-parameter family of such planes. (Just imagine a bunch of planes stacked on top of each other). Each plane represents space at a certain time. Planes that are higher in the "stack" represent later times.

What we have done here is to "slice" spacetime into hypersurfaces that represent space at different times. Now we get to the point: The "slices" of spacetime that represent space at different times to a moving observer are not perpendicular to the planes that we think of as space at different times.

In the galaxy frame, the event "B launches" is located on a plane that is higher in the stack than the plane that contains the event "A launches". That's why we say that B launches at a later time. But observer C is not using the same "slicing" of spacetime as we (the galaxy frame) are. His "slices" are tilted towards him, so much that to him, "B launches" is on a lower plane than "A launches".

Why are the the "slices" tilted towards him, and not away from him? How much are they tilted? I'm not going to try to explain this here, but if you would like to understand it I recommend that you read about spacetime diagrams, in particular the stuff about how to draw another observer's coordinates inside your own coordinate system. The relativity book by Schutz does this really well.

 

[MiGUi]

I think that we use our actual logic to imagine that kind of problems, as in the 30s they imagine a world full of high zeppelins instead of planes, and more years before they imagine vapour trains with wheels of seven meters to reach 400 km/h.

Maybe in the future, we are able to reach hyperspace, as Asimov thaught.

 

[Phymath]

right...so about those calcs...im much more a symbol person so that would greatly help

 

[Doc Al]

Lorentz Transformations

right...so about those calcs...im much more a symbol person so that would greatly help

Are you familiar with the Lorentz transformations? They allow you to translate the space-time coordinates of events (for example: the position and time that each ship took off) from one frame (the galaxy frame) to another (the frame of observer C).

 

[Phymath]

yes, ok let me just clearify everyone this is not any type of homework its just a question in a textbook at the library and was wondering if someone could show me the calcs...

 

[daredevil_23]

calc relativistic gamma (δ~7.088); Δt = 50000 yrs; v = 0.99 l.y./yr; c= 1 l.y./yr; Δx = 10^5 l.y.

Δt' = δ(Δt-(v/c^2)*Δx)

gives Δt' ~ -347,000 yrs (therefore B launches before A)