Can Spaceships Travel Faster Than the Speed of Light?

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multiix
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Two spaceships are traveling relative to Earth (stationary). One spaceship is going to the right at 0.8c the other is going to the left at 0.8c. Could you say their relative speed to one another is .8c+.8c? I'm thinking not since you can't possible go faster then the speed of light, doesn't matter what the frame of reference is.

Please Help me with the Theory behind this
 
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multiix said:
Two spaceships are traveling relative to Earth (stationary). One spaceship is going to the right at 0.8c the other is going to the left at 0.8c. Could you say their relative speed to one another is .8c+.8c? I'm thinking not since you can't possible go faster then the speed of light, doesn't matter what the frame of reference is.

Please Help me with the Theory behind this

That is their relative speed wrt the earth, not the speed of one to another (note that "relative" can be omitted for the last). So, if for relative speed you use the definition of "difference of speeds" (as Einstein did and as I learned it) then it does matter what the frame of reference is. Further, see the links already provided.