Does time go backwards if object is going faster than light?

[adimantium]

Lets pretend I am in my spaceship going in one direction at 0.9c. My brother is in his spaceship going the opposite direction also at 0.9c. Oh and there is a big clock on the side of our ships. When we cross paths, to me it looks as if I'm not moving and my brother is moving at 1.8c. I am aware that the formula for time dilation is t0 = t√1-\frac{v^{2}}{c^{2}} and that velocities don't simply add together, the formula for that is V_{3} = \frac{v_{1}+v_{2}}{1+\frac{v_{1}v_{2}}{c^{2}}}. Using that formula for velocity the speed would be about 0.9945c. this only makes sense to me if the two velocities are in the same direction. So let's just forget the formula for velocity. I see my brother moving faster than light. Let's also pretend I have some kind of telescope that can perceive vision instantaneously. Using the time dilation formula, I would be left with t√-0.8 I know you can't really find the square root of a negative number, so what would I see? Would I see his clock run slow but forward like normal, not move at all, or backwards?

 

[Bill_K]

I am aware that the formula for time dilation is t0 = t√1-\frac{v^{2}}{c^{2}} and that velocities don't simply add together, the formula for that is V_{3} = \frac{v_{1}+v_{2}}{1+\frac{v_{1}v_{2}}{c^{2}}}. Using that formula for velocity the speed would be about 0.9945c. this only makes sense to me if the two velocities are in the same direction. So let's just forget the formula for velocity.

No, please don't forget it! It's correct. The formula the way you've written it assumes that the velocities are in the opposite direction. Moreover there's a recent thread which discusses how to add velocities that are in any direction.

 

[Ibix]

You can't just "forget" the formula for velocity addition. That's the way velocities add. So you don't see your brother traveling faster than light.

On a related note, nothing goes faster than light so you cannot perceive faster than light. It's common practice to imply that all players in an experiment are smart enough to subtract out lightspeed delay, which can confuse some students. But if something happens a light year away, we cannot know about it for a year.

So: you would see his clock running slow because of time dilation, but sped up (as he approaches) or slowed even more (as he moves away) because of the Doppler effect. You would never see the clock running backwards, or showing an imaginary time.

 

[D H]

So let's just forget the formula for velocity. I see my brother moving faster than light.

You do not see your brother moving faster than light. That formula that you want to forget is precisely what you need to use to explain why you see your brother moving at a speed less than the speed of light.