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- Summary
- I have been working on this problem for days, and I can easily do the math, but I really can’t seem to conceptualize it. Please help!

In the Earth’s reference frame, a tree is at x=0km and a pole is at x=20km. A person stands at x=0 (stationary relative to the Earth), and at t=10 microseconds, this person witnesses two simultaneous lightning strikes. One of these strikes hits the tree he is standing under, and the other hits the pole at x=20km.

Now let’s say that a rocket is traveling at 0.5c relative to the Earth (and therefore Bob) in the positive x direction. If we synchronize the clocks of Bob and the Rocket, so x=x’=0 at t=t’=0, then when did the rocket view each of the lightning strikes occurring? (End Problem)

The math is just a little bit of algebra, and when you do this you get that the rocket views the lightning striking the tree at about 11 microseconds rather than the 10 microseconds that Bob measured. This makes perfect sense because the rocket is moving away from the tree.

Here’s what doesn’t make sense, the rocket views the lightning striking the pole at -27 microseconds. I understand that the rocket is moving towards the pole, so the time should decrease, but the time shouldn’t be negative here.

The reason for this is NOT because negative times can’t happen. If we go back to Bob’s frame, and you view the time it would take for the light to Reach Bob’s eye from the pole, it is about 60 microseconds or so. This means that the original strike, relative to the pole, would have occurred at about -50 microseconds.

Here’s the problem, we shouldn’t be getting a negative time in this case, because that would infer that the rocket is closer to the pole than Bob. I say this because we originally synchronized Bob and the rocket by saying that x=x’=0 at t=t’=0. Since this is true, if we have a negative t’, x’ will also have to be negative, meaning that the rocket is further away than Bob is, and this is significant because then the light would travel and hit Bob before it hits the rocket.

This is the huge dilemma that I have been having for days, so will someone please help me. My professor that taught me Special Relativity said that he isn’t able to understand why this is happening, the graduate students in my lab don’t understand why this is happening, and I definitely don’t.

Please let me know if I need to clarify anything further.

Now let’s say that a rocket is traveling at 0.5c relative to the Earth (and therefore Bob) in the positive x direction. If we synchronize the clocks of Bob and the Rocket, so x=x’=0 at t=t’=0, then when did the rocket view each of the lightning strikes occurring? (End Problem)

The math is just a little bit of algebra, and when you do this you get that the rocket views the lightning striking the tree at about 11 microseconds rather than the 10 microseconds that Bob measured. This makes perfect sense because the rocket is moving away from the tree.

Here’s what doesn’t make sense, the rocket views the lightning striking the pole at -27 microseconds. I understand that the rocket is moving towards the pole, so the time should decrease, but the time shouldn’t be negative here.

The reason for this is NOT because negative times can’t happen. If we go back to Bob’s frame, and you view the time it would take for the light to Reach Bob’s eye from the pole, it is about 60 microseconds or so. This means that the original strike, relative to the pole, would have occurred at about -50 microseconds.

Here’s the problem, we shouldn’t be getting a negative time in this case, because that would infer that the rocket is closer to the pole than Bob. I say this because we originally synchronized Bob and the rocket by saying that x=x’=0 at t=t’=0. Since this is true, if we have a negative t’, x’ will also have to be negative, meaning that the rocket is further away than Bob is, and this is significant because then the light would travel and hit Bob before it hits the rocket.

This is the huge dilemma that I have been having for days, so will someone please help me. My professor that taught me Special Relativity said that he isn’t able to understand why this is happening, the graduate students in my lab don’t understand why this is happening, and I definitely don’t.

Please let me know if I need to clarify anything further.