Both you and the earth-bound observer will agree that the two reflected flashes of light get back to you at the same time. You both will also agree about the total round-trip distance covered by each flash of light
They will not agree on the total distance traveled by the flashes. For the Earth observer, the time between emission and detection is longer due to time dilation and the flashes therefore travel further as their speed is c.
I'm sorry, I wasn't clear. I was trying to say that they will agree that the forward-directed and the rearward-directed flash cover the same round-trip distance. They won't agree about what that round-trip distance is, for exactly the reason that orodruin gives.
The reflections will happen at different moments, but both front and rear paths will arrive back to the flashlight at the same moment.
If you're saying that when using the Earth frame to do or calculations, the reflections of the two flashes from their respective mirrors are not simultaneous events, that is correct.
@Zephaniah - just to stress this: if two flashes of light arrive at a point at the same time in one frame they must do so in all. Why? Because you could build a simple brightness detector that returns signal strength zero when not illuminated, strength one when illuminated by one pulse, and strength two if illuminated by two pulses at the same time. Then you wire it to a bomb (or something similarly irrevocable) that will detonate if it receives a strength two signal. If the frames disagree on whether or not the pulses arrive at the same time then they disagree on whether or not everything is in little pieces or not. This kind of non-consistency wouldn't make sense.
Both front and rear paths will arrive back tl the flashlight at the same moment but the they are reflected are not the same. The light reflected from the rear part will be reflected first before the front.
Question is "What will someone on Earth see?"
Let us just apply the two postulates of Einstein.
I think you understand it, but your explanations are not clear. Earlier, you wrote:
It's not clear what is being hit in this sentence. Since you've already talked about the reflection events, SlowThinker, Nugatory and I all read it as referring to the observer in the middle of the rocket. That would be wrong, as discussed above. If you intended it to repeat your statement about the reflection events then it is correct, but you didn't completely answer the question about what the observer in the rocket sees.
No it is not. The only questions in the OP are:
This clearly refers to the light coming back to you, not its reflection on the wall.
The second question is a clear reference back to the first in my opinion. There is never a question regarding whether or not the flashes hit the mirrors at the same time. The bolded part would have sufficed as an answer to the OP.
It is physically impossible to travel at the speed of light, so the laws of physics won't be able to answer that question. You're basically asking how to apply the laws of physics in a situation in which they cannot be applied.
If the ship is traveling at constant speed it would be possible to define an inertial reference frame in which it is at rest. If it were traveling at the speed of light then light would be at rest in this frame. But one of the two postulates of relativity is that the speed of light is the same in all inertial reference frames, so your question contains a direct contradiction (a frame in which light is both at rest and moving at 3×108m/s) and therefore has no answer, as Nugatory says.
No. The answer is that you traveling at the speed of light is an incoherent concept in relativity (see posts 21 and 22). There is no way to describe a headlight traveling at the speed of light, so asking what it would do if it did cannot be answered.
Yes, it is impossible to travel with a speed of light but take note that it is just a "What if" question. And as what I am always saying, please refer to the 2 postulates of Einstein.
You cannot expect a theory to tell you anything about a "what if" question that violates its basic postulates.
"What if" questions with impossible premises are impossible to answer.
Let me ask you a what if question: what if there were a single sheep that was both completely black and completely white at the same time. What colour would it be? Is the answer black, white, grey, or "this question makes no sense"?
You are always saying it. You don't seem to be doing it. Please re-read my post #22, where I explicitly use the invariance of the speed of light to show how the question is self-contradictory.
What color is that sheep again?Yes, it is a what if question, but wouldn't an outside observer see a light?
Not really a helpful way of thinking about it. Your inability to reach one hundred miles per hour is a mere technical challenge, not a logical impossibility.Well, try to think of it this way: It is impossible for me to run a hundred miles an hour, but if I could, would I get to that town 100 miles away in one hour?
That isn't the question you are asking. You are asking how much energy you would use in the run. But a realistic model of you running at 100mph would involve you tearing ligaments and collapsing - so there's no way to answer that question.Well, try to think of it this way: It is impossible for me to run a hundred miles an hour, but if I could, would I get to that town 100 miles away in one hour?
The answer is: it depends relative to what frame your speed is measured and relative to what frame the time to get there is measured.Well, try to think of it this way: It is impossible for me to run a hundred miles an hour, but if I could, would I get to that town 100 miles away in one hour?