# Relative simultaneity

• I
• Kiley

#### Kiley

Imagine you are in the center of a ship moving at V to the right relative to earth. You have a flashlight in your hand and two perfect reflectors on each end of the ship. If you turn on the flashlight will you observe the reflected light from both ends to hit you simultaneously? What will someone on Earth see?

## Answers and Replies

Imagine you are in the center of a ship moving at V to the right relative to earth. You have a flashlight in your hand and two perfect reflectors on each end of the ship. If you turn on the flashlight will you observe the reflected light from both ends to hit you simultaneously? What will someone on Earth see?
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

You will find that the two reflection events happened at the same time, and that both flashes of light traveled the same distance on the outbound and return legs.

The earth-bound observer will disagree: for him the forward-moving flash traveled a longer distance on the outbound leg than on the return leg; the rearwards-moving flash traveled a shorter distance on the outbound leg and a longer distance on the return; and the reflection from the rear mirror happened before the reflection from from the forward mirror instead of at the same time.

Turning on the flashlight is a single event, so there's no simultaneity issue - it has to be simultaneous with itself. Likewise, "your eye and the two flashes are all at the same place" is a single event. However the two reflection events, one at each end of the ship, are two different events and different observers moving relative to one another may disagree about their simultaneity.

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David Lewis, Chestermiller, phinds and 1 other person
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.

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.

Imagine you are in the center of a ship moving at V to the right relative to earth. You have a flashlight in your hand and two perfect reflectors on each end of the ship. If you turn on the flashlight will you observe the reflected light from both ends to hit you simultaneously? What will someone on Earth see?

Event1 : His/Her flashlight flashes and lights start forward and backward at the same time.
Event2 : He/She receives lights coming from forward and backward at the same time.
These are common observed results in any IFRs. Since light speed is c in every IFR, lengths of two light tracks are same in any IFRs, though their values depend on specific IFRs chosen.

On your own inertial frame of reference, the light will hit you simultaneously because for you who is riding on a ship you are at rest and the Earth is moving.

Person on Earth's inertial frame of reference: The light will hit the rear part of the ship first than in front because the ship is moving at v to the right. And so therefore the light that hit the rear part of the ship will reflect first than in front. I'm saying that the light will not hit simultaneously.

Remember the two postulates of Einstein?

First postulate: The laws of physics are the same in all inertial frames of reference.

Second postulate: The speed of light in vacuum has the same value c in all inertial frames of reference

Person on Earth's inertial frame of reference: The light will hit the rear part of the ship first than in front because the ship is moving at v to the right. And so therefore the light that hit the rear part of the ship will reflect first than in front. I'm saying that the light will not hit simultaneously.
The reflections will happen at different moments, but both front and rear paths will arrive back to the flashlight at the same moment.

Person on Earth's inertial frame of reference: The light will hit the rear part of the ship first than in front because the ship is moving at v to the right. And so therefore the light that hit the rear part of the ship will reflect first than in front. I'm saying that the light will not hit simultaneously.
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.
However, the question being asked is: what does the person in the middle see? That is, what flashes of light reach their eyes at what times? If we calculate that both flashes of light reach their eyes together using one frame, then we must get the same result if we do the calculation in some other frame.

That is, what flashes of light reach their eyes at what times? If we calculate that both flashes of light reach their eyes together using one frame, then we must get the same result if we do the calculation in some other frame.
@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.

Kiley and Zephaniah
The reflections will happen at different moments, but both front and rear paths will arrive back to the flashlight at the same moment.
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.

The
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.
However, the question being asked is: what does the person in the middle see? That is, what flashes of light reach their eyes at what times? If we calculate that both flashes of light reach their eyes together using one frame, then we must get the same result if we do the calculation in some other frame.
Question is "What will someone on Earth see?"

And my answer is someone on Earth will see that the light will hit the rear part of the ship first than in front because the ship is moving at v to the right. And so therefore the light that hit the rear part of the ship will reflect first than in front and since the ship is moving at v to the right both the reflected light from the rear and front will arive at the same time in the middle.

If you really insist the question of what the person in the middle will see? The answer will be, he/she will see the light was reflected simultaneously.

@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.
Let us just apply the two postulates of Einstein.

If you really insist the question of what the person in the middle will see? The answer will be, he/she will see the light was reflected simultaneously.
I think you understand it, but your explanations are not clear. Earlier, you wrote:
Person on Earth's inertial frame of reference: ...I'm saying that the light will not hit simultaneously.
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.

Precise language is very important when discussing relativity (when discussing anything, really, but doubly so for relativity) since it is very easy to confuse yourself and others about what you are talking about.

Kiley
Question is "What will someone on Earth see?"
No it is not. The only questions in the OP are:
If you turn on the flashlight will you observe the reflected light from both ends to hit you simultaneously? What will someone on Earth see?
This clearly refers to the light coming back to you, not its reflection on the wall.

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.
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.

Precise language is very important when discussing relativity (when discussing anything, really, but doubly so for relativity) since it is very easy to confuse yourself and others about what you are talking about.

Imagine you are in the center of a ship moving at V to the right relative to earth. You have a flashlight in your hand and two perfect reflectors on each end of the ship.

A. If you turn on the flashlight will you observe the reflected light from both ends to hit you simultaneously?

B. What will someone on Earth see?

A. The reflected light will hit you simultaneously.

B. Someone on Earth will see the light to hit the rear part of the ship first than in front. Why? Because the ship is moving at a certain v to the right giving the rear part a shorter distance compared in front. There is a long distance in front because the ship is moving to the right. It mean that the light will have to catch up to the moving ship to hit the mirror. And so therefore the light that hit the rear part of the ship will reflect first than in front. The light will not hit the mirror simultaneously but the reflected light will arrive to the person in the middle at the same time.

Kiley
B. Someone on Earth will see the light to hit the rear part of the ship first than in front. Why? Because the ship is moving at a certain v to the right giving the rear part a shorter distance compared in front. There is a long distance in front because the ship is moving to the right. It mean that the light will have to catch up to the moving ship to hit the mirror. And so therefore the light that hit the rear part of the ship will reflect first than in front. The light will not hit the mirror simultaneously but the reflected light will arrive to the person in the middle at the same time.
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.

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.

I'm just explaining how did I come up with my answer.

Kiley
Thank you all for your responses. I appreciate everything you guys wrote including going beyond my original two questions and answering what will happen at the reflectors themselves.

Zephaniah
Imagine you are in the center of a ship moving at V to the right relative to earth. You have a flashlight in your hand and two perfect reflectors on each end of the ship.

What would be seen if the ship is traveling at the speed of light? Just a single flash at the center of the ship?

Zephaniah
What would be seen if the ship is traveling at the speed of light? Just a single flash at the center of the ship?
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.

What would be seen if the ship is traveling at the speed of light? Just a single flash at the center of the ship?
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.

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Kiley
What would be seen if the ship is traveling at the speed of light? Just a single flash at the center of the ship?

Maybe it would be interesting if you ask this,
What will happen if you are traveling at the speed of light and you opened your headlight?

Maybe it would be interesting if you ask this,
What will happen if you are traveling at the speed of light and you opened your headlight?

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.

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.

Yes, it is impossible to travel with a speed of light but take note that it is just a "What if" question.
You cannot expect a theory to tell you anything about a "what if" question that violates its basic postulates.

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.
"What if" questions with impossible premises are impossible to answer.

From a mathematical point of view, anything follows from a contradiction. So every answer is correct and no answer is meaningful.

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.

Here's the problem with this kind of "What if" question: It is that you have to assume that what we know about physics is wrong, while at the same time expecting to get an answer based on what we know about physics. You would have to replace the laws of physics with some new laws to allow for the scenario, and we have no idea as to what those new laws would entail, or what they would predict happens under those conditions.

Yes, it is impossible to travel with a speed of light but take note that it is just a "What if" question.
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"?

The question of what happens in an inertial frame traveling at the speed of light is just as nonsensical. It's just harder to see that, so people ask it in all innocence. The question makes no sense regardless, and your attempt at an answer is analogous to replying "black" to my sheep question. The only correct answer is to point out the contradictory premises and go from there. All other answers, yours included, lie between wrong and not-even-wrong.
And as what I am always saying, please refer to the 2 postulates of Einstein.
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.

Maybe it would be interesting if you ask this,
What will happen if you are traveling at the speed of light and you opened your headlight?

Yes, it is a what if question, but wouldn't an outside observer see a light?

Yes, it is a what if question, but wouldn't an outside observer see a light?
What color is that sheep again?

phinds and Ibix
What color is that sheep again?

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?

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?
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.

Your original question involves asking what happens if you are in a situation where light is both stationary and traveling at 3×108m/s. There can be no coherent answer to a question that doesn't make sense. I realize it isn't obvious that your question isn't coherent. I've explained (post #22) why it isn't, and I'm happy to help you understand that answer. But at some point you need to accept that there is no answer in the terms you want.

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.

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