# Two oposite beams and earth and rocket again

## Main Question or Discussion Point

I am sure this question in some form gets posted here all the time again and again, but I somehow can not find it in the form I would recognize, so my appologies for probably posting it again.

So one of the classics: Two light beams - A and B get launched from Earth to the opposite directions at the same moment from the same place. A rocket with some man inside of it launches in the direction of B beam at the same time the beams get launched and from the same place. Another man stays on earth at that particular spot. Let's assume light moves 1 megameter per second and rocket immediately accelerates to 0.5 megameters per second.

.........=>......
A<----|--->B

I kind of had a good and intuitively pleasing explanation on what happens with the rocket man, earth man and beam B. So after 1 earth man's second he says that beam is 1 megameter away from earth, but the rocket man objects that after 1 rocket man's seconds the beam is 1 megameter away from his ship - as his ship is already 0.5 megameters away from earth then it's 1.5 megameters away from earth and not 1. Here the slowing down of the rocket man's clock would be a very cool and easy to understand explanation of the phenomena that both see beam B leaving them with the same speed of 1 megameter per second, even though rocket man is chasing it. I kind of got the feeling that now I understand everything:) And then I started to think about beam A...:)

Ok, just to be closer to the real situation I included into the calculations the time that is needed for the information about the location of both beams to be delivered to the ship and earth. So the picture from earths point of view after 1 second looks the following:
1) A is 0.5 megameters away from Earth (it actually is further but that information has not reached Earth yet)
2) B is also 0.5 megameters away from Earth
3) Rocket man should see beam B being 0.75 megameters away from the rocket,
4) Rocket man should see beam A being 0.25 megameters away from the rocket.

So my common sense and the so often heard word simetry (not intuition of course) says that rocket man says the same replacing Rocket <> Earth and A <> B.

And the results of the experiments with light say that rocket man in reality should see both beams being away the same distance all the time, i.e., there can be no such moment that the rocket man sees beam B being 0.75 megameters and beam A being 0.25 megameters away from the rocket.

So - how do you grasp this from the Earth man's point of view? How is the rocket man misinterpreting the data? Is it so that from Earth man's point of view the rocket man sees everything behind him squeezed by ~0.375 and everything in front of him expanded by ~2 and what about the clock then... Or this question does not make sense due to some reason?

## Answers and Replies

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Mentz114
Gold Member
jviksne : welcome to the forum.

So after 1 earth man's second he says that beam is 1 megameter away from earth
I must point out to that if you shine a beam of light away from yourself, you have no way of knowing where the wavefront is unless some of it is reflected back to you.

So in your thought-experiment, you need a line of matter along the path of the beams, in order to follow the wavefront. This means there is another delay because the reflected light has to get back to the rocket or earth guy.

This changes the setup and your conclusions may well be different.

I must point out to that if you shine a beam of light away from yourself, you have no way of knowing where the wavefront is unless some of it is reflected back to you.

So in your thought-experiment, you need a line of matter along the path of the beams, in order to follow the wavefront. This means there is another delay because the reflected light has to get back to the rocket or earth guy.

This changes the setup and your conclusions may well be different.
It doesnt matter if you can detect the light or not... Hes talking about the predictions SR makes as to where the light is. Plus, you ALWAYS take travel times into account so that the delay of the reflected light is irrelevent.

Ok, just to be closer to the real situation I included into the calculations the time that is needed for the information about the location of both beams to be delivered to the ship and earth. So the picture from earths point of view after 1 second looks the following:
1) A is 0.5 megameters away from Earth (it actually is further but that information has not reached Earth yet)
2) B is also 0.5 megameters away from Earth
3) Rocket man should see beam B being 0.75 megameters away from the rocket,
4) Rocket man should see beam A being 0.25 megameters away from the rocket.
here is where your mistake is. Beam A and B are always t megameters away from the earth from the earths frame for all t. Similarly they are t megameters away from the rocket in the rockets frame.

Therefore after 1 second in earth's frame:
1) A is 1 megameter away from Earth
2) B is 1 megameter away from Earth
3) Rocket man is .5 megameters from beam B and 1.5 megameters from beam A

after 1 second in rocket man's frame:
1) A is 1 megameter away from Rocket man
2) B is 1 megameter away from Rocket man
3) Earth is .5 megameters from beam A and 1.5 megameters from beam B

Mentz114
Gold Member
michael879:
He's talking about the predictions SR makes as to where the light is.
Why does jviksne say 'see' ?
3) Rocket man should see beam B being 0.75 megameters away from the rocket,
4) Rocket man should see beam A being 0.25 megameters away from the rocket.
Your analysis is probably right.

Why does jviksne say 'see' ?
eh idk, maybe I misinterpreted him. Its pretty clear you cant see a beam of light moving away from you so I assumed he was talking about its (undetectable) position.

Thanks for the replies!

In the first situation with beam B only I was talking about the predicted positions. Let's discard this completely.

In the second situation I was talking about the detected situation on Earth and what would the Earth man think should be the detected situation for the rocket man.

So there are the following situations (location of both beams) after one second:
1) Earth man's detected situation for Earth (A&B 0.5m away),
2) Earth man's predicted situation for rocket's detected situation if he would not know the Special Relativity theory at all (A 0.75 m away, B 0.25 m away).

Point 2 seems messy but it is actually what the rocket man would see if there was no relativity (I do not say that such a world is possible here. In other words - in the Earth man's world (frame of reference) after one second the rocket man should see A beam 0.75 m away and B beam 0.25 meters away. The question is how the world looks to the rocket man at this moment.

I think I myself now can answer the question (i.e., how the world that earth man sees looks to rocket man at that moment).

The earth man should wait for half the second for the image of the rocket man to arrive, then check what rocket man's clock shows in that image and then remember how the distances between the beams, earth and rocket looked to him when his clock showed that time to him and just exchange both beams and earth <> rocket.

Now the question is what time would he see in the image that arrived. So the image arrives from one particular spot from earth man's frame. As soon as the rocket man accelerated this spot appeared to him to be closer and thus with his speed reachable faster than in one second. So I guess his clock shows ~0.5 seconds in the image.

After 0.5 seconds Earth man predicted rocket being 0.25 m away, beam A being 0.75 m away from it and beam B being 0.25 m away. So if we symmetrically switch then in the image the earth man receives he sees the rocket man thinking that beam A is 0.25 m away from earth, rocket is 0.25 from earth and beam B is 0.5 m away from rocket and 0.75 m away from earth. And he sees the earth compressed towards him. And all the objects that are in front of him will visually look more stretched than they look to the earth man.

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