Understanding Simultaneity in Special Relativity

[neurotoxin]

Hi everyone!

I am new here. I like physics and so I am trying to understand a few things. I think I understood the Newton physics. Now I am reading about relativity.
I began wiht special relativity. I just learn the two postulates. I think I can accept them without problems. I also read about the simultaneity issue. But before I proced I would like to be sure that I anderstood what I have learned so far. So I will try to post a litle question to see if someone can help me on this... Sory about my english... Ok, let's go!

Let's supose the following situation:
There is a rectilinear path A-B-C where B is half way from A to C. An observer is on his way from A to C at velocity "V". At the exact time when he passes through position B, two gun shots are fired. One from A and the other from C. Both in B direction. The shotguns also emited a flash of light at the time of the shots. So both bullets and light beams are on their way to position B.
I belieave I have learned so far that the observer in movement from A to C will first see the light from C than the one from A, and then will take the shot from bullet coming from C also first than the one coming from A.

Is this correct?

If so, then I have to conclude that there is no diference in the behavior of the light and the bullet.
But from the postulates of special relativity, I understood that light travels always at "c" from the point of view of any observer, independently of his velocity. So, will it be supid to say that the observer from my experiment should see both light beams at the same time??
If not, than for me the light behaves just as a simple bullet...

Can someone write a few words about this please?
But please go easy on me, because I am a slow learner...

Thank you all!

daniel

 

[JesseM]

Let's supose the following situation:
There is a rectilinear path A-B-C where B is half way from A to C. An observer is on his way from A to C at velocity "V". At the exact time when he passes through position B, two gun shots are fired. One from A and the other from C. Both in B direction. The shotguns also emited a flash of light at the time of the shots. So both bullets and light beams are on their way to position B.
I belieave I have learned so far that the observer in movement from A to C will first see the light from C than the one from A, and then will take the shot from bullet coming from C also first than the one coming from A.

Is this correct?

That's correct, if you assume that the guns were at rest at points A and B. On the other hand, suppose the guns were also moving at velocity V in the A-B-C frame, one behind the observer and one ahead of him. Suppose that the distances are such that, at the moment the observer passes B, the first gun is passing A and the second gun is passing C, and at that moment the guns both fire in the direction of B (since simultaneity is relative, assume all these events happen simultaneously in the A-B-C frame). In this case, in the A-B-C frame the gun at A is firing in the same direction as its motion, and the gun at C is firing in the opposite direction as its direction of motion, so the bullet from the gun at A will be moving faster than the bullet from the gun at C in the A-B-C frame. In the frame of the observer between the two guns, the guns are at rest, so both bullets move at the same speed in his frame and will both reach him at the same time.

In contrast, if you have two laser guns, all observers will measure the photons they emit to move at c in their own frame, regardless of how the laser guns are moving. Even if the laser guns are moving at speed V in the A-B-C frame as in my example above, the photons from each gun will still move at c in the A-B-C frame, so if the two laser guns fire simultaneously in the A-B-C frame, the photons from the laser gun at C will reach the observer in the middle before the photons from the laser gun at A. And yet in this observer's own frame, the laser guns are at rest, and he will also measure both photons to move at c towards him, so the only way he can account for the fact that the photons from the laser gun at C reached him first is to assume that laser gun reached point C and fired before the other laser gun reached point A and fired (which makes sense since in his frame the distance between A and C is smaller than the distance between the laser guns due to Lorentz-contraction).

 

[paw]

Let's supose the following situation:
There is a rectilinear path A-B-C where B is half way from A to C. An observer is on his way from A to C at velocity "V". At the exact time when he passes through position B, two gun shots are fired. One from A and the other from C. Both in B direction. The shotguns also emited a flash of light at the time of the shots. So both bullets and light beams are on their way to position B.
I belieave I have learned so far that the observer in movement from A to C will first see the light from C than the one from A, and then will take the shot from bullet coming from C also first than the one coming from A.

Is this correct?

As far as it goes yes.

Let's look at the light first. Assuming the flashes were simultaneous in B's frame then the observer will see the light from C before the light from A.

As for the bullets, if the bullets are traveling at v<=V then the bullet fired from A will never reach the observer while the bullet from C will reach the observer some time after the flash. This is different from the case of light in which both flashes will always reach the observer.

 

[RandallB]

... I also read about the simultaneity issue.
… supose the following situation:
There is a rectilinear path A-B-C where B is half way from A to C. An observer is on his way from A to C at velocity "V". At the exact time when he passes through position B, two gun shots are fired. One from A and the other from C. Both in B direction. The shotguns also emited a flash of light at the time of the shots. So both bullets and light beams are on their way to position B.
I belieave I have learned so far that the observer in movement from A to C will first see the light from C than the one from A, and then will take the shot from bullet coming from C also first than the one coming from A.

Is this correct?

NO IT IS NOT CORRECT.
The problem comes in understanding the simultaneity issue which you’ve only read about.
A fundamental principle defined from SR is how reality treats the “simultaneity issue” in that for spatially separated events (things separated by distance) there is no such thing a “real simultaneity”. Except where two inertial reference systems are essentially the same internal reference system no two will agree on the time for each of the three events you describe. And based on SR no individual reference system can be defined as the “correct” preferred frame to actually identify if your three events (“At the exact time when he passes through position B, two gun shots are fired. One from A and the other from C.”) in fact happened at the same time.

Based on SR, it can only be measured as having appeared to be simultaneous for a particular reference frame. And no option for defining a preferred frame is offered by SR.

This makes a big difference in how you can describe and interpret such examples, so it is important you gain an understanding of the simultaneity issue.

 

[neurotoxin]

Well, maybe its better for my understanding to separate things... I think that one can say that two events are simultaneous if he received the information from the light from the two events at the same time.
But let's try to forget simultaneity for now, just to see if I can clarify things in my mind.
OK?

I'll try to put it in the simplier way I am able to:
I am traveling in the direction to a photon that is also moving in my direction. I don't know that I am moving, but I am! At a given time in my watch I am at 300000Km from the photon. If I start measuring time in my watch at that distance, how long will the photon take to reach me?
Can I put it this way?
I just did it because one of the SR postulates says that the ligth always travels at "c". So I can say that no matter what my velocity is, I see the photon traveling to me at "c". Then it will take one second!
My question is really a basic one, but I really would like to understand it!

Thanks a lot for your answers.

daniel

 

[JesseM]

Well, maybe its better for my understanding to separate things... I think that one can say that two events are simultaneous if he received the information from the light from the two events at the same time.

Only if both events happened the same distance away from me! If they didn't, then I can receive light from two events at different times and still call them simultaneous in my frame. For example, if on Jan. 1 2010 I receive light from an event exactly 5 light years away (both time and distances measured in my frame), and then on Jan. 1 2015 I receive light from an event exactly 10 light years away, then I'll say these events happened simultaneously in my frame, on Jan. 1 2005.

I'll try to put it in the simplier way I am able to:
I am traveling in the direction to a photon that is also moving in my direction. I don't know that I am moving, but I am!

In relativity it is meaningless to ask whether someone "is moving" or not, all motion is relative. What we can say is that in the frame of some other observer, you may be moving in one direction while a photon is moving towards you in the opposite direction, and in this frame (as in all frames) the photon is moving at c.

At a given time in my watch I am at 300000Km from the photon.

300000 km from the photon in your rest frame, or 300000 km away in the frame where you are moving? Remember that different frames measure distance differently, because each frame defines distance in terms of rulers at rest in that frame, and rulers which are moving in some frame will be measured to be shrunk in that frame.

If I start measuring time in my watch at that distance, how long will the photon take to reach me?

If the photon is 300000 km away from you in your frame, then the light will take about 1 second to reach you in your frame.

I just did it because one of the SR postulates says that the ligth always travels at "c". So I can say that no matter what my velocity is, I see the photon traveling to me at "c". Then it will take one second!

But it's meaningless to ask what "my velocity is" in any absolute sense. There is only velocity relative to some frame or another. But yes, in your own rest frame the photon is always coming towards you at c, so if it's 300,000 km away from you at some time in your frame, then it will take about 1 second to reach you in your frame.