grav

2008-Nov-14, 01:15 AM

I've decided to start this thread again fresh. I'm still trying to get the simultaneity thing down pat. In the thread "Twin paradox (relativity)", SeanF provided a scenario very similar to the one I'm about to present.

Alice and Bob are born at the same time in the same reference frame (stationary to each other) at some distance from each other. Carl is born in a ship that is moving directly past Alice where their births coincide. Danielle is born in a ship that is moving directly past Bob where their births coincide. Carl and Danielle are in the same frame of reference and moving along the line from Alice toward Bob.

So let's say Alice and Bob observe that they, Carl, and Danielle were all born at the same time. That means that Alice and Bob measure the same distance between themselves as the distance between Carl and Danielle. Due to a simultaneity effect, Carl and Danielle cannot agree that all four were born simultaneously. That also means that Carl and Danielle cannot measure the same distance between Alice and Bob as themselves. So a length contraction must take place for the distance between observers in each frame. If Alice and Bob measure the same distance between observers in each frame, then Carl and Danielle must see their own distance greater and Alice's and Bob's as shorter. In that case, Carl would say that Danielle coincides with Bob first, so they are born at the same time and both older than himself, and then Alice and Carl coincide later.

Okay, now here's another scenario somewhat similar to the one from the end of "Lorentz contraction 2" after some discussion with KenG, which so far seems to be about the only way things can work out, but I'm still examining it. All four observers are originally stationary to each other. Alice and Carl coincide at some distance from where Bob and Danielle coincide. At T=0, Carl and Danielle then instantly accelerate to some relative speed to Alice and Bob. Or instead of instant acceleration, one can figure the acceleration is tremendous but acts over infinitesimal time, so there is virtually no distance gained and no time dilation over the time of acceleration.

According to Alice and Bob, then, Carl and Danielle will still coincide with them after the acceleration takes place and therefore the distance between them remains the same before and after the acceleration, so no contraction has taken place of the distance between them. Carl, on the other hand, has experienced a simultaneity shift so that he now views Bob and Danielle as future forward. So Carl says that Danielle and Bob have already separated, while Bob and Alice remain in the same places, so their distance stays the same, but since Danielle has already moved, Carl and Danielle's distance has elongated.

Danielle has also experienced a simultaneity shift so she views Alice and Carl as past. Yet in the past, Carl had not yet accelerated so he still coincides with Alice. Then Danielle should still see the distance between Carl and herself as the same as that between Alice and Bob.

So what's going on?

1) Why do each of the observers in the first scenario see the distance between observers in the other reference frame contracted while things occur differently in the second scenario?

2) Why is Carl the only one who will see an elongated distance of his own frame in the second scenario while the other three observe the same distances between observers in each frame as before, or do they?

3) How could we tell the true length of a ship or the distance between observers in another frame as the observers in that other frame observe it if each sees different lengths as in the second scenario where Alice and Bob, for instance, might not even see a contraction between Carl and Danielle after they have attained a relative speed, even if Carl and Danielle were within a ship that accelerated all at once?

Alice and Bob are born at the same time in the same reference frame (stationary to each other) at some distance from each other. Carl is born in a ship that is moving directly past Alice where their births coincide. Danielle is born in a ship that is moving directly past Bob where their births coincide. Carl and Danielle are in the same frame of reference and moving along the line from Alice toward Bob.

So let's say Alice and Bob observe that they, Carl, and Danielle were all born at the same time. That means that Alice and Bob measure the same distance between themselves as the distance between Carl and Danielle. Due to a simultaneity effect, Carl and Danielle cannot agree that all four were born simultaneously. That also means that Carl and Danielle cannot measure the same distance between Alice and Bob as themselves. So a length contraction must take place for the distance between observers in each frame. If Alice and Bob measure the same distance between observers in each frame, then Carl and Danielle must see their own distance greater and Alice's and Bob's as shorter. In that case, Carl would say that Danielle coincides with Bob first, so they are born at the same time and both older than himself, and then Alice and Carl coincide later.

Okay, now here's another scenario somewhat similar to the one from the end of "Lorentz contraction 2" after some discussion with KenG, which so far seems to be about the only way things can work out, but I'm still examining it. All four observers are originally stationary to each other. Alice and Carl coincide at some distance from where Bob and Danielle coincide. At T=0, Carl and Danielle then instantly accelerate to some relative speed to Alice and Bob. Or instead of instant acceleration, one can figure the acceleration is tremendous but acts over infinitesimal time, so there is virtually no distance gained and no time dilation over the time of acceleration.

According to Alice and Bob, then, Carl and Danielle will still coincide with them after the acceleration takes place and therefore the distance between them remains the same before and after the acceleration, so no contraction has taken place of the distance between them. Carl, on the other hand, has experienced a simultaneity shift so that he now views Bob and Danielle as future forward. So Carl says that Danielle and Bob have already separated, while Bob and Alice remain in the same places, so their distance stays the same, but since Danielle has already moved, Carl and Danielle's distance has elongated.

Danielle has also experienced a simultaneity shift so she views Alice and Carl as past. Yet in the past, Carl had not yet accelerated so he still coincides with Alice. Then Danielle should still see the distance between Carl and herself as the same as that between Alice and Bob.

So what's going on?

1) Why do each of the observers in the first scenario see the distance between observers in the other reference frame contracted while things occur differently in the second scenario?

2) Why is Carl the only one who will see an elongated distance of his own frame in the second scenario while the other three observe the same distances between observers in each frame as before, or do they?

3) How could we tell the true length of a ship or the distance between observers in another frame as the observers in that other frame observe it if each sees different lengths as in the second scenario where Alice and Bob, for instance, might not even see a contraction between Carl and Danielle after they have attained a relative speed, even if Carl and Danielle were within a ship that accelerated all at once?