Acceleration effect

this is a good explanation and revision on relativity of simultaneity by dr. Gary Felder

we shall ask if a body {A} is accelerating relative to resting body , how will the clock of resting body {B} seen by the accelerating body ?

1-if {A} is accelerating towards {B} ,{A} will see clock of {B} running faster than his own.

2-if {A} is accelerating away from {B} , {A} will see clock of {B} running slower than his own.

To answer why this is, I have to say a bit about how simultaneity works in special relativity (SR). In Newtonian physics, there's never any ambiguity about which two events are and aren't simultaneous. You can synchronize all of the clocks in the universe and they will always stay synchronized, no matter where they are and no matter how they move. Every observer agrees about the time at which any given event takes place. In SR, things work differently. Because different clocks move at different rates, two observers can disagree about what time a given event occurs. Thus the statement "These two events happened simultaneously" is something that can be true in one reference frame but not in another.

To make this more concrete, let's consider two reference frames, which I'll call A and B. Reference frame A consists of a planet. Reference frame B consists of a series of rockets flying by this planet, all at rest relative to each other. From A's point of view all of the rockets are moving with the same velocity v. From B's point of view all of the rockets are at rest and the planet is moving with velocity -v.

Now consider Bob, who lives in rocket number 0. At some moment Bob's rocket passes by planet 0, where Alice lives. Let's suppose that at that moment both Bob's clock and Alice's clock read 12:00. I've drawn the situation below:

... B:-2 --> B:-1 --> B:0 --> B:1 --> B:2 ...
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The arrows show the direction that the rockets are moving (to the right) according to Alice. Remember that Bob says the rockets aren't moving and the planet is moving to the left, but either way they both agree that some time later Alice will be next to rocket B:-1, where she'll meet Bruce. Here's the crux of the argument. Bob says that all of the clocks in all of the rockets are perfectly synchronized. From Bob's point of view none of the rockets are moving and they have had plenty of time to send signals back and forth getting all of their clocks perfectly in synch with each other. When Bob passes Alice, he therefore says that not only does his clock read 12:00, so does Bruce's. Let's imagine that according to Bob and Bruce it's going to take an hour before Alice is next to Bruce. In other words at the moment they pass each other, Bruce's watch will read 1:00. What will Alice's watch say? Since Bob and Bruce say her clock is running slowly, it will only say 12:30. To recap, when Alice is next to Bob their watches both say 12:00. When Alice is next to Bruce his watch says 1:00 and hers says 12:30.

How does Alice resolve this seeming contradiction? According to her Bruce's watch should be running slower than hers. Since her watch only ticked off half an hour in between the two meetings, she has to say that Bruce's watch only ticked off a quarter hour. And yet she sees that when they meet Bruce's watch says 1:00. The only way Alice can reconcile these facts is to say that at the moment when she was with Bob, Bruce's watch said 12:45.

Let's stop for a moment and see what we've just said. We can consider three separate events here. One is the meeting of Alice and Bob, which occurs at 12:00 on both of their watches. The next one is the event of Bruce looking at his watch and seeing 12:00. Finally, there's the event of Bruce looking at his watch and seeing 12:45. If I call these events 1, 2, and 3 respectively, then in reference frame B events 1 and 2 are simultaneous (and event 3 happens later), while in reference frame A events 1 and 3 are simultaneous (and event 2 happens earlier). Note that everyone agrees that all of these events happened. Perhaps when his watch said 12:00 Bruce drew a dog and when it said 12:45 he drew a cat. Everyone can get together afterwards and agree that both drawings are there; all of those events took place. They will even agree that he drew the dog before he drew the cat. However, Alice will say that he drew the dog long before her meeting with Bob, while Bob and Bruce will both say that Bruce drew the dog at the exact moment when, many miles away, Alice and Bob were saying hello.

From what I've said so far, we can figure out what an accelerated observer should see. Suppose someone else, call her Carol, is traveling along with Bob. Being in reference frame B she knows that her watch, which she keeps in synch with Bob's, is also in synch with Bruce's watch, many miles away. Now suppose that at the moment when Bob passes Alice, Carol hops off the ship and lands on the planet with Alice. In so doing Carol accelerates and thus jumps from one reference frame (B) to another (A). When she does so, a strange thing happens from her point of view. Her clock says 12:00, before and after she jumps ship. Moreover she agrees that Bob's and Alice's both say 12:00 before and after the jump. In other words in the one second it takes her to switch reference frames she doesn't see anything odd happen right where she is. However, when she was in reference frame B she said that Bruce's watch said 12:00. When she switches to reference frame A she suddenly says that Bruce's watch says 12:45. This is an example of the phenomenon I described before. During the one second when she is accelerating, she says that Bruce's watch is running much faster than her own. This is a result of the fact that she is switching from a reference frame in which Bruce's clock reads 12:00 to a reference frame in which it reads 12:45, so from her accelerated point of view Bruce's clock jumped ahead 45 minutes in the one second it took her to jump ship.

here ends the explanation and I think it is so clear thanks to dr. Gary Felder.

but when I knew these information a new question jumped to my mind about one idea which may seem confusing and so I set this thought experiment:

WE HAVE 2 BODIES [A] AND [B] AT REST AND AWAY FROM EACH OTHER WITH THEIR CLOCKS SYNCHRONIZED,

A THIRD BODY [C] IS BETWEEN THEM AND START TO ACCELERATE TOWARDS [B] THUS [C] IS ACCELERATING TOWARDS [B] "I.E. SEES CLOCK OF [B] READING MORE" AND ALSO ACCELERATING AWAY FROM [A] "I.E. SEES CLOCK OF [A] READING LESS"

HOW COULD THIS HAPPEN ,IT IS A CONTRADICTION { THEIR CLOCKS MUST READ THE SAME}

IT IS NOT A CONTRADICTION BUT IT IS A RESULT WHICH MUST BE EXPECTED AS ACCORDING TO [A] & [B] THE TICKS OF THEIR CLOCKS ARE SIMULTANEOUS

SO THESE TICKS MUST BE NOT SIMULTANEOUS ACCORDING TO [C] AS HE MUST SEE TICKS OF [B] HAPPENS BEFORE [A] IN [C] FRAME.

by this point we shall conclude that the key point for solving many paradoxes in special relativity is to take care of "relativity of simultaneity" and we will use this point in the next paper for solving some paradoxes.

there is also another explanation for why {A} sees clock of {B} running faster when {A} is accelerating towards {B} and slower when {A} is accelerating away from {B}.

it depends on general relativity and equivalence principle {explained within general relativity}, when {A} is accelerating he can consider himself resting and refer the changes happening to a gravitational field its source is behind him and thus act in an opposite way of acceleration of {A}.

we knew from general relativity that the clock of {A} -nearer to gravity source and has higher gravitational potential-, runs slower than {B} -farther from the gravity source and has lower gravitational potential- .this happens when {A} is accelerating towards {B} , but when {A} is accelerating away from {B} , {B} becomes behind {A} and thus nearer to gravity source and have higher gravitational potential so clock of {B} runs slower as seen by {A}.

remember that the explanation in the above paragraph is from point of view of {A} ,since {B} never feels this gravity.
Equivalence principle preserves the concept of relative motion as it says that even the body in a non inertial frame of reference can consider himself resting and refer the effects he sees to a gravitational field.

Effect of acceleration on time flow