Thought expriments

## Some thought experiments and their explanations

### by :Ahmed Khaled

in this paper we will recall the first thought experiment in the first paper and try to make its explanation clearer, and we will introduce another thought experiment.

Notes:

For better understanding of the subject of this paper you need to understand special relativity , you can read the other papers in the special relativity page of this site .

If you are familiar with the equivalence principle you can read the second experiment, other wise you had to read the other paper named
"acceleration effect"

### Thought experiment 1:

You're on Earth, and I fly by in my rocket as before. Right as we pass each other, we both start our stopwatches. When your stopwatch says that one minute has passed, you check my stopwatch. Because I'm in a different frame, my watch is running slow: it only says thirty seconds.

Now let's play that exact situation back from my frame. You looked at me after only thirty seconds; but your clock was running slow, so it said only fifteen seconds. CONTRADICTION! We agree that when you looked at me, my watch said thirty seconds: but did your watch say fifteen seconds (as I thought), or sixty (as you thought)? So we have taken what we intuitively felt made no sense, and exploited that to come up with a paradox that will test relativity: if there isn't a way out of that paradox, Relativity falls.

So, as you probably suspected, here is the way out of the paradox. The problem, as with most of modern Physics, comes in making the measurement. Suppose that when I passed you the first time, and we synchronized our watches, we were right next to each other. That means that sixty seconds later (your frame), when you checked my watch, I was a long way away. How do you look at my watch a long way away? Your eyes take in light that bounced off it; your ears take in sound coming from it; whatever you do, you're using something that traveled from me to you. And it took time to do it.

The point is, you can't say "I'm looking at his watch now." You have to say "I'm looking at light that came from his watch a while ago," and I have to say the same thing when I look at you. So when you and I are in different places, whatever we see about each other is old news. And we have to take that into account when we say "This is what I'm seeing on his watch," admitting that this is simply what his watch used to say. When we take that into account, we can plug through the math of Einstein's equations and we wind up without a paradox.

#### comment:

you may understand that the time dilation seen is only because that light takes time traveling from you to me or vice versa, but this is not the truth and the explanation doesn't mean that so I will say it in more clear way.

the contradiction was {did your watch say fifteen seconds (as I thought), or sixty (as you thought)?} , we really shall say that there is no contradiction , it says 15 in my frame but 60 in your frame.

the key is "the relativity of simultaneity" , the event of my clock reading 30 sec. is simultaneous with the event of your clock reading 15 sec. in my frame but it is simultaneous with the event of your clock reading 60 sec. in your frame, so time dilation is not an illusion but it is real thing.

### Thought experiment 2:

now another thought experiment which may be some way harder

A & B ARE 2 BODIES WHICH ARE AT REST IN EARTH'S FRAME AND THEIR CLOCKS ARE SYNCHRONIZED IN REST.

SIMULTANEOUSLY , THEY STARTED TO MOVE TOWARDS EACH OTHER.

{THEY ACCELERATE BY SAME RATE OFF COURSE}  UNTIL THEY REACH SAME VELOCITY AND THEN CONTINUE MOVING TOWARDS EACH OTHER.

{SO THEY ACT AS EACH OTHER ALL THE TIME}
AT THE POINT THEY PASS BY EACH OTHER EACH ONE LOOKS AT OTHER'S CLOCK.

what will they see???

really they see their clocks reading the same !! this has a very simple explanation,

WE CAN SAY THAT SINCE BOTH [A] & [B] ARE ACCELERATING THEY ARE OUT OF WORK OF SPECIAL RELATIVITY , AND THE RIGHT CALCULATIONS ARE THOSE WHICH RESTING BODY (IN EARTH'S FRAME ) DO.

AND ACCORDING TO RESTING BODY THEY ACT LIKE EACH OTHER SO THEIR TIME IS DILATED BY SAME PERIOD AS SEEN BY THE RESTING BODY SO NO CONTRADICTION OCCUR.
DEFECT: WHAT ABOUT THEIR OWN VIEW.
THIS IDEA IS ESCAPING FROM THE PROBLEM AND NOT A SOLUTION TO IT.

and another difficult one which I will explain in a very clear way by an explanation which would support many experiments of this type:

I will explain it from point of view of [A] and we can apply it by same way on [B]

from point of view of [A] ,he is resting and THERE ARE 3 PHASES:

1- A GRAVITATIONAL FIELD FROM BEHIND HIM CAUSES EARTH AND [B] TO RUSH TOWARDS HIM, BUT OFF COURSE [B] HAS HIGHER ACCELERATION THAN THE EARTH DUE TO HIS OWN ENGINES.
HERE THERE IS 2 EFFECTS AND NOT ONE:

i- [A] HAS HIGHER GRAVITATIONAL POTENTIAL SO HE SEES CLOCK OF [B] RUNNING FASTER THAN HIS OWN

ii-[A] CAN'T CLAIM THAT [B] IS MOVING ONLY UNDER THE EFFECT OF GRAVITATIONAL FIELD BUT HE MUST DECLARE THAT [B] IS ACCELERATING SO [A] SEES CLOCK OF [B] RUNNING SLOWER THAN HIM.
I meant here that time dilation is due to [B] movement {i.e. velocity}

THE 2 EFFECTS ARE EQUAL{ [A] & [B] ARE ACCELERATING By SAME RATE} SO THEY CANCEL EACH OTHER, in this experiment the 2 effects will not be equal but the first effect is more . but the 2 effects will be equal if they continue in this phase until they meet.

simply when they are far A will see for example the clock of B reading 10 before his own clock by 2 seconds (as his clock read 8) but as they get closer these 2 seconds diminish ,e.g. after some time A will see the clock of B reading 15 before his own clock by only 1 second (as his clock read 14) and so on , so as if they continue accelerating they will see their clocks reading the same at their meeting point.

* WHAT WILL CANCEL THE EFFECT OF MOVING  WITH UNIFORM VELOCITY???

2- THIS IS THE KEY PHASE ,  [A] & [B] START TO MOVE WITH UNIFORM VELOCITY SIMULTANEOUSLY IN EARTH'S FRAME SO [A] MUST SEE [B] START TO MOVE WITH UNIFORM VELOCITY {i.e. UNDER THE EFFECT OF GRAVITATIONAL FIELD ONLY} BEFORE HIMSELF IN FRAME OF [A].
IN THIS PHASE [B] WILL BE MOVING ACCORDING TO [A] UNDER THE EFFECT OF GRAVITATIONAL FIELD SO [A] SEES CLOCK OF [B] {IN THIS STAGE} RUNNING FASTER THAN HIS OWN ONE.

3- [B] MOVES WITH UNIFORM VELOCITY AND NO GRAVITATIONAL FIELD SO [A] WILL SEE CLOCK OF [B] RUNNING SLOWER THAN HIS OWN.

THUS THE EFFECTS IN SECOND AND THIRD PHASE CANCEL EACH OTHER

WE CAN REPLACE THE GRAVITY BY  EXPLANATION ABOUT [A] SHIFTING THROUGH SEVERAL FRAMES BUT HE ALSO MUST DECLARE THAT [B] IS ALSO SHIFTING THROUGH SEVERAL FRAMES AND HE MUST DECLARE THAT [B] START TO MOVE WITH UNIFORM VELOCITY BEFORE HIM {WHILE HE IS STILL SHIFTING}.

HERE  A NEW QUESTION RAISED AND THIS QUESTION MAY BE RAISED IN MANY EXPERIMENTS.

WHAT IF THE EFFECT IN THIRD PHASE IS MORE THAN THAT OF SECOND PHASE, MAY BE THEY MOVE WITH UNIFORM VELOCITY  FOR A LONG TIME???????

ANSWER: TO MOVE FOR A LONG TIME WITH UNIFORM VELOCITY , THEY MUST START THIS PHASE WHEN THEY ARE SO FAR {VERY HIGH POTENTIAL DIFFERENCE IN PHASE 2} AND SO THE 2 EFFECTS WILL BE ALWAYS EQUAL.

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