some questions

[TrueHeart]

.. can you provide a website which teachs everything about the math in a simple manner?

You don't need a whole web site because it's pretty simple stuff. Use the formula 1/sqrt(1-v^2) to arrive at what's known as the gamma. [NOTE WELL that in the formula I just gave, v is the velocity of the observed entity/frame expressed as a fraction of lightspeed.] The observed (reckoned) length of the moving frame is equal to its native length divided by gamma. Of course you know that length contraction is only along the direction of motion. Observed time spans of the moving clocks are their native amount divided by gamma. And -- don't forget this one! -- the amount by which separated clocks are out of sync (does not involve gamma) is equal to the time it would take light to travel their uncontracted distance apart, multiplied by the frame's velocity expressed as a fraction of lightspeed. A trailing clock reads a later time than a forward located clock (of course, only if their separation is along the direction of motion). That's a complete summation of the basic SR Lorentz Transform. More to follow.

[TrueHeart]

.. So, we say there are two points, A and B, 0.866 lightyears apart. On A is the earth twin while on B is the astronaut twin. The astronaut twin would then instantly accelerate (or consider him already moving) to 0.866c where gamma=2 (the time dilation factor, right?). The whole journey will take 1 year according to the earth twin and will see the other twin's time run at half speed (6 months) while the astronaut twin will take 6 months to complete the journey and see the earth twin's time run at half the speed (3 months). Now, what is the solution to the situation?

The resolution to that apparent contradiction lies in the fact that clocks separated along an elongated moving frame are not in sync -- as reckoned by the presumed still observer of course. The astronaut twin is just such a presumed still observer, and the "real estate" consisting of A-to-B is just such an elongated moving frame. Because of the length contraction of that frame, only 6 months of the astronaut's time is required for it to pass by him, at the stated .866c speed. Only 3 months are witnessed to elapse on Earth's clock during that period, but the Earth frame time at point B was 0.75 years (9 months) earlier than Earth's time, when the astronaut twin was at point B. So according to the Earthbound twin, the astronaut journeyed from a clock reading -9 months to a clock reading 3 months... hence one whole year elapsed (as the A & B clocks are perfectly synchronized to Earth natives). It's tough to fathom alright; and I am sorry if my wording leaves yet an iota of doubt. Maybe someone else can word it better.

[youngone]

Only 3 months are witnessed to elapse on Earth's clock during that period, but the Earth frame time at point B was 0.75 years (9 months) earlier than Earth's time, when the astronaut twin was at point B. So according to the Earthbound twin, the astronaut journeyed from a clock reading -9 months to a clock reading 3 months... hence one whole year elapsed (as the A & B clocks are perfectly synchronized to Earth natives).

 

Can you explain on this part some more? I realize that both clocks are out of sync but I want to know how is it in the very end both of their clocks agree that the earth twin has elapsed more time.

[TrueHeart]

Can you explain on this part some more? I realize that both clocks are out of sync but I want to know how[/b'] is it in the very end both of their clocks agree that the earth twin has elapsed more time.

Both clocks are not out of sync. And both earth and the astronaut do not agree that the earth twin has aged more. There are actually three clocks at issue so let's get it straight.

 

First, let's clarify that in the scenario you describe, point B is some "space buoy" or something that is unmoving with respect to Earth. That makes it easier to get a handle on things. And you're calling Earth point A.

 

You've allowed for only a one-way segment of travel in the scenario you've drawn up. So... according to the earth twin, the astronaut aged only half as much as he himself did. According to the astronaut twin, the earth twin aged only half as much as he himself did.

 

Reviewing; the earth twin knows that he ages 1 year and the astronaut aged only 6 months. The astronaut knows that he ages 6 months and the earth twin aged only 3 months. The discrepancy is attributable to the two parties disagreeing on exactly when the journey began.

[TrueHeart]

Let's say that point B is a space buoy (unmoving with respect to Earth) that has a clock on it which is perfectly synchronized with Earth's clock. When the astronaut was at point B, the clock on the buoy read zero, and he takes a snapshot to prove it. When the astronaut gets to Earth, the clock there reads 1 year, and both twins can bear witness to that reading.

 

Now according to the Earth twin, the buoy clock is in perfect sync with his own, so the data indicates that one year elapsed. But according to the astronaut twin, the buoy clock reads 9 months earlier than what Earth's does (at any given instant), so the data indicates that only 3 months elapsed on the Earth-to-buoy frame.

 

The foregoing assumes that accelerations are not an issue because the astronaut was already in relative motion when he passed the buoy, and he keeps moving as he passes his twin on Earth.

[youngone]

Ok, so if the astronaut twin was already in relative motion when he passed the space buoy, he would conclude that the earth twin started his watch 9 months in his own time before he passed the buoy, right? But he would still compute the clock on the space buoy would read 9 months earlier than on the earth even though according to the earth's frame of reference, both clocks are in sync. Now what is the cause for the clocks going out of sync?

 

One more thing (We can do this after we handle the above situation). Instead of considering the astronaut twin moving before he reaches the buoy, let us say he starts on the space buoy and accelerates to 0.866c in a certain amount of time and reaches the earth twin. What is the difference between the other situation and what happens in this scenario?

[TrueHeart]

.. what is the cause for the clocks going out of sync?

That's the theory of relativity... that clocks and rulers have to be attributed some certain variances in order to allow the perception of lightspeed to be the same from all viewpoints.

.. say he starts on the space buoy and accelerates to 0.866c in a certain amount of time and reaches the earth twin. What is the difference between the other situation and what happens in this scenario?

Complications! Give it a rest, will you please.

[youngone]

Ok, let me just get this straight: Two clocks separated by a distance that are in sync in one frame of reference will be computed (not seen) as being out of sync to an observer travelling at a certain velocity relative to the clocks' frame of reference, right? So that means that the astronaut twin will see the clock on the space buoy have an earlier time than the clock on the earth even after factoring and taking into account the Doppler Shift and distance between those two clocks?

[TrueHeart]

Ok, let me just get this straight: Two clocks separated by a distance that are in sync in one frame of reference will be computed (not seen) as being out of sync to an observer travelling at a certain velocity relative to the clocks' frame of reference, right? So that means that the astronaut twin will see the clock on the space buoy have an earlier time than the clock on the earth even[/i'] after factoring and taking into account the Doppler Shift and distance between those two clocks?

That's fairly accurate. If the clocks are in sync to a native of the frame, then the clocks are out of sync to a non-native, meaning to someone who is in relative motion. The dissynchronicity of the clocks is a fact to such a non-native observer. Yes, I mentioned in an earlier post that you can't really trust what you see at such high speeds, at near light speeds, because of the Doppler shift and other thorny dynamics. That's why I prefer to use the term "reckoned". But the distortions of relativity are a fact, to the observer. Various different observers, moving at various differing speeds, will reckon various differing distortions... so those distortions are not an objective (absolute) fact, but they are nevertheless totally REAL to each observer.

 

For example: a house is engulfed in flames. An observer 3 feet away will get scorched; an observer 30 feet away will feel intense heat; an observer 300 feet away will feel warm, and an observer 3000 feet away will feel nothing. All of those effects are totally real, yet they are not "universal"... they differ for each observer.

 

I suppose I have to say "Happy Thanksgiving". Do I have to say that?? Maybe I have to say that.

[youngone]

Heh heh, no reason to say Happy Thanksgiving. I live in Brunei, a place nobody has ever heard of and we don't celebrate Thanksgiving. Anyway I hope you had a Happy Thanksgiving.

 

Okay, I still don't get much about the dissynchronized clocks in the same frame of reference. So I will tell you what I know about the whole situation again and then you correct me, Ok?

 

The astronaut twin travels from point A (space buoy) to point B (Earth) 0.866 lightyears apart at a speed of 0.866c whereas the earth twin stays on Earth. When the astronaut twin passes both twins will start their watches and later measure their times when they meet up at B. To prevent any confusion we ignore any Doppler shift effects.

 

To the earth twin, he starts his watch as soon he computes the astronaut twin passes point A. The earth twin measures 1 year for the journey and reckons the astronaut twin took only 6 months in the astronaut twin's time. To the astronaut twin the journey takes 6 months and reckons the earth twin recorded the journey as taking only 3 months. But actually the astronaut twin saw the earth twin start his watch 9 months before he passed the sun so they end up agreeing that the astronaut twin had elapsed less time. This part I now understand.

 

Now, you suggested a clock placed at the space buoy that was in sync with the earth's time. But when the astronaut twin passed it, it read time that was 9 months earlier than the earth's time. What I want to know is if the clock on the space buoy would still read 9 months earlier than the earth's clock as the astronaut passed by it or would it read 9 months later because the astronaut twin was closer to the earth's clock? Can you also tell me everything else that you know about this?

[TrueHeart]

Heh heh, no reason to say Happy Thanksgiving. I live in Brunei, a place nobody has ever heard of and we don't celebrate Thanksgiving. Anyway I hope you had a Happy Thanksgiving.

Many thanks! Of course we Americans have heard of Brunei --an extremely wealthy kingdom, free housing and medical care for all the citizens.

.. Now, you suggested a clock placed at the space buoy that was in sync with the earth's time. But when the astronaut twin passed it, it read time that was 9 months earlier than the earth's time. What I want to know is if the clock on the space buoy would still read 9 months earlier than the earth's clock as the astronaut passed by it or would it read 9 months later because the astronaut twin was closer to the earth's clock? Can you also tell me everything else that you know about this?

As I stated in my post #27, the buoy clock reads 9 months earlier than Earth's clock at any given instant, from the astronaut's perspective. No matter where the astronaut is located, the buoy clock will read 9 months earlier than Earth. The astronaut twin can rightly claim himself to be stock still, all the time. So to him, the Earth-to-buoy "real estate" is a frame in relative motion.

 

I don't see clearly where to go from here. Perhaps 15 is too young to fully grasp the concepts of relativity, but I refuse to believe that. Just realize that length contraction and time dilation are meaningless on their own -- you must cipher in the time dissynchronicity element as well, in order to arrive at any coherent analysis. The three distortions all conspire together to make relativity work, and be consistent.

 

Remember: I said that the astronaut took a photograph of the buoy clock as he passed it, so there are no illusions or tricks. When later analyzing the data, the clock readings, photographs of clock readings, etcetera; the Earth twin will conclude that the journey took 1.0 of his years... the astronaut will conclude that the journey took 6 of his months while only 3 Earth months elapsed. Realize that this is not a round trip scenario, merely one-way; so the two twins will disagree on how much time elapsed. But, by applying the formulas of relativity, each will reason why the disagreement exists. There is no universal time, no universal space, no "bigger picture". Humans are always yearning to "play God" and see things from the top down, to see the bigger picture, the larger truth; but relativity taught us the lesson that such efforts will always be in vain. And the entire field of Physics is consequently somewhat vain: what is true here and now is something that can be ascertained, not what is true from some supposed "master viewpoint".

[TrueHeart]

.. an extremely wealthy kingdom, free housing and medical care for all the citizens.

Oh hey! check that! I think I've confused Brunei with Abu Dhabi. Please forgive me!

[youngone]

Ha ha ha!! Everyone makes mistakes so you are pardoned. Living in Brunei is actually very difficult, generally because of its slow education system. There are no proper Physics lessons unless you are a Form 4 (which I will be next year!) because all Science subjects such as Biology and Chemistry are taught as General Science. I am also guessing that the only university in my country does not offer any Advanced Physics Courses. So apparently, the only way I'll ever become a physicist is to go overseas. I am considering going to Cambridge in the UK but I a might feel a bit alienated because I am Chinese and I don't think there are many Chinese in UK.

 

I feel that you're right about me being too young to fully grasp everything about relativity. I understand the concept of time dilation and length contraction but maybe not for relative dissynchronicity and simultaneity. Maybe when I grow up and learn additional mathematics I should be able to understand the complex equations behind relativity.

 

Looks like I have to be going now. I sincerely thank you for all your help and patience in helping me sort through some of my problems.

[TrueHeart]

.. if one observer, traveling at 0.9c in one direction, is traveling away from another observer traveling at 0.9c in the opposite direction (both relative to a stationary object as lightSword pointed out), light emitted from one observer would still catch up to the other observer, and it would take (300,000 x L) seconds (where L is the distance between the two observers when the light was emitted). ..

I happened across this oldish post of yours, gib65, and although you have grown more astute in subsequent posts, I wish to offer some correction here. First, you obviously meant L divided by 300,000 -- not multiplied. But more importantly, the formula is only half right. It would take that long (L/300k sec.) only according to the vantagepoint of the light signal recipient. From the viewpoint of the signal sender it would require extra time to catch up to the other receding entity. Please get it straight. Also get straight that there is only one "a" in "time dilation".

[gib65]

I happened across this oldish post of yours, gib65, and although you have grown more astute in subsequent posts, I wish to offer some correction here. First, you obviously meant L divided by 300,000 -- not multiplied. But more importantly, the formula is only half right. It would take that long (L/300k sec.) only according to the vantagepoint of the light signal recipient. From the viewpoint of the signal sender[/i'] it would require extra time to catch up to the other receding entity. Please get it straight. Also get straight that there is only one "a" in "time dilation".

 

Although you are correct in a few of these points, I suppose I now know how to push your buttons. I think I'll be putting this to good use if we ever got into a heat discussion in these forums.

[TrueHeart]

Huh?? whaddya mean? I have only the one (belly) button, and no, you will never have occasion to "push" it.

[gib65]

Huh?? whaddya mean? I have only the one (belly) button, and no, you will never have occasion to "push" it.

 

LOL!