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What happens in the restframe with lightsource?

by faen
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faen
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Mar5-12, 11:58 AM
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I read somewhere that special relativity and time dilation has been proven to really occur. Isn't this a contradiction according to what has been said so far?

Consider the following experiment:

There is a rest frame of reference, with available clocks anywhere. There is another person with a clock traveling very close to light speed such that the traveling clock should almost stop its ticks relative to the restframe. After traveling in a straight line for some seconds, the person stops traveling to compare the differences of the clocks. According to experiments the traveling clock has been ticking slower. I am wondering why? Because according to the traveling clock, it was the other clock which slowed down?

Is it because the moving frame had to stop and deaccellerate? Doesn't this mean that time dilation does not really occur because of traveling faster, but that accelleration is what causes time dilation? There is some contradiction here about that special relativity slows time, since it is simply a contradiction that both clocks are slow relative to eachother.

I would appreciate if somebody could help me out again to understand this better.
Fredrik
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Mar5-12, 02:15 PM
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Quote Quote by Tantalos View Post
This is against logic. According to you if B travels first and then A goes that same distance with the same speed as B to meet him then A will be younger.
I don't think I said anything that can be interpreted that way. If A and B both leave Earth, going at the same speed in opposite directions, and after a while turn around and go back, they'll be the same age when they meet. If instead A stays here while B leaves and later comes back, B will be younger when they meet.

In the scenario that you describe now, where B goes from Earth to some distant location and stays there, and A makes the same journey some time later, then they will certainly be the same age when they meet.

Quote Quote by Tantalos View Post
And what if they decide to travel both in one space ship the same distance and speed? Logically they will be of the same age, but with the previous result their age depends on whether they travel alone or with a company.
Huh?
faen
#21
Mar5-12, 03:22 PM
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Why is nobody replying to my questions anymore? :/ If there's anything I need to explain better please let me know and I'll try..
ZikZak
#22
Mar5-12, 03:45 PM
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Quote Quote by faen View Post
I read somewhere that special relativity and time dilation has been proven to really occur. Isn't this a contradiction according to what has been said so far?
No. If it weren't observable, then we wouldn't be talking about it and it wouldn't be science.

Consider the following experiment:

There is a rest frame of reference, with available clocks anywhere. There is another person with a clock traveling very close to light speed such that the traveling clock should almost stop its ticks relative to the restframe. After traveling in a straight line for some seconds, the person stops traveling to compare the differences of the clocks. According to experiments the traveling clock has been ticking slower. I am wondering why? Because according to the traveling clock, it was the other clock which slowed down?
The reason depends on which observer you are. The unaccelerated observer attributes the disagreement in the clocks as being due to time dilation while the spacecraft was in motion.

The accelerated observer attributes the difference to a combination of factors, but mainly failure of simultaneity. Suppose your rest observer, with clocks stationed everywhere, in particular has a clock next to himself where the race begins, and a clock at the "finish line" where the traveling observer slows down and stops, and that these clocks are synchronized in his frame.

Then they will not be synchronized in the traveling frame. The traveling observer observes both clocks running at the same slow rate, but the finish line clock will read a value that is vastly ahead of the starting line clock. So it is no surprise to him that when he gets there, it is reading many years ahead of his own clock, even though it runs more slowly.

it is simply a contradiction that both clocks are slow relative to eachother.
No it isn't.
faen
#23
Mar5-12, 04:10 PM
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Quote Quote by ZikZak View Post
The reason depends on which observer you are. The unaccelerated observer attributes the disagreement in the clocks as being due to time dilation while the spacecraft was in motion.

The accelerated observer attributes the difference to a combination of factors, but mainly failure of simultaneity. Suppose your rest observer, with clocks stationed everywhere, in particular has a clock next to himself where the race begins, and a clock at the "finish line" where the traveling observer slows down and stops, and that these clocks are synchronized in his frame.

Then they will not be synchronized in the traveling frame. The traveling observer observes both clocks running at the same slow rate, but the finish line clock will read a value that is vastly ahead of the starting line clock. So it is no surprise to him that when he gets there, it is reading many years ahead of his own clock, even though it runs more slowly.
Why will he read that the clock at the finish line is years ahead of his own clock, even if it is running the same speed as the one at the starting line? If there was a person in the rest frame, he would predict that time went slower for the person in the space ship. If this was true as well, why isn't he the one who is younger than the person who traveled?

Quote Quote by ZikZak View Post
No it isn't.
The theory says that time goes slower for both the person in the space ship and in the rest frame. It says that time goes slower in rest frame relative to space ship frame, and time goes slower in space ship frame relative to rest frame. This can't be true if there is only one truth. Also when the two frames arrives at equal velocity, they predict only one truth. However it seems like some kind of acceleration is necessary for them to predict and arrive at the same truth. Thus I am curious about the role of acceleration as well.
ZikZak
#24
Mar5-12, 04:23 PM
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Quote Quote by faen View Post
Why will he read that the clock at the finish line is years ahead of his own clock, even if it is running the same speed as the one at the starting line?
For the same reason each observer observes the other's clock(s) to run slow: that both of them must observe the speeds of every light ray to be c. That requirement leads logically to the necessity for moving clocks to run slow, for moving meter sticks to be shorter than their rest counterparts, and for clocks synchronized in one frame to be unsynchronized in another. That is to say, the Lorentz Transform.



The theory says that time goes slower for both the person in the space ship and in the rest frame. It says that time goes slower in rest frame relative to space ship frame, and time goes slower in space ship frame relative to rest frame. This can't be true if there is only one truth.
I live in the U.S. If I point in the direction of "up," I point in the opposite direction from someone who lives in Australia. We completely and utterly disagree on which direction is up, and yet we are both right, AND there is one truth to the matter.
ghwellsjr
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Mar5-12, 04:43 PM
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Quote Quote by John232 View Post
No problem, I have wrestled with this idea for some time. I still haven't been able to get an answer that resovles the confusion of this issue. I have thought about trying to publish my own theory of special relativity that only switchs the time variables and doesn't consider the time as being a change in time, and I don't know how far into the mathmatics I would have to go into other theories that depend on this equation. I am sure it would find a lot of opposition since it would mean that everything we know about modern physics could be slightly wrong, but their is a growing opionion that relativity may still need some work done on it inoder to obtain grand unification and that may conclude that relativity as we know is not the final answer. Or, that a more accurate theory could get rid of dark matter or something of the like, I think it could be that something that physics has been looking for...
Let me see if I can resolve your confusion so you won't be tempted to publish your own theory of special relativity.

Part of the confusion comes from a misunderstanding of the nomenclature. In the usual presentation of the Lorentz Transform the equations are stated with t' and x' on the left side of the equation and t and x on the right side of the equations. You shouldn't think of the primed symbols as being associated exclusively with just a primed frame like S' and the unprimed symbols associated exclusively with an unprimed frame like S. Rather, you should think of the LT as providing a way to convert the coordinates of any frame into the coordinates of any other frame and back again if you want. I think it is better to refer to each frame with unprimed symbols to avoid this confusion.

So, for example, let's say that you have an event in frame A at t=18 and x=10 and you want to find the coordinates in frame B moving at 0.6c in the x direction with respect to B. (I'm going to use compatible units where c=1.) First we need to calculate gamma, γ and note this is not the English letter y, it is the Greek letter γ. You can get it by going to the advanced editing mode and clicking on the fourth Quick Symbol in the second row. Unfortunately, it looks very much like the letter y but you can tell the difference with the tail going straight down instead of angled.

OK, since β=0.6, we can calculate γ:

γ = 1/√(1-β2) = 1/√(1-0.62) = 1/√(1-0.36) = 1/√(0.64) = 1/0.8 = 1.25

Now we are ready to apply the LT formulas:

t' = γ(t-xβ) = 1.25(18-10*0.6) = 1.25(18-6) = 1.25(12) = 15
x' = γ(x-tβ) = 1.25(10-18*0.6) = 1.25(10-10.8) = 1.25(-0.8) = -1

So if we represent the coordinates as [t,x], then [18,10] in frame A is [15,-1] in frame B.

Now if we want to go back the other way, we do the same thing except that now frame A is moving at -0.6c along the x axis with respect to frame B. Gamma is of course the same value.

t' = γ(t-xβ) = 1.25(15-(-1)*(-0.6)) = 1.25(15-0.6) = 1.25(14.4) = 18
x' = γ(x-tβ) = 1.25(-1-15*(-0.6)) = 1.25(-1+9) = 1.25(8) = 10

We have confirmed that [15,-1] in frame B transforms to [18,10] in frame A, the original coordinates that we started out with.

So you see, the primed symbols can apply temporarily to either frame, they are just intended to mean the new values in whatever frame you are converting the coordinates into. It's also important to recognize that the values that t and x refer to are coordinate values, that is, coordinate time and coordinate distance.

Now I want to get to the confusion over the Time Dilation factor. Since we use t' and t in the Lorentz Transform for two different frames, we don't want to use both of these symbols in the Time Dilation formula because they are both coordinate times (t' being used just temporarily). The Time Dilation formula applies in just a single frame and allows us to determine the time on a moving clock in that frame so we use Einstein's symbol for Proper Time, the Greek letter tau, τ. Einstein presented this formula as τ=t√(1-v2/c2) but it is more common to see it τ=t/γ. When presented these ways, there is no confusion because τ is always the Proper Time for the moving clock and t is always the Coordinate Time for the stationary clocks.

So if we want to find out how much time progresses on a clock moving at 0.6c in any frame compared to the coordinate clocks, it is simply 0.8 times the progress of time on the coordinate clocks (since 1/1.25=0.8).

Now let's consider a clock that starts at the origin in our Frame A from above and moves in a straight line at a constant speed to the event [18,10]. What speed will it move at? That's pretty easy to calculate because it has traveled a distance of 10 in a time of 18 so the speed is 0.555556c. If the time on the clock was 0 at the start of the trip, what time will be on the clock when it reaches 10? First we have to calculate gamma, like we did before:

γ = 1/√(1-β2) = 1/√(1-0.5555562) = 1/√(1-0.308642) = 1/√(0.691358) = 1/0.831479 = 1.202676

Then we divide the coordinate time of 18 by 1.20267 and we get 14.96663.

We could have used the Lorentz Transform calculate the coordinates in Frame C moving at 0.555556c to arrive at this same value as follows:

t' = γ(t-xβ) = 1.202676(18-10*0.555556) = 1.202676(18-5.55556) = 1.202676(12.44444) = 14.96663
x' = γ(x-tβ) = 1.202676(10-18*0.555556) = 1.202676(10-10) = 1.202676(0) = 0

Well, look at this, the distance coordinate came out zero and the reason why is because we have gone from Frame A in which the clock was moving at 0.555556c to Frame C in which it is stationary so the x-coordinate better come out zero because that is where it started and it isn't moving in Frame C.

Now the final point of confusion has to do with length contraction and why the distance coordinate isn't also divided by gamma in the Lorentz Transform. The answer to that question has to do with that zero coordinate for distance. In order to properly arrive at the correct time dilation factor, we had to use an event in Frame A that would result in a coordinate of zero (because the clock started at location zero in Frame A) for distance in Frame C. This happens automatically when we calculate where the clock is, based on its speed in Frame A.

But in order to see the correct length contraction, we have to use two events in Frame A that result in the time coordinates being the same at both ends of the desired length in Frame C. How do we do that? There are several ways but the easiest is to simply multiply the distance coordinate by the speed and use the same x-coordinate as before.

Remember, what we are trying to do is calculate the distance that the clock thinks it has traveled in Frame C. So starting from Frame A the clock moved from [0,0] to [18,10]. In Frame A, the distance is 10 and we expect it to be divided by gamma resulting in a value of 8.314794. All we have to do is multiply the distance coordinate by the speed so that is 10 times 0.555556 which is 5.55556 and we create a new event of [5.55556,10] in Frame A which we transform to Frame C:

t' = γ(t-xβ) = 1.202676(5.55556-10*0.555556) = 1.202676(5.55556-5.55556) = 1.202676(0) = 0
x' = γ(x-tβ) = 1.202676(10-5.55556*0.555556) = 1.202676(10-3.08642) = 1.202676(6.91358) = 8.314794

Here we see the requirement that the time coordinate is the same as it was when the clock started moving and this gives us the same length contraction for the distance the clock traveled as when we simply divide the original length by gamma.

Keep in mind that this is an easy calculation because one end was at the origin. If you are calculating the length of an object or a distance in which neither end is at the origin, you need to multiply the speed by the delta between the two ends and then add that number to the time coordinate of the first event.

I hope if you study this, all your confusions will be cleared up and you won't have to publish your own theory.
Fredrik
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Mar5-12, 05:04 PM
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Quote Quote by faen View Post
As far as I've understood while the person is in the space ship he turns around, accellerates, and he will feel that he is in a gravitational field.
This is just a much more difficult way of looking at these things. I would recommend that you avoid it. Actually, the whole concept of "gravitational field" is problematic. That concept isn't really used in GR (or SR), and there's no need to involve anything but SR here. The counterintuitive aspects of the problem show up in the SR treatement of the problem as well.

Quote Quote by faen View Post
However this accelleration lasts only a very short amount of time compared to the whole trip. Therefor he will only feel as if he is in a gravitational field slowing his time only for as long as he accellerates. After he is finished accellerating both observers will experience that the other persons clock is slower, right?
This is not a right or wrong issue. It's a matter of what coordinate system we choose to think of as describing his "experience". If we choose to use the comoving inertial coordinate systems, then he "experiences" that the guy on Earth is aging slowly both before and after the turnaround. But the fact that the simultaneity lines of the two comoving inertial coordinate systems before and after the turnaround are very different means that the moment after the turnaround, he would describe the guy on Earth as much older than before the turnaround.

Quote Quote by faen View Post
So is it only the time during the accelleration that the person in the rockets time is really going relatively slower, or his time is really going relatively slower the whole trip?
It's the other parts of the trip. The turnaround just makes us associate a different coordinate system with his motion.


Quote Quote by faen View Post
I read somewhere that special relativity and time dilation has been proven to really occur. Isn't this a contradiction according to what has been said so far?
It has, and no, it's not.

Quote Quote by faen View Post
Consider the following experiment:

There is a rest frame of reference, with available clocks anywhere. There is another person with a clock traveling very close to light speed such that the traveling clock should almost stop its ticks relative to the restframe.
You shouldn't say "the" rest frame, because the other frame is also a rest frame...of another object.

Quote Quote by faen View Post
After traveling in a straight line for some seconds, the person stops traveling to compare the differences of the clocks. According to experiments the traveling clock has been ticking slower. I am wondering why? Because according to the traveling clock, it was the other clock which slowed down?
I don't like to think of moving clocks as "slowing down". Instead I would say that every clock always does what it's supposed to, which is to display the proper time of the curve that describes the motion it has done so far. Some curves just have shorter proper times than others. The "straight lines" that represent non-accelerating motion have the longest proper times.

Quote Quote by faen View Post
Is it because the moving frame had to stop and deaccellerate? Doesn't this mean that time dilation does not really occur because of traveling faster, but that accelleration is what causes time dilation?
No, it's the speed, not the acceleration. The following spacetime diagram, made by DrGreg, following a description by yuiop, illustrates this point.



Here the twins are doing exactly the same acceleration, but spend different amounts of time at the higher speed relative to Earth. The one who spent the most time at the higher speed ends up being younger when they're both back on Earth.

Quote Quote by faen View Post
There is some contradiction here about that special relativity slows time, since it is simply a contradiction that both clocks are slow relative to eachother.
It's not a contradiction. I explained this in post #4.
John232
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Mar5-12, 06:00 PM
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Quote Quote by ghwellsjr View Post
Now I want to get to the confusion over the Time Dilation factor. Since we use t' and t in the Lorentz Transform for two different frames, we don't want to use both of these symbols in the Time Dilation formula because they are both coordinate times (t' being used just temporarily). The Time Dilation formula applies in just a single frame and allows us to determine the time on a moving clock in that frame so we use Einstein's symbol for Proper Time, the Greek letter tau, τ. Einstein presented this formula as τ=t√(1-v2/c2) but it is more common to see it τ=t/γ. When presented these ways, there is no confusion because τ is always the Proper Time for the moving clock and t is always the Coordinate Time for the stationary clocks.
I was saying that I think the wiki is wrong.

http://en.wikipedia.org/wiki/Time_dilation

I think this calculation should give the proper time, but it doesn't because it misassigned the time variables. It says the time dialation forumla is t'=yt, but I think it should be t'=t/y. If the wikki is correct there then it would in effect be a different theory, unless you are saying that it is also wrong....

The observer in motion doesn't see the light ray to travel a longer distance, it is the opposite. The observer in motion sees the light ray travel straight up and down. They then use their own time to measure this, that would have to be smaller.

If you used the the time dialation equation given there, you would get a larger value for time not a smaller one. That is because it assumes that the observer in motion see's the light to travel a longer distance, so then they would have to experience more time to allow that to happen.
ghwellsjr
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Mar5-12, 08:40 PM
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Quote Quote by John232 View Post
Quote Quote by ghwellsjr View Post
Now I want to get to the confusion over the Time Dilation factor. Since we use t' and t in the Lorentz Transform for two different frames, we don't want to use both of these symbols in the Time Dilation formula because they are both coordinate times (t' being used just temporarily). The Time Dilation formula applies in just a single frame and allows us to determine the time on a moving clock in that frame so we use Einstein's symbol for Proper Time, the Greek letter tau, τ. Einstein presented this formula as τ=t√(1-v2/c2) but it is more common to see it τ=t/γ. When presented these ways, there is no confusion because τ is always the Proper Time for the moving clock and t is always the Coordinate Time for the stationary clocks.
I was saying that I think the wiki is wrong.
Really??? Where did you say anything about the wiki???
Quote Quote by John232 View Post
http://en.wikipedia.org/wiki/Time_dilation

I think this calculation should give the proper time, but it doesn't because it misassigned the time variables. It says the time dialation forumla is t'=yt, but I think it should be t'=t/y. If the wikki is correct there then it would in effect be a different theory, unless you are saying that it is also wrong....
It is confusing but if you read the whole article, it's very clear that it is the moving clock that is determined by each observer to have its time dilated, that is, seconds are bigger, which means the clock is running slower. So their formula t'=yγt is meant to show that the time it takes for a tick on the moving clock takes longer than a tick on the stationary clock. But we usually use t to refer to the time showing on a ticking clock rather than its inverse which is the time it takes for a tick to occur. (I wish you would use the correct symbol for gamma.)
Quote Quote by John232 View Post
The observer in motion doesn't see the light ray to travel a longer distance, it is the opposite. The observer in motion sees the light ray travel straight up and down. They then use their own time to measure this, that would have to be smaller.

If you used the the time dialation equation given there, you would get a larger value for time not a smaller one. That is because it assumes that the observer in motion see's the light to travel a longer distance, so then they would have to experience more time to allow that to happen.
Even in these comments of yours, it's confusing. The way I would say it is, ignoring gravity, every observer cannot determine that his own clock is running abnormally but any other clock that is moving with respect to him is running slower than his own. In Special Relativity, no one ever determines that any other clock runs faster than his own, always slower.

But regarding the rest of my post, does it help you to understand the other points of confusion so that you don't feel the need to publish your own theory of Special Relativity?
PAllen
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Quote Quote by Fredrik View Post
Here the twins are doing exactly the same acceleration, but spend different amounts of time at the higher speed relative to Earth. The one who spent the most time at the higher speed ends up being younger when they're both back on Earth.
The intent of this phrasing is admirable, but can lead to errors if taken too seriously. In fact, I conclude no simple, intuitive statement about which twin ages less can cover all cases, even in SR:

http://physicsforums.com/showpost.ph...9&postcount=33
Fredrik
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Quote Quote by PAllen View Post
The intent of this phrasing is admirable, but can lead to errors if taken too seriously. In fact, I conclude no simple, intuitive statement about which twin ages less can cover all cases, even in SR:

http://physicsforums.com/showpost.ph...9&postcount=33
I agree that there's no statement similar to the one I made that works for all situations, but it certainly works in this case, where we can say once and for all that "time spent at the higher speed" refers to the description in terms of the inertial coordinate system that's comoving with Earth, there are only two speeds involved (0 and 0.8), and the segments that represent the acceleration phases have identical shapes (in that same coordinate system).

In general, there's no substitute for the statement that the number displayed by a clock is the proper time of the curve that represents the motion the clock has done so far.
ghwellsjr
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Quote Quote by PAllen View Post
Quote Quote by Fredrik View Post
Here the twins are doing exactly the same acceleration, but spend different amounts of time at the higher speed relative to Earth. The one who spent the most time at the higher speed ends up being younger when they're both back on Earth.
The intent of this phrasing is admirable, but can lead to errors if taken too seriously. In fact, I conclude no simple, intuitive statement about which twin ages less can cover all cases, even in SR:

http://physicsforums.com/showpost.ph...9&postcount=33
Rather than read just one post, I urge everyone to read the entire thread, Dumb twin paradox question and you will see that I addressed every one of your concerns and you never responded to my last post. If you still believe that my simple statement (for example, post #16 in the linked thread) can lead to errors or cannot cover all cases in SR, then I urge you to present such a case. I already showed how your one example is not such a case (post #43) and I don't know why you have this concern. So, please, rather than make nebulous charges, show us a specific example where my simple process doesn't work or leads to errors.
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Quote Quote by ghwellsjr View Post
Rather than read just one post, I urge everyone to read the entire thread, Dumb twin paradox question and you will see that I addressed every one of your concerns and you never responded to my last post. If you still believe that my simple statement (for example, post #16 in the linked thread) can lead to errors or cannot cover all cases in SR, then I urge you to present such a case. I already showed how your one example is not such a case (post #43) and I don't know why you have this concern. So, please, rather than make nebulous charges, show us a specific example where my simple process doesn't work or leads to errors.
You answers are just restatements of my option #5 - you have to define 'more time at higher speed' in a way that is completely at odds with what the English words mean (as effectively equal to: add up 1/gamma times coordinate time for each segment - possibly via integration - which is my option #5, and does not correspond to the English words). I didn't respond after a certain point because I felt your additional posts added no information or insight to what had already been said.
harrylin
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Quote Quote by ghwellsjr View Post
[..] But it does help to consider that in the ground's rest frame, the clock on the rocket is ticking slower and it is moving away from the clock on the ground. So between each tick of the rocket clock, as it observes the ground clock, it has moved farther away and so the image of the ground clock's ticks have farther to travel resulting in a longer time compared to its own ticks. It turns out that the ratio of the ground clock's tick interval compared to the rocket clock's tick interval as determined by the rocket is the same as the ratio of the rocket clock's tick interval compared to the ground clock's tick as determined by the ground. Work it out, you'll see that this is true.
Very good George - I've rarely seen such a clear explanation. Thanks I'll try to remember that one!
ghwellsjr
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Mar6-12, 08:45 AM
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Quote Quote by PAllen View Post
Quote Quote by ghwellsjr View Post
Rather than read just one post, I urge everyone to read the entire thread, Dumb twin paradox question and you will see that I addressed every one of your concerns and you never responded to my last post. If you still believe that my simple statement (for example, post #16 in the linked thread) can lead to errors or cannot cover all cases in SR, then I urge you to present such a case. I already showed how your one example is not such a case (post #43) and I don't know why you have this concern. So, please, rather than make nebulous charges, show us a specific example where my simple process doesn't work or leads to errors.
You answers are just restatements of my option #5 - you have to define 'more time at higher speed' in a way that is completely at odds with what the English words mean (as effectively equal to: add up 1/gamma times coordinate time for each segment - possibly via integration - which is my option #5, and does not correspond to the English words). I didn't respond after a certain point because I felt your additional posts added no information or insight to what had already been said.
You didn't state any options, let alone 5. You did state in post #42:
Quote Quote by PAllen View Post
This is what I've been saying: pick a frame, accumulate dilated time (=proper time) along different paths. Compare. Result same no matter what frame you use for the analysis. Where I have a problem is attempts to state some other simple rule to predict or explain this - all such that I've ever seen I consider simply wrong.
which is a more succinct version of what I stated in post #16:
Quote Quote by ghwellsjr View Post
...you can analyze the scenario in any single inertial Frame of Reference and the "time spent at a higher speed" is defined uniquely in that FoR and the "higher speed" is defined uniquely in that FoR and we're talking about the coordinate time of each body in that FoR and we apply Einstein's time dilation formula to convert coordinate time into proper time for each body and then we see how much proper time has accumulated for each body as it travels at different speeds according to the FoR for whatever coordinate time intervals from the time they separated until the time they reunite and we get the amount that each one aged and subtract them and we have the differential aging...
So why is your restatement of my statement acceptable and mine not?
PAllen
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Quote Quote by ghwellsjr View Post
You didn't state any options, let alone 5. You did state in post #42:

which is a more succinct version of what I stated in post #16:
Originally Posted by ghwellsjr View Post

...you can analyze the scenario in any single inertial Frame of Reference and the "time spent at a higher speed" is defined uniquely in that FoR and the "higher speed" is defined uniquely in that FoR and we're talking about the coordinate time of each body in that FoR and we apply Einstein's time dilation formula to convert coordinate time into proper time for each body and then we see how much proper time has accumulated for each body as it travels at different speeds according to the FoR for whatever coordinate time intervals from the time they separated until the time they reunite and we get the amount that each one aged and subtract them and we have the differential aging...


So why is your restatement of my statement acceptable and mine not?
The restatement is fine, but it bears no resemblance to the ordinary meaning of "more time spent at higher speed". There are any number of ways you can talk about accumulating proper time in a given frame - these are correct - but "time spent at a higher speed" is not a reasonable summary of this unless you remove all normal meaning from the words.
ghwellsjr
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Mar6-12, 09:59 AM
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Quote Quote by PAllen View Post
The restatement is fine, but it bears no resemblance to the ordinary meaning of "more time spent at higher speed". There are any number of ways you can talk about accumulating proper time in a given frame - these are correct - but "time spent at a higher speed" is not a reasonable summary of this unless you remove all normal meaning from the words.
Fredrik's comment:
Quote Quote by Fredrik View Post
Here the twins are doing exactly the same acceleration, but spend different amounts of time at the higher speed relative to Earth. The one who spent the most time at the higher speed ends up being younger when they're both back on Earth.
and my similar comment:
Quote Quote by ghwellsjr View Post
I'm glad you mentioned both bodies experiencing acceleration because we can have another variant of the Twin Paradox in which both of them accelerate exactly the same except that one returns home immediately while the other one continues far away from home before matching the acceleration of his twin and returning home a lot later. This clearly shows that it's not the acceleration that causes the differential aging but rather time spent at the relatively higher speed that causes the differential aging.
were both made in the context of both twins experiencing the same acceleration and is perfectly clear English. The whole point of these statements is to show that acceleration is not what causes the difference in aging. I fail to understand what you think you are offering to help people who think that it is the acceleration that is what makes the difference because they have heard that "it is the one who accelerates that ages less" (which is true if only one accelerates). We're trying to help novices who may not yet even know what Proper Time is to take a small step from a point of misunderstanding to a better understanding and I don't know why you think it is helpful to create a debate in the middle of this attempt.


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