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It's actually really easy to explain...

First I think you guys are using the word relative pretty horribly, or at least one person is. What you mean is when two bodies are moving at different velocities relative to each other one is must be moving slower and the other is moving faster. However if two bodies are moving at the same velocity then they are both standing still. It's only with reference points that we can begin to understand speed at all.

That being said it has nothing to do with why two identical clocks that move at different speeds would read differently. The reason is that an increase in speed effects time space, increasing gravity and slowing time in that specific area through some reason i don't know cuz I just know the basics... The gravities and flow of time is different in the two different areas and thus one clock runs slower than the other...or faster, depending on how you look at it.

When the two clocks "stop" or return to velocities that are equal they read seperate times because even though they started at the same time the flow of time was altered in their local areas separately. At the moment they begin going at the same velocity their flow of time is equalized and begin ticking at the same intervals.

The OP assumes that once both clocks both return to the same velocity they both read the same time though. This is wrong. They read different times but tick at the same rate...assuming their tick is perfect and never slow or speed up.

So in the end the reason it all works is more or less because because they are moving faster through time...You know... one might make an argument that there is a balance that the faster one goes the slower time goes for them and if one were to go fast enough time would reverse >.>

2. Originally Posted by mugaliens
I think the easiest way to understand the twin "paradox" is to put it in it's simplest terms:

1. Two twins in two space ships in empty space. They synchronize clocks.

2. One twin remains where he is (no acceleration of any kind).

3. The second twin rockets away at 1 G for 1 day (shipboard clock), decelerates at 1 G for one day, reaccelerates at 1 G back towards his twin, then decelerates again, coming back to rest alongside his twin.

4. To the moving twin, 4 days have passed, exactly.

5. To the stationary twin, how many days have passed? Is it more than 4 days? Exactly 4 days? Or less than 4 days?

I would contend that it's more than 4 days. And thus, the "paradox," is no more.
I also think both would agree that the younger one used more fuel. All acceleration requires energy, hmmmmm.

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I just thought of something... why is it that a moving object which would have to be losing mass be creating more gravity than something that is standing still >.> That sounds weird to me.

4. Originally Posted by Durakken
It's actually really easy to explain...
You've covered what time dilation is (or might be) but I think you've missed what makes the "paradox" get called a "paradox" in the first place.

...which is that each observers view is equally valid.

(Bob in the spaceship can view himself as standing still, and Alice, sitting on Earth as zooming away then coming back again. Bob's view is entirely valid, because there is no absolute reference frame which which to say it's Alice or Bob who is moving "faster". So why doesn't Alice, on "spaceship Earth", come back younger? While there is relative motion between them - they each see each others clock as running slower than their own. It makes no difference who is "faster" or "really moving".)

The twins paradox is not about time dilation, as such, but about the apparent lack of symmetry - given that all points of view are equal.

The answer (as I understand it) is not that Bob moves "faster" but that Bobs' reference frame changes, and as a result he moves further through space-time.

(While Bob in a spaceship uses acceleration to change frames, messenger clocks synchronised in some way, don't need to invoke acceleration, to shift reference frames.)

5. Originally Posted by SeanF
We can synchronize two clocks, A and B, as long as they are stationary relative to each other - even if they are spatially separated. We can have two people (Ann and Bob) who are born at the two clocks simultaneously, in that reference frame.

We can have a third person, Carl, who is born at the same point in space-time as Ann's birth, but on a ship that is in relative motion to Ann and Bob. When Carl's ship reaches Bob, Carl will be younger than Bob. Isn't that effectively the "twin paradox," without any acceleration?
Hmm, that's very interesting also. It appears we cannot now even say that the resulting time lag depends upon who is switching frames, much less accelerating, since there is not even any frame switching occurring in your example, only a comparison between frames with time dilation and a simultaneity effect taking place. So what could we say now that might help to clarify who ages less?

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That's wrong.

A paradox is two opposite things being held as being true when there is no possible way for it to be.

If someone suddenly starts walking on the ceiling it's their floor because of their perspective but that does not make it a paradox that the other views it the opposing way.

And as far as what you're talking about speeds great enough to create this illusion have less to do with speed than it does with distance and area. Not the speeds at which they travel... In other words, it's several different things that create your so called paradox than it is just plain physics.

7. Originally Posted by Durakken
A paradox is two opposite things being held as being true when there is no possible way for it to be.
But that's exactly what I've been saying:

1. All points of view are equal and it doesn't matter who is "really" faster - they all see each others clock slower.

2. Bob ends up younger than Alice.

Those are the two opposite things that make this a "paradox" in the first place.

(Or to put it another way: what are the "two opposite things" that you think are what gets the "twins paradox" get called a "paradox"?)

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No what you are saying is that something that is moving away at increased speed appears to be moving slower from the perspective of viewer that is watching that something but the truth of the matter is that anything that can move at speed and still be seen must be pretty big or moving across a distance from a far enough distance so one can track. What you are perceiving is not any sort of paradox but rather an illusion created by the perspective of the viewer due to tracking that object while ignoring the background OR having such a large background that is far enough away that it is outside our average range of reference.

That is why from the side that is moving faster technically it would be moving slower unless your say a car appears to be moving slower than you when you are on a bike...

9. Originally Posted by Durakken
No what you are saying is that something that is moving away at increased speed appears to be moving slower from the perspective of viewer that is watching that something but the truth of the matter is that anything that can move at speed and still be seen must be pretty big or moving across a distance from a far enough distance so one can track. What you are perceiving is not any sort of paradox but rather an illusion created by the perspective of the viewer due to tracking that object while ignoring the background OR having such a large background that is far enough away that it is outside our average range of reference.

That is why from the side that is moving faster technically it would be moving slower unless your say a car appears to be moving slower than you when you are on a bike...

That's way off. I'm not talking about perspective or visual illusion.

I'm talking about time dilation due to the speed of light being constant for any observer.

The bit you are missing, still, is that according to relativity, it doesn't matter which observer is doing the observing; they will see/calculate/consider the others clock to be slower than their own.

This is not about perspective or optical illusion.

This is relativity.

10. Originally Posted by pzkpfw
It still seems to me that you have a more complex than required "version" of the twins' paradox.
When I agreed with you earlier, it was when you said that in the twin paradox, one twin "really does" age less. That is the crux of the twin paradox, and it simply never occurs without acceleration of an observer. That's not more complex than required, it is the twin paradox-- one twin really does age less. Otherwise, there's no paradox, it's just two people thinking the other is younger (that's time dilation, which also is a bit paradoxical, but it's not the significantly more subtle twin paradox because it doesn't break any symmetry between twins.)
Q: Is it or is it not true that:

For any two observers in relative motion, each will observe the others clock running slower than their own.
Yes, but that is symnetric between twins, so is not the twin paradox. It's just time dilation, which if you like, is only one pillar of the twin paradox (the other being acceleration of a twin, which breaks the symmetry).

At my simple level, that's it. That's all that is needed to "create" the apparent "paradox".
It may seem paradoxical, but the twin paradox is something very different, and more difficult to explain. You starr by explaining time dilation, and once someone has that down, then you bring in the twin paradox, which establishes the additional effects of acceleration (or gravity).
Alice, Bob, Carl are all zooming around, or not. They are in relative motion, so they all see each others clocks running slower than their own. The apparent "paradox" is: why does one actually age more than the other?
But that's the whole flaw in the Alice, Bob, Carl scenario-- none of them "actually" age more. They are all completely correct in thinking they each age the most, that's why it's just not the twin paradox. You are talking about nothing other than time dilation, that's why the Alice-Bob-Carl scenario misses the point. Time dilation is strange, but it's not a paradox, because no one ever said that there had to be one person who actually aged more-- unless there's acceleration, and then there really has to be one who ages more. It's a higher-order surprise in relativity than simple time dilation, and it's called a paradox because people who don't understand the importance of acceleration will think that the twin paradox is pure time dilation, and will thus reason to a contradiction (the symmetry of the twins).

I don't understand why you write this off as "simple time dilation". Maybe it's a really easy, obvious, simple explanation - but that doesn't make it invalid, does it?
Time dilation is a perfectly good explanation-- of something other than the twin paradox! The twin paradox itself comes from using only time dilation and nothing else, it is not resolved by that. Its purpose is to get beyond time dilation into understanding global simultaneity shifts, which start out purely as a convention but end up getting "fixed" into the reality when there's acceleration of an observer.
Messenger clock answers seem to show that a) is irrelevant; and if it isn't then all this is a debate over semantics anyway.
You cannot arrive at the twin paradox by using messenger clocks, but that doesn't mean they resolve it-- it means they are irrelevant to it. You described the paradox perfectly well yourself:
1. All points of view are equal and it doesn't matter who is "really" faster - they all see each others clock slower.

2. Bob ends up younger than Alice.
Point 2 is exactly what does not happen in the messenger-clock scenario, as it lacks acceleration of Bob. Thus the A-B-C scenario is simply not the twin paradox, and it is completely described by time dilation-- and it can only lead to the twin paradox if B goes with C rather than handing off his watch to C.
On the other hand, if b) is true, does that mean it's part of i) a more detailed version of the twins paradox - or ii) does it specifically replace and invalidate my simpler understanding of it?
I think we had better understand what is meant by the twin paradox. What is meant is not that two twins each think the other is younger (which is all you ever get with the A-B-C scenario), but rather than two twins agree that one is younger-- so how did that happen? Acceleration (or gravity).

I apologise in advance; I expect I'm causing frustration (let's talk about how many event horizons a black hole has...).
No frustration, I'm just trying to find the crux of the disconnect here.

11. Sorry, have to get back to work (it's 1:30 pm my time), so this is a quickie (I don't mean to be rude and skip most of your post - will come back to it):

Originally Posted by Ken G
No frustration, I'm just trying to find the crux of the disconnect here.
Agreed.

Originally Posted by Ken G
What is meant is not that two twins each think the other is younger (which is all you ever get with the A-B-C scenario), but rather than two twins agree that one is younger-- so how did that happen? Acceleration (or gravity).
In my concept of the twins paradox, it is also about both twins agreeing that one has aged differently. The "paradoxical" part is that by the principle of equivalence, they shouldn't. It's the changing of reference frames that resolves the issue (or explains it). That may or may not have been caused by acceleration.

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Originally Posted by pzkpfw
It still seems to me that you have a more complex than required "version" of the twins' paradox.
Originally Posted by Ken G
When I agreed with you earlier, it was when you said that in the twin paradox, one twin "really does" age less. That is the crux of the twin paradox, and it simply never occurs without acceleration of an observer.
Ken, you are quite correct.

The original 1905 SR paper always leads to a paradox, if one tries to think of what BOTH of two equal observers “see” or “observe” while “moving relatively” and while neither is accelerating, because, both will see themselves as being the “stationary” one, and they will see the other as being the “moving” one. That is why this debate about the 1905 paper has been going on for more than 100 years.

Since acceleration and gravity are disregarded in the 1905 paper, and only “relative motion” is considered, that’s what creates the “paradox”. In order to try to get rid of the “paradox”, Einstein himself had to add acceleration and gravity to his 1905 thought experiments, and he did that in a science-magazine article he wrote in 1918. The article was translated into English only in 2002, and it’s still not widely known. I mentioned this a few years ago, back before the English version was available on the internet. But now, it is finally on the internet.

Einstein wrote this article in a “dialogue” conversational style, much like Galileo’s “Dialogue Concerning the Two Chief World Systems”. In this article, “Critic” is someone who criticizes the 1905 paper, while “Relativist” is Einstein. Of course Einstein wrote both parts of the conversation:

Einstein, 1918:
http://en.wikisource.org/wiki/Dialog..._of_relativity

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The thing about relativity is that it claims that both objects are speeding away from each other at the exact same speed which is semi true, but then people try to apply this to the clock thing which isn't.

If I was attached to a point in space between two objects. One that flies away while the other stays still I would see that both object move away at the same pace if I am attached to the point exactly in the middle no matter what. This isn't because the non-moving object is moving but because from my perspective if i stayed in between them as one increases it's distance i have to too. That however doesn't mean the both have the same velocity and it is this Velocity that actually alters the flow of time...

The real interesting thing to look at is if you have a warp drive vessel traveling at say 2 times the speed of light and a thrust drive engine that travels at the same speed going right next to each other...what happens ^.^

14. Originally Posted by pzkpfw
In my concept of the twins paradox, it is also about both twins agreeing that one has aged differently.
It is absolutely all about just that. That's exactly what you will never find happening in these other versions that don't include acceleration of one of the parties.

That may or may not have been caused by acceleration.
No, it is always caused by only acceleration (or gravity).

15. Originally Posted by SeanF
Ken G, I think you're making a mistake when you tie the simultaneity difference to acceleration.
No, the twin paradox is more than just simultaneity differences, which are essentially purely conventional. The "closed loop" character of the paradox is absolutely essential, which requires acceleration or gravity, because that's the topology that makes the conventional elements "come out in the wash" in actual observations. The observations are invariants, the simultaneity conventions are not.
I mean, Special Relativity is all about comparing two reference frames that are in relative motion to each other.
Actually, that's really not what it's about, because you are basically talking about fairly arbitrary conventions (like global simultaneity). What special relativity, as a physical theory, is really about is its invariants. Yes the standard conventions are built into the common language of special relativity, but not into its testable predictions, which are the guts of any theory. I like to say that special relativity is actually less than most people think it is, because of the added untestable baggage that goes into its most common language usage.
We can have a third person, Carl, who is born at the same point in space-time as Ann's birth, but on a ship that is in relative motion to Ann and Bob. When Carl's ship reaches Bob, Carl will be younger than Bob. Isn't that effectively the "twin paradox," without any acceleration?
No, it isn't. The crux of the twin paradox was summarized well:
Originally Posted by pzkpfw
1. All points of view are equal and it doesn't matter who is "really" faster - they all see each other's clock slower.

2. Bob ends up younger than Alice [unequivocally, and having started at the same age, unequivocally].
If you can think of way to get both points 1 and 2 without acceleration, by all means do so, but the Alice-Bob-Carl scenario (even your modification where Alice and Bob are born at different places) does not accomplish both 1 and 2 here. Neither time dilation, nor even time dilation plus an arbitrary global simultaneity convention applied to inertial frames, can do it, in terms of any unequivocal testable outcomes. You need to have an observer who, if he neglects his own acceleration, reaches a wrong conclusion because he expects a symmetric result between the twins that does not play out in the observed invariants. That's the twin paradox.

Originally Posted by SeanF
Carl will insist both he and Ann were born after Bob was. But it is a simultaneity issue with simple relative motion, not an issue with acceleration.
True, but it's also not the twin paradox, by #1 and #2 above.

16. Ken, I see what you're saying.

But let me try something else to explain why I think pinning the twin paradox on "acceleration" is misleading, at best.

Consider three triplets, all born in the same reference frame at the same time. Ann stays behind, Bob and Carl are both accelerated away (identical accelerations). At some point, Bob decelerates back to the original reference frame but Carl continues "moving". Then, at some later time, Carl decelerates back to the original reference frame (same rate of deceleration as Bob).

Carl then accelerates back towards Bob (and, further in the distance, Ann). As Carl approaches Bob, Bob begins accelerating towards Ann (same rate of acceleration as Bob) so that he matches Bob's speed exactly as he and Bob come alongside each other.

They then continue together and undergo identical decelerations to meet up with Ann at the original starting point, original reference frame.

Ignore for the moment that Ann will be older than both Bob and Carl, and note that Bob will be older than Carl. But did they not experience identical accelerations? The only difference was the amount of time they spent in each inertial frame and the spatial distance between their respective "turning around" points. But the acceleration(s) themselves were identical.

And yet...Bob is older.

EDIT: Two predictions: 1) KenG will agree that Bob will be older than Carl. 2) Sam5 will be very disappointed when KenG acknowledges this.

17. Originally Posted by SeanF
But did they not experience identical accelerations? The only difference was the amount of time they spent in each inertial frame and the spatial distance between their respective "turning around" points. But the acceleration(s) themselves were identical.
Yes that is what will happen, but all it says is that both acceleration, and time dilation, are essential aspects of the twin paradox. I agree with that. In a sense, the time dilation is what allows for the times to differ, but it is the acceleration that breaks the symmetry and allows Alice and Bob to agree on an invariant that would otherwise be in dispute. You cannot get a twin paradox with only one or the other, where the twin paradox is defined as an acceleration-blind expectation that is in contrast with a measured invariant. This is evidenced by the fact that as yet there are no examples of getting this without both acceleration and time dilation. No one describing an A-B-C scenario has been able to say "here are two twins that agree which one is older" without acceleration. But that's the twin paradox-- not that they disagree who is older, but that they agree, since that is non-symmetric.

18. Originally Posted by Ken G
This is evidenced by the fact that as yet there are no examples of getting this without both acceleration and time dilation.
Phew, 5 pm and things have moved on.

1. There's a clock on Earth. There's a sticker on it labelling it as "Alice".

2. A spaceship zooms by at constant velocity. When it passes Earth, a clock on board (labelled "Bob") is synchronised with the Earth clock*.

3. Later another spaceship zooms by the first, back in the direction of Earth. It is also not accelerating. It gets a clock (labelled "Clone of bob") synched to the first spaceships "Bob" clock.

4. When the second spaceship passes Earth, it's reading is compared to the "Alice" clock.

I'd expect the "Clone of bob" clock to have a lesser reading than the "Alice" clock, though none of the clocks were accelerated.

While it wasn't one physical clock that left and came back, why would this be an issue? The information left and came back... and experienced different frames.

* say, by a beam of light, which when received is corrected for known effects. (I'm trying to avoid the need for any concept of "simultaneous" in the syncing of the clocks)

19. Originally Posted by pzkpfw
3. Later another spaceship zooms by the first, back in the direction of Earth. It is also not accelerating. It gets a clock (labelled "Clone of bob") synched to the first spaceships "Bob" clock.
You can call it a "clone" if you like, but Bob won't even think that clock stays synchronized with Bob! So why should Alice? There's no twin paradox there, as you defined it. Yes the clone of Bob will agree that Alice is older, but the "clone" is not Bob, nor is it synchronized with Bob, nor did it ever think it was as old as Alice ever since it synchronized to the young Bob.
I'd expect the "Clone of bob" clock to have a lesser reading than the "Alice" clock, though none of the clocks were accelerated.
Of course you'd expect that-- it just comes from understanding time dilation. You cannot say the paradox was resolved when in fact it was never even encountered!

Let's look at the world according to each of A, B, and C:
A says: B is aging slowly, and so is C, so there's no surprise A is older than C.
B says: A is aging slowly, but C is aging really slowly, so there's no surprise that A is older than C.
C says: B is aging more slowly than A, so even though B started life at the same time as A, B is more time dilated than A. So when C synchronizes their clock to B, they are synchronizing to a clock that has elapsed less time than A. That lag persists even though A is being dilated as A approaches C. So again, C is not surprised that A is older than C.

So you see, with all inertial frames, it's all 100% pure time dilation, and no one reaches any contradictions using nothing other than time dilation. There's no twin paradox there.

But, let's say that, at the last minute, B decides to join C in the ride home. C will say "you do realize that you are already so much younger than A, you will not catch up to her on the way home?" And B will say "what do you mean, A is being time dilated, so has always been younger than me and should still be younger when I get back". To which C will say "look again, as soon as you joined my reference frame (by accelerating), A just got a whole lot older for you (I already thought she was older than we are, by the way)." That is the only way to encounter, and subsequently resolve, the paradox. Look again what happens if B says "in that case, I won't join you, I'll stay inertial". Then C says "OK, then I see Alice as older than us as she was less time dilated during your journey, but you still see her as younger than us as she was more time dilated. We just can't agree unless you accelerate into my reference frame, and if you don't then you will expect A to age more than I will during my return, so you won't be surprised when I show up and she's older than me, but younger than you." And in that lack of agreement, the paradox never appears.
While it wasn't one physical clock that left and came back, why would this be an issue? The information left and came back... and experienced different frames.
Follow your own points #1 and #2 and tell me the two people who understand time dilation enough to expect to each be older than the other, yet find one is younger, in your scenario. You can't say C should expect to be younger than A, because as I said, C is synchronizing to B, who has always been more time dilated than A since birth, according to C.

The bottom line is, you just never get any twin paradox with all inertial observers. Such observers never need to undertand anything more than time dilation. It is only when you have acceleration that observers need to understand more than just time dilation to avoid contradictions, and that's why the twin paradox is so important to teach people who think everything is about time dilation in gravity-free relativity.
Last edited by Ken G; 2008-Nov-12 at 05:41 AM.

20. Originally Posted by Ken G
Yes that is what will happen, but all it says is that both acceleration, and time dilation, are essential aspects of the twin paradox. I agree with that. In a sense, the time dilation is what allows for the times to differ, but it is the acceleration that breaks the symmetry and allows Alice and Bob to agree on an invariant that would otherwise be in dispute. You cannot get a twin paradox with only one or the other, where the twin paradox is defined as an acceleration-blind expectation that is in contrast with a measured invariant.
You're missing my point, Ken G. People like Sam5 believe that Special Relativity is fundamentally flawed, that there is no time-dilation, and that General Relativity is talking about a physical effect that acceleration has an actual atomic clocks. When you insist that "acceleration causes the twin paradox," they see it as an agreement with that position.

You talk about an "acceleration-blind expectation." That doesn't necessarily mean no acceleration, it can mean "any accelerations cancel out," or "both observers expect the same acceleration effects." That's what I'm trying to provide with my latest thought experiment.

I know where symmetry breaks down in this last thought experiment, why the accelerations don't actually cancel out, and I'm sure you do, too, but it's got to be made clear that it's not acceleration making someone older (or younger). The symmetry is not broken by "one observer accelerated and the other didn't," nor "one observer accelerated more than the other did."

21. Originally Posted by SeanF
Consider three triplets, all born in the same reference frame at the same time. Ann stays behind, Bob and Carl are both accelerated away (identical accelerations). At some point, Bob decelerates back to the original reference frame but Carl continues "moving". Then, at some later time, Carl decelerates back to the original reference frame (same rate of deceleration as Bob).

Carl then accelerates back towards Bob (and, further in the distance, Ann). As Carl approaches Bob, Bob begins accelerating towards Ann (same rate of acceleration as Bob) so that he matches Bob's speed exactly as he and Bob come alongside each other.

They then continue together and undergo identical decelerations to meet up with Ann at the original starting point, original reference frame.

Ignore for the moment that Ann will be older than both Bob and Carl, and note that Bob will be older than Carl. But did they not experience identical accelerations? The only difference was the amount of time they spent in each inertial frame and the spatial distance between their respective "turning around" points. But the acceleration(s) themselves were identical.

And yet...Bob is older.
Ahah, very good. I like your scenarios. They are breaking things down to what is really going on here. In another thread, I did something similar. I had identical relativity of speeds and of accelerations as you have done here, but still found an age difference, or something of that nature if I remember correctly. The only thing left, then, was a possible relativity of distances to explain the difference which I never see discussed. But simultaneity does just that. It is directly proportional to the distance between points in different frames of reference. So if Carl travels further than Bob at the same relative speed from Alice and turns around with the same acceleration applied, there will still be a greater simultaneity shift between Carl and Alice due to the larger distance between them.

I guess it could also be consider a relativity of time, though, since Carl travels away from Alice for a longer period, but it would be different from just time dilation, though it will figure into that as well as the simultaneity shift. Depending on whether we use a relativity of distance or time, then, the formula for the simultaneity shift will become either tl = 2 L d v / (c^2 - v^2) = 2 d (v/c) / L, or tl = 2 Z t v^2 / (c^2 - v^2) = 2 t (v/c)^2 / Z, where L and Z are the Lorentz contraction and time dilation, respectively, and d and t are the distance travelled and the time of travel according to the traveller.

22. Originally Posted by cjameshuff
Doppler effect depends on velocity of approach or separation, time dilation only depends on relative velocity.
Yes, a good example for this are geostationary (geosynchronous?)sattelites. No approach, no separation, still time dilation (ignoring gravitational effects)

If you mean you doubt whether either is younger than the other...
Well, this was actually meant to be a joke because of the "huge" time difference (7000+ ns/d)

23. Originally Posted by Durakken
why is it that a moving object which would have to be losing mass ...
There must be a misunderstanding. Why should a moving object lose mass? Do you think the Earth is permanently losing mass on its way around the sun???

... be creating more gravity than something that is standing still >.> That sounds weird to me.
A moving object is creating gravity?? Where did you get this from?
On the other hand, between "standing still" and "moving" there must have been some acceleration. And if you had done this with your eyes closed you wouldn´t be able to tell the difference between acceleration and gravity (greetings from Einstein´s elevator )

24. Originally Posted by SeanF
When you insist that "acceleration causes the twin paradox," they see it as an agreement with that position.
That is of no concern, I would not reject a fact simply because someone else could unite that fact with some other type of erroneous reasoning. What I have said is, in a world where acceleration is impossible, no one would have ever dreamed of a twin paradox. It simply would never come up, and to see that, note that such a world would be like my "world according to A, B, and C" above. All time dilation, no twin paradox, no breaking of any symmetry between observer's views. If a world where acceleration is impossible could never need to confront a twin paradox, then clearly acceleration is crucial to the twin paradox. That's all I said, yet it is being disputed, though no one has yet given an example of all-inertial observers who encounter a twin paradox.
I know where symmetry breaks down in this last thought experiment, why the accelerations don't actually cancel out, and I'm sure you do, too, but it's got to be made clear that it's not acceleration making someone older (or younger).
If there's no acceleration, no one is unequivocally made younger! Both observers think they are older, it is simply a disputed issue. It is only with acceleration that anyone has to confront that one is really younger, that's the whole point. Draw whatever conclusions you will from that, it is nevertheless true.
The symmetry is not broken by "one observer accelerated and the other didn't," nor "one observer accelerated more than the other did."
That is precisely what breaks the symmetry-- give me an example of a case where a symmetry is broken without that. I already said above why none of the A-B-C scenarios break any symmetries, because in all cases, every age difference that is encountered in a face-to-face meeting always had that age relationship, the entire time. But the twin paradox contrast two separate age relationships between the same two people, once when they are the same (ergo, "twin"), and once when they are different in a non-symmetrical way. The latter simply never happens in any purely inertial scenario, and if anyone still thinks it does, why are there still zero examples of it?

25. Originally Posted by Ken G
Originally Posted by SeanF
The symmetry is not broken by "one observer accelerated and the other didn't," nor "one observer accelerated more than the other did."
That is precisely what breaks the symmetry-- give me an example of a case where a symmetry is broken without that.
That's what I think I did in this post.

1) Did Carl and Bob begin the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? Yes.

2) During the duration of the experiment, did...
a) Carl accelerate more than Bob? No.
b) Bob accelerate more than Carl? No.

3) Did Carl and Bob end the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? No.

In light of the "No" answers to 2a and 2b, what explains the "No" answer to 3c?

26. Originally Posted by Ken G
You can call it a "clone" if you like, but Bob won't even think that clock stays synchronized with Bob!
I agree, but I don't see why that's an issue..

(Say there are triplets, in the acceleration-included version: When Bob accelerates to trun back towards Alice, Craig, who was with Bob, is jettisoned into space and continues on the original path. Craig does not remain synchronised with Bob - but that does not change the result of the coming Alice-Bob comparison.)

Originally Posted by Ken G
So why should Alice?
Well, if she understands enough of relativity she won't; but the "paradox" is only a "paradox" when using an incomplete understanding - after all: no-one is saying it's an unsolved puzzle.

Originally Posted by Ken G
There's no twin paradox there, as you defined it.
I still think there is; clocks have been in relative motion. That's it. By equivalence, they should each have been slower than the other - but that's not what eventuates. The shifting of reference frames breaks the symmetry.

Originally Posted by Ken G
Yes the clone of Bob will agree that Alice is older, ...
The Clone bob clock might not have expected that, using only time dilation and the equivalence principle - that his view that he is stationary and the Alice is moving is equally valid. (This is point 1. of my description of the two "facts" in the "paradox" - as in the post of mine you quoted.)

Of course, this would have to be after the Clone clock made a similar assumption for the Bob clock that his setting was synched to. It's a bit contradictory that the Clone clock could assume the Bob clock is stationary and Alice clock moving; then follow that with his own clock stationary and Alice moving - but then, the "answer" to the "paradox" is the shifting of reference frames!

Originally Posted by Ken G
...but the "clone" is not Bob, nor is it synchronized with Bob, ...
I don't see why that's an issue.

Originally Posted by Ken G
nor did it ever think it was as old as Alice ever since it synchronized to the young Bob.
He might (think that), if he only uses partial knowledge of relativity. (Which is what allows it to be called a "paradox" in the first place.)

Originally Posted by Ken G
Of course you'd expect that-- it just comes from understanding time dilation. You cannot say the paradox was resolved when in fact it was never even encountered!
In contrast it seems to me that you are using more complete knowledge of relativity to say a paradox doesn't exist, when the paradox itself requires that incomplete knowledge.

Why couldn't I say in answer to your resolution of the paradox "Of course you'd expect that-- it just comes from understanding acceleration under GR. You cannot say the paradox was resolved when in fact it was never even encountered!".

I think we still disagree on what the "paradox" is.

(I've been Googling for the web page where I "learned" the no-acceleration-required resolution to the "paradox"; no luck yet. The text wasn't pink on a yellow background, in multiple fonts, and there were no exclamation marks or claims of suppression - so I think it wasn't ATM...)

27. Originally Posted by SeanF
That's what I think I did in this post.

1) Did Carl and Bob begin the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? Yes.
Check, check, and check. But, now look at Carl's history prior to the beginning of the experiment. He sees the approaching Bob as more time dilated than the distant Alice, yes? So when he synchronizes his age to Bob, does he think he is synchronizing to an age less or more than Alice's? So why should he be surprised that Alice is still older when he later gets to Alice? That's a twin paradox? Are you saying Carl has some reason to think Alice and Bob have to be the same age to Carl? Not if he understands time dilation. But even if you understand that, you still get the real twin paradox.

3) Did Carl and Bob end the experiment...
a) at the same point in space-time? Yes.
No, certainly not.
b) in the same reference frame? Yes.
Again, no. Not in either version of the A-B-C scenarios we've seen. I think you may mean Carl and Alice here, but it doesn't matter-- either they began at the same place and time, or ended it there, but no pair started and ended it that way, as you claim here.

28. Originally Posted by SeanF
In light of the "No" answers to 2a and 2b, what explains the "No" answer to 3c?
The distance at which the accelerations occur - the size of the "slice" of space-time involved. The further away an observer is, when they change their inertial frame relative to your own, the larger the shift in simultaneity, the larger the difference in your relative definitions of now.

29. Originally Posted by Ken G
Check, check, and check. But, now look at Carl's history prior to the beginning of the experiment. He sees the approaching Bob as more time dilated than the distant Alice, yes?
Approaching Bob? Distant Alice?

You're looking at the wrong experiment. Rather than linking, I'll cut and paste the experiment and the questions back together into this post.

The Experiment (I've changed my original 'Ann' to 'Alice' and corrected some typos in this! ):
Originally Posted by SeanF
Consider three triplets, all born in the same reference frame at the same time. Alice stays behind, Bob and Carl are both accelerated away (identical accelerations). At some point, Bob decelerates back to the original reference frame but Carl continues "moving". Then, at some later time, Carl decelerates back to the original reference frame (same rate of deceleration as Bob).

Carl then accelerates back towards Bob (and, further in the distance, Alice). As Carl approaches Bob, Bob begins accelerating towards Alice (same rate of acceleration as Carl) so that he matches Carl's speed exactly as he and Carl come alongside each other.

They then continue together and undergo identical decelerations to meet up with Alice at the original starting point, original reference frame.
The Questions:
Originally Posted by SeanF
1) Did Carl and Bob begin the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? Yes.

2) During the duration of the experiment, did...
a) Carl accelerate more than Bob? No.
b) Bob accelerate more than Carl? No.

3) Did Carl and Bob end the experiment...
a) at the same point in space-time? Yes.
b) in the same reference frame? Yes.
c) at the same age? No.

30. Originally Posted by SeanF
Approaching Bob? Distant Alice?

You're looking at the wrong experiment.
What I was referring to as the general class of Alice-Bob-Carl experiments is that class in which all the observers are always inertial, dating back to hhEb09'1s link on the topic, and the erroneous arguments contained therein. You have been talking about one in which they are accelerated. That's not even relevant to my point, because what I have said is that if you never have any acceleration, you never have any twin paradox, and if you do have proper acceleration, you can have a twin "paradox". Ergo, acceleration is crucial to the twin paradox. That's just a logical conclusion.

Now, you are apparently talking about something different, which is a claim, that I haven't made and is not the A-B-C issue, that all that matters in the twin paradox is acceleration. So for example, you show that where the acceleration occurs does matter. But I know that where the acceleration occurs does matter, as pointed out by speedfreek as well. That was never the claim that is being discussed-- the claim being discussed is whether you can have a twin paradox in the absence of any accelerated observer. That was the whole point of the A-B-C formulations. I now see that you have been talking about something quite different, so we can put that to bed by saying, the twin paradox must always involve acceleration, and where the acceleration happens does matter to the outcome.
Last edited by Ken G; 2008-Nov-12 at 09:12 PM.

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