I can understand why this works. For the person traveling in the spaceship near the speed of light, time has slowed down so they age less than the one one Earth. But, to the person on the spaceship, time is running normal and the people on Earth appear to be moving more slowly. So wouldn't they expect to come back to Earth to find a younger twin?

Our own Great and Angry Grape has written about this. Try the short version or the long version. Also there are helpful links to FAQ's at the bottom of those pages.

The Twin "paradox" always seems to cause confusion. I've found that one thing that helps is to not think of people in the spaceship "seeing things on earth". This thinking of one being able to check simultaneously what is happening in the spaceship and what is happening on earth is completely against SR. It is easier to think of the total journey of one observer then compare it to the other observer upon return.

Christine,

While the rocket is moving away from the Earth, both observers say the other's clock is running slow. While the rocket is moving back towards the Earth, both observers say the other's clock is running slow.

However, the rocket stops and changes direction, while the Earth does not. At that time, the two observers do not need to have reciprocity on what they see the other's clock as doing.

Think about it with two rockets instead of a rocket and a planet (lets call them Rocket A and Rocket B). Now, let's envision three distinct scenarios:

1) Rocket A moves away from Rocket B, then stops and moves back.

2) Rocket B moves away from Rocket A, then stops and moves back.

3) Rocket A moves away from Rocket B, then stops. Rocket B moves towards Rocket A.

It would be possible to describe all three of these situations as "Rocket A and B moved apart, then moved back together", but they are different because there are differences in which rocket(s) changed inertial frames and when. Do you see?

For what it's worth, in scenario 1, Observer A is younger at the end. In scenario 2, Observer B is younger at the end. In scenario 3, they are the same age at the end.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

As SeanF said, it is a matter of who changed inertial frames. In the original scenario, the rocket accelerates away from Earth, decelerates to a stop, accelerates back to Earth, and decelerates to a stop. Note that the rocket is the one that changed inertial frame every time. The Earth continued merrily on its way. So the twin on the rocket comes back younger than the twin who stayed on Earth.

_________________
TANSTAAFL!


<font size=-1>[ This Message was edited by: Kaptain K on 2002-02-15 15:37 ]</font>

Thanks for the nod, Wiley. Here is my GR version of the twin paradox, also.
::Jake on::
Why would you say that? One of the principles of SR, as delineated in the original paper, was that you could synchronize clocks across the entire inertial reference frame.
::Jake off::

But why does the short period of time that the rocket decelerates and stops make such a difference in their aging? For most of the trip, they are moving (or seeing the Earth/ Rocket B moving). And what if the rocket does not stop, but say orbits around a planet and continues back home, without changing their velocity?

Christine

You ask why a short period of decelleration would make such a difference. The answer is that the decelleration wouldn't be for a short period of time, but for half the journey. With these sorts of questions, the effect doesn't arise to any noticeable extent when you're travelling at the speed an Apollo spacecraft travels at (which was a few kilometres a second), but at relativistic speeds (tens of thousands of kilometres a second) it does arise.

Therefore, with regard to your second question, decellerating merely to orbital speed means decellerating to such a slow speed compared to what you were travelling before that you might as well be stationary compared to the Earth.

I disagree, I think. The GR variation of the twin paradox link I gave earlier is my attempt to deal with that aspect of it, although there are other approaches that you can find at the sci.physics faq links.

The one in the spaceship is not in an inertial frame during the turn around. Therefore, on the way back, he finds that the universe that was far away from him during the turn around "speeded up."
According to Einstein's 1905 paper where he defined SR (more or less) he defines a "stationary frame is one where both Newtonian mechanics and Maxwell's equations are true." An inertial frame was one which "moved at a constant velocity relative to the stationary frame." From this, one deduces that an inertial frame is any frame where both Newtonian mechanics and Maxwell's equations hold true. Not all frames are inertial frames.

Well, during the turn around, Newtonian mechanics does not strictly hold true for the guy in the turn around spaceship. He feels a gravity-like force, yes. This force is a type of "action." However, there is no force corresponding to a "reaction" to this force. Therefore, Newton's Third Law does not hold for the gravity-like force.

The guy who stayed behind, who never is in a rocket ship, always has all the Laws of Newtonian mechanics (and Maxwell's equations) working for him. Therefore, for him, the time scale of distant objects do speed up. However, the speed up in time increases with distance in the direction of the acceleration. Therefore, he does not see a speed up in time in his nearby suroundings. Furthermore, he has to wait until light from distant objects gets to him before he can deduce that part of the rest of the universe speeded up.


The constancy of the speed of light comes from Maxwell's equations that apply in every inertial frame. The speed of light is a consequence of a solution to Maxwell's equations. Maxwell's equations apply to electric fields, magnetic fields, and optics. However, without SR, Maxwell's equations and Newtonian mechanics contradict each other.

In 1922, Einstein changed his definition slightly to, "An inertial frame is one where the laws of physics are simplest." This allows SR to apply to nonNewtonian subjects (quantum mechanics, thermodynamics, etc.) Of course, this implies that an observer who is accelerating (i.e., in a noninertial frame) has laws that are more complicated than those in inertial frames.

The thing that is confusing you is Einstein's law of reciprocity: "The laws of physics are the same in all inertial frames." Note that this is not a corrollory of the definition. In principal, having two frames with different but equally simple laws would be possible but for the law of reciprocity. You think that the guy in the rocket and the guy who is stationary should have the same simple law, that he sees time in a moving space ship slow down. However, during the turn around, the guy in the spaceship is NOT in an inertial frame. He will soon deduce that the universe in the direction of his acceleration speed up, and that the universe in the direction opposite his acceleration slowed down. The effect increases with distance.

Really, it's not the acceleration (or deceleration) of the spacecraft that is the issue, it's simply the fact that it is now moving in a different direction.

Let's say you're receiving broadcast clock signals from a distant planet.

If the planet is motionless relative to you and is right now 100 light years away, you are receiving a signal that left the distant planet 100 years ago.

If the planet is moving away from you at .6c and is right now 100 light years away, you are receiving a signal that left the distant planet only 62.5 years ago.

If the planet is moving toward you at .6c and is right now 100 light years away, you are receiving a signal that left the distant planet a full 250 years ago.

So, what if we have two spacecraft, one travelling towards Earth and one travelling away from Earth, that pass each other 100 light years from Earth? Let's say that when they pass each other, both of their clocks read "1200 hours on February 18, 2100." They would both receive the exact same clock signal (let's say "1200 hours on February 18, 2002") from Earth at that moment. However, one would say that signal left Earth 250 years ago, and the other would say that signal left Earth only 62.5 years ago!

Therefore, one says that Earth's clock read Feb 2002 when his own clock read Aug 2037 (62.5 years ago), and the other says that Earth's clock read Feb 2002 when his own clock read Feb 1850 (250 years ago). Both spaceship clocks see Earth's clock as running at the same slower rate relative to their own (at .6c, the dilation would be 80%), so since they disagree on how long ago it was 2002 on Earth, they disagree on what year it is on Earth right now. One says 2052, the other says 2200.

If we have an observer who is riding the out-bound rocket, and he "leaps" onto the in-bound rocket at the moment they pass, what changes for him? His "current time" stays at 1200 on Feb 18, 2100. His rate of aging (relative to Earth) stays the same. The clock signal he's receiving from Earth stays at "1200 on Feb 18, 2002." His measurement of Earth's rate of aging remains at 80% of his own. However, his measurement of Earth's current time immediately jumps from 2052 to 2200!

He would have left Earth when his clock said 1933 and Earth's clock said 1919. He will arrive at Earth on the new ship when his clock says 2266 and Earth's clock says 2334. He says it took 166 years out and 166 years back. He says Earth's clock counted off 133 years during the trip out and 133 years during the trip back. But that 148-year jump in "Earth time" when he changed directions is what makes Earth older.

This is not a result of deceleration and reacceleration. It is only a result of the synchronicity difference in SR which is direction dependent, unlike the time dilation and spatial contraction which are direction independent.

I'm probably just making this even more confusing than it already was . . . but I think I'll go ahead and submit this post anyways! [img]/phpBB/images/smiles/icon_smile.gif[/img]

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

But SeanF, that is acceleration.

At least, that is the way that we define acceleration in this context (modern physics). Constant speed but a change in direction is an acceleration.

All right, technicality point granted.

However, if you have two spaceships that are moving at the same constant speed but in different directions relative to Earth, and those two spaceships measure the current time on Earth differently, would you argue that that difference is a result of acceleration?

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

I would need a few more specifics of the setup here. How are they moving differently? And when?

If two spaceships start out in opposite directions at the same speed, would they necessarily see Earth anyway differently at all?

You're asking if two spaceships start out at Earth and move off in opposite directions? In that case, there would be no way to define any simultaneity between the two spacecraft, so trying to discuss whether they see Earth the same is kind of meaningless.

However, see the situation I described in my post above. At the moment the two spacecraft pass each other 100 light-years from Earth (at which time they can have an agreement with each other on simultaneity), they measure different times for the current time on Earth, and that difference is necessary for the infamous "twin paradox" to work out.

It comes down, basically, to the simultaneity issue. Observers on the two spacecraft would disagree as to what "event" (or "time") on Earth was simultaneous with the "event" of the two spacecraft passing each other. Actually, if we throw in an observer on Earth, we can have three distinct Earth-bound "events" that are seen to be simultaneous with the ships' passing, one by each of the three different observers.

So, is that difference in simultaneity a result of acceleration?

(As an aside - Grapes, I absolutely love having SR discussions with you. You have an uncanny capability of asking just exactly the right questions to make me clarify my thoughts in my own mind and on screen!)

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

<a name="20020218.8:34"> page 20020218.8:34 aka Graphic thoughts / HUb'
.1 Vertical scan rate {60} arb units
...2 Horizantal . RATE .of. SCAN TBA
...... anyway I was trying to delete some
POSTs today in the Apogee to Perigee thread.
Not that this matters .. and also trying to
consieve of a TV picture beinng sent to a
TV set on board an orbiting space station
about EARTH aproaching Texas & leaving Dallas2
I guess its about the same story as GPU or is it GPI maybe GiP?

SeanF

That's exactly why I'm here. (No, not for your clarification, for mine.)

Check out my webpage that Wiley referenced. The bottom paragraph talks about "Carl" who passes Bob and returns to Earth. For all intents, I believe that satisfies your scenario (except I have their meeting occur 6 lightyears from Earth).

Then, how did the one going towards Earth (Carl) originally establish "current time on Earth?" Don't you have your simultaneity problem there? I assume the one going away (Bob) established it when he left Earth?

Yes, that's essentially the same thought experiment on your page . . .

Einstein's original 1905 paper established how one determines synchronicity with distant clocks (I know you know about it, GoW! [img]/phpBB/images/smiles/icon_wink.gif[/img] ), and his method of determining that synchronicity is not limited to clocks which are stationary relative to one another. Both outgoing and incoming observers can use the signals received from Earth to determine how far away Earth is and how fast (and in what direction) it is moving, as well as what "time" it is on Earth. To be more accurate, the observers can only determine what Earth's status was at the time the signal was sent -- However, continuous monitoring will allow both to determine "after the fact" what "Earth time" was at the moment they passed each other. While the outgoing observer could have established "Earth time" at the moment of passing, he would still need to continue to monitor the signal to maintain that knowledge.

Now, I would like to take this opportunity to re-phrase my previous objection to "acceleration." I probably should have been objecting to the terms "non-inertial frame" or "not in an inertial frame."

Consider the thought experiment wherein we have the Earth and the two spaceships already travelling in opposite directions. Our single observer starts out on Earth and "leaps" onto the first spaceship as it passes. He then "leaps" from the first spaceship to the second as they pass each other, and then again from the second spaceship to Earth (before we get any futher, let me acknowledge that it is physically impossible in the real world to have this kind of instantaneous change in inertial frame - but this is just a thought experiment, so please bear with me).

The practical upshot of this is that the observer spends exactly zero time "in a non-inertial frame" or "not in an inertial frame." None. Never. This is similar to the situation Einstein was describing in his 1905 paper with the observer in the "closed loop of constant velocity" that brought him back to his starting point - the observer was constantly changing from one inertial frame to another, but was never "not in an inertial frame" (or so I believe Einstein intended).

Now, since neither our traveling observer nor the one left on Earth ever spent any time in non-inertial frames, why does the traveling observer wind up younger? Because the Earth-bound observer spent the entire duration of the experiment in the same inertial frame, whereas the traveling observer did not. Although the traveling observer "changed inertial frames," he never spent any time in a "non-inertial" or "accelerating" frame, which is why I asserted that "acceleration" is not responsible for the time dilation.

I also once described a thought experiment where two rockets experienced identical accelerations, decelerations, and re-accelerations, with one merely spending more time cruising in the final inertial frame before decelerating and turning around. Although the two spacecraft's experience with acceleration and non-inertial frames would be identical (albeit not simultaneous nor colocated), the traveler who gets more "cruising time" would experience a greater time dilation.

While General Relativity predicts consequences of "acceleration" or "non-inertial frames," Special Relativity does not and SR's "twin paradox" is not dependent on them.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

I admit i'm lost, but doesnt this have some bearing on the matter ie thought experiment or no we are talking about physical laws & wouldnt such an instantaneous jump of inertial frames still involve an acceleration of sorts?
Please feel free to ignore this, I probably dont know what i'm talking about but finding it interesting! [img]/phpBB/images/smiles/icon_smile.gif[/img]

__________________
N6MAA10816
Faber '62 ΔTX
Are you a Bright?

Roy,

It does have bearing on the matter - in actual practice, the acceleration involved in actually doing an experiment like this would have an effect on the observer. However, SR predicts that the simple relative motion as described would create time dilation "above and beyond" any effects caused by the acceleration, which is why I tried to describe a situation where we can ignore the acceleration-induced effects and focus on the others.

Another way to think about is to just have separate observers on Earth and the two ships. Both ship observers say the Earth clock is running more slowly than their own. The observer on the outgoing ship says x time passed between his ship passing Earth and the two ships passing each other; the observer on the incoming ship says x time passed between the two ships passing each other and his ship passing Earth, but the observer on Earth says more than 2x time passed between the first ship passing Earth and the second.

Same apparent paradox, no acceleration involved . . .


_________________
SeanF

<font size=-1>[ This Message was edited by: SeanF on 2002-02-18 16:23 ]</font>

Well....

As near as I can tell, that jumping from one inertial frame to another (see Twins Redux link) avoids the acceleration of physical objects (why have the observers change frames--just pass notes somehow to each other as they pass) but clearly it is an acceleration of some sort.

So, in Einstein's 1905 paper, he cobbled together a finite set of such paths, where the inertial paths were linked at endpoints--"avoiding" acceleration, as you say. However, that is a consequence of acceleration, so I'd hesitate to say that SR does not predict such consequences.

In fact, it's just that sort of thing that led Einstein to General Relativity. It is Special Relativity taken to the limit. You can do it mathematically, if you assume that the limit is valid. In his 1905 paper, he said he didn't know why it wouldn't be, but he didn't go farther than that, in the paper.

So, one of the consequences of SR does involve acceleration, and Einstein even made that point in his first paper.

<font size=-1>[Fixed link]</font>

<font size=-1>[ This Message was edited by: GrapesOfWrath on 2002-02-19 06:40 ]</font>

We may be just arguing semantics and definitions, but I still think I need to disagree. The "acceleration," such as it is, is necessary in order to get the observer back to his original starting point, but I still don't think it contributes to the time dilation.

New thought experiment! [img]/phpBB/images/smiles/icon_smile.gif[/img]

You have two stationary clocks separated by six light-minutes' distance and synchronized. A spaceship moving at 0.6c passes first by one clock and then by the other. The spaceship observer says it only takes eight minutes from when he passes one clock to when he passes the second, but the two stationary clocks show a difference of ten minutes.

Now put the two stationary clocks in the same place (or replace them with a single clock) and just send the spaceship out and back on a "constant" 0.6c that lasts eight minutes of spaceship time, and the stationary clock(s) will have ticked off ten minutes.

Now, there's no difference in the results, even though the second experiment involves acceleration and non-inertial frames while the first does not. So how can those results be "due to" acceleration and/or non-inertial frames?

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

We're going to fry each others brains.

Now, with your new experiment, I need one more piece of information. Since everything appears to be in inertial reference frames, how do you account for the symmetry between them? What do the observers stationed with each set of clocks see, on their clocks and the others clocks?

Mmmmm . . . did you ever see "Hannibal"?
Observers at either of the two relatively stationary clocks see the two clocks as being synchronized, per Einstein's definition in his 1905 paper.

In other words, an observer at one clock will be receiving signals from the other that are exactly six minutes behind his own. By bouncing his own signal off the other clock, he can determine that the other clock is motionless with respect to himself and is synchronized with his own. An observer at the other stationary clock would see exactly the same thing.

Both of those observers can use the same method to measure the spaceship clock, although it requires a bit more math on their parts to compensate for Doppler. They would both recognize that the spaceship clock is running slow (by a factor of .8 ) compared to their own clocks.

The spaceship observer, using essentially the same math, would also recognize that the two "stationary" clocks are running slow (by a factor of .8 ) compared to his own clock. However, he would conclude that the two stationary clocks are not synchronized, but that the "second" clock is set three minutes and 36 seconds ahead of the "first" clock. This is due to the simultaneity factor of SR.

[Edited to correct auto-"smilies"]

_________________
SeanF

<font size=-1>[ This Message was edited by: SeanF on 2002-02-19 09:57 ]</font>

Sorry it took so long to answer this question. The key seems to be in that first sentence. You claim that there is no difference in the results, but
Notice that in the second experiment of your new thought experiment, the spaceship observer would not be allowed to conclude this--because the first clock is the same clock as the "second" clock.

The only way to break the symmetry (and come up with truly different results) is by acceleration.

What the spaceship observer sees during the experiment is not the "results" of the experiment, is it?

The experiments are not identical - if they were, there'd be no point. There're two clocks in the first version, so the observer can see both clocks simultaneously. There's only one clock in the second version, so he can't. Obviously, then, they're going to see different things. However, the first observer's observations of the first clock during the first half of the experiment will be identical to the second observer's observations of his clock during the first half of his experiment (while he's moving away from it). Second clock, second half, same observations. It would not be incorrect to say that in the single-clock experiment, the clock is not (or does not remain) synchronized with itself as viewed from the spaceship.

Bottom line is that in both cases, the spaceship spends eight minutes travelling at 0.6c relative to the "stationary frame" and ends up two minutes behind it.

The idea of physically separating the "stationary" observer into two so the spaceship doesn't have to come back is mere convenience. An "inertial frame" is not a point, or a spaceship, or a planet - it's a coordinate frame that extends throughout spacetime and can be thought of as a whole.

I once gave JW an analogy of a mountain. The air is thinner at the top, so a person will have a harder time breathing at the top than at the bottom. The difference in breathing is a result of being at the top rather than being at the bottom; but is it correct to say that the difference in breathing is caused by the climbing or the moving up? I don't think so. Likewise, the difference in that single clock is a result of the spaceship being in a different inertial frame, but it's not correct to say it's caused by the acceleration.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

But the breaking of symmetry is. The point is that in the first half of your experiment, if you had another observer with your clocks, both observers would see each other grow old and die while they stayed young--or they would infer that from the clocks they were passing. Totally different outcome, as far as their experience.

I feel like we may be going in circles here . . . I'm not arguing that the turn-around is irrelevent, just that it doesn't contribute to the time dilation. Really, my problem is that I think the wording of some Relativity explanations is misleading, but I don't know that my own wording is any better! I would make a horrible teacher . . .

The classic SR "twin paradox" is a spaceship that accelerates, cruises, decelerates, turns around, accelerates, cruises, decelerates, and stops back at Earth, right? The astronaut ends up younger than his twin left behind on Earth.

If you leave all the accelerating and decelerating the same but increase the time spent "cruising" (both ways, of course), you will end up with an even bigger difference in age. If you reduce the "cruising" time, you end up with less difference in age.

My concern is when I read things that suggest that it's something that happens during acceleration that causes the time dilation.

The fact that only one twin changes direction is, as you point out, what breaks the symmetry postulate of SR, but it's really not what causes the twins to age at different rates.

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF

Yes, but without the turnaround, it happens to both of them.

That's the genesis of what appears to be a paradox--if SR is a symmetric effect, and the dilation depends upon relative velocity, how does an asymmetry develop when they meet back up again? That's why the turnaround is basic to the twins paradox.

Yes, it's true that the turnaround time is important in the paradox, which I mentioned in my first post in this thread:

But then later posts by others said things like:

and:

And it was really those types of statements to which I was intending to "object" (although in re-reading, I have less objection to that second one than I did initially).

__________________
SeanF

"Ask to understand, but don't challenge unless you have the knowledge."--NEOWatcher

The contents of this post are ©2009 by SeanF and may not be copied or retransmitted in any form without the express written consent of SeanF