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Author Topic:   The Twins Paradox and the speed of light
tis---strange
Junior Member (Idle past 5244 days)
Posts: 14
From: Oslo, Norway
Joined: 11-11-2009


Message 121 of 230 (535129)
11-13-2009 2:35 AM
Reply to: Message 120 by lyx2no
11-12-2009 5:55 PM


Re: Why it is called the Twin PARADOX
But the problem does not make any physical sense if you make this simplification. If you just assume that you can solve the problem for the time dilitation on the one way and add the time dilitation on the other way (as the book does), the two twins come to different conclusions about the age of the other twin. Therefore, we can not ignore the acceleration.

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 Message 120 by lyx2no, posted 11-12-2009 5:55 PM lyx2no has replied

Replies to this message:
 Message 122 by lyx2no, posted 11-13-2009 8:23 PM tis---strange has replied

  
lyx2no
Member (Idle past 4716 days)
Posts: 1277
From: A vast, undifferentiated plane.
Joined: 02-28-2008


Message 122 of 230 (535226)
11-13-2009 8:23 PM
Reply to: Message 121 by tis---strange
11-13-2009 2:35 AM


School Me
But the problem does not make any physical sense if you make this simplification.
Ok, you're going to have to help me out on this one. Why? As far as I understand it, there's nothing special about this acceleration. At any given instant the accelerating clock has such and such dilation relative to the other. Replace v in the LT with the acceleration function and integrate for the interval, right? But because it's only in the latter parts of the acceleration that the velocity becomes relativistically significant it seems to me that it would be easier to ignore then the acceleration period in the Bos-Den problem. (I say this assuming, of course, that the acceleration periods all round are comparatively short.)
I certainly wouldn't be surprised if I were missing something important. It's not like I know what I'm talking about, or anything. I'd appreciate the lesson.

It's not the man that knows the most that has the most to say.
Anon

This message is a reply to:
 Message 121 by tis---strange, posted 11-13-2009 2:35 AM tis---strange has replied

Replies to this message:
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Bolder-dash
Member (Idle past 3630 days)
Posts: 983
From: China
Joined: 11-14-2009


Message 123 of 230 (535254)
11-14-2009 4:23 AM
Reply to: Message 1 by Jester4kicks
06-30-2008 4:57 PM


Paradox within a paradox
I enjoy this discussion, but as in everything in life, one must approach all "facts" with some skepticism. Here is a paradox I have with this paradox: If someone cares to answer it, (preferably without math formulas) I would be most grateful:
Premise: When one object is accelerating it will experience time slower relative to an object not accelerating.
So, what if the object (one of the twins in this case) is simply going in circles around the other twin, and they can see each other?
What if one of the twins is not changing his orientation at all, but is simply spinning on a fixed axis at close to the speed of light, is the parts on his body furthest from the axis experiencing time at a different rate from the parts of his body closer to the axis (which are obviously moving slower)?
Take it another step further...the object that is moving is a pocket-watch-does the way in which it is moving matter? Can it be spinning around an axis? How about if you could stare at the center of the face of the pocket-watch, but the numbers are spinning clockwise (or counterclockwise if you prefer)?
And what if it is just part of the watch that is accelerating, like a ring around the outside of it? Can parts of the watch age more while other parts age less?
And to take it even one step further if I may. What if one of the twins (or a watch) is simply vibrating at close to the speed of light, will it experience time differently than the twin not vibrating, even though they have not moved apart from each other at all? It is after all moving while it is being vibrated, correct?
Edited by Bolder-dash, : Grammar, ..poor eyesight

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Iblis
Member (Idle past 3895 days)
Posts: 663
Joined: 11-17-2005


Message 124 of 230 (535258)
11-14-2009 5:03 AM
Reply to: Message 123 by Bolder-dash
11-14-2009 4:23 AM


yes and no, with a side of maybe
When one object is accelerating it will experience time slower relative to an object not accelerating
Not "accelerating", accelerated. Accelerating an object dilates its proper time; that proper time remains dilated (in respect to objects that have undergone less acceleration) even after it stops accelerating; the only way to "un-dilate" it is to decelerate the object a corresponding amount.
what if the object (one of the twins in this case) is simply going in circles around the other twin
Three parts:
a) Traveling in a circle around something at a steady rate constitutes circular acceleration, the source of "centrifugal force"
b) Because it's circular, though, it's progressively equal acceleration in all directions, so there's as much deceleration to it as there is acceleration
c) It becomes somewhat more complex when bound in the circle by gravity, but doesn't affect the basic equalization, the extremely tiny time-warp associated with being in orbit has to do with gravitation rather than classical acceleration
What if ... spinning ... around an axis ... just part ... vibrating
It's all the same question from there on in. Spinning, circling, orbiting, and vibrating all involve equal amounts of acceleration and deceleration by direction.
You are kind of spooking yourself by using phrases like "at the speed of light" though. The forces necessary to create circular or vibratory acceleration-deceleration such as to create relativistic speeds will reduce your twin to plasma and then energy.
Imagine how much force is necessary to speed something up to the speed of light in say a minute, or a second. Then imagine having to subject it to that much force to decelerate it back to "0". Then imagine having to continue to subject it to that much force to get it back up near C in the opposite direction. Then do it again, and again, and again, and again, every minute or second.
* I'm seriously wrong here somewhere, btw. For example, in the vibrating version, the acceleration forward will dilate the proper time, a tiny bit, and then the deceleration will un-dilate it, and the acceleration backward will dilate it some more (not reverse it!) and then that deceleration will un-dilate it, ad nauseam.
After a bit that ought to add up to a chunk of time lost wouldn't it? Why wouldn't the same thing happen in an orbit situation? Does it get just drowned out by the significantly larger differential the other way due to distance from the gravity source?
Edited by Iblis, : jot and tittle
Edited by Iblis, : more Big Dope

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 Message 123 by Bolder-dash, posted 11-14-2009 4:23 AM Bolder-dash has not replied

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lyx2no
Member (Idle past 4716 days)
Posts: 1277
From: A vast, undifferentiated plane.
Joined: 02-28-2008


Message 125 of 230 (535272)
11-14-2009 8:29 AM
Reply to: Message 124 by Iblis
11-14-2009 5:03 AM


Re: yes and no, with a side of maybe
I'm seriously wrong here somewhere, btw.
Well, for the orbiting body the acceleration is always pointing down. It is its velocity that is progressively in all directions (in the plane).
I'd pretty much go along with the bits would add up if your own bits wouldn't fly to bits.

Welcome Bolder-dash
Yes, the bits would age differently; just as your bits are aging differently head to toe wise as you stand in Earth's gravity well.
AbE:
For the case of going in circles around the other twin: Yes, the circling twin would age slower, but, assuming they're not a point source twins, not all parts of the spinning twin would age slower at the same rate.
The fixed axis spinning twin's distal bits would age faster then his proximal bits. This was what I was implying in post 99 where Zeus was aging at a different rate then I because he lived closer to the equator.
All the bits of the vibrating twin would age at the same rate as they are vibrating in unison. But it's a less efficient fountain of youth then the revolving twin uses as only a small portion of his time is spent at vmax.
The watch is the same as a twin for all this.
Google time dragging around a black hole. These weird effects do happen. Well, not the vibrating.
Edited by lyx2no, : grammar.
Edited by lyx2no, : It's raining. I can't be raking in this storm.
Edited by lyx2no, : Grammar (imply not infer).

It's not the man that knows the most that has the most to say.
Anon

This message is a reply to:
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tis---strange
Junior Member (Idle past 5244 days)
Posts: 14
From: Oslo, Norway
Joined: 11-11-2009


Message 126 of 230 (535281)
11-14-2009 11:08 AM
Reply to: Message 122 by lyx2no
11-13-2009 8:23 PM


Re: School Me
I am certanly not qualified to school you, but what I have of recollections of the two ways of computing the time age of the twin on earth from the perspective of the twin on the spaceship, most of the aging of the twin on earth happens while the second twin is accelerating.
We can try calculating that using GR and assuming an infinately short(in the referance frame of the spaceship) acceleration with an infinite acceleration g (as cavediver said, it is not wrong to do it that way, and I am not used to using hyperbolic motion... so therefore I use GR ;-)
We will split the problem in three parts. Part one is moving from earth in direction proxima centauri (4.1ly away at rest distance) and part three is moving back with a constant speed 0.8c.
Part two is the acceleration part, I will come to that.
We consider sitting in the spaceship, thus "being at rest". At start, earth (and proxima centauri) is moving with a speed 0.8c. Since the bodys are moving, we observe a lorentz contracted distance between the two bodies s=s0sqrt(1-v^2/c^2) = 2.4ly. When proxima centauri arrives at our ship we will have aged 2.4ly/0.8c = 3 years. Earth however has moved, so we calculate that the time elapsed on earth is given by 3years * sqrt(1-v^2/c^2) = 1.8 years.
Then we experience a gravitational field (we accelerate) with a constant gravitational-acceleration g. Earth is falling freely in this field. At this point we observe earth at a distance x1=2.4ly. We will then observe earth slowing down until it comes to rest at a distance x2=4.1ly. Earth will then accelerate back against us until it reaches v=0.8c again at the distance x1=2.4ly.
We will now need to use the proper time intervall deltatau (the time experienced in the free falling frame/earth while the acceleration lasts). It is not trivial to find the expression for this (the way I was taught to do this, you need to know a bit about lagrange functions), and I hope you can believe me when I say that in this case it is given as:
delta tau = c/g *sqrt(((1+gx2)/c^2)^2 - ((1+gx1)/c^2)^2)
Now, we want the acceleration to last a very short amount of time (this makes calculating the age of the traveler from the earth frame easyer), meaning that we want g to approach infinity giving (by using L'hopitales rule):
delta tau = 1/c sqrt(x2^2 - x1^2)
for x1 = 2.4ly and x2 = 4.1ly, this gives:
delta tau = 6.4 years
on the way back, we calculate the time elapsed on our planet in the same way as in part one, giving:
Time elapsed for us: 3 years + 3 years + nearly nothing = 6 years
Time elapsed for earth: 1.8 years + 1.8 years + 6.4 years = 10 years
Which is the same result as expected by calculating the age of the traveler from earths frame.
So if we eliminate the acceleration by making it very short and then saying it doesn't have any influence, we are 6.4 years off in the end result.
I realize that this is not exactly what you had in mind, you wantet to integrate over an infinite amount of frames moving with constant velocity to get the result. I think the result would be the same (if you take the amount of time you accelerate to be very short)...

This message is a reply to:
 Message 122 by lyx2no, posted 11-13-2009 8:23 PM lyx2no has replied

Replies to this message:
 Message 128 by lyx2no, posted 11-17-2009 7:59 PM tis---strange has replied

  
Trae
Member (Idle past 4306 days)
Posts: 442
From: Fremont, CA, USA
Joined: 06-18-2004


Message 127 of 230 (535761)
11-17-2009 6:36 PM
Reply to: Message 114 by lyx2no
11-11-2009 6:00 PM


Re: Back to the basics
Thanks. This was an aspect I hadn't seen address before, so while it seems like it applies, it really isn't significant enough to matter.

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lyx2no
Member (Idle past 4716 days)
Posts: 1277
From: A vast, undifferentiated plane.
Joined: 02-28-2008


Message 128 of 230 (535766)
11-17-2009 7:59 PM
Reply to: Message 126 by tis---strange
11-14-2009 11:08 AM


School Me More
You've confused me. I've been going over this for several days and have made little progress in its unraveling.
Then we experience a gravitational field (we accelerate) with a constant gravitational-acceleration g.
I don't know why we consider a gravitational field at all. Are you just saying that an acceleration is akin to a gravitational field? Isn't "g" Earth's surface gravity? We'd not feel that from 2.4 ly.
I hope you can believe me when I say
Of course I can believe ya', buddy What's a lagrange function? (I have been reading up I don't expect you to do my work but my maths aren't there yet.)
To make a long story short Huh?

It's not the man that knows the most that has the most to say.
Anon

This message is a reply to:
 Message 126 by tis---strange, posted 11-14-2009 11:08 AM tis---strange has replied

Replies to this message:
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tis---strange
Junior Member (Idle past 5244 days)
Posts: 14
From: Oslo, Norway
Joined: 11-11-2009


Message 129 of 230 (535794)
11-18-2009 1:36 AM
Reply to: Message 128 by lyx2no
11-17-2009 7:59 PM


Re: School Me More
I don't know why we consider a gravitational field at all. Are you just saying that an acceleration is akin to a gravitational field? Isn't "g" Earth's surface gravity? We'd not feel that from 2.4 ly.
Yes! In GR we can associate an acceleration with a gravitational field. In fact: We consider ourselves standing still in this gravitational field (kind of like standing on the surface of earth) while earth is falling freely in this field. It seems strange, but it is physical identical with what you experience in the space ship: You feel a "force" (this picture on wikipedia makes a point of this) and earth is accelerating towards you at the right rate. I am shure cavediver has a better explanation up his sleeve ;-)
g is only a variable I defined. Call it for a if you think that is easier. But I did not consider Earth's surface gravity at all (we neglect the suns gravitational field and proxima centauris grav field, earth grav field is much less), and remember g goes to infinity (to simulate an infinitly short acceleration).
Of course I can believe ya', buddy What's a lagrange function? (I have been reading up I don't expect you to do my work but my maths aren't there yet.)
A lagrange function describes a system in classical mechanics (in this case we had to generalize it to apply to GR, but the principal is the same).
In the case of uniform acceleration it is given by:
L = -1/2(1+ gx/c^2)^2c^2dt/dtau + 1/2dx/dtau
Where tau is the proper time/time expirienced in the accelerated system.
The Lagrange function is a way to discribe a physical system using conservation of energy and conservation of momentum. The point is: When you have the Lagrange function, you can use the Euler-Lagrange functions of motion to discribe the system.

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jaywill
Member (Idle past 1941 days)
Posts: 4519
From: VA USA
Joined: 12-05-2005


Message 130 of 230 (538125)
12-03-2009 11:30 PM
Reply to: Message 123 by Bolder-dash
11-14-2009 4:23 AM


Re: Paradox within a paradox
I dare not comment on this without reviewing the issues. But isn't it UNIFORM motion that is always discussed in time dialation?
The one ship has to go in a straight line out and back. I don't think going out in a big ellipse or turn around is used as and example of time dialation.
Isn't it uniform motion in relation to some reference point ?

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lyx2no
Member (Idle past 4716 days)
Posts: 1277
From: A vast, undifferentiated plane.
Joined: 02-28-2008


Message 131 of 230 (538130)
12-04-2009 1:23 AM
Reply to: Message 130 by jaywill
12-03-2009 11:30 PM


Re: Paradox within a paradox
But isn't it UNIFORM motion that is always discussed in time dialation?
Only because it makes the math easier.
I don't think going out in a big ellipse or turn around is used as and example of time dialation.
It is the accelerating twin whose time is dilated, so an ellipse would satisfy that distinction telling us who stepped out of the initial frame of reference.
Isn't it uniform motion in relation to some reference point ?
The twins paradox is used to generally examine an odd effect of relativistic time dilation, not the actual rate of the time dilation. In as much, one doesn't really get into the specifics. Nonuniform velocities only complicate the situation.
But at any instant the dilation has a certain value. If the motion is uniform all instants have the same value: τ=(1-v2/c2)0.5. If the twin is accelerating uniformaly, say v=gt, then at t=10million seconds our astronaut twin would be aging at 94.5% the rate of his Earth bound, reference point brother. At t=2107, 75.6%; and at t=3107, 19.4%. (Not that he'd be able to maintain g.) figuring out the mean τ for the interval 0≤t≤3107 is difficult. Figuring out the average τ for the complex acceleration of a planar curved motion is very difficult. Neither lend themselves to an unraveling of the twins paradox.

The world breaks everyone, and afterward many are strong at the broken places. But those it cannot break, it kills. It kills the very good and the very gentle and the very brave impartially. If you are none of these, you can be sure that it will kill you too, but there will be no special hurry.
Ernest Hemingway

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Maartenn100
Member (Idle past 4592 days)
Posts: 39
From: Belgium Antwerp
Joined: 08-13-2011


Message 132 of 230 (628835)
08-13-2011 11:25 AM


another view on the twin paradox and gravitational relativity.
Hello,
I'm new here and from Belgium. My English is not very well, but I will try and I hope you will forgive me when I don't formulate something correct.
I'm a student in psychology (in my free time as an adult) and tried to think about perceiving time and space by an observer.
I think I found an interesting issue, related to relativity. I want to post it on the forum for criticism. To get some feedback.
The twinparadox
I believe that the twinparadox is for relative movements in a uniform gravitational field.
Why?
Because when an astronaut leaves earth, he must accellerate to leave the gravitational field.
While he is accellerating away from Earth, he sees the 'object Earth' more and more turning around.
First the Earth stood still, no he sees the earth more and more turning around. So the heavy object were he is moving away from is not only moving away from him from his reference point of view. This heavy object is also turning around itself more and more.
When the astronaut is leaving the solarsystem, he is not only measuring that the heavy object Earth is moving away from him relative to his reference point of view.
No, he sees that the heavy object Earth also succesively is turning around the sun more and more till it reaches the speed of 30 m/s around the sun.
When the earth is moving away from him - relative to his reference point of view - it's also spinning around the sun at 30 m/s, then the astronaut himself is outside the solarsystem and is not turning around the sun anymore.
So the timedilation of the object by progressively spinning in the gravitational field by the measurements of the moving observer is is not calculated in the measurements of relativity in the gravitational field.
The Earth or any other object is not only going away from us from our point of view, but is also beginning to move around its axis, around the sun, the sun begins to move in the milkeyway. While we are leaving the solarsystem.
When an heavy object as the sun is not only moving away from our point of view (we as astronauts, escaping the gravitational influence from the sun), but also begins to move in the gravitational field (g) in the Milkey Way, while we are leaving the Milkey Way, according to us, then there is no paradox anymore for the timedistortions.
Both objects will have the same time while coming back together.
The twins will have the same age when they meet again.
Because the twin who stood on earth was not only accelarating away relative to the traveling twin. He was also turning around more and more. Spinning around the earth, wobbling with a moon, spinning more and more around a sun and so on.
The timedilations caused by these measurable spinning movements are not involved in the calculations for gravitational relativity.
Therefore I think that the twinparadox is only a paradox in a uniform gravitational field, but not when an observer is moving away from an object in space.
When an observer is moving away from an object in space, that object is not only moving away from him from his point of view. But while he or she is accellerating to escape the gravitational field, that object begins also to spin in the gravitational field that he is leaving.
The gravitational accelerations of the bodies will be measured too as movements of these bodies where we, as observers, are moving away from, and will be the cause for the measured timedistortions of these bodies.
Then the timedilations caused by these movements will cancel eachother out.
The twins will have the same age.
Edited by Maartenn100, : No reason given.
Edited by Maartenn100, : No reason given.

Replies to this message:
 Message 133 by Adminnemooseus, posted 08-13-2011 11:39 AM Maartenn100 has replied
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Adminnemooseus
Administrator
Posts: 3974
Joined: 09-26-2002


Message 133 of 230 (628839)
08-13-2011 11:39 AM
Reply to: Message 132 by Maartenn100
08-13-2011 11:25 AM


We've just had a time dilation event happen!
Back in your proposed topic, I suggested that you read through this topic AND THEN maybe add your input to this topic.
10 minutes passed between my posting of the above cited message and your posting to this topic.
Boy, for someone not good with the English language, you sure read a lot of messages in what seemed to be a very short amount of time. Apparently I was accelerating and/or moving at a high velocity while you were stationary, such that much more time passed for you than for me.
Nah, that probably didn't happen. You really should read the early part of this topic. A lot of smart people posted some pretty good information there. There might even be smart people posting good information in the later part of the topic.
PLEASE, NO REPLIES TO THIS MESSAGE. YOU DON'T HAVE TIME - YOU SHOULD BE READING!
Adminnemooseus

Please be familiar with the various topics and other links in the "Essential Links", found in the top of the page menu. Amongst other things, this is where to find where to report various forum problems.

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Maartenn100
Member (Idle past 4592 days)
Posts: 39
From: Belgium Antwerp
Joined: 08-13-2011


Message 134 of 230 (628842)
08-13-2011 11:59 AM
Reply to: Message 133 by Adminnemooseus
08-13-2011 11:39 AM


Re: We've just had a time dilation event happen!
yes I know, but I already know a lot about relativity and the twin paradox. I've read more books than the few articles here about relativity. But I understand your concern.

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 135 of 230 (628847)
08-13-2011 12:21 PM
Reply to: Message 132 by Maartenn100
08-13-2011 11:25 AM


Re: another view on the twin paradox and gravitational relativity.
While he is accellerating away from Earth, he sees the 'object Earth' more and more turning around.
No, he will see the Earth turn more slowly - the Earth will appear red-shifted.

This message is a reply to:
 Message 132 by Maartenn100, posted 08-13-2011 11:25 AM Maartenn100 has not replied

  
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