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Author Topic:   The Twins Paradox and the speed of light
lyx2no
Member (Idle past 4716 days)
Posts: 1277
From: A vast, undifferentiated plane.
Joined: 02-28-2008


Message 20 of 230 (473678)
07-01-2008 7:50 PM
Reply to: Message 19 by NosyNed
07-01-2008 6:33 PM


Re: spatial
Set y and z to 0 then solve for x.

Kindly
Everyone deserves a neatly dug grave. It is the timing that's in dispute.

This message is a reply to:
 Message 19 by NosyNed, posted 07-01-2008 6:33 PM NosyNed has replied

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


Message 22 of 230 (473685)
07-01-2008 9:34 PM
Reply to: Message 21 by NosyNed
07-01-2008 8:38 PM


Re: More help please
x=(s2 + t2).
It's the Pythagorean theorem. x, the spatial separation is the hypotenuse of a right triangle. s, the spacelike spacetime interval; and, t, the time interval make up the adjacents. The hypotenuse is always the longest side.
Edited by lyx2no, : Meant time interval, not timelike spacetime interval. Got carried a way with parallel sentence structure.
Edited by lyx2no, : Typos, confusing ones.

Kindly
Everyone deserves a neatly dug grave. It is the timing that's in dispute.

This message is a reply to:
 Message 21 by NosyNed, posted 07-01-2008 8:38 PM NosyNed has replied

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


Message 31 of 230 (473799)
07-02-2008 11:38 PM
Reply to: Message 30 by fallacycop
07-02-2008 11:05 PM


Re: Calculation
If dt is larger then ds you'd have dτ2 = dt2 - ds2, and would be calculating proper time rather than proper distance.
AbE: It looks like farther down in the tread ds has been used for time while I've been thinking of it as d(spatial). Sorry if I've confused the issue. Or maybe I'm confused now.
Edited by lyx2no, : No reason given.

Kindly
Everyone deserves a neatly dug grave. It is the timing that's in dispute.

This message is a reply to:
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lyx2no
Member (Idle past 4716 days)
Posts: 1277
From: A vast, undifferentiated plane.
Joined: 02-28-2008


Message 83 of 230 (511120)
06-06-2009 8:45 AM
Reply to: Message 81 by Kev The Thiest Evolutioni
06-06-2009 4:53 AM


An Acre Per Hour
velocity times distance.
The E=mc2 of lawn mowing theory.

Ridicule is the only weapon which can be used against unintelligible propositions. Ideas must be distinct before reason can act upon them.
Thomas Jefferson

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


Message 99 of 230 (534615)
11-09-2009 8:20 PM
Reply to: Message 98 by Trae
11-09-2009 6:09 PM


Re: Back to the basics
Under what variables, if ever, would the time dilation effect be significantly great enough in this two planet scenario? Would we have worlds in our own galaxy which would experience time very much faster than we ourselves experience? Do we ever get scenarios along the line of a day is equal to a year or more?
One would be hard put to locate a planet where the time is exactly the same as ones own. Even another Earthly home is not exactly the same. I live at 18 feet above sea level; Zeus lives at 9,577 feet above sea level. I live 42.45N; Zeus at 40N. I live on 325 feet of soggy glacial till over granite basement; Zeus lives on a few thousand feet of carbonates over basaltic basement. Each makes an absolutely miniscule difference, but none-the-less there.
The difference only become significant at the extremes of velocity and mass density. Do you have a reasonably different circumstance from our own that an alien would be living under? A planet orbiting its super-dense sun in a matter of minutes is not a likely home. Nor would a 100,000g planet.
However, in a galaxy far, far away enough your aliens would be travailing away from us fast enough to make any time dilation you care to name.

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

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


Message 101 of 230 (534633)
11-09-2009 11:09 PM
Reply to: Message 100 by Iblis
11-09-2009 9:24 PM


Re: Back to the basics
To begin with would come from in this case.
In our 3D view of the Universe we still see the expansion as motion; hence, the red shift.
But, let's skip that for now. Let's say expansion of space does accelerate them somehow. Fine. If so, it accelerates both planets equally. This would be similar to a twins problem where the guys both get into spaceships, rocket off on identical trips in opposite directions, stop "at the same time" and turn around and zoom back, to meet on earth again; and are very surprised after hearing all this jargon about warp-drive messing up your family chronology, to discover that they are actually still the same age!
Both see the others times a dilated. It's when one of them gets into a ship and accelerates into others reference frame that both agree to who's lagging. The traveler will be the younger and see that it is his world that is slow; only to get back in his ship with his sister world friend to travel back to his home where where he'll find he and his friend were slow and his world was fast, while the friend would see and agree that his world was indeed slow.
So then when you "teleport" there everything will be happening much slower than it would here on earth, and be much more massive. This would probably kill you, imagine a bunch of very slow but massive air molecules sort of perforating you.
To truly be considered tele-ported "onto" the other world one would have to, sort of, change reference frames or you'll be splattered against that other world at 0.7c. That, too, would probably kill you. But if you're in their frame you get their time and mass being normal. No poky, massive O2. This is the bit where cavediver wondered if he'd end up in a westward listing head-stand if he tele-ported to Fremont.

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

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Replies to this message:
 Message 102 by Iblis, posted 11-10-2009 12:20 AM lyx2no has replied

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


Message 104 of 230 (534810)
11-11-2009 6:58 AM
Reply to: Message 102 by Iblis
11-10-2009 12:20 AM


Re: Back to the basics
Or sure, if we compound our magic with even more magic and "change our frame of reference too"
When one buys a plane ticket it is not entirely unreasonable to assume that that plane have landing gear.
Trae's aliens and teleporter are window dressing to his question. cutting to the chase: were it possible to observe two clocks separated by half a universe would they keep the same time? Not bloody likely.

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

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


Message 109 of 230 (534861)
11-11-2009 1:24 PM
Reply to: Message 106 by cavediver
11-11-2009 7:54 AM


Re: Back to the basics
The birdbrain bows to the egghead.

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

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


Message 114 of 230 (534914)
11-11-2009 6:00 PM
Reply to: Message 112 by Trae
11-11-2009 5:07 PM


Re: Back to the basics
Would say galaxies 100,000 light years be sufficiently far apart from each other
You'd want to multiply that by a thousand for it to even start getting interesting, yet alone relativistic. With Hubble's constant being 71 km/sec/Mps, these galaxies are experiencing only 2.2 km/sec of expansion. 20% of Earth's escape velocity.
AbE: ‘yvind Grn is, himself, a twin so may have a special interest in this problem.
Edited by lyx2no, : AbE.

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

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


Message 120 of 230 (535067)
11-12-2009 5:55 PM
Reply to: Message 119 by tis---strange
11-12-2009 5:16 PM


Re: Why it is called the Twin PARADOX
Well, I think it follows from the wrong assumption that you can ignore the acceleration in the problem
One can ignore the acceleration in the problem in the same way one can ignore the acceleration in the problem: I travel from Boston to Denver, a trip of 1770 miles, on a train at 85 miles per hour. How long did it take? It's not a assumption; it's a simplification.

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

This message is a reply to:
 Message 119 by tis---strange, posted 11-12-2009 5:16 PM tis---strange has replied

Replies to this message:
 Message 121 by tis---strange, posted 11-13-2009 2:35 AM lyx2no 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

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 Message 121 by tis---strange, posted 11-13-2009 2:35 AM tis---strange has replied

Replies to this message:
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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

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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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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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