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normdowling
2008-Mar-27, 05:16 AM
I cant understant why the twins ages should end up different?

Dont they see each other as moving away from each other?

From twin A frame of reference, twin B is moving away with a slower clock.

From Twin B frame of reference, Twin A is moving away with a slower clock as well.

Im sure the answer has to to do with the issue of simultanity . However ,

can someone give me a good conceptual understanding as to why????

Jens
2008-Mar-27, 06:35 AM
The problem has to do with which one is accelerating, in other words, which one is using energy to move away from the other. The one that is accelerating is the one for whom time goes slowly in relative terms.

AstroSmurf
2008-Mar-27, 08:06 AM
Alternatively, if you want to side-step the acceleration problem, you could say that one twin "switches" his reference frame from one moving away from the other twin to one that moves back towards him. That switch causes the assymmetry.

normdowling
2008-Mar-27, 09:49 AM
it still feels like both have switched from each others reference frames.??????

when the moving twin slows down he sees the stay at home twin slow down and change direction.

once the moving twin stops accelerating and is is uniform motion, Why doesnt he

see the other twin moving away??????????and with a slower clock????????????

sorry if im repeating myself..

normdowling
2008-Mar-27, 10:37 AM
revised question-

why should it matter which twin is moving away?????????????

How can the twin in the space ship, in uniform motion, know that he is moving and

not his brother back on earth.???????

grant hutchison
2008-Mar-27, 11:42 AM
So long as the moving twins are in uniform motion, they can't say which is moving and which isn't. And each measures the other's clock running slowly: and that happens whether they're approaching or receding.
Trouble is, so long as they're in continuous uniform motion, they can't ever compare their clocks more than once when they're in the same place: they can synchronize them as they pass, but can't come back together to compare elapsed time later. The "same place" thing is important, because under special relativity they disagree about the simultaneity of widely separated events. While they're moving apart, for instance, each sees himself as being simultaneous with events in the other twin's worldline that the other twin sees as being in his past.
So, they need to get back together to compare clocks in the same place. One of them needs to accelerate, to turn round and catch up with the other. The one who accelerates experiences forces during acceleration; the one who doesn't, doesn't. So the symmetry is broken, right there, as one twin turns around to return.
The acceleration moves the "travelling twin" from one state of uniform motion (receding from the other twin) to another state of uniform motion (returning towards the other twin). This change in motion flips the traveller's measurements of simultaneity: in a short period of his own time (during acceleration), his simultaneity scans futureward along a big chunk of the home twin's worldline. The unaccelerated home twin experiences no such change, and just carries on measuring the traveller's clocks as running slow.

So it's the distant turnaround, and the shift in simultaneity under acceleration, which breaks the symmetry and resolves the paradox.

Grant Hutchison

dcl
2008-Mar-27, 05:47 PM
Suppose that both twins A and B are initially at rest on earth.

Twin A takes off in his trusty space ship, bound for the Andromeda galaxy, 2.7 million light years away. That is, it takes light 2.7 million years to travel that distance. Twin A really puts the pedal to the metal and is soon zipping along at just slightly less than the speed of light. Twin B, back on earth, soon also sees twin A zipping along at very close to the speed of light.

Back on earth slightly more than 2.7 million years later, twin B's descendants watch through their telescopes as twin A arrives at the Andromeda galaxy. To Twin B, twin A traveled 2.7 million miles, just slightly longer than it took light to travel that distance.

Twin A, moving at nearly the speed of light relative to everything around him, witnessed a hugr Lorentz contraction of the entire univserse along his line of travel during his outbound trip. His speed was such that the contraction reduced the distance between earth and the Andromeda galaxy to less than a minute more than two light weeks. He arrives at the Andromeda galaxy in slightly more than two weeks.

His rocket ship screeches to a halt during the next minute or so. He looks back at a calendar on earth through his telescope and sees that slightly more than 2.7 million years have passed. The Lorentz contraction that he observed throughout his outbound trip disappeared as he came to a stop, so the universe appears normal to him now.

He immediately heads for home, within the first few minutes again achieving a speed close enough to that of light, so that he sees the distance to earth again shrink to two light weeks. Two weeks later, he's back on earth and finds that approximately 5.4 million years have passed on earth while he was away. He probably has difficulty in finding a nearby Starbucks.

The space and time dilations described in the above narrative are calculable from the equatons of special relativity. These effects embody what has come to be known as the Twin Paradox.

clint
2008-Mar-27, 08:11 PM
Now suppose the descendants of twin B colonize the entire Milky Way in a million years,
and then find a way to build a wormhole to Andromeda.

They take another million years to colonize Andromeda,
and when twin A arrives, he will be welcomed by great-great-great-...-great-grand-nephews and -nieces,
who have long ago joined an intergalactic Milky-Andromeda Federation.

Weird stuff

Jens
2008-Mar-28, 03:02 AM
why should it matter which twin is moving away?????????????


Again, it doesn't matter which one is moving away. In fact, you can't know that.

What matters is which one accelerates. If we are standing together, and I fire rockets, then I am the one whose clock will seem to go slower.

Jerry
2008-Apr-07, 04:33 AM
He probably has difficulty in finding a nearby Starbucks.

If current trends continue, there should be one Starbucks every seven anstrom by then.

You can construct the Twin Paradox so that both twins experience identical forces of acceleration for the entire episode; nominally the earth bound twin experiencing 1 g on earth, and the 'traveling twin' accerating in a much wider arc and always accelerating at 1g, too. When the 'travelin twin' zips past the earth at ~98% of the speed of light but still only accelerating at one g, which twin is aging fastest?

grant hutchison
2008-Apr-07, 11:15 AM
You can construct the Twin Paradox so that both twins experience identical forces of acceleration for the entire episode; nominally the earth bound twin experiencing 1 g on earth, and the 'traveling twin' accerating in a much wider arc and always accelerating at 1g, too. When the 'travelin twin' zips past the earth at ~98% of the speed of light but still only accelerating at one g, which twin is aging fastest?The Earth twin.
If you're going to fret about the effects of gravity, you need to invoke General Relativity. Although the two twins are experiencing the same force, the metric they're embedded in is different. The twin on Earth is sitting at the bottom of a dimple in spacetime, which levels off to an approximation of "flat space" nearby. So the Earth twin's clock runs slow only by the relatively slight difference in potential between the Earth's surface and flat space. The accelerating twin sees the whole Universe accelerating in the opposite direction at a uniform rate, and so under GR is at the bottom of a very long and uniform potential gradient. As the traveller accelerates back towards Earth, she therefore sees Earth as being much "higher" than she is, and therefore its clocks run much faster than hers.

Grant Hutchison

Kaptain K
2008-Apr-07, 11:40 AM
You can construct the Twin Paradox so that both twins experience identical forces of acceleration for the entire episode; nominally the earth bound twin experiencing 1 g on earth, and the 'traveling twin' accerating in a much wider arc and always accelerating at 1g, too. When the 'travelin twin' zips past the earth at ~98% of the speed of light but still only accelerating at one g, which twin is aging fastest?

You have made the common mistake of equating scalars and vectors! While it is true that both experience 1g of acceleration (scalar), the direction of the acceleration of the traveling twin is constantly changing (vector). The two (vector) accelerations are not equal!

grant hutchison
2008-Apr-07, 11:52 AM
You have made the common mistake of equating scalars and vectors! While it is true that both experience 1g of acceleration (scalar), the direction of the acceleration of the traveling twin is constantly changing (vector). The two (vector) accelerations are not equal!The vector for the stay-at-home twin changes constantly, too, if you consider the rotation of the Earth! :)
You can set it up so that they twins experience equal and opposite accelerations throughout the experiment. The Earth twin hovers above the surface of the Earth as it rotates, maintaining a constant acceleration vector. The traveller shoots by at high velocity, and they synchronize clocks. The traveller immediately begins to accelerate towards the Earth, gradually reversing her velocity vector and eventually returning to compare clock settings with the hovering twin.
With that scenario, you really need to invoke GR to explain why the traveller comes back younger than the Earth twin.

Grant Hutchison

jfribrg
2008-Apr-07, 05:58 PM
Back on earth slightly more than 2.7 million years later, twin B's descendants watch through their telescopes as twin A arrives at the Andromeda galaxy.

Wouldn't it take another 2.7 million years for the light from the twin A's arrival to travel back to Earth?