| From: James Richmond (Avatar) | 11/03/99
15:59:20 |
| Subject: Twin paradox explained | post id:
3546 |
| A lot people seem to be confused
about the twin paradox. When does time dilation occur? What causes it -
relative motion, acceleration, gravity or a combination of these? Here's
my attempt to clear up some of the confusion. The scenario Observers A and B are twins, on Earth. A stays at home, while B jumps into a spaceship and heads off into space. After travelling at constant speed for a while, B slows down, turns around, and comes back to Earth, again at constant speed for most of the trip. Arriving at Earth, B slows down, lands and greets sibling A. The result When B arrives back on Earth, s/he has aged less than A. The explanation. Part 1: Constant velocity parts of B's motion While B is travelling away from OR towards Earth at CONSTANT VELOCITY: A notices nothing unusual about the rate at which his/her time seems to pass. But when s/he looks at B though a telescope, B's clocks seem to be running slowly, and B seems to be aging more slowly than A. This is time dilation, explained by special relativity. B notices nothing unusual about the rate at which his/her time seems to pass. But when s/he looks at A through a telescope, A's clocks seem to be running slowly, and A seems to be aging more slowly than B. This is also time dilation. Now, the reason the two observers see the same thing is that there is NO PREFERRED FRAME OF REFERENCE. In other words, we can't say which of A and B is "really" moving. The "paradox" arises because both A and B see the other as aging more slowly while they are travelling. Obviously they can't both be the oldest when they meet up again, so what's going on? The explanation. Part 2: Accelerated parts of B's motion A and B don't have the same experiences of the trip. As B speeds up and slows down the spaceship, s/he experiences the affects of acceleration (i.e. being pushed towards the rear or front of the ship). A DOESN'T experience the acceleration. So although we can't say whether A or B is "really" moving, we CAN say that B is accelerating and A isn't. During the accelerated parts of the trip, A and BOTH see A's clocks as running faster than B's clocks. The net effect of this, together with the constant velocity parts of the trip, is that A ends up being older than B when they meet again. The effects of gravity Gravity may not seem especially relevant in the above discussion. However, in many ways acceleration is very similar to gravity. For example, it would be difficult to tell the difference between accelerating at 1 g in a rocket in deep space and standing in the rocket while it is stationary on Earth. In a strong gravitational field, general relativity tells us that clocks run slower than in a weak gravitational field. When B turns around, s/he feels acceleration effects which are similar to being in a strong gravitational field, so B's clocks run slower than A's during the turn around phase of the trip. Actual experiment: Atomic clocks An experiment which has ACTUALLY BEEN DONE is to start off with two identical, synchronised atomic clocks, keep one on the ground and fly the other one around in a plane for a while. When the plane lands, the clock that was in the plane is found to have run a little slower than the one on the ground. The precise amount by which this is the case agrees with the combined predictions of special relativity (due to the speed of the plane relative to the ground) and general relativity (due to the fact that clock in the plane in the air is in a weaker gravitational field than the clock on the ground). JR | |
| From: Chris (Avatar) | 12/03/99
8:50:01 |
| Subject: re: Twin paradox explained | post id:
3622 |
Spanners in the works: James... what if the travelling twin doesn't accelerate to return to earth? Suppose we had her/him execute a smooth free-fall slingshot around a massive object. Now which twin is oldest upon return, and more importantly, why?. ;o) Challenge? | |
| From: James Richmond (Avatar) | 12/03/99
10:25:38 |
| Subject: re: Twin paradox explained | post id:
3635 |
| Chris, in order to compare the
twins' ages correctly, they must at some stage be in the same inertial
frame. If one is then going to travel relative to the other, there must be
a period of relative acceleration. As for your slingshot around a massive object, there would, of course, be gravitational time dilation effects. In addition, from my GR lectures I vaguely recall certain problems with synchronising clocks around a spherical mass such as a planet. What are your ideas on this? JR | |
| From: Chris (Avatar) | 12/03/99
10:45:13 |
| Subject: re: Twin paradox explained | post id:
3642 |
Just trying to demonstrate that using acceleration as the distinguishing factor in the two journeys can be limiting. Suppose the clocks are synchronised as the stellar twin passes by the stationary twin (this time on a satellite in geosynchronous orbit, by the window) already travelling at 0.99c (gamma = just over 7). The pass-by is within a metre. The trip is over a year in the subjective frame of the traveller. Instead of accelerating to turn around the stellar twin either free falls around a massive object or exploits a region of curved or cylindrical topology to return, bypassing the satellite bound twin and synchronising. One should have aged by 7 years more than the other. But which? Neither twin accelerated during the journey, and the gravitational effect of the remote star puts the stellar twin at the bottom of the grav well... if anything making her age faster! How do we explain that the twin who stayed at home aged faster?? | |
| From: Dr. Ed G (Avatar) | 12/03/99
10:59:58 |
| Subject: re: Twin paradox explained | post id:
3643 |
| ... the
gravitational effect of the remote star puts the stellar twin at the
bottom of the grav well... if anything making her age faster!
... I thought one aged slower at the bottom of a gravitational well. Soupie twist, Ed G.  | |
| From: Halogen Fisk | 12/03/99
12:10:29 |
| Subject: re: Twin paradox explained | post id:
3651 |
| Hi, me again, Chris said "Suppose the clocks are synchronised as the stellar twin passes by the stationary twin" I thought the whole point was there is NO stationary. All our local stars, planets & people may well be moving at 0.5C (relative to any cosmic stationary). If our travelling twin goes off in the direction we came he would reduce his speed relative to C. If there is such thing as 'Stationary', the travelling twin would age more!! p.s. I'm booking my tickets to Salt Lake City | |
| From: Dr. Ed G (Avatar) | 12/03/99
12:18:50 |
| Subject: re: Twin paradox explained | post id:
3655 |
| p.s. I'm booking
my tickets to Salt Lake City. You'd better learn the proper spelling of "Mormon", then :-) Soupie twist, Ed G. | |
| From: Chris (Avatar) | 12/03/99
14:18:27 |
| Subject: re: Twin paradox explained | post id:
3672 |
I thought one aged slower at the bottom of a gravitational well... Ooops! Yes, you're exactly right Eds! (Thanks for the pick-up :o) Will the jury please disregard the relevant remark in my last post... Thanks :o) Chris | |
| From: Terry Frankcombe | 12/03/99
14:50:11 |
| Subject: re: Twin paradox explained | post id:
3684 |
| Chris, doesn't the stellar twin
have to accelerate to get away from the satellite-bound
twin? | |
| From: Chris (Avatar) | 12/03/99
15:02:47 |
| Subject: re: Twin paradox explained | post id:
3688 |
The idea is that it is possible to construct a scenario without an acceleration component. To be obtuse, I could remove the people and have simple atomic clocks do the travel, instantaneous turnaround via a signal, travel across a curved reinmann manifold - whatever it takes to eliminate the acceleration answer. But the dilation still occurs. There is a far more surefire way of telling why the travelling twin ages. Draw a simple 2-D space-time diagram (a "Minkowski 2-space"). If you map both journeys you will see that one diverges markedly. Since the proper time interval (denoted delta-Tau squared) is a combination of space and time, it becomes obvious which has aged. In addition this way you can see the relative simultaneity points, etc. I'll see if I can draw some, and stick them up somewhere for you to see... Chris | |
| From: Yoda Oz | 15/03/99
8:56:07 |
| Subject: re: Twin paradox explained | post id:
3841 |
| What if the earth stopped moving
around the sun or even stopped rotating so it is dead stationary? Would
that mean that everything on earth would stop
aging? | |