Posted: Thu Apr 15, 2004 11:38 pm Post subject: Time Dilation in Special Relativity
I've heard that an experiment has taken place in which two atomic clocks, one was carried in a super fast jet and the other was stationary on the ground. Although they both had been precisely synchronized before the trip but after the trip, the one which was in the plane had ticked a little slower therefore the time it showed was a little less than the time the atomic clock on the ground showed.
But my question is why this happens, as the atomic clock on the ground has its right to consider the plane as a stationary object consider the earth and itself as moving fast away from the plane. So the result would be vice versa.
Posted: Fri Apr 16, 2004 4:39 am Post subject: non-symmetry
Einstein's theory of relativity was thought of as paradoxical in the days before this effect could be observed and precisely measured experimentally. Your way of thinking about the symmetry in the problem is called the twin paradox. Your way of thinking is wrong.
The mathematics that models this particular situation isn't trivial. Both clocks are accelerating in different ways along two radically different trajectories. The symmetry you imagine doesn't exist.
If you want to simplify the problem a bit conceptually, it's easier to think of one clock as being absolutely stationary (not accelerating) and the second clock moving away and then needing to accelerate to change its direction to return to the first clock for a comparison check. The clock that undergoes the least acceleration will measure the greatest elapsed time. The measured times will be different on the two clocks at the end of the experiment.
Why do clocks behave in this way? Because it's the nature of Minkowski spacetime to always yield that outcome for that experiment. Minkowski spacetime is defined by the Lorentz transformation. The mathematics of the Lorentz transformation only measures the effect and gives consistent answers. It offers no explanation why. It's just the nature of space and time and mathematics that produces consistent results.
Joined: 15 Mar 2005 Posts: 8 Location: Baton Rouge, LA
Posted: Tue Mar 15, 2005 1:29 pm Post subject: Re: Time Dilation in Special Relativity
Popen wrote:
I've heard that an experiment has taken place in which two atomic clocks, one was carried in a super fast jet and the other was stationary on the ground. Although they both had been precisely synchronized before the trip but after the trip, the one which was in the plane had ticked a little slower therefore the time it showed was a little less than the time the atomic clock on the ground showed.
You're thinkg of the Hafele-Keating experiement of 1971. This experiment actually tested special and general relativity. Time for both planes speeds up relative to the ground clock due to experiencing slightly less gravity than the ground clock. This effect is actually the larger of the two effects. But there is also a contribution to the time difference from the motion of the planes - the westbound plane will have its clock slow down and the eastward will have its clock speed up.
But my question is why this happens, as the atomic clock on the ground has its right to consider the plane as a stationary object consider the earth and itself as moving fast away from the plane. So the result would be vice versa.
The difference in the two observing frames is that the plane had to undergo an acceleration in order to achieve its higher velocity and a deceleration to come back down to earth. If you and I are at constant, different velocities, its equally valid to say I'm at rest and you're in motion as it is to say you're at rest and I'm in motion. But if I am accelerating away from you, I will experience a force ("G-forces"), and you will not, so it would not be valid to say you are accelerating and I am not.
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