From: Ronald Wong (ronwong@inreach.com)
Date: Thu Mar 27 2003 - 00:34:17 PST
Message-Id: <l03102800baa83e11b5cb@[209.209.18.102]> Date: Thu, 27 Mar 2003 00:34:17 -0800 From: Ronald Wong <ronwong@inreach.com> Subject: RE Relativity Question
Eric recently said:
>What I always try to tell my kids is that with regards
>to time dilation (at least in terms of special
>relativity) you can't trust the opinion of anyone who
>accelerates.
>...
>...that the only way the travelers will agree upon
>the time when they return to Earth is if they take a
>side-by-side trip and undergo the same accelerations.
>...
It would seem, from the recent posts regarding time dilation, that we are
dealing with an esoteric physics concept that only a physicist could love.
The mathematics may be daunting but actually, in one sense, it really isn't
as complicated as it seems - and it need not be an esoteric physics concept
that one brings up in their classroom only when time allows.
Take a clock and place it at some point on the equator. Relative to a clock
sitting in the middle of the earth it is moving with a speed of around 1000
mi/hr. Special relativity says that it's clock will run slower than the
clock at the center of the earth - which here represents an inertial frame
of reference. We can compute what the difference in time will be between
these two clocks for any given time interval.
Let's have an airplane fly eastward (the direction of the earth's rotation)
along the equator at a speed of 500 mi/hr. Because of this motion, it is
traveling even faster around our inertial clock than the one fixed to the
equator. So not only will it's time be slower than the one at the center of
the earth but it will be slower than the clock sitting on the equator. We
can compute the difference between the times for this situation as well.
Let's have a second airplane fly westward at 500 mi/hr along the equator.
It's still going to be moving eastward about our clock at the center of the
earth so it will still run slower than the one at the center of the earth.
BUT it will not be running as slow as the one fixed to the equator because
this airplane is going about the center of the earth at a rate slower than
the clock sitting at the equator. So, relative to the one at the equator,
the clock on this plane will actually be ticking away at a faster rate!
And we can compute the difference between the times for this situation as
well.
In all three cases, the frame of reference of the clocks are accelerating.
In fact the accelerations are all different.
Talk about complications!
Despite that, not only can we can compute the various differences in time
for all these clocks - trust me - but we can compare them as well.
Comparing the clocks is a no-brainer. After all, if you fly around the
equator long enough, you end up right back where you started. We don't have
to travel away from the earth and somehow get back (or pursue any other
complicated scenario that one might come up with) in order to observe the
twin paradox.
It may come as a surprise to some of you, but in the early 70's (1971?) a
couple of physicists placed a couple of clocks on a couple of jet airliners
and sent them on their way with one traveling east and the other traveling
west.
The situation was a little more complicated than the one I've described above.
Airplanes can't fly at the same elevation as a clock sitting on the surface
of the earth. They can crash at the same elevation as the clock but they
can't fly.
Unfortunately, the difference in elevation introduces the need to consider
a difference in spacetime (here comes General Relativity). The higher up
you go, the less the distortion of spacetime due to the earth's mass and
the greater the rate of change for the clock when compared to a clock
sitting at the surface (i.e. clocks run faster at higher elevations). As
with the other examples, we can compute this also (using the equations of
G.R. - as Eric would say).
Interestingly enough, the increase in rate for the clocks due to elevation
is greater than the decrease in rate for the clocks due to their motion (by
a factor of about 2 depending on the elevation). So, whether the airliners
went east or west, their clocks net rate was one in which they ran faster
than the clock sitting on the earth - and we can compute all of this.
The differences over 24 hours only amounts to a couple of hundred
nanoseconds - at most - so the clocks on the airliners weren't
run-of-the-mill Timex's. They were the latest rage - atomic clocks.
By taking into account the time differential due to the airliners'
elevation and then factoring in the time differentials due to their
motions, the physicists were able to predict what the time differences
would be for any given time interval. When they compared the clocks on the
two airliners with the clock sitting on the ground (after they had been
flying for a long period of time), there was total agreement.
In one neat experiment, they added further evidence for the validity of
both the Special and the General Theory of Relativity.
____________________________________
>Of course if they knew General Relativity they could
>predict the time difference and be satisfied with the
>time difference . . . But who REALLY knows G.R. anyway?
Well, for sure, J.C.Hafele and R.E. Keating.
They used both the Special Theory of Relativity and the General Theory of
Relativity to "predict the time differences" and, NOT being "satisfied with
the time difference", conducted a "simple" experiment in the early 70's
that confirmed their predictions.
It doesn't get any better than that.
____________________________________
Today, both civilians and members of the military use the Global
Positioning System (GPS) to determine their location on the surface of the
earth. The system utilizes a large number of orbiting satellites to achieve
this purpose. The accuracy with which individuals can determine their
position is dependent on the accuracy of the clocks found in these
satellites. By means of coded signals sent to these satellites, the clocks
are regularly adjusted to take into account both their motion and their
elevation.
The "twin paradox" is not an esoteric topic in physics. It's something that
is being addressed every day of the year for all kinds of reasons.
Cheers.
ron
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