112
R. Barrett and P. P. Delsanto
case, they can never get back together to compare their clocks or lament their
wrinkles. The only way this can happen is if Mary turns the spaceship around
and brings it back home. In doing so, she undergoes an acceleration, positive
and/or negative, and thereby violates the conditions of Special Relativity. The
paradox is therefore resolved. However, time dilation will still occur, and as a
consequence of the acceleration she has experienced, Mary will age less than
Peter.
Time dilation is extremely small, except for velocities v close to c. The
energy required to accelerate a rocket ship increases rapidly as its speed
approaches that of light, for reasons that will become apparent later in this
Chapter. The highest speed attained by a rocket was achieved in 2006, when
an Atlas V Rocket, carrying the New Horizons probe to Pluto, was launched
from Cape Canaveral in Florida, USA. Its maximum speed, relative to the
launch pad was 58,536 kph (about 16.3 kms per second), which yields a
v/c ratio of 0.0000542. Accordingly, its relativistic time dilation effect was of
the order of one in a billion, which is very small, but significant over a long
journey.
The first direct test of time dilation for normal objects and velocities was
carried out by Hafele and Keating [4] in 1971. They flew four caesium atombeam clocks around the world in commercial jet airliners, both eastwards and
westwards, and compared the clocks afterwards with reference clocks that had
remained behind in the U.S. Naval Observatory. The clocks lost 59 ± 10 ns
during the eastward flight and gained 273 ± 7 ns during the westward flight,
compared with the land-based clocks. The difference between the eastward
and westward results is explained by taking into account the rotation of the
earth. These figures agree well with the predictions of Einstein’s theory of
Relativity.
It should be noted that the altitude of the airliner varied throughout the
flight, but was generally around 9000 m. At this altitude, the gravitational
force experienced by the clocks in the aircraft was less than that experienced
by the ground-based clock. As we shall see in the next Chapter, gravitational
fields produce another form of time dilation, which must be included in the
analysis of the results of the Hafele-Keating experiment.
A routine application of Einstein’s theories may be found in a device that
most of us use regularly. Because of the difference in altitude and speed
between GPS satellite transmitters and the receivers in the navigators of our
vehicles and mobile phones, corrections for time dilation—due to the relative motion of the satellites and our phones, and to the different gravitational
fields that they experience—must be included in the software that is used to
calculate GPS positions.
R. Barrett and P. P. Delsanto
case, they can never get back together to compare their clocks or lament their
wrinkles. The only way this can happen is if Mary turns the spaceship around
and brings it back home. In doing so, she undergoes an acceleration, positive
and/or negative, and thereby violates the conditions of Special Relativity. The
paradox is therefore resolved. However, time dilation will still occur, and as a
consequence of the acceleration she has experienced, Mary will age less than
Peter.
Time dilation is extremely small, except for velocities v close to c. The
energy required to accelerate a rocket ship increases rapidly as its speed
approaches that of light, for reasons that will become apparent later in this
Chapter. The highest speed attained by a rocket was achieved in 2006, when
an Atlas V Rocket, carrying the New Horizons probe to Pluto, was launched
from Cape Canaveral in Florida, USA. Its maximum speed, relative to the
launch pad was 58,536 kph (about 16.3 kms per second), which yields a
v/c ratio of 0.0000542. Accordingly, its relativistic time dilation effect was of
the order of one in a billion, which is very small, but significant over a long
journey.
The first direct test of time dilation for normal objects and velocities was
carried out by Hafele and Keating [4] in 1971. They flew four caesium atombeam clocks around the world in commercial jet airliners, both eastwards and
westwards, and compared the clocks afterwards with reference clocks that had
remained behind in the U.S. Naval Observatory. The clocks lost 59 ± 10 ns
during the eastward flight and gained 273 ± 7 ns during the westward flight,
compared with the land-based clocks. The difference between the eastward
and westward results is explained by taking into account the rotation of the
earth. These figures agree well with the predictions of Einstein’s theory of
Relativity.
It should be noted that the altitude of the airliner varied throughout the
flight, but was generally around 9000 m. At this altitude, the gravitational
force experienced by the clocks in the aircraft was less than that experienced
by the ground-based clock. As we shall see in the next Chapter, gravitational
fields produce another form of time dilation, which must be included in the
analysis of the results of the Hafele-Keating experiment.
A routine application of Einstein’s theories may be found in a device that
most of us use regularly. Because of the difference in altitude and speed
between GPS satellite transmitters and the receivers in the navigators of our
vehicles and mobile phones, corrections for time dilation—due to the relative motion of the satellites and our phones, and to the different gravitational
fields that they experience—must be included in the software that is used to
calculate GPS positions.