110
R. Barrett and P. P. Delsanto
However, although very large, c is not infinite. 5 The error of 10 kph,
compared with the value of c, amounts to roughly 1 part in 100 million, and
in most circumstances it could be completely disregarded. However, when,
instead of balls, subatomic particles are shot out in nuclear reactions, they
may be moving at speeds comparable with c. In this case the error obtained
by using Galilean transformations would be quite large.
Indeed the consequences of Special Relativity, as the new field springing out
of Einstein’s conjecture was called by Einstein himself, are astonishing and
manifold, resulting in some very bizarre effects, rivalling those we encountered with QM in the last Chapter. They made Einstein an instant (and
sometimes controversial) celebrity, even among the general public. In the next
Sections, we shall discuss briefly some of these effects: notably time dilation,
Lorentz contraction, the puzzle of simultaneity and mass/energy equivalence.
6.6 Time Dilation
In the real world, as distinct from the world of fiction and fairy tales, time
has always flowed inexorably from the past to the present, and at the same
rate for everybody, no matter where they are or what is their state of motion.
Or so it was believed, Giang Huong and Tu Thuc notwithstanding. However,
the Special Theory of Relativity put an end to this complacency.
Let us remove Mary from the comfort of her railway carriage, train her
as an astronaut, and place her on a high-velocity rocket ship, which can
attain speeds comparable to (but never equalling or exceeding) that of light.
When Peter looks into the spaceship moving away from him, he notices an
amazing thing: everything and everyone on board appears to be in a state of
slow motion. Even the cabin clock has slowed down. Comparing it with his
own earthbound timepiece, Peter observes the second hand of Mary’s clock
completing only one revolution of the dial in the time it takes his own clock
to complete two. Time is actually moving more slowly in Mary’s frame of
reference than in his own. She is indeed in a sort of Land of Bliss. This effect,
which is known as Relativistic Time Dilation, is a direct consequence of the
Lorentz transformations. However, even without using these transformations,
the effect is easily deduced from Einstein’s assumption that the speed of light
is the same for all observers in inertial frameworks.
Imagine Peter is peering into Mary’s spaceship, which is at rest on its
launch pad. He observes a ray of light passing between two points in the ship
5 To be precise its value is 299,792,458 m per second. This value is exact, as since 1983, the metre
has been defined as the distance travelled by light in a vacuum in 1/299,792,458 s.
R. Barrett and P. P. Delsanto
However, although very large, c is not infinite. 5 The error of 10 kph,
compared with the value of c, amounts to roughly 1 part in 100 million, and
in most circumstances it could be completely disregarded. However, when,
instead of balls, subatomic particles are shot out in nuclear reactions, they
may be moving at speeds comparable with c. In this case the error obtained
by using Galilean transformations would be quite large.
Indeed the consequences of Special Relativity, as the new field springing out
of Einstein’s conjecture was called by Einstein himself, are astonishing and
manifold, resulting in some very bizarre effects, rivalling those we encountered with QM in the last Chapter. They made Einstein an instant (and
sometimes controversial) celebrity, even among the general public. In the next
Sections, we shall discuss briefly some of these effects: notably time dilation,
Lorentz contraction, the puzzle of simultaneity and mass/energy equivalence.
6.6 Time Dilation
In the real world, as distinct from the world of fiction and fairy tales, time
has always flowed inexorably from the past to the present, and at the same
rate for everybody, no matter where they are or what is their state of motion.
Or so it was believed, Giang Huong and Tu Thuc notwithstanding. However,
the Special Theory of Relativity put an end to this complacency.
Let us remove Mary from the comfort of her railway carriage, train her
as an astronaut, and place her on a high-velocity rocket ship, which can
attain speeds comparable to (but never equalling or exceeding) that of light.
When Peter looks into the spaceship moving away from him, he notices an
amazing thing: everything and everyone on board appears to be in a state of
slow motion. Even the cabin clock has slowed down. Comparing it with his
own earthbound timepiece, Peter observes the second hand of Mary’s clock
completing only one revolution of the dial in the time it takes his own clock
to complete two. Time is actually moving more slowly in Mary’s frame of
reference than in his own. She is indeed in a sort of Land of Bliss. This effect,
which is known as Relativistic Time Dilation, is a direct consequence of the
Lorentz transformations. However, even without using these transformations,
the effect is easily deduced from Einstein’s assumption that the speed of light
is the same for all observers in inertial frameworks.
Imagine Peter is peering into Mary’s spaceship, which is at rest on its
launch pad. He observes a ray of light passing between two points in the ship
5 To be precise its value is 299,792,458 m per second. This value is exact, as since 1983, the metre
has been defined as the distance travelled by light in a vacuum in 1/299,792,458 s.