6 Special Relativity
117
motion, its total mass is greater than its rest mass because of the contribution
from the conversion of kinetic energy into mass, as we have discussed in the
previous paragraph. Photons, having no rest mass, must spend their entire
existence zipping hither and thither at speed c. They can never slow down.
This upper limit on the speed at which material objects, e.g. astronauts, can
travel has long been the bane of science fiction writers, as it puts restrictions
on how far one can travel in a human lifetime. Given that the closest stars,
located in the Alpha Centauri system, require 4.3 years of travel at speed c to
reach them, it is clear that by far the vast majority of the cosmos is beyond the
reach of humankind. The invention of Hyperspace, a region outside the realm
of Relativity, has become an accepted method in the domain of science fiction
to overcome the limits imposed by Einstein’s theory. In the real world, we can
only sit and peer through our telescopes in frustration or find something else
nearer to home to sate our curiosity.
Let us now put our wistfulness aside and return to the application of
Einstein’s formula to more earthly pursuits. Its importance and huge impact
on the history of the twentieth century is due to the magnitude of the coefficient c 2 in our lonely equation. To give a simple example, if one kilogram of
matter collides with one kilogram of antimatter (we will discuss antimatter
in Chaps. 8 and 9), they annihilate each other: the two masses disappear and
as much as fifty billion kilowatt-hours (kwh) of energy are produced.
To put this number into perspective, we recall that in the oil industry, the
unit toe (tonne of oil equivalent) is defined as the amount of energy released
by burning one tonne of crude oil, and is approximately equal to 11,600 kwh.
Hence the annihilation of 1 kg of matter and 1 kg of antimatter would yield
the same energy as burning 4.3 million tonnes of crude: i.e. almost enough
to provide for the entire energy needs of the United States for one day (about
6 million toes).
In reality, however, kilograms of antimatter are difficult to find, and the
practical transformation of mass into energy relies on one of the two processes
of nuclear fission and nuclear fusion. The result is either nuclear energy,
released under controlled conditions and deployable for practical purposes,
or a violent burst of a huge quantity of destructive energy. The latter is
the atomic bomb, if nuclear fission is employed, or the H-bomb, with the
potential for an even more devastating effect, if nuclear fusion is adopted.
Given the consequences, should we blame Einstein (or science) for having
incautiously opened such a Pandora’s Box ? Or rather humans, for their stockpiling of a terrifying arsenal of weapons of mass destruction? This question
has been debated for the past seventy years, and we shall not discuss it further
here.
117
motion, its total mass is greater than its rest mass because of the contribution
from the conversion of kinetic energy into mass, as we have discussed in the
previous paragraph. Photons, having no rest mass, must spend their entire
existence zipping hither and thither at speed c. They can never slow down.
This upper limit on the speed at which material objects, e.g. astronauts, can
travel has long been the bane of science fiction writers, as it puts restrictions
on how far one can travel in a human lifetime. Given that the closest stars,
located in the Alpha Centauri system, require 4.3 years of travel at speed c to
reach them, it is clear that by far the vast majority of the cosmos is beyond the
reach of humankind. The invention of Hyperspace, a region outside the realm
of Relativity, has become an accepted method in the domain of science fiction
to overcome the limits imposed by Einstein’s theory. In the real world, we can
only sit and peer through our telescopes in frustration or find something else
nearer to home to sate our curiosity.
Let us now put our wistfulness aside and return to the application of
Einstein’s formula to more earthly pursuits. Its importance and huge impact
on the history of the twentieth century is due to the magnitude of the coefficient c 2 in our lonely equation. To give a simple example, if one kilogram of
matter collides with one kilogram of antimatter (we will discuss antimatter
in Chaps. 8 and 9), they annihilate each other: the two masses disappear and
as much as fifty billion kilowatt-hours (kwh) of energy are produced.
To put this number into perspective, we recall that in the oil industry, the
unit toe (tonne of oil equivalent) is defined as the amount of energy released
by burning one tonne of crude oil, and is approximately equal to 11,600 kwh.
Hence the annihilation of 1 kg of matter and 1 kg of antimatter would yield
the same energy as burning 4.3 million tonnes of crude: i.e. almost enough
to provide for the entire energy needs of the United States for one day (about
6 million toes).
In reality, however, kilograms of antimatter are difficult to find, and the
practical transformation of mass into energy relies on one of the two processes
of nuclear fission and nuclear fusion. The result is either nuclear energy,
released under controlled conditions and deployable for practical purposes,
or a violent burst of a huge quantity of destructive energy. The latter is
the atomic bomb, if nuclear fission is employed, or the H-bomb, with the
potential for an even more devastating effect, if nuclear fusion is adopted.
Given the consequences, should we blame Einstein (or science) for having
incautiously opened such a Pandora’s Box ? Or rather humans, for their stockpiling of a terrifying arsenal of weapons of mass destruction? This question
has been debated for the past seventy years, and we shall not discuss it further
here.