Bondi k-calculus
Encyclopedia
Bondi k-calculus is a method of teaching special relativity
originated by Professor Sir Hermann Bondi
, and now common in university and college level physics classes.
The usefulness of the k-calculus is its simplicity. It has been successfully used to teach special relativity to young children and also in relativity textbooks.
Many introductions to relativity begin with the concept of velocity and a derivation of the Lorentz transformation
. Other concepts such as time dilation
, length contraction
, the relativity of simultaneity
, the resolution of the twins "paradox"
and the relativistic Doppler effect
are then derived from the Lorentz transformation, all as functions of velocity.
Bondi, in his book Relativity and Common Sense, first published in 1962, reverses the order of presentation. He begins with the Doppler factor, denoted by the letter
. From this he explains the twins paradox, and the relativity of simultaneity, time dilation, and length contraction, all in terms of 
. It is not until later in the exposition that he provides a link between velocity and the Doppler factor 
. The Lorentz transformation appears towards the end of the book.
Special relativity
Special relativity is the physical theory of measurement in an inertial frame of reference proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".It generalizes Galileo's...
originated by Professor Sir Hermann Bondi
Hermann Bondi
Sir Hermann Bondi, KCB, FRS was an Anglo-Austrian mathematician and cosmologist. He is best known for developing the steady-state theory of the universe with Fred Hoyle and Thomas Gold as an alternative to the Big Bang theory, but his most lasting legacy will probably be his important...
, and now common in university and college level physics classes.
The usefulness of the k-calculus is its simplicity. It has been successfully used to teach special relativity to young children and also in relativity textbooks.
Many introductions to relativity begin with the concept of velocity and a derivation of the Lorentz transformation
Lorentz transformation
In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frames of reference. It is named after the Dutch physicist Hendrik...
. Other concepts such as time dilation
Time dilation
In the theory of relativity, time dilation is an observed difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses. An accurate clock at rest with respect to one observer may be measured to tick at...
, length contraction
Length contraction
In physics, length contraction – according to Hendrik Lorentz – is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non-zero velocity relative to that observer...
, the relativity of simultaneity
Relativity of simultaneity
In physics, the relativity of simultaneity is the concept that simultaneity–whether two events occur at the same time–is not absolute, but depends on the observer's reference frame. According to the special theory of relativity, it is impossible to say in an absolute sense whether two events occur...
, the resolution of the twins "paradox"
Twin paradox
In physics, the twin paradox is a thought experiment in special relativity, in which a twin makes a journey into space in a high-speed rocket and returns home to find he has aged less than his identical twin who stayed on Earth...
and the relativistic Doppler effect
Relativistic Doppler effect
The relativistic Doppler effect is the change in frequency of light, caused by the relative motion of the source and the observer , when taking into account effects described by the special theory of relativity.The relativistic Doppler effect is different from the non-relativistic Doppler effect...
are then derived from the Lorentz transformation, all as functions of velocity.
Bondi, in his book Relativity and Common Sense, first published in 1962, reverses the order of presentation. He begins with the Doppler factor, denoted by the letter
. From this he explains the twins paradox, and the relativity of simultaneity, time dilation, and length contraction, all in terms of . It is not until later in the exposition that he provides a link between velocity and the Doppler factor . The Lorentz transformation appears towards the end of the book.