Chapter 9
Natural Measuring-Rods and Clocks
On the one hand, it is correct that we can choose our units of measure arbitrarily.
A yard as a unit of length and a pile of sand running through an egg timer as a unit
of time are completely sufficient to formulate our physical laws. However, we will
not find this too pleasurable, because randomly chosen units or units specifically
chosen for a certain problem can lead to tedious parameters. The largest problem is
however its constancy and reproducibility. If we wish our observations to become
more detailed and accurate, then our measuring devices also have to become more
precise. It is also most unsatisfactory if we have to invent random units of measure
when concerning ourselves with such fundamental conceptions as space and time.
One thus began to search for natural units of measure, units of measure given to us by
the physical objects for which we made our laws, for example, the earth’s revolution
period of the sun and the circumference of the earth. Modern examples would be the
caesium atomic clock and the wavelength of the yellow sodium line.
Here, we wish to do the same when observing our mechanical objects and their
motions in the crystal (replaced by a continuum). Due to the fact that we are dealing
purely with mechanical processes, we will try to define our standard lengths and
clocks with the help of those mechanical ‘objects’ that can be found inside of our
crystal. Here, the sine-Gordon equation comes to our help. As we know, the solutions of this equation describe certain mechanical states such as one-dimensional
imperfections distinguished by the crystal. It is thus near at hand to take these easily
reproducible and identical lines found inside of our crystal and examine them for simple and characteristic forms suitable to be used as a standard length—a measuring-rod
as it will be called hereafter—and a well-defined unit for an oscillation period.
Here, we once again wish to bring your attention to a characteristic of physical
quantities: The correct description of any physical quantity contains two details, the
unit of measure that gives us a quantity to compare something with and the coefficient
of measure that tells us how often we have to take our measure of comparison in
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_9
81
Natural Measuring-Rods and Clocks
On the one hand, it is correct that we can choose our units of measure arbitrarily.
A yard as a unit of length and a pile of sand running through an egg timer as a unit
of time are completely sufficient to formulate our physical laws. However, we will
not find this too pleasurable, because randomly chosen units or units specifically
chosen for a certain problem can lead to tedious parameters. The largest problem is
however its constancy and reproducibility. If we wish our observations to become
more detailed and accurate, then our measuring devices also have to become more
precise. It is also most unsatisfactory if we have to invent random units of measure
when concerning ourselves with such fundamental conceptions as space and time.
One thus began to search for natural units of measure, units of measure given to us by
the physical objects for which we made our laws, for example, the earth’s revolution
period of the sun and the circumference of the earth. Modern examples would be the
caesium atomic clock and the wavelength of the yellow sodium line.
Here, we wish to do the same when observing our mechanical objects and their
motions in the crystal (replaced by a continuum). Due to the fact that we are dealing
purely with mechanical processes, we will try to define our standard lengths and
clocks with the help of those mechanical ‘objects’ that can be found inside of our
crystal. Here, the sine-Gordon equation comes to our help. As we know, the solutions of this equation describe certain mechanical states such as one-dimensional
imperfections distinguished by the crystal. It is thus near at hand to take these easily
reproducible and identical lines found inside of our crystal and examine them for simple and characteristic forms suitable to be used as a standard length—a measuring-rod
as it will be called hereafter—and a well-defined unit for an oscillation period.
Here, we once again wish to bring your attention to a characteristic of physical
quantities: The correct description of any physical quantity contains two details, the
unit of measure that gives us a quantity to compare something with and the coefficient
of measure that tells us how often we have to take our measure of comparison in
© The Editor(s) (if applicable) and The Author(s), under exclusive
license to Springer Nature Singapore Pte Ltd. 2020
H. Günther, Elementary Approach to Special Relativity,
https://doi.org/10.1007/978-981-15-3168-2_9
81