3.2 Newton’s Laws Applied to a Biosystem
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The Concept of Time and of Space
Time is a count of the number of repetitions which occur in a ‘periodic system’.
A system is periodic if it deviates from a given state, returns, and then repeats this
same sequence of changes. The ‘period’ of a system is the smallest unit of repeat. A
periodic system may serve as a ‘clock’. A good clock is one for which many copies,
put under varying but ordinary conditions, all agree in count with the original, to
within an acceptable tolerance. Since nature gives us a number of good examples of
a periodic system, time is correspondingly given a unit according to which system
is being used as a clock, and how larger periods are put together from the smallest.
In modern use, the heart is not a good clock. But it served Galileo, while sitting
in church watching a swinging lamp, when he noticed, using his own heartbeat, that
a pendulum’s period appears to be independent of its amplitude.
Atomic clocks can presently be constructed which would agree with each other
to within a second in a few 100 million years.
Bodies occupy and are separated by what we call space, which we define through
a measure of separation called ‘distance’. A spatial separation exists between two
bodies if light takes time to move between them. The calibration of distance is called
‘length’. Recognizing that the speed of light, c, is a universal and fixed number,
length is defined by the time it takes for light to travel the length multiplied by the
speed of light. 2 In our Universe, determining the unique position of bodies from
a give one requires at least three independent distances. Giving the extent of these
three distances gives the ‘location’ of the body relative to the first.
Neural networks making a brain capable of thinking are easier to construct in at
least three spatial dimensions.
Starting from a given origin and set time, the measured location and the time of
observation of a localized body or entity determines an ‘event’, often communicated
by four numbers, (ct, x, y, z). Because of conservation laws, it follows that each
atom within you follows a contiguous sequence of events. 3 The track of a body in
space-time is called a ‘world line’.
The Concept of Mass
Mass is a measure of the inertia of a body, i.e. the body’s resistance to change of
motion. Note that mass is a concept defined independent of weight. Astronauts have
inertia even far from the gravitational pull of planets.
In ‘classical’ descriptions (i.e. with Newton’s laws combined with Maxwell’s
equations), the mass, length, and time are independently defined. Standard unit sizes
2 The speed of light is set to be c = 299, 792, 458 m/s, thus defining the meter in terms of a time
measurement.
3 In this case, local baryon and lepton number conservation insures that isolated atoms detected in
one region of space will be found a short time later near that same region.
29
The Concept of Time and of Space
Time is a count of the number of repetitions which occur in a ‘periodic system’.
A system is periodic if it deviates from a given state, returns, and then repeats this
same sequence of changes. The ‘period’ of a system is the smallest unit of repeat. A
periodic system may serve as a ‘clock’. A good clock is one for which many copies,
put under varying but ordinary conditions, all agree in count with the original, to
within an acceptable tolerance. Since nature gives us a number of good examples of
a periodic system, time is correspondingly given a unit according to which system
is being used as a clock, and how larger periods are put together from the smallest.
In modern use, the heart is not a good clock. But it served Galileo, while sitting
in church watching a swinging lamp, when he noticed, using his own heartbeat, that
a pendulum’s period appears to be independent of its amplitude.
Atomic clocks can presently be constructed which would agree with each other
to within a second in a few 100 million years.
Bodies occupy and are separated by what we call space, which we define through
a measure of separation called ‘distance’. A spatial separation exists between two
bodies if light takes time to move between them. The calibration of distance is called
‘length’. Recognizing that the speed of light, c, is a universal and fixed number,
length is defined by the time it takes for light to travel the length multiplied by the
speed of light. 2 In our Universe, determining the unique position of bodies from
a give one requires at least three independent distances. Giving the extent of these
three distances gives the ‘location’ of the body relative to the first.
Neural networks making a brain capable of thinking are easier to construct in at
least three spatial dimensions.
Starting from a given origin and set time, the measured location and the time of
observation of a localized body or entity determines an ‘event’, often communicated
by four numbers, (ct, x, y, z). Because of conservation laws, it follows that each
atom within you follows a contiguous sequence of events. 3 The track of a body in
space-time is called a ‘world line’.
The Concept of Mass
Mass is a measure of the inertia of a body, i.e. the body’s resistance to change of
motion. Note that mass is a concept defined independent of weight. Astronauts have
inertia even far from the gravitational pull of planets.
In ‘classical’ descriptions (i.e. with Newton’s laws combined with Maxwell’s
equations), the mass, length, and time are independently defined. Standard unit sizes
2 The speed of light is set to be c = 299, 792, 458 m/s, thus defining the meter in terms of a time
measurement.
3 In this case, local baryon and lepton number conservation insures that isolated atoms detected in
one region of space will be found a short time later near that same region.