3.2 Newton’s Laws Applied to a Biosystem
31
The Concept of a Force
Force characterizes the effect on one body due to other nearby bodies, causing a
change in the momentum of the affected body if the net force is non-zero. The
Newtonian momentum of a body is its mass times its velocity. Einstein’s Special
Relativity Theory makes momentum the mass times velocity divided by the square
root of one minus the square of the velocity over the speed of light. For slow speeds
compared to the speed of light, Einstein’s theory reduces to Newton’s.
Observations indicate that in Nature, no more than four types of forces are
needed to explain all interactions. As we have noted, two of these (the ‘Nuclear
force’ and the ‘Weak force’) have ranges which do not measurably extend much
beyond the diameter of a proton. The other two, the ‘Gravitational force’ and the
‘Electromagnetic force’, act over distances we can see. They are called ‘long-range’
forces.
Our successful mathematical descriptions of the known interactions uses the
concept of a ‘field’. A field is any quantity defined at each point in space. In our
models of all interactions, we say that bodies with mass or charge ‘create a field’
around them. Other masses or charges in the vicinity are then affected by this field.
The force of one body on another due to gravity or electromagnetism diminishes
with increasing separation r between the bodies, with a power law 1/r 2 for bodies
with mass or electric charge. In Einstein’s theory, gravity is always attractive and, in
Newtonian theory, is proportion to the mass of bodies, while electromagnetic forces
can be attractive or repulsive, and, in Maxwell’s theory, are proportional to the size
of the electric charge on each of the interacting bodies.
As there is no negative mass in our best models of nature, we cannot ‘cancel’
the gravitational field outside a mass. 6 However, because there are both positive and
negative electric charges, we can shield bodies from the effect of an electric field.
For example, to protect sensitive electronics or people, one can surround a system
with a ‘Faraday cage’, which will exclude any external electric field. ‘Mu-metal’
(made from a nickel-iron alloy) can shield against an external magnetic field. A
superconducting material can also prevent a magnetic field from penetrating. (This
is called the Meissner effect.)
The local interactions from one molecule to another in life systems can be
explained in terms of electromagnetism and quantum behavior. Of course, longer
6 This inability to cancel the Earth’s gravitational field over a finite region is not just a matter of
not finding negative mass: The nature of the gravitational interaction seems to not allow repulsive
gravity. In Einstein’s General Theory, gravity must be attractive, as the gravitational acceleration of
a body is due to the distortion of space-time, and not any internal property of the body. In quantum
theory, a supposed ‘graviton’ carries a spin of two units times Planck’s constant over two pi. A
spin-2 interaction is sufficient to explain the purely attractive nature of gravity, to be contrasted
with a spin of one unit for the photon, the particle that carries the electromagnetic interaction. An
odd-integer spin particle exchange allows for both attractive and repulsive interaction. For details
on this topic, see Anthony Zee’s book, Quantum Field Theory in a Nutshell, Princeton Univ
Press (2003).
31
The Concept of a Force
Force characterizes the effect on one body due to other nearby bodies, causing a
change in the momentum of the affected body if the net force is non-zero. The
Newtonian momentum of a body is its mass times its velocity. Einstein’s Special
Relativity Theory makes momentum the mass times velocity divided by the square
root of one minus the square of the velocity over the speed of light. For slow speeds
compared to the speed of light, Einstein’s theory reduces to Newton’s.
Observations indicate that in Nature, no more than four types of forces are
needed to explain all interactions. As we have noted, two of these (the ‘Nuclear
force’ and the ‘Weak force’) have ranges which do not measurably extend much
beyond the diameter of a proton. The other two, the ‘Gravitational force’ and the
‘Electromagnetic force’, act over distances we can see. They are called ‘long-range’
forces.
Our successful mathematical descriptions of the known interactions uses the
concept of a ‘field’. A field is any quantity defined at each point in space. In our
models of all interactions, we say that bodies with mass or charge ‘create a field’
around them. Other masses or charges in the vicinity are then affected by this field.
The force of one body on another due to gravity or electromagnetism diminishes
with increasing separation r between the bodies, with a power law 1/r 2 for bodies
with mass or electric charge. In Einstein’s theory, gravity is always attractive and, in
Newtonian theory, is proportion to the mass of bodies, while electromagnetic forces
can be attractive or repulsive, and, in Maxwell’s theory, are proportional to the size
of the electric charge on each of the interacting bodies.
As there is no negative mass in our best models of nature, we cannot ‘cancel’
the gravitational field outside a mass. 6 However, because there are both positive and
negative electric charges, we can shield bodies from the effect of an electric field.
For example, to protect sensitive electronics or people, one can surround a system
with a ‘Faraday cage’, which will exclude any external electric field. ‘Mu-metal’
(made from a nickel-iron alloy) can shield against an external magnetic field. A
superconducting material can also prevent a magnetic field from penetrating. (This
is called the Meissner effect.)
The local interactions from one molecule to another in life systems can be
explained in terms of electromagnetism and quantum behavior. Of course, longer
6 This inability to cancel the Earth’s gravitational field over a finite region is not just a matter of
not finding negative mass: The nature of the gravitational interaction seems to not allow repulsive
gravity. In Einstein’s General Theory, gravity must be attractive, as the gravitational acceleration of
a body is due to the distortion of space-time, and not any internal property of the body. In quantum
theory, a supposed ‘graviton’ carries a spin of two units times Planck’s constant over two pi. A
spin-2 interaction is sufficient to explain the purely attractive nature of gravity, to be contrasted
with a spin of one unit for the photon, the particle that carries the electromagnetic interaction. An
odd-integer spin particle exchange allows for both attractive and repulsive interaction. For details
on this topic, see Anthony Zee’s book, Quantum Field Theory in a Nutshell, Princeton Univ
Press (2003).