To Nick: By the word "gravity" what a physicist means is merely "that
kind of interaction that masses have with each other, mediated by the
effects mass has on space".
The word is useful, because there are four known kinds of
"interactions": gravitational, electromagnetic, "weak" (the
interaction responsible for example for the instability of the
neutron, which when outside of a nucleus spontaneously decays into a
proton, an electron, and an antineutrino), and "strong" or "nuclear"
(the non-electromagnetic interaction among protons and neutrons in the
nucleus which binds them together despite the electric repulsion
between the protons). After these four kinds of interaction were
identified in mid-20th-century, a framework was discovered within
which the electromagnetic interaction and the weak interaction are
seen to be different manifestations of the same underlying type of
interaction, mediated by the exchange of photons (electromagnetism)
and "vector bosons" (the weak interaction). Then a bit later it was
discovered that the "electroweak" interaction could be unified with
the "strong" or "nuclear" interaction. This unification is called the
Standard Model. There are strenuous efforts to find some way to unify
the Standard Model with gravitational interactions.
So there's nothing mystical about "gravity" -- it's just a useful word
for distinguishing a type of interaction that is very different from
the other kinds. At the same time, it's silly to teach young children
that things fall "due to gravity". That's a tautology.
A comment on the contemporary physics concept of "interaction"
(something we deal with in some detail in the first chapter of our
intro physics textbook): Following the deep insights of Galileo and
Newton, we expect an object to move with constant (vector) velocity
(constant speed and constant direction, with no motion at all being a
special case of constant speed) except to the extent that there are
interactions with other objects. We in fact observe that when objects
are isolated from other objects, they do tend to move with constant
velocity (in the case of gravitational interactions you may have to
get quite far away from other objects to see this).
This gives us a rule for identifying when an interaction occurs: look
for a change of speed and/or direction. If you see such a change, look
for objects that might be responsible. This interaction-identification
rule gets broadened to include as evidence of interaction any change
in an object, such as a change of temperature. To put it succinctly,
change we take as evidence of interaction.
And a subrule: If you see no change in a situation where change is
expected, that is indirect evidence for additional interactions that
you might have failed to account for. As an example, consider a book
lying on a table. Because there is a gravitational interaction between
the book and the massive Earth, one expects the book to fall toward
the Earth. That it doesn't fall is evidence for some additional kind
of interaction, in this case the electric interaction between atoms in
the bottom surface of the book and the top surface of the table. As
another example, we observe that the speed of an object sliding along
the floor decreases, and we therefore suspect an interaction, and we
notice contact between atoms in the object and atoms in the floor and
infer that there is an interaction between these atoms.
Having established a way to identify interactions, the next step is to
seek ways to quantify the amount of interaction, with it being
implicit that we expect more interaction to cause more change
("constant velocity except to the extent that...."). Examples of such
quantification are Newton's gravitational force law and Coulomb's
electric force law. The "Newtonian Synthesis" then relates
quantitatively the amount of interaction ("force") to the amount of
observed change (change in speed, change in direction).
Note carefully that this is not circular reasoning, though it is
sometimes characterized as such. Relative positions, amount of mass,
amount of electric charge, are used to predict amount of interaction,
and amount of interaction is used to predict something about entities
that are very different, such as speed and direction of motion.
Newton's famous equation "rate of change of momentum is equal to net
force" (dp/dt = F_net, alas bowdlerized in most intro physics courses
to the far less powerful form F = ma, a form Newton never used), is
powerful precisely because it relates two quantities that are utterly
different in their ontology.
To take a specific example, consider two electrically charged
electrons repelling each other. Coulomb's force law is written in
terms of the electric charge of the electrons and their relative
positions and says absolutely nothing about mass or motion. The effect
of the electric interaction is written in terms of electron mass and
velocity. In the equation dp/dt = F_net, the equal sign can be deeply
misleading. These quantities dp/dt and F_net are not the same entities
but completely different. It was a deep insight on Newton's part to
see that they were nevertheless connected causally.
I can offer some additional insight into the issue of "action at a
distance". For Newton and his contemporaries, the problem was its
mysticism. For Einstein the problem was much more concrete: action at
a distance is inconsistent with Special Relativity, and the limitation
that nothing, not even information, can travel faster than the speed
of light. Newton's (gravitational) and Coulomb's (electric)
one-over-r-squared force laws do not contain time in their algebraic
statements and therefore must be wrong, since they imply immediate
effects at large distances. The fundamental concept that addresses
these issues is the concept of "field", first introduced by Faraday,
then broadened and deepened by Maxwell, Einstein, and the many
mid-20th-century physicists who created "quantum field theory".
The basic idea is that charged particles surround themselves with a
web of interaction called a "field", and other charged particles that
wander into this web are affected by the field. Similarly, masses
surround themselves with a gravitational field, which affects other
masses that wander into the region. If the "sources" of the field
(charged particles or masses) move, there is a delay or retardation
before distant locations experience a change in the value of the field
at that location. So in a sense there is no action at a distance.
Rather objects create fields, and another object interacts with the
value of the field at the second object's location, NOT with the
source object directly.
For an introduction to the field concept, I can offer two videos. The
first is a talk I gave to Santa Fe city government people motivated by
the fact that public meetings on the citing of cell phone towers
showed that even technically educated people often have no real
concept of what an electromagnetic "field" is, and are accordingly
fearful of such fields. You can see my talk "Electric Fields, Cell
Towers, and Wi-Fi" on my home page,
http://www4.ncsu.edu/~basherwo
Another source of insight is a lecture given by Ruth Chabay from the
electromagnetism section of our physics course, "The Reality of
Electric Field", Chapter 14, Lecture 4b, in this series of videos:
http://courses.ncsu.edu/py582/common/podcasts/
Here she engages students in a thought experiment outlined in our
textbook in which one sees retardation effects that show that the
field is in some sense "real", not just a useful computational tool.
You might also find interesting her lectures on mechanics:
http://courses.ncsu.edu/py581/common/podcasts/
In these mechanics lectures, Chapter 1 Lecture 2 deals with the
concept "interactions".
Bruce
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