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something called qi is believed to circulate through the body on specific, mappable pathways
called meridians. This idea pervades the contrived explanations/rationalizations of acupuncture,
and the qi is generally translated into English as energy. No one has ever found this so-called
'energy', nor confirmed the uniqueness of its meridian pathways, nor verified, through proper
double-blind tests, that any therapy or treatment based on the theory actually works. The
proponents of qi can't say whether it is a fluid, gas, charge, current, or something else, and their
theory requires that it doesn't obey any of the physics of known carriers of energy. But, as soon
as we hear someone talking about it as if it were a thing we know they are not talking science,
but quackery.
The statement 'Energy is a property of a body' needs clarification. As with many things in physics,
the size of the energy depends on the coordinate system. A body moving with speed V in one
coordinate system has kinetic energy ½mV2. The same body has zero kinetic energy in a
coordinate system moving along with it at speed V. Since no inertial coordinate system can be
considered 'special' or 'absolute', we shouldn't say 'The kinetic energy of the body is ...' but
should say 'The kinetic energy of the body moving in this reference frame is ...'
Equal. [Not all 'equals' are equal.] The word equal and the symbol '=' have many different uses.
The dictionary warns that equal things are 'alike or in agreement in a specified sense with respect
to specified properties.' This we must be careful about the specified sense and specified
properties.
The meaning of the the mathematical symbol, '=' depends upon what stands on either side of it.
When it stands between vectors it symbolizes that the vectors are equal in both size and
direction.
In algebra the equal sign stands between two algebraic expressions and indicates that two
expressions are related by a reflexive, symmetric and transitive relation. The mathematical
expressions on either side of the '=' sign are mathematically identical and interchangeable in
equations.
When the equal sign stands between two mathematical expressions with physical meaning, it
means something quite different. In physics we may correctly write 12 inches = 1 foot, but to write
12 = 1 is simply wrong. In the first case, the equation tells us about physically equivalent
measurements. It has physical meaning, and the units are an indispensable part of the quantity.
When we write a = dv/dt, we are defining the acceleration in terms of the time rate of change of
velocity. One does not verify a definition by experiment. Experiment can, however, show that in
certain cases (such as a freely falling body) the acceleration of the body is constant.
The three-lined equal sign, =, is often used to mean 'defined equal to'. Unfortunately this symbol
is not part of the HTML character set, so in this document we use an underlined equal sign
instead.
When we write F = ma, we are expressing a relation between measurable quantities, one which
holds under specified conditions, qualifications and limitations. There's more to it than the
equation. One must, for example, specify that all measurements are made in an inertial frame,
for if they aren't, this relation isn't correct as it stands, and must be modified. Many physical laws,
including this one, also include definitions. This equation may be considered a definition of force,
if m and a are previously defined. But if F was previously defined, this may be taken as a
definition of mass. But the fact that this relation can be experimentally tested, and possibly be
shown to be false (under certain conditions) demonstrates that it is more than a mere definition.
Additional discussion of these points may be found in Arnold Arons' book A Guide to
Introductory Physics Teaching, section 3.23, listed in the references at the end of this
document.
Usage note: When reading equations aloud we often say, 'F equals m a'. This, of course, says
that the two things are mathematically equal in equations, and that one may replace the other. It
is not saying that F is physically the same thing as ma. Perhaps equations were not meant to be
read aloud, for the spoken word does not have the subtleties of meaning necessary for the task.
At least we should realize that spoken equations are at best a shorthand approximation to the
meaning; a verbal description of the symbols. If we were to try to speak the physical meaning, it
would be something like: 'Newton's law tells us that the net vector force acting on a body of mass
m is mathematically equal to the product of its mass and its vector acceleration.' In a textbook,
words like that would appear in the text near the equation, at least on the first appearance of the
equation.
Error. In colloquial usage, 'a mistake'. In technical usage error is a synonym for the experimental
uncertainty in a measurement or result. See: uncertainty.
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