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Date: Sun, 18 Apr 1999
Measurement II
Thomas M. Miovas, Jr.
In Relativity, Einstein deals with spacetime as if it
is a real physical existent with real physical qualities, such
as curvature; but as far as I know, this is not something that
is directly measurable, except perhaps by measuring the curved
path of a body sufficiently close to another body (which is what
the tensor represents). There may be other methods of giving
particular quantities to the variables of the equations, but the
tensor itself is not what is being measured.
Charge is a relational concept, it is the effect of certain
types of bodies on other certain types of bodies (two electrons,
say). When we say an electron has such and such charge, we are
saying it has such and such effect. If we get to the point where
we can identify the attribute of an electron that gives rise to
this effect, I think it would be improper to say that attribute
is the charge of the electron. Rather, a new term would have to
be coined. Since I haven't discovered this attribute, I can't
officially coin the term; but for the sake of making a point,
let's that attribute is the "swiggle" of the particle. A swiggle
of X gives rise to what we now refer to as positive charge, and
a swiggle of Y gives rise to what we now call a negative charge.
I think this is the only way would could differentiate the cause
from the effect.
Similarly for gravity. Regardless of the theory under
discussion, it is the effect of (any) two bodies moving towards
one another that we call gravity. If we discover the attribute
of particles that gives rise to gravity, it would have to be
given it's own name, say "gritty." A big gritty would give rise
to a big attractive force, and a little gritty would give rise
to a little attractive force (using Newtonian terminology and
keeping in mind that the elementary particles don't have the
same mass).
So, an electron could have a swiggle of X, and a gritty of A;
whereas a proton could have a swiggle of Y, and a gritty of B.
And this doesn't say anything about the attribute of that which
is in-between that "carries" these effects. This attribute would
have to be given yet its own name, probably one name for charge
("zingle") and another for gravity ("droble").
In other words, for an electron, a swiggle of X leads to a
zingle of Q, and for a proton, a swiggle of Y leads to a zingle
of R [charge]; whereas, for an electron, a gritty of A leads to
a droble of E, and for a proton, a gritty of B leads to a droble
of F [gravity].
I hope this makes the point, even though I made up the
terminology. Charge would not be the same thing as the swiggle
or the zingle, but would be how one leads to the other and how
this effects other particles; and gravity would not be the same
thing as the gritty or the droble, but would be how one leads to
the other and how this effects other particles.
Date: Tue, 20 Apr 1999 03:11:53 -0400 (EDT)
Measurement and Calculation
Thomas M. Miovas, Jr.
While I'm sure I can't handle the mathematics as well as
Stephen, since I only have a B.A. in physics and dealt mostly
with partial differential vector calculus equations and only a
few tensors (and that was fifteen years ago), my issue was not
so much the mechanics of the equations, but rather the way
Stephen phrased his reply. The amount of information contained
in certain equations is absolutely amazing, especially if one
knows how to use specialized mathematical skills to draw out the
particulars one didn't directly measure. However, his statement
made it sound as if the tensor was the physical thing being
measured, and that was what I was questioning.
Perhaps I jumped the gun, but I see two related issues as the
point of contention in the measurement thread: 1) Is an
equation the thing that is being measured? and 2) Is a
calculation the same thing as a measurement?
1) A mathematical equation is a condensation of observations and
integrations about the relationship of various aspects of
existence that uses units of measurement in a very precise
organization. These observations, integrations, and
relationships are represented by symbols. The symbols and their
organization are no more the things (or actions of the things)
they represent than the word "dog" is a dog, or even no more the
things (or their actions) than the concept "dog" is a dog. A dog
is a dog, the concept "dog" is a mental integration of
observations about various dogs, and the word "dog" is a set of
symbols representing the metal organization of the integration
of observations about dogs.
I'll take it for granted that Stephen understands this, and that
he was simply using the terminology loosely. Even if Einstein's
theory of General Relativity was true, the spacetime curvature
tensor would not be spacetime or its curvature. Spacetime would
be the physical thing out there, and the tensor would be an
equation representing it, its curvature, and other aspects of
spacetime.
2) Though mathematics is the science of measurement, and
mathematics uses equations, I draw a distinction between a
measurement and a calculation.
A mathematical measurement requires finding a standard unit
among certain aspects of existence that have similar
characteristics, such that the other units or their
characteristics differ from the standard unit by a *quantity* of
that standard unit, thus making that standard unit a unit of
(mathematical) measurement.
A mathematical equation is a mental organization of various
units of measurement and their relationship to each other;
1+1=2, a+b=c, dx/dt + dy/dt = dz/dt, and so on.
A (mathematical) calculation utilizes a mathematical equation to
arrive at a solution when every quantity of the units of
measurements of the equation may not be known, at least for
algebra and above. For 1+1=2, one can directly measure a length
of one inch, another length of one inch, add them together to
get two (total) inches. The result, in this simple case, can be
confirmed simply by measuring the total length of the object,
say two inches; but it's not always possible to do this.
Volume can be directly measured by dunking an object, say a
child's toy block, into water; the volume of the water displaced
by the object is the volume of the object. The volume of the
displaced water can be measured by using a graduated cylinder or
even kitchen utensils, such as those used for measuring cups,
tablespoons, and teaspoons. The volume of the block can also be
calculated by the equation LHW=V, if one measures the length,
the height, and the width of the block. The results will be the
same, but I think it's obvious that the process used to get the
result is different. For something like a child's block, either
procedure is possible; but it's not possible to use the dunking
procedure on the entire Earth, the volume of the Earth must be
calculated, not directly measured.
As far as I know, every valid mathematical equation reduces to
1=1, if one simply looks at the units of measurement while
omitting the specific measurements. For example, length times
width times height equals volume (LWH=V). The units of
measurement of L, W, and H are, say, inches, whereas the units
of volume are cubic inches. So, just looking at the units of
measurement, we have [inches][inches][inches] = [inches^3], or
1=1 if we divide each side of the equation by [inches^3].
It becomes more complicated when one is dealing with equations
that are organizations of different units of measurement, say:
Fg=Gm1m2/(d^2) (the equation for gravitational force). In this
type of case, one isn't really able to divide distance into
mass, but it can be handled as if one can, and the equation
reduces to 1=1.
Since a valid equation does reduce to 1=1, it implies that maybe
a calculation is a type of measurement even though the units of
measurement on either side of the equation are not the same
units of measurement. But I don't know how to prove that *all*
valid mathematical equations *must* reduce to 1=1; so, at this
point, I draw a distinction between a measurement and a calculation.
As to an instrument like an odometer, I think one is directly
measuring distance, because there is a mechanical causal link
between how far one moves an odometer over a surface and the
numbers that show up in the read-out. The odometer isn't making
any calculations, even if it uses a computer as part of the
causal mechanism. When the ground wheel turns, everything else
connected to it changes in a precise, causal manner -- and that
is as direct as one can get.
