"The Failure to Define Mass". There is no such failure. Formal systems are built in basis to elementary concepts, not defined in terms of anything more fundamental and characterized only by formal properties laid down for them; and derived concepts, which are defined in terms of the elementary concepts; and of other derived concepts. Mass is an elementary concept.
"It was not understood how to formally define both mass and force from f=ma". "The equation f=ma is the introduction of mass. The equation f=dp/dt is not the beginning equation. Physicists did not understand how one could define both mass and force in f=ma". Not even close. F=ma is neither the definition of force nor the definition of mass. Mass is an elementary concept, and force is defined in other ways. The expression F=ma is an equation of motion, and it is introduced as an axiom in the formal system. Truesdell gives a nice presentation of the formal structure of the theory of mechanics (see attachment).
"Mass is pervasive in physics equations. It is absolutely necessary that it be known what it is; otherwise, that lack of knowledge is spread widely
throughout theory". Not only mass doesn't need to be defined (because it is a elementary concept), but this argument about 'absolutely necessity' is invalid because it is circular. Imagine that we decide mass isn't elementary and define it using one or more concepts. Those concepts will be now elementary in the formalism, and so they will be undefined, so we are back to the starting point. And if we consider those new concepts also require definition, we will only define them using a new set of concepts... the whole argument is absurd. A finite formal theory has to rely on a set of elementary concepts, which cannot be defined in terms of anything more fundamental, because there is nothing more elemental, obviously.
"one must define both mass and force using a combination of only length and time", which doesn't make any mathematical or physical sense.
"The best choice is to accept mass as an inverse representation of some property that is undergoing acceleration." Besides all the above criticism, doing something as (m = 1/ u) where u is "some property" doesn't add any new physics to the description. It is basically replacing a concept by other. There is no net advance in our understanding of Nature by a mere change of labels.
"Force would then be defined as a ratio of two accelerations." Assuming same mass, the ratio of two accelerations is the ratio of two forces.
"The newton would be defined as a ratio of the units of acceleration". Since both accelerations share the same unit the ratio is dimensional and cannot be used to define the newton. But this was obvious because the ratio of two accelerations is not a force, but an adimensional quantity, a mere number.
"The units of mass tell us that we are being led to learning that there is a very fundamental property that has velocity and undergoes changes of velocity. What is the property? It is light. It is true that the speed of light always measures locally C". Light doesn't have velocity, it has only speed, because photons cannot be localized. C is not only valid locally, but also globally (in absence of gravitation).
"However, physics would still have the same ailment when it got to thermodynamics. Temperature has been and remains an undefined property ever since it was introduced". Another invalid claim. Several definitions of the concept of temperature are available on the literature since more than one century. The usual definition in modern thermodynamics literature is T == (partial S / partial U)-1. Temperature can be also defined without using entropy.
"2. Lack of Attention to Detail". It is kind of ironic this article accuses physicists of lack of attention to detail.
"What is the meaning of k in Coulomb's Law? [...] The k in Coulomb's law is the most important term in the equation". k is the coupling constant and it measures the strength of the interaction for given set of distance and charges; k is important, but it isn't the most important. The functional dependence on distance or the dependence on charges are as important as k.
"The only place for new knowledge to enter Coulomb's Law is in the proportionality constant". Not true, in fact new physics enters in the distance part, when we do corrections to physics for small scales. The part related to the charges is also a place for new physics; e.g. when we consider the physical effect of screening of charges in a polarizable medium, or when we consider electric currents.
"Removing 4pi from k and placing it with r^2 gives us ko the true pure constant of proportionality." Which is useless, because (i) the physics doesn't change by simply moving a constant from one place to another, (ii) because 4pi would be still needed in other expressions as that for potentials, and (iii) because two different concepts of distance would be needed at once.
"here has been no experimentation directly upon the properties of space or time". Space and time aren't objects that one can manipulate.
"The way in which this can be known is to recognize that there are no units of measurement for either one. The units of seconds are not units of a fundamental property of time. The units of meters are not units of a fundamental property of space". No. One can measure both 'space' and time, we have well-known operational definitions and apparatus to measure both even to very high accuracy and precision. Moreover, claims such as "units of seconds" are meaningless; the unit is "second" (without plural) and second is unit of time, so "units of seconds" is as saying "units of units of time", which doesn't make sense.
"Space is not an object. There are no specimens of either space or time contained in any laboratory anywhere. Both are completely inaccessible to us for the purposes of measuring, or affecting them, or being affected by them." The first part is absolutely correct. They aren't objects. The late part is so wrong as pretending that we cannot measure velocities or the concentration of a substance because velocity and concentration aren't objects. Velocity, concentration, 'space' (really position) and time are physical properties associated to objects, and those properties can be measured, as the long history of science demonstrates.
"The letter 't' represents our substitute for the indefinable property of time." Time is an elementary concept, as mass.
"For those who are not aware of this, Empirical evidence is communicated to us in terms of meters and seconds only". First, there is here a glaring confusion between the property and some specific unit associated to it (I can measure time in other units aren't the second). Moreover, a complete description of Universe cannot be build only over the concepts of position and time; we need masses, charges,...
Next section repeats the same misguided claims such as "The units of a defined mass are units of inverse acceleration."
"This result shows that temperature is the rate of transfer of energy between molecules". This is not temperature; the temperature of noninteracting molecules is well-defined.
"However, the use of these units allows for the discovery that the Universal Gravitational Constant is actually the square of the gravitational force between two neutrons, as measured by an observer located on one of the neutrons, separated at a distance of the radius of the hydrogen atom locally measured as 4.8x10^-11 meters". I don't know what is this radius, Bohr radius is 5.3 10-11; but the numerical value is of little importance here; the really important here is that gravitational constant is not the square of the force. Such claim is completely meaningless because force (Newtonian) is the product of G, the masses, and inverse of square distance.
Similar remarks about meaningless claims made in the Essay, such as "This makes for a very big change. Fundamental unity allows for just one cause for all
effects. That one cause is the property that mass is inversely representing. It is the variation of the speed of light. All effects currently credited to one of the four fundamental forces are actually due to the variation of the speed of light".
The quote from the "anonymous physicist" is incorrect. It is not possible to derive Newtonian mechanics, thermodynamics, E&M, etc... from the principles of conservation of momentum and conservation of energy/mass alone. I have searched the source for such quote. Google only reports two results, and both are docs from James A Putnam. In one of docs the phrase is typed without quotation marks; so I conclude that the quote wasn't said by any physicist, but it is a quote from Putnam himself.
Additional comment: The pair of http links in the references section aren't "Usenet files".Attachment #1: FORMAL_MECH.png
