The Physics Preview for the 21st Century -

March-April 2000 current project - Part 1

johnreed's take on mass

If you think strictly in terms of object-space, as in something-nothing, then any granular manifestation of any quantity must be a particle. Any motion is secondary to a moving object. And the particle is fundamental.

Consider the solar system. We essentially have objects in space, traveling in a reasonably ordered array. We have interpretted this system in terms of mass and force, and in terms of mass and curved space-time. On the face, it may appear that the ultimate fundamental focus, in both cases, is on the object itself, however, with GR we have side-stepped this locked in manner of thinking.  Before I address that, the following discussion is in order.

There are two distinct (perceivable) aspects of this solar system: 1)The object. 2)The trajectory of the object. Wrt (1), two sensory channels are involved. We see the object in the sky, and, we feel the Earth attractor. This causes us to consider, both, what we see, and what we feel. The question is: can we freely apply this bi-directional information in a generalized description of the physical process we relate it to?

The answer is: Yes we can attribute the trajectory of the object, to the object itself, and treat the trajectory as a function of the object. This enables us to include other detectable properties of the object, as fundamental functions as well, which is essentially what we have done with classical mechanics. In this manner we combine the local properties of the object with the non-local properties of the object. Since this works in a mathematical formalization, we have an operational theory.

The question we must ask is, why does it work so well when it is mathematically formalized?

In a short paper I wrote a few years ago, I explained the reason the mathematics works so well on the universe. This can be found at:

(http://members.aol.com/randamajor/mathuniv.html).

It is not necessary to read that paper to understand the ideas presented in this paper. It is merely supplemental for anyone who is interested.

In our study of the universe, our necessary primary focus, is on stable systems. From the data so far gained, as a result of these investigations, it is reasonable to conclude, that all systems that approach stability in the field, exhibit efficient action. I am not stating that any system is stable forever. I am only stating that to the degree a system is stable, its action is efficient.

This observation is a special case of a more general observation. All the natural motion in the universe that we have observed, can be approximately categorized, under the general heading of "conic sections". This is a very close approximation.

If we analyze a conic section trajectory, figuring from our locally derived quantities of force and mass, which we base on our feel (sensory channel number 1) of the Earth attractor, we discover that a least action principle is always met. Can we therefore conclude, that the local conic section trajectory results from the quantities we use? Do these trajectories result from forces and masses and accelerations?

La Grange and Hamilton derived the least action principle (if I am not mistaken) analytically from these quantities? On the face then, it appears that we can attribute the conics to the locally derived quantities. At least that is what our mathematics tells us.

If we do conclude that the local conics derive from the local quantities, is it also reasonable to conclude that far away trajectories result from the local quantities we use? And if this is a reasonable conclusion, is it reasonable to conclude that the trajectories at smaller scales, are the result of the local quantities we use?

Or, do the quantities we use function, merely because they are defined in terms of time-space, or space-time, units, which are the same units that describe the conic section trajectories?

Apparently, the answer to these questions center around how we view the quantity we call mass. Consider F=ma and p=mv. Both force and momentum are built from inertial mass and [s/t^2] or [s/t]. We can easily see that the quantities [a] and [v] are kinematic and operate within time-space boundaries. In terms of natural motion in the universe these boundaries are trajectories that approach conic section regularity. The only indication that our quantity of force generates the conics, is in our quantity called mass. We regard mass as a fundamental property of matter.

So, we can rephrase our question: Does a least action trajectory arise, as an unexplained property of an object in motion, in real space, or does the quantity called mass influence the motion? (There is another possibility to entertain: Is the motion influenced by something other than mass. Something that would result in efficient action, as a logical consequence of the manner it exerts its control? I will discuss this possibility in another paper). To shed light here, we must turn to some simple mathematics.

If we roll billiard balls on a collision course we learn that a quantity called momentum is conserved. Momentum is represented as the quantity [mv]. So in the collision: [m1v1] and [m2v2], we can interpret the conserved result as: 1) the velocity of the masses have changed, to conserve momentum, or 2) the masses of the velocities have changed, to meet least action principles. Either description applies equally well.

However, since the quantity mass does not change, wrt to each billiard ball, and since we can apply any number of velocities to the billiard balls, we see this as a mass controlled conservation principle. It should be noted, that we can also apply any number of masses, to the velocities, by using different billiard balls.

To avoid confusion here wrt gravity, we can do this experiment in a gedanken, in the free space frame. This is the frame Newton used to set his First Law. While we can view this in terms of momentum conservation, it can also be seen as a least action principle. Since we cannot discern which quantity, [m] or [v] controls, we can only (rigorously) conclude, that the principle of least action has been obeyed. This is, of course, the common thread for all action in the universe.

So, how is it that we have determined that mass is fundamental ? Our feel of force is the basis for this conclusion. It is obvious that some cohesive force holds the Earth together. We are a part of the Earth, born of its elements. We are held to the Earth. This state of attraction existed on each of our attracted parts long before we were ever assembled. We feel this attraction and quantify it in terms of weight.

The attractor at Earth doesn't care what we weigh. The stuff we are made of, is the stuff of the Earth. Alive or dead, flesh and blood, or dust and ashes, we are born, we grow. The weight of our bodies change, as we consume the food and air and water, that, like our bodies, is the stuff of the Earth.

An analogy: Combining hydrocloric acid with sodium hydroxide. In just the right proportion they become water and sodium chloride. Nothing has changed wrt the Earth attractor and weight. The combined inertial mass of the compounds has not changed.

We know by sensory channel 2), that the Earth attractor does not differentiate between object masses. This is clear wrt to orbit, free fall, and escape velocity.

However, we also know that the Earth attractor does differentiate between object masses, through our sensory channel 1). This is our FEEL of attraction toward the Earth. Larger masses are more difficult to place in orbit. They are harder to send into space. They land with greater impact after free fall.

We have returned to the original point of this discussion. And we note a significant discrepancy between what we see and what we feel, wrt force and inertial mass. In view of this discrepancy, do we assume that the object is fundamental, and generalize the properties of the object to all the universe? Or do we assume the trajectory is fundamental and generalize the trajectory to all the universe?

We have assigned the attraction we feel as weight, as a property of all the objects in the universe. We have taken this option, even though, by my argument, so far, it is not the most compelling conclusion. Up until now, no problems with this decision have been expressly noted. The reason for this is somewhat subtle.

Mass has no effect on the orbits, no effect on free fall, and no effect on escape velocity. The trajectories are pretty much covered. We can see that the object mass, does not enter into the calculations that describe the trajectory.

Since mass has no influence on the Earth attractor trajectories, it's a safe generalization, to say, that mass has no influence on any planet trajectories in the universe. Consequently we can generalize our quantity mass, to any planet motion frame in the universe, with assured impunity, as long as it is generalized to a non-local frame we cannot directly measure, mass magnitudes in. We can arbitrarily include our FEEL channel results, as an integral part of the generalization.

In this context, we must now analyze the FEEL of force that we experience. This is a subjective quantity that results from two factors. 1) Our bodies 2) the Earth attractor. However, we have quantified this subjective FEEL of force, by defining it in terms of mg. The two factors above are represented here, as, 1) [m] mass our bodies 2) [g] the Earth attractor.

Because the quantity [g] does not differentiate between objects, we can compare the relative (inertial) masses of objects using a balance scale (an aside: it is humbling to note: the balance scale had been in use since perhaps 3000 years before Aristotle. Perhaps 5000 years passed before Galileo deduced that all objects fall at the same rate). So, we have the question, what is it that we feel? Do we feel what is actually quantitatively measured on the balance scale? Our mass?  If we were on the Moon we would feel a smaller attraction than we feel on Earth. So, no, we can't be feeling our mass, because our mass does not change.

Are we feeling the Earth attractor [g], acting on our mass? Well, [g] at Earth is larger than [g] at the Moon, so this is what we feel. But is it our mass it acts upon? This hardly appears likely, since we see that the Earth attractor does not differentiate between masses. Therefore, this attraction does not differentiate between atoms (follows from principle of equivalence). So we feel the total force as the sum of the equivalent force the Earth exerts on each atom of our bodies.

Let's look at the balance scale again. It is assumed that when we use such a device, we are measuring gravitational mass (what we feel), rather than inertial mass (what we think we feel). But if we place a balance scale on the moon, the inertial mass of an object will be the same as its inertial mass measured at Earth.  On the moon we will feel a much smaller gravitational attraction. Our inertial mass however, has not changed, as we can readily verify on the balance scale. So the balance scale gives us a reading of inertial mass and not what we call gravitational mass. Therefore, our feeling of gravitational mass is a consequence of an attractor that does not influence inertial mass.

my regards,

johnreed

Unfinished

April 17, 2000