The entire history of physical science has been a tragedy of errors. Oog, the son of Moog, was willing to believe his senses that space had directional characteristics. He definitely knew which way was up. With the concept of an infinite, linear, homogeneous space; the philosophers did not. The trouble with an idea is that the originator comes to believe it. When this happens, he finds himself stuck with it. With the best of intentions, he lets it be known to the world. The difficulty is that once it gets loose, there is no way under heaven to get rid of it. I have no doubt that the concept of the Euclidian space will be carried on to the end of time.

The basic difficulty was that Euclid had no intention of applying it to the field of physical science. Once it was loose, Euclid had no control over it. Then the natural philosophers applied it to their description of physical space in spite of the fact that it had no physical reality. The idea of a linear space is convenient in developing the principles of geometry, but there its significance should have ended.

It is said that the influence of Aristotle was such that he prevented any real progress in the field of physical science for a thousand years. It was not until the time of Galileo that any progress was made. Let us observe the nature of that progress.

To Galileo space was homogeneous, linear, and infinite in extent. It may be that we can assume the progress to be indicated by the fact that the descriptive words were used in a different order. The concept of the inertial reference frame as introduced by Galileo made it impossible to distinguish the effect of the magnitude of mass on any motion. All inertial reference frames were equivalent and massless in application. Since there were no provisions for the recognition of such a thing as the center of mass of a two body system, it reduced to an either-or situation. Either the one mass point or the other mass point had to be used as reference. Nothing was said about the velocity of light.

The laws of momentum and inertia were known to Galileo, but the nature of forces as derivative forms had not yet been developed. Since this is the extent of Galileo's knowledge of physical laws, his statement: "The laws of physics take the same form with respect to all inertial reference frames," referred only to the measurement of momentum and inertia. Somehow or other the present author is not exactly overwhelmed. The relativity principle certainly does not apply to rotating systems.

Don't let your right hand know what shenanigans your left hand is up to. The strangest fact of all is that Galileo accepted the Copernican system which required the earth to be in motion around the sun. This obviously required a system in which the sun was the center of mass. There is no evidence that Galileo saw this fact as a denial of his own relativity principle.

The fact that the tail can wag the dog appears in the analysis of the spectral series of hydrogen. The correction required that the heavy mass and the light mass rotate with respect to a common mass center determined by the equation of moments.

Einstein swallowed the bait, the hook, the line, and the sinker. By this time, the work of Lorentz and others had changed the nature of Euclidian space to that of the Luminiferous Ether. The ether was linear, homogeneous, and infinite, but it had to act as a medium for the propagation of light waves. Since it was now a mechanical medium, the energy per unit volume was out of this world, but the density was too small to interfere with objects passing through it. Einstein denied its existence by renaming it the space-time continuum. We are struck by the truth of the adage: "The more things change, the more they remain the same."

The point to be made is that there is nothing out there. Oog, the son of Moog, observed that as the days passed and the seasons came and went, up remained up, down remained down, and the whole shooting match continued as before. This could not be true unless the space of the earth was a part of the earth and continued to be so with time. Space can have no existence apart from the mass object which determines it. Since the mass object is finite, so is its space.

There is a flaw in physical theory that creates a gap so wide that a Mack truck can be driven through it and never touch on either side. This is to the effect that an inertial force does no work. This error in concept required that an applied contact force acting through a distance to accelerate an object caused a mass increase in the object. The reasoning is flawless. The object had work done upon it by the applied force. Since work was done, the energy of the accelerated object was increased. Since there exists an equivalence between mass and energy, it follows that the mass of the accelerated object was increased by the act of putting it into motion.

We observe that Newton's third law of motion was neglected in the analysis. The concept that forces of action and reaction are equal and opposite requires that the action of contact forces without permanent deformation or damage should be conservative.

There is a "yes, but" to be considered. The mass increase actually can occur in a particle accelerator. In spite of the fact that the action of contact forces is conservative, the concept of a variable mass associated with the emission and absorption of radiation is one of the most important developments in the field of physics.

The work of Einstein considered translations only. The work of Mach considered rotations. His analysis of the rotating water bucket is a good example. Let us consider a cylindrical bucket half filled with water. A rope is tied to the bail and suspended on the vertical. If the rope is attached to a rotor, the spinning of the bucket is gradually translated to the water. In the final analysis, the surface of the water takes the shape of a paraboloid of revolution under the action of gravity and centrifugal force.

Mach claimed that if the bucket was at rest and the universe was rotating around it with the same angular velocity, the effect on the surface of the water would be the same. He did not explain how a test could be performed.

In the process of teaching my classes in physics, I used the basic idea to demonstrate my own power. One rotation on my heel through 360 degrees was equivalent to my standing still and rotating the universe through 360 degrees. It is doubtful that the universe was much affected.

Quantum theory has been described to require that everything goes steady by jerks. The work of de Broglie indicated that an electron in motion produced a diffraction pattern very much like that of light but with a much shorter wavelength. The use of this wavelength multiplied by the internal frequency of an electron at rest was assumed to yield the wave velocity. It was found that the predicted wave velocity varied from infinity to the velocity of light.

The odd part is that no one ever got around to observing the error and making a correction. Instead, endless proposals were made to explain how the matter wave could so greatly outrun the particle and still remain attached to it. The one finally accepted was that the matter wave was a phase wave carrying no energy, and the velocity of the matter wave was a phase velocity. Such a conclusion is worthy of the world of Alice in Wonderland. It certainly has no place in science.

The correction can be made by observing that an integral number of wavelengths of the matter wave must describe one complete orbit of a planetary electron in an atom. Then the frequency of the matter wave multiplied by its wavelength must describe the orbital velocity of the electron on its path. In this case we can observe that the hypothetical phase wave never had any existence in the first place.

Quantum theory is supposed to have no other basis than experimental fact. This is not exactly true considering the nature of wave mechanics and the Schrodinger matter wave equation. As presently understood, certain errors and certain limitations appear. The spin of the photon is one-half integral rather than the integral value presently assigned. One very distinct limitation is to be observed in the fact that as applied to the atom, only integer quantum numbers appear. As a matter of fact, electron spin numbers appear as well as the requirement that orbital angular momentum numbers are given by odd half integers. The extension of the quantum numbers into reciprocal integers is necessary to explain the formation of neutrons and protons from electrons and positrons. The existence of the simple neutrino as the end result of the decay of positronium negates the reality of the Pauli neutrino.

The most puzzling characteristic of the standard physicist is that of complete complacency. Everything in the field is absolute truth and not subject to question. I have never talked to a physicist in excess of ten years of age that didn't know more about the subject than I did. Each one gave the impression that he knew at least three things more than God.

As a matter of actual fact, the field of physics is in the doldrums so deep that it may never get out. Every error in the field that has been generated over the span of 2000 years has been very carefully preserved and glorified as the highest expression of human genius. It is quite comforting to the author to realize that physicists of the past were a bunch of Fuddy-Duddies like himself.

Earlier in the day, the nonsense rhyme," Fuddy and Duddy went up a hill, if they haven't come down, they're up there still", kept going through my mind. If I accept the present view, I can't even be sure of that. If Fuddy was composed of matter and Duddy was antimatter, they may have annihilated each other.

A number of years ago, the observatory at Jodrell Bank in England gave a news release to the effect that they had detected a flow of matter in a distant galaxy that exceeded the velocity of light. Just about every scientist in the world came up with a paper explaining how the flow could seem to exceed the velocity of light without actually doing so.

The Einstein composition of velocities is taken to be an expression of genius. The requirement is that any combination of velocities cannot exceed the velocity of light. Then if we combine two velocities of light we get the velocity of light. In terms of simple addition this is equivalent to one plus one equals one. We are forced to conclude that the author of that one had seen the elephant. In that case all lesser wonders were taken in stride.

Since space acts somewhat like an atmosphere, we should investigate that medium. The atmosphere exhibits a variable mass density with elevation. There is also a temperature reduction in the same sense. The medium is highly compressible and certainly has a viscosity. In this case it is far from perfect, but necessary to sustain life.

The bane of modern existence is noise. The medium propagates any disturbance. It is also true that the viscosity in the medium will damp out any wave motion with distance. Since any manifestation of viscosity depends on a shearing effect, we state: Any shearing effect imposed in a viscous flow will result in the generation of acoustic waves.

The Mach number in the atmosphere is determined by the velocity of sound. The Mach number as applied to atmospheric flight is variable with altitude. The definition is given as the ratio of the velocity of the aircraft to that of the ambient velocity of sound. Since the air itself may have a motion of translation, the speed of the plane must be measured with respect to the ambient air.

The speed of sound is reduced as the temperature of the air is reduced. It follows that for a given air speed, the Mach number at altitude is greater than that at sea level. It is true also that the atmospheric density is reduced with elevation so that high speed flight can be accomplished to better advantage than at sea level.

Shock waves occur when the medium cannot react fast enough to get out of the way of the plane in flight. This certainly results in a high rate of shear and a high intensity of noise. The exhaust from a jet engine is also a shearing flow resulting in the generation of noise. The work of M. J. Lighthill in England requires that the acoustic power generated depends on the eighth power of the flow velocity. His eighth power law required a multiplier called the Lighthill parameter that could only be determined by experiment. My own analysis indicates that a ninth power law applies with no multiplying constant. Considering the nature of the power law, it can be seen that the onset of damage to structures in the flow can be quite sharply defined and quite severe.

The boundary layer is a region of transition between the flow and the surface of a structure. If we consider a flat metallic surface with a flow of air parallel to it, we must observe that the air molecules in contact with the surface do not enter into the flow. No surface can be flat at the molecular level of size, and there are forces of cohesion and adhesion present. The standard view is that the layer of molecules in contact with the surface is at rest. The second layer is subject to a slight effect of slippage. This effect continues as we move away from the surface, layer by layer, until the free stream is finally reached. This boundary layer must have a finite thickness and must act as an acoustic generator if the given analysis is correct. In extreme cases, acoustic damage may result from the action of the flow.

In a real application, the flow cannot be expected to remain parallel to the surface. Then we can expect boundary layer thickness variation to occur from point to point. If impact flow at 90 degrees incidence occurs, a stagnation point or stagnation area results. As expected, impact flow is the most destructive.

"Sweet are the uses of viscosity." I somehow get the impression that the above is a misquote. Without viscosity and friction acting between airfoil and the atmosphere, no plane would ever leave the ground. The shape of the wing is such that the flow velocity is increased as it passes over the wing and retarded below the wing. This provides a net upward thrust which could not apply in the absence of friction and viscosity. The effect is like that of a rotating drum which carries some of the air in the direction of rotation. If the drum is translated as it rotates, assuming the net flow velocity increased on top and reduced on the bottom, the final effect is that of lift. The action depends on Bernoulli's law. The increase in velocity on the top reduces the pressure of the atmosphere in this region. Retardation of the flow underneath the wind increases the pressure with the net difference providing the lift.

The same effect applies to a baseball that is given a high forward velocity and a high rate of spin. Depending on orientation of the spin, the ball can be made to curve sidewise or otherwise at the will of the pitcher. The effect of the spin can be augmented if the well-known "foreign substance" is applied to increase the effect of the boundary layer. As any pitcher knows, the spitball is an illegal pitch.

The Navier-Stokes flow equations have never been solved in their entirety, but they can be applied to advantage in many cases. The use of dimensional analysis in the study of aerodynamics requires a great deal of wind tunnel testing. The question then becomes the interpretation of those tests in the light of human understanding and preconceived notions. These facts apply to flow problems in hydrodynamics as well.

We consider the problem of cavitation damage in marine propellers and in hydrofoils in general. The existence of bubbles which collapse and disappear is too obvious to be missed.

Now we have a "therefore." This particular therefore as applied to the cavitation problem requires the collapse of the bubbles to be the cause of cavitation damage. This is an obvious fact since the pressure in the bubble depends inversely on the radius which applies. In the limit, a zero radius requires an infinite pressure. Since no structure can stand an infinite pressure, damage occurs.

Now we go back and consider a "but." The but in question has to do with the force equation. Since pressure is force per unit area, it follows that any force applied must be given by pressure times area. The area of the bubble depends in the square of the radius. The force is then directly proportional to the radius itself. Then it follows that in spite of the fact that a hypothetical infinity was found for the pressure, the force it can exert on collapse is zero.

It seems to this author that he has spent his life in the process of correcting the errors of others. There can be no more certain way to lose friends and insult people than that of revealing their mistakes. Even if the process of pointing out the error could be tolerated, the process of correcting it cannot. It is a futile gesture to claim that someone must do it.

The entire analysis of the bubbles assumes a hypothetical medium which is continuous to all extremes. The analysis assumes that the definition of surface tension in unmodified form applies to all extremes. If the smallest unit is the molecule, the radius of the bubble cannot be less than that of the molecule. Surface tension as applied to the molecule has no meaning. It is obvious that a new approach to the problem is required.

The appearance of the bubbles is a symptom and not a cause of cavitation. The fact that the boundary layer acts as an acoustic generator comes into play. The term acoustic applies well to the jet engine in the atmosphere, but the frequency range found for the marine propeller is of the order of 10⁹ cycles per second. This is in the range of molecular frequencies.

Application of the wave equation developed to fit the case showed that the attenuation of the wave in water was quite severe. Pressure variations to be expected were of the order of 700 pounds per square inch. The bubbles appear in the wake and soon collapse with a luminescence which should indicate their origin as a frequency source. Since the attenuation with distance is so severe and the original frequency is so high, any external manifestation is more thermal than acoustic.

In the blade structure of the propeller, the effects are quite different. With no attenuation, the intensity of the acoustic wave in the interior must reach the intensity of that in the boundary layer before it is attenuated in the free stream. Further, at any blade boundary internally, reflections must effectively double the pressure on the internal surface. Calculation showed internal pressures could be well in excess of the destructive limit for metals.