While observing a discussion between a famous senior science professor and an uneducated student from a distant land the following dialog was observed. The student, while ignorant of current scientific concepts, was known to possess an extraordinarily high level of intelligence. DIALOG
The abbreviation of P and S will be used to indicated when the speaker is the professor (P), or the student (S).
S: Professor, what is 'science'? DAY 1: MEASUREMENTS INVOLVING TIME AND SPACE
P: Science is an area of study wherein man attempts to explain natural occurrences. Man observes his surrounding reality and postulates philosophical thoughts. He then attempts to prove or disprove that thought through experimental evidence. When possible, the philosophic concept is expressed in terms of exact mathematical equations. Through use of those equations, the original philosophical thoughts may be extrapolated into generalized rules which are then referred to as the 'Laws of Nature'.
S: Yes, I understand. The philosophical thought is first verified by actual experiment and generalized through use of mathematics.
P: Exactly!
S: Can you explain the process of experimental verification?
P: Yes. The experiment required to verify the philosophic thought is first designed through use of creative imagination. Then the needed equipment is built or purchased to conduct the experiment. Next, notes and measurements are made while the experimental procedures are performed. And finally, the recorded notes and measurements are analyzed to determine if the experimental data confirms the original philosophic thoughts.
S: That is almost clear. But please tell me what is a 'measurement'?
P: Ahhh, I forgot that you have not been previously informed about the concept of measurements. Let me back up and explain what a measurement is. But first you need a little background information about the experimental observations which will be 'measured'.
As we observe the physical world around us, we do so through the use of our 'perceptions' of sight, sound, smell, taste, and feel. This includes an ability to perceive differences between various objects, which enable us to identify specific unique objects which are located at unique 'separation distances' from each other at the time of each instantaneous observation.
In addition to our ability to perceive the current physical characteristics and instantaneous relative locations of physical objects, man is endowed with mental capacities of 'memory' about prior states of relativity, and 'imagination' about possible future states of relativity. If it were not for our capacities of memory and imagination, then we simply would remain unaware of the reality of change. That mental capacity enables us to compare the current state of relative locations with prior and future states of relative locations. The relocation of objects between observations is referred to as 'motion'.
To avoid confusion about the changes in relative locations of objects, we need to organize our thoughts about the sequence of those changes. Without organization we would be in a situation similar to attempting to understand the information documented in a book if the pages in the book were randomly scattered around us. In the case of books, we avoid that possibility by adding 'page numbers' which enable us to assemble the scattered pages into a logical order. Man created the imaginary concept he refers to as 'time' to enable him to organize his mental thoughts about the changes - such as locations - he perceives during sequential observations. Time, like page numbers, may be insignificant unto itself - but it is a necessary tool for mental organization of the changes which occur between sequential observations.
Now to answer your question about measurements directly: Man postulated the concept of fixed predefined 'units' of measure to enable him to communicate his thoughts about the differences in relative magnitudes of distance and time lapse. A fixed 'unit' of measure was arbitrarily agreed upon which could then be used as the denominator of a ratio for which any other magnitude of distance and time lapse could be compared through use of an agreed on sequence of increasing 'numbers'. This ratio enabled man to communicate the thought that a distance or a time lapse of current interest was equal to the number associated with the ratio of the distance or time lapse of current interest divided by the previously agreed on 'unit of measure' for distance and time lapse. For example, the concept enabled man to communicate that one state of relativity about distance was equal to four times the amount of distance which has been agreed on as the 'unit of measure' for distance. Similarly, man could advise that the amount of time lapse between two observations of current interest was four times that amount of time lapse that had been agreed on as the unit of measure' for time lapse.
The number associated with the ratio of the magnitude of interest divided by the pre-agreed unit of measure for distance or time lapse is referred to as a 'measurement'. To aid in the determination of these measurements, man created 'rulers' and 'clocks'.
S: I understand. But how was it determined that the units of measure are independent of all other considerations? What experiment was conducted to prove this assumption?
P: That is an interesting question. I don't really think anyone questioned that before. I suppose you might say that the concept of fixed units of measure which are independent of all perceivable conditions is just accepted without question. It is a basis which all the other parts of science accept without question.
But never mind, let us continue.
S: When making a measurement, what reference point is used as the base, or 'zero', location for distance and time lapse?
P: Well actually, the zero reference point may vary. For example, if we are considering the motion of a single object in empty space, then the zero reference point is assumed to be the location of that object at the time of the first observation. The change of interest is that number of units of distance and time lapse between the first and the second observations. The motion is then defined in terms of either a number representing the ratio of the change in location divided by one 'unit' of distance, or a number representing the ratio of the lapse in time divided by one 'unit' of time lapse. We refer to this as an 'absolute' motion.
However, if we are considering the motion of one object relative to a second object, then we measure the differences in distances between that amount of distance between the two objects at both the first and second observation. We refer to this as 'relative' motion. If the first object does not move from it's initial location between the two observations, then the absolute and relative motions have equal mathematical values for distance. However, if the both objects move between the first and last observation, then the values of relative distance and absolute distance will not be equal.
S: That is rather confusing, but I think that I understand the difference between absolute and relative measurement of distance is due to the variation of the base 'zero' point of reference. I think this is what might be referred to as a difference which occurs due to a change in the center of a 'coordinate system' on which measurements of distance are based.
P: Very good! You are indeed a brilliant student. Now let me introduce another form of measurement. As we observe the world around us, we note that the amount of change in distance associated with motion is variable - depending on the historical time at which the observations are based, or on the selection of the objects of current interest. These differences are referred to as the relative 'rate of motion'.
The measurement used for 'rate of motion' is actually only an imaginary mathematical equation. The equation is simply a ratio of the number of units of change in distance divided by the number of units of time lapse between two sequential observations. That mathematical ratio is then reduced to it's simplest form by dividing both the numerator and denominator of the ratio by the denominator. This results in a single number representing the averaged number of units of distance which would be associated with the motion during one single unit of measure of time lapse. Hence, by definition, 'velocity' is simply the number of units of distance through which motion is perceived to have occurred during one unit of time lapse.
S: So then the unit of measure for 'velocity' is actually an identity to the unit of change in distance when the number of units of time lapse is also equal to one. And when we measure the actual rate of motion of an object the mathematical value assigned to velocity and associated distance are always identical.
And the mathematical value named velocity is actually a dimensionless, or pure number because it is simply a ratio of a dimensionless numerator indicating number of units of change in location and dimensionless denominator of 1.0 indicating a single unit of time lapse? The mathematical value named 'velocity' must be dimensionless also because both numerator and denominator are both actually dimensionless numbers.
P: Well, yes. But it is common practice to add a suffix to that dimensionless number. The suffix is necessary because man has agreed on several different units of measure for both distance and time lapse. In order to communicate the intended thought, it is therefore necessary to add a suffix to the pure number to explain which set of units of measure are being used during the current report.
What you say is significant however, because the numbers referred to as 'distance' and 'time lapse' must also be pure 'dimensionless' numbers because they are actually ratios of like type perceptions. And here too, it is customary to add a suffix to the pure number to explain which of the arbitrary type of units the pure number refers to.
Your reference to the concept of a unit of measure of 'velocity' when the distance and time lapse are equal to one is also a little unusual, but I suppose it might be considered that way. If so, then we might think of the speedometer on an automobile in the same way we think of a ruler or a clock.
S: This all seems unnecessarily complex. It seems that a single state of reality about the actual motion of any single object, may be assigned many different mathematical values - dependent not on the singular reality of the motion, but on the arbitrary choice of the units of measurement for distance and time lapse as well as the location and state of motion of the coordinate system on which the motion is being defined.
Furthermore, the number assigned to the equation named 'velocity' is always an averaged value which may vary greatly from the actual rate of motion occurring between the first and last actual observations - as well a during any single pre-defineed unit of time lapse.
However, when we consider velocity as a measurement indicated by the speedometer of a car, then that value is an actual instantaneous value rather than an averaged number because the speedometer value is based on current instantaneous rate that the wheels of the car are spinning.
P: Perhaps that is all true. But one eventually learns to understand and use all these words. And without the words it would be impossible to communicate about the differences in distances and time lapses, and rates of motion that we perceive around us.
These words and rules were all developed centuries ago, and it is now considered foolish to question the logic of their origins and continued usage.
I think we should take a break now so that you can reflect on all we have discussed so far. We still have two more perceptions, named force and mass, to cover before we move on to how all these perceptions fit together in current concepts of science.
The conversation between the distinguished professor and student continued the following day: DAY 2 MEASUREMENT OF FORCES AND INERTIA
P: Yesterday we discussed the meaning of 'science', the concepts of fixed, pre-defined 'units of measure' for separation distances and time lapses, and the concept of motion as defined by the mathematical ratio named 'velocity'.
We have another basic concept that must be discussed - a factor that we refer to as 'force' and 'inertia'. These factors are associated with a change in the mathematical value of 'velocity' of physical objects.
Have you ever had to push your car to get it to start after the battery failed?
S: Yes, unfortunately that happened one morning after I left the car lights on overnight.
P: Well the effort that you exerted to push the car is referred to by the word 'force', and man has agreed on fixed amounts of force which we refer to as the 'unit of measure' for force. Just like with distance and time lapse, the magnitude of any force of current interest is defined by a mathematical ratio of the magnitude of the force of current interest divided by the pre-agreed unit magnitude of force.
S: OK, so then values assigned to forces are actually pure dimensionless numbers, just as the values of distance, time lapse, and 'velocity' that we discussed yesterday were pure dimensionless values?
P: Well, yes. But again it is customary to add a suffix to that number so that we can communicate about our arbitrary choice involving the 'unit of magnitude' of force that we are currently interested in. For example we might describe the same amount of force as having a value of 2000 'pounds' or as one 'ton'. The determination of the number depends on the choice of the magnitude of the named unit of measure.
S: Are the unit values of force considered to be fixed and independent of motion - like the units of distance and time lapse were?
P: That's right. You catch on fast. Now, when you pushed on the car the velocity of the car increased. We refer to that change in the value of velocity as 'acceleration'. And we define the mathematical value of acceleration by use of still another ratio. This ratio is the amount of change in the value of velocity divided by the number of units of time lapse that the force is applied during the change in velocity. That ratio is then reduced by dividing both the numerator and denominator by the denominator so that we end up with the number of units of acceleration during one single unit of time lapse.
S: Then the value assigned to the ratio named 'acceleration' is actually an averaged value. This is similar to the value which was assigned to the ratio named 'velocity' being an averaged value. And like the other factors 'acceleration' is actually a dimensionless factor? In effect, the word 'acceleration' is another form of measurement for which the unit of measure would correspond to a change of one single unit of distance divided by one single unit of time lapse?
P: Yes, that's true. But we usually think of those values as being current instantaneous values rather than as averaged values. And you need not remind me again that the actual instantaneous values might possibly vary considerably from averaged values.
S: I'm sorry. It is just that I am trying to understand all that you are telling me.
I notice that since the actual rates of motion are defined by ratios, and that the ratios are all mathematically reduced to one unit of time lapse. Then it must follow that the mathematical value assigned to the word 'velocity' must be identical to the mathematical value of the number of units of distance on which the word 'velocity' was based. So mathematically, 'velocity' and 'distance' are identical values when both are based on the a single unit of time lapse.
And also that the mathematical value of the word 'acceleration' must be identical to the change in the number of units of units of distance which occurs during one single unit of time lapse.
P: Hmmm. This is an interesting observation. Even though the named concepts imply entirely different perceptions, they are indeed dimensionless mathematical identities.
And that mathematical identity is especially true because we have already determined that the descriptive suffix is not actually a reality of the math, but only an added communication tool needed to explain the concept of reality of current interest (such as distance, motion, or change in motion) and the choice of the units of magnitude of current interest (such as inches, feet, or miles).
S: Yes, and also all the concepts involving motion are averaged values rather than exact values. And the potential error between the exact and averaged values are all dependent on the magnitude that was originally defined as the single unit of measure for time lapse. The longer the unit of time lapse (for example, hours rather than seconds) the greater the probability of error between the actual motion and the mathematically defined motion.
P: Young man, you are bringing up thoughts that have never occurred to me before. I have an answer for you about this potential error problem - involving a mathematical process called 'calculus' - but lets come back to that subject aftter we finish our discussion about forces.
S: OK. We can discuss calculus at a later date.
P: Now, where was I? You applied an effort when you pushed on the car, and we measure that effort by use of units of measure of force. did you notice that the harder you pushed (that is the greater the force) that the faster the car accelerated?
S: I don't think that I did notice that. But I did notice that it did not start to move until I pushed very hard. And also that as the rate of motion increased it seemed to take more energy to continue pushing as hard as I pushed before. I was exhausted when the car engine finally did start up.
P: Well never-the-less, it is a fact that we can prove by experiment that the rate of change in motion is directly proportional to the magnitude of the applied force. There are a couple of side considerations that explain why you tired more quickly as the rate of motion increased. I again want to postpone detailed discussion of these side considerations, but they have to do with factors we call 'friction' - which has to do with the characteristics of the car and environment; and 'energy' - which has to do with the rate of motion of the car while you were pushing it.
But first, I want to tell you about a factor we call 'inertia'. As I said before, it can be experimentally demonstrated that the rate of 'acceleration' of a physical object (the car in this case) is directly proportional to the magnitude of the force (how hard you pushed). We refer to that effect as being due to magnitude of a naturally existing opposing force that we call 'inertia'. For any specific objecct, the magnitude of the Inertia force is directly proportional to the associated 'acceleration'. The ratio of the value of acceleration divided by the inertial force is referred to as the 'mass' of the object which is accelerating.
Because the value of acceleration divided by the inertia force varies for different objects, we say that 'mass' is a property which is 'owned' or is characteristic of each specific physical object. And because the ratio of the acceleration divided by the inertial force is constant for any specific object, we say that the value of the 'mass' of the object is a constant which is independent of the current velocity as well as the magnitude of the pushing force.
This combination of factors involving pushing force, inertial force, and acceleration forms the most basic of all scientific concepts. It is indicated in mathematical format as F = MA where F is the pushing force, M is the mass to which the push is applied, and A is the resultant magnitude of acceleration.
S: The value of 'acceleration' is directly proportional to the value of 'force', and the value of 'velocity' is directly proportional to the change in travel distance that occurs between two observations separated by one unit of time lapse.
Why not simply assume that the ratio of force is to acceleration is equal to the ratio of velocity to time lapse. In mathematical form it would appear as F/A = (S2/1 - S1/1)/1
That could then be simplified to mass is equal to acceleration, or even to mass is equal to the change in the number of units of velocity: M = (V2 - V1),
Or that mass is a change in the magnitude of travel distances that occurs during one unit of time lapse: M = (S2 - S1) during sequential units of time lapse.
When the value of 'mass' is equal to the 1, then the value of 'acceleration' would also be equal to one. Which means that the change in 'velocity' is equal to one. Which means that the change in distance of travel is equal to one during each sequential unit of time lapse. In effect, the ‘unit of measure’ for mass is a mathematical identity to one unit of change in travel distance during each sequential unit of time lapse. That unit of measure for mass is therefore another imaginary mathematical function of the other imaginary mathematical equations named ‘velocity’ and ‘acceleration’.
The unit of measure for mass is actually totally independent of the static characteristics (ie zero rate of motion) of the specific object to which it’s value has been assigned.
P: Woooaaw, boy. This is not the way we scientists think. And all that may be true, but it would only be true when all those differently named forms of perception were equal to one. Obviously they all may have many different values of separation distance, velocity, acceleration, force, and mass.
S: True but all those named forms of perception are simply words and equations which refer to the same singular type of reality. And the numbers that man has assigned to all those named forms of reality are based not on the reality itself, but rather on the original assumption that the imaginary agreed upon 'units of measure' for distance and time are independent of the reality of changes that occur during one imaginary agreed on unit of time lapse.
What if the units of measure for distance and time lapse were not actually independent of rates of motion, but were directly proportional to the rate of motion? Then the equation named 'velocity' would never vary from a constant, and that constant could be set at 1.0 which would be totally independent of the actual reality of changes in rates of motion.
P: Frankly, I'm quickly tiring of trying to teach you about science as you seem to be off on a wild tangent from all that I have learned and now know to be true.
But, there is something about science, referred to as 'relativity' that gives me reason to want to pause before we continue our discussion. Let's stop now, and continue our discussion tomorrow.
S: OK. I'm sorry if what I have said upsets you. I mean no offense, but it does seem that the concepts of science that you are teaching me is unnecessarily complex. The simply singular reality of the sequential locations of objects seems to be clouded by many imaginary assumptions about names and numbers.
P: I did not get much sleep last night. My prior explanations about science were about units of measure, locations, motions, forces and inertial mass of physical objects all described in terms of pre-defined fixed units of measurement. These explanations were based on concepts first documented in the 15th century, and generally classified as 'classical' science. DAY 3 RELATIVITY
But classical science itself was based on the previously accepted concept of fixed units of measure which remain unaffected by the environment in which measurements are made. That concept of fixed units of measure probably dates back to an earlier time when man needed a comparative system of measures to conduct the practices of trade and commerce here on the surface of the Earth. At that early stage of civilization, these practices of trade and commerce did not involve differences in rates of motion. It therefore was very reasonable to ignore the possibility that the units of measure might be affected by changes in rate of motion.
You upset me a bit when you began to talk about units of measure being variables which might be proportional to rates of motion - which has never even been considered in science before. I think you may have touched on that idea of variable units of measure during the first day of our discussion. But we simply brushed that idea aside at that time.
Yesterday you again brought up the idea of units of measure being variables dependent on rates of motion. It seemed to me that you were simply going astray at the time. I was about to discontinue our discussions out of frustration. But then you used the word 'relative'. And that triggered a thought in the back of my mind about a much more modern scientific concept, referred to as 'relativity'. This is a concept documented in the 20th century at a time when mankind's interests had expanded from simple commerce and trade on the surface of the earth to concepts of very high rates of motion.
This modern concept of science advises that the actual magnitudes of distances, time lapses, and masses do vary with changes in rates of motions. But those changes are expressed in terms of the numbers of fixed units of measurement, rather than in the concept that you were suggesting about variations in the magnitude of the units of measure themselves due to changes in the rates of motion.
Last night I began consideration of the affect that such a paradigm change in thought might have on currently accepted scientific concepts. The more that I analyzed this paradigm, the more interesting it became. You may have just stumbled across something that science has been pursuing without success for centuries. We refer to that goal the 'general unification' of science because the goal would explain how various branches of scientific inquiry all follow one common set of rules. These different branches are in areas of study named nuclear, atomic, electromagnetic, and physical science. The perceivable differences between these areas involve both size and force. But variations in the relationships of size, force, and motion are all explained by many different mathematical equations and words that apply only to each specific branch of interest.
It occurred to me that if we considered that the units of measure are treated as variables proportional to size and rates of motion, as you were talking about yesterday, that all these different scientific fields of interest may indeed follow the same set of rules of behavior. The differences currently believed to exist would not be due to the actual reality, but rather only to the confusion involved in the currently accepted equations and words. But then all the equations and words may only be due to an improper assumption that the numbers associated with fixed 'units of measure' are more important than the reality of the observable magnitudes.
S: Well, professor, I have never even heard of all these various branches of science before, but from what you are saying now, it might be that all that unnecessary complication that I was referring to yesterday may be very significant. Maybe there is no need for the complication, but only a need to give a little bit of consideration to the very basic ground rules on which the first scientific postulations were made. If the first basic postulations became 'scientific laws' only because the verifying mathematical equations were based on one original false assumption, then it would be possible that all the subsequent 'laws' might fall as soon as the original error was recognized.
That might seem catastrophic to current scientists who have built a life time of belief of prior errors. But it might result in vast simplification which would be advantageous for all the future generations of scientists who have not yet been indoctrinated into the old set of beliefs.
But now I still need for you to explain more about the currently accepted scientific thoughts so that we can jointly evaluate the effects of a new set of rules involving the new concept of relative units of measure.
Also you mentioned in passing a few concepts that you promised to explain later. I recall the word 'calculus' in reference to a mathematical process that would minimize the affect of errors associated with units of time lapse greater than zero. Also, I made a note to return to the concepts you call 'friction' and 'energy' when we were talking about pushing a car. Can we continue again tomorrow?
P: Indeed we can. I am beginning to wonder at this point which of us is the Professor and which is the Student in this discussion.
P: Yesterday I promised we would discuss mathematical procedures named calculus, and also the concepts of friction and energy. However, I want to postpone that discussion a little longer because that concept of variable units of measure that you suggested continues to haunt me. DAY 4 - ELECTROMAGNETIC WAVES AND PHOTONS
We have been discussing the field of science that has to do with the motion of physical objects in terms of fixed units of measure of distance, time lapse, and force. And we have discussed how changes in the rate of motion of physical objects relates to unbalanced forces and inertial affects - all of which is associated with the word 'acceleration'.
There is however, another, newer field of science, referred to as electromagnetics. In this study, the concept of massive physical objects is replaced with a concept of 'waves' and 'photons'. Waves and photons are considered to have zero mass, and therefore are free of inertial resistance forces. The rate of motion of waves and photons is also independent of the concept of unbalanced applied forces.
The magnitude of distance through which a photon moves is referred to as a 'wave length', when the associated amount of time lapse is a fractional part of one unit of time referred to as 'frequency'.
The velocity of photons and wave lengths is considered to be a constant (ie independent of the affects of applied forces, inertia, and acceleration), and is said to be equal to the product of the wave length times the frequency.
Interestingly, when we recall that the word 'frequency' is actually a reference to a reciprocal value of the concept of time lapse, then the constant velocity equates to one relative unit of distance (wave length) divided by a fractional portion of one unit of time (seconds), that is 'relative' to the factor named 'velocity'.
In effect, the factors named wave length and time lapse are both proportional to the rate of motion. By the same token a sequential train of photons combine to form one complete 'wave'. And when the number of waves is equal to the factor named 'frequency', then the overall length of the wave train is equal to both one full predefined fixed unit of measure for time lapse and also that amount of distance which is referred to as the 'velocity' of the individual waves.
That descriptive set of definitions seems to be exactly what you were wondering about when you first asked why the units of measure and time lapse had been assumed to be independent of the rate of motion for an object. If we defined the distance of travel corresponding to one unit of time lapse the same way for physical objects that we do for photons and 'waves' then it would be impossible for the value of the ratio named 'velocity' assigned to the motion of physical objects to vary.
S: But if the velocity of the physical object could not vary, then the concept of 'acceleration' and associated 'unbalanced force' and 'inertial resistance force' would be meaningless - or at least independent of the actual rate of motion, wouldn't they?
P: Yes they would at least be independent of the actual rate of motion. In fact, the whole idea of any connection between actual rates of motion and the word velocity would be without meaning.
But then it becomes unclear how we would communicate our thoughts about obvious, perceivable variations in the rate of motion. For we do indeed perceive that different objects move at different rates of motion, and the same object may move at different rates of motion during different times in history.
S: Well Professor, what if the actual perceivable rate of motion - rather than the concepts named distance and time lapse - was considered to be the primary factoor upon which units of measure were based? Then the number of units of measure for both distance and time lapse would be variables which are directly proportional to the actual perceivable rate of motion, but the mathematical ratio named 'velocity' could not possibly vary, and would be totally independent of the actual perceivable rate of motion.
P: And in which case, the concept of an unbalanced force either would no longer exist - or at least would not affect the value of 'velocity' and 'acceleration'. That seems too far removed from all that I know to make much sense.
S: There is something that has been bothering me, Professor. You have used the concept of 'unbalanced forces' repeatedly during discussion of objects in motion. But it seems totally impossible that any force could ever be 'unbalanced'. Before I can push on any thing, that thing must push back equally hard. For example, when I push on the wall of this building, the wall must resist with equal force. If it did not, my hand would move right on through the wall. And if the wall resisted with more force than I was pushing on it, then it would cause me to slide backwards.
This same principle applies when I push on the car. Even though the rate of motion of the car may change when I push on it, the surface of the car must resist the push of my hand with equal force, or else I would bend the surface of the car. And if the car resisted with more force than I was pushing on it, then the car would cause me to move backwards - or else it would run over me.
But based on those thoughts, it follows that the entire concept of an 'unbalanced' force is impossible. In the case of the wall, the equal but opposite push is called structural strength. In the case of the car, the equal but opposite push by the surface where I am pushing is also called structural strength - but the same resistance is called 'inertia' when we talk about the compete car rather than just the surface of the car.
Anyway, by any name, it seems to me that the idea of an 'unbalanced' force must be wrong.
P: Oh no, it can not possibly be wrong. For it is the underlying basis for all of physical science. Way back in the fifteenth century, a man named Isaac Newton established that basis when he postulated that an unbalanced force is mathematically identical to the product of mass times acceleration. We show that in mathematical format as F = MA. And all physical science was based on that equation - at least until the twentieth century when the concepts of 'relativity', electromagnetics, and quantum mechanics were postulated.
S: Well Professor, I don't know about all those new postulates, but we have already proven that the entire concept of variable 'velocity' is based on an unquestioned belief in fixed units of measure for distance and time lapse which are independent of the actual perceivable rate of motion. And also that same belief has already been discarded in favor of the use of variable units of measure when we speak about the motion of photons and wave lengths.
Doesn't it seem strange that rates of motion for physical objects must be variable while rates of motion for photons and electromagnetic waves must be constant only because the base assumptions about the factors of distance and time lapse have been defined differently for the concepts - or 'fields of science? Both physical objects and non-physical objects would act the same if their action was based on a common definition of units of measure.
P: Ummm. Let's continue our discussion tomorrow. I have other business to attend to just now.
S: Good morning, Professor. I have a new question based on your statement yesterday that the underlying relationship for all physical science is that an unbalanced applied force is equal to the product of mass times acceleration, or as you said in mathematical form F = MA. DAY 5 - INERTIA IS SIMPLY AN EQUAL BUT OPPOSITE FORCE
P: Good morning. Sorry that I left so abruptly yesterday, but you had raised another question that caught me by surprise. But what is your question?
S: Well, remember how I had indicated that the concept of unbalanced force seems illogical? And that for every 'applied force' there must be an equal but opposite resistance force?
P: Yes I do. That was the part that caught me off balance yesterday. Although it is counter to the basis of physical science, it seems to be absolutely correct. Last night as I was considering this, it occurred to me that science has created many different words for the concept of forces which oppose an 'applied force'. For example we refer to friction when we are talking about objects sliding against each other, and viscosity when an object moves through a liquid medium, and aerodynamic drag when an object moves through the atmosphere. But aside from all those words, we use the concept of 'inertia' when we think about the resistance of an object to changes in the rate of motion after all those other recognized concepts of resisting force have been subtracted from an 'applied force'. But rather than referring to that remaining amount of resistance as a 'force', we refer to it as 'inertia'.
It occurred to me that 'inertia' is actually a concept which must exist to account for any unaccountable differences between an 'applied force' and all other known 'resistance' forces. Now we don't usually think of 'inertia' in terms identical to a 'force' - but actually that seems to be exactly what it is.
But go ahead with your question.
S: Well that equation F = MA states that in mathematical values that the product of M times A must be identical to F. If we think of that factor of M in terms of a pure force, being the resistance force which counterbalances the applied force, F, and rearrange the equation from F = MA to the form F / M = A, then it must follow that the only possible value for A is simply 1.0.
In that form, the factor A might be thought of as a 'stress' which exists at the location where the applied force, F, and the equal resistance force, M, come together. Then the stress could exist at that point even though the net force must be zero. Is that right?
P: Yes the thought seems correct. But the concept of A in terms of a 'stress' rather than in terms of a change in 'velocity' is certainly unusual. And we know from experience that when an object is free to move that when an 'unbalanced applied' force exists, then the rate of motion changes. That is apparent from observation - even if the net force is actually equal to zero.
S: Yes. But remember our discussion that when the concept of units of measure is relative to the rate of motion, then the concept of 'velocity' is independent of the actual rate of motion of an object. Well based on those relative units of measure, the rate of motion would be allowed to change when 'stress' exists. But that change in the rate of motion would not be reflected by a change in the value of the mathematical ratio named 'velocity', because both the relative distance and relative time lapse would change in direct proportion to the change in the rate of motion.
Now if the mathematical ratio named velocity is constant and independent of the actual rate of motion, then the currently accepted concept for that mathematical ratio named 'acceleration' would be meaningless because it is based on a change in the value of the mathematical ratio named 'velocity'.
Furthermore, if the distance of travel and associated time both increase as the actual rate of motion (not 'velocity') increase, then this is exactly the same sort of relationship that exists when we refer to the distance of travel as 'wave length' and the time lapse is converted to the word 'frequency'. In other words, this is the same relationship we discussed for photons and wave motion before (on day 4).
Do you follow what I'm saying - it's rather hard to grasp, and took me quite a while to understand?
P: I think so. Your thought is that the concept of an 'unbalanced' force is impossible, but 'stress' may exist even when the net force is zero. And that when a stress exists on an object which is free to move, then the actual rate of motion of that object will change. But if the measurements of distance and time lapse are proportional to the actual rate of motion of the object, then the mathematical value of 'velocity' remains constant, and the mathematical value named acceleration is therefore a meaningless mathematical constant of one.
S: That's right. And we can then think of the concept of the word acceleration now in terms of the existence of a stress at the point where the applied force meets it's equal but opposite resistance force which results in an actual change in the perceived rate of motion of the stressed object.
And one more thing. The magnitude of the change in the actual rate of motion would be directly proportional to the magnitude of the stress. The main reason that this is important is that it ties this new line of thought back into the currently accepted line of thought that for any given object the change in rate of motion (not 'velocity') is directly proportional to the magnitude of an 'unbalanced' force.
P: You are describing a completely new way to explain the same concepts that are currently accepted about motion, distance, time lapse and force. But the new way still satisfies all of the scientific information which has already been proven by actual demonstration.
And all of this is based on a change in our prior arbitrary, unproved assumption that the units of measure for distance and time lapse are independent of the rate of motion of that which we desire to measure.
You have tied together two fields of science which were previously considered completely separate - involving the characteristics of motion of physical objects and the characteristics of electromagnetic waves.
In addition, it seems to me that you may also have hit upon an entirely new and extremely simple explanation for the concept of 'relativity'. A simple and logical explanation for a concept that up till now has contained several postulates that could only be documented in terms of imaginary mathematical equations that seemed totally illogical in terms of reality.
I need another break to think about all this some more.
P: We have discussed some rather amazing concepts during the past few days. But there seems to be a big problem with some of our reasoning. We have treated the concept of 'mass' as simply a force, rather than a unique physical reality in it's own right. That seemed to make sense in view of that which we were discussing. But if it were true, then the whole concept currently applied to astronomy and gravity would be flawed. That is because science associates 'mass' with an attractive force field that holds our solar system together, and also keeps us from falling off the surface of the Earth! DAY 6 - MASS, MASS ATTRACTION AND GRAVITY
S: Please tell me more about this currently accepted concept of 'mass attraction', Professor?
P: Well, mass attraction is a concept first presented in the fifteenth century by Isaac Newton. His thought was based on earlier work by Copernicus and Kepler which indicated that the planets all orbit around the Sun while the Sun remained stationary in space. Newton realized that for that to be true, the orbital paths of the planets would result in an outward 'centrifugal force' that would cause the planets to fly off along a tangent to the orbital path. Since there was no other recognized inward 'centripetal' force to counter balance that outward 'centrifugal force', Newton postulated that a new type of unrecognized force must exist. He called that unrecognized force 'mass attraction'.
S: How did Newton know that a centrifugal force existed on the planets? And how did he determine the magnitude of that force?
P: Actually, he only assumed that the centrifugal force existed. That assumption was based on mathematical equations that can be used to show that as an imaginary point moves through an arc around an imaginary center point, that the equation needed to define the path relative to the center point is equal to the square of the tangential velocity divided by the radius of the arc. This is shown by in equation form as V^2 / R.
Newton realized that the dimensional factors associated with that equation resolve down to 'distance' divided by 'time squared'. That is the same combination of dimensions used to describe the acceleration of an object moving along a straight line. He also was aware that when physical objects accelerate along a straight line that the unbalanced force causing that acceleration is directly proportional to the weight of the object on the surface of the Earth.
He had previously created the word 'mass' for the mathematical equation of weight divided by acceleration which resulted in the equation that 'force' equals 'mass' times 'acceleration' (F = MA).
Newton postulated that the same relationship must exist for mass and that same combination of factors that equated to orbital motion, but in the case of orbital motion, the force would be directed radially outward rather than being aligned with the direction of the linear motion. He referred to that as 'centrifugal force'. Which indicated that the outward radial force acting on a planet in orbit around the fixed Sun was also F = MA or F=M(V^2 / R). Newton concluded that an unbalanced force of magnitude MV^2/R must exist on the planets which would result in them flying off along a tangent - rather than remaining in orbit.
He concluded that the magnitude of the unbalanced centrifugal force existing on the planets was equal to a mathematical value equal to MV^2/R.
S: But professor, we agreed during the first day of our discussions that that the concept of 'dimensions' being associated with numbers does not represent a reality, but simply a descriptive suffix needed by man to define the referenced magnitude of the fixed unit of measure being referred to.
P: Yes.
S: Well then, why did Newton decide that the 'dimensions' of a truly dimensionless number used to describe linear acceleration must be extrapolated to the concept of orbital motion? That seems to me like saying that if the name of one person is Adam, then that same name must apply equally to all other persons. It is obviously illogical.
P: Perhaps. But it did seem logical to Newton at the time he postulated his theory of mass attraction. What Newton did after he had postulated that an unbalanced centrifugal force must exist on a planet in orbit about the fixed Sun was to postulate that that unbalanced force must be counterbalanced by some other unrecognized centripetal force. And that the planets therefore remained in orbit because of a balance between centrifugal and centripetal forces. He named that equal and opposite centripetal force 'mass attraction'.
S: Then Newton advised that the magnitude of the centripetal force was equal to the centrifugal force or MV^2/R also?
P: Well not exactly. He postulated that the magnitude of the centripetal force was defined by another equation that was represented by a new constant times the product of the mass of the Sun times the mass of the planet and divided by the square of the distance between the Sun and the planet. In mathematical terms this equation was written as F = GMm / R^2.
S: Why not simply F = mV^2/R ? How could he define one force in terms of the rates of motion and the other equal but opposite force being independent of motion?
P: Boy, you certainly do pose some difficult questions! I don't know why Newton did it that way, but he did. And we simply do not question what Newton did after accepting it without question for over four hundred years. You asked me to tell you what science is, and I am simply trying to answer your question. I did not know that I was going to have to justify the currently accepted concepts when we started this discussion.
Lets quit for today, and we will try again tomorrow.
P: You brought up more questions than I was able to answer yesterday. That tends to frustrate me because in all the years that I have been teaching science these questions have never occurred to me before, nor have any of my very best students posed such questions in the classroom. DAY 7 - AN INTERLUDE OF PHILOSOPHY
My first reaction to that frustration is toward anger at you for not simply accepting what I say without question. It has been in response to that tendency to anger that I have terminated some of our daily discussions.
But afterwards, when I reflect on your questions, and my own tendency to anger, then I begin to realize some important insights. There is a major difference in the environment of the formal classroom and here in our study. In the classroom, many students simply accept whatever they are told because they are more motivated to pass the course than they are in doubting what I say. This is a habit they have learned after many years of schooling. And I, as the learned expert, not only expect that student response to my authoritarian position as a professor, but I encourage it because it gives me a kind of sense of power over the students.
By the same token, as I look back at my own years as a student, it occurs to me that I also was more interested in getting high grades than in expressing doubts about what the professors were telling me in the classroom. I prided myself on memorizing the lessons so that I could obtain high grades. And when the high grades were obtained, it gave me a kind of satisfaction and pleasure that prompted me to go ever forward in the formalized school system. Until eventually I became the professor rather than the student. And now, as the professor, I proudly parrot back all that I memorized without question to the new generation of students.
I now suspect that this same cycle of education has gone on for many generations, with each successive generation of professors parroting what every he was told by the prior generation. It is only when a very unusual student - such as Copernicus, Galileo, Newton, or Einstein - comes along that the prior parroting oof lessons are modified in favor of new scientific concepts. If and when those very unusual students become accepted as having knowledge greater than their instructors then the concept of science undergoes a major change. And the entire process of education continues along that modified line of thought until another truly unusual student once again gains recognition.
You, my boy, may have the characteristics of just such an unusual student. But we should anticipate a very difficult time if we hope to promote your thought over the currently accepted educational dogma. For mankind has never tended to accept paradigms involving new thoughts about currently accepted beliefs. In ancient times, men were jailed and even burned at the stake for professing new thoughts. We may no longer be burning educators at the stake, but society truly does tend to crucify such educators through use of ridicule, political and social expulsion.
We must each decide if we wish to continue in our search for new knowledge at the expense of such ridicule, or if we prefer to take the easy path of acceptance without question.
I must be honest in telling you that while I find the search for new knowledge that you are taking me to fascinating. But also that I lack the courage to give up my current prominent position as a well paid professor in order to attempt to promote the new knowledge.
You, in your optimistic youth and enthusiasm, may choose to continue in your pursuit and presentation of advanced knowledge. It is entirely your choice. But it is also only fair that I warn you about the potential difficulties you will encounter.
I want you to think about this overnight, and we will continue with our discussion of science tomorrow if you wish to continue. If we do continue, then I will try to help in your pursuit of new knowledge, but will not help in making that knowledge available to the public. If we do not continue, then I would welcome you as any other student in my public classrooms where I can teach you more about currently accepted scientific concepts - even knowing that they may be based on false premises.
Go now and reflect on what I have said today. If you choose to return to my study tomorrow we will continue our pursuit of new knowledge. If not, then let me congratulate you on your exceptional capacity, and I look forward to seeing you in my pubic classroom.
S: Thank you, Professor, for sharing this with me. I very much appreciate your honesty, and will indeed give this consideration before we meet again.
S: Professor, I would like to continue our discussions even though it may not be socially or politically wise. Will you continue to help me in gaining understanding about science? DAY 8: CELESTIAL ORBITS & MASS ATTRACTION - PART 2
P: Yes I will. I was in hopes that you would return today. I have made some notes summarizing our prior discussions that it might be helpful to review for starters.
You have recognized that all measurements are actually pure dimensionless mathematical numbers because a measurement is always obtained by means of a mathematical ratio of identical type dimensions which are self canceling. The current practice of adding dimensional suffixes to those pure numbers is only to verbally clarify the type of observation of current interest. Because of that, the entire scientific concept that we currently refer to as 'dimensional analysis' may be questionable.
You have recognized that the concept of fixed pre-defined magnitudes of measure that we call the 'units of measure' has never been questioned - even though there is no valid experimental proof that such an assumption is valid. You pointed out that that concept has already been ignored in the scientific field of electromagnetics wherein the fixed units of measure for time and space have been replaced by a concept of variable 'wave lengths' and 'frequencies' which result in constant values for the mathematical ratio named 'velocity'. And, as you pointed out, if that same concept of measurement was applied to the motion of physical objects, then it would be impossible for the value of velocity to vary because 'velocity' would be independent of the actual rate of motion., and the concepts of unbalanced forces and acceleration would be invalidated.
You have pointed out that the currently accepted concept of an 'unbalanced force' is obviously false, and that the factor named 'mass' is simply the equal but opposite force that must coexist with each and every 'unbalanced force'. As a result the net force can never vary from zero, and the ratio of force to mass must be 1.0. As a result, the factor named 'acceleration' when associated with the currently accepted equation of F=MA can be indicated from F/M = A to represent the magnitude of 'stress' existing at the location where the equal but opposite force and mass meet and combine to zero net force.
And finally, you have questioned the logic used by Newton when he postulated the concept of 'mass attraction' being independent of motion even though he created that concept in order to counterbalance a centrifugal force which is dependent on the rate of motion. It was at that point that I last broke off further discussion about scientific considerations.
S: That is a good summary, Professor. I went to the library after we met yesterday to study the work of historically great scientists that you named during our philosophic discussion yesterday. You mentioned Copernicus and Kepler. According to the books in the library Copernicus discovered that the universe does not rotate around the Earth as the authorities of his day insisted. It was he who the church authorities imprisoned?
P: Yes. And it was Bruno who they burned at the stake for the same reason.
S: Well, Copernicus advised that the Earth and other planets revolve in circles about a fixed Sun. And it was Kepler who advised that the orbital paths were elliptical rather than circular.
P: Yes.
S: Professor, why were these thoughts of Copernicus and Kepler so upsetting to the authorities? Obviously the actual motion of the Sun and planets did not change just to agree with what Copernicus and Kepler had postulated. These were not great discoveries at all. They were simply changes in the mathematical equations used to describe the orbital paths. And the mathematical equations changed only because the location of the imaginary coordinate system on which the equations were based was mentally relocated by Copernicus and Kepler. The authorities wanted to base the equations on a coordinate system centered on the Earth, Copernicus wanted to base the equations on the center of the Sun, and Kepler wanted to base the equations of motion on an imaginary point in space referred to as a 'focal point' of an ellipse.
Based on the assumed location of the coordinate system, all three concepts were equally correct, and there was no significant 'discovery' made by anyone. It was all just a mathematical game and misunderstanding about the difference between reality and mathematics.
P: Oh my heavens! Son, you have done it again! You are absolutely correct. If we moved the coordinate system to the north star, we could come up with still another set of equations. That would not change realty one bit - but might be considered as the same kind of great discovery that Copernicus and Kepler made.
S: The books indicated that Newton went on to develop his postulates (now 'scientific laws') based on Kepler's concept of elliptical orbital paths of the planets around a fixed Sun. But then later on Newton observed that the when two celestial bodies are in orbit, both bodies move in circular orbits at a common rate of rotation around a common center of rotation.
P: Yes.
S: Well Newton said that the common center of rotation for mutually rotating celestial bodies is located along an imaginary line extending between the two mutually rotating celestial bodies. And the ratio of the radial distances of the bodies from the common center of rotation was equal to the inverse ratio of the 'mass' of the two bodies.
P: I'm not certain that Newton explained his observations in those words, but that is a correct interpretation of his observation. I think Newton may have referred to the common center of rotation as the 'center of gravity' for the combination of the two masses when they are treated as one single celestial system. It boils down to the same thing you say. In fact, there are three different ratios with identical mathematical values involved. Because the angular rate of motion is common to both bodies as they rotate around a common center, the ratio of the radii must be equal to the ratio of the tangential velocity, and also equal to the inverse ratio of the 'masses'.
S: Right. And as a result that concept that you referred to as a 'centrifugal force' which was defined as F= MV^2/R must be identical for both of the two mutually rotating celestial bodies. But because the bodies are on opposite sides of the center of rotation, the centrifugal forces are equal in magnitude, but opposite in direction.
P: True
S: Well, don't you understand, Professor? If the centrifugal forces are equal but opposite in direction, then that is the source of the centripetal force that Newton was searching for when he created the concept of 'mass attraction'.
There was never any need to create a new force of mass attraction, because the centripetal force that Newton was searching for already existed. The Sun is not fixed in space as Copernicus and Kepler had postulated. The Sun is in mutual rotation with the planets! It may be true that the center of rotation of the Sun to planet combination is much closer to the center of the Sun than it is to the Earth - but only because that resistance force that Newton called 'mass' must be much greater for the Sun than the planets. But the Sun does move. It is not stationary as Copernicus, Kepler, and then Newton all postulated. But more importantly, Newton's concept of 'mass attraction' is simply unnecessary.
The force that Newton called 'mass attraction' is not a variable value between the Earth and Sun, but is a line of constant tensile force acting along the imaginary line between the Earth and Sun, and which is balanced to zero net value at the common center of rotation.
The effect is exactly like that which is currently referred to as a 'tensile' force in a balanced physical flywheel spinning around a mechanical axle. We may not be able to see that two body flywheel, or the line of tensile force between the celestial bodies and the center of rotation - but it is much more real and explainable than the concept of a variable and invisible force field of 'mass attraction' that Newton postulated.
P: Oh my, oh me. Oh for heavens sake. Lets break for the day. I really need to think about this some more. To tell a professor like me that Newton's concept of 'mass attraction' is false is very much like telling the Pope that God does not exist!
P: Good morning once again. OK. We have concluded that the concept currently referred to as 'mass' is simply an equal but opposite 'force' which must coexist with any 'unbalanced applied force'. In which case the concept currently referred to as 'acceleration' is simply a 'stress' which exists at that point where the force and mass meet. DAY 9: REALITY
How do we account for the concepts named 'momentum', 'work', and 'energy' when there can be no unbalanced force?
S: Well, remember the other postulate that the units of measure for time and space are directly proportional to the actual rate of motion of an object, rather than being pre-defined fixed constants which are independent of the rate of motion. Recall that this is the same concept already used in the science pertaining to electromagnetics where the 'velocity' of a wave or photon is constant because the variable terms 'wave length' and 'frequency' have replaced the fixed concept of 'distance' and 'time lapse.
As a result, the mathematical value of the ratio named 'velocity' is not actually related to the reality of the actual rate of motion of an object - be that object called a 'wave' or a physical object.
P: I remember.
S: When the factor named 'unbalanced applied force' is zero, then so too is the equal but opposite force named 'mass'. Stress is zero or non existent. The rate of motion of the object remains unchanged, and therefore the unit of distance as well as the actual distance of travel per unit of time remains unchanged. In short no work is being performed when this condition of constant rate of motion exists. Nor does any 'stress' exist when both the forces are zero. This condition corresponds to a lack of the concepts currently referred to as 'work' and 'energy', and the magnitude of the concept referred to as the 'momentum' of the object of interest remains unchanged.
P: That zero force would correspond to the currently accepted concept referred to as the 'conservation of momentum'. That value may differ for different objects, but for any specific object (where the 'mass' is currently considered to be constant) the magnitude of the change in momentum is directly proportional to the actual change in the rate of motion.
S: Right. When both the applied and resistance forces are zero, the object is not stressed, there is no change in the rate of motion, so the values of associated with work and energy are zero, while the value associated with momentum is proportional only to the actual rate of motion.
P: There is a point that needs to be made here however. When we speak of the applied force and equal resistance force in this situation, the magnitude of the values must include all forms of the resistance forces. That would include not just the unexplained portion of the force we attribute to a change in the rate of motion, but also the otherwise defined portion of the force that we attribute to concepts such as friction, viscosity, and drag. For if we did not include these later forms of resistance force, then even when the rate of motion was unchanged, the work and energy factors would exist in proportion to those recognized factors of friction and viscosity and drag.
That's interesting, and it's important. When we speak about the balance of 'applied force' and it's equal but opposite resistance force of 'mass' we must be sure to include all those recognized forms of resistance force as well as the factor currently referred to the 'unbalanced' part of both the applied and resistance forces. Science currently associates only that 'unbalanced' part of the total applied force with mass, momentum, and acceleration.
S: Now, let's look at the relationships when the factors named 'applied force' and resistance force (or 'mass') is any magnitude greater than zero. The currently perceived concept of an 'unbalanced force' still does not actually exist. But now the object is 'stressed' by the equal and opposite force and 'mass' factors.
The actual rate of motion of the stressed object will change, and the magnitude of that change will be directly proportional to the magnitude of the stress.
As the rate of motion changes, the relative units of measure for both distance and time lapse change in direct proportion to that change in the actual rate of motion. The mathematical ratio named 'velocity' however continues to remain constant.
The factor currently named 'momentum' for any object of interest increases in direct proportion to the change in the rate of motion. By the same token, the factor currently referred to as 'work' or 'energy' does now have a value, and that value is directly proportional to the change in the actual rate of motion - which is of course directly proportional to the change in the relative units of measures for both distance and time lapse.
P: Go on.
S: The factor named momentum is just a different name for the magnitude of the actual rate of motion - which is the same as the magnitude of the relative units of measure for both distance and time lapse.
The factors named work and energy are just different names for a change in the relative rate of motion - which is the same as the change in the relative units of measure for both distance and time lapse, as well as the magnitude of the existing 'stress'.
The actual magnitudes are all independent of the concepts of 'unbalanced force' and 'mass', but are all mathematically proportional to any actual 'stress' and resultant change in the relative rate of motion of that object to which the factors are attributed.
The reality is very simple. But the simplicity of that reality was been clouded by currently accepted science because of the original unproved assumption that arbitrarily chosen units of measure are independent of the actual rate of motion of that which is being measured.
Because of that clouded reality, science has created many false concepts involving unnecessary complicated mathematical equations which have been given special names. And then those imaginary names have been falsely assumed to represent the simplicity of the actual reality.
P: Wow! It would seem that we need to re-define all of the theoretical physical science which has been developed since the fifteenth century. And it all goes right back to recognition that the arbitrarily pre-defined fixed units of measure for distance and time lapse should have been defined as being variables which are directly proportional to the rate of motion of that which is being measured.
S: That's right, Professor. And when we recognize that the units of measure are directly proportional to the actual rate of motion of current interest, then for each specific object of current interest, the change in value for every equation and special name that has been generated in the name of physical science turns out to be identical in actual significance and mathematical value to that one single factor involving the actual relative rate of motion of the single object of current interest.
The concepts currently referred to as 'unbalanced force', 'mass', work, energy, and torque are insignificant when there is no change in the actual rate of relative motion. And when the change in actual rate of motion occurs, then the concept of 'mass' is simply the equal but opposite resisting force which must coexist with that 'unbalanced force', which demands that the values of momentum, work, and energy are simply mathematical identities to the magnitude of the resultant stress.
Different locations, as defined by 'objects' of current interest, may have different magnitudes for these factors. But at any specific location every factor will be mathematically identical to all the other factors.
If the ratio of the difference of any one specific type of perception for any two different locations (or objects) is perceived, then that same ratio automatically applies for every other pair of like characteristics for those same two different locations.
Furthermore, the magnitude of all currently accepted measurements for theories about physical science are totally dependent on the arbitrary selection of the location of that point in space which will be defined as the fixed center of the coordinate system on which measurements of distance, time lapse, and rates of motion are based. That is the real significance of relativity.
As a result even the comparative ratios between two different locations or objects is not an absolute factor, but only a relative factor which is totally dependent on the assumed location selected as the center of a coordinate system used to determine the magnitude of the measures for distance and time lapse.
There are no absolute values in nature. There are only ratios of relativity which apply as the result of man's arbitrary selection of a coordinate system which should be used as the basis for measurements.
P: This is utterly fascinating in it's total simplicity. Time for another break. Let me compare all of this to some other currently accepted concepts that we have not yet discussed. There have been other radical changes suggested in more recent times since that of the time of Newton. These are referred to as the 'special theory of relativity' which has been closely associated with a man named Einstein. I want to study if and how your thoughts apply to that.
P: Most of what we have discussed before today has applied directly to science that was developed before the twentieth century, and generally categorized as 'classic physics'. About the start of the twentieth century, a new concept in physical science was developed. The new development was generally categorized as 'relativity'. DAY 10: SPECIAL RELATIVITY
S: Ohhh. That sounds very interesting in light of our prior discussions..
P: Yes. And it is mainly because of your continued use of that word during our prior discussions, that you have held my interest.
The new theory of relativity continued the prior practice that the units of measure for time space and force remained independent of the rate of motion of objects, but postulates that the actual magnitude of that being measured in terms of those fixed units is proportional to the relative rate of motion of the object of interest.
S: Sounds very similar to my thoughts wherein the relative magnitude of the units of measure themselves change, but the actual number of units of measure remains unchanged?
P: But there is one major difference. In this currently accepted concept of relativity, it is postulated that a maximum possible rate of motion exists. That maximum rate is referred to as the 'speed of light' in a vacuum type environment.
A mathematical equation was presented by Einstein indicating that as the rate of motion of a physical object increases, then the values assigned to distance, time lapse, and 'mass' all change at a variable rate. When the rate of motion is low, the rate of change in the distance, time lapse, and mass is almost insignificant. But when they object approaches the speed of light, the rate of change becomes very rapid. The magnitude is then asymptotic to either infinity or else vanishing to zero. And at the speed of light, the characteristics of the physical object change completely and assume the characteristics associated with electromagnetic waves and photons. Having assumed the characteristics of electromagnetic waves, it is of course impossible for the rate of motion to increase farther - for the reasons we have already discusssed in some detail.
In order to bring that theory into conformance with prior scientific concepts, it was necessary to redefine the older classical concept of 'mass'. As a result the old concept of mass that was originally postulated by Newton was revised and referred to as 'inertial mass'. But then a new definition for mass was that mass is actually a combination of 'inertial mass' and 'relativistic energy'. This theory postulated that the inertial mass increases to infinity just below the speed of light, but is instantaneously converted into pure energy with zero remaining inertial mass exactly at the speed of light.
This new theory provided a means to comply with the old concepts as postulated by Newton when the rate of motion was low, but then to comply with the newer concepts which had been developed to explain electromagnetic science.
S: That sounds very confusing and complicated. How did they know that the fastest possible rate of motion was that 'speed of light' value?
P: Well, that was not actually known. It was just assumed because it was thought to be the fastest thing in the universe at the time the theory was postulated. That thought is currently under very serious question today as the result of recent laboratory experimental work. It appears that some very small objects actually do move faster than the speed of light.
S: How can an object have an infinite 'mass' at the speed of light minus 1, and go to zero mass at the speed of light plus one?
P: That was not actually demonstrated by experiment, but was simply assumed and then postulated through use of an imaginary mathematical equation. Also, as I said, it required a redefinition of the older concept of the word 'mass'.
S: Well, Professor, it has been you who has been tempted to walk out on our prior days of discussion. I must admit that that same feeling is beginning to come to me. That currently accepted concept of relativity sounds totally ridiculous to me! It seems to be based on imaginary mathematics and the creation of new words to fit the nonsensical mathematics.
Lets take our break here so that I can check some things out at the library. OK?
P: (Chuckle). Sounds like a good idea.
S: As best as I can determine, that concept of special relativity was initially headed in the right direction, but completely missed the boat when it overlooked the concept of relative units of measure in favor of a concept of relative magnitudes of reality. The introduction of a maximum rate of motion was a complete fraud which had nothing to do with reality, but was simply an attempt to pull two flawed and contradictory schools of thought about physics and electromagnetics together. That whole concept was not about a search for understanding about natural reality, but rather was only an attempt to justify a bunch of prior errors. DAY 11 - SPECIAL RELATIVITY & QUANTUM THEORY
The concept simply added more confusion to that which already existed!
If the scientists had simply recognized that the original unexplained assumption that units of measure are absolutely independent was in error, then not only would the errors of 'mass' and 'mass attraction' introduced in classical physics have been recognized, but the other concepts of classical physics would have been adequate to encompass the problems that theory of special relativity was attempting to resolve.
There would have been no need to postulate a maximum 'speed of light', and the concepts of physical and electromagnetism would have meshed automatically as soon as it was recognized that the concepts named 'wave length' and 'frequency' represented nothing other than a concept of relative units of measure that justify a constant mathematical value for the imaginary equation named 'velocity'.
P: Wonderful. You have just expressed the very same thoughts that have been haunting my mind for several days. I'm sure that we are right, but remember my warning about what happens to those people who would dare to present an entirely new concept to the public. We may have stumbled into a new source of knowledge that others would prefer to have us 'burned us at the stake' rather than to attempt to understand.
While you were at the library searching for information about the currently accepted concept of special relativity, did you also come across the concept of quantum mechanics?
S: Yes, I did. But I was so excited about the relativity nonsense, that I did not take time to pursue that concept of quantum mechanics. Can you give me a quick outline of that concept?
P: Gladly. It was developed about the same time that Einstein was postulating his own theory of special relativity. Based on laboratory experiments, it was observed that when radiated energy is transmitted it did not occur in a completely smooth analog fashion. Rather, the transfer of energy occurred in very very small steps. And the amount of energy associated with each step was referred to as a 'quantum' of energy.
The theory was then postulated that the amount of energy associated with one quantum was proportional to the electromagnetic 'frequency' associated with that unit of quantum. As a result, the magnitude of energy of referred to as a 'quantum' is a variable having a mathematical value equal to it's frequency times a constant mathematical conversion factor. The constant conversion factor was named 'Planck's Constant'. And that relationship between energy and frequency was shown in mathematical terms as E = hf where h was the Planck constant.
This new theory worked very well to explain some new concepts about the arrangement and behavior characteristics of tiny objects called 'electrons' and 'atoms' which were then thought to form the basic building blocks for physical materials. However, the new theory did not work at all with the explanations of other new concepts about the motion of electromagnetic waves. There was a great debate among the scientists of that time about all the newly developing concepts and mathematical explanations given for those new concepts.
S: Here we go again, Professor. When we recognize that the word 'frequency' is just another way of expressing the concept of a relative unit of time lapse in inverted form, then that E = hf equation is actually a statement that E = the number of times that the value 'h' re-occurs during one predefined fixed unit of time referred to a one 'second' of time lapse. Then the value of energy, E, is simply the product of one single unit or step of energy (h) times the number of those units (f) that occur during one pre-defined fixed unit of time lapse.
The equation might then be interpreted as if that factor of 'h' being a universal constant applicable for all 'quantum' while the magnitude of energy was simply the result of the number of identical quantum that are measured during one second of time. In effect Planck's constant is that amount of energy that every quantum possesses (independent of the concept of it's frequency), and the frequency is simply the number of identical quantum that arrive at the sensor during one second of fixed time lapse.
The old problem of a confusion between different words being used for identical realities seems to be at work here - just as it was in the other scientific equations and explanations.
P: If what you have just said is true, then here in the quantum theory, we again find that the only significant reality boils down to the relative rate of motion of an object of current interest. That is because the rate of arrival of a sequence of quantum would increase in direct proportion to the frequency, and the distance between the individual quantum would correspond to the 'wave length' associated with the value referred to as 'frequency'.
The factor named frequency is not an actual indication of a variance in the magnitude of energy associated with each individual quantum, but rather is a reference to the number of identical quantum that arrive at a sensor during one pre-defined fixed unit of time. Planck's constant is therefore simply the mathematical value associated with the energy content of one single quantum, and that amount of energy is a constant which is independent of the word frequency.
In which case the differences, such as (sound tones, colors or heat, and radiation effects) that we now attribute to frequency is not due to the energy level of unique parts (such as quantum or wave properties), but simply due to the rate of arrival of identical quantum parts at the sensors which we use to record the amount of arriving energy. The higher the frequency the greater the arrival rate of identical units of energy, and every single unit of energy is simply that value referred to as Planck's constant.
Very interesting. Let's think about that a little more. Tomorrow I want to discuss one of the problems that lead to the arguments between the scientists when the quantum theory was first presented. This argument revolved differences observed in motion of objects and the motion of waves.
P: A big problem has been encountered in laboratory experiments involving differences in the motion of physical objects and 'wave motion'. When a physical object is in motion and encounters another physical object which is fixed in space, then the forward motion of the moving object is either blocked entirely, or else both of the objects ricochet off in a manner that is attributed to a sharing of the original momentum of the moving object. This is similar to the interaction of a baseball when it encounters a baseball bat. DAY 12: - MOTION OF OBJECTS AND WAVE FRONTS
But when wave motion is obstructed by another physical object, then the wave behaves differently. This is currently attributed to the wave acting like an entire line of parallel moving physical objects, which is called a 'wave front'. If the entire wave front encounters a solid wall, then the behavior of the wave is reflected backward: that is not too much different than the behavior of a physical object, such as the baseball meeting the bat. In this format, the wave is said to have been reflected by and from the obstruction.
When the wave motion is wider than the obstruction however, then portions of the wave front on each side of the obstruction move on past the obstruction. And those portions that do move on then tend to spread back out again and form an entirely new and complete wave front. This behavior is referred to as refraction of the wave.
How can we explain that difference in behavior referred to as refraction?
S: I understand what you are saying, Professor. I went to the library again last night and read through some text books sections that discussed the reflection and refraction of wave motions.
It seems to me that when we refer to the motion of single physical object, such as the baseball, the entire activity involving that motion is consolidated, and the path of the motion is therefore one single straight line.
However when we refer to the motion of a 'wave', we are no longer referring to the motion of a single isolated object, but rather to the motion of the entire environmental medium through which the 'wave' is perceived to be moving. And it is the motion of that entire medium that becomes the subject of interest. A wave should not be thought of as a 'thing' unto itself, unless that 'thing' is actually the entire environmental medium which consists of a whole ocean of individual parts rather than one single consolidated object.
The characteristics of the environmental medium therefore determines the characteristics of 'wave' motion. Perhaps this is best illustrated by the mathematical equations which have been postulated to represent the motion of waves when the medium changes. There is one equation used to explain wave motion along the solid linear string of a guitar, another to explain wave motion of sound through air or water, still another equation to explain light waves.
The equations all appear to be quite different. However, that difference is not in the basic thought presented in the state of motion, but in the exponent of the number used to express the magnitude of the length associated with the units of a force and mass. For example, the velocity of wave motion along a guitar string is expressed as a function of force divided by the 'line mass' of the string. But the velocity of a sound wave is expressed as a function of pressure and density; in which case the factor of distance associated with line mass (in the numerator) has been changed to the square of distance associated with 'pressure' while the factor of 'line mass' concept has been changed to the concept of mass density (in the denominator). Both the numerator and denominator have both been modified through an increase in the exponent of the distance factor, and given new names. That added exponent is self canceling from both numerator and denominator, so that the resultant relationship is actually identical to the equation used to define wave motion of the guitar string. Similarly the equation used to explain the rate of motion of an electromagnetic wave involves newly defined words for conduction and resistance of the medium that can be reduced right back to simply force and length with exponents of one.
The transformations may seem difficult to recognize when looking at the descriptive part of the equations, but that transformation is obvious when we look at the other side of the equation which always boils down to simply 'velocity' of the moving waves.
Here once again, the differences are not in the actual reality that is of interest, but only in the unnecessary complications that science has introduced through faulty understanding about the underlying simplicity of that actual reality. It is almost as if the scientists were trying to make things seem much more complex than nature really is. Failing to see the simplicity, the scientists simply create more words and equations that duplicate the meaning of other words and equations that were previously accepted.
P: But how does that change the experimental demonstration of differences between the motion of a single physical object and a 'wave'?
S: Because the wave is not motion of one single consolidated object. It is motion involving many separate objects - all the objects that combine to make up that which we refer to as the 'environmental medium' through which the wave is moving.
If you were to throw thousands of baseballs and in every direction at one time, then that combined family of baseballs would take on the same kind of characteristics that we currently attribute to a a wave front. Especially if the environment in which the thrown baseballs moved consisted of an otherwise stationary sea of widely spaced similar baseballs. As the thrown baseballs struck the environment of stationary baseballs, obviously the resultant motion would involve some of the thrown baseballs bouncing back toward one another on the far side of a partial obstruction.
It might help clarify this if you think of the thrown family of baseballs as being red in color and the stationary environment of widely spaced baseballs being white in color After you throw the family of baseballs then watch only the red ones while ignoring the white ones. The red ones make up a 'wave front' that is reflected and refracted just as we currently envision electromagnetic waves to do.
P: All right! That all seems very logical. But again, lets take our break so that I will have time to reflect on these new ideas.
APPENDIX
CALCULUS MADE SIMPLE
GEOMETRY MADE SIMPLE
LOGARITHMS MADE SIMPLE
ORBITS MADE SIMPLE
SIGNIFICANCE