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These statements are general and as scarce as possible.
For example :
It is " the experience of observing the small scale patterns of motion( rotational) leading to a resultant large scale motion " that is labelled duration. Thus it is an experience, a specified one, that is labelled duration.
Before I quantify inertia I must identify what I am experiencing and thus labelling inertia.
The process of quantification involves establishing and agreeing a common standard for all relevant experiences. It is an inductive refining process that eventuates to an agreed standard object or behaviour as a measure or Metron.
For example eventually the behaviour of a pendulum came to be set as a standard for a Period, and later set to determine the second. Now of course we use the more complex decay period of excited caesium " atoms" and we count the number of emissions in that decay!
Despite its obvious complexity it is still an experience of observing a large scale pattern develop from smaller ones
It behaves me to establish a development of them so as to guide any reader through a method or system of synthesis using them .
Currently I am working through Justus Grassmanns pamphlet " To the purchasers of Mathematical and a Natural (Things)", as a precursor to finishing Hermanns work on finding Quaternions in the Ausdehnungslehre.
I believe once I have completed that project, when I return, then, to the 1844 Ausdehnungslehre I will be able to develop a detailed Doctrine of Thought Patterning expression of the above that will be replete with labels and symbols accessible to the mathematical physics community.
But I refer you to professor NJWildberg for a detailed reconstruction attempt of mathematics using robust physical and data types .
In short ,yes I think I can but not at this specific moment in time.
Take two balls of the same size - one is made of gold the other is made of aluminum. We all have an intuitive notion of inertia, i.e. before we even get to the difficult task of quantifying this notion, we can tell that one object has more inertia than the other. For example, we all know that the gold ball has more inertia than the aluminum one. I repeat, we have not defined yet how to measure inertia but we have no doubt whatsoever that the gold ball has more inertia than the aluminum one. Note also that we firmly believe that the gold ball has more inertia than the aluminum one whether the balls are located on the surface of the Earth, or in the open space far away from the Earth, or the balls are in freefall.
Now, if someone offers a schema for quantifying inertia that contradicts our unshakable conviction that the gold ball has more inertia than the aluminum one, then we, naturally, will reject that schema. Wouldn't you agree?
Now hang each of the two balls on a thread of its own of the same length, i.e. make two pendulums, which are identical except the bobs are made of different materials, and measure the inertia of the two balls as you have suggested: "The quantity of motion has a transfer duration which is a measure of inertia", and compare the measures you get.
Your way of measuring the inertia leads to the conclusion that the gold and aluminum balls are of the same inertia! Therefore we have to reject your schema.
I am not even going to the additional difficulties you have introduced by linking your "Metron" for inertia to gravitation. What if the pendulums are in free space, or in freefall?
Simply I do not accept it.
You may ask why, and I may give many reasons , but at the heart of any discourse is " Aitema" . Sometimes mistranslated as axiom, but better understood as demands Or more supplicantly as a postulate. The art of rhetoric Erin's ith begging for common terminology and a common starting point..
That being said I do not accept that we all intuitively know what inertia is. I hope that we have enough life experience between you and I that you can give good experiences by hich you can illicit from me a response that convinces you that I am identifying the same experience you are.
I have seen demonstrations in whichn an aluminium mass falling through a magnetic field behaves differently, to one in a weaker, supposedly, magnetic field. I have not seen similar demonstrations with gold.
I have seen people struggle to lift gold, but I have also seen them struggle to lift aluminium.
Of course I u dear stand that your experimental design is based on the volume of the materials, but in determining that volume it is usually remarked that the density of the materials is differing! So now is inertia that "we" all know really what "we" all refer to as density?
The question is rhetorical because my point is that I can not intuitively tell you what you mean by inertia.
As to the pendulum, my point is that historically we start with this dynamic structure in the case of understanding the gyre of the gyroscope. If I recall, the large pendulum experiment that lead to the understanding that pendulums , all being equal, cn be said to swing in a plane came to this conclusion by assuming the earth rotated beneath the pendulums swing . This seemed to account for the observed pattern traced out relative to the ground over a known duration.https://en.wikipedia.org/wiki/Foucault_pendulum
Newtons conception of a measure for motion relied on the product of two notionally independent quanties : mass and velocity. These were associated to a point in space surrounded by a defined volume or bulk. The corpus or body was abstracted from the design in certain definitions, later the topology of the corpus was given some simple role in designing the representative formulation of the desired proportionalities.
Newton struggled to deal adequately with more complex fluid dynamical volumes, but his genius is evident in the robustness of his methodology. Using modern computing power we can make up for what he lacked. His conclusions on vortex dynamics for example are unsound , but the best he could do. He left it for future Naturally philosophers to do better!
So when Newton introduces the concept of inertia it is within a developmental discourse and built upon previous definitions of quantities and general Postulates, later called Axioms. There are linking Lemmas, side issues to consider, before he makes his main postulations and theorems. The conception of inertia starts off as a definition of a resistive force( vis) within matter ( insita) and it is a resistance to change. Newton himself associates it to density but as an allied property.
Thus the quantity of motion is foundational to Newtons postulation of an experience called inertia, but Newton was careful to identify all the matter "insita", and therefore capable of giving resistance to change, the consequences of inertia are therefore in Newtons method dependent on the complexity of the observed circumstance. . In addition, inertia is conceived as transferable by Newton, because the body at rest has one inertia , while that same body in motion has Differing inertia relating to the inertia of the colliding body that imparts change .
Newtons concept of inertia is relative , and properly underpins his notion of equilibrium . A system in say static equilibrium will exhibit no net " force" but immediately destabilised will exhibit stabilising forces or an inertial " force" to the change, insita!
I write only in regard to Newtons defined inertia, not to any intuitive notion or belief of inertia.
Your assertion/ prediction that your pendulum arrangement for measuring inertia using my schema gives the identical result is interesting to say the least ! If it does then that would be a cause for enquiry, not rejection .
You have not seen similar demonstrations with gold because gold is an expensive
material - not because gold would behave any different. In fact, the effect you are referring to would be more pronounced with gold because gold is a better conductor than aluminum is. Not to mention, this has nothing to do with the notion of inertia as defined by Newton, or with the intuitive notion of inertia as I have defined it above with the sled experience. So? I presume here that "I u dear stand" means "I understand". If so, then you understand it wrong. Reread my sled example above carefully, and you'll see that my intuitive notion of inertia has nothing to do with volume or with density.
Now you can tell what I mean by inertia - it is exemplified by sled experience and many other experiences of that type.
I am afraid you are confusing here Newton's notion of inertia with your own. It is hard for me to imagine Newton making such a confused assertion. But, to give you the benefit of the doubt, bring some quotations from Newton himself showing that your take on Newton's understanding of inertia is valid. Very well, let us do some enquiry. I predict that pendulum arrangement for measuring inertia using your schema will give identical results not only for gold and aluminum balls of the same size, but also for ANY two ball of the same size - no matter what material the balls are made of! Not only that, you can even use balls of different sizes - you still get identical results. Therefore, according to your understanding of what inertia is, all bodies - irrespective of their volumes, or materials they are made of - are of the same inertia!?
Jehovajah, now I am really worried about you! Are you ok, man?
I hope you too are well in this coldest part of the year.
Clarify for me what you mean by size, please.
Also, love the festive sled example! Imagine if it was ladened with presents for all the good children in the world ! Xxx
However the volume or the bulk of those presents intuitively leads to an expectation of greater exertion ! Imagine my surprise when I find it is as easy to accelerate as if there was only one present on the sled !
Or as another surprise, suppose I had one gold ingot on it., imagine my surprise if it was harder to accelerate the sled with that one present than with the great bulk of presents!
My first guess would be : that's inertia unrelated to volume or density!
But then my curiosity would lead me to investigate, and to in the course of my analysis , invent distinctions like volume nd density. Then I might say to myself :" the density seems to be the important notion in understanding ( sorry about the typo) the differing sensations of inertia. "
As for Newton here is a link
https://books.google.co.uk/books?id=lSoJ2tJKfIEC&pg=PA5&dq=Motive+newton&hl=en&sa=X&ei=3IzRU-zrO4ep7AbakoFQ#v=onepage&q=Inertia&f=false
Gold is a fantastic conductor, so I m told, but I would still like to see the demonstration .
Your prediction is intriguing . Do you have experimental results? Does size not matter? Fascinating .
At this stage I am inclined to diminish the electrical aspect of the theory of radiation in favour of a magnetic/ rotational description .
I thought that there might be a straight forward demonstration of measuring the electric and magnetic components of light, and their relative orientation, at least in the linearly polarised light case.
If there is one let me know.
The recollection I have is the measurement of microwave radiation , polarised , in which the magnetic and electrical components are istinguihed.
Here I assume the reading on the ammeter is a measure of the " electrical " component of the microwave. The emitter design produces polarised microwave emissions and the experiment defines linear polarisation .
When you are told that polarisation is defined in terms of the electric component, this is why. It is easier to use existing ammeters to measure signal response and associate that through existing theory to an electric component in microwave radiation .
So now is there a similar demonstratption for the so called magnetic component?
Based on radio wave theory the electric " field" dominates in the explanation. Measuring the electric field at a point in space on an assumed sphere is a reading of an ammeter or led, demonstrating a received broadcast signal. The magnetic component is effectively ignored for measurement, or calculated from the incident electrical reading.
So far no direct Gaussian field intensity measurements are forthcoming.
I hope you will not ask me to clarify for you what I mean by the words like thing, dimension, magnitude, big, etc. Send me a gold bar of the same size (see the meaning of the word size above) as that of the aluminum bar in the following demonstration:
We could even say that the pendulum period T varies with L only, for g is practically constant.
In this radiation and oscillatory phenomenon is depicted as a orthogonal combination of electric and magnetic components.
How this view emerged is romanticised around James Clerk Maxwell, but this misleads the enquiring mind.
William Kingdom Clifford for example took it upon himself before he died to demonstrate mathematically the undulatory mature of light. Faraday by experimentation demonstrated a connection between polarised light behaviour and magnetic material acting on a translucent material called lead glass . Malthus had discovered that Felspar was a material that diffracted light into two "polarised " rays or beams , and reflected light was found to be polarised..
Young and Fresnel and Arago worked to establish the mathematical "wave" theory based on sine curves as a depiction of a physical oscillation, neglecting the Cosine curve , and thus a physical rotation as a means of propagation, generation or initiation of the behaviours.
Volta,Örsted, Ampere, Gauss, Franklin ,Grimaldi, stand for the many people who contributed to the plethora of observations fed into the Royal Society regarding light and the effects of magnetic behaviour on it, or the effect of light on the needle of a compass .
So the heretical nature of light is an amalgam of many different observations I which the explanatory structure was concocted to give a wide possible interpretation and application to the observations.
The bivector ( E X H ) was eventually adopted as the most useful mathematical depiction of the related effects on measuring devices. This lead to the concept of orthogonally oscillating components which were magnetic and electric.
Originally the phase difference was depicted in the diagrams of this wave Ingram. Later the phase shift was removed and in phase magnetic and electric oscillations presented .
Since it was the electric signal that was used to detect the radiation the electric component was given preeminence.
Measuring the magnetic component was, is and usually is found o be very tricky,even today, the determination involves supetconucting materials, and statistical methods of analysis to determine a measure. As a consequence, the magnetic component is usually calculated from the electric signal so called.
I am still looking for justifications of this model more than simple assertions.
An analogicall demonstration of E X H
Some of these demonstrations reflect Ampères experimental investigations.
So I found the measuring equipment for these field effects are described as emf meters . They are designed to respond to electro magnetic fields of radiation from magnetic and electric sources. Those specific to magnetic fields use the Hall effect , to detect changes in a current, the others generally use a coil to detect alternating current fields/ regions of influence, thus they measure an induced current or current change.
My knowledge of radio transmission and microwave transmission is scant, almost laughably so! I don't mind admitting it as I am here to learn
http://www.lessemf.com/rf.html
It would appear that most broadcast signals are linearly polarized by the method of producing the transmission. To obtain a circularly polarised transmission a different transmitter and receiver arrangement has to be made.
Given this fact it becomes clear why net name are directional in the main, that is so as to gain the most from the signal falling on them, and why the reflection, diffraction of linearly polarized signals create reception/ receiver problems.
It is also the case that despite the theorists defining polarisation by the electric component, in practice it is the induced electric potential / current from the oscillating/ rotating Magnetic influence!
When that induction is read off against a Gauss scale we deceive ourselves into thinking we are detecting a physically different quantity, when in fact we are detecting the same physical behaviour, just reading it against a different scale.
The Hall effect detects a different physical behaviour, but still uses a change in current to calibrate against magnetic induction intensity.
Thus the reason the wave is structured as it is is to make the magnetic induction comply with the Fleming rules.
The receiver horn is said to be directed onto a crystal receiver . That is a very simple radio receiver but a profundity that reveals the disconnect in my thinking about electrical circuits.
So I startwithbŌrsted: he perceived that a rod with a battery attached established a dual vortex pair that were screwing opposite to each othe that is abc / emf against acb/fme wher the trip,ets lie in orthogonal planes that both contain m .
In addittion the vortices were connected to the surrounding environment by gaining or losing vortex " swirls" .
What Ampère did was to divorce the vortices from the surrounding swirls and to pace causality in the circulating " courantes" that themselves were moving in the rod as a whole. These currents were the electro dynamical cause of magnetic behaviour at the g
Ivan level of his inductive development of his model.
Thus both Ōrsted and Faraday looked for an external cause of magnetic and electric power, while Ampère and Maxwell sought an internal mechanism for a conductor.
That lightning was electricity in free space was demonstrated by Franklin and the earth was a magnet as supposed by Gilbert was not connected causally until Tesla, and even then hardly understood as fundamental.
Enid's school of thought was to demonstrate the consistent principle of a magnetic base to understanding this.
So the magnetic behaviour of the earth induces magnetic patterning in all sorts of maerials. Especially in the lodestone crystal and the organic amber crystal.
The lodestone crystal exhibited a dynamic polar mode caled magnetism. While the mere crystal exhibited a higher frequency polar mode calked dielectric
The dielectric was said to have capacitance, that is stored magnetic patterning that gave off sparks, while the Lodestone was said to have inductance , that is stored magnetic patterning that ephemerally changed.
The conductor was found to be dynamically changing its magnetic patterning and this was called an alternating current after Tesla pointed it out. But it is in fact a dynamically alternating dual vortex pattern.
The capacitor spread the dynamic pattern into and over an area. The wire guided the vortex pattern into a tubular structure that reciprocated between the two ends, the solenoid coil concentrated the vortex patterns into dipolar / bipolar inducting magnets that radiated it's unique magnetic pattern over and above the induced pattern from the earths magnetic "field. "
The chemical battery used the interleaving material to store more of the magnetic patterning just like the Leyden jar, and released it into the closed circuit to drive the circuits patterning above the induced natural background resonances.
On the larger scale the earths magnetic patterning is driven by the suns magnetic vortex patterns. But in free space with low density per unit volume of space the magnetic power I able and free to drive all interplanetary rotations, and our simple circuits can be tuned to pick out those magnetic variations that drive our solar system.
And yes I do find Huygens formula truly fascinating! At one time I thought it logically defined what time(T) is! But very quickly I realised it was a conundrum. The gravitational constant g has dimensions [M]/[T]^-2 . So dimensions of time appear on both ides of the Equation.
It was only much later that I understood the proportionality Relation that this is .
Then I grasped that all units are derived from proportions that have been standardised by agreements, including the electron.
Now I think I see the train of your thinking . Remember, you designed this particular experiment, claiming it used my schema .
What was my schema, as you understood it?
Lol! Xxx you would be welcome to it if I had it to give you, for you share with me your golden nuggets of thought and empirical data from actual experiments , for which I am grateful .
That these surfaces are dy amic at all scales is masked by a relativity of motion that is scale dependent, and which is only seriously addressed by the so called Rayleigh number of a material,fluid continuum .