Measurements, probability and statistics

In the world – there are visible formed shapes, structures (from atoms and cells to galaxies) – their appearance is always in probabilistic forms of their frequency distribution. Not only Gaussian curve but also other curves of distribution. There are common characteristic of species, or structures, or processes. After that there is a simplicity of mathematical models – to take out unimportant details, especially omnipresent chaotic behaviour – see noise versus „stabilized“ resp. renewed shapes despite the noise.
Mathematics predicts stable (invariant) base unit and and the relationships between them and the measured values. However, mathematics cannot be different by its very nature – the numbers 1, 2, 3, … , mark the sum of two equal (identical) values. Such mathematics cannot be mindlessly applied in the real world, where no two entities are the same and something is always changing. Mathematical equations are valid for an ideal world, a world with ideal given changes. For a world removed from Reality, i.e. a dead world. And that’s what everyone who tries to evaluate the world with this idol look like.  Mathematics is like language – only to direct us, to lead us to inexpressible and changing Reality. Nothing against equations, they are unmissable, but they must be subordinated to Reality and not vice versa.
The agreement of mathematical equations of idealized models with reality – see crank mechanism or pendulum. Likewise thermodynamics and many other examples. Many scientists were then literally fascinated by the mathematical possibilities which led them to explain or predict events in areas that could no longer be verified. See Archimedes, fascinated by the power of the lever to move the Earth. Which is theoretically and practically impossible.
Ideal models are valid, even 100% valid for given ideal conditions. The validity of the prediction is limited by the computational accuracy. So nothing against ideal models determining absolute temperature, the expansion time of the universe, or the position of the crank mechanism. One can take into consideration a real crank mechanism – determine (scan) the dimensions of the connecting rod, piston and other parts, determine the structures of the materials used, the locations of the greatest forces and thus the locations of breakage or wear. At the point of sliding movement – the greater the tightness the greater the accuracy but also the greater the wear and the greater the freedom in sliding the less the accuracy but also the worse the wear. Precisely because mechanisms, like all processes in the universe, are subject to wear. Even if we determine the point of highest wear, we cannot determine the exact location of the wear and its progression. It will always have a probabilistic course. In other words, a random, unpredictable element will enter into the idealized real mechanism, or predictable, but within a certain range. This range will be many orders of magnitude away from the original accuracy of the calculation (scan of dimensions, positions of interacting parts, etc.). Thus, the original high accuracy of the idealized real mechanism will be fatally broken. The accuracy of the prediction will be completely off in this case as well.

For an idealized crank mechanism from an ideal steel, we can predict for millions of years or billions of years with sufficient accuracy. It is not possible to predict the position of a real crank mechanism for x-turn, let alone for x-days or years. We don’t know what will happen. The same is true for all mechanisms. No two steels are exactly the same even if they are in the same category under the same code. The same code provides validity of mechanical properties to 98% or 99.98%, but these steels are very expensive. The greater the simplification from reality, the greater the illustration and clarity, but the shorter the validity of the prediction over time. Not to mention – weather forecast for ½ year or 10 mil. years. We know „exactly“ the weather on Mars, we „exactly“ know processes in the beginning of our universe, but we are unable to predict weather report more then several days. Not to mention so-called three body problem in mechanics.

Measurement and control is necessary in the real world- both in the case of the crank mechanism and in the case of all mechanisms and all natural processes in general. The extent of control, the possible states, the deviations, are determined by a detailed calculation, but they must be regulated. Without this, no technical process is possible. It is absurd, on the basis of idealized models, to predict the operation for hundreds of days or years, or in astrophysics for billions of years. Nothing against idealization and initial calculation, one has to start somewhere, but one has to know this and go further according to experience with Reality.

Measurement, probability and statistics

Where is the right value N? We are unable to measure directly right value N of something – diameters of balls or anything else. We are only able to measure a certain amount of values that, in effect, when plotted, resemble Gauss’s distribution curve of random errors. In other words, we consider the peak of this curve to be the right value N.

Measured values oscillate at interval N ± d over the right value N, which is irrational (see rational numbers oscillate around irrational ones to infinity) and, crucially, the indescribable right value N keep changing – it’s “alive”.
The prove – t
he Gaussian distribution curve also oscillates, slightly, through the time, when we take several sets of measurements of the value N – e.g. a diameter of a ball. We could say “Probability of probabilities”. We don’t measure all values at the same time, but we measure sequentially over time. Each value has its own time when it was measured. The measured values change – they oscillate with the frequency of their appearance according to the Gaussian curve of the frequency distribution of the measured values. Each value differs both in value and in the time at which it was measured. It cannot all happen at once for a matter where there is a difference between time and distance. That would not be matter then, but radiation, where there is no difference between time and distance.

Let´s go to the emission of light. E.g. the wavelenght N of emitted light from hydrogen atom. Specifically, the line spectra, so characteristic of each element from hydrogen, helium, through sodium, etc. The line spectrum needs to be taken realistically and not strictly mathematically. There is no ideal line without thickness in the world, just as there is no ideal point or ideal circle. Reality, then, is always a bit of a blur. It follows that our measurements are inaccurate. Nor is there an absolutely sharp scratch of the measuring instrument. Thus, even the so-called sharp line spectrum of emitted light has a very small yet fuzzy nature. It is best expressed again by the Gaussian distribution curve.

We will never measure two identical values at the wavelength level of light – see orange lines in an image below. Light is part of an ocean of quantum field full of random quantum fluctuations. Never repeatable. The idea for theory of dissipation or irreversibility. 

We take the distance between two peaks h of the two curves for the value of the “correct”  wavelength. It should be added that there is no exact value of the wavelength of light emitted, for this nature – a kind of blurism is inherent in the nature of real nature in and around us. So it would be better to no longer call this attribute, in the form of a mathematical notation and graph, the distribution curve of measurement errors. However, this is a natural characteristic of real nature.  We also don’t call the error the movement of molecules or we don’t call the error the range of the oscillating movement of the spring. Would we then call the movement of an elephant or a human in a restricted place the error? However, it is meant to sit in the middle and not walk at different distances from chair to room? Or shall we call pregnancy a disease?

It should be remembered that the calculation of Planck’s constant was done in the above mentioned way. The same way as the calculation of the gravitational constant or the speed of light. There have always been a range of accuracy in the calculated values. Now the calculated values were taken to be invariant. But in reality they are not constant in a changing world. The point is that simplification through the fixation of fundamental constants can bring later complications.
Certainly the logic of fixing the base constants is clear. The constant is fixed to a certain value and the other values change with a much larger tolerance range. This is exactly what makes this method misleading. Even a unit is subject to change and these changes (tolerance range) cannot always be included in derived or interacting variables. 

Resolution versus regulation. It’s impossible to regulate processes that we can’t distinguish. For regulation, we need a distinguishable impulse. The more precise the scale, the more precise the regulation. However, there is some regulatory limit, or limit of distinguishability, not only for optical instruments in terms of diffraction, or the thermal movement of molecules, but above all the fundamental law of quantum mechanics – the Heisenberg uncertainty principle.