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The Theory of Measurements

An Introduction

  18th September 2024

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"However, this divine rather than human science, which investigates the loftiest
subjects, is not free from perplexities. The main reason is that its principles and assumptions, called "hypotheses" by the Greeks, have been a source of disagreement, as we see, among most of those who undertook to deal with this subject, and so they did not rely on the same ideas. An additional reason is that the motion of the planets and the revolution of the stars could not be measured with numerical precision and completely understood except with the passage of time and the aid of many earlier observations, through which this knowledge was
transmitted to posterity from hand to hand, so to say."

-  Nicolaus Copernicus, On the Revolutions of the Heavenly Spheres.









"The quantity of matter is the measure of the same, arising from its density and bulk conjointly.

The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjointly."

- Isaac Newton, Philosophiæ Naturalis Principia Mathematics.


 











"Therefore two difficulties: (1) Can we transform psychologic time, which is qualitative, into a quantitative time? (2) Can we reduce to one and the same measure facts which transpire in different worlds?"

- Henri Poincaré, The Foundations of Science
translated by George Bruce Halsted, Source Wikipedia.













"....the same laws of
electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good. We will raise this conjecture (the purport of which will hereafter be called the “Principle of Relativity”) to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty
space with a definite velocity c which is independent of the state of motion of the emitting body."

Albert Einstein, On the Electrodynamics of moving bodies.



















"Physics introduces new theories not because the theories in a particular domain are found to be unsatisfactory, although they may be so also, if the technique of experiment becomes finer and finer and new phenomena are found which pass beyond the level of accuracy in the earlier theories, but primarily because the domains of physics which come into question are ever extended."

- Julian Schwinger, Quantum Mechanics: Symbolism of Atomic Measurements.

   
 

    "Every entity, simultaneously an observer and an object, is in a state of measurement and shall continue to measure until the measurement is complete."



    The idea of measurements has been with us since the beginning of the human development, when we learned to observe and then make decisions based on our observations.  In fact, the increasing sophistication in our measurements and insights thus gained can be directly correlated to the advancements we have made as a civilization. 

      Over millennia of evolution,  we incorporated measurements into observations to make them more precise.  These measurements were related to Length ( Arm length, Steps, Height, Rulers), Time (Lunar, Solar, Clocks) and Weight (Stones and Scales), which eventually resulted in what we now call Mass Length and Time or MLT system of dimensions.  Later Temperature K,  Charge Q or Current I, Mole N, Candela J, and Angle oDegree, were added to the description of a physical system.

     The most advanced and hence the simplest measurement, is Counting.  In scientific terms,  Counting requires associating a Scalar to a physical quantity of interest such as, mass, time, spatial dimensions, charge etc. 

    In similar manner,  "Theoretical Counting" means that any theory we develop, must map the description of an event(s) or an entity(s) from a complex illustration in n-dimensions to a real number in 1-dimensional Real space ℝ1, if possible.  How we accomplish this, is not necessarily straight forward.

     Our ideas on conventional measurements underwent a rather disruptive change when the theory of Special Relativity was published by Einstein.  And even more so later on when Quantum Mechanics came along. 

    Ever since then there has been this ongoing discourse, between “Should we count?” aka Determinism combined with Locality (DL),  or “Should we make a measurement with maximum possible precision?” aka Determinism combined with Local Realism (DLR), which has profoundly fascinated some of us.1
  
    When we speak of measurements, for example, either in Astronomy or in High Energy Physics, we usually think of them being of two different domains (energy scales), and hence two different underlying mechanisms.  And these mechanisms seem to be not aligned with each other. 


    Subsequently we keep trying to develop new ideas and new theories to reconcile these mechanisms.  However the central idea which ties everything together eludes us.  So we must ask ourselves as follows:

 
Should we not first comprehensively understand the measurement an observer is making, and then let different mechanisms and subsequent theories evolve from our understanding?
 

    In doing so, we are making our observations and measurements precursors to the theories required to explain fundamental mechanisms, theories which would provide us with further insights.  A really neat example, is Dirac's theory of Fermions.  It will be worthwhile to note that the concept of spin and the incorporation of Special Relativity into Quantum Mechanics in Dirac's formulation, was preceded by Stern-Gerlach experiment.


     In next few blogs we will be discussing the following:

1.    What does a measurement conceptually mean to an observer?

2.    Why do we need resources to make a measurement?

3.    Where do these resources come from?

4.  What is the role of Hamiltonian and Lagrangian in making a measurement?

5.  Once we have completely understood a measurement then how to develop theoretical concepts to express our understanding and gain further insights?

 
to be continued 
____________________
 
 
 1. In j-space language, DL is equivalent to performing Zero-Entropy Measurements and DLR is equivalent to performing finite-entropy measurements.  We also note that both types of measurements require finite resources.   DLR resource requirements are likely to be extremely high (HEP).

 
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Previous Blogs:


An Ecosystem of δ-Potentials - IVB
 
An Ecosystem of δ-Potentials - IVA

An Ecosystem of δ-Potentials - III

An Ecosystem of δ-Potentials - II

An Ecosystem of δ-Potentials - I

Nutshell-2019

Stitching Measurement Space - III

Stitching Measurement Space - II

Stitching Measurement Space - I

Mass Length & Topology

A Timeless Constant

Space Time and Entropy

Nutshell-2018

Curve of Least Disorder

Möbius & Lorentz Transformation - II

Möbius & Lorentz Transformation - I

Knots, DNA & Enzymes

Quantum Comp - III

Nutshell-2017

Quantum Comp - II

Quantum Comp - I

Insincere Symmetry - II

Insincere Symmetry - I

Existence in 3-D

Infinite Source

Nutshell-2016

Quanta-II

Quanta-I

EPR Paradox-II
 
EPR Paradox-I

De Broglie Equation

Duality in j-space

A Paradox

The Observers
 
Nutshell-2015
 
Chiral Symmetry

Sigma-z and I

Spin Matrices

Rationale behind Irrational Numbers

The Ubiquitous z-Axis

 

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