What does one measure?

Turn an aggregate effect into a number

E.g. pressure , temperature

Did something happen or not?

E.g. Geiger counter

Measuring e.g. mass or amount of substance

E.g. balance measuring mass
cf A to D converter

Measurement by comparison

Length, mass, time, ....
[ Is this rod longer than that rod? ]

Measurement by counting

[ How many rods does it take to cover this? ]

In WPP everything is graph theoretic

E.g. time is a counting of events for an observer in the causal graph

E.g. energy is flux of causal edges

When can one measure?

How much fluid is in the Great Red Spot?
We’ve got to identify an object about which we make a measurement
E.g. liquid has a definite volume; gas does not
E.g. solid has a definite length (as well as volume); liquid does not have a definite length
E.g. an electron has a definite mass, but it can have any momentum
E.g. what things have nontrivial expectation values in QM (e.g. distance from nucleus to an electron has meaningful value; orientation of a S electron does not)

What is the length of water flowing through a river?

Pressure is meaningful for a gas, not a solid
Length is meaningful for a solid, not a gas
For a liquid, there is potentially a meaningful distance between eddies....
E.g.
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M-band apparent magnitude
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absorbed dose of ionizing radiation
,
dissociation degree
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precipitation
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sound energy density
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electric conductivity space-time tensor density
,
ambient pressure
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relative mass ratio of vapor
,
bending moment of force
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proton count

Measured quantities need systems in which they are occuring

Function of measurement: “standardize” some actual phenomenon

Transform the phenomenon to something that we humans intrinsically sense

Pressure measurement

Transducing from properties of a gas to properties of a solid/liquid
Each individual molecule from a gas hitting a solid surface just has a small effect on the solid overall, as opposed to making a tiny pit in the surface
In a manometer ... one could have every gas molecule collision produce a local deformation in the liquid surface
For what coordinate system is the fluid surface in a manometer “easy to describe”
What about a manometer that is made of another gas?
As the “measurement gas” gets more and more nonideal, it becomes a more convincing measuring device

The fact that liquids and solids are useful for measurement is a consequence of our features as observers

The position of the liquid surface is somehow robust

Set up a coordinate system to measure the position of the liquid surface

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ListLinePlot[Evaluate[Table[i,{i,0,1,.05},50]]]
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-0.2
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Vision

Only works because there are blobs of light from things we consider to be objects
A random photon field would be incomprehensible to our brain
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igneous rock
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0.356241,
material
0.356241,
substance
0.356253,
component
0.356253,
black pepper
0.0121276,
black cottonwood
0.00436992,
Sitka spruce
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States of matter

Infinite number of dof all coherently work together to make something that can be classified as a state of matter....
In a definite phase, the system is characterized by a small number of e.g. order parameters

Measurement is about taking a large number of dof and filtering to a small number of dof

E.g. for vision, we go from a photon field to object recognition

Fundamentally an observer wants to “make a decision”

The observer has a bounded brain, so it’s got to reduce out most of the detail of the actual system

Liquid is also basically “going to an attractor”

https://writings.stephenwolfram.com/2021/05/the-problem-of-distributed-consensus/

Metamodel:
1. system goes to an attractor
2. the observer can tell “which attractor” it went to

Consider the case of all being cycles:

This effectively has an invariant that characterizes the different “attractors”

Compare:
[[ need to find the attractor states here ]]
cf https://www.wolframscience.com/nks/p597--statistical-analysis/

Measurement in the hypergraph

Use black hole formation to do your measurement

Above the Schwarzschild mass you’ll make a black hole; otherwise you won’t

Can we turn a state of the system into an “observer identifiable” “attractor feature”

E.g. from bubbling atoms of space, particles can emerge;
or from emes, identifiable axiomatic structures

Examples

E.g. scintillation counter

lots of details of the ionizing particle and the crystal etc. end up just producing “the same photon”

E.g. semiconductor thermometer

Lots of detailed heat ... promotes electrons to the conduction band ... where they are easy to identify

E.g. rain gage

The drop fall in many positions and patterns; but when they fill up the rain gage, it’s an attractor because the only thing that matters is the total volume of fluid

Measurement: turning things into a recognizable “standard form”