What does one measure?
What does one measure?
Turn an aggregate effect into a number
Turn an aggregate effect into a number
E.g. pressure , temperature
Did something happen or not?
Did something happen or not?
E.g. Geiger counter
Measuring e.g. mass or amount of substance
Measuring e.g. mass or amount of substance
E.g. balance measuring mass
cf A to D converter
Measurement by comparison
Measurement by comparison
Length, mass, time, ....
[ Is this rod longer than that rod? ]
Measurement by counting
Measurement by counting
[ How many rods does it take to cover this? ]
In WPP everything is graph theoretic
In WPP everything is graph theoretic
E.g. time is a counting of events for an observer in the causal graph
E.g. time is a counting of events for an observer in the causal graph
E.g. energy is flux of causal edges
E.g. energy is flux of causal edges
When can one measure?
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?
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.
In[]:=
RandomEntity["PhysicalQuantity",10]
Out[]=
,,,,,,,,,
Measured quantities need systems in which they are occuring
Function of measurement: “standardize” some actual phenomenon
Function of measurement: “standardize” some actual phenomenon
Transform the phenomenon to something that we humans intrinsically sense
Transform the phenomenon to something that we humans intrinsically sense
Pressure measurement
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 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
The position of the liquid surface is somehow robust
Set up a coordinate system to measure the position of the liquid surface
Set up a coordinate system to measure the position of the liquid surface
In[]:=
ListLinePlot[Evaluate[Table[i,{i,0,1,.05},50]]]
Out[]=
In[]:=
ListLinePlot[Evaluate[Table[i+.1Sin[100t]+.1Sin[100Sqrt[2]t],{i,0,1,.05},{t,0,50}]]]
Out[]=
Vision
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
In[]:=
RandomImage[]
Out[]=
In[]:=
ImageIdentify
,All,10,"Probability"
States of matter
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
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”
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”
Liquid is also basically “going to an attractor”
Metamodel:
1. system goes to an attractor
2. the observer can tell “which attractor” it went to
Metamodel:
1. system goes to an attractor
2. the observer can tell “which attractor” it went to
1. system goes to an attractor
2. the observer can tell “which attractor” it went to
Consider the case of all being cycles:
Consider the case of all being cycles:
This effectively has an invariant that characterizes the different “attractors”
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
Measurement in the hypergraph
Use black hole formation to do your measurement
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”
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
E.g. from bubbling atoms of space, particles can emerge;
or from emes, identifiable axiomatic structures
or from emes, identifiable axiomatic structures
Examples
Examples
E.g. scintillation counter
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
E.g. semiconductor thermometer
Lots of detailed heat ... promotes electrons to the conduction band ... where they are easy to identify
E.g. rain gage
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”
Measurement: turning things into a recognizable “standard form”