Well, as for the last point about experiments, you know what they say in physics: if your experiment needs a statistician, you need a better experiment [attributed to Rutherford but I have no idea if that's a true quote]
And I'm joining the comments before me in unshamefully claiming that if this series is heading to physics land, StatMech also deserves some attention [if only to materialize my prediction about the self-averaging argmin post...]
Thank you for another awesome article, Professor! Apologies if this is a silly question, but how often do we need to consider the effect of measurement upon a system in non-QM statistical contexts? In most cases, do we assume that the measurement doesn't affect the results of the parameters/data we are estimating?
I kinda get annoyed about this discussion of QM being focused on measurement as AFAICT the uncertainty thing doesn't come from measurement at all mostly it comes from the fact that quantities that are independent classically (time and energy, or position and momentum), are defined as fourier transforms of each other in QM, and if something is localized in frequency space it is not localized in position space, regardless of how you measure it (i.e. it's that the quantities are not defined, not that they are hard to measure, and it's the inability to define these things independently that is weird). But what do I know.
An old paper by Shalizi and Moore, _What is a Macrostate?_(https://arxiv.org/abs/cond-mat/0303625) seems relevant in this conversation. I am curious if control theoretic perspectives can build upon the arguments of that paper and add to the discussion here.
"The impossibility of measurement highlights the dirty secret of physics."
This reminds me of Hasok Chang's book "Inventing Temperature." There is always this race between theory - using models to say estimate the temperature of the sun - which themselves are validated from tools that have obviously never "directly" measured the sun. Does the theory still apply at the sun?
There have been many cases where theories accord with the measurements at local levels, but they are contradicted at more macroscopic or microscopic levels - and only once we have better tooling are we able to confirm this.
The tooling also of course depends on the theory. You need to have a sense of what you are measuring - if you do get a thermometer near the sun, are you actually measuring temperature, or picking up something else? How would you know?
I have seen few books investigate the dialectic between theory and empiricism as well as Chang's.
I think (though I am about as far away from physics as you can get) that your post concerns inescapable quantum uncertainty - i.e. the fundamental uncertainty which plops out of a mathematical model.
I believe there is also fundamental empirical uncertainty. When you make a measurement, you must control the experiment such that the conditions are as close as possible across multiple iterations.
Even after controlling for all these conditions - we use the same measuring device from the same operator in the same lab during roughly the same time period - we will _still_ have variance in our measurements. This is perhaps self-evident - we can never of course control every single possible bit of variance involved in taking a measurement. And so, we will be left with irreducible uncertainty at the empirical level.
Well, as for the last point about experiments, you know what they say in physics: if your experiment needs a statistician, you need a better experiment [attributed to Rutherford but I have no idea if that's a true quote]
And I'm joining the comments before me in unshamefully claiming that if this series is heading to physics land, StatMech also deserves some attention [if only to materialize my prediction about the self-averaging argmin post...]
Thank you for another awesome article, Professor! Apologies if this is a silly question, but how often do we need to consider the effect of measurement upon a system in non-QM statistical contexts? In most cases, do we assume that the measurement doesn't affect the results of the parameters/data we are estimating?
I kinda get annoyed about this discussion of QM being focused on measurement as AFAICT the uncertainty thing doesn't come from measurement at all mostly it comes from the fact that quantities that are independent classically (time and energy, or position and momentum), are defined as fourier transforms of each other in QM, and if something is localized in frequency space it is not localized in position space, regardless of how you measure it (i.e. it's that the quantities are not defined, not that they are hard to measure, and it's the inability to define these things independently that is weird). But what do I know.
An old paper by Shalizi and Moore, _What is a Macrostate?_(https://arxiv.org/abs/cond-mat/0303625) seems relevant in this conversation. I am curious if control theoretic perspectives can build upon the arguments of that paper and add to the discussion here.
"The impossibility of measurement highlights the dirty secret of physics."
This reminds me of Hasok Chang's book "Inventing Temperature." There is always this race between theory - using models to say estimate the temperature of the sun - which themselves are validated from tools that have obviously never "directly" measured the sun. Does the theory still apply at the sun?
There have been many cases where theories accord with the measurements at local levels, but they are contradicted at more macroscopic or microscopic levels - and only once we have better tooling are we able to confirm this.
The tooling also of course depends on the theory. You need to have a sense of what you are measuring - if you do get a thermometer near the sun, are you actually measuring temperature, or picking up something else? How would you know?
I have seen few books investigate the dialectic between theory and empiricism as well as Chang's.
I think (though I am about as far away from physics as you can get) that your post concerns inescapable quantum uncertainty - i.e. the fundamental uncertainty which plops out of a mathematical model.
I believe there is also fundamental empirical uncertainty. When you make a measurement, you must control the experiment such that the conditions are as close as possible across multiple iterations.
ISO defines these "repeatability conditions" here in 0.3: https://www.iso.org/obp/ui/#iso:std:iso:5725:-1:ed-1:v1:en.
Even after controlling for all these conditions - we use the same measuring device from the same operator in the same lab during roughly the same time period - we will _still_ have variance in our measurements. This is perhaps self-evident - we can never of course control every single possible bit of variance involved in taking a measurement. And so, we will be left with irreducible uncertainty at the empirical level.
I write about this topic more here: https://alexpetralia.com/2023/01/31/what-does-it-mean-for-data-to-be-precise-part-4/#the-iso-definition-of-precision