it's difficult to talk about measurement. It's one of those things that resists description. Like slime; the tighter you squeeze it the more it slips out of control. Or like the opposing ends of a magnet; the closer you bring them together the greater the repulsion.
unfortunately, I want to hold it as tightly and closely as possible but I don't know if I can but I can try.
1.
i think we get the most intuitive understanding of measurement from our body. We use our skin to measure our immediate surroundings, vision and hearing for the not so immediate surroundings.
consider how you 'see' light. A photon of some wavelength hits your retina and fires a network of neurones and you consciously detect that photon. But how precisely do you measure that photon? Is it 456.314 nanometres or are you more precise say 456.31415926... nm ? Or are you most precise and you measure it to infinite precision.
there is ambiguity in my use of infinite precision above. But say infinite precision is the most detailed picture of a system. For example; the most detailed picture of a container of gas would be where all the atoms are, how they're moving, how they interact with each other etc. In principle, the most detailed picture of a system is everything about the system.
well, you can't ever measure anything to infinite precision. In other words, you can't ever measure the most detailed state of a system and it is not because of how good your measuring instrument is.
this is the crux of my argument and is contrary to what one would think at first.
I'm arguing that you can never know the most detailed picture of a system by measurement.
Infinite precision, like infinity, is unattainable.
2.
ive made a strong statement above. Which I hope doesn't seem rational yet. Why might it be the case that you can never in principle measure the most detailed state of a system? That seems to be a real barrier to what we can know. Surely there must be some method of measuring that gives you the complete picture. It doesn't have to be something massive like the planet or the universe. Can you not even in principle measure the most detailed picture of a small container containing some gas or a group of atoms?
no, not really.
measurement by nature is an interaction between a measuring device and a system. The most precise measurement would be one that's least invasive because then it won't change the system.
consider an analogy: imagine you go for a checkup. It can't be the case that the doctor merely touches your forehead and gets the most detailed picture of your body. They would have to be more invasive. They would test you but that act of testing itself alters your state by raising your heart rate or decreasing your level of attention.
the above is an analogy but the act of measuring itself alters the state of the system.
say your system exists in some state A prior measurement. The act of measuring itself alters the state of the system from A to B. What I'm arguing here is not a practical shortcoming of your measuring instrument. It's not the case that, 'oh if only I had a better measuring instrument I would be able to measure the system with infinite precision without altering the state from A to B'.
in our daily experience, this doesn't seem to be the case at all. You measure the position of a tennis ball by detecting the light reflected off it. Just by looking you don't change the state of the tennis ball from A to B. That is from a classical perspective where you are a giant in comparison to an atom some 10 magnitudes bigger and so is the tennis ball; measurement doesn't really affect the ball directly.
But the universe is inherently quantum mechanical; everything is made up of microscopic particles. So in reality when you see the tennis ball, which is just detecting the light reflecting off it; the tennis ball is different from before you observed it because that photon that reflected off the tennis ball and entered your eye interacted with some atom/s of the ball and therefore changing the most detailed picture of the tennis ball.
the most precise measurement would be the one that didn't change the tennis ball at all. But that can't happen. You have to interact with it in some manner to measure it but just doing so changes it. This argument doesn't just apply to tennis balls but rather to everything in the universe.
measurement is like a heist in that aspect; the most precise measurement is the one that never happened.
3.
the universe is inherently shy at the most detailed scale. There is a fundamental limit to knowing its truest nature; Heisenberg's uncertainty principal is that idea's mathematical analogue.
it is without a doubt that physicists think about the abstract idea of measurement more than the average person. But I hope the argument above resonated with you at some level even if you might disagree with it.
measurement and observation are inherently our nature. It is the one thing that is so deeply linked to consciousness and is perhaps one of the most mysterious concepts.
for me, it is both a powerful yet humbling idea that merely observing changes the nature of things at the most fundamental level in the universe. It is as if we are the threads of the tapestry which is this universe.
maybe for some this invokes the idea of a greater power or spirituality; I don't know what it is but at the moment I seem to be convinced that I surely can't measure it.