When I go to the supermarket and think about whether there is milk there or not, I imagine an empty shelf
Yes, you indeed imagine it. And people also imagine a world that macroscopically looks just like ours on a human-scale, but instead follows the laws of classical mechanics (in fact, for centuries, this was the mainstream conception of reality among top physicists).
The problem is that such a world cannot exist. The classical picture of a ball-like electron orbiting around a proton inside a hydrogen atom cannot happen; classically, a rotating electrically charged particle radiates away energy (and, to compensate and ensure conservation of energy, must lose potential energy as a result). As such, the electron would collapse into the center of the proton a billion times faster than the blink of an eye.[1]
At a deep, fundamental level, the fact that we imagine such a world is a fact about us, not about the world. It’s not that there are some weird phenomena around the edges that appear when you move really fast or you fly millions of light-years away from Earth or you get down to quarks, so that you’re forced to use QM or relativity because they are “appropriate,” but as long as you only think about sufficiently “mundane” matters, you are ok. No! The “weirdness” is baked into everything that exists. Even a bar magnet, the likes of which you might stick onto a fridge, cannot be explained by classical mechanics; ferromagnetism is a fundamentally quantum phenomenon.[2]
Logic runs on (appropriately-named) logical deductions. But as soon as you have any contradiction whatsoever, the principle of explosion makes everything… well, explode. Every statement inside the system becomes both true and false, i.e., it becomes useless. If you can prove “observation-X implies observation-Y a time-step later” but also know that both “observation-X” and “not observation-Y” (i.e., you reason about a logical counterfactual), then you are fully within the ambit of the principle of explosion.
So that’s the problem with the milk-free supermarket. And it’s a genuine problem, since naive resolutions break the laws of math and physics typically used to parse through such matters. Nevertheless, I suppose there are solutions, at least if you believe in the MWI and the notion of different quantum “branches,” for example.
More precisely, classical-inspired Stat Mech models (like the Ising model) might serve as fine approximations of reality, but the assumptions lurking in the background (i.e., what causes the dipole moments to be systematically oriented a certain way?) necessitate QM as a justification
Yes, you indeed imagine it. And people also imagine a world that macroscopically looks just like ours on a human-scale, but instead follows the laws of classical mechanics (in fact, for centuries, this was the mainstream conception of reality among top physicists).
The problem is that such a world cannot exist. The classical picture of a ball-like electron orbiting around a proton inside a hydrogen atom cannot happen; classically, a rotating electrically charged particle radiates away energy (and, to compensate and ensure conservation of energy, must lose potential energy as a result). As such, the electron would collapse into the center of the proton a billion times faster than the blink of an eye.[1]
At a deep, fundamental level, the fact that we imagine such a world is a fact about us, not about the world. It’s not that there are some weird phenomena around the edges that appear when you move really fast or you fly millions of light-years away from Earth or you get down to quarks, so that you’re forced to use QM or relativity because they are “appropriate,” but as long as you only think about sufficiently “mundane” matters, you are ok. No! The “weirdness” is baked into everything that exists. Even a bar magnet, the likes of which you might stick onto a fridge, cannot be explained by classical mechanics; ferromagnetism is a fundamentally quantum phenomenon.[2]
Logic runs on (appropriately-named) logical deductions. But as soon as you have any contradiction whatsoever, the principle of explosion makes everything… well, explode. Every statement inside the system becomes both true and false, i.e., it becomes useless. If you can prove “observation-X implies observation-Y a time-step later” but also know that both “observation-X” and “not observation-Y” (i.e., you reason about a logical counterfactual), then you are fully within the ambit of the principle of explosion.
So that’s the problem with the milk-free supermarket. And it’s a genuine problem, since naive resolutions break the laws of math and physics typically used to parse through such matters. Nevertheless, I suppose there are solutions, at least if you believe in the MWI and the notion of different quantum “branches,” for example.
You can run the calculations yourself, if you want to; a single-semester course of E&M would suffice to give you all the background you need
More precisely, classical-inspired Stat Mech models (like the Ising model) might serve as fine approximations of reality, but the assumptions lurking in the background (i.e., what causes the dipole moments to be systematically oriented a certain way?) necessitate QM as a justification