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In a quantum experiment, does the leakage of the electromagnetic fields lead to the suppression of quantum effects? For example if I have an electron in a box, in some quantum superposition. Can I use an electrostatic fieldmeter to collapse its wavefunction? How does this problem scale with larger number of particles?

Can it always be screened or is there some uncertainty in the field too that allows to retain its quantum coherence?

What could be said about larger systems if we start to be able to measure their gravitational effects? Why doesn't the leakage of gravitational field collapse the wavefunction of all electrons?

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Quantum effects are suppressed by the environment or measurements copying information out of a quantum system - this process is called decoherence. If the environment interacts with a system so that it copies information about the value of an observable then the different values of that observable can't interfere. Decoherence takes place over time because the interaction that copies the information out takes place over time. So as long as that interaction is negligible for a system over the time during which you're conducting an experiment you will see interference. For larger objects the decoherence times tend to be shorter because their interactions with the environment are stronger. For a review, see

https://arxiv.org/abs/1911.06282

The long range electromagnetic fields produced by charges prevent interference between states with different charge as explained in Section 2.4 of the above reference and its citations: this effect is called environment induced superselection.

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  • $\begingroup$ Could you be more technical, what exactly do you mean by copying? $\endgroup$
    – Mauricio
    Commented Mar 10, 2023 at 18:31
  • $\begingroup$ Perfect copying means perfect measurement $|a\rangle_S|0\rangle_M\to|a\rangle_S|a\rangle_M$, where the $|a\rangle$ states are orthogonal. Imperfect copying means the states aren't necessarily orthogonal and this means you can't perfectly distinguish them. $\endgroup$
    – alanf
    Commented Mar 10, 2023 at 20:20
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Schrodinger's Cat is a thought experiment. As such things behave in idealized ways. So unlike their real behavior you have to imagine the box completely shields the observer from the contents while not actually interacting with the (idealized) Cat and contents.

You've discovered another reason why this is a very confusing thought experiment which you and generations of students world wide find more confusing than helpful.

In reality the entire experiment behaves classically with no quantum effects apart from the random decay of the radioactive material. Please do not test this with a real Cat (or poison) because you'll annoy the Cat and several Cat lovers here. They way macroscopic objects "forget" they're made of quantum objects is called decoherence, by the way.

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  • $\begingroup$ I am aware of many of the problems of this thought experiment. My question addresses the leakage problem specifically and its validity as a counter-argument. Please consider editing your answer to address this specific problem. $\endgroup$
    – Mauricio
    Commented Mar 10, 2023 at 12:24
  • $\begingroup$ @Mauricio It's a thought experiment, not a real one. It is folly to analyze this as if it were real and it is clear (as you can read in many answers about the Cat on Physics SE) that Schrodinger never intended it to be deep dived in this way. Decoherence is the answer you're looking for, whether you like it or not. $\endgroup$ Commented Mar 10, 2023 at 12:38
  • $\begingroup$ Your answer as currently written is just a general no-go argument on Schrödinger cat experiment.Please read the question, I have even changed the title to make it more clear that this is about true quantum experiments. I am discussing the argument that leaked fields may perturb the system even for microscopic quantum systems. You are welcome to provide an argument on that topic based on decoherence formalism. $\endgroup$
    – Mauricio
    Commented Mar 10, 2023 at 12:59
  • $\begingroup$ @Mauricio The cat is used as a Geiger counter in in this cruel thought experiment. Any influence on the outcome has to come from the interaction of fields you propose at the level of the decay of the radioactive source. So it will depend on the source of radioactivity. I think that nuclear decay lifetime will not be affected by external fields because of the coupling constants (strong)involved. Other decays have been affected but are not energetic enough for the thought experiment . See aip.scitation.org/doi/10.1063/1.3142386 for electromagnetic ones. $\endgroup$
    – anna v
    Commented Mar 10, 2023 at 13:22
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    $\begingroup$ If you want to discuss what you call the "leakage problem" in real experiments I'd suggest you just write a completely new post and close this one. The Schrodinger's Cat stuff is just irrelevant if you want a real world scenario. In real lab experiments great effort is made to ensure that interference and unwanted interactions are avoided and it's not trivial and experiment specific. $\endgroup$ Commented Mar 10, 2023 at 13:30

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