Question about quantum superposition

[evelk86]

TL;DR Summary

If an atom is a sphere of influence, can an atom in superposition influence two places at once- even if for a brief moment? And is it possible for the wave function of an atom to not collapse after being observed?

All of my speculation is based on my current understanding of quantum physics as an art high school student who just has this as an interest, which is in no way at a quantum physicist's level so I apologize if this question is stupid. Also sorry for my English.
Most, if not all of you reading this have probably heard of the Schrödingers cat- a theory based on superposition, stating that a cat in a closed box has a 50/50 chance of being alive or dead.

Most of the time when I read about the Schrödingers cat in simplified explanations, the explanation implies that in superposition, the cat is both alive AND dead at the same time, in the same reality. And I was wondering, is this really a good interpretation of this theory?

From the way I understand it, the cat »may as well« be dead or alive from the perspective of you, the observer.
If the only way for me to in any way observe the cat in the box, is to open the box, and if neither me or the cat have any influence on each other until i physically see the state of the cat with my own eyes by opening the box, then again, the cat may as well be dead or alive to me.

But, that wouldn't mean the cat is in two states at once. It is only either dead or alive. Say a mouse named Fred was in the box with the cat (this mouse is immortal and isn't affected by whatever can kill the Schrödingers cat, for the sake of the argument). It can see that the cat is there, and can observe wether or not it is dead or alive- collapsing the possible superpositions of the cat, relative to Fred. Me, looking at the box, has no idea that Fred's in there- as much as i have no idea of the cat's livelihood, which means that the cat is still in superposition for me. But Fred sees that the cat is alive meaning that it really is in only one state at a time.

If I transfer these assumptions to an atom in superposition:
An atom, to my understanding, is considered to be a sphere of influence. And an observation, is any sort of interaction with a force or particle by (in this case) an atom.

So by this logic, is an atom that isn't observed by anything, really even there? And if an atom in superposition would truly be in two positions at once, therefore influencing it's surroundings in two positions at once, what if it gets observed, therefore collapsing it's wave function into one sphere of influence; was the other superposition of the atom, that wasn't observed truly even there in the first place? And if it was, is there any circumstance in which an atom in superposition, after being observed, still stays in two or more positions at once? And is it possible that quantum entanglement is particles in superposition, that haven't collapsed their wave function?

If possible, please do not write a simplified version of the answer- I truly want to know the answer to at least one of these questions so I can actually wrap my head around superposition. Please include math as well if needed (I assume it is needed).

Thanks for reading :)

 

[Nugatory]

Most, if not all of you reading this have probably heard of the Schrödingers cat- a theory based on superposition, stating that a cat in a closed box has a 50/50 chance of being alive or dead.

This is a very common misunderstanding of Schrodinger's cat, one of those things that "everyone knows" but isn't right.

When Schrodinger proposed this thought experiment, he was not saying that the cat would end up in a superposition of dead and alive. He was suggesting that something was wrong with the then-current (almost a hundred years ago now) understanding of quantum because the then-current understanding of the math seemed to require that the cat would end up in such a state - even though that outcome is nonsensical and no one has ever taken it seriously, then or now.

We've made a ton of progress understanding the math of quantum mechanics since then, and the problem of the cat was substantially resolved with the discovery of decoherence a few decades after Schrodinger brought it up. Start by Googling for "quantum decoherence" (but you may find the math to be daunting - the initial price of admission is at least several years of college level math) and also try David Lindley's much more layman-friendly book "Where did the weirdness go?"

If possible, please do not write a simplified version of the answer- I truly want to know the answer to at least one of these questions so I can actually wrap my head around superposition.

There's no sensible answer until you have a more solid understanding of what quantum mechanics really is. Although it is not a substitute for a real textbook, Giancarlo Ghirardi's book "Sneaking a look at God's cards" is a good overview of how the math of superposition works and how it relates to entanglement.

We will leave this thread open for other replies and followup questions for a while, but all posters are reminded that it is a B-level thread. We wil close it if it seems to be getting out of hand.

 

[PeroK]

Summary: If an atom is a sphere of influence, can an atom in superposition influence two places at once- even if for a brief moment? And is it possible for the wave function of an atom to not collapse after being observed?

The wave function collapse is part of some interpretations of QM, which try to give some heuristic narrative to the core mathematics of QM. Wave function collapse is not a physical process that could be inhibited but part of an explanation of QM.

Most, if not all of you reading this have probably heard of the Schrödingers cat- a theory based on superposition, stating that a cat in a closed box has a 50/50 chance of being alive or dead.

QM is designed to model the behaviour of elementary systems. It doesn't replace classical mechanics, biology or veterinary medicine in terms of explaining a cat. That's part of the point of Schrödingers cat: that by a clever use of radioactive decay (that is governed directly by QM), we can impose quantum criteria on a cat, which is potentially absurd.

Most of the time when I read about the Schrödingers cat in simplified explanations, the explanation implies that in superposition, the cat is both alive AND dead at the same time, in the same reality. And I was wondering, is this really a good interpretation of this theory?

The fact that a cat cannot be both dead and alive is supposed to highlight that there is something wrong or missing in QM.

From the way I understand it, the cat »may as well« be dead or alive from the perspective of you, the observer.
If the only way for me to in any way observe the cat in the box, is to open the box, and if neither me or the cat have any influence on each other until i physically see the state of the cat with my own eyes by opening the box, then again, the cat may as well be dead or alive to me.

Yes, but in QM it's not a question of not knowing, it's a question of properties being undefined until measured - which doesn't fit very well with the way a macroscopic object like a cat behaves.

But, that wouldn't mean the cat is in two states at once. It is only either dead or alive. Say a mouse named Fred was in the box with the cat (this mouse is immortal and isn't affected by whatever can kill the Schrödingers cat, for the sake of the argument). It can see that the cat is there, and can observe wether or not it is dead or alive- collapsing the possible superpositions of the cat, relative to Fred. Me, looking at the box, has no idea that Fred's in there- as much as i have no idea of the cat's livelihood, which means that the cat is still in superposition for me. But Fred sees that the cat is alive meaning that it really is in only one state at a time.

Yes, that sort of argument is part of the puzzle. The mouse must logically be in a superposition as well: 1) hiding from a live cat; and, 2) relaxing upon seeing a dead cat!

If I transfer these assumptions to an atom in superposition:
An atom, to my understanding, is considered to be a sphere of influence. And an observation, is any sort of interaction with a force or particle by (in this case) an atom.

So by this logic, is an atom that isn't observed by anything, really even there?

The existence of an atom is not defined or determined by having certain classical properties, such as well-defined position. It's a mistake to think that if an atom is quantum mechanical, then it somehow doesn't exist. It exists, but behaves non classically.

And if an atom in superposition would truly be in two positions at once

The atom is not in two places at once. It simply does not have a position until measured.

, therefore influencing it's surroundings in two positions at once, what if it gets observed, therefore collapsing it's wave function into one sphere of influence; was the other superposition of the atom, that wasn't observed truly even there in the first place? And if it was, is there any circumstance in which an atom in superposition, after being observed, still stays in two or more positions at once? And is it possible that quantum entanglement is particles in superposition, that haven't collapsed their wave function?

This is confused thinking based on a basic misunderstanding of QM, superposition and atomic position measurements.

If possible, please do not write a simplified version of the answer

The true answer is to learn the mathematics of QM. That is the language that describes QM fully and without ambiguity. It's only when you try to describe things in everyday terms that the problems start.

- I truly want to know the answer to at least one of these questions so I can actually wrap my head around superposition.

Then learn the mathematics. Superposition is a simpe idea in mathematical terms.

Please include math as well if needed (I assume it is needed).

You are better with a textbook for that.