What I'm doing
Note before reading: I've made two edits for clarification
The first starts at: "To clarify based on answers, I think ya'll are missing the meat of the question:"
The second starts at: "Alright, I think I see the problem here"
I've been trying to understand quantum superposition for a while now and back in high school physics I got the whole lecture on the double slit experiment and I saw the age old video Dr Quantum - Double Slit Experiment (itself pulled from the film "What the Bleep! Down the Rabbit Hole - Quantum Edition (2006)", which tried to explain the results of that experiment.
I understand that observing (adding a detector to the slits) the electron changes its behavior from that of a wave to that of a particle. I understand that that can be observed through the diffraction pattern (or lack thereof) on the back board (where the electron eventually lands) that contains the results of the experiment, thus the whole thing proves electrons are both wave and particle like. The problem I'm having is when they try to explain why. The video doesn't really do it for me and when I asked my teacher in high school and later my physics professors in college they would always say something like "observing the electron collapses the wavefunction".
How I try and see it from a math point of view after researching it
Now that I've taken differential equations and linear algebra I have a basic idea of eigenvalues and linear equations because we had to use them to solve linear differential equations. While I was researching quantum computers I happened upon this Saturday Morning Breakfast Cereal comic on "The Quantum computer talk". In the comic there is a part about superposition that told me that (paraphrasing here) "quantum superposition is not two things at once but it is it's own unique state". This got me curious and So I looked up many questions on this topic with one of the good ones being:
This question seemed to affirm that I can't think of superposition as a mix of classical states (here or there) or both at the same time (here and there) but rather something else entirely, a unique state. I'm having trouble thinking about what this 'Unique state' actually means. I currently understand that electrons are governed by wavefunctions and that these wavefunctions have eigenstates. I think that somehow superposition is like a linear equation where the eigenstates of the wavefunction are their own smaller solution.
To put this in terms of my differential equations/linear algebra understanding this seems to me to be a parallel to linear equations and a basis of vectors, like how you can write a vector as a linear equation of other vectors and both are equivalent. eigenvalues in differential equations were used almost like those individual 'vectors' when solving the equation and the 'linear' ish combination of them is what enabled you to solve the differential equation. I think something similar is happening with wavefunctions, eigenstates and quantum superposition but I just can't see the connection here. Is there a parallel to be made there? Upon reading the tag description for quantum superposition it seems to be somewhat related but I can't 'see' it, like in a deep understanding kind of way.
The core question
Anyways the whole point of this is to understand mathematically/visually this question:
If I was Schrödinger's cat, what would I feel? would I feel alive? dead? The question I researched seemed to assert that I would feel like some unique state but not both dead and alive. Does the fact that I would be the cat count as 'observing' the superposition and thus 'collapse the wavefunction'? Can I even observe my own superposition? electrons obviously can't really observe themselves but observing my own superposition might be impossible because it seems that the very act of photons hitting me (and hence me receiving them in my eyes) seems to disrupt the superposition BUT maybe I just close my eyes and don't 'observe myself' and then maybe the whole collapse doesn't happen and then that re-begs the question.
According to my research I would be in some unique state that isn't just a probability mixture of being dead or alive (i.e. I'm not just alive with a 75% chance or something) but that I'm not both alive and dead nor am I alive or dead. So again, what exactly would I feel? Is it not even possible to describe because the very thought of describing it confines us to classical interpretations? Would the act of 'feeling it' count as observation? I want to understand on a math level (and possibly a visual level) with the basic ideas of solving linear differential equations being (maybe) a parallel to whats going on.
The reason I need (really want) to understand this is because I want to understand quantum computers. These two things relate because I'm told (by the comic mentioned earlier) that qubits aren't actually 1 and 0 at the same time but in a 'superposition' which is a 'unique state' not definitely 1 or 0 with some probability, not 1 and 0 at the same time. How do you describe a linear combination of two states of 'being'? Is it possible?
To clarify based on answers, I think ya'll are missing the meat of the question:
I appreciate the insight about de-coherence but I think the point is being missed. The general consensus seems to be: the cat isn't ever actually in a superposition because it interacts too much with it's environment. I get that realistically it would be impossible for us (now anyway) to actually get a cat into a superposition, but I think the more important insight for me is this: assuming it IS in a superposition (and if you can't deal with that then feel free to substitute cat for electron) what does that actually look like? what does that 'feel' like? I get that the whole act of feeling/seeing/it interacting with outside stuff implies and causes de-coherence but what I want to know is basically summed up by 'what would it feel like to be in a superposition provided I could feel what was physically true regardless of the fact that observation causes that superposition to decay back to normal.' I want to know if superposition itself IS being two things at once or NOT and if its NOT then what IS it, physically. I don't know how to describe a 'linear combination of solutions to a wave function' physically if we talk about 'wave functions' as 'states' and I want to know what the equivalent physical analogy is. What does superimposed mean physically? what would it look like IF we could see it? Assume I'm ignoring the actual engineering ramifications for preventing de-coherence (I'm not trying to build a cat sized quantum computer yet anyways).
If the whole 'feeling' thing bothers you still then just answer this instead: If I was an electron, or still Schrodinger's cat in superposition and I was unable to interact with my environment somehow, what would ACTUALLY happen to me (I'm not observing anything I'm simply asking about the physical reality of whats going on. No interactions are taking place). Would I ACTUALLY BE dead, alive, both, neither, in two universes, something else until I interacted with my environment, something else entirely (explain this in depth if true), Or can we not explain it yet? A linear combination of dead and alive 'states' doesn't correlate (to me anyway) to anything physically. So far the only real physical based explanation is: the universe splits in two. The problem I have with this is that implies like, infinite universes beyond comprehension because there are all kinds of particles constantly in-n-out of superposition that are constantly being observed/interacted with. The 'pilot wave' thing I saw in one answer looked interesting but the idea of being 'entangled with the rest of the universe' and some universal wave propagating at FTL and changing the state of the universal wave function like some sort of giant state machine seems a little implausible, So I'm going with the Copenhagen interpretation for now. what does a Copenhagen superposition ACTUALLY physically mean and if possible what WOULD it look like if/assuming it was possible to 'observe' without 'interacting'.
Note that it is OK if 'we can't actually explain this because its impossible its some sort of paradox, philosophical thing, or the math is too complicated/not invented yet' is the answer, I just need to KNOW its impossible to describe (and then maybe list attempts at describing it).
The core point is IGNORE the 'feel' part of this and focus more on the 'superposition' part because I feel like the 'you aren't in a superposition anyways' answer is more of a cop-out than an actual answer.
Alright, I think I see the problem here
I'm asking something philosophical here. If quantum superposition is only possible when said quantum object doesn't interact with it's environment, then the only time it 'exists' is when we can't shoot photons at it, detect it's field, or detect anything from it really. So then (in terms of the Copenhagen interpretation) the question that Einstein himself posed was 'If you don't look at the moon does it go away?' he considered that absurd, as do I. I did some research on quantum erasure, the copenhagen interpretation, re-read the wikipedia page on shrodinger's cat for the tenth time and I think the problem is that we don't have a way to describe the physical aspects of this simply because there isn't a way to physically see it without interaction of some kind.
Consequences I've thought about. Pictures of electrons?
The other thing I'm wondering is this: electrons are in superpositions when they aren't interacting with the enviroment at all, so logically that means that when they bind to atoms and 'interact' they must de-cohere into the two states (wavefunctions) possible: waves, or particles. The thing is, We've taken pictures of atomic nuclei so we have an idea of what the electron cloud looks like, so then my question is, is that the picture of the electron as a wave? or the electron as a particle? I know the particle wouldn't look like a billiards ball and nor would the wave due to uncertainty principle, and my research on quantum erasure made it seem like it should (in both cases) look like a smudge, which it does in the photos I've seen of atomic nuceli (might be a correlation there but thats probably a future question). But then could we possibly know which one it is?
The big issue
I think the problem with 'describing a superposition' is we clearly can't experimentally observe it and short of finding some mystical thing that can observe it without interacting with it, all we have is all kinds of opinion based interpretations (its two universes, it can't be observed classically, theres some pilot wave, some other theory)
the math angle?
I want to think of it from this angle: Thinking about superposition as a Unique Linear Combination of smaller solution wavefunctions (states) that are superimposed that is in and of itself a solution wavefunction (state or even states) that represents a probability distribution that when interacted with causes the solution to break down into one of its eiganstate solutions. what math to physical correlation does that allow us to draw when IN the superposition? I could consider a possible solution to be exiting the weird world of qunatum mechanics and simply asking "what does a linear combination of two states as its own state as a superimposed wave really look like". We can't observe the superposition itself, I get that goes philosophical so instead lets think in math terms, concrete demonstrable, non-opinion based and lets just think about it from there. What would superimposing two (even classical) states really look like physically disregarding quantum mechanics for just a second. Is that something beyond comprehension?
electrons might hold the key
Maybe it just looks like some sort of smudge just like the electron looks like in our photos and the 'image' doesn't actually ever change but the behavior does. We know the results of the electron superposition decohereing must (I think anyways) look like the smudge we are seeing, because we are seeing decoherent electron superpositions in our pictures of atoms which means we should be seeing both the wave electron and the particle electron. In the quantum erasure experiment thats what was observed as well when the two states were superimposed on the backboard detector as a combination of the wave and particle states going through the slits. This makes more sense when you think about a superimposed wavefunction, maybe the 'image' never changed at all, the electron always looks like a smudge even if you can't actually look at it while its in superposition.
A smudge would probably be the first thing I would think of if I had to imagine a 'superimposed image' of classical states. The cat (if it actually was/could be in superposition) might look like a cat but physically BE different (a dead cat only looks different really when it starts interacting with its environment but a superposition cat might not look different because if it did look different it wouldn't be in superposition in the first place) So maybe thats it, superposition might change the physical nature of the cat but not actually the look because by the time the look of the cat has changed, the superposition has decohered.
heres how maybe We can think about it
The cat goes in the box, assuming it can be completely isolated from its environment for a while (even a plack time unit might be acceptable here) it goes into a superposition. Then it starts to interact with its environment and it decoheres into either alive or dead. At this point (instant in time at the moment of decoherence we stop the clock on the universe), the box hasn't been opened but instead the actual decoherence happens when 'the universe observes the cat'. The image of the cat hasn't yet changed (only one or two planck times might have passed and the image can't have possibly changed, nothing with the photons can happen instantaneously) but the physical state of the cat has in fact changed (because thats the event for which we stopped the clock). We start time up again and since decoherence just happened, the cat continues on classically being alive or dead and by the time you open the box, the decoherence has already occurred so you observe the cat classically.
in terms of electrons, What I just thought of
The electron gets isolated from its environment and goes into a superposition of states. We then shoot a photon at it (or it interacts with something) and at that instant, its state changes but it's image does not. then after that instant of decoherence and interaction, the electron continues it's day as either a wave or particle. the thing is, since we know what an electron looks like after decoherence, and since the above says (the image shouldn't change immediately after decoherence) then maybe (if the image doesn't change quickly due to a change in state) the superposition just looks like what the image is now. Its possible this could even be tested if we developed technology to
Take a picture of a superpositioned electron and cause it to decohere and receive the one photon we hit it with
The crux of this being that the image of the electron can't change when decoherence occurs if that decoherence is caused by the act of taking a picture because somehow the photon bringing that information back would have to change before it was received OR the electron would have to anticipate the photon hitting it OR some sort of transition process would have to occur that changes the image of the electron from a superposition to a non-superposition
I don't think photons can change like that on their way back if left undisturbed by anything weird
I don't think electrons anticipate photons hitting them, they aren't sentient and can't predict the future and if they could that'd be weird
Its possible there might be a 'de-coherence transition period' but then in principle we could advance our technology and record ever more infitesimal amounts of time and EVENTUALLY see this. which again, would be weird
The biggest thing is, any change in appearance suggests decoherence has already occured, so the moment (instant) decoherence occurs there SHOULDN'T BE any change yet (instants in time don't allow for changes) because if there was change, decoherence would already have occured. So if our photon is sending back data from that instant in time (since the 'capture' was the thing that caused decoherence) that data should represent the 'picture' at that instant unless something REALLY WEIRD is happening to the photon on the way back.
I want to know what you think of this line of thinking (not opinion wise but is it valid/correct): Is it possible I'm onto something here? I don't want opinions of the different interpretations I want a math-based explanation or something based on the above tangent, and if the answer is no thats not possible THEN put it in an answer because thats a concrete non opinion fact that needs to be known.
a change in appearance implies decoherence has already occured, thus since decoherence must cause the change in appearance, causing decoherence by viewing the electron in superposition must capture the photo the instant decoherence occurs, thus that picture represents what the superposition 'looked like' assuming we say it actually exists when in superposition. (simpler): We can't view the superposition, but if we capture it the moment it's changing, we know what it was in the past even without seeing it.
very simple explanation of whats going on
Imagine you have a camera, and you have a friend phil, when you take a picture of phil he screams, (he hates photos). When you take a picture of phil, you see phil as a calm human being in the picture because the act of taking the picture is what causes the change in behavior/appearance. Only after the photo is taken do you see phil as an angry human being. Phil was the electron, the photo was a photon and 'taking the picture' is 'de-cohereing the electron'.
Or you know I could be completely wrong
Feel free to let me know why.
really why I think the question should be unclosed
I think that this edit makes the question non-philosophical because I'm no longer trying to describe the undescribeable, I'm only ever viewing the thing when its decohered, talking about the math angle, or talking about possible analogous classical interpretations. Those are concrete and not opinion based. Feel free to suggest further improvements.