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If I was Schrödinger's cat, what would I feel?
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What I'm doing
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 a funny xkcd comic on "The Quantum computer talk" (I think it was titled 'Saturday Morning Breakfast Cereal' and was a parody of the birds and the bees but with quantum computing) and in the comic there was 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:
Is "quantum superposition" just a fancy way of saying that a system is in one state or another with some probabilities?
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?
quantum-mechanics superposition observables schroedingers-cat
edited 2 hours ago
Emilio Pisanty
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up vote
2
down vote
favorite
What I'm doing
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 a funny xkcd comic on "The Quantum computer talk" (I think it was titled 'Saturday Morning Breakfast Cereal' and was a parody of the birds and the bees but with quantum computing) and in the comic there was 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:
Is "quantum superposition" just a fancy way of saying that a system is in one state or another with some probabilities?
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?
quantum-mechanics superposition observables schroedingers-cat
edited 2 hours ago
Emilio Pisanty
78.6k21187385
asked 2 hours ago
Redacted
385
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6
If you were Schrödinger's cat, then you wouldn't be Schrödinger's cat - you would be Wigner's friend (that being the equivalent paradox where the being in a superposition state is a conscious human). (Unless, of course, you're actually a cat.)
– Emilio Pisanty
2 hours ago
4
In addition to that, the standard advise when it comes to the 'What the bleep' so-called documentary is: drop it and find a better source. The whole film is so riddled with errors, misconceptions, quantum woo and outright misinformation that you simply won't come out ahead when getting your information from there.
– Emilio Pisanty
2 hours ago
Its funny, the more I learn about something, the more I realize my past teachers were misleading me in so many ways. good to know they're using bad resources. Now if only I could really understand the real math behind this stuff
– Redacted
1 hour ago
1
@Redacted You can understand the real math behind this, if you have a background of differential equations and linear algebra all you have to do is get an introductory book on the subject. I would recommend Griffiths or Shankar. There are many good sources to learn QM from.
– Hugo V
1 hour ago
found the book you're talking about. I'm going to start with the Griffiths one. found a pdf of the whole thing, downloaded it free of charge. Hopefully it'll help with my Diff EQ and linear algebra and calculus skills. Thanks for the recommendation.
– Redacted
55 mins ago
 |Â
show 1 more comment
up vote
2
down vote
favorite
up vote
2
down vote
favorite
What I'm doing
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 a funny xkcd comic on "The Quantum computer talk" (I think it was titled 'Saturday Morning Breakfast Cereal' and was a parody of the birds and the bees but with quantum computing) and in the comic there was 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:
Is "quantum superposition" just a fancy way of saying that a system is in one state or another with some probabilities?
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?
quantum-mechanics superposition observables schroedingers-cat
edited 2 hours ago
Emilio Pisanty
78.6k21187385
asked 2 hours ago
Redacted
385
New contributor
Redacted is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
What I'm doing
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 a funny xkcd comic on "The Quantum computer talk" (I think it was titled 'Saturday Morning Breakfast Cereal' and was a parody of the birds and the bees but with quantum computing) and in the comic there was 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:
Is "quantum superposition" just a fancy way of saying that a system is in one state or another with some probabilities?
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?
quantum-mechanics superposition observables schroedingers-cat
quantum-mechanics superposition observables schroedingers-cat
edited 2 hours ago
Emilio Pisanty
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asked 2 hours ago
Redacted
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edited 2 hours ago
Emilio Pisanty
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asked 2 hours ago
Redacted
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edited 2 hours ago
Emilio Pisanty
78.6k21187385
edited 2 hours ago
Emilio Pisanty
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edited 2 hours ago
Emilio Pisanty
78.6k21187385
78.6k21187385
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Redacted
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asked 2 hours ago
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New contributor
Redacted is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Redacted is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
6
If you were Schrödinger's cat, then you wouldn't be Schrödinger's cat - you would be Wigner's friend (that being the equivalent paradox where the being in a superposition state is a conscious human). (Unless, of course, you're actually a cat.)
– Emilio Pisanty
2 hours ago
4
In addition to that, the standard advise when it comes to the 'What the bleep' so-called documentary is: drop it and find a better source. The whole film is so riddled with errors, misconceptions, quantum woo and outright misinformation that you simply won't come out ahead when getting your information from there.
– Emilio Pisanty
2 hours ago
Its funny, the more I learn about something, the more I realize my past teachers were misleading me in so many ways. good to know they're using bad resources. Now if only I could really understand the real math behind this stuff
– Redacted
1 hour ago
1
@Redacted You can understand the real math behind this, if you have a background of differential equations and linear algebra all you have to do is get an introductory book on the subject. I would recommend Griffiths or Shankar. There are many good sources to learn QM from.
– Hugo V
1 hour ago
found the book you're talking about. I'm going to start with the Griffiths one. found a pdf of the whole thing, downloaded it free of charge. Hopefully it'll help with my Diff EQ and linear algebra and calculus skills. Thanks for the recommendation.
– Redacted
55 mins ago
 |Â
show 1 more comment
6
If you were Schrödinger's cat, then you wouldn't be Schrödinger's cat - you would be Wigner's friend (that being the equivalent paradox where the being in a superposition state is a conscious human). (Unless, of course, you're actually a cat.)
– Emilio Pisanty
2 hours ago
4
In addition to that, the standard advise when it comes to the 'What the bleep' so-called documentary is: drop it and find a better source. The whole film is so riddled with errors, misconceptions, quantum woo and outright misinformation that you simply won't come out ahead when getting your information from there.
– Emilio Pisanty
2 hours ago
Its funny, the more I learn about something, the more I realize my past teachers were misleading me in so many ways. good to know they're using bad resources. Now if only I could really understand the real math behind this stuff
– Redacted
1 hour ago
1
@Redacted You can understand the real math behind this, if you have a background of differential equations and linear algebra all you have to do is get an introductory book on the subject. I would recommend Griffiths or Shankar. There are many good sources to learn QM from.
– Hugo V
1 hour ago
found the book you're talking about. I'm going to start with the Griffiths one. found a pdf of the whole thing, downloaded it free of charge. Hopefully it'll help with my Diff EQ and linear algebra and calculus skills. Thanks for the recommendation.
– Redacted
55 mins ago
6
6
If you were Schrödinger's cat, then you wouldn't be Schrödinger's cat - you would be Wigner's friend (that being the equivalent paradox where the being in a superposition state is a conscious human). (Unless, of course, you're actually a cat.)
– Emilio Pisanty
2 hours ago
If you were Schrödinger's cat, then you wouldn't be Schrödinger's cat - you would be Wigner's friend (that being the equivalent paradox where the being in a superposition state is a conscious human). (Unless, of course, you're actually a cat.)
– Emilio Pisanty
2 hours ago
4
4
In addition to that, the standard advise when it comes to the 'What the bleep' so-called documentary is: drop it and find a better source. The whole film is so riddled with errors, misconceptions, quantum woo and outright misinformation that you simply won't come out ahead when getting your information from there.
– Emilio Pisanty
2 hours ago
In addition to that, the standard advise when it comes to the 'What the bleep' so-called documentary is: drop it and find a better source. The whole film is so riddled with errors, misconceptions, quantum woo and outright misinformation that you simply won't come out ahead when getting your information from there.
– Emilio Pisanty
2 hours ago
Its funny, the more I learn about something, the more I realize my past teachers were misleading me in so many ways. good to know they're using bad resources. Now if only I could really understand the real math behind this stuff
– Redacted
1 hour ago
Its funny, the more I learn about something, the more I realize my past teachers were misleading me in so many ways. good to know they're using bad resources. Now if only I could really understand the real math behind this stuff
– Redacted
1 hour ago
1
1
@Redacted You can understand the real math behind this, if you have a background of differential equations and linear algebra all you have to do is get an introductory book on the subject. I would recommend Griffiths or Shankar. There are many good sources to learn QM from.
– Hugo V
1 hour ago
@Redacted You can understand the real math behind this, if you have a background of differential equations and linear algebra all you have to do is get an introductory book on the subject. I would recommend Griffiths or Shankar. There are many good sources to learn QM from.
– Hugo V
1 hour ago
found the book you're talking about. I'm going to start with the Griffiths one. found a pdf of the whole thing, downloaded it free of charge. Hopefully it'll help with my Diff EQ and linear algebra and calculus skills. Thanks for the recommendation.
– Redacted
55 mins ago
found the book you're talking about. I'm going to start with the Griffiths one. found a pdf of the whole thing, downloaded it free of charge. Hopefully it'll help with my Diff EQ and linear algebra and calculus skills. Thanks for the recommendation.
– Redacted
55 mins ago
 |Â
show 1 more comment
4 Answers
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In practice, you can't actually get yourself into a quantum superposition of dead and alive. Exposing a quantum system to a thermal environment causes the state to lose coherence and collapse into one state or another. In the double slit experiment, you are the thermal environment that causes the collapse.
"Observation" in quantum mechanics has nothing to do with eyesight. Closing your eyes does not make the difference between the state being observed or not. You can think of an observation having occurred whenever some macroscopic state of an incoherent system (like a cat) is made dependent on the microscopic state of a coherent quantum system.
So, in short, you would be either dead or alive, not in a superposition at all.
answered 2 hours ago
Chris
8,77362839
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I think the easiest resolution of the Schrodinger cat situation is to think that the state of a macroscopic system is never in a superposition of states, you can search about decoherence to understand this a little bit better.
So in this case, you have a cat in a box, a bit of radioactive material, a geiger counter and some poison that is released if the geiger counter detects a particle from the radioactive decay. It is fine to talk about an atom being in a superposition of states, the atom can be sufficiently isolated so that it is truly in a superposition of states. But the geiger counter is never in a superposition of states, independently of wheter you look at it or not(since observation has nothing to do with an actual person, or consciousness oberving), it either detects a particle or it doesn't, so the poison is either released or it isn't, which makes the cat not both dead and alive, not neither deade nor alive, but as expected, either dead or alive.
answered 2 hours ago
Hugo V
2086
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Understanding the math taught in quantum mechanics textbooks doesn't mean you know answers to questions like "what does it mean for a physical system to be macroscopic or to decohere" or "what does it mean to have a conscious being in a quantum superposition". Once you know a little bit of the basic math (most of the stuff in proper quantum mechanics textbooks is actually useless for discussing such questions), you can for example read about the "many worlds interpretation of quantum mechanics" in papers by B. DeWitt (For example the article in "Physics Today 23, 9, 30 (1970) called "Quantum Mechanics and Reality") or the thesis of H. Everett. In my opinion "many worlds" is a misnomer, in fact Everett's thesis doesn't use the term "world" at all, so don't be scared off by a thought like "I don't care about other universes, this has to be bullshit".
While I can't answer the questions well, I think when you think about what you feel when being in a quantum superposition you should keep in mind that you are a very complicated physical system and "feeling something" is also an extremely complicated process. Suppose for example there was a way to clone you with every atom in your body kept in exactly the same state inside your copy (this is impossible according to quantum mechanics, but never mind that for the moment). Both you and the copy then have equal claim to "being the real you". Would you mind, for example, being killed immediately after the copying process with only your copy surviving)? (This question has been discussed in the context of what "beaming" entails in science fiction films) The concept of some lump of matter being you and having a continuous and coherent experience is something your mind assumes by default but this is a simplification of what is really happening.
I will now try to address the question. This is the way I personally think about it and anyone is free to disagree. In a very lax manner, I would venture to say that at least in the "many worlds interpretation" of quantum mechanics (which is among the more popular "interpretations" among scientists in recent years) "each superposition" of you in "your quantum state" has its own independent experience. One could then imagine that this implies having "many copies of you" around at the same time. However, the question "which copy will I become when my state is shown to be a superposition" doesn't make sense. They are all just as valid. At the same time the question "am I currently in a quantum superposition?" doesn't make sense because in order to answer it you have to define yourself as a quantum system as opposed to the system asking the question (We always have to discuss the relative state of one system to the system "asking a question". Since all systems in the universe are in principle entangled, that is the only meaningful way to talk about "the state" of some object). It does make sense to ask if your friend over there is in a macroscopic quantum superposition (trust me, he is not, but you can still check if you like) and it also makes sense to ask if your right index finger is in a quantum superposition. You need to leave some system though that can record the answer to the question for the question to make sense.
Of course there are other "interpretations" which might try to answer such questions differently.
answered 46 mins ago
Adomas Baliuka
831215
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up vote
0
down vote
Regarding the double slit experiment you could read up on the single photon experiments, you would conclude that the high school point of view is very simplistic. Single one at a time photons still form the pattern ( the photons choose a path that is most probable, based on 1) interacting with the EM field of the slit and 2) finding the shortest path that tends to be n multiples of its wavelength (Feynman path integral). About Schrodinger's cat, it is trying to say that until we observe something we will not know what state it was in and it also says by observing it we may even force the system to adopt one state or another. If you are trying to observe yourself and determine your state your actions would equally affect the observed result. Superposition of states in the experiment means a state that is not one or other of 2 possible observations but in an another intermediate state or even states.
answered 2 hours ago
PhysicsDave
60426
"the photons [...] interacting with the EM field of the slit" - Photons don't interact with the EM field. "finding the shortest path [...] (Feynman path integral)" - The path integral refers to the least action, not the shortest path.
– safesphere
29 mins ago
add a comment |Â
4 Answers
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4 Answers
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active
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up vote
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In practice, you can't actually get yourself into a quantum superposition of dead and alive. Exposing a quantum system to a thermal environment causes the state to lose coherence and collapse into one state or another. In the double slit experiment, you are the thermal environment that causes the collapse.
"Observation" in quantum mechanics has nothing to do with eyesight. Closing your eyes does not make the difference between the state being observed or not. You can think of an observation having occurred whenever some macroscopic state of an incoherent system (like a cat) is made dependent on the microscopic state of a coherent quantum system.
So, in short, you would be either dead or alive, not in a superposition at all.
answered 2 hours ago
Chris
8,77362839
add a comment |Â
up vote
2
down vote
In practice, you can't actually get yourself into a quantum superposition of dead and alive. Exposing a quantum system to a thermal environment causes the state to lose coherence and collapse into one state or another. In the double slit experiment, you are the thermal environment that causes the collapse.
"Observation" in quantum mechanics has nothing to do with eyesight. Closing your eyes does not make the difference between the state being observed or not. You can think of an observation having occurred whenever some macroscopic state of an incoherent system (like a cat) is made dependent on the microscopic state of a coherent quantum system.
So, in short, you would be either dead or alive, not in a superposition at all.
answered 2 hours ago
Chris
8,77362839
add a comment |Â
up vote
2
down vote
up vote
2
down vote
In practice, you can't actually get yourself into a quantum superposition of dead and alive. Exposing a quantum system to a thermal environment causes the state to lose coherence and collapse into one state or another. In the double slit experiment, you are the thermal environment that causes the collapse.
"Observation" in quantum mechanics has nothing to do with eyesight. Closing your eyes does not make the difference between the state being observed or not. You can think of an observation having occurred whenever some macroscopic state of an incoherent system (like a cat) is made dependent on the microscopic state of a coherent quantum system.
So, in short, you would be either dead or alive, not in a superposition at all.
answered 2 hours ago
Chris
8,77362839
In practice, you can't actually get yourself into a quantum superposition of dead and alive. Exposing a quantum system to a thermal environment causes the state to lose coherence and collapse into one state or another. In the double slit experiment, you are the thermal environment that causes the collapse.
"Observation" in quantum mechanics has nothing to do with eyesight. Closing your eyes does not make the difference between the state being observed or not. You can think of an observation having occurred whenever some macroscopic state of an incoherent system (like a cat) is made dependent on the microscopic state of a coherent quantum system.
So, in short, you would be either dead or alive, not in a superposition at all.
answered 2 hours ago
Chris
8,77362839
answered 2 hours ago
Chris
8,77362839
answered 2 hours ago
Chris
8,77362839
answered 2 hours ago
Chris
8,77362839
8,77362839
add a comment |Â
add a comment |Â
up vote
1
down vote
I think the easiest resolution of the Schrodinger cat situation is to think that the state of a macroscopic system is never in a superposition of states, you can search about decoherence to understand this a little bit better.
So in this case, you have a cat in a box, a bit of radioactive material, a geiger counter and some poison that is released if the geiger counter detects a particle from the radioactive decay. It is fine to talk about an atom being in a superposition of states, the atom can be sufficiently isolated so that it is truly in a superposition of states. But the geiger counter is never in a superposition of states, independently of wheter you look at it or not(since observation has nothing to do with an actual person, or consciousness oberving), it either detects a particle or it doesn't, so the poison is either released or it isn't, which makes the cat not both dead and alive, not neither deade nor alive, but as expected, either dead or alive.
answered 2 hours ago
Hugo V
2086
New contributor
Hugo V is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
1
down vote
I think the easiest resolution of the Schrodinger cat situation is to think that the state of a macroscopic system is never in a superposition of states, you can search about decoherence to understand this a little bit better.
So in this case, you have a cat in a box, a bit of radioactive material, a geiger counter and some poison that is released if the geiger counter detects a particle from the radioactive decay. It is fine to talk about an atom being in a superposition of states, the atom can be sufficiently isolated so that it is truly in a superposition of states. But the geiger counter is never in a superposition of states, independently of wheter you look at it or not(since observation has nothing to do with an actual person, or consciousness oberving), it either detects a particle or it doesn't, so the poison is either released or it isn't, which makes the cat not both dead and alive, not neither deade nor alive, but as expected, either dead or alive.
answered 2 hours ago
Hugo V
2086
New contributor
Hugo V is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
up vote
1
down vote
up vote
1
down vote
I think the easiest resolution of the Schrodinger cat situation is to think that the state of a macroscopic system is never in a superposition of states, you can search about decoherence to understand this a little bit better.
So in this case, you have a cat in a box, a bit of radioactive material, a geiger counter and some poison that is released if the geiger counter detects a particle from the radioactive decay. It is fine to talk about an atom being in a superposition of states, the atom can be sufficiently isolated so that it is truly in a superposition of states. But the geiger counter is never in a superposition of states, independently of wheter you look at it or not(since observation has nothing to do with an actual person, or consciousness oberving), it either detects a particle or it doesn't, so the poison is either released or it isn't, which makes the cat not both dead and alive, not neither deade nor alive, but as expected, either dead or alive.
answered 2 hours ago
Hugo V
2086
New contributor
Hugo V is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I think the easiest resolution of the Schrodinger cat situation is to think that the state of a macroscopic system is never in a superposition of states, you can search about decoherence to understand this a little bit better.
So in this case, you have a cat in a box, a bit of radioactive material, a geiger counter and some poison that is released if the geiger counter detects a particle from the radioactive decay. It is fine to talk about an atom being in a superposition of states, the atom can be sufficiently isolated so that it is truly in a superposition of states. But the geiger counter is never in a superposition of states, independently of wheter you look at it or not(since observation has nothing to do with an actual person, or consciousness oberving), it either detects a particle or it doesn't, so the poison is either released or it isn't, which makes the cat not both dead and alive, not neither deade nor alive, but as expected, either dead or alive.
answered 2 hours ago
Hugo V
2086
New contributor
Hugo V is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 hours ago
Hugo V
2086
New contributor
Hugo V is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 2 hours ago
Hugo V
2086
answered 2 hours ago
Hugo V
2086
2086
New contributor
Hugo V is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Hugo V is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Hugo V is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |Â
add a comment |Â
up vote
1
down vote
Understanding the math taught in quantum mechanics textbooks doesn't mean you know answers to questions like "what does it mean for a physical system to be macroscopic or to decohere" or "what does it mean to have a conscious being in a quantum superposition". Once you know a little bit of the basic math (most of the stuff in proper quantum mechanics textbooks is actually useless for discussing such questions), you can for example read about the "many worlds interpretation of quantum mechanics" in papers by B. DeWitt (For example the article in "Physics Today 23, 9, 30 (1970) called "Quantum Mechanics and Reality") or the thesis of H. Everett. In my opinion "many worlds" is a misnomer, in fact Everett's thesis doesn't use the term "world" at all, so don't be scared off by a thought like "I don't care about other universes, this has to be bullshit".
While I can't answer the questions well, I think when you think about what you feel when being in a quantum superposition you should keep in mind that you are a very complicated physical system and "feeling something" is also an extremely complicated process. Suppose for example there was a way to clone you with every atom in your body kept in exactly the same state inside your copy (this is impossible according to quantum mechanics, but never mind that for the moment). Both you and the copy then have equal claim to "being the real you". Would you mind, for example, being killed immediately after the copying process with only your copy surviving)? (This question has been discussed in the context of what "beaming" entails in science fiction films) The concept of some lump of matter being you and having a continuous and coherent experience is something your mind assumes by default but this is a simplification of what is really happening.
I will now try to address the question. This is the way I personally think about it and anyone is free to disagree. In a very lax manner, I would venture to say that at least in the "many worlds interpretation" of quantum mechanics (which is among the more popular "interpretations" among scientists in recent years) "each superposition" of you in "your quantum state" has its own independent experience. One could then imagine that this implies having "many copies of you" around at the same time. However, the question "which copy will I become when my state is shown to be a superposition" doesn't make sense. They are all just as valid. At the same time the question "am I currently in a quantum superposition?" doesn't make sense because in order to answer it you have to define yourself as a quantum system as opposed to the system asking the question (We always have to discuss the relative state of one system to the system "asking a question". Since all systems in the universe are in principle entangled, that is the only meaningful way to talk about "the state" of some object). It does make sense to ask if your friend over there is in a macroscopic quantum superposition (trust me, he is not, but you can still check if you like) and it also makes sense to ask if your right index finger is in a quantum superposition. You need to leave some system though that can record the answer to the question for the question to make sense.
Of course there are other "interpretations" which might try to answer such questions differently.
answered 46 mins ago
Adomas Baliuka
831215
add a comment |Â
up vote
1
down vote
Understanding the math taught in quantum mechanics textbooks doesn't mean you know answers to questions like "what does it mean for a physical system to be macroscopic or to decohere" or "what does it mean to have a conscious being in a quantum superposition". Once you know a little bit of the basic math (most of the stuff in proper quantum mechanics textbooks is actually useless for discussing such questions), you can for example read about the "many worlds interpretation of quantum mechanics" in papers by B. DeWitt (For example the article in "Physics Today 23, 9, 30 (1970) called "Quantum Mechanics and Reality") or the thesis of H. Everett. In my opinion "many worlds" is a misnomer, in fact Everett's thesis doesn't use the term "world" at all, so don't be scared off by a thought like "I don't care about other universes, this has to be bullshit".
While I can't answer the questions well, I think when you think about what you feel when being in a quantum superposition you should keep in mind that you are a very complicated physical system and "feeling something" is also an extremely complicated process. Suppose for example there was a way to clone you with every atom in your body kept in exactly the same state inside your copy (this is impossible according to quantum mechanics, but never mind that for the moment). Both you and the copy then have equal claim to "being the real you". Would you mind, for example, being killed immediately after the copying process with only your copy surviving)? (This question has been discussed in the context of what "beaming" entails in science fiction films) The concept of some lump of matter being you and having a continuous and coherent experience is something your mind assumes by default but this is a simplification of what is really happening.
I will now try to address the question. This is the way I personally think about it and anyone is free to disagree. In a very lax manner, I would venture to say that at least in the "many worlds interpretation" of quantum mechanics (which is among the more popular "interpretations" among scientists in recent years) "each superposition" of you in "your quantum state" has its own independent experience. One could then imagine that this implies having "many copies of you" around at the same time. However, the question "which copy will I become when my state is shown to be a superposition" doesn't make sense. They are all just as valid. At the same time the question "am I currently in a quantum superposition?" doesn't make sense because in order to answer it you have to define yourself as a quantum system as opposed to the system asking the question (We always have to discuss the relative state of one system to the system "asking a question". Since all systems in the universe are in principle entangled, that is the only meaningful way to talk about "the state" of some object). It does make sense to ask if your friend over there is in a macroscopic quantum superposition (trust me, he is not, but you can still check if you like) and it also makes sense to ask if your right index finger is in a quantum superposition. You need to leave some system though that can record the answer to the question for the question to make sense.
Of course there are other "interpretations" which might try to answer such questions differently.
answered 46 mins ago
Adomas Baliuka
831215
add a comment |Â
up vote
1
down vote
up vote
1
down vote
Understanding the math taught in quantum mechanics textbooks doesn't mean you know answers to questions like "what does it mean for a physical system to be macroscopic or to decohere" or "what does it mean to have a conscious being in a quantum superposition". Once you know a little bit of the basic math (most of the stuff in proper quantum mechanics textbooks is actually useless for discussing such questions), you can for example read about the "many worlds interpretation of quantum mechanics" in papers by B. DeWitt (For example the article in "Physics Today 23, 9, 30 (1970) called "Quantum Mechanics and Reality") or the thesis of H. Everett. In my opinion "many worlds" is a misnomer, in fact Everett's thesis doesn't use the term "world" at all, so don't be scared off by a thought like "I don't care about other universes, this has to be bullshit".
While I can't answer the questions well, I think when you think about what you feel when being in a quantum superposition you should keep in mind that you are a very complicated physical system and "feeling something" is also an extremely complicated process. Suppose for example there was a way to clone you with every atom in your body kept in exactly the same state inside your copy (this is impossible according to quantum mechanics, but never mind that for the moment). Both you and the copy then have equal claim to "being the real you". Would you mind, for example, being killed immediately after the copying process with only your copy surviving)? (This question has been discussed in the context of what "beaming" entails in science fiction films) The concept of some lump of matter being you and having a continuous and coherent experience is something your mind assumes by default but this is a simplification of what is really happening.
I will now try to address the question. This is the way I personally think about it and anyone is free to disagree. In a very lax manner, I would venture to say that at least in the "many worlds interpretation" of quantum mechanics (which is among the more popular "interpretations" among scientists in recent years) "each superposition" of you in "your quantum state" has its own independent experience. One could then imagine that this implies having "many copies of you" around at the same time. However, the question "which copy will I become when my state is shown to be a superposition" doesn't make sense. They are all just as valid. At the same time the question "am I currently in a quantum superposition?" doesn't make sense because in order to answer it you have to define yourself as a quantum system as opposed to the system asking the question (We always have to discuss the relative state of one system to the system "asking a question". Since all systems in the universe are in principle entangled, that is the only meaningful way to talk about "the state" of some object). It does make sense to ask if your friend over there is in a macroscopic quantum superposition (trust me, he is not, but you can still check if you like) and it also makes sense to ask if your right index finger is in a quantum superposition. You need to leave some system though that can record the answer to the question for the question to make sense.
Of course there are other "interpretations" which might try to answer such questions differently.
answered 46 mins ago
Adomas Baliuka
831215
Understanding the math taught in quantum mechanics textbooks doesn't mean you know answers to questions like "what does it mean for a physical system to be macroscopic or to decohere" or "what does it mean to have a conscious being in a quantum superposition". Once you know a little bit of the basic math (most of the stuff in proper quantum mechanics textbooks is actually useless for discussing such questions), you can for example read about the "many worlds interpretation of quantum mechanics" in papers by B. DeWitt (For example the article in "Physics Today 23, 9, 30 (1970) called "Quantum Mechanics and Reality") or the thesis of H. Everett. In my opinion "many worlds" is a misnomer, in fact Everett's thesis doesn't use the term "world" at all, so don't be scared off by a thought like "I don't care about other universes, this has to be bullshit".
While I can't answer the questions well, I think when you think about what you feel when being in a quantum superposition you should keep in mind that you are a very complicated physical system and "feeling something" is also an extremely complicated process. Suppose for example there was a way to clone you with every atom in your body kept in exactly the same state inside your copy (this is impossible according to quantum mechanics, but never mind that for the moment). Both you and the copy then have equal claim to "being the real you". Would you mind, for example, being killed immediately after the copying process with only your copy surviving)? (This question has been discussed in the context of what "beaming" entails in science fiction films) The concept of some lump of matter being you and having a continuous and coherent experience is something your mind assumes by default but this is a simplification of what is really happening.
I will now try to address the question. This is the way I personally think about it and anyone is free to disagree. In a very lax manner, I would venture to say that at least in the "many worlds interpretation" of quantum mechanics (which is among the more popular "interpretations" among scientists in recent years) "each superposition" of you in "your quantum state" has its own independent experience. One could then imagine that this implies having "many copies of you" around at the same time. However, the question "which copy will I become when my state is shown to be a superposition" doesn't make sense. They are all just as valid. At the same time the question "am I currently in a quantum superposition?" doesn't make sense because in order to answer it you have to define yourself as a quantum system as opposed to the system asking the question (We always have to discuss the relative state of one system to the system "asking a question". Since all systems in the universe are in principle entangled, that is the only meaningful way to talk about "the state" of some object). It does make sense to ask if your friend over there is in a macroscopic quantum superposition (trust me, he is not, but you can still check if you like) and it also makes sense to ask if your right index finger is in a quantum superposition. You need to leave some system though that can record the answer to the question for the question to make sense.
Of course there are other "interpretations" which might try to answer such questions differently.
answered 46 mins ago
Adomas Baliuka
831215
answered 46 mins ago
Adomas Baliuka
831215
answered 46 mins ago
Adomas Baliuka
831215
answered 46 mins ago
Adomas Baliuka
831215
831215
add a comment |Â
add a comment |Â
up vote
0
down vote
Regarding the double slit experiment you could read up on the single photon experiments, you would conclude that the high school point of view is very simplistic. Single one at a time photons still form the pattern ( the photons choose a path that is most probable, based on 1) interacting with the EM field of the slit and 2) finding the shortest path that tends to be n multiples of its wavelength (Feynman path integral). About Schrodinger's cat, it is trying to say that until we observe something we will not know what state it was in and it also says by observing it we may even force the system to adopt one state or another. If you are trying to observe yourself and determine your state your actions would equally affect the observed result. Superposition of states in the experiment means a state that is not one or other of 2 possible observations but in an another intermediate state or even states.
answered 2 hours ago
PhysicsDave
60426
"the photons [...] interacting with the EM field of the slit" - Photons don't interact with the EM field. "finding the shortest path [...] (Feynman path integral)" - The path integral refers to the least action, not the shortest path.
– safesphere
29 mins ago
add a comment |Â
up vote
0
down vote
Regarding the double slit experiment you could read up on the single photon experiments, you would conclude that the high school point of view is very simplistic. Single one at a time photons still form the pattern ( the photons choose a path that is most probable, based on 1) interacting with the EM field of the slit and 2) finding the shortest path that tends to be n multiples of its wavelength (Feynman path integral). About Schrodinger's cat, it is trying to say that until we observe something we will not know what state it was in and it also says by observing it we may even force the system to adopt one state or another. If you are trying to observe yourself and determine your state your actions would equally affect the observed result. Superposition of states in the experiment means a state that is not one or other of 2 possible observations but in an another intermediate state or even states.
answered 2 hours ago
PhysicsDave
60426
"the photons [...] interacting with the EM field of the slit" - Photons don't interact with the EM field. "finding the shortest path [...] (Feynman path integral)" - The path integral refers to the least action, not the shortest path.
– safesphere
29 mins ago
add a comment |Â
up vote
0
down vote
up vote
0
down vote
Regarding the double slit experiment you could read up on the single photon experiments, you would conclude that the high school point of view is very simplistic. Single one at a time photons still form the pattern ( the photons choose a path that is most probable, based on 1) interacting with the EM field of the slit and 2) finding the shortest path that tends to be n multiples of its wavelength (Feynman path integral). About Schrodinger's cat, it is trying to say that until we observe something we will not know what state it was in and it also says by observing it we may even force the system to adopt one state or another. If you are trying to observe yourself and determine your state your actions would equally affect the observed result. Superposition of states in the experiment means a state that is not one or other of 2 possible observations but in an another intermediate state or even states.
answered 2 hours ago
PhysicsDave
60426
Regarding the double slit experiment you could read up on the single photon experiments, you would conclude that the high school point of view is very simplistic. Single one at a time photons still form the pattern ( the photons choose a path that is most probable, based on 1) interacting with the EM field of the slit and 2) finding the shortest path that tends to be n multiples of its wavelength (Feynman path integral). About Schrodinger's cat, it is trying to say that until we observe something we will not know what state it was in and it also says by observing it we may even force the system to adopt one state or another. If you are trying to observe yourself and determine your state your actions would equally affect the observed result. Superposition of states in the experiment means a state that is not one or other of 2 possible observations but in an another intermediate state or even states.
answered 2 hours ago
PhysicsDave
60426
answered 2 hours ago
PhysicsDave
60426
answered 2 hours ago
PhysicsDave
60426
answered 2 hours ago
PhysicsDave
60426
60426
"the photons [...] interacting with the EM field of the slit" - Photons don't interact with the EM field. "finding the shortest path [...] (Feynman path integral)" - The path integral refers to the least action, not the shortest path.
– safesphere
29 mins ago
add a comment |Â
"the photons [...] interacting with the EM field of the slit" - Photons don't interact with the EM field. "finding the shortest path [...] (Feynman path integral)" - The path integral refers to the least action, not the shortest path.
– safesphere
29 mins ago
"the photons [...] interacting with the EM field of the slit" - Photons don't interact with the EM field. "finding the shortest path [...] (Feynman path integral)" - The path integral refers to the least action, not the shortest path.
– safesphere
29 mins ago
"the photons [...] interacting with the EM field of the slit" - Photons don't interact with the EM field. "finding the shortest path [...] (Feynman path integral)" - The path integral refers to the least action, not the shortest path.
– safesphere
29 mins ago
add a comment |Â
Redacted is a new contributor. Be nice, and check out our Code of Conduct.
Redacted is a new contributor. Be nice, and check out our Code of Conduct.
Redacted is a new contributor. Be nice, and check out our Code of Conduct.
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6
If you were Schrödinger's cat, then you wouldn't be Schrödinger's cat - you would be Wigner's friend (that being the equivalent paradox where the being in a superposition state is a conscious human). (Unless, of course, you're actually a cat.)
– Emilio Pisanty
2 hours ago
4
In addition to that, the standard advise when it comes to the 'What the bleep' so-called documentary is: drop it and find a better source. The whole film is so riddled with errors, misconceptions, quantum woo and outright misinformation that you simply won't come out ahead when getting your information from there.
– Emilio Pisanty
2 hours ago
Its funny, the more I learn about something, the more I realize my past teachers were misleading me in so many ways. good to know they're using bad resources. Now if only I could really understand the real math behind this stuff
– Redacted
1 hour ago
1
@Redacted You can understand the real math behind this, if you have a background of differential equations and linear algebra all you have to do is get an introductory book on the subject. I would recommend Griffiths or Shankar. There are many good sources to learn QM from.
– Hugo V
1 hour ago
found the book you're talking about. I'm going to start with the Griffiths one. found a pdf of the whole thing, downloaded it free of charge. Hopefully it'll help with my Diff EQ and linear algebra and calculus skills. Thanks for the recommendation.
– Redacted
55 mins ago