- #1
Negatratoron
- 25
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Context of this post (skim or skip, but read the last paragraph):
I like to teach things to people, especially those who believe that they won't understand. For those hard cases you almost have to trick them into learning something. That is, just start building up concepts in simple terms, and only at the very end reveal what it is you're talking about. Because if you say "Here, I'm going to explain quantum superpositions to you" they think "I can't", turn their brains off, and go into hopeless-but-politely-attentive mode.
It feels like a dance, speaking only in ways that do not trigger them to stop thinking. Never giving them a place where they can say "yeah but that's beyond my ability to comprehend". And walking away smiling, as they struggle with the cognitive dissonance they get from understanding something they wanted to think they could not. But that's a rant for another time.
Anyway, my worst fear is always that I give someone a misconception. Misconceptions are extremely troublesome. Having one is like having a proof of "false" banging around in your head, going around proving other falses. And the more damage has been done, the more reluctant one is to change their mind. So I take misconceptions very seriously.
I am not a physicist. This post is to clear up my own misconceptions about superpositions so I can help other people clear up theirs. Please read over it and let me know whether I'm on the right track by describing superpositions this way.
The Post:
I used to have the misconception (a common one, I think) that "superposition" means a particle is literally in two places at once. The truth is way more mundane than that.When someone says "A particle's location is in superposition", they just mean "I have not recently measured the location of the particle, but here's my guess as to where it might be".
For instance, consider an electron in a superposition of two locations. We needn't think of it as being in two places at once - we simply don't know which location it is at. Its electric field is also in superposition. When we compute how this electric field affects another particle, we do not "sum" or "average" over the superposition of electric fields and apply the result to the other particle. Instead, the other particle is pulled into superposition too. It could be affected by the electric field one of the two ways (not by both). We simply don't know which it was, until we measure an appropriate observable.The superposition of a system is relative to a given observer. It is based on what information that observer has about the system.
The uncertainty principle tells us that an observer can never have perfect information about a system. So during measurement, the system's superposition "collapses" to some extent (meaning the observer now knows some of the specifics of the system). Then the superposition "grows" again, as the variables the observer was unable to measure do affect the evolution of the system.Schrodinger's cat is in a superposition of being alive and dead. It is in no way both alive alive and dead simultaneously. Nor does it have a 50% chance of being alive and a 50% chance of being dead. It has a 100% chance of being one and a 0% chance of being the other, our observer just doesn't know which is which. (oh how the media likes to sensationalize Schrodinger's cat)
Really, the superposition corresponds to our observer's confidence in each alternative. With a 50-50 superposition, our observer has no idea whether the cat is alive or dead. When they look in the box, they become highly confident in one alternative over the other, and the superposition is said to collapse.
If our observer's partner looks in the box, then THEY are in superposition of having seen a living cat and having seen a dead cat. When our observer observes their partner, perhaps a look of relief on their face conveys some information and the superposition collapses a little bit. But it collapses more fully when our observer looks in the box themselves.A superposition is just the (possibly infinite, of course) set of states a system might be in, along with the confidence level for each alternative. Different observers might even consider the same system to be in different superpositions, depending on what information they have about it.That's all.
Thanks for reading (or at least scrolling) to the bottom of this long post. Happy new year all.
I like to teach things to people, especially those who believe that they won't understand. For those hard cases you almost have to trick them into learning something. That is, just start building up concepts in simple terms, and only at the very end reveal what it is you're talking about. Because if you say "Here, I'm going to explain quantum superpositions to you" they think "I can't", turn their brains off, and go into hopeless-but-politely-attentive mode.
It feels like a dance, speaking only in ways that do not trigger them to stop thinking. Never giving them a place where they can say "yeah but that's beyond my ability to comprehend". And walking away smiling, as they struggle with the cognitive dissonance they get from understanding something they wanted to think they could not. But that's a rant for another time.
Anyway, my worst fear is always that I give someone a misconception. Misconceptions are extremely troublesome. Having one is like having a proof of "false" banging around in your head, going around proving other falses. And the more damage has been done, the more reluctant one is to change their mind. So I take misconceptions very seriously.
I am not a physicist. This post is to clear up my own misconceptions about superpositions so I can help other people clear up theirs. Please read over it and let me know whether I'm on the right track by describing superpositions this way.
The Post:
I used to have the misconception (a common one, I think) that "superposition" means a particle is literally in two places at once. The truth is way more mundane than that.When someone says "A particle's location is in superposition", they just mean "I have not recently measured the location of the particle, but here's my guess as to where it might be".
For instance, consider an electron in a superposition of two locations. We needn't think of it as being in two places at once - we simply don't know which location it is at. Its electric field is also in superposition. When we compute how this electric field affects another particle, we do not "sum" or "average" over the superposition of electric fields and apply the result to the other particle. Instead, the other particle is pulled into superposition too. It could be affected by the electric field one of the two ways (not by both). We simply don't know which it was, until we measure an appropriate observable.The superposition of a system is relative to a given observer. It is based on what information that observer has about the system.
The uncertainty principle tells us that an observer can never have perfect information about a system. So during measurement, the system's superposition "collapses" to some extent (meaning the observer now knows some of the specifics of the system). Then the superposition "grows" again, as the variables the observer was unable to measure do affect the evolution of the system.Schrodinger's cat is in a superposition of being alive and dead. It is in no way both alive alive and dead simultaneously. Nor does it have a 50% chance of being alive and a 50% chance of being dead. It has a 100% chance of being one and a 0% chance of being the other, our observer just doesn't know which is which. (oh how the media likes to sensationalize Schrodinger's cat)
Really, the superposition corresponds to our observer's confidence in each alternative. With a 50-50 superposition, our observer has no idea whether the cat is alive or dead. When they look in the box, they become highly confident in one alternative over the other, and the superposition is said to collapse.
If our observer's partner looks in the box, then THEY are in superposition of having seen a living cat and having seen a dead cat. When our observer observes their partner, perhaps a look of relief on their face conveys some information and the superposition collapses a little bit. But it collapses more fully when our observer looks in the box themselves.A superposition is just the (possibly infinite, of course) set of states a system might be in, along with the confidence level for each alternative. Different observers might even consider the same system to be in different superpositions, depending on what information they have about it.That's all.
Thanks for reading (or at least scrolling) to the bottom of this long post. Happy new year all.