Superposition in quantum mechanics describes a quantum state existing in all possible states simultaneously until observed. This concept is mathematically represented as an infinite-dimensional vector, where any state can be decomposed into a superposition of basis states. The discussion emphasizes that superposition is not limited to certain states; rather, all quantum states can be expressed as a linear combination of basis states. The double-slit experiment serves as a practical illustration of superposition, demonstrating how a single photon can interfere with itself due to being in a superposition of states.
PREREQUISITESStudents of physics, quantum mechanics enthusiasts, and educators seeking to deepen their understanding of superposition and its implications in quantum theory.
Do you know how superposition works, mathematically, with classical fields, e.g. the electric field?Sundown444 said:Can anyone please describe to me how superposition in quantum mechanics works,
Sundown444 said:Can anyone please describe to me how superposition in quantum mechanics works, preferably using real life places and objects as examples? I am having trouble understanding the concept.
jtbell said:Do you know how superposition works, mathematically, with classical fields, e.g. the electric field?
Stephen Tashi said:What's your education, so far? What mathematics have you studied?
Sundown444 said:Not by much. Please tell me if you can.
I have Algebra and some Calculus, and I know a good amount of physics, though I haven't gone much into Quantum Mechanics yet. What I recall is that superposition is the idea that a system is in all possible states at the same time until it is observed.
PeroK said:If you know what a vector is, then you will be familiar with resolving a vector into the components in different directions.
For example, gravity near the surface of the Earth is a vertical vector. But, you can decompose that vector into, say, components tangential and normal to an inclined plane. And, in fact, you are free to decompose the vector into components in any pair of directions.
A quantum state is in fact an infinite dimensional vector. And superposition is the term used to describe its decomposition in a given basis of states.
Many people labour under the delusion that some states are in superposition and some are not. But, that is as absurd as saying some vectors can be decomposed and some cannot.
In short, given any state and any set of basis states, the state is in a superposition of those basis states. If you think, therefore, that superposition just means linear combination, then you'd be correct. Of course, if the basis you choose has the state in question as one of the basis states, then the superposition is trivial.
The role that linear algebra plays in QM goes much deeper than that. But, that's what a superposition is.
I don't know much about the Many World's interpretation of QM. But, superposition is part of the core mathematical framework, so it's not specifically related to anyone interpretation.Sundown444 said:I see. Does it have anything to do with that many worlds theory thing?
The Many Worlds Interpretation in a nut shell gives each possible outcome its own "universe" to exist in, where the observed outcome relates to the universe we continue to exist in. Pilot wave theory simply gives a deterministic approach to the same probabilistic reality which is quantum superposition.Sundown444 said:Does it have anything to do with that many worlds theory thing?
Schrödinger's cat is an example from way back, when QM was fairly new. Macroscopic objects don't behave this way but the thought experiment gives some clue as to why superposition is hard to conceptualize.Sundown444 said:Can anyone please describe to me how superposition in quantum mechanics works