The discussion revolves around the concept of superposition in quantum mechanics, with participants seeking clarification and examples to aid understanding. The scope includes theoretical explanations, mathematical interpretations, and conceptual challenges related to both quantum mechanics and classical fields.
Participants express a range of views on the nature of superposition, with some seeking clarification while others provide technical explanations. There is no consensus on the applicability of superposition to macroscopic objects or the interpretation of quantum mechanics, indicating ongoing debate and uncertainty.
Participants' understanding of mathematics and physics varies, with some having limited exposure to quantum mechanics. The discussion includes assumptions about familiarity with concepts like vectors and linear algebra, which may not be universally shared.
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