Question about superposition....

[Sundown444]

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.

 

[anorlunda]

Sorry but no. Quantum mechanics is not like anything in everyday life. You can learn how QM works by study, but :

It is safe to say that nobody understands quantum mechanics. Richard Feynman.

 

[Sundown444]

So it only applies to subatomic particles then, not objects?

 

[jtbell]

Can anyone please describe to me how superposition in quantum mechanics works,

Do you know how superposition works, mathematically, with classical fields, e.g. the electric field?

 

[Stephen Tashi]

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.

What's your education, so far? What mathematics have you studied?

 

[Sundown444]

Do you know how superposition works, mathematically, with classical fields, e.g. the electric field?

Not by much. Please tell me if you can.

What's your education, so far? What mathematics have you studied?

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]

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.

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.

 

[Sundown444]

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 see. Does it have anything to do with that many worlds theory thing?

 

[PeroK]

I see. Does it have anything to do with that many worlds theory thing?

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.

 

[lekh2003]

I think a good place to start is by looking at the double slit experiment. I hope you are familiar with this experiment.

The experiment with two slits proves that two light waves can interference constructively and deconstructively just like any wave. The interesting part of the experiment comes when you only shoot single photons at a time. Either photon can only go through one slit, so we shouldn't see a constructive or deconstructive pattern. How can a photon interfere with itself? Well, surprise surprise, it can interfere with itself. The photon is in a superposition of several states and these states can interact with each other.

If you are not aware of the experiment and what I am talking about, it would do you good to study the mathematical properties of waves and review a high school physics textbok.

 

[jerromyjon]

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.

 

[jerromyjon]

Can anyone please describe to me how superposition in quantum mechanics works

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.