Practical examples of superposition?

[ayladarcy]

Hello,

I am a first time poster and this post will be long, but I wanted to make clear my understanding of superposition so that you can all correct me. Thanks for your patience/interest.

I am not a physicist but a critical theorist working with Bohr's complementarity. I thought I understood superposition (from Bohr's essays and Heisenberg's Physics and Philosophy and from other quantum physics books written for non-physicists) but the more I read (Omnes's Quantum Philosophy specifically) the more confused I get. I would like to explain what I understand and what I don't and see if someone can help me. I am actually onceptualising this in my own way/words from all that I have read.

My understanding of a quantum state is that it is not reality but an expression of a range of potential realities which we cannot know, ie observe. When we do observe something it resolves into a classical determined state that falls within the range of the quantum state and is then 'reality'. Superposition is then an interpretative and mathematical term that allows us to calculate and talk about observations resulting from an experiment in which particles behave in ways we cannot see.

Superposition is something that happens to fields, waves or things dispersed within a field, wave or area of dispersal. These waves are either real, i.e. energy, or conceptual, ie a wave function.

The only way I can come to any grips with physics is when I am given an example experiment rather than a mathematical formula.

The double-slit experiment I think I get. The Schroedinger cat is nonsense to me. In the same way, quantum superposition makes sense to me but macroscopic doesn't - mainly because we always do observe the macroscopic world and therefore things are determined and not fields of possibility that describe what we cannot know. Yet Omnes writes that tunnel effects theoretically can effect the macroscopic world, it is just that their probability is so low its basically nil. I don't get that.

In the double slit experiment there is an actual observation of interference effects that are traces of a path(s) that we cannot observe. When we do observe it the traces tell a different story and we get a distribution pattern. I tend to interpret this as the difference between a photon behaving as a wave or a particle rather than as a particle simultaneously going through two slits; or the interference of an actual wave long enough to pass through two slits rather than a point that is in two places at the same time. Therefore, the mystery isn't that the particle made a quantum jump at some point to choose only one hole but that a particle will appear to behave the way an observer chooses.

From what I gather of the Schroedinger cat thought-experiment there is no interference. What is the interference effect of a dead and alive cat? A sick cat? And if so how would this sickness manifest itself as a trace that we could observe only if we never open the box but would disappear once we did? It just doesn't seem in any way equivalent to the double slit experiment.

The Wikipedia page on superposition uses an example I get: the superposition of probabilities that a photon has either a negative or positive spin state cancels each other out and an atom isn't jumped to a new level. But if we actually measure (determine) the spin state as plus or minus then the atom will jump. And there's even a way this kind of makes sense in that the observation changes the system so what happens under observation is always different than what happens when not observed ('course maybe it did jump, who knows, we didn't observe it).

But Omnes's example of a pendulum that measures spin I don't get because apparently the pendulum begins in a state of superposition and I understand superposition to be something that happens not something you begin with.

Anyway, I guess this is a loooong way of asking if you all could provide me with other actual examples of real interference interpreted as superposition that somehow collapses into determination independent of the act of being measured or observed. If there is not such experiment then why is decoherence necessary and how do observed things show superposition? Clearly, I'm not getting this because none of this bothers me philosophically the way it apparently does actual physicists... To me there is logic in uncertainty and complementarity and the fact that unobservable and observed realms must be understood mutually exclusively yet both can only be talked about in the classical language that describes what is observed.

Thanks for your patience and I look forward to your answers.

 

[DrChinese]

... But if we actually measure (determine) the spin state as plus or minus then the atom will jump. And there's even a way this kind of makes sense in that the observation changes the system so what happens under observation is always different than what happens when not observed ('course maybe it did jump, who knows, we didn't observe it).

Spin entanglement of a pair of photons is a good example of superposition. A typcial scenario is the Bell state:

H>V> + V>H>

In this state, regardless of where you choose to set the H axis, there is a statistical connection between these two photons. Now it should be clear that the observation of one would NOT classically affect the other. Yet there is wave function collapse for both when one is measured, and that collapse occurs FTL (probably instantaneously). So then the particles move into a specific state and they are no longer in a superposition.

Now, this state occurs naturally all the time: all virtual particle pairs are entangled.

 

[f95toli]

You can also look up a few papers on solid state qubits (which, btw, are definately macroscopic), one advantage with them in this context is that we are dealing with something more tangible than e.g. photons.
Examples of states that can be in a superpositions in this case would e.g be
*Charge qubit: 0 and 1 extra electon on an superconducting island (which is basically a small capacitor)
*Flux qubit: Current flowing clockwise and counter-clockwise

More "modern" qubits use slightly more sophisticated systems, but these are quite good to start with since it is quite easy to understand what the two states represent (since these states also exist in the classical regime)

 

[Naty1]

This may be to too basic but if a quantum system can be found in one of two states, say A and B with different properties, it can also be found in a combination of them say xA and yB where x and y are any numbers...each combination is a superposition...

In quantum theory the concept of a state is limited to as complete a description as may be given subject to the uncertainty of the Heisenberg uncertainty principle. Lee Smolin implies he doesn't fully believe it, but uses it because it's part of the only theory he knows that explains the main observed facts about elementary particles. As you may have implied in your post, if we choose to measure different quantities, this can have an effect on the state of the system.

Lee Smolin has a decent non mathematical introductory discussion in THREE ROADS TO QUANTUM GRAVITY chapter 3.