# Superposition of charges

1. Mar 13, 2015

### lucas_

In the superposition of charges, both directions is said to occur at the same time.. question: is this simultaneous occurrences observable (viewable) at the same time? I presume the left an right direction are eigenstates, but it is commonly said you can only observe one eigenstates at a time... so how does the left and right charges work.. alternatively? and most important.. what theorem forbid the simultaneous observation of eigenstates.. maybe the law of conservation of energy, what exactly?

Thanks.

2. Mar 14, 2015

### Simon Bridge

You need to be clear about what is being measured.

In general: an eigenstate of A may be a superposition of eigenstates of B ... so a system prepared in an eigenstate of A will yeild a definite state when A is measured, but B will be uncertain. iirc. The superposition itself is said to be "simultaneous" if the mix is not time dependent. It's just maths.

By "superposition of charges" do you mean a superposition of charge states?

3. Mar 14, 2015

### lucas_

so there is no situation that eingenstate of A and B will simultaneous? what do you mean time independent.. an example?

4. Mar 14, 2015

### Simon Bridge

Ah - charge state superposition as in cooper-pairs ...

If |a> is an eigenstate of A with eigenvalue a, similar for B, then we may have the system prepared in state $|b\rangle = \frac{1}{\sqrt{2}}(|a_1\rangle+|a_2\rangle)$ ... i.e. |b> is a superposition of two states of |a>.

A measurements of A will get you either a1 or a2 with 50:50 chance.
But that probablility need not be constant in time. You could have:

$|\psi\rangle = c_1(t)|a_1\rangle+c_2(t)|a_2\rangle): c_1^\star c_1 + c_2^\star c_2 = 1$

5. Mar 14, 2015

### lucas_

non-physics education...

I got confused.. I wasn't referring to superposition of charges.. but superposition of currents in opposite direction like mentioned here:

http://physicsworld.com/cws/article/news/2000/jul/05/schrodingers-cat-comes-into-view
http://www3.amherst.edu/~jrfriedman/NYTimes/071100sci-quantum-mechanics.html

I was asking if the 2 currents in opposite directions are actually measured at the same time.. or only one at a time... and whether there are experiments where both are measured at same time

I was (and am) wondering whether when you have superposition of A and B.. both A and B are contained in the system at the same time and what conservation laws it can violate if it were true...

Last edited: Mar 14, 2015
6. Mar 14, 2015

### Staff: Mentor

Here is Lukens's and Friedman's paper here, the experiment that those two articles are reporting on: http://www.nature.com/nature/journal/v406/n6791/abs/406043a0.html. It's worth reading, if only to get a sense of just how much both of those articles are leaving out.

Currents in opposite direction are not being measured in any experiment of this type. Instead, we measure something else and conclude from that measurement that the state of the system can be written as a superposition of the current-clockwise and the current-counterclockwise states (it can also be written as a superposition of many other things if we'd rather).

There are no violations of conservation laws here. A superposition of A and B does not mean that system state is both A and B at the same time, nor does it mean that the system state is A or B but we don't know which. It means that the system is in some state that is neither A nor B, and that if we make a measurement there is some probability that immediately after the measurement the state will be A and some probability that it will be B. Either way, all conservation laws will be respected (although we have to remember to include any possible transfers of momentum, charge, energy, other conserved stuff to the device doing the measuring).

7. Mar 14, 2015

### Simon Bridge

Context is everything ...

From a general ed perspective then ... breaking things down into parts like this is common in mathematics. Consider long-division ... just because you do the calculation like that does not mean the actual thing is divided-up anything like the process suggests. It's just that breaking the process into parts can make the calculation easier to carry out.

8. Mar 14, 2015

### lucas_

Finally I understood why they have to propose Many Worlds, here system state A and B both occur (why haven't you mentioned this). No conservation laws violated because they don't occur in one world. Because if it can occur in one world, you can duplicate things like making 2 electrons out of one in the double slit experiment if state A and B both exist. But in the Feynman Path Integral, all paths exist so state A and B both exist.. so why didn't this violate conservation laws? Maybe like in the virtual particles because of HUP?

9. Mar 15, 2015

### Simon Bridge

He did, this bit...
(my emph.) ...its just maths. The way you do the calculations need not resemble what physically happens. No need for "many worlds".

There is a sticky about interpretations someplave.

10. Mar 15, 2015

### Staff: Mentor

You don't need the Many Worlds Interpretation (MWI) to explain this. The standard collapse interpretation (and any other interpretation, for that matter) works and conserves energy just as well. You say:
Whether you use the MWI or not, a superposition of state A and state B does not mean that both A and B exist; in fact, neither exists unless and until some interaction (this interaction is often and misleadingly called a "measurement") with something else (for example, a detector in the slits) happens. The double slit experiment shows that the electron is in a superposition of "went through first slit" and "went through second slit" when it arrives at the screen, and this is true in both MWI and the various single-world interpretations. That superposition does not mean that the electron actually went through both slits, nor that the electron somehow "exists" in both slits, nor that it was ever in two places at once.

All the MWI does is give you a particular way of thinking about what happens after that interaction with the detector happens. MWI says that the the world splits into two worlds, one in which the measurement result is A and the other is B; we find ourselves in one or the other so see only the A result or only the B result, and we don't don't care about the other. We could just as well say that the interaction "collapses" the wave function to either A or B so that's the only result and of course that's what we see. Whether we end up with A or B, energy is conserved.
The path integral doesn't say that all the paths exist, it says that if you perform a particular calculation for each possible path and add up the results, you will get the right answer for the probability of getting a particular measurement result. Virtual particles are just another part of this mathematical trick; you include the paths in which virtual particles appear and disappear when you're doing the calculation, but that doesn't make them real or violate any conservation laws.

If you're really serious about understanding how the path integral works, you'll need a serious book on quantum field theory. Quantum field theory for the gifted amateur is excellent, but requires a fairly strong math background. Feynman's book "QED: The strange theory of light and matter" is a good start if you just want a decent but math-free overview.

Last edited: Mar 16, 2015
11. Mar 16, 2015

### Simon Bridge

Still looking for the definitive post on interpretations ... did find this:
... it goes on to discuss why people bother with interpretations.
Interpretations of Quantum Mechanics