When are particles in a superposition of states?

[AidenPearce]

Hi guys, I hope you all are doing great.

If we take the double slit experiment for instance, before measurement particles are in a superposition of states. Once they are "measured", or non arbitrarily interfered with, their wave function collapses and only one state remains. So my question is this : how long does that state remains "fixed" ? When it comes to the particles that compose us / the environment, what state(s) are they in ? Aren't they being "measured" every time they hit another particle and thus never really are in a superposition of states ?

My understanding of "measurement" is most definitely flawed and is probably the source of my misunderstandings.

This video actually raised these questions :



Starting around 6:00, we can see the effects of quantum tunnelling, where the photons that tunnel through the glass become visible. From my understanding, they can only tunnel if they are in a superposition of states, except as they are always "hitting" other particles (firstly the ones that compose the guy's finger), how come they still are in a superposition of states ?

I so hope someone has some answers for me

Cheers mates !

 

[PeroK]

I don't think being in a superposition of states is relevant to the tunnelling effect demonstrated.

I think you have quite a few questions in there.

1) A particle (or any quantum system) is always in a superposition of states. But, it is also always in a defined (possibly mixed) state. This is because any state can be expressed as a superposition of other states (in an infinite number of ways). You may have a system in an energy eigenstate (that's a well-defined state). But, that eigenstate may be a superposition of infinitely many position eigenstates. If you measure position, the state "collapses" to a position eigenstate, which is a superposition of energy eigenstates.

Simplistically, a system is in an eigentstate of what you last measured; and that is a superposition of eigenstates of anything else you could measure. It's not either in a superposition or not. It's both at the same time.

2) What happens in large "macroscopic" system is best expained by decoherence. Rather than write about that here, I'll let you look it up. It's actually very difficult to describe in QM terms what is happening in "large" systems.

3) The behaviour of light is also not that easy to describe quantum mechanically. Feynman wrote a book called QED: The Strange Theory of Light and Matter. That's definitely worth a read.

https://en.wikipedia.org/wiki/QED:_The_Strange_Theory_of_Light_and_Matter

 

[vanhees71]

It doesn't make sense to say a system is in a superposition. You have to specify the basis you use to expand the state vector in. E.g., if you have a spin of a spin-1/2 particle in the state where $\sigma_x=1/2$, it's in the corresponding eigenstate represented by the ket $|\sigma_x=1/2 \rangle$.

Using the eigenbasis of $\hat{s}_z$, it's in a superposition,
$$|\sigma_{x}=1/2 \rangle=\frac{1}{\sqrt{2}} (|\sigma_z=1/2 \rangle+|\sigma_z=-1/2 \rangle).$$

A particle cannot be in a position eigentstate, because the position eigenstate in the position representation is given by $u_{x_0}(x)=\delta(x-x_0)$, i.e., it's a generalized function or distribution, not a square-integrable wave function. There's always a finite uncertainty in position, though you can make it arbitrarily small, i.e., there are arbitrarily sharply peaked wave functions in position space (e.g., Gaussian wave packets).

Whether or not a system is in an eigenstate of the operator representing the measured observable or not depends on the measurement device and how it couples to the measured system. The collapse hypothesis is quite problematic and at best a hand-waving heuristic way to discuss socalled von Neumann filter measurements.