reflection wrote:
Nice post, except I don't understand "The presence or absence of the particle can in principle be detected with however little disturbance to the particle itself". This is not true according to the Heisenberg uncertainty principle.
But this would turn into a discussion about QM. I'm no expert (just know some basics) and this is not my intention in this thread, so Ill leave it at this.
It can be very tricky to state matters in a precise way, and it seems very easy to try, and wind up with a somewhat involved explanation, but then find that one is still being a bit imprecise.
When I wrote of detecting the presence or absence of the particle before, I meant detecting whether the particle is going through the left slit or the right slit. This is not the same as if one were to try to detect the precise location of the particle. By the Heisenberg uncertainty principle, if the position is observed to be within a small enough radius of a given point, then the momentum (hence velocity) can't also be determinately within a certain small range of a fixed value at the same time. In our case, though, all I'm describing our doing is observing which side of the apparatus the particle is on, and the uncertainty in momentum forced by doing that is minuscule. In a two slit experiment the slits usually have to be somewhat close, but one can do similar experiments where the two paths taken by the particle are meters or even kilometers apart before they come back together and one gets interference fringes. The Heisenberg limit for detecting whether a particle is in New York or Los Angeles isn't something to worry about. But the mere fact of having made it possible to distinguish afterward which side of the experiment the particle passed through is enough to get rid of the interference fringes.
Physicists sometimes denote quantum states with a notation like this: |s>. A system made up of two pieces can sometimes be described by giving the states of the two pieces, like this: |s1>|s2>. Suppose that it's a question of a particle like an electron that might be observed to be in a state |e_L> going through the left slit, or a state |e_R> going through the right slit. A superposition of the two can be written as |e_L>+|e_R> (and I'll leave off dividing by the square root of 2 here, which typically would be done to keep the magnitude of the result the same). Suppose there is also a detector with possible states |D> that it starts in, |D_L> and |D_R> the state of having detected the electron on the left or on the right. If |e_L> and |e_R> are states in which the electron is in two genuinely separate regions, then they are orthogonal and in principle there is a measurement process that distinguishes them without disturbing them. That is, a process in which |e_L>|D> would evolve to |e_L>|D_L> and |e_R>|D> would evolve to |e_R>|D_R>. The rules of quantum physics allow a process like this as long as it satisfies a property called unitarity, which this does as long as |e_L> and |e_R> are orthogonal. Unitarity means essentially that the angles, corresponding to the degree to which states are reliably distinguishable from each other, is preserved (and that superpositions also are preserved).
The two things I meant to say were that in this observation process, where one can have an electron passing on the left and being observed there, or likewise on the right, the two component states of the electron don't have to be disturbed. Limitations of experimental technique may mean that |e_L>|D> really evolves into |e_L'>|D_L> where |e_L'> is very slightly different from |e_L>, but there's no Heisenberg-enforced lower limit on how small the disturbance is. Second, just the fact that the detector has made a detection, that |D_L> and |D_R> are now orthogonal, is enough to get rid of the interference fringes.
But if I want to be 100% accurate in what I'm saying, the measurement really is a change in the state of the electron, just a more subtle change. Before the measurement, one says the electron is in a "pure" superposition of the two states, |e_L> and |e_R>. After measurement, one says that the electron and the detector have become "entangled", and the state of the electron is described now as being a "mixture" of |e_L> and |e_R>, and they don't interfere as before. That's the essential difference. It does have an effect on the momentum but a very small one not particularly responsible for the change in the interference fringes.
Fig Tree
