# Quantum double slit which-way problem

I recall reading that if you put a parallel polarizing filter over one slit and a perpendicularly polarizing filter over the other slit, and send a singe photon to the slits, then there is no interference pattern produced beyond the slits. The explanation was that the filters provided a "which-way" tagging of the photon and so, if that information is known, there can be no interference because the photon could only have gone through one slit. I think this view also implies wave function collapse at the slits

Suppose the photon is in a pure state before reaching the slits. I think another explanation might be:

one emergent wave is tensor multiplied by one eigenstate of polarization and the other emergent wave is tensor multiplied by a different eigenstate of polarization.

When the two tensor products are added, we get a state vector (representing the joint polarization and position states) where each state of that state vector is described by a single wave.

Therefore, when probabilities are calculated, there is no cross-term and no interference. Further, the polarization can be reversed by a simple matrix multiplication of the state vector of the photon. (Note, the photon remains in a pure state, after its wave function passes through the slits)

So, in this interpretation, there are no interference patterns, but the wave goes through both slits (without wave function collapse at the slits), unlike the information interpretation, where it goes through only one as a particle.

What do you think?

• @CuriiousOne If instead photons, we spoke of polarized electrons, would that be better for you to consider? – David Dec 21 '15 at 5:34
• We would be talking about the exact same misconception. Electrons are not particles, either. They are (massive) states of the same quantum field. High energy physicists are only talking about "particles" because their detectors are never even coming close to the resolution needed to test the uncertainty principle. At the interaction point, though, all calculations in the theory are performed as exchanges of field quanta, not as interactions of classical point particles. – CuriousOne Dec 21 '15 at 5:45
• I am looking at this from more of a quantum mechanical point of view, not a QED point of view, which I think is how we differ on this subject. – David Dec 21 '15 at 5:47
• You would be still wasting your time musing about photons as particles. Photons are not particles and never have been. They are field quanta and that means they only show up when you perform certain types of measurements on the quantum field. Between those measurements they are simply not defined and they can not be observed as particles. Science is not about pounding square pegs into round holes. It's about knowing when something is a square peg and something else is a round hole and when it's neither. Quantum objects fall right into the last category. – CuriousOne Dec 21 '15 at 5:57
• @CuriousOne: Is it equally a waste of time to understand special relativity because spacetime is not flat, or to understand classical mechanics because quantum mechanics is not classical? Or is there something unique about your obsession with theories that assign a meaning to the word "particle"? (Incidentally, I notice that you recently answered a question about a planet's angular momentum. Why didn't you stop to mention that there are no planets?) – WillO Dec 21 '15 at 6:54

I recall reading that if you put a parallel polarizing filter over one slit and a perpendicularly polarizing filter over the other slit, and send a singe photon to the slits, then there is no interference pattern produced beyond the slits. The explanation was that the filters provided a "which-way" tagging of the photon and so, if that information is known, there can be no interference because the photon could only have gone through one slit. I think this view also implies wave function collapse at the slits.

This does not imply wave function collapse, just that the components of the field that go though the polariser all have a particular polarisation. This would also be true in the many worlds interpretation, and so doesn't depend on collapse. The real problem with what you have stated above is that whether the interference happens doesn't depend on whether anybody knows the information in question. Rather, it just depends on whether there is a system other than the amplitude of the field that contains the relevant information. See http://arxiv.org/abs/1212.3245 for a discussion of how information is relevant.

The other description you gave in terms of tensors etc. describes the same issue at a different level of abstraction. That explanation works only for the system you are considering. The discussion in terms of information works at a higher level of abstraction but gives you a way to understand what is happening in many other kinds of systems.

One more note. CuriousOne objects to you discussing this issue in terms of photons. It is true that photons are just patterns of excitation in a field that look a bit like particles in certain approximations. However, the fact that in a certain experimental apparatus only one of those excitations can be detected in the time it takes a disturbance in the field to propagate through the experiment is relevant to ruling out explanations for what is happening in terms of lots of particles bumping into one another. What is happening in reality is more complex than that simple picture. It is useful to talk about photons as long as you understand that it is shorthand for a way of decomposing a field, not an actual particle.

• "The other description you gave in terms of tensors etc. describes the same issue at a different level of abstraction. That explanation works only for the system you are considering." Indeed, that is true. I am just thinking that each case where the info approach is used, which works in many other kinds of systems, always has an alternative "traditional", non-info explanation. That is, the info approach is never necessary, though is certainly most general and very helpful. – David Jan 8 '16 at 0:34
• You say that the info approach is never necessary. But that's not true. For example, the low abstraction approach doesn't explain what set of operations a computer has to be able to perform to be able to simulate a quantum system. You don't need a bespoke computer for every Hamiltonian as a result of computational universality. The low abstraction approach is necessary to discover the Hamiltonian of any specific system, but it is not the be all and end all of explanation. – alanf Jan 8 '16 at 13:51

In an experiment where in the path between the particle emission and the observer are placed polarizers the state of the particles is changed. In addition to the change of the photons state from randomly distributed by 360° electric field component to some polarisation from the edges of the slits (google wire slit polarizer) now you place two additional polarizers. Of course this will change the influence of the slits on the distribution on a screen.

I. wave form and particle form do not exist at the same time One or the other. When photons,electrons or atoms are emitted toward the 2 slits they are only in their wave form and pass through the 2 slits as such producing an interference result. When we turn on the detector the electric current in the detector some how acts to convert the waves to their particle form as they approach the 2 slits(decoherence)Possibly as a result of their wave actions. Turning off the current restores the interference pattern.

• So, the polarizers at the slits make the two emerging waves be decohered from each other (went from a pure state to a mixed state)? – David Jan 7 '16 at 3:51