In a double-slit experiment, interference patterns are shown when light passes through the slits and illuminate the screen. So the question is, if one shoots a single photon, does the screen show interference pattern? Or does the screen show only one location that the single photon particle is at?
Quantum Mechanics – Slit Screen and Wave-Particle Duality
double-slit-experimentphotonsquantum mechanicswave-particle-duality
Related Solutions
The photon in transit between the light source and the screen is described by a wavefunction. Specifically, the wavefunction describes a photon that is delocalised i.e. it does not have a well defined position. Because the wavefunction is delocalised it encompasses both slits, which is why we say the photon goes through both slits.
Whenever you interact with this wavefunction you change it, and typically you will change it in such a way as to localise it. This is because the interaction happens at a point, and the result is to localise the photon at that point.
Now, when the photon interacts with the screen this does happen at a point, and indeed the interaction creates a spot on the photographic film/CCD/whatever at the point where the interaction happened. We can't say in advance where the interaction will occur, only that the probability of it happening is given by the wavefunction. So any one photon interacts at a point, but when we take many photons the points where they interact with the screen are distributed according to the wavefunction and together they build up the interference pattern.
However, if you interact with the photon before it has reached the slits then your interaction localises the wavefunction so the photon can no longer go through both slits. Because the wavefuntion immediately prior to the slits has changed, the effect the slits has on the wavefuntion changes as well and therefore so does the final pattern at the screen on the other side of the slits.
The answer by Craig Gidney is quite adequate for the question, but I want to address the word "collapse" in the title, since search engines will be homing in on it. From webster.com
1: to fall or shrink together abruptly and completely : fall into a jumbled or flattened mass through the force of external pressure <a blood vessel that collapsed>
2: to break down completely : disintegrate <his case had collapsed in a mass of legal wreckage — Erle Stanley Gardner>
3: to cave or fall in or give way <the bridge collapsed>
4: to suddenly lose force, significance, effectiveness, or worth <fears that the currency may collapse>
5: to break down in vital energy, stamina, or self-control through exhaustion or disease; especially : to fall helpless or unconscious
6: to fold down into a more compact shape <a chair that collapses> Definition of the word "collapse", Webster's dictionary
Note how the word describes a physics situation.
A wave function is a mathematical formula with complex numbers, posited for all particles in the quantum mechanical framework, from which the classical dimensions we live in emerge. It is a mathematical expression of a very successful model which, when squared with its complex conjugate gives a probability density distribution for observing with real numbers the problem at hand. In the case of the double slit experiment, the probability of finding the photon at the specific (x,y) of the screen.
The wavefunction exists in our copy books and our computers as a mathematical formula valid continuously. It is an unfortunate label that the word "collapse" has been attached to any property of the wavefunction. The wave function does not break down in any of the senses of the definition of the world collapse. It is always there, in our copy books and computers. A single measurement picks up an instance, and accumulation of measurements gives the probability distribution that the wavefunction so successfully models.
Example:
Take this paper which gives Probability of delivery within x days of a given date, the date given by the doctor from the data the mother gave.
The birth of a baby will be an instance of this plot, which accumulated with more instances should verify the distribution shown. Is anything in any logical way collapsing, according to the definitions of Webster?
I hope this makes clear that collapse is a wrong word to use for a mathematical distribution, attributing reality values. It is at worst an anthropomorphic word, giving human attributes to a mathematical formula, at best a misguided identification of the complex mathematical formula to the real formula of a collapsing balloon. The wave function is not a balloon either.
Best Answer
The answer is yes to both questions: yes, the screen does show one location for one particle and yes, the accumulated picture after repeating the experiment many, many times does show the interference pattern.
There is a set of beautiful pictures and a video of the double slit experiment in one-particle-per-time mode that can be found here (the experiment is with electron but conceptually there is no difference).