# How fast does the collapse travel in a multiple slit experiment?

If we have a kilometer long million slit light source and make an observation on a slit at one of the ends, will the interference pattern fully collapse or partially collapse? is there any delay in the propagation of the collapse or is the collapse instant?

http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslidi.html#c3

Additional information. I am thinking that if Alice is at one end, point A and is looking at the pattern on the wall from the million slits. Bob is at the other end a kilometer away at point B. Bob then makes an observation to detect if a photon is going through a slit. Wouln't Alice see the pattern on the wall disappear?

My understanding of how this is not faster than light in the 2 slit experiment is because the change in light travels from the slit to the wall at c after the instant collapse. In the multiple slit though the collapse travels a lot further instantly and then the change in light travels at c from the slits to the wall. For Alice that is. Where is my mistake?

There is no real collapse because there is no real wavefunction. Physicists unfortunately speak of "wavefunction" for $\psi(x) = \langle x|\psi\rangle$, where $|\psi\rangle$ is the state of the system, but it is a probability amplitude and nothing else. Probability amplitudes (and even probabilities in probabilistic classical physic) may perfectly change instantaneously, independently of any consideration of spatial distances, if one operates on the system by a way or an other, for instance a measurement or an interaction. The state $|\psi\rangle$ of the system may be seen (Heinsenberg representation is the best one for this) as some set of (quantum) "initial conditions". As long as you do not interact with the system, the "initial conditions" stay the same. If you interact with the sytem, by a measurement of the position, for instance, these quantum "initial conditions" $|\psi\rangle$ are reset, so the probability amplitude $\psi(x) = \langle x|\psi\rangle$ is reset too.

Nothing of this violates causality/locality, because causality/locality corresponds to a completely different protocol which is : sending an information/energy from some space point to an other. The result is that you cannot send a signal quickest than the speed of light.

• That makes sense if every photon going through one slit is interfering with photons at every other slit. Do they all interfere with each other or is it only the slit next door? – Jitter Jan 11 '14 at 12:38
• Quantum mechanically, you cannot say that "a photon" goes through one slit or an other (if you don't put any measurement apparatus to differentiate the slits, but, in this case, you have no more interference pattern). Now, classically, all the "waves" coming from all the different slits interfere, yes (not only two neighbours) – Trimok Jan 11 '14 at 12:50
• Quantum mechanically, you may say that the different slit states $|\psi_i\rangle$ are added to build the resulting state (with some normalization), so the different probability amplitudes $\psi_i(x) = \langle x|\psi_i\rangle$ are added to have the resulting probability amplitude (with some normalization). – Trimok Jan 11 '14 at 12:53
• If I had a multiple slits one thousand kms long could I use it to communicate from one end to the other end by stopping and starting measurements? – Jitter Jan 11 '14 at 14:44
• I am not sure to perfectly understand your question, but it is not possible to send information (or energy) quickest than the speed of light. And it is not possible to control the outcome of measurements. – Trimok Jan 13 '14 at 11:05

I assume we are talking quantum mechanics here.

In quantum mechanic "collapse" is a fancy terminology for "measurement." A measurement in quantum mechanics picks one out of the probable values of a variable, where the probability is given by the square of the wavefunction describing the system.

If we have a kilometer long million slit light source and make an observation on a slit at one of the ends, will the interference pattern fully collapse or partially collapse? is there any delay in the propagation of the collapse or is the collapse instant?

The measurement of an interference pattern needs a lot of statistics, i.e. a lot of photons hitting the screen ( individual measurements/dots on the screen). Each measurement builds up the interference pattern . You might learn something if you watch how the interference pattern is built up, photon by photon in this two slit video. Each dot is a measurement according to the probability distribution for the quantum mechanical solution of the boundary conditions set up by the two slits.

Collapse has nothing to do with it and thus the concept of instant or propagation is erroneous.

• Is there a video of photon by photon buildup for 3 and 4 slit experiments? – Jitter Jan 11 '14 at 14:11
• Not that I know of. In general, because the quantum mechanics of photons has been shown to blend smoothly with the classical electromagnetic wave framework people do not bother on the obvious. When the numbers are large it is best to use the classical formalism which is equivalent to the ensemble of photons. – anna v Jan 11 '14 at 15:07