# What pattern would emerge in a double slit experiment in which you tried to measure the particle before the slits?

Asked this question many times before, on different sites as well, but i still haven't gotten a good answer for some reason. Some will say one thing, others another, some won't really give me a direct answer at all. Probably going to get downvoted but what the heck.

We all know that if you shoot a single particle at the slits, the probability distribution that you will find on the screen after multiple trials will be that associated with a wave-like entity (interference pattern). However, if you decide to measure which slit the particle goes through, the probability distribution pattern that emerges will change, it will be a pattern consistent with a particle-like entity (the "particle" is most likely to be detected directly behind the slits and the probability will taper off everywhere else). My question is this, what pattern, "wave" or "particle", will emerge if we decide to take a measurement before it goes through the slits?

• Try this site. It goes through a few steps in the experiment. genesismission.4t.com/Physics/Quantum_Mechanics/… May 9, 2015 at 15:57
• I deleted a comment discussion that was getting a little out of hand. May 9, 2015 at 19:19

The pattern on the screen depends on where before the slit you measure the particles.

• If you measure the particle's position in a way, that it will propagate on in a way that will cover both slits later on, then you will just see the interference pattern as before.
• If you measure directly before the slits, the results will be (almost) the same as when measuring after the slits.
• If you measure somewhere such that the particle flux on the both slits becomes uneven you get results, where you have an interference pattern and "ballistic" background.

These results are easily obtained by considering, that position measurement puts the particle in the measured position eigenstate (this obviously only holds approximately and, depending on the measurement device, not at all for other observables).

You can even construct measurement devices that measure only with a certain probability, then you will get "intermediate" results (material on this can easily be found).

In other words the important thing about measuring the particle at a position, is whether the measurement predicts the taken slit, then the quantum coherence is obviously no longer given and you measure the "ballistic" results.

The correct mathematical formalism to handle this is a density matrix approach, (and then you could easily describe the measurement by taking the partial trace over the environment and getting the results from decoherence theory, by-passing the above assumption about the measurement process).

You can use this logic to answer your own question: The particles you measure before the screen form a simple ballistic pattern that is determined by the source! The measured particles are not coherently related with the interference. In otherwords, the measurement before the slits is completely unaffected by the presence of the slits (but may affect the pattern observed after the slits).

• By ballistic i'm guessing you mean results consistent with the classical intuition of a particle? Sorry if i'm not understanding your question but you're saying that if you measure a particle position before the slits, that you will get the same "ballistic" pattern than you do when you measure which slit the particle goes through? May 9, 2015 at 20:25
• On ballistic: Yes, its imprecise wording, sorry. But I could not think of something better at the moment. On the rest: it depends on where (i.e. how close) you measure before the slits (and how), if the particles are absorbed by the measurement (photo plate), then of course not (all measured particles do not contribute to the interference pattern), if you do something like a short drift chamber and are sufficiently close to the slits, do determine which slit the particle will go through, then yes (because the procedure is equivalent to measuring which slit the particle goes through). May 9, 2015 at 22:52
• To make this all clear: Most of the time I discuss the pattern observed on the screen after the slits. The pattern on the screen before the slits will not depend on the presence of the slits (assuming the particles that do not pass are absorbed and not scattered back), the pattern observed before the slits will depend only on the source! May 9, 2015 at 23:02

We all know that if you shoot a single particle at the slits, the probability distribution that you will find on the screen after multiple trials will be that associated with a wave-like entity (interference pattern).

Yes, you see a parttern like this one, courtesy of Brown University:

Note though that each photon has energy E=hf or E=hc/λ. It has a frequency and a wavelength. It's a wave, it goes through both slits. See weak measurement work by Jeff Lundeen et al. Don't think the photon is some point particle because detection leaves a dot on the screen. For all you know that detection could involve some kind of interaction that's akin to the optical Fourier transform, see Steven Lehar's web page:

However, if you decide to measure which slit the particle goes through, the probability distribution pattern that emerges will change, it will be a pattern consistent with a particle-like entity

Detection at one slit would presumably involve something akin to a Fourier transform that converts the wave into a dot that goes through that slit only. So there's no interference pattern any more.

My question is this, what pattern, "wave" or "particle", will emerge if we decide to take a measurement before it goes through the slits?

I imagine it would be a wave pattern of dots, similar to what you'd get if the photon was emitted from your measurement point.

• So you think you would get the wave pattern? Thank you for actually trying to answer my question. May 9, 2015 at 20:19
• @Yogi DMT : my pleasure Yogi. There is of course no substitute for experiment, but I'll wager it's been done already. May 10, 2015 at 12:13