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I have been reading/learning about the double slit experiment, its implications in quantum theory, and how it explained that “particles” can behave as both waves and particles.

I know that the wave function is a probability of the location of the particle, and that shooting the electrons through the double slits causes an interference pattern associated with multiple waves. This, though not making intuitive sense (in relation to how anything can even exist as a wave), is something I can follow.

However, I have read/heard that an “observer” collapses the wave function into a single point. This is what caused the electrons to actually show up on the wall behind the slit; however Feynman (admittedly, as a thought experiment) suggested that putting an “observer” prior to the slits would cause the electrons to fly through as particles, and leave no interference pattern on the back wall.

What is an “observer”? How and why would the electron “know” it is being observed and therefore cause it to change behavior?

Qmechanic
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Runeaway3
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    The subject of decoherence may be of some interest to you. https://en.wikipedia.org/wiki/Quantum_decoherence Basically, you might say the "collapse" happens when the electron becomes entangled with a measuring device. Because the measuring device is extremely entangled with the surrounding environment (air molecules, etc.) all expectation values will appear classical from that point on. This book may be too advanced but "Decoherence" by Schlosshauer gives a very good description. – user1379857 Oct 23 '19 at 19:46
  • As my2cts said “ wave function collapse is only in the heads of physicist “ Not only that but no one can physically describe what a light wave is. Any light phenomena can be derived with a particle theory. *What is a light wave if not billions of coherent photons?? The term correlation is what’s needed instead of entanglement. Not only can you correlate to particles but you can describe how to do it. What is entanglement if not correlation??* – Bill Alsept Oct 23 '19 at 21:19
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    in relation to how anything can even exist as a wave The electron $\neq$ the wave function – BioPhysicist Oct 23 '19 at 21:59
  • Small correction: "I know that the wave function is a probability of the location of the particle" is not right. The wave function is the probability amplitude (see this post) which is not the same thing as a probability density (also called a distribution, the thing you normally encounter in your basic probabilty course). To get the actual probability (density) you need the square of the modulus of the wave function (viz., Born's rule). –  Oct 24 '19 at 15:48
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    An observation is fundamentally an interaction. This trips people up because we instinctively think of 'observing' something as being a way of "looking" at a system to gain information from it at a distance without interacting with it. At the quantum level this notion of separation goes away, and the interaction part of an observation becomes so significant as to be incapable of not altering the state of the object under observation. – J... Oct 25 '19 at 17:17

6 Answers6

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The other answers here, while technically correct, might not be presented at a level appropriate to your apparent background.

When the electron interacts with any other system in such a way that the other system's behavior depends on the electron's (e.g., it records one thing if the electron went left and another if it went right), then the electron no longer has a wave function of its own: the electron+"detector" system has a joint state. The two are entangled.

The electron doesn't have to "know" anything. The simple physical interaction results in a state vector which, by the laws of quantum mechanics, will preclude interference by any of the subsystems of this larger system. That said, the joint state can itself show a kind of "interference effect" (though not the kind you normally think of in the two-slit experiment).

If this entanglement is well-controlled (as in a lab), then (a) showing this "joint interference" might be practical, and (b) undoing the entanglement is also possible, thus restoring the electron's sole superposition. This is how we know that it hasn't "collapsed."

But if the entanglement is caused by stray photons, air molecules, etc., then any hope of controlling them becomes almost immediately dashed, and we can no longer exhibit interference in practice. From here on out, the system will appear to behave classically, with the different branches evolving independently. This fact is called decoherence. The superposition still hasn't "collapsed," but we no longer have the ability to show or exploit the superposition.

You may notice that this still leaves open a crucial question: when do the many branches become one? This is called the measurement problem, and physicists don't agree on the answer even today.

A_P
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    The way I understand it: there's no way to "telepathically" measure something about the electron. We either need to bounce another electron (or proton, or whatever) off of it, or perhaps we can get something to be affected by its electrical field - but the electron will be equally affected by the measuring device's field. In other words, in order to measure the electron, we are forced to disturb it. And that's when the "collapse" happens. That is "observing". – Vilx- Oct 24 '19 at 15:37
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    In the macro world we can observe things without (noticeably) affecting them because there are tiny things (photons) that can bounce off of big things without significantly affecting them. But when we enter the quantum realm, there is nothing smaller still, because the quantum particles are already (by definition) the smallest things in existence. – Vilx- Oct 24 '19 at 15:39
  • @A_P It would be great if you could speak to why negative or interaction free results like Renninger’s are equally effective in reducing the wave function to classical values. – JPattarini Oct 26 '19 at 23:59
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    @JPattarini Thanks for mentioning this. The lack of a detection event can be just as telling as the presence of one. In the Renninger gedankenexperiment, the wave function isn't reduced to a point, but to the hemisphere of trajectories where it wasn't detected. The simple way to understand this all is that whenever information is gained about a state, this constitutes an entanglement. And clearly information can sometimes come via negative means. Rather than being "forced to disturb it," here we tried and failed to disturb it, in a sense. But trying was enough. – A_P Oct 27 '19 at 03:21
  • @A_P I think I’ll have to post a dedicated question on this, but it seems that if a negative result from a detector is enough to update the wavefunction, then we should see Quantum Zeno effects in any Renninger-like setup. Basically if detection and non-detection are both measurements on equal footing, it feels like state evolution should hardly be able to occur at all – JPattarini Oct 27 '19 at 03:27
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    @JPattarini Another question is a good idea. I'm not a physicist. But why do you think we would see a Quantum Zeno effect? There's only one detector, at a fixed distance, that's responsible for the partial collapse. Also, the state still evolves; it just doesn't do so as a coherent superposition. – A_P Oct 27 '19 at 04:03
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    If we let $D_+$ mean detector states where there was detection and $D_-$ where there wasn't, then $|\psi\rangle$ evolves to $|D_+\rangle\otimes|\psi_1\rangle + |D_-\rangle\otimes|\psi_2\rangle$, where $|\psi_2\rangle$ is a superposition of position eigenstates. Those can still interfere with each other; they just couldn't interfere with any $|\psi_1\rangle$ states (ignoring that the particle has been absorbed on that branch anyway). – A_P Oct 27 '19 at 04:42
  • @A_P I'm afraid I also need simplistic explanation, but I do watch a lot of science lectures. How does your answer agree/conflict with a "many worlds" interpretation of quantum mechanics? – Jack R. Woods Oct 28 '19 at 13:35
  • @JackR.Woods We call a superposition decoherent when it grows beyond our ability to manage (or detect). Because the branches of the superposition are exceedingly unlikely to interfere beyond that point, some people like to say that we should call them "different worlds." But there's no special event that happens that could demarcate a clear boundary, so I feel this is a bit silly. Why should "nearly impossible for modern humans to reverse" be the boundary for world creation? (cont'd) – A_P Oct 29 '19 at 00:15
  • Cavepeople couldn't detect even a single-particle superposition, and every particle is in such a superposition when looked at in some basis. Does this mean every particle was in "two worlds" back then? Of course not. Besides, many people make the mistake of thinking that when the worlds branch, there is a single result. This isn't true. All possibilities are still there, even if they don't interfere. It's only when the whole thing entangles with you that something distinct happens (from your perspective). Then again, I'm just a nobody, so probably better to read "the experts." – A_P Oct 29 '19 at 00:17
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Wavefunction collapse is a feature of the Copenhagen interpretation, which is one interpretation of quantum mechanics. It isn't the only one. These days people don't really talk about interpretations of quantum mechanics. They talk more in terms of decoherence. One of the things that was always unsatisfactory about the CI was that it never defined what was meant by terms like "observer" and "measurement."

A more natural way to think about this is in terms of decoherence. When a quantum-mechanical system interacts with an environment, there is a tendency for its phase information to get scrambled. Decoherence is a theory that allows us to calculate this sort of thing, and, e.g., find the time-scale on which this phase information is lost. When the environment is a big thing with a lot of energy, the time scale for decoherence is very short. When people talk about observers and measurement, they're talking about objects so big and containing so much energy that this time scale is much shorter than any other time scale in the problem, and therefore it makes sense to treat it as an instantaneous collapse, as in CI.

  • also, decoherence doesn't map superpositions to eigenfunctions, but pure states to mixed ones that can be interpreted as "classical" probability distributions: Decoherence per se does not address individual measurements – lurscher Oct 24 '19 at 17:53
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    @Ben Crowell How does decoherence explain wavefunction partial collapse in Renninger’s setup? – JPattarini Oct 27 '19 at 00:00
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Wave function collapse only happens in the head of the physicist.

What we are dealing with is entanglement of the electron and the detector wavefunctions. In the double slit problem we can write the electron wave function as $\psi_L + \psi_R$. The detector has two orthogonal states, $L$ and $R$. If there is no detector we have interference. If there is one and if it distinguishes the two possibilities with 100% certainty then the wave function must be $\psi_LL + \psi_RR$. This is an entangled state where interference is absent as $\langle\psi_LL | \psi_RR\rangle$

$= \langle\psi_L | \psi_R\rangle\langle L|R\rangle =0$.

No collapse occurs unless during the installation of the detector.

BioPhysicist
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my2cts
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The early years of quantum theory were dominated by a school of thought known as the Copenhagen interpretation.

According to that school of thought the wave function of a particle could undergo an instantaneous change when some property of the particle was measured. The act of measurement was assumed to cause the change (which is sometimes called the 'collapse' of the wave function). So the short answer to your question, according to the Copenhagen school, is that an observer brings about a collapse of the wave function by making a measurement. For example, if a photon interacts with a photographic plate to produce a dark spot, the position of the photon is suddenly localised.

Many physicists have raised objections to this interpretation, those objections being on three main grounds. Firstly, the collapse seems to be instantaneous, with no supporting theory about what mediates or triggers it. Secondly, a 'measurement' is just an interaction between the particle and some other particle that happens to be part of the measuring apparatus. And thirdly, that the measuring apparatus itself is just a collection of particles with wave functions, so why should it not be subject to the same sort of discontinuous change along with the object it is measuring?

These objections still haven't been been fully resolved. Many resolutions have been proposed, and each has its proponents and detractors.

Marco Ocram
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A photon is, or is associated with, an electromagnetic wave packet. Its energy can be thought of as being embodied in the energy density of the electric and magnetic fields. A wave function describes this wave packet. Observing a photon generally means that it has been captured (as in a CCD or on a piece of film). In being captured, the photon looses its energy to the capturing device and the wave disappears. There is nothing left for the function to describe.

R.W. Bird
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Physics students are taught the following three things: 1) A wavefunction is a probability density function, infinite in size, which serves as a useful fiction, allowing us to calculate properties of a particle. 2) Wavefunction collapse is a real event, a non-fictional event, initiated by something external to the particular wavefunction in question. 3) Physicists have some idea what's going on in the universe, so we should take them seriously.

Clearly, one of these three things needs to go.

J Daniels
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