#quantum behavior

Since the number of electrons that arrive at a particular point ≠ the number of electrons that arrive through hole 1 + the number of electrons that arrive through hole 2, we logically conclude that it's NOT true that electrons go through EITHER hole 1 or hole 2. But is it really not true? This is the aspect of electron behavior for which we said a conceptual explanation is elusive. So let's try to test this conclusion with another experiment:

Electric charges scatter light, which we can use to test whether electrons do go through either hole 1 or hole 2, not both at the same time. If an electron passed through hole 2 (see diagram), it would cause a flash of light near hole 2 (point A on the diagram). Similarly, if an electron passed through hole 1, it would cause a flash of light near hole 1.

So whenever we hear a click, we can tally the flashes at each hole and get the probability of an electron arriving at the detector via hole 1 (P'1) and the probability of an electron arriving at the detector via hole 2 (P'2).

What we see is that no matter where we put the detector, every time we hear a "click" from the electron detector, we also see a flash of light either near hole 1 or near hole 2, never both at once. This means electrons DO arrive either through hole 1 OR hole 2. If this is true, then why does P12 ≠ P1 + P2?

This experiment is problematic because light is an electric field perpendicular to a magnetic field (hence light is a form of electromagnetic radiation) and its electric field exerts a force on charges. Trying to watch the electrons (i.e. using light) changes the electrons' motions such that the probability of an electron arriving at the detector through hole 1 or hole 2 is changed so P'12 = P'1 + P'2. The probability of an electron arriving at the detector through hole 1 or hole 2 (P'12) shows no interference. When we turn off the light, we get the original idea that P12 ≠ P1 + P2 and that P12 shows interference.

If we were to dim the light source, i.e. decrease its intensity, all we discover is that light are also particle-waves like electrons. Decreasing light's intensity means that the rate at which particles of light aka photons are emitted decreases. This means that sometimes we hear a click from the detector (electron arrived) and there is no flash of light - there was no photon emitted at the moment the electron passed by. The size of the photons doesn't change when you decrease the light's intensity, so when you DO see light, the flashes are always the same size as when the light was brighter.

If we were to do this experiment with a dimmed light, these are the results we'd get:

"When we do not see the electron, no photon disturbs it, and when we do see it, a photon has disturbed it. There is always the same amount of disturbance because the light photons all produce the same-sized effects and the effect of the photons being scattered is enough to smear out any interference effect."

If, the greater the photon's momentum, the more the electron is disturbed, perhaps we should lower the frequency of light if we don't want to disturb the electrons as much.

This would work if we could tell where the electrons come from at a low enough frequency. But we can't. I don't get why the wave nature of light creates this limit but I'm pasting the explanation here so I can review it later:

You remember that when we discussed the microscope we pointed out that, due to the wave nature of the light, there is a limitation on how close two spots can be and still be seen as two separate spots. This distance is of the order of the wavelength of light. So now, when we make the wavelength longer than the distance between our holes, we see a big fuzzy flash when the light is scattered by the electrons. We can no longer tell which hole the electron went through! We just know it went somewhere! And it is just with light of this color that we find that the jolts given to the electron are small enough so that P′12 begins to look like P12—that we begin to get some interference effect. And it is only for wavelengths much longer than the separation of the two holes (when we have no chance at all of telling where the electron went) that the disturbance due to the light gets sufficiently small that we again get the curve P12 

This demonstrates Heisenberg's uncertainty principle which states that there's a limit to how accurately we can [experimentally] predict from initial conditions the values for certain pairs of physical properties of a particle (e.g. particle position and momentum). "It is impossible to design an apparatus to determine which hole the electron passes through [electron position], that will not at the same time disturb the electrons enough to destroy the interference pattern [due to photon momentum changing the electron's motion]."

Tbh I didn't really get all the details of the later parts of the chapter (especially the math). Maybe I will if I come back to this someday. Anyway, all in all, the book's a good read.