Young's slit experiment with single photons

In summary, Marilyn is having trouble understanding Young's slit experiment with single photons. She is confused by the popular science description that the photon interferes with itself, and believes that it is actually different photons interfering with each other. She also questions how the mathematical formalism of quantum mechanics can predict this phenomenon. However, Dale explains that a single photon can indeed interfere with itself, and that this is due to the fact that a photon is not a point-particle but rather a one-quantum Fock state of the quantized electromagnetic field. This explains the probability distribution observed in the interference pattern.
  • #71
HomesliceMMA said:
would a more/less correct statement be: Things we think of as photons and electrons (and I guess any classical "elementary particles" and maybe any other mass in classical sense?) is neither a particle nor a wave
Yes.

HomesliceMMA said:
but behaves either as a wave (before a decoherence event or whatever its called) or as a particle (after a decoherence event)?
No. Again, this kind of reasoning will lead you to wrong answers (for example, in post #67).
 
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  • #72
PeterDonis, you have officially blown my mind LOL. Can you explain how that second part is wrong? It does not behave like a wave before the measurement in those experiments? I thought that was like the crux of those experiments, behaves like wave before, but if you measure then wave function collapses and you see it go one way or the other as a single particle? What is the subtlety I am missing?

As always, I appreciate the help with these baby steps!
 
  • #73
HomesliceMMA said:
Can you explain how that second part is wrong? It does not behave like a wave before the measurement in those experiments?
You reasoned yourself to a wrong answer in post #67 by assuming that it did behave like a wave before the measurement. (Although you might want to take a look at the classical wave theory of diffraction to see if you might want to revise your intuitive guess about what classical wave behavior would result in.)

However, there's a clearer case: Compton scattering. The behavior "before measurement" is most easily modeled as simple billiard-ball type collisions between X-ray photons and electrons--i.e., particle behavior (though you have to use the relativistic energy-momentum relations). But the measurement itself, where you see the effect on the X-rays (their frequency decreases and their wavelength increases), is a wave measurement--you measure the frequency and wavelength before and after and compare them. So this case is exactly backwards from your description: the "particle-like" behavior occurs while the quantum object is not being measured, and the "wave-like" behavior occurs when it is.
 
  • #74
HomesliceMMA said:
I thought that was like the crux of those experiments, behaves like wave before, but if you measure then wave function collapses and you see it go one way or the other as a single particle?
In some experiments, the actual measurement does show more or less "particle-like" behavior, yes. But not all of them (I gave a counterexample in post #73 just now). Similarly, in some experiments, the "in between measurement" behavior can be seen as "wave-like" behavior--but not all of them (again, I gave a counterexample in post #73).
 
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  • #75
PeterDonis said:
You reasoned yourself to a wrong answer in post #67 by assuming that it did behave like a wave before the measurement. (Although you might want to take a look at the classical wave theory of diffraction to see if you might want to revise your intuitive guess about what classical wave behavior would result in.)

However, there's a clearer case: Compton scattering. The behavior "before measurement" is most easily modeled as simple billiard-ball type collisions between X-ray photons and electrons--i.e., particle behavior (though you have to use the relativistic energy-momentum relations). But the measurement itself, where you see the effect on the X-rays (their frequency decreases and their wavelength increases), is a wave measurement--you measure the frequency and wavelength before and after and compare them. So this case is exactly backwards from your description: the "particle-like" behavior occurs while the quantum object is not being measured, and the "wave-like" behavior occurs when it is.
Man, this is so weird to me (and almost certainly so far above me). I ask anyone that can help - can ANYONE explain this in simple terms to me? And everything I've read (behaves like wave before, particle after, measurement) is dead wrong? I mean, I could google it now and get hundreds or thousands of people saying that same thing effectively. They are all wrong?
 
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  • #76
HomesliceMMA said:
Man, this is so weird to me (and almost certainly so far above me). I ask anyone that can help - can ANYONE explain this in simple terms to me? And everything I've read (behaves like wave before, particle after, measurement) is dead wrong? I mean, I could google it now and get hundreds or thousands of people saying that same thing effectively. They are all wrong?
In another of your threads I suggested two books you might find helpful. Whether these are simple enough I don’t know, but I do know that no simpler explanation will be adequate.

Yes, just about everything you have read so far is wrong, although I wouldn’t say “dead wrong”, I’d rather say “seriously misleading.”
Some of the problem is that (as you also heard in that other thread, from PeterDonis) quantum mechanics cannot be properly described without math, so any math-free description is going to be somehow misleading. A further difficulty is that our common sense intuition about how things behave are all based on a lifetime of experience with things that don’t behave quantum mechanically, so we cannot depend on that intuition to help us over the gaps in an incomplete description.
 
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  • #77
Shoot Nugatory, I missed that (and I just spent several minutes trying to go back and find it, could not off hand). Might you tell me again? Thank you!!!
 
  • #80
HomesliceMMA said:
I would have thought as you narrow the slit in a single-slit test, the interference pattern would get a little bit narrower.
From my link for single-slit diffraction, the distance from the center of the pattern on the viewing screen to the first minimum (##m = 1##) on either side is $$y \approx \frac {\lambda D} a$$ where ##\lambda## is the wavelength, ##D## is the distance from the slits to the screen and ##a## is the width of the slit. The width of the central maximum is twice this. Clearly as ##a## increases, ##y## increases.

This is for small angles, less than 10 degrees or so depending on how much accuracy you want. For larger angles the calculation becomes more complicated, but you still have ##y## increasing as ##a## decreases.

One way to make this plausible might be to consider that if ##a## becomes small enough, the slit "looks" a lot like a line with a point-like cross section. After passing through it, light spreads out in half-cylindrical waves with a semicircular cross-section. Think of replacing the slit with a glowing, very thin straight wire with a diameter maybe less than a wavelength.
 
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  • #81
HomesliceMMA said:
Man, this is so weird to me (and almost certainly so far above me). I ask anyone that can help - can ANYONE explain this in simple terms to me? And everything I've read (behaves like wave before, particle after, measurement) is dead wrong? I mean, I could google it now and get hundreds or thousands of people saying that same thing effectively. They are all wrong?
The confusion comes from the fact that unfortunately many popular-science book writers or, even worse, youtubers like to have quantum theory to present "something weird". They think they'd make the subject more interesting to sell their stuff better or getting higher click numbers. However, the really exciting aspect of science is that it describes the objectively observable phenomena of Nature in ever more clear and complete mathematical (!) models and theories.

All the "quantum weirdness" goes away, when you are accepting that the currently valid version of this theory is the one discovered in 1925-1926 in three equivalent forms: Born, Jordan, Heisenberg -> "matrix mechanics" (including the quantization of the electromagnetic field!), Schrödinger -> "wave mechanics", and Dirac -> "transformation theory". The latter is the most general scheme, which is based exclusively on the idea that the observables are described as a algebra of so-called self-adjoint operators on a Hilbert space, enabling the description of the symmetry principles already known from classical physics.

This mathematical formalism allows you describe the probability for the outcomes of measurements on a quantum system, which has been prepared in some way described by the quantum state. That's all that can be described by quantum theory (QT), and it's, as far as we know today, also the only description with is consistent with all observations ever made in attempts to testing the theory.

The confusing ideas of "wave-particle dualism" etc. is due to an old predecessor description of the behavior of nature in the quantum realm, rightfully dubbed "the old quantum theory". It was a collection of guesses, based on classical physics, adding some ad-hoc "quantum rules". This only leads to an apparent success for discribing the most simple systems. In fact it only works for the free particle, the hydrogen atom, and the harmonic oscillator (including the free electromagnetic field and thus also Planck's black-body radiation law). Today we know that's just, because these systems are described by equations of motion that have an exceptionally high symmetry, and in this sense that's just by sheer luck. It doesn't work already for the next-most simple atom, the Helium atom.

On top it leads to obviously wrong qualitative conclusions: E.g., according to the Bohr-Sommerfeld model of the hydrogen atom, you'd expect that such an atom is geometrically seen as a little disk, i.e., the electron runs around the proton in a planar circular or elliptic orbit (similar to the planets running around the Sun according to Kepler's laws). In fact a hydrogen atom in its ground state is a spherical object, and that's what's indeed observed in scattering experiments.

Even worse, as you realize yourself, the picture the "old quantum mechanics" provides as a description of nature, is intrinsically contradictory. Wave-particle dualism is the most infamous example for this: Of course, it's intrinsically inconsistent to think that a particle like an electron is both a wave and a particle at the same time, and that's resolved by modern quantum theory by an admittedly quite abstract description of what's observable about an electron in real-world experiments. The solution of the apparent wave-particle paradox is the probabilistic meaning of the quantum state, i.e., that all you can know about an electron are the probabilities for the outcome of measurements of some observables (its position, momentum, magnetic moment, etc.) given the state this electron is "prepared" in before making these measurements. In the wave-mechanics formulation the most determined states (so-called "pure states") are described by Schrödinger's wave function, whose meaning is that its moduluse squared provides the probability distribution for its position and the probability for finding one of the components of the spin in direction of an applied magnetic field used to measure it (e.g., in a Stern-Gerlach experiment) in either spin up or spin down direction (##\sigma_z \in \{\hbar/2,-\hbar/2 \}##).
 
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  • #82
HomesliceMMA said:
everything I've read (behaves like wave before, particle after, measurement) is dead wrong?
How many of these things you've read were textbooks or peer-reviewed papers?
 
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