[PmbPhy]

The evil twin of an autobra.

Why can't you be serious? You waste a lot of my time with these silly remarks.

Come on, even Dirac had a sense of humor - he nearly offered me a job!

That's not merely humor. It's sarcasm, the lowest form of humor. And there's a huge difference between having a sense of humor and using it to disguise whether you're being insulting or not.

[Atomic-S]

There is no such thing as " time at which the position occurs remains highly indefinite."  Position is measured at a specific time. That means when you measure the position of a particle you simultaneously look at the clock and record what it reads.

Let's see if we can get a clearer grip on the question by attempting to be more detailed in analysis. How would the middle detector operate?  I envision three energy levels, or more exactly, bands of closely spaced levels, having electrons in the lowest. The others will be assumed to be unoccupied.  The photon comes along, hits the middle detector broadside and energizes an electron in the lowest band that most closely matches the photon's waveform. The electron is kicked into the highest band by a process that replicates that waveform spatially (in the transverse plane), temporarily absorbing the photon. Then the electron drops into the intermediate band, again replicating the wave distribution in the transverse directions, a process which re-emits the photon with the same transverse wave pattern but at a slightly different frequency.  At some time after entering the intermediate band, the detected electron is recorded by other processes, which need not take place before the photon finally reaches the final detector. During the time the photon is engaged with the electron, it is detained in the detector and thus its X position is "measured"; however if I am correct, doing so under these conditions does not permanently efface the shape of its wave function in any major way, and also does not establish with accuracy when the photon was in the detector. The fact that the photon re-emerges in substantially its original form, particularly as to still having a narrow bandwidth, has to do with the nature of the absorbtion and re-emission processes, which are assumed to take place between electron states having narrowly-defined energies. But to have such energies, the electron states have narrowly-defined frequencies, meaning that the lifetimes of the states must be long compared to one cycle of the photon.  But that means that the photon will be trapped within the detector for a while, not being re-emitted instantly. In this way, the photon's having a narrowly defined x coordinate is reconciled with its retaining its narrow bandwith and being re-emitted with close to its original wavelength, made possible by the indefiniteness of the time of its presence in the detector that is created by the accurately defined frequencies of it and the electron.

[PmbPhy]

How would the middle detector operate?

What middle detector? Your writing is extremely dense and as such very hard to read and recall. Therefore you can't expect people to recall what it is that you're referring to days after they've made their last post. We're carrying on several conversations at once in multiple forums so please don't expect everyone to recall exactly what your set up is. Please provide a simple description of the set u before you start the explanation, okay? Thank you my friend.

I read what you wrote below and it's all confused. It appears as if you have several misconceptions about quantum mechanics. First of all you said "The photon comes along, hits the middle detector " but you didn't tell us anything about what this detector is and why you refer to it as the "middle" one. Then you started talking about electrons in bands and photon waveforms. What are these "bands" that you're referring to? It sounds like you're referring to the band theory of solids. Is that it? And apparently you're under the wrong impression that photons have a wavefunction.
See: http://en.wikipedia.org/wiki/Photon

And the term "waveform" is never used in quantum mechanics so I don't know what you mean by it.

The electron is kicked into the highest band by a process that replicates that waveform spatially (in the transverse plane), temporarily absorbing the photon.

What exactly do you mean here? Electrons don't absorb photons. Only a system of charges like a solid or an atom/molecule can do that. Is that what you're referring to?

Then the electron drops into the intermediate band, again replicating the wave distribution in the transverse directions, a process which re-emits the photon with the same transverse wave pattern but at a slightly different frequency.  At some time after entering the intermediate band, the detected electron is recorded by other processes, which need not take place before the photon finally reaches the final detector.

All of that makes no sense. Photons are never "re-emitted". A photon is either emitted or absorbed. Nothing in between. It can never meaningfully be said that the same photon is re-emitted after it's absorbed. And what is this wave form that you're referring to? Waveform of what?

During the time the photon is engaged with the electron, it is detained in the detector and thus its X position is "measured";

A photon is never "engaged" with an electron for any period of time. Also photons cannot be detained.

The fact that the photon re-emerges in substantially its original form, ..

I'm sorry but when you say things like this it only tells me that you don't know quantum mechanics in the sense that your knowledge is seriously and almost hopelessly flawed. Where/how did you come to know what you do about quantum mechanics?

[Atomic-S]

Further explanation:

Figure 1:  The photon has passed through the slits (located at the left and out of the picture), and is described by its "waveform", by which I mean its state function Ψ(x,y,z,t) whose absolute square at any point is the probability that a photon would be found there, which is represented by the orange wavefronts having come from the slits, and is travelling toward the middle, or preliminary, detector (which sits between the slit plate and the final screen or film), which can be thought of as a wafer that contains three energy bands.  In the diagram, the detector is represented in cross-section so that it appears as lines, though in practice it would be  a plate in which the three energy bands would be effected by three physical layers, and that is the way it is represented in the diagram.  The layer nearest the incoming photon has the lowest energy level, and is occupied by electrons. The middle layer has the highest potential energy level (the energy that an electron would acquire if present) but is empty. The final layer is likewise empty but has a potential energy that falls between the other two.

[Atomic-S]

Figure 2:

The photon now interacts with the intermediate detector through its state function, shown in orange, entering the first layer. There it finds the electron that it most closely matches, in terms of the way the electron's state function lays the electron out spatially compared to the spatial distribution  of the photon's state function.  Because of the agreement in spatial layout between the photon's and the electron's state functions, the electron is excited and begins transitioning into the middle layer by raising its own (electron's) frequency (the temporal part of its state function) by an amount that equals the frequency of the photon.  In so doing, the electron effectively becomes an antenna that absorbs the photon, having an oscillating charge-probability density made possible by being in the combined state that consists of its initial state in the first layer and its final state in the second layer. An essential feature of the process is that the electron occupies both layers simultaneously for a short while.   

[Atomic-S]

Figure 3:

Eventually the electron has transitioned to the middle layer. Its state in the middle layer replicates the state it had in the first (left) layer except that the temporal part of the function is at a higher frequency, because the energy is higher by the amount absorbed from the photon. That is important, because by being such, the state preserves the original spatial information, from which the diffraction pattern will be recovered. That is, the absorbtion of the photon by this process did not collapse its wave function in such a way as to localize it in the transverse plane.

 The electron will then begin a second transition, into the right layer, dropping in energy. Actually, this process may well begin before the absorbtion process is fully completed, so that for a brief moment there could be some photon energy still present within the system, represented by the orange and red lines.  Whether in this form or in a fully excited electron in the middle plane, the energy is contained within the wafer and thus the x position of the photon can be said to have been determined to within the thickness of the spacing between layers.  But note that this does not mean that the momentum, and therefore wavelength, of the emitted photon will be indeterminate. The reason it won't be is because the excited electron has a well defined frequency of state-function oscillation, from which a definite wavelength will be recovered. [ Invalid Attachment ]

[Atomic-S]

Figure 4:

The electron then transitions into the exit (right) layer by a process similar to the earlier absorbtion, by entering a mixed state in which it  temporarily has significant probability to be found in either the middle or right layer. The right layer has a lower potential energy, causing, again, a beat frequency between the two states, and therefore an oscillating charge-probability density. Correspondingly, a photon wave function corresponding to that, as per the antenna principle, is created, and the photon is sent on its way (red wavefronts). The spatial information is preserved as before, causing the photon state function to have the original pattern it did when it had arrived at the wafer, and therefore the interference information is preserved intact.
 [ Invalid Attachment ]

[Atomic-S]

Figure 5:

The photon, represented by its state function having the diffraction information (red), continues on to the conventional screen, forms a probability pattern based on the fringes, and is detected as a specific spot (bronze color). That detection in itself does not prove that the fringe patterns are present, but we will repeat this experiment many times and establish the fring pattern by statistics.
 [ Invalid Attachment ]

[Atomic-S]

Figure 6:

After the one specific photon in question has been detected, the right layer of the wafer is accessed and the electron, if present, is read out.  The fact that the electron was found to be present demonstrates that the photon passed through the wafer.  If no electron had been found on read-out, that would tell us that no photon had passed through.  Note that the verification that the photon was in the wafer does not occur at a specific instant of time, and therefore has nothing to do with uncertainties as to its energy and frequency.  Indeed, as noted with respect to Figure 3, the photon or its equivalent energy is expected to dwell for a short while in the wafer, which is how a definite x position for it (at that time) can be reconciled with preserving a definite exit wavelength.
 [ Invalid Attachment ]

[sunshaker]

Atomic-s I've only skimmed trough thread, is this the experiment you are trying to explain?

http://www.sciencealert.com/reality-doesn-t-exist-until-we-measure-it-quantum-experiment-confirms?utm_content=bufferdc7d6&utm_medium=social&utm_source=twitter.com&utm_campaign=buffer [nofollow]

They then randomly added a second grating that recombined the paths, but only after the atom had already passed the first grating.

When this second grating was added, it led to constructive or destructive interference, which is what you'd expect if the atom had travelled both paths, like a wave would. But when the second grating was not added, no interference was observed, as if the atom chose only one path.

The fact that this second grating was only added after the atom passed through the first crossroads suggests that the atom hadn't yet determined its nature before being measured a second time.

[sciconoclast]

The experiment you described would not work but an experiment to achieve the results you are looking for has been done by Aephraim Stienberg at the University of Toronto.

"They succeeded in experimentally reconstructing full trajectories which provide a full description of how light particles move through the two slits and form an interference pattern."
http://phys.org/news/2011-12-toronto-breakthrough-physics-world.html

This experiment is a problem for the more wilder claims of quantum theory and as it relates to this thread for the requirement of observation.

In 2011 this was voted the experiment of the year in several publications. How did you guys miss it.

   

[lightarrow]

Further explanation:
Figure 1:  The photon has passed through the slits (located at the left and out of the picture), and is described by its "waveform", by which I mean its state function Ψ(x,y,z,t) whose absolute square at any point is the probability that a photon would be found there,

No, such a function doesn't exist for a photon.
For electrons or others non-zero-mass particles it exists, but not for photons.

If you want to modify your question using other particles, e.g. electrons, make us know.

--
BlueRay

[PmbPhy]

For electrons or others non-zero-mass particles it exists, but not for photons.

Where'd you get such a notion from? See: The Photon Wave Function by J. H. Eberly, L. Mandel, Coherence and Quantum Optics VII, Eds., Plenum, New York 1996, p. 313. This is available online at http://www.cft.edu.pl/~birula/publ/CQO7.pdf

[lightarrow]

For electrons or others non-zero-mass particles it exists, but not for photons.

Where'd you get such a notion from? See: The Photon Wave Function by J. H. Eberly, L. Mandel, Coherence and Quantum Optics VII, Eds., Plenum, New York 1996, p. 313. This is available online at http://www.cft.edu.pl/~birula/publ/CQO7.pdf

See post 42. You have written:
"And apparently you're under the wrong impression that photons have a wavefunction"
 []

Anyway, the document you linked doesn't show that exists a wave function which square modulus is the probability to find the photon, as Atomic wrote.

--
lightarrow

[PmbPhy]

For electrons or others non-zero-mass particles it exists, but not for photons.

Where'd you get such a notion from? See: The Photon Wave Function by J. H. Eberly, L. Mandel, Coherence and Quantum Optics VII, Eds., Plenum, New York 1996, p. 313. This is available online at http://www.cft.edu.pl/~birula/publ/CQO7.pdf

See post 42. You have written:
"And apparently you're under the wrong impression that photons have a wavefunction"
 []

Anyway, the document you linked doesn't show that exists a wave function which square modulus is the probability to find the photon, as Atomic wrote.

--
lightarrow

You're right. That topic falls under quantum electrodynamics and relativistic quantum mechanics, neither of which I've studied yet. I looked them up. Unfortunately I got conflicting answers in both cases that I looked them up and forgot what my answer was the first time when I posted the second. I'll contact someone I know and ask him.

The problem with the Wikipedia article is that I didn't read it closely enough. Had I done so I'd have seen this

More generally, the normal concept of a Schrödinger probability wave function cannot be applied to photons.[57] Being massless, they cannot be localized without being destroyed; technically, photons cannot have a position eigenstate |\mathbf{r} \rangle, and, thus, the normal Heisenberg uncertainty principle \Delta x \Delta p > h/2 does not pertain to photons. A few substitute wave functions have been suggested for the photon..

So what I misunderstood was that the "normal" concept of a wave function doesn't apply but "A few substitute wave functions have been suggested ..."

[Atomic-S]

Atomic-s I've only skimmed trough thread, is this the experiment you are trying to explain?

http://www.sciencealert.com/reality-doesn-t-exist-until-we-measure-it-quantum-experiment-confirms?utm_content=bufferdc7d6&utm_medium=social&utm_source=twitter.com&utm_campaign=buffer

No, but it sounds interesting. More details would have been helpful.

[Atomic-S]

So what I misunderstood was that the "normal" concept of a wave function doesn't apply but "A few substitute wave functions have been suggested ..."

May I suggest as the wave function, the classical electromagnetic field equation that would describe the light at high intensity passing through this region, times some very small constant.  After all, such an equation describes, in the case of full-strength radiation, the intensity we would observe if we took intensity measurements at various points, and thus corresponds, in the case of very weak radiation, to the probability that we would detect a photon at any particular place and moment of time if we tried.

[PmbPhy]

May I suggest as the wave function, the classical electromagnetic field equation that would describe the light at high intensity passing through this region, times some very small constant.

You don't need to suggest it. That's the way that it's done. It's not a real wave function though since that's defined as the inner product of the bra <r| with the state ket and no such bra exists for photons. The constant has to be chosen to normalize the resulting function.