[Atomic-S]

As Pascual Jordan put it: “Observations not only disturb what has to be measured, they produce it….We compel [the electron]
to assume a definite position…. We ourselves produce the results of measurements.”

.
I find this an interesting concept, which brings up the following question regarding the double-slit experiment. As it is typically conducted, a particle is sent through two parallel slits, behaving wave-like, during which, I suppose, it has no position.  Then it hits a screen as, for example, photographic film, is detected at a specific position, and is deemed to be a particle having that position.  I have wondered if there is any way of detecting it that does not demand that it assume a definite position, and if so, that would be a significant experimental breakthrough showing that a particle indeed not need be in a definite position to be a particle.  It would appear that the nature of the detector is significant in this regard. When photographic film is placed there, it becomes part of the experiment. What if we used something else?  We would have to be clever about what it was in order to elicit the desired result. We want something that would indicate the presence of the particle, but in a way that did not demand that it assume a definite position.  If we were able to do that, it suggests the possibility that the particle could continue to travel beyond there still following much of its original wave configuration, that would become evident in a second detection of some kind. With the conventional double-slit experiment, particles hit the detector with a distribition governed by their wave nature up to that point, but whemn each hits, it is recorded in a specific place, and as such, now has a state function that is different, so that (assuming the particle has enough energy to continue on from that point), its subsequent behavior should be different than its original wave distribution indicated. The point is t hat the first detection, by requiring it to assume definite position, has altered its subsequent behavior.  So the objective would be to show that if we could detect its presence in a way that did not require it to assume a definite position, then its subsequent behavior would be much less disrupted and would largely be the same as its earlier wave function would indicate.  Can such an experiment be done?  The first thing that comes to mind as a possible way of doing so is to change the chemistry of the detector so that it is characterized by large molecules having electron orbits that run throughout their entire length and thus do not have narrowly localized locations. You would also want to try to set this up so that the molecules had a dearth of closely-confined electron orbits that would be sensitive to the particular particle to be detected.  The result would be that when the particle interacted, an electron from a wide-ranging orbit would be kicked up into another higher-energy wide-ranging orbit, which could triger other phenomena that would be recorded.  But because the process did not pin the detected particle to a particular location, its wave function would not have "collapsed" as much as would ordinarily be the case, allowing the particle, with such residual energy as it had, to proceed further on and be detected a second time by a conventional detector. The result of that would be, executed on many particles, a diffraction pattern more closely resembling what would have come out of the slits (probably some weak fringes), rather than what would have come out of a narrow-position detector (probably diffuse). 

[PmbPhy]

I find this an interesting concept, ...

And it might be interesting to read if you didn't write it as one long sentence. It's easier to read when you break things up into paragraphs. If you choose to do so I'd like to read what you wrote. Otherwise it's a strain on my eyes.

[Atomic-S]

To make a long story short, we do the double slit experiment as follows: There are the slits, and there is a conventional detection screen. It produces an indication of where each particle hits. Between the slits and the screen we place another detector.  It is to detect the passage of the particle without detecting its position.  When the particle passes through it, its presence is recorded but its position is not. Because its position was not, it remains indefinite.  The purpose is to test to see if, by leaving it indefinite, the wave characteristics that emerged from the slits remain in force.  We find the answer to that by allowing the particle to strike the final detection screen and record a position. We repeat the experiment with many particles. If the statistical pattern on the final detection screen is consistent with the diffraction expected from the slits, then we would know that the wavelike behavior was not nullified by the earlier detection as a particle.  That would be interesting because this experiment would have demonstrated an object possessing both particle-like and wave-like properties at the same time.

The detector to be first encountered might be constructed of a semiconductor having two conductive energy bands separated by a small energy difference.  Because such energy bands are characterized by electrons free to wander extensively,  their electrons are of indefinite position. If the energy difference is substantially less that that of the incident photon (for example), the amount of energy lost from the photon when it kicked an electron from the lower band to the upper band would not greatly affect it, so that as it proceeded from that point on toward the final screen, the photon's wavelike character would undergo only limited change. This change would probably appear as an increase in wavelength. The result of that could be that the diffraction pattern would widen a little.  But the experiment should still be doable.

[PmbPhy]

To make a long story short, we do the double slit experiment as follows: There are the slits, and there is a conventional detection screen. It produces an indication of where each particle hits.

So far so good.

Between the slits and the screen we place another detector.  It is to detect the passage of the particle without detecting its position.

What you just said is impossible. One can't merely make such statements and expect them to be taken as a valid statement. You have to state exactly how such a thing is possible by stating at least one way on how to do it. And detecting a passage of something means that you've taken a position measurement. You don't appear to understand that those two things are identically the same thing.

  When the particle passes through it, its presence is recorded but its position is not.

Again, impossible. To demonstrate what I mean please draw a diagram of what you're saying and the actual physics of how it would be accomplished.

Things like this are the main problems with ideas in this forum. The ideas presented are so vague as to appear possible but so vacuous that it can't be accomplished in practice.

[Atomic-S]

The position of the particle has three components.  The component in the direction from the source to the final target is indeed recorded to the precision of the position of the central detector, but the position in the other two dimensions is not.  It is those transverse measurements that matter in this experiment.

[Atomic-S]

As for the first detection itself, I turn to the antenna principle to attempt to discuss it in a bit of detail.  The antenna principle attempts to understand the absorption and emission of radiation on the basis of the behavior of radio antennas, which, although it may seem inapplicable to a quantum situation, actually is if you examine the mathematics closely.

  The state function of an electron in a specific energy state is a function of x, y, z, and t in a way such that the absolute square of the function is everywhere time-independent, although the function itself varies with time according to the factor exp(iω₁t), ω₁ being determined by the energy level.  If the electron moves to a different orbit with a different different energy level, its state function is again of x, y, z, and t in like manner, except that the dependence on x, y, and z will in general be different, and that  the time dependency will be exp(iω₂t), with ω₂ being determined by the different energy of that state.  But as before, the time dependency of the absolute square will be constant.  The absolute square is associated with the probability that a process to find an electron at a given point would find it there, and thus can be thought of as equivalent to a classical charge density, and what this all says is that when the electron is definitely in one or the other state, its charge-density distribution is independent of time, which corresponds to a classical electrostatic situation.  (Note that this is true despite the kinetic energy the electron possesses).

 When, however, the electron is absorbing or emitting EM radiation, it will be, for a short time, in both states at once.  Now if you add the two states, you will find that the absolute square is no longer time-independent, but varies at a frequency 2π(ω₂ - ω₁), a frequency that corresponds to the frequency of the emitted or absorbed radiation.  During this time, the charge probability density is varying with time, very much like the currents in a classical antenna. As such, this gives us a method of calculating the radiation pattern, i.e., the probability that the photon will be found in the various possible directions of flight. For the purposes of this experiment, therefore, the task is to devise a first detector that will have such available electron orbits so that when the photon encounters it, the electron that it excites will conform itself to its wave pattern during the transition to the higher energy level, in such a manner as to replicate that wave pattern as nearly as the loss of energy will permit. 

Of course, when so doing, the photon must not lose all its energy to the transition process, but only a small part of it.  Thus we must contrive that the electron when being energized by the photon not simply be ejected from the detector as in a phototube.  Achieving this will likely require that the detector be carefully designed. It must absorb the photon, but then retransmit as much of it as possible on nearly the same frequency and with as near to the original wave pattern as possible.  Properly designed, the detector would be able to respond to any wave pattern (within the wavelength range of interest) that were to impinge upon it, retaining that wave pattern and re-emitting the photon with slightly less energy to continue its journey. I am not able to describe the exact details of such a detector, but believe it can be done through a system of wide-ranging electron orbits made available through a correctly structured system of conduction bands that give us electrons that have no definite position in the transverse directions, as well as slight energy gaps that can be crossed using substantially less energy than in the incident photon.  It may be that more than two such energy bands would have to be provided, and that the detector may have to have layers of differing material that would allow these processes to be carried out in sequence. It may be necessary, for example, to have an intermediate energy band whose energy is high enough to absorb most of the photon energy (so that the electron is not ejected from the material), from which the electron would then transition into the final energy band that would be just a little different than the incident energy.  But the key to everything is that all this takes place in spatial phase, so that the original wave pattern is maintained.  Doing all this may require cooling the material to a very low temperature to depopulate the higher energy levels and make them available to clearly receive the activated electron. With a first detector build on these general principles, the process should be possible.

[SciencyGummyWorms]

Process of observation: kick it

Observation: landmine explodes

Very well said.

[lightarrow]

The position of the particle has three components.  The component in the direction from the source to the final target is indeed recorded to the precision of the position of the central detector, but the position in the other two dimensions is not.  It is those transverse measurements that matter in this experiment.

In practice you say that the particle, after the slits, crosses a plane parallel to the screen before this one, without interacting in a specific point of this plane but making the generation of a signal when it crosses it. Correct? I don't know if what you say is actually possible.

Assuming it is possible, measuring the position x of the particle means to put its state in an autoket eigenvector of position so its momentum Px (x component of momentum) is then completely undetermined in this new state.

As a result, I think, you would have an interference pattern which should be the overlap of infinite patterns of different momentum, that is colours (now I assume to use photons) each, that is, a white diffuse area on the screen.
But it's just a thought, not sure of it.

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[PmbPhy]

Assuming it is possible, measuring the position x of the particle means to put its state in an autoket of position so its momentum px is then completely indetermined in this new state.

What in God's name is anautoket??

[alancalverd]

The evil twin of an autobra.

[Bill S]

It's something you snort on your own; or possibly in your car.

[lightarrow]

Assuming it is possible, measuring the position x of the particle means to put its state in an autoket of position so its momentum px is then completely indetermined in this new state.

What in God's name is anautoket??

[]Yes, you're right. For some mysterious reason I made a mix between italian language and Dirac denomination! I intended "eigenvector".

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[lightarrow]

The evil twin of an autobra.

LOL 😂

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[Atomic-S]

In practice you say that the particle, after the slits, crosses a plane parallel to the screen before this one, without interacting in a specific point of this plane but making the generation of a signal when it crosses it. Correct?

Yes.

[Atomic-S]

I think, you would have an interference pattern which should be the overlap of infinite patterns of different momentum, that is colours (now I assume to use photons) each, that is, a white diffuse area on the screen.
But it's just a thought, not sure of it.

I believe your analysis is correct, as pertains to what it analyzes. However, I believe I have not described the experiment clearly enough. The purpose of the experiment is not to measure the position in the direction of propagation, although doing so to within certain margins of error would be an inevitable consequence, in the sense that if the intermediate detector detects the particle, then the particle has necessarily been found within it, hence its position has been measured. However we also need to take the time factor into account. We have absolutely no need of finding the particle's X position except to the extent of verifying that it is a single particle.  The existence, upon exiting the slits, of a well-formed diffraction pattern implies that the particle has a narrowly-constrained wavelength, and therefor a very vague position.  What we do not want to do is change that situation in the first detector.  Can we detect the particle's presence in the first detector without altering its wavelength to something highly indefinite?  Yes, if we do not insist on knowing just when the particle passes through the first detector.  Therefore, the nature of the first detector's operation will be such that we are unable to say with any precision just when the particle passes through it, but we can still affirm that a particle, and only one particle, has passed through it if the original source is very weak.  For this experiment to work, we need a source that has a narrow wavelength band but also a very low photon rate so that the probability of having more than one photon between the slits and the final detector is negligible. Under these conditions, when the first detector records action, we know a photon has passed, even though we don't have a good idea of exactly when, in relation to the recorded signal, it did so. (And the recorded signal could itself occupy many times the time required for transit from slits to final screen). The temporal uncertainty of the transit of the first detector would probably be associated with the times required for the agitated electron to jump through three energy levels.

[Atomic-S]

Assuming it is possible, measuring the position x of the particle means to put its state in an autoket eigenvector of position so its momentum Px (x component of momentum) is then completely undetermined in this new state.

No, because the time at which the position occurs remains highly indefinite.

[PmbPhy]

The evil twin of an autobra.

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

[PmbPhy]

Assuming it is possible, measuring the position x of the particle means to put its state in an autoket eigenvector of position so its momentum Px (x component of momentum) is then completely undetermined in this new state.

No, because the time at which the position occurs remains highly indefinite.

That's incorrect and probably based on a misconception of the time-energy uncertainty principle. 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. Take a photon hitting an array of photon detectors or CCD for example. When the photon hits a "pixel" which the array of photon detectors or the CCD is composed of the time is recorded. Time is a parameter in QM, not an observable.

[lightarrow]

I think, you would have an interference pattern which should be the overlap of infinite patterns of different momentum, that is colours (now I assume to use photons) each, that is, a white diffuse area on the screen.
But it's just a thought, not sure of it.

  Can we detect the particle's presence in the first detector without altering its wavelength to something highly indefinite?  Yes, if we do not insist on knowing just when the particle passes through the first detector.

If you don't know when the particle passes, I could even say that it hasn't passed at all, yet! So, how can you say that you have measured its position?  []

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[alancalverd]

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!