Stefan, you asked"

"May I ask you to deduce the cause of the change in the following experiment?"

You already answered you own question: "we determine that - due to the property..."

My point is, that the "we" you refer to, by exploiting its memory, determined whatever "we" thinks it is, that has been determined. The experiment did not make this determination. "WE" did. The issue is what the observer did, not what the experiment did.

To be more specific, the only type of behavior that QM accurately models, without EXPLICITLY taking into account each and every one of the trillion, trillion bits of information in "we's" brain, are ones in which everything "we" does, is INSTANTLY erased from "we's" memory, as soon as it happens. Under these conditions, "we" does not even know that "we" even did an experiment, much less know how to "determine that - due to..."

Let me put it this way. You CANNOT use the law of gravity to "determine that - due to.." the nature of the law, all by itself, that the Earth will be in EXACTLY the orbit it is. You MUST specify the initial conditions. Similarly, if you are going to try to determine what a "WE" is going to determine, you MUST either specify the initial conditions, or conduct the experiment in such a way that NONE of the initial conditions could EVER make ANY difference. The continuous, instant erasure of "WE's" entire memory will accomplish that. I doubt that anything else will. The experiment you describe, is badly designed to determine, how entities like "we" determine anything. Consequently, it sheds no light on why "we" behave and why "we" deduce and determine whatever it is that "we" deduce and determine. Your experiment is designed to determine what the particles can and cannot do. That may be very interesting, but it is irrelevant to my point. You need to design an experiment to determine what "we" the observer can and cannot do, and under what circumstances. The only circumstances of interest are concerned with the contents of the observer's memory, because, it is known for a fact, that without that memory, "we" is unlikely to be able to deduce or determine anything.

QM has made the unstated assumption, that the content of the observer's memory has no significant impact on ANY experimental outcomes. But one of those outcomes is precisely the production of the "meaning" and "significance" and "interpretation" of the other outcomes! So do the experiment. It is not difficult. Erase all of "we's" knowledge and observe if "we" is still able to produce the same "meaning" and "significance" and "interpretation" of the other outcomes. What those other outcomes are, is of absolutely no interest, to the question of the validity of that unstated assumption.

Rob McEachern

Let me add a clarification to my statement that: "QM has made the unstated assumption, that the content of the observer's memory has no significant impact on ANY experimental outcomes."

The equations of QM do indeed assume this; it assumes that there is no "mind or matter". But this seems to be at odds with the observation that "the presence of the observer sometimes seems to impact the results."

My point is that one of the primary mechanisms by which the observer impacts the results, is not by some weird "mind over matter", but rather by "mind over mind". The observer's mind is not impacting the "other outcomes" mentioned in the previous most. But it has a major impact on the outcome generally known as the "production of the "meaning" and "significance" and "interpretation" of the other outcomes."

Dear Robert, Stefan,

Robert's answer above may be subtle, and may even appear to be 'crawfishing', a sideways skedaddle to avoid the challenge. Not so. As I understand it he is saying that, knowing nothing else, the experimenters would probably not rush to conclusions that deny local realism. But they DO know other stuff, and are biased by it.

If, in all cases, Alice and Bob choose filter angles a=b, then the correlation is perfect (-1) and there is absolutely no hint of anything questioning local realism. But when the angles change, the treatment changes. Let me quote Zeilinger from his book, Dance of the Photons:

"We detect only about 30% of the photons, because our detectors are not perfect ... but -- and this is really funny -- each experiment leaves at least one loophole open." Now this is interesting, but I find more significant statements on page 230:

"How can the measurement results now reflect that B and Y are entangled, just because Alice decided to perform a Bell-like measurement on A and X? Even though, before, when Alice measured her photons separately, Bob's photons B and Y were not entangled, their measured results were completely uncorrelated? How is that possible?"

"So what Alice and Bob do [is] they sort Bob's data ... into four different bins. ... if we mix together all four bins, the results all together are completely random and do not indicate any entanglement. So Alice's results allows us to sort Bob's data into the right sets, which individually are not completely random anymore, while the complete set was."

"...very different physical explanations for the same data result can be obtained by us [and] the experimental results clearly confirm that the photons registered earlier by Bob can be seen as entangled, IF SORTED THE RIGHT WAY, on the basis of Alice's measurement results."

"In the end we will, for Bob's results, present a different interpretation depending upon what Alice at a later time decides to do." Thus, although "the observed events are just events, ... the explanation of the events depends on later actions and decisions we or someone else might make. ... The mathematical description, the quantum state we assign to the situation, is very different depending on what Alice decides to do."

There's more, but it seems to me quite clear that "logic" and "deductive reasoning" are applied in very specific fashion, and many equally intelligent physicists find reasons to argue about the conclusions. For this reason I am more and more inclined -- forced to choose between realism, deductive reasoning, and locality -- to choose local realism and to tell the logicians, "get your act together".

Edwin Eugene Klingman

Hi, Robert

You are right, of course, that one can only speculate. My own suspicion is that the only truly simple things are artifacts--products of definition or design.

Dear Robert, Edwin,

thanks so much for your detailed lines of reasoning.

Don't get me wrong, i am not a person who will insist to be right, even if not. The whole motivation of my essay was the same as your both motivations to think about the open questions concerning QM. I just want answers that are consistent and "get the act together".

Edwin and Robert, you both are right by determining that there is much confusion in the attempts to explain/interpret the QM behaviour. Let me just give an example recently made by Menzel et al.

In their paper ("Wave-particle dualism and complementarity

unraveled by a different mode", Ralf Menzela,1, Dirk Puhlmanna, Axel Heuera, and Wolfgang P. Schleichb) they write:

"The precise knowledge of one of two complementary experimental

outcomes prevents us from obtaining complete information

about the other one. This formulation of Niels Bohr's principle of

complementarity when applied to the paradigm of wave-particle

dualism--that is, to Young's double-slit experiment--implies that

the information about the slit through which a quantum particle

has passed erases interference. In the present paper we report a

double-slit experiment using two photons created by spontaneous

parametric down-conversion where we observe interference in

the signal photon despite the fact that we have located it in one

of the slits due to its entanglement with the idler photon. This surprising

aspect of complementarity comes to light by our special

choice of the TEM01 pump mode. According to quantum field theory

the signal photon is then in a coherent superposition of two

distinct wave vectors giving rise to interference fringes analogous

to two mechanical slits."

Their experimental results are interpreted as outsmarting the classical "dictum" of complementary between interference and which-way information. But there are some differences here to state. First of all, the "thing" that comes from the source is in a "superposition". Secondly, if we believe in superpositions, due to this superposition the down-converted thing going through the double-slit aperture cannot be thought of as being attributed in the sense "the lower maxima goes through the lower slit, the upper maximum goes through the upper slit". Despite the fact that the two maxima are macroscopically distinct, if we want to speak meaningfully about A PATH it went/will go through, we must take into account that due to the superposition of the maxima it is undecidable which path the thing went. Despite the fact that in this experiment the idler detector was fixed to a certain maximum of the down-converted control-beam, the 1 to 1 assignment of a "collapsed" superposition at the idler detector and the fact that interference occurs at the signal detector isn't possible. The reason for this is, that the state of the signal-beam was entangled with the double-slit until the signal-detector measured it. After this, the superposition of position at the slits "collapsed" but the superposition of the original beam is still there and produces the interference pattern in the far field.

So, D1 and D2 don't "speak" about the same "thing".

I will reply in more detail to yours post, Robert and Edwin, in the evening of my time zone (Germany), because today my day is occupied with some activities and i must carefully think about what Robert wrote to me.

Thanks to both of you for an exciting exchange!

Best wishes,

Stefan Weckbach

Dear Robert,

I have read your essay and I appreciate your viewpoint. Your essay is very well-written, most interesting and very impressive. I wish you good luck in the contest.

Recently, I have noticed some wild variations in community rated list of contest essays. There is a possibility of existence of a biased group or cartel (e.g. Academia or Relativists group) which promotes the essays of that group by rating them all 'High' and jointly demotes some other essays by rating them all 'Low'. As you know, we are not selecting the 'winners' of the contest through our ratings. Our community ratings will be used for selecting top 35 essays as 'Finalists' for further evaluation by a select panel of experts. Therefore, any biased group should not be permitted to corner all top 'Finalists' positions for their select group.

In order to ensure fair play in this selection, we should select (as per laid down criteria), as our individual choice, about 50 essays for entry in the finalists list and RATE them 'High'. Next we should select bottom 50 essays and rate them 'Low'. Remaining essays may be rated as usual. If most of the participants rate most of the essays this way then the negative influence of any bias group can certainly be mitigated.

I have read many but rated very few essays so far and intend to do a fast job now onwards by covering at least 10 essays every day.

You are requested to read and rate my essay titled,"Wrong Assumptions of Relativity Hindering Fundamental Research in Physical Space". Kindly do let me know if you don't get convinced about the invalidity of the founding assumptions of Relativity or regarding the efficacy of the proposed simple experiments for detection of absolute motion.

Finally I wish to see your excellent essay reach the list of finalists.

Best Regards

G S Sandhu

everyone might find the Rousseaus' entry interesting concerning the bottom level and "simple entities":http://www.fqxi.org/community/forum/topic/1539?search=1

I posted this a little earlier, under Lorraine Ford's essay. It is part of an ongoing discussion that Lorraine, I and others have been having, about the nature of information. Since that discussion is directly relevant to my own essay, I thought I would also post it here.

No need to apologize. You are in good company. Most of the world's physicists have their wires crossed in exactly the same way. Imagine a "Skyscraper of Perception", built on "The Foundations of Reality." As one journeys upwards, bottom to top, one passes through realms of increasing levels of perception; Physical behaviors, chemical behaviors, biological behaviors, and at the top, conscious behaviors.

You and the physicists are on the roof, looking downwards, through the mists, trying to "See", "The Foundations of Reality". I went to graduate school, in physics, expecting to spend my career doing the same thing. But before I had even finished school, I had noticed all the communication antennae on the roof, and began to wonder what all that was about. That was much nearer, and not surrounded by mists, and thus more readily discerned. Then, after having satisfied my curiosity about information and communications systems, I once again took note of all my former colleagues, the physicists, still peering intently down into the mists. But now, rather than joining them, I began to peer at them. I wondered if they were really doing anything all the different than the other antennae on the roof. They certainly believed that they were. But I had my doubts. They believe that they are "seeing", but like all the other antennae on the roof, they are only "perceiving". And when they set up their instruments, to enhance their "seeing", they merely perceive the perceptions of the instruments, in addition to their own.

The difference between "seeing" and "perceiving" is important. As noted elsewhere, in these posts, you can "see" "data", but "information" can only be "perceived." Data is what exists "out there", but perceptions and "information" only reside at the output, not the input, of an information recovery process. By confusing the two, you confuse everything you can ever know about what actually resides within the mists. Physicists have assumed that they were "seeing" "The Foundations of Reality", But they merely perceive "Our Reality", the false-colored, coded information, generated by our entire collection of perceptual apparatus.

By failing to take into account the "instrumental effects" produced by their own perceptual apparatus, they have convinced themselves that "Our Reality" must be necessarily identical to "The Foundations of Reality." But that is not in fact necessary, and as I attempted to demonstrate in my essay, it is in fact not the case. At present they are still quite different. The subject of this essay contest, is ultimately about why they no longer seem to be growing any closer together. My reply is "Because you have failed to clearly perceive perception itself", because you do not clearly understand what information even is.

Thus, while the physicists continue to debate if information is lost, when a book is dropped into a black-hole, I respond "NO!" Information only exists at the output of a recovery process, a perception. For information to be lost, all the observers capable of reading the book must be dropped into the black-hole.

Dear Robert,

you are right, unstated assumptions are relevant. They for example stem from the observers memory.

You wrote above:

"The only circumstances of interest are concerned with the contents of the observer's memory, because, it is known for a fact, that without that memory, "we" is unlikely to be able to deduce or determine anything".

True. But without memory, what would be left over from physics/maths/science in general? Surely nothing. Sience has at least some useful "stories" to offer which result in practical innovations. Science in this sense "works" - with the help of human memories and maybe some other ingredients.

You further wrote:

"Similarly, if you are going to try to determine what a "WE" is going to determine, you MUST either specify the initial conditions, or conduct the experiment in such a way that NONE of the initial conditions could EVER make ANY difference."

I understood these "initial conditions" as the unstated assumptions you mentioned above. In this fashion, most of us do more or less build our lines of reasoning. We assume somthing. Some assume something as real and FORGET it - the price is that there may occur serious contradictions, because the "initial conditions" simply do not take into account that they could be wrong.

Conducting an experiment "in such a way that NONE of the initial conditions could EVER make ANY difference" does not make any sense to me. Science, physics, human logics, maths, human social behaviour - all of these areas and all "information" originating from these areas need neccessarily an act of differentiation to deduce/induce/conclude something. I give you an example:

Referring to the erasing of ones memory is sometimes usefull, sometimes not. Because it can produces serious problems - if one erases the information about his/her own a priori assumptions.

I am a little bit disappointed that you don't even try to deduce what could be going on in my mentioned experiment without referring to the erasure of memory. If there is a certain "memory" in physical nature without the need for a human brain - we simply don't know! It could be, it could be not the case.

I claim that you cannot explain this experiment other (but in all cases consistent - with or without the help of your memory) than deducing a non-local effect being "at work" in this experiment. See this challenge as an Gedankenexperiment and keep in mind (or not) that whatever initial conditions you attach to the experiment - by being aware that those conditions are at first only your personal constructions - you will not be able to construct a consistent model for the experiment.

You are overly concerned with human retrodicitons, but what is your opinion about human predictions - predictions that can be proven and in the history of science were to be found correct?

That's for now,

best wishes,

Stefan Weckbach

  • [deleted]

  • Post #90

Hi Robert

Would you like read my essay?

http://fqxi.org/community/forum/topic/1413

Stefan,

It has long been the position of Science, that the burden of proof lies with whoever is making an extraordinary claim. It is the claimant's job to prove it, not Science's job to disprove it. I am not the one making an extraordinary claim. My only claim is so non-extraordinary, that I seriously doubt that anyone will ever even bother to test it; namely, that the contents of the observer's memory has a significant impact on the "interpretation" of the experiment, produced by that observer.

The claimants claim, in effect, that without plugging a single "bit" of the relevant initial conditions (the observer's memory) into the equations, they can deduce, from the structure of the equations alone, that the observer must, of NECESSITY, conclude whatever the claimant thinks they have concluded, regarding the aforementioned "interpretation". That is a rather extraordinary claim. They have not even attempted to proved it. But it is their job, not mine or Science's, to do so. My point is, the claimants claim is equivalent to the statement, that they can predict the behavior of the observer (he or she MUST conclude thus and such), with even greater accuracy than they can predict the phenomenon that is being observed. That is an extraordinary claim. In effect, they claim that the equations of QM, enable them to predict the behavior of the observer, regarding this "interpretation", with CERTAINTY, from the mere structure of the equations alone, without even having to specify a single, relevant initial condition.

My essay and comments are simply my attempt to lend the claimants a helping hand, as time permits. I have attempted to point them in the direction of the path they will have to take, in order for them to prove their claim. But it is they, not I, that must trudge along that arduous path. For example, to start with, after erasing the relevant memory, they might slowly restore it, bit-by-bit, to determine exactly at what point in that process, does in again become possible for the observer to deduce the "interpretation" he was able to deduce before the memory erasure.

Rob

This is a post I made on Sept. 3, 2012, while discussing the essay: Is Quantum Linear Superposition an Exact Principle of Nature? by Angelo Bassi, Tejinder Singh, and Hendrik Ulbricht. It might help to understand my concern with what the observer is doing, rather than what the observed is doing.

Inger,

Your question is not silly at all. It is very near the heart of the issue. One need only go a little bit deeper to arrive at "the issue."

What is the significance of the particles all being "identical" in the first place? If they remain, forever identical, then they cannot change with the passage of time. If they cannot change with the passage of time, then they cannot store any information whatsoever, within their internal structure.

But a larger entity, constructed from a number of such identical particles, can store information, by the relationships (like distances) between them. Entities that store information, can behavior towards other entities in a "symbolic" manner, and not just a "physical" manner. Even a tiny virus particle has genetic information stored within it, that enables it to exhibit such "symbolic" behavior.

What is the significant difference between "symbolic" and "physical" behavior? It is this: in the latter, observed data measurements are treated as "real numbers", in the former, they are treated like "serial numbers." Real numbers have most significant and least significant digits. Serial numbers, like credit-card numbers do not; change one digit anywhere, and it symbolizes someone else's account number; introduce one genetic mutation, and it may code for a different protein.

All the "interpretations" of mathematical models in physics have assumed that entities only interact "physically." That is true for entities devoid of any information storage capacity, like subatomic particles. But it is not true of macroscopic entities, especially human observers. Physical behaviors can be viewed as encoded into the equations. But symbolic behaviors are coded into the initial conditions. By ignoring the exact (individual digits) of the initial conditions of the information stored within complex entities, physicists has thrown the baby out with the bath-water.

All the supposed "weirdness" in the "interpretations" of quantum theory, derives from the fact that physicists have failed to take into account that human observers interact "symbolically" with their experiments, as well as "physically."

Sketches Among the Ruins of My Mind (with apologies to Philip Jose Farmer)

Let us conduct a global scale, double slit experiment. I, Rob McEachern, will be the entity traveling through the slits. Here are the observable facts of the matter:

1) I will repeat the following journey many times, to enable observers to determine my probability of arriving at any particular destination:

2) I arrive at Los Angeles airport, and ask to be put on the first available flight to anywhere the airline travels.

3) The airline only has flights, from Los Angeles, to two destinations (the slits), Washington and New York, and the flights are equally probable to either destination.

4) I arrive at either New York or Washington, and ask to be put on the first available flight to anywhere the airline travels.

5) The airline only has flights, from these two airports, to airports in Europe. The probability distributions of the flights (the routing system as constructed by the airline) is such that, when the arrival destinations are graphed as a histogram of probability of arrival versus latitude, it looks just like an "interference pattern."

6) Observers record my arrival destinations, and generate the histogram noted above.

7) The observers then deduce, the I, Rob McEachern, must be some weird, supernatural entity, that must necessarily have traveled through both New York and Washington, simultaneously, because that is, without doubt, the only possible mechanism for producing the observed "interference pattern."

SPOILER ALERT: do not read any further until you have thought about the above.

If observers misattribute an attribute of the slits (the routing system) to be an attribute of the traveler, then observers can come to some pretty weird conclusions.

Dear Robert,

You only can arrive at the belief that observers have misattributed an attribute of the slits to be an attribute of the particle(s), because of suppressing (forgetting?) some additional information. By suppressing this information, you indeed can come to the conclusion you made in the referring post. Here's the missing information:

I presume that the routing system you spoke of does not change if an independent observer looks - throughout the overall course of your many journeys - which airplane you enter at the Los Angeles airport (towards New York or towards Washington). Even if this routing system changes from day to day or somewhat other, the result must - as defined by you - be your "interference pattern". I also presume that you only fly from one and the same airport in L.A.. Even if we don't know at which time you arrive at this airport, the same interference-pattern is assured by you.

If the observers you spoke of, at the end hold their finished histogram in their hands and see the interference pattern, the independent observer from L.A. airport will find his data embedded within the "interference pattern". His data is consistent with the data sheet of the observers you spoke of, because we easily can imagine that the independent observer always traveled with you forth to europe and back to L.A.

But now a contradiction between the "Rob McEachern"-journeys and the "journeys" of single particles arises. For observed particles, even when observed not at "New York or Washington", but "europe", the "interference pattern" changes into a "non-interference"-pattern. We surely can "imagine" to travel with single particles, but we cannot prove (in the same way we *can* prove for example your journey's route by traveling with you) the trajectory of a particle and at the end obtain nonetheless the same "interference pattern". Even if we want to prove the particles' trajectory (your flight ticket) just a moment before it hits its layer of final measurement (the observers at the different airports), the frequencies for your visited airports in europe change dramatically - for every control sample some observers make in those cases. This must logically be the case, if you assume your thought experiment to be in a one-to-one relationship to the observations gained from the double-slit experiments. If you don't assume this, your thought experiment is just badly designed.

If we bring together the referring information (namely your flight tickets and the fact that you arrived at specific, but different airports in europe), we can "prove" the route you should have been taken. Logically, at the basis of your example, we should conclude (deduce) that it should not make a difference for the histogram if the observers at airports in europe only identify you or additionally want to see your flight tickets or not. But if they want to see your flight tickets - the only way for you to escape the contradiction is to assume that the tickets are at least in such cases we want to see them, faked. Because I as an independent observer was always with you - from L.A. to europe (and back). Maybe the whole passenger list was for every single flight filled with people who traveled with me for the only purpose of validating my final reports about the reality of your flight routes.

In the double-slit experiment, we have no such observers like the people I just mentioned. But the contradiction between a route you seemingly took (namely the particles' path through one of the slits and its final arriving at one of possibly a multitude of independent detectors - (observers at the european airports) and the final localisation at a certain detector (observer at a certain european airport) which does no more contribute (if your flight ticket is checked!) to the final histogram you mentioned (but to a *different* histogram! which is *not* the inverse pattern of your "interference-pattern"), is penetrating. I think you cannot explain this contradiction with some new "routing system" at every airport in europe - for the case you give away your flight tickets to the observers.

Rob, sience is not only about defending ones' own model against counter-examples. It is also about necessarily *give* counter-examples to others for the sake of the intellectual honesty of science and its developement. In this sense I would ask you to give me a counter-example that shows that my lines of reasoning about non-locality in my previous post are inconsistent. Not because I want you to make a bad job, but intending you to make a good job.

I want you to remember that you made a claim within your essay (be it "extraordinary" or not lies in the eye of the beholder) that "There is no 'spooky action at a distance' ", and your only arguments circle around the non-existence of the widely assumed spin-properties of electrons (cube instead of coin). You are stuck into a position where you cannot prove something with physical or mathematical methods that seems for you as not existing (the cube). Non-existing things (or things that are assumed to be non-existing) cannot be proven to be non-existing in ones model via physical procedures or logical deduction (You only can give metaphysical arguments for or against them).

Why not look at other experiments (for example the one I outlined in one of my previous posts, the double-double-slit-experiment) for which it seems to the scientific community that there is a spooky-action-at a-distance involved and try to prove them wrong by some reductio ad absurdum? From a logical point of view, you *CAN* prove that an assumption about the non-existence of something is false by giving counter-examples. I think this would be the better way than complaining yourself about all that hybris within academical and/or non-academical physical communities.

Best wishes,

Stefan

Stefan,

I'm having a bit of a hard time following your argument. You seem to be making some additional assumptions that I did not make. What does your independent observer in LA know, other than the time I departed? No one knows the flight's destination, for example, other than that it is equally likely to be headed to either NY or Wash. (it may not actually arrive, it may crash).

The routing distributions are given by the Fourier Transform of the slit geometry:

When both NY and Wash are open, the arrival pattern in Europe looks like the Fourier Transform of a double slit, an "interference pattern". When Wash is closed, the arrival pattern in Europe is set by the Fourier Transform of the Northern slit, a sinc function. When NY is closed, the arrival pattern in Europe is set by the Fourier Transform of the Southern slit, another sinc function, but offset in latitude. So the slit geometry is fixed, and the probabilities are fixed by the Fourier Transform of that Geometry. And they are independent of time, except that whenever you close, or open a slit, the changed geometry changes the Fourier transform, and hence the routing arrival distributions. When both airports are open, you see an "interference pattern", but when only one is one, you see a sinc function (its magnitude).

Note also, that many flights never arrive at all; they have crashed into the sides of the "slits". In this system, there is indeed a none-local phenomenon. But it resides within the routing system, not the travelers. It only appears "spooky" to an observer that attributes it to the traveler.

If you like, you can let your observer be the air-traffic controller, that blinks the airports (slits) open or shut, in any way you wish. But as soon as you change the slit geometry, you also, as a mathematical necessity, change it's Fourier Transform, and hence the routing distributions.

In other words, instead of thinking about this as a system of "wave-like" entities that produce an "interference pattern", think of it as an analog computer, that computes an approximation of the Fourier transform of the slit geometry, as in Fourier Optics. Consequently, the slit geometry "is" the routing system, whenever you change it, you change the routing.

    I was not being very precise in the previous post, when I stated "the Fourier Transform of the Southern slit, another sinc function, but offset in latitude." The Fourier Transform is a complex function. By "offset in latitude", I mean the latitude is encoded into the phase of the Fourier Transform. Hence, the Fourier Transform of the North and South slits differ in phase, but not magnitude.

    Dear Robert,

    if the slit geometry is/was the routing system that is/was responsible for the routing distributions (frequencies of the particles' impact), the inconsistency remains.

    Because you write "Consequently, the slit geometry 'is' the routing system, whenever you change it, you change the routing". Obviously, following from your statements, in delayed-choice experiments the slit geometry must have changed *after* a particle succesfully went through the aperture with both slits open. Because the arrival distributions have suddenly changed for those cases - despite the fact that both slits were open.

    But you assumed "The routing distributions are given by the Fourier Transform of the slit geometry". Even if i consider the system to be an analog computer in the classical fashion, this computer would be limited to only propagate its information with maximally the speed of light from the measurement plane ("europe") back to the slit geometry at the "east coast of the U.S.A." (double-slit geometry). If this would be the case, it would contradict the experimental observations obtained by delayed-choice experiments which exclude a backwards propagation of information with maximally the speed of light. The contradiction is, logically your routing system cannot at the same time be 'X' and be 'NOT X', if you think of it in classical terms like analog computers and such.

    Consequently, you neither can think about the system as equipped with wave-like nor equipped with particle-like entities which "travel" between the U.S.A. and europe.

    Best wishes,

    Stefan

      Stefan,

      An inconsistency does indeed remain. But that too is caused by additional misinterpretations of what is happening. Physicists have been using the wrong analogies, to think about this, for a very long time.

      I want you to look at a diagram, while I describe this. But to avoid violating someone's copyright, I don't want to copy and paste it here. Please open another browser window. Under Wikipedia's page for "Wheeler's delayed choice experiment", there is a heading for "External links", the first of which is "Wheeler's Classic Delayed Choice Experiment by Ross Rhodes". If you click on that, it should take you to "www.bottomlayer.com/bottom/basic_delayed_choice.htm". The figure of interest is on that page.

      Imagine "1" to be a radio transmitter antenna. "5" are two radio receivers, attached to highly directional, large, parabolic antennae. The slits at "2" create "Multi-Path" Interference. The radio antenna is simultaneously transmitting multiple stations, or channels. So there is also "Multi-Channel" Interference.

      To receive a signal with no interference, you must use a frequency band-limited filter to remove "Multi-Channel", and a spatial beam-limited filter to remove the "Multi-Source". The telescopes (large parabolic antennae) at "5" act as the spatial filters.

      Next, consider that, in addition to producing the "Multi-Path", the two slits act as a crude diffraction grating, dispersing the spectrum into the interference "fringes", which are the different "channels", that when combined together, result in the "Multi-Channel", so by "tuning" to just one "fringe", you have effectively tuned to just one channel, and thereby eliminated the "Multichannel" Interference. Consequently, there is no surprise that you see no interference, since the apparatus filtered out both the "Multi-Path" and the "Multi-Channel". So called Quantum erasers", in effect, merely remove the filters to restore the interference.

      The last sentence in the Introduction, on the Wiki page cited above, reads "The fundamental lesson of Wheeler's delayed choice experiment is that the result depends on whether the experiment is set up to detect waves or particles." Yes indeed they do, and for exactly the reasons given in my essay and the related posts under both my essay and Lorraine Ford's. More specifically, it depends on whether the experiment was set up to detect a Fourier Superposition (waves) or a single frequency (particle). Thus, on page 6 of my essay, I stated that "...the correct model for the observations is not a superposition, but is indeed a single frequency wave..." Having the correct model matters, It matters a LOT; why it matters was discussed, at some length, in the posts under Lorraine Ford's essay. Basically it boils down to this; knowing what to look for, enables one to recognize and filter out all the "crap", that does not look like what one is looking for.

      This brings us to the two Gaussian filters described in my essay. Look again at the figure cited above. Replace each of the two receiver/telescopes at "5", with a pair of of identical receivers/telescopes. Carefully design the frequency filter passbands to have Gaussian responses, as described in the essay. Now, as described, you have a pair of particle counters that can be used to INFER, not measure, the single frequency, via the ratio of particle counts, with an accuracy that greatly exceeds the uncertainty principle. That is why having the correct model matters.

      Next, consider the following:

      The Fourier transform of a Gaussian function, is itself, another Gaussian function. Furthermore, a Gaussian function yields the minimum possible time-bandwidth product, and thus the minimum "uncertainty" in the Fourier uncertainty principle.

      Returning, for the moment, to the radio signal analogy, remove the slits at "2", digitize the signal, multiply it (windowing) by a Gaussian shaped "window" and compute a Discrete Fourier Transform (DFT). Voila! You have just constructed not just a pair of Gaussian filters, but an entire "filter bank", each consecutive pair of which, can be used as described in my essay. Each of these pairs can be used to estimate the signal frequency. But, of course, due to the narrow bandwidths, pairs that are tuned closest to the signal frequency, have much higher signal-to-noise ratios, and thus provide much more accurate frequency estimates. In the formula for a Fourier Transform, multiplying by the complex exponential represents a tuning operation. The subsequent integration is a lowpass filtering operation. Multiplying by the Gaussian shapes the frequency response of that lowpass filter, to be another Gaussian function. Hence, a Fourier Transform can be viewed as a filter bank; a large number of tuned receivers. In a DFT, these receivers may be numbered, 1,2,3...n, and are spaced "D" Hz apart.

      In the formula in the essay: f = nD+D/2-(cD/2)ln(a(f)/b(f)). nD+D/2, is thus the center frequency of a receiver pair. The amplitude ratio term, in effect, yields a fine frequency interpolation. The reason I mention all this is to point out that the amplitude (particle count) ratio only yields the frequency offset from the pair's center frequency. The complex exponential in the formula for the Fourier Transform, acts a a single-stage, frequency tuner, known in the old radio receiver literature as a heterodyne. Now replace the two-slit "diffraction grating" and you have introduced a second-stage of frequency tuning, a superheterodyne.

      In effect, this entire apparatus is nothing more than a crude superheterodyne tuner, feeding into a spacial filter, followed by an AM receiver. Adding the paired AM receivers converts it into an FM receiver.

      Rob McEachern

      Like the 26 letters of the English alphabet, the representations created by De Broglie and Fourier are sufficient, but not necessary, in order to describe probabilities of detection. De Broglie associated a frequency with an energy. But that is not necessary. Fourier enabled superpositions to be described in terms of frequencies and phases. But that is not necessary. They are merely sufficient.

      It is often asked what exactly is the QM probability distribution, the probability of? Why does only the magnitude of the wave function matter? Because descriptions in terms of frequency and phase are merely sufficient. They are not necessary.

      It should be clear from my previous post, that the magnitude of a Fourier Transform may me viewed as a filter-bank of tuned energy detectors. The point is, they can be DIRECTLY viewed as being tuned in ENERGY, rather than frequency. For example, in the Gaussian detection curves used to construct an FM detector, one can substitute (make a change of variables) energy, for frequency, and everything will still work. Instead of being viewed as a Frequency Modulation detector, it can be DIRECTLY viewed as an Energy Modulation detector. De Broglie's association of a given Energy with a given Frequency, becomes superfluous. It is sufficient, but not necessary.

      Consequently, instead of viewing the description as a Fourier superposition of sinusoids, each associated with a given energy, one can directly view it as a superposition of tuned Energy Detectors. If a detector, a receptor, has a probability of detection versus energy that is a Gaussian function, then the paired detectors may be used to infer estimates of that energy, from the ratio of a pair of detectors' "total energy received" outputs. The process by-passes the wave versus particle distinction as unnecessary; what matters is energy detection. Whether you view the energy as arriving in single particles, or waves of particles, becomes superfluous.

      In case it is not obvious, let me point out, that when the Discrete Fourier Transform is used, the Energy Detection Filter Bank, noted in the previous posts, produces detectors that are tuned to Discrete Energies. So, if Energy is quantized, you end up with detectors, with specified probabilities of detection versus energy, tuned to each of the quantized energy values.