Dissolving Quantum Paradoxes

Rob,

As you admitted, buffering up signals requires introducing artificial delays. They hide the fact of causality which was formulated by Claude Shannon in terms of past and future. You are following Einstein's mainstream dogma that the distinction between past, (present), and future is just an albeit obstinate illusion. While Einstein took Fourier's mathematics for reality, Shannon obeyed common sense.

If you really were open minded and made comparisons between FT in IR and CT in IR, you should know that the latter omits redundant non-causal data, merely fictitious data that are not anchored in measurable samples out of reality.

"Perhaps you have never encountered a situation in which they [you meant not yet existing data] are highly advantageous. I have."

Professionals like us who dealt thoroughly with signal processing for decades should respect each other. Being well aware of the benefits of FT and all that, and even in position to causally explain them, I merely hope getting your support when I take the view of Shannon over the belief of Einstein. Let's not take any mathematics for reality. I see non-causal physics as closer related to mathematics rather than as to reality.

Hopefully you understand me, although my command of English is poor.

Eckard,

All filtering processes delay signals. There is nothing artificial about that. My only real disagreement with your position, is that I do not believe that a cosine transform is any more "physically real" than a Fourier transform. I have never encountered any evidence of nature employing any orthogonal functions. Mother nature does not appear to have ever discovered such things, and consequently does not use them anywhere. The problem is, orthogonal transforms require maintaining precise phase relationships between their different components. Nature does not seem to be able to do that. Consequently, it has always puzzled people, why senses like vision and hearing seem to be so insensitive to phase, when all the mathematical models that they have developed in an attempt to explain sensory signal processing are very sensitive to phase. The resolution to this problem, seems to be that nature employs an entirely different principle, to INFER (not measure) "frequency" like color and pitch, by transducing pairs of amplitude measurements made at the output of discrete, bandpass filters, like the cone-cells in the retina of the eye.

A similar problem with phase, is at the heart of the misinterpretation of quantum theory. The wave-function has a phase, so people have come to believe that the phase really matters. But computing the sum of the squares of the real and imaginary parts (Born rule) eliminates the phase information. The phase ultimately does not matter. Only signal amplitudes matter - because that is the only thing nature "knows" how to process.

Rob McEachern

Rob,

You hit a decisive coffin-nail on the head. Decades ago, I wondered why the ear is well known to be pretty phase-deaf. Does it disdain half of the information it receives? Steven Greenberg argued that the mere spectral analysis in cochlea cannot account for the huge richness of audible signals. He invited me to a NATO Advanced Study Institute on Computational Hearing, about twenty years ago in Il Chiocco, Italy where I met most of the belonging leading experts.

In my FQXi essays, I repeatedly tried to explain that and how Fourier analysis introduces fourfould redundancy. Realvalued Cosine transformation (CT) avoids these redundancies. Therefore I consider CT as well as a real filter bank more similar to reality than FT. Many physiological facts show: Cochlea can definitely not perform a complex analysis. You are right: Cochlear function evolved by trial and error in combination with subsequent neural time (alias phase) coincidence detection to a performance that is still superior to non-causal complex theory of signal processing. Oliver Heaviside cheated us.

This doesn't mean that complex calculus isn't computationally very elegant.

I appreciate your hint to Born's rule as a key to dissolve quantum paradoxes.

Eckard,

"the mere spectral analysis in cochlea cannot account for the huge richness of audible signals." That is because neither vision nor hearing operate anything like a spectrum analyzer. They operate as AM and FM modulation detectors, in which the FM is derived from pairs of AM detectors! The latter principle was one of the earliest forms of FM radio demodulators, long before things like phase-locked-loops were invented. At typical signal-to-noise ratios, the "instantaneous" frequency can be estimated several orders of magnitude more accurately than is possible via standard Fourier Analysis (picking the bin-frequency with the most power in an FFT).

Rob McEachern

Rob,

Hopefully you will be ready to question assumptions that are basic to your modulation interpetation too: In reality, no signal extends over time from minus infinity to plus infinity. Mirror symmetry between past and future and negative frequencies are also just fictions. So I see your view and arXiv: 1801.06347 (by Adan Cabello) close to a final solution but perhaps not yet fundamental enough. A nail is not yet the whole coffin.

What about hearing, I wonder if there is physiological support for your idea that it may operate as A and F demodulator. So far, all evidence confirms strong tonotopy from cochlea to CN and beyond. While your hypothetical carrier for AM is unknown at least to me, the temporal structure of the signal remains available for also confirmed subsequent neural coincidence detections.

I guess, physicists will not benefit from being confronted with technical terms like modem, PLL, etc. instead of truly elementary insight based on common sense.

Eckard

Rob,

In the 2013 contest "It from Bit or Bit from It?" I wrote an essay Shannon vs. Wheeler where I put the question "Did Alan Oppenheimer improve John Tukey's (real-valued) cepstrum? Do you agree on that the correct answer is no, and it may relate to your approach eyplaining the quantum paradoxes?

Eckard

Speaking of a play within a play:

https://www.researchgate.net/publication/326380733_simultaneity

Eckard,

"truly elementary insight based on common sense" That is exactly what the early FM radio engineers had, that physicists, enamored with Fourier analysis and orthogonal functions, have missed.

It is as simple as this:

(1) if a frequency-modulated signal is sent through a filter (like a resonator) with a sloping (non-flat) amplitude-vs-frequency response curve, then any change in frequency will be TRANSDUCED into a change in amplitude.

(2) This makes it possible to DETECT small frequency changes, without ever actually measuring either frequency or phase. Only simple-to-make amplitude measurements are necessary. But the output is ambiguous; a changing input amplitude, and not just a change in frequency, will also produce an change in the output amplitude.

(3) A simple procedure to eliminate this ambiguity, is to employ a pair of filters, with opposite slopes; taking the ratio of their output amplitudes will cancel out the effect of changes in the input amplitude, leaving a frequency-change as the only cause for a detector-output-amplitude change.

(4) This is how two-cone cells in the retina can produce the sensation of color, that is highly correlated with input frequency, even though the cone-cells are only sensitive to slow amplitude changes.

(5) What type of resonator-like bandpass filter has the minimum-possible time-bandwidth product? A Gaussian filter.

(6) How accurately does a pair of Gaussian filters, employed as above, enable the estimation of an input frequency? Exactly, unlike most other filter-types, that only yield an approximate estimate.

(7) This is all related to the Heisenberg uncertainty principle and Shannon's Capacity theorem, both of which are concerned with minimal time-bandwidth processes.

Rob McEachern

Rob,

The Gaussian filter is non-causal which means the filter window is symmetric about the origin in the time-domain. This makes the Gaussian filter physically unrealizable.

Karl Weierstrass, teacher of G. Cantor, didn't influence mathematics by own scientific papers but rather by lessons he gave for a crowd of his students.

I hesitate accepting him since he e.g. allegedly meant "it is impossible to distinguish two infinitely large numbers a and b from each other". In my understanding, infinity is a property, not a number, even if engineers like me often benefit from using it as if it was a number.

Admittedly, I am only familiar with cochlea, not with retina. I nonetheless guess in (4) "cone-cells" is correct. Could "two-cone cells" be a typo?

Eckard,

A truncated, FIR filter approximation to an IIR Gaussian filter is perfectly causal, when the FIR filter taps are applied to buffered samples in a "tapped delay line"; this is the actual, physical structure of the synaptic-connections between neurons - neurons implement FIR filters via a tapped-delay-line architecture. Here is a graph depicting color perception based on a pair of such filters.

In the retina, the three cone-cells can form a blue-green pair and a green-red pair.

Note that by simply making a change of variables (relabeling the axis) from "frequency" to either "log(frequency)" or "mel-scale-frequency", the same technique will compute pitch estimates like those observed in the auditory system. Note also that it is trivial to process multiple audio harmonics, to produce a single pitch-estimate, by summing the high or low filter output amplitudes, from harmonically-tuned filter pairs, and then estimating the pitch from the pair of sums. This is why "missing harmonics", including the absence of the fundamental, nevertheless yield the same perception of pitch, as when the harmonics are present. Longer (narrow bandwidth) filters result in longer delays, that are reflected in the delayed perception of their outputs. Such delays are observed in auditory perception experiments.

Rob McEachern

Rob,

You "do not believe that a (real-valued) cosine transform is more "physically real" than a (complex) Fourier transform". This is indeed almost unbelievable, but I keep it for justified.

You also wrote:"... phase, is at the heart of the misinterpretation of quantum theory. The wave-function has a phase, so people have come to believe that the phase really matters. But computing the sum of the squares of the real and imaginary parts (Born rule) eliminates the phase information. The phase ultimately does not matter. Only signal amplitudes matter - because that is the only thing nature "knows" how to process". Here we might be close to each other.

I just doubt that arbitrarily chosen phase reference, arbitrary truncation in case of choosing a window and FIR and the like reflect something physically real.

Couldn't the huge diversity of remedies not just in signal processing indicate that non-causal theories may suffer from arbitrarily added redundancies. You are certainly aware of Kramers-Kronig relations. Wasn't Kramers bound to tradition when he was involved in Heisenberg's approach?

I see the reality of past time more immediately anchored to the admittedly uncommon range of just positive elapsed time in IR rather than to abstract time in IR where time and absolute phase are arbitrarily shiftable.

Can we make the Gaussian bellshaped filter causal? Years ago I had the idea of enforcing zero future time by assuming a mirror at the border between past and future that adds the time reversed caudal part. Perhaps there is a better solution. Isn't CT simpler than FT in that it immediately provides its own inverse? In any case, the modified Gaussian bell shape cannot be symmetrical on ordinary scales of time and frequency.

By the way, instead of critical remarks on your interpretation of hearing I reveal favoring Tukey's cepstrum.

Eckard

Eckard,

"I just doubt that arbitrarily chosen phase reference... reflect something physically real" I agree. But, you have not taken that far enough: since all orthogonal transforms are based on just such phase references (between the orthogonal basis functions themselves), none of them seem to correspond to any process in the physical world. I have never seen Mother Nature do either a Fourier Transform, a cosine transform, or anything else of similar ilk.

"I see the reality of past time..." as nothing more than previously acquired, stored values, that PRESENTLY exist, and thus enable processing, in the present moment. We cannot process past events, that we failed to acquire and store, at the only moment at which they were actually present. The only things that can ever be processed, is whatever exists at the moment. If stored memories of the past exist, then they can be processed just as current measurements are processed.

"Can we make the Gaussian bellshaped filter causal?" Absolutely, if you truncate it, and align the resulting FIR with past data values, stored in a memory.

Nothing ever has to worry about processing a value "from the future", since, if you wait long enough (add sufficient delay), everything needed for processing what had once been "future" will have already transitioned to being "past" and consequently, if stored in memory, can be processed NOW.

Rob McEachern

Rob,

While it depends on the chosen reference whether a sinusoidal function sin(x+phi) is called e.g. a sine or a cosine function, only the sum of positive and negative cosine components, not sine components, may realistically describe a (bound to reality) signal which can be physically different from zero at its beginning (t=+0).

Perhaps in contrast to you, I consider phase up to complex calculus an appropriate and very useful description of a RELATION between two physical quantities. However, the only objective reference point for time and phase is the now, the ignored by abstract theory of physics border between past and future. When the late Einstein seriously worried about the now, he suspected it something outside science. I prefer distinguishing between the level of abstract laws and the underlying reality.

Instead of "aquired and stored values" I prefer speaking of traces that allow to reconstruct what happened to some extent. Objective history, as Shannon understood it too, exists unchangable for good, no matter whether or not is known.

Deliberately fuzzy expressions like at the very moment, today, nowadays, or in this millennium must not be misused in physics as to attribute existence only to a timespan called present between past and future.

Truncation and FIR are no non-arbitrary basic alternatives to the symmetry of Gauss's bell. Also, it is silly to wait long enough for the NOW.

Eckard,

"I consider phase up to complex calculus an appropriate and very useful description of a RELATION between two physical quantities." I do to. It is very useful as a computational device and in the analysis of many man-made communication systems etc. I just don't find it to be a good model for very many natural, fundamental, physical phenomenon. For example, while a water wave may exhibit interference, and that interference may be usefully described via phase, the underlying interactions between water molecules, that are the ultimate cause for the existence of the waves, are not fundamentally due to phase. The molecules do not "know" anything about the "big picture" in which the waves appear.

"it is silly to wait long enough for the NOW" Every time I order a meal in a restaurant, I have to wait for the moment it will arrive. It is no different with data collection and analysis - I have to wait for the data to arrive, before I can analyze all of it, as a complete set. Some processes, such as the IIR filters you prefer, may commence processing some of the data, before all the data that will influence the output has arrived. But if, for any reason, you wish to have all such data available, before the analysis even begins (as is necessary with most orthogonal transform algorithms) then you will have to wait, until all the data has arrived.

Rob McEachern

Rob,

My dictionary tells me: A phenomenon is something that is observed to happen or exist. Phenomena is the plural of phenomenon.

Largely agreeing with you, I'll give a different example for the "inability" of nature to know a human choice: Whilen the ear can sense RELATIVE phase, it is definitely unable to "know" the reference of agreed GMT used in science. This deficit indicates that science is sometimes too much abstracted from reality.

Do I have "to wait for the data to arrive, before I can analyze ALL of it, as a complete set"? No. Of course, I can only analyze data that already arrived. However, what means ALL data, what constitutes a complete set?

If something commences, it begins. I don't wish commencing to analyse data before they are available. Is it really necessary for me with CT to cheat myself in Heaviside's manner? Or is CT not an orthogonal transformation?

"Whilen the ear can sense RELATIVE phase" Can it? Detecting a time delay, which the auditory system can certainly do, is not the same physical process as detecting a corresponding phase delay. Can the auditory system sense the difference between sin(?t) and cos(?t)? No.

"However, what means ALL data, what constitutes a complete set?" Whatever is required to complete the task at hand. In the case of an FIR filter, you cannot complete the computation of an output point, until you know the data sample to be multiplied by each filter coefficient.

Rob McEachern

Rob,

Anonymous was me, and I should have written "our two ears" instead of "the ear". Sensation of interaural time alias phase difference is physiologically based on a direct comparison between simultaneously transmitted signals from the right and the left nuclei cochlearis, referring to each other.

My point is, the auditory system can use the difference between cos(omega t phi_1) and cos(omega t phi_2) for location of a sound source with just the RELATIVE phase phi_2 - phi_1.

While ordinary time and also position in space don't have naturally preferred points of reference, delay and distance are always positive which means the latter ones are ABSOLUTE quantities like e.g. absolute temperature too.

A set of measured data belonging to a function of time must be complete in the sense of containing ALL data that will be subject to the frequency analysis at the moment it will be performed. Being based on a time notion that makes no distinction between past and future, neither IIR nor FIR filter do a priori obey this causality.

I would like have to correct my mistakeable sentence "Is it really necessary for me with CT to cheat myself in Heaviside's manner?" I meant, with FT, not with CT, we follow Heaviside who evidently cheated us. Using the CT instead, I need not cheating myself but I avoid non-causalities as well as arbitrary choices.

I see the CT an also orthogonal transformation with functions of time and of frequency orthogonal to each other. Admittedly, this contradicts to the traditional notion of time in IR.

Eckard,

"the auditory system can use the difference between cos(omega t phi_1) and cos(omega t phi_2) for location of a sound source with just the RELATIVE phase phi_2 - phi_1." I understand what you are saying, but I disagree with the implicit assumption that you have made, about what is enabling this. The actual physical process being employed, does not involve phase detection. Rather, it is caused by detecting the time-differences between induced amplitude variations. In other words, a sudden phase shift will always produce a sudden amplitude spike, in a band-limited signal. These amplitude spikes will occur at different times, between the two ears, due to the difference in arrival times at the two ears. The detection process within the auditory system is not sensitive to the phase itself, but it is highly sensitive to these induced amplitude spikes. If you play a cosine into one ear and a sin into the other, there will be no amplitude spike, except at the turn-on and turn-off times of the signal. Consequently, the system will not detect any difference, between the two ears, except at those two points in time.

Rob McEachern

Dear Patient Closer To Truth Support Grouper,

I have attached the contemptuous email answer I got from Professor Elizabeth R Loftus after I had asked her to comment on my REALITY AM NOT ROCKET SCIENCE essay that was published on line on January 10, 2018 by FQXi.org. She evidently thinks that her ability to accurately memorize the name of a washing detergent am far more essential than her learning about natural visible reality would be.

Joe Fisher