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A Quantum Epistemology Blog

A dilettante exploration by , Copyright © 2000 - 2004, All Rights Reserved

The purpose of this document is to entertain the reader with an ongoing account of a newly converted enthusiast's plunge into quantum mechanics and quantum computing.

Days

2000-11-12

I'm going to put this page up here and keep it up until I feel foolish enough about what I have written to take it down.

I have recently come to an intuitive grasp of quantum mechanics. It seems to me to have a few rules I haven't seen stated anywhere as general propositions, so let me state them here.

  1. The universe is infinite in all directions in all dimensions as far as we can understand infinity.
  2. That which is called "classical physics" should be termed local physics, physics between objects on approximately the same scale.
  3. Quantum mechanics deals with phenomena individually governed by local physics when viewed as quanta from another scale.
  4. Thus, whatever are the essential priniciples of quantum mechanics, they must apply to the macroverse equally as to the microverse.
  5. Incidentally, the set of correlations of local physical laws or conditions which are internally consistent correlations is a set of membership > 1.
A galaxy looks very much like an atom. The dark center is reminiscent of the atomic nucleus; the opening and closing arms of a spiral galaxy look like the probabilistically governed quanta called electrons. A quasar is reminiscent of a quantum dot, squeezing off immense (from our scale) macroversal
"photons" in discreet quanta.

All phenomena interact on a quantum scale, even sociologically. The year 2000 American election was a quantum sum which represented "None of the Above" in the mathematical semantics of the American electoral system, and this because, like subatomic quanta, human political postures are entagled with all postures with which they are in direct contact, e.g., "You votin' for Nader? Then I'll vote for Gore 'cause I don't want Bush." A cyclone is a quantum interaction. A traffic jam is also.

As a computer programmer and theorist, this view is pleasing to me, because it finally makes me comfortable with electrical theory, with which I have more familiarity than with nuclear physics. Previously, belief in their operation required something like an act of faith. Now I have made my peace with semiconductance.

I hope to write more as I study the math specific to quantum mechanics and quantum computing at greater depth. I'm plowing through that now.
Helpful have been the following:

A thought later that day

The most general principles of the interaction of quanta composed of innumerable immeasurable discreet phenomena should be applicable equally to the macroverse as to the microverse.

Still later that day

Think about cars entering a toll plaza, then remerging, as on the Oakland side of the Oakland-San Francisco Bay Bridge. You can see an interference pattern as they remerge. QM is about an empirically observed aspect of the universe, to wit, that "if you have enough li'l stuff viewed from a sufficiently detached perspective, stuff looks like quanta." This includes ants in an anthill, consumers buying deodorant, the spiral arms of galaxies, and emissions from pulars/quasars.

Benoit Mandelbrot said he was talking not about abstract math, but about the "fractal geometry of nature". Similarly, there's a quantum mechanical nature to all systems which are sufficiently complex so as to render analysis of their constituent phenomena impossible except in statistical fashion.

Let's return to the example of automobile traffic flow. The observer is a county road inspector. He's not a traffic cop, he's studying usage patterns. He doesn't care if he sees an individual car weaving, that's the problem of the highway patrol. However, he might care if he saw many drivers going over the white line on the shoulder to pass cars on the right. Likewise, our observations of subatomic phenomena and astronomical phenomena are focussed on certain kinds of measurements to the exclusions of others of less interest, or which are more difficult to make or which might not have occurred to us.

The planet Earth is a wave, if measured once a millenium by a single measurement which might find the Earth itself, or merely one position in the wave form of Earth's orbit where there is high probability the Earth might be encountered. Of course, if you are on humanity's scale relative to the scale of the Earth, the Earth is undoubtedly a particle. Still, phenomena such as the precession of the equinox nag at the collective mind of mankind to remind us of the wave nature of the celestial role known as "planet".

I don't mean to suggest an onionskin theory of the universe. Astronomical phenomena are easy to differentiate from subatomic phenomena. However, quantum analysis of either end of our perceptual scale is remarkably similar to quantum analysis at the opposite end of the scale. Among those worthy of examination in this regard are quantum phenomena such as hurricanes, tidal waves and freeway traffic congestion, all residing close enough to our human scale that we may examine them both from a quantum perspective and as composites of perceptible and measurable discreet phenomena.

2000-11-13

Early A.M. musings.

It is interesting to read the lives of the quantum theorists. They were generally a pretty odd bunch.

...

I think we already see something very like quantum coherence on the mundane scale when we observe traffic flow on a limited access highway such as a freeway. Consider all on-ramps and all off-ramps. At a given instant, from the point of view of the observer at rush hour, there's some kind of balance between flow onto the freeway here and flow off of the freeway there, whichever exits "here" and "there" might be. The balance is measurable statistically. Faster-than-light coherence exists between the quanta of cars exiting and entering because of reasons outside the scope of the measurment, i.e., that a certain flow is established during rush hour based on the statisical of distribution of commuters going to any given destination from any given origin.

Late evening

An article in New Scientist entitled " Prime Time " makes some points seemingly related to my intuition of the general applicability of the principles of quantum measurement:
If ... physicists prove the Riemann hypothesis using a quantum system, the link will be firmly established. Then ... the field will blossom. Using the mathematics of the zeta function, scientists will be able to predict the scattering of very high energy levels in atoms, molecules and nuclei, and the fluctuations in the resistance of quantum dots in a magnetic field.

And it turns out that the same mathematics applies to any situation where waves bounce around chaotically, including light waves and sound. So the performance of microwave cavities and fibre optics could be improved, and the acoustics of real concert halls might profit from the music of the primes.

Thanks go to Dennis Wilson for pointing out this article to me on the Well .

Mitsu Asks Why

Also on the Well, Mitsuhara Hadeishi made the following interesting comment:
[T]he mystery of quantum mechanics is of a very different kind from the mystery of, say, why the fine structure constant is 1/137. The QM mystery is not just "why are the equations that way and not some other way" --- but rather --- what do the equations mean? What is a measurement? What does consciousness have to do with measurement? Why do we measure anything at all?

There is a big fuzzy hole at the center of QM, and the fundamental question of why we observe collapse to the particular set of observables we observe (and not, for example, a set of superpositions of those observables) --- that's a really big question. NOTHING in the mathematics makes this clear whatsoever.

Presumably, quantum mechanics is describing physical systems, and presumably we, the physicists, are also physical systems. So what is the relationship between us and these systems that we observe? What is so special about an "observer" that they have the power to "observe" and thereby force a "collapse" of a quantum system?

Or, to put it another way, how is it that we can make the observations necessary to even determine the fine structure constant is 1/137?

I replied that epistemology suggests that the "collapse" in measurement is a measurement of the measurement as much as of the measured quantum.

Bedtime reading

People sometimes used to believe that computer programmers are mathematicians gone to seed. Some years ago I purchased two books at a public library used book sale which I somehow felt that I must have and someday read. I have poked around at them over the years but never completed either. Now I find myself opening them by my bedside to refresh my mathematical grasp so as to deal with relativity and quantum physics. These two books are: Vectors is very readable and helpful in a way that gives the reader a sense that the author liked students. Tensor Calculus and Relativity seems a little less friendly to the student, but it is still very pithy and useful. I conclude I was very fortunate in these inexpensive chance purchases. 

2000-11-14

More thoughts on the architects and architecture of quantum theory

I continue reading with interest biographies of the quantum pioneers of physics and mathematics presented by Univ. of St. Andrews Scotland MacTutor History of Mathematics .

It stands out that these individuals were all part of what we might today call a "network" at the highest circles of European academia. While most of the practical applications of particle physics took place in America immediately before, during and after World War II, due to America's vast resources, her industrial ingenuity, and the haven she provided to members of the European intellegentsia fleeing the Nazis, the theoretical framework was erected by a rather small group of pioneers, many of whom were lauded prodigies, many of whom had studied with the same professors, and who were continually engaged ("entangled"?) with one another in intellectual discourse and sometimes combat.

I have read that Newton and and Leibniz independently arrived at the calculus, but that Leibniz's notation was superior to Newton's and was therefore universally adopted over the following decades. I mention this because, although adept at computer programming, I have always had a bit of trouble with classical math. Although fluent in several foreign languages, including those with non-latin and even non-phoenician alphabets, some of the approaches and notations of classical math are, for some psychological reason, off-putting to me. I pondered this same point many years ago when I found the Forth programming language, which is syntactic rather than notational, much easier at first to assimilate than the highly notational C language. I strongly suspect that this is the result of an intellectual-cum-cultural bias on my part. I am partly of Jewish extraction, and find the Forth programming language subtly reminiscent of Hebrew, compared to the C language which evokes for me the flavor of Latin or Greek. Or perhaps it is just the savage American in me rejecting the mincing and the flourishes of European thought.

Now in middle age and revisiting the maths which I treated casually decades ago, I find the task a bit easier, but am still uneasily conscious of the overbearingly European flavor of the theoretical framework. This leads one to suspect that some of the difficulties of quantum theory lie in the memetic framework of the observer. This intuition is bolstered by a year's experience teaching high school math in the Hawai`ian Islands, where Euclidean geometry left the students gaping and slack-jawed, but casual discussions of relativity found a much more receptive hearing, the furniture of relativity, such as the variance of time depending on the observer and the inherent curvature of space-time, according more closely with island and ocean life than does the blander Euclidean architecture founded on measurements made in the flat floodplain of the Nile.

More helpful links

Bright Gaps and Traffic Jams

In discussing today my quantum mechanical intuitions, I summarized for my interlocutor as follows:
I suppose that what I am saying is primarily epistemological, but the point is that if you factor electron volts and spin numbers from quantum physics, there still remains a kernel of truth about quantum measurement itself that is applicable to all scales.
My interlocutor asked if there were practical implications for subatomic physics to be derived from this perception. I replied with another traffic jam analogy.
In measuring a freeway stop-and-go jam, what are you measuring? Really, you are measuring the frequency of openings between the cars. The individual cars, green or blue, long or short, are irrelevant to your concern, which is focussed on wave intervals of the absence of cars, because this lessened density of cars recurring periodically denotes flow of traffic, which is your interest. This is not the perception of the drivers of the cars to whom their individual car and its precise location at any instant is of supreme interest.

In fact, for the traffic observer stationed above the freeway on a footbridge, it would be helpful and intutive for the pavement upon which the cars roll to be back-lit in some fashion so that free-flowing traffic showed as a wave motion of light which possessed broader and broader darkened bands as traffic became more congested.

It seems thus a physical science corollary implicit in my epistemological observations that, in measurements at the subatomic level, some of the things which subjectively seem to us "bright" and "positive" and connote to our gut-level human view of the world a sense of presence may equally turn out denote absence, as in the backlit pavement showing through the absence of cars in the traffic flow.

I suspect that a likely candidate for exploration in this regard is electromagnetic radiation. This seems to be a partial reply to Mitsuharu Hadeishi's rhetorical questions above about what we measure and why we measure.

2000-11-17

One More Traffic Jam!

Thinking in the wee hours about quantum measurement again since I got stuck in a reduced traffic flow situation on I-70 between Denver and Denver International Airport earlier in the evening!

The essence of driving in stop-and-go traffic is, as every good driver knows, not being one of the stop-and-go'ers. Instead, you let space open up between you and the driver ahead so you may have to relent and slow down but you never have to hit your brakes. Actually, what you are doing is driving the average speed of the traffic.

The jam was cause by heavy right-to-left merging from on-ramps. As drivers in the second and third lanes to the left relented, cars periodically moved over leftwards from the first and second lanes in the open spaces. It's like watching gas molecules in a envelope under constant deformation.

Workin' Class Blues

As naive as it may sound, I tried applying for a job in quantum computing with one of the firms trying to build an actual quantum computer. My programming skills are excellent and mature, but of course, what is really wanted in these jobs at this point is a PhD in an applicable field, whereas I am an autodidact who only got his high school diploma by luck.

The PhD who answered my email was very gracious. I'm going to keep trying applications because that is how, a couple of decades ago, I got started in programming after spending the '70's in mystico-philosophical bemusement so characteristic of those times, with an income provided by farm and industrial work. So maybe in middle age (I just became a grandfather) I can slide over into quantum computing.

How to hop over decades of sort of thumbing my nose at the hard math of quantum physics and learn something practical is the challenge! Maybe my exploration will merely remain an epistemological exercise without ever leading to work in developing quantum computers.

So I have changed the title of this page from "A Quantum Mechanics Daybook" to "A Quantum Epistemology Daybook".

Shall we proceed?

Quanta, Quanta Everywhere ... The Simple Syllogism of Quantum Epistemology

Quantum epistemology we are defining as an audit of the rational basis of observation and measurement of quanta.
  1. A quantum is an aggregate of local phenomena observed with detachment.
  2. Observing a quantum renders it a local phenonemon.
  3. Ergo, any aggregate of quanta observed with detachment is another quantum.
By "observed with detachment", I mean that the observation is focussed on the aggregate, not on the local phenomena of which the quantum is composed.

Quanta exist and are perceived in daily living. Even the human body itself is measured in quanta: we call some of these quanta "organs", for instance. At every level we are only perceiving quanta. Each of those quanta is an aggregate of local phenomena. Each of these quanta is to us a local phenomenon, a "dog", a "rock", a "jelly donut", but of course, it's an immesurably complex entity composed of quanta. In the aggregate, these local phenomenon on some scale are constitute a quantum on some other scale of measurement, ad infinitum.

If this is true, then the notion that subatomic phenomena behave paradoxically in relation to our mundane frame of reference simply because they are quantum phenomena must be incorrect. It is obvious that we interact in an intuitive fashion with an infinity of quantum phenomena in every moment of our existence, because everything we see is an aggregate of complexity beyond our ability to fathom except in quantum fashion.

The ballot count in Florida in the year 2000 United States presidential election proves that the principles of the measurement of quanta whose constituent phenoma are inscrutable apply to our daily lives. All our observations and measurments in daily life confront precisely that difficulty of quantum measurement. There is no stable, provable frame of reference for making the assumptions which we are compelled to make in our daily struggle for existence outside of highly statistical quantum theories such as religion, ethics, and folk wisdom.

Observeration commits the observer with respect to subsequent observation.

The paradoxes of particle physics are local phenomena in our frame of reference, an inability to see, a desire to see what we infer must exist. These paradoxes are not specifically intrinsic to the subatomic frame of reference, unless Seussian Whos exist at the subatomic level in a state of perplexity comparable to our own.

"Expect a Surprise"

The principal attraction of an epistemological approach to quantum measurement is that one can benefit from both the wisdom and the folly of mankind throughout history. For instance, as scientific eras change, the previous era's accomplishments tend to be obscured by disdain. The ancient concept of matter consisting of earth, air, fire and water, is skewed from our present point of view by the use of the term "elements". We still claim four states of matter, solid (earth), liquid (water), air (gas) and fire (plasma).

Ergo, if one pays close, or even perverse attention to the hubris and blind spots of the modern scientific viewpoint, one can choose from a wide assortment of phenomena currently viewed as implausible which are likely candidates for discovery. The most striking epistemological feature of the practice of quantum physical research is the narrowness of focus. Not much focus has been placed upon quantum measurement of the behavior of subatomic particles in situ in large composites from homely everyday life.

Therefore, there could exist in the common scientific viewpoint a tacit assumption loosely based on Occam's Razor that subatomic quanta in the fine should behave as subatomic quanta in the rough, within a certain similarity of scale as regards molecular ordering and density. Yet the case can be made on epistemological grounds that carbon atoms found in a large, handworked block of finely polished mahogany should exhibit perceptibly different quantum taxonomy than those of a crude, unworked block of inferior wood. The case is made, briefly, something like this:

  1. In shamanic societies, to the extent that their practitioners could be made to understand quantum physics, those practitioners would assume the constituents of a finely polished block of good wood to be of a nature somewhat different than those of a crude, unworked block of bad wood.
  2. In the conflict between Lamarckian evolution and Darwinian evolution, Darwin won a complete victory in Western thought which endured for over a century before it was entirely clear that neither Darwinian nor Larmackian evolution was entirely satisfactory, and that elements rejected out of hand from the Lamarckian school of thought were attempts to deal with empirical phenomena explained away too hastily by the Darwinian argument.
While a better and more finely reasoned case may be made in this particular matter, the above should be a sufficent toy example to prove that quantum epistemology is capable of predictive reasoning.

Beam me up, Charm!

Quantum teleportation is similarly an artifact of observation.
Heisenberg understated the case:
The approach of the observer interacts with the observed.
This is because, statistically speaking, the observed will appear to seek to evade the observer.
On the scale of practical infinity, anything can happen and does happen.
There is an infinity of individual constituent phenomena behind a measurable subatomic event. Unless one wishes to model an entirely deterministic model of universal existence, which is, I think, a sterile excercise, each constituent event may be said to have its own agenda.

2000-11-19

An interesting use of single photons to form a data stream to allow quantum detection of data interception is resported by Stanford University News . 

2000-11-29

Reconciliation

Fool that I am, I've been debating on the Well with people much better informed than myself on Quantum Mechanics. The debate goes round and round and runs something like this:
Me: Quantum measurement and chaos theory have to be the same thing.
Better-informed: No they don't because the definition of observation in QM is non-classical thus-and-such and Chaos is a classical physical system.
Me: But the issue of quantum measurement itself seems to me perfectly intuitive by my definition of a quantum.
Better-informed: You have invented your own definition of quantum measurement.
And then the discussion stalls because I have not managed to convey my vision of the reconcilabilty of quantum measurement with classical measurement. Well, maybe I'm being foolish. Still ...
Can paradoxes of quantum physics be resolved with classical physics to some extent by the correct grasp of quantum measurement itself?
It seems to me that they can be. One more traffic analogy follows which attempts to explain instantaneous quantum communication. I used the same example above in 2000-11-13 but I didn't present it very well, so let me try again.

Traffic Flows and Instantaneous Quantum Communication

Say we have a high-speed limited-access modern automobile highway with on-ramps and off-ramps.

Let there exist on this highway a specific downtown on-ramp 'A' and a specific suburban off-ramp 'B'.

During evening rush hour, there are a certain number of cars forming a somewhat steady stream entering A which will exit at B.

As the A->B'er on-ramp traffic at A increases, the off-ramp traffic at B increases subsequently. Assuming traffic is flowing smoothly, attempt to graph the flow onto A and the flow off of B and correlate their amplitudes second by second.

Since there is traffic entering A that does not go to B, and traffic exiting B that does not originate at A, the correlation may be easy or difficult depending on the volume of this extraneous traffic on either ramp relative to the volume of A->B traffic. But if you can see the correlation, the waves will be offset. As traffic diminishes on A, the diminishment on B will be subsequent by some offset, and so for augmentation.

Suppose there are many people wanting to do the A->B trip and they are periodically metered by surface-street traffic lights as they approach the ramp. So every 90 seconds you have a burst of A activity followed sometime later by a burst of B activity. The graph of A superimposed on B becomes recognizably periodic to the eye with an offset between B and A.

Here's the crux. Here's where it comes down to quantum measurement explaining instantaneous quantum communication, in these two points:

  1. If the time to travel between B and A is an integer multiple of 90 seconds, B and A will appear synchronized. If A is measured low, B is low. If A is high, B is high, and so for intermediate amplitudes.
  2. If an observer has a stroboscopic view of the ongoing graph, A & B can appear not only synchronized, but stable at one absolute amplitude once the measurement is made and the offset and regular period of the stroboscopic view established.
This applies not only to speed and location of measured quanta but to all characteristics, since the definition of the quantum as a composite of myriad constituent phenomena implies that all characteristics are agglutinations of periodic behavior of the sub-phenomena.

I intuit that this is the nature of instantaneous quantum communication.

After Some Discussion on the WELL

The special, figurative usage of the term "stroboscopic" in the discussion above is meant to imply that the ideas presented above may be verifiable experimentally at the particle level. If you assume that there is some hidden periodic time base þ in our observations of subatomic phenomena, all you have to do find a way to make paired measurements skewed by some non-integer multiple or divisor of þ and you will observe something palpably other than you were given to expect by the canonical interpretation of quantum paradox.

Mitsu points out an interesting discussion thread on an optical QM delayed-choice experiment .

2000-11-30

Interesting discussion on the WELL today about particle/wave duality in the context of the optical QM delayed-choice experiment mentioned earlier. In the context of the discussion, I posted the following:
I have no problem with the idea that a quantum called a "photon" is a composite of myriad constituent phenomena, and that it can exhibit wave and particle nature. I'd have called it a "bolus" if I'd invented the terminology, at least as far as I currently misunderstand it :-) "Bolus" because that's what your dinner is called when it goes down your esophagus, during which trip it exhibits both wave and particle nature.
The quantum paradox relative to the photon argument seems to me to resolve itself into a circular argument dictated by observation technique. The circular argument goes something like this:
  1. We know the behavior of the photon because we measured statistically.
  2. When we try to study one photon we become enmeshed in paradox.
  3. But we only or mostly measure statistically. We never or rarely measure one photon.
Really the crux of it all is summed up in "An End to Uncertainty" in New Scientist, where the authors write:
In a two-slit device, however, it effectively splits its own existence, and goes through both slits.
But of course this can only be proven statistically. And if you observer, you observe it acting as an unsplit particle and spoil the effect.

Of course. Because particles don't split their existence and go through both slits. This is the "American family with 2-1/4 children" paradox.

Boluses and the observer spoiling interfernce

The article says that it had been assumed that some random kick was imparted which spoiled the reunion of the "split" particle. Then they refuted that, and went with the metaphyisical "entaglement" which is nonetheless very satisfying.

Here's the entanglement. Visualize this.

Here we have a photon emitter. It will burble up an average of x.y photons per n nanoseconds.

When does it burble them up precisely? Can't be said. Just statistical.

Okay. It starts burbling. A cluster of boluses come burbling outwards jostling each other. Each of these boluses is wealthy in consituent sub-phenomena on the order of a galactic subcluster.

A megabolus of boluses locked in a formation launch together from the emitter. A megabolus of (z>(x.y))/m can satify x.y/n by some m>n, statistically.

Some go one way, some another. They meet at the target, their tremendous velocity helping preserve their orientation and spin. They meet focussed off kilter and bands appear. It's well known that sound behaves precisely in this fashion. Why should light be different? It seems to explain the behavior.

I'm ready to explain why observation ruins interference, if you're with me this far. It's even more fanciful.

The bolus represents a sort of "petrified forest". It subconstituents are subject to accretion and excretion. Whatever fleas on littler fleas constitute the dust of interquantum space, the bolus accretes and leaves behind some discarded subconstituent mass. It is indeed a bolus.

That which the observer observes is a bolus. The creation of a channel for the bolus to interact with the bolus of observation transforms the orientation in many dimensions of the observed bolus. Imagine a lightspeed collision of two trembling globules of unimaginably low density.

The two boluses interpenetrate and transform one another profoundly without transforming significantly the momentum of either bolus. Momentum is preserved. It's like the comedy sketch where two guys run towards one another and collide and emerge from the collision each going his original direction at the same momentum but they're wearing each other's clothes.

The bolus is a possible explanation of the dual wave/particle nature of light and of why observation ruins interference.

This also happens, I suspect, at the astrophysical scale. A pulsar is emitting quanta of energy, galaxy-sized quanta, bursts of boluses in relation to which our galaxy is an interacting but vastly denser entity.

2000-12-03

A Bad Day for the Bolus

Mitsu managed to convey to my thick skull the paradox pointed out by interference experiments. I was ready to surrender on my "bolus" theory but I think I have salvaged it, or at least deepened the error into which I am tumbling :-)

Given:

  1. That we have an apparatus with a beam splitter and recombiner as shown in the optical QM delayed-choice experiment
  2. (Except that the illustration should show, but doesn't, that phase is shifted for interefence by making one path between split and recombine longer than the other)
  3. That apparatus can emit as few as one photon per shot.
  4. That in either path, the photon can be observed between splitter and recombiner if desired.
Mitsu informs me that empirically the following result can be obtained:
Number of apparati Emitted Observed between split and recombine? View of all exposed plates superimposed
1 Continuous stream of photons No Interference
1 Continuous stream of photons Yes No interference
1 One photon per second No Interference
1 One photon per second Yes No interference
Many Continuous stream of photons No Interference
Many Continuous stream of photons Yes No interference
Many One photon per emitter once No Interference
Many One photon per emitter once Yes No interference

That is, one photon going through an apparatus designed to demonstrate interference shows that interference whether or not in synchronously encountered another photon whose wave phase it may interfere with.

Save The Bolus!

So what happens when a bolus encounters this setup?

Let's restate and perhaps expand on our hypothetical bolus-style photon:

Now imagine viewing a photon from a perspective where a photon seems to the observer somewhat smaller than a galaxy, but on that scale. What are its surroundings? Let's call its surrounding "the ambient subatomic universe".

There is a density of dust, of free atoms in intergalactic space on the astrophysical scale of about 1 atom per 1000 cubic centimeters (thanks again, Mitsu). To an observer to whom a galaxy of our astrophysical universe was roughly the size of a photon, that intergalactic dust would be immeasurably evanescent. Mathematically, its mass and charge would have been subsumed in constants describing the overall system.

So then for the bolus theory to survive, the following must be true:

When a photon hits a beam splitter, it imparts a light-speed shock wave to the ambient subatomic universe in the path opposite to that taken by the photon. It recombines and interferes with that wave at recombination.
Since the mass to which the shock is imparted is zero to our measurements, the momentum lost by the photon in imparting the shock wave is zero to our measurements.

Voila ... have we saved the bolus? Well, tomorrow people from the Well will read this and someone will no doubt stump me again!

2000-12-04

Mitsu and I are down to it on the Well. I have to correlate my intuitions to Bell's Theorem or my apparently locality-based bolueses and shock waves go into the ashbin of dilettante speculation.

The web page on Bell's Theorem purports to explain Bell's proof that quantum mechanics can't be explained by any locality-based theory. I am reading it now and trying to grok if I am refuted or no.

After reading the paper on Bell's Theorem

Okay, I think I get the point. Using the example of the electron:
  1. electron spin has a statistical probablity of being measured in one of two orientations on any arbitrary axis, but the measurement affects the electron and orients it definitively either 1 or -1 with respect to that axis.
  2. Once its orientation of 1 on one axis is determined, it probability of being measured 1 on another axis offset from the measured orientation by angle q is cos2q.
  3. The empirical observation is that the probabilistic result of measuring each of two entangled electrons in one of three orientations offset by 120° separately with one measurement preceding the other conforms to predictions based on the assumption that the second becomes oriented inversely from the first with respect the axis upon which the first was measured as a result of that measurement itself, rather than conforming to probability predictions of an assumption of a "hidden variable" shared by the entangled electrons.

What is Spin Measurement?

I suppose I will have to study spin measurement more, because the paradox presented in the electron spin experiment seems no paradox to me.

What is spin and spin measurement?

  1. Picture an electron as a penny spinning and precessing in all axes.
  2. Its north pole fractally describes a globe.
  3. Effectively, spin measurement must be measuring direction of spin during the time an electron's north pole is in the measured orientation.
Ergo, information travels faster than light because no new information is transmitted. Electron B which is quantum entangled with electron A is in a statistically reliable orientation in some regards with relation to a measurement of electron A. The observed behavior is that for any orientation measured the result for B will be the inverse of A. The formula cos2 q for the probability of measuring the same orientation at some angle q (sorry, no theta in this browser) subsequent to a prior measurement appears then to reflect in some fashion the period of the precession of the eletron pole.

In this line of thought, measurement appears to change and "latch" electron A (using the term "latch" analogous to the digital microelectronic sequencing use of the term). This appearance is the measurement instrument identifying the direction of spin for that orientation of the electron. There is no change-via-observation in A to be communicated to B.

Bell Sidestepped?

Have I salvaged the hidden variable? I cannot have, because others assure me that Bell proves no hidden variable can account for the observed behavior. But if a challenge to the interpretation of the observed behavior can be sustained, there is no paradox to pass through Bell. Then Bell remains valid and consistent, but without application to quantum physics.

Isn't it possible that Bell is inapplicable, at least to the electron spin paradox we have been dealing with, if it is plausible that spin measurement does not measure the electron pole orientation, but rather measures the direction of the spin for the polar orientation of the direction of measurement. The electron whose pole precesses through the globe has a direction to report for any orientation.

2000-12-06

I've been wrestling with Bell's inequality and I have a question.

Is the Study of Probability Itself Flawed?

Independently and preceding my interest in quantum measurement, I came to some empirical conclusions regarding probability. I am convinced that certain assumptions of probability as expressed in textbooks are not valid from a game theory point of view. A real-world illustration of the sort of thing that I am talking about is the comment made to me privately by a senior and world-renowned professor of mathematics that he frequently played the California lottery when the prizes got large, because, "If you have no other chance of obtaining a million dollars, you should buy lottery tickets when the odds are the most in your favor. Then it's a reasonably good bet."

It can be argued that this insight of the professor does not change his formal assessment of the percentage likelihood that he will win. But Benoit Mandelbrot has pointed out the fractal geometry of nature, and that studies of fractal geometry were dismissed by mathematicians in earlier decades as the study of freaks and sports. Mandelbrot argues in reply that here are no true circles, no straight lines, no perfect squares in nature. Analogously, the study of classical odds in a bet like winning the big one in the California lottery appears a sterile and academic excercise compared to a iteratively refined estimate of amount by which the longshot payoff had shifted in your favor, the feasability of forming a syndicate, etc, concomitant with the increase in the size of the prize due to carryovers.

Classical probability is suspect on similar epistemological grounds to those offered by Mandelbrot as objections to the sterility of geometry as he encountered it. If the classical assessment of probabilistic expectations resulting from a hidden variable theory can be cast into doubt, it seems to me that the Bell inequality has no meaning.

Storming the Citadel

If the only proof that "spooky action at a distance" is inconsistent with a sufficiently sophisticated hidden variable theory is the discrepancy of probabilistic assessment, then the best chance to Save the Bolus is to storm the citadel of classical probability.
The word random can be shown epistemologically to reduce to "I don't know".

All phenomena exhibit patterns. The more real-world the phenomenon, the more intricate the patterns until we reach an assessment of "I can't follow the pattern" and we call that randomicity. Or more practically, "I didn't determine the pattern" which works among us humans in games of chance, as long as the determinism of the pattern transcends the wit and the will of the participants.

Einstein didn't like things left to chance. He archly asserted that "God does not play dice with the universe." Perhaps if he had recognized that God is playing with loaded dice, Einstein would have been more sanguine.

It may be a ferocious battle to storm the citadel of classical probability, but if we succeed, we'll have done less violence with Occam's razor than does the metaphysical assumption that a particle extratemporally knows that its entangled particle has been measured, an assumption forced upon us by Bell's Inequality.

Synopsis and Summation

  1. Over several days, I have proposed an amusting theory which seems to account for one allegedly mysterious quantum phenomenon, single-photon interference.
  2. Physics buffs toyed with my theory then dismissed it for violating Bell's Theorem.
  3. Bell's Theorem was illustrated to me by Gary Felder's paper on Bell's Theorem .
  4. As a result, in my limited understanding it appears to me that if one could tinker only slightly with some assumptions about probability, the objections to the bolus theory of light would vanish. All that would matter then would be consistency for experimental results.
  5. The two issues are related: one has to offer a good local theory even if we can toy slightly with probability.
  6. I assert that there is a plausible if difficult experiment suggested by my explanation of single-photon interference. Can the reader deduce it?
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2000-12-07

I seem to be losing the debate on Bell's Theorem. Ah, well, we dilletantes must remember that Rome wasn't burned in a day :-).

I think I'll wander off on another tack. Since Bell's Theorem proves that my idea is impossible, I'll use the heuristic of setting aside the theory and going for some experimental evidence. At worst, I just confirm Bell.

If what the scientists call locality supported by a hidden variable were possible, the most plausible theory I can come up with for single-photon interference would be my bolus + shock-wave-in-the-ambient-quantum-universe idea. Now, as far as I can grasp, if there were such a thing as a shock wave in the ambient quantum universe, the closest thing to this I can find so far which quantum physics has seriously posited is the elusive neutrino. I have read its description as massless and moving at the speed of light. Sounds like a shock wave, huh?

So, in other words, the bolus/shock wave theory could be easily disproved without Bell. You'd just have to see if when a photon went down one side of a beam-splitter a neutrino went down the other side. No neutrino, no local theory (presuming I'm correct in making my shock wave a neutrino). I wonder if this sort of experiment is possible.

2002-07-25

Misunderstanding what a neutrino is gave me pause for about 18 months. The attempt to flesh out a bolus is amusing but distracting from the gist of the argument. The bolus amounts to trying to point to one vanishingly small ripple of a wave travelling through the ambient subatomic universe and invest it with cosmological significance. It's an angel on the head of a pin.

However, the principal assertions of this document found as the entry for 2000-11-12 seem to me still to stand.

Let's tackle it this way: Say that Bell's theorem with respect to its application to the discussion at hand is something like a tautology.

What is quantum entanglement?

Quantum entaglement is the result of a continuum which we are perceiving, or measuring, in discrete observations. Two events are entangled because they are the same event. This resolves the paradox of time travel : the perceived cannot be other that that perceived by the perceiver in the branch in which the perceiving occurs.

This seems to me in no way to contradict Bell's theorem, which is merely predictive and not fully ontological .

Same event or same substance?

To say that two entangled events are the same event is not to assert they are the same substance, to speak figuratively of substance.

An event is a stream of constituent events in the subatomic universe. This is why it is, as well known, an error to separate the wave nature of a quantum event from its physical nature, because we are dealing with waves of events, mass movements, figuratively, that have a regularity sufficient to allow their measurement. We can't see the event; we see the echo of myriad events within a continuum in the ambient subatomic universe in which the event occurs.

Durable entanglement

Within the past week or so, it was announced that experiments in entanglement had allow events to continue entangled as their perceived particles travelled through metal. While excellent engineering, this is hardly surprising, since there must be some way to impart a wave into the ambient subatomic universe sufficient to knock the golf ball through the woods and back out onto fairway, so to speak.

No paradoxes

I see no paradox in the paradoxes of quantum physics. I continue to assert that:

2003-01-01

Predictive capacity of my theory

From a conversation on the WELL :

Topic 550 [science]: Quantum Mechanics
#512 of 512: Jack J. Woehr (jax) Wed Jan 1 '03 (22:23) 32 lines

Anyway, <mitsu>, you and I agree on one thing: That the nexus is
something about our perception of the matter.

I assert that the perceptual nexus is our inability to see the logical
implications of viewing as unitary entities phenomona composed of
innumerable component entities.

You have (at times) challenged this theory by demanding of it some
predictive capacity.

I offer now a prediction implied by my theory. The prediction lies
outside of our ability to apply an experiment, but perhaps we'll
be lucky enough that the predicted outcome will manifest itself
in our lifetimes. Here it is:

If, indeed, quantum effects such as entanglement arise as I
suggest, then at some time, we should see within our astronomical
range of vision a phenomenon such as this:

Something big, like a pulsar or quasar, suddenly changes
state. Maybe it explodes and takes out an arm of a galaxy.
Maybe it suddenly changes spin. AT THE SAME TIME, another
similar body, say a million parsecs away, SIMULTANEOUSLY
exhibits a complementary change in state.

Of course, the chance of us seeing something like that ... they'd
have to be roughly the same distance from our observation point
so that within recorded history both events could be witnessed
and correlated ... seems pretty slim.

BUT ... if it were to happen ... you see.
 

2003-07-16 (Summary restatement of the theory)

2004-01-29 The Zen of QM methinks

Quantum measurement is measurement at the point where quantity becomes quality.

2004-04-09 Mitsu Describes Quantum Measurement's Paradox

Mitsu Hadeishi on the WELL once again drummed the paradoxical nature of quantum measurement into my head.

First he had me read the following websites:
Then an interesting exchange took place. I had described the structure of an electron as perhaps being a "roiling cloud". Mitsu grabbed my terminology as a cudgel :-)
The following transcript is edited somewhat in the interests of brevity and clarity.

science.552.1145: Pseud Impaired (mitsu)  Thu 8 Apr 04 02:26

 >If the composite we call an electron is a roiling cloud of myriad
 >infinitesimal sub-entities, why is the angular correlation with
 >spin measurement surprising?
 
 The correlations are surprising because they depend on how
 you're measuring at A and B, not just on the measurements you
 get at A and B.  As I keep saying, correlations by themselves are
 hardly surprising.  It doesn't take roiling clouds or whatever
 to produce correlations.  The strange thing is how the
 correlations vary with the different setups of the measurement
 apparatuses at A and B.
 
 The key hinges on whether the two particles (roiling clouds,
 whatever) are *independent* or not.  In a classical world, the
 measurement at A couldn't possibly depend in any way on what the
 observer at B decides to do.  The observation at A should depend
 only on the "roiling cloud" and its interaction with the
 apparatus at A.  *But that's not what we observe in nature*.
 What Bell's Theorem says is that no matter how complex you
 try to imagine the particle at A is, what you observe at A
 will not only depend on the particle at A, but on what the
 observer decides to observe at B.  The correlations will depend
 on something that is happening far away, and it could
 be a spacelike separated interval.
 
 But the "quotidian picture" says that what the observer does
 at B couldn't have any bearing on what is observed at A.  But
 it does.

science.552.1147: Pseud Impaired (mitsu)  Thu 8 Apr 04 09:45

 >The observations coincide
 
 As I keep saying, they don't merely coincide --- they exist in a specific
 statistical relationship that depends on the relative angle between the two
 measuring instruments at A and B.  What's spooky is that no local theory can
 explain this relationship.
 
 Let me try to lay it out a bit more specifically.  Suppose you were to
 choose three possible orientations of your instruments at A and B, zero
 degrees, 120 degrees, and 240 degrees.  Let's call these orientations 1, 2,
 and 3.  We know that if we measure in orientation 1 at A and orientation
 1 at B they will perfectly anti-correlate --- spin "up" will always
 correspond to spin "down" at B, and vice-versa.  The same, of course, goes
 for orientations 2 and 3.
 
 So far so good --- nothing spooky yet.
 
 Now suppose at A we measure along orientation 1, but at B we measure along
 orientation 2.  Because the cosine of the relative angle is -.5, we will
 find, over time, that the measurements at A and B have a statistical
 correlation of 50%, which is to say, 75% of the time they will
 come up with the same measurement, and 25% of the time they will come
 up with the opposite measurement.
 
 The same could be said for choosing orientation 1 at A and orientation 3
 at B, and so forth for every other pair of orientations.
 
 If the world were as you suggest, the measurement of the particle at any
 given orientation at A would be determined in advance (by whirling vortices
 or whatever).  Measured along orientation 1, the particle at A would be
 spin up, say, and along 2 it's spin down, along 3 it's spin up, or whatever.
 
 Let's say we write down what the measuring device at A is going to say for
 orientations 1, 2, and 3 for each particle at A, and do the same for
 each particle at B.
 
 If we have this big table of observations, to make it consistent with
 quantum mechanics, we have to set it up the table so that the observations
 are always opposite in the corresponding columns of the tables at A and B.
 
 In other words, if column 2, particle 567A says "up", column 2, particle
 567B will say "down".
 
 Now, the test: can you make a table so that the corresponding columns (1,
 2 and 3) are all 100% anticorrelated, AND all pairwise columns are 50%
 correlated?  I.e., if column 2, particle 567A says "up", there is a 75%
 chance that column 1 particle 567B says "up" AND a 75% chance that column 3
 particle 567B also says "up"?
 
 The answer, in short, is no.  Bell's Theorem says no matter how hard you
 try to make a table that satisfies both conditions at once, you can't do it.

science.552.1159: Pseud Impaired (mitsu)  Thu 8 Apr 04 11:32

 To be more specific, for a specific roiling cloud, there could be eight
 possibilities:
 
 If the specific roiling cloud hits the measuring apparatus at A in
 a given orientation, we could see:
 
 Orientation 1 | Orientation 2 | Orientation 3
   spin up-1   |   spin up-2   |   spin up-3
   spin up-1   |   spin up-2   |   spin dn-3
   spin up-1   |   spin dn-2   |   spin up-3
   spin up-1   |   spin dn-2   |   spin dn-3
   spin dn-1   |   spin up-2   |   spin up-3
   spin dn-1   |   spin up-2   |   spin dn-3
   spin dn-1   |   spin dn-2   |   spin up-3
   spin dn-1   |   spin dn-2   |   spin dn-3
 

science.552.1160: "Quantum mechanics is where quantity becomes quality," says (jax)  Thu 8 Apr 04 11:34

 Yes.

science.552.1161: Pseud Impaired (mitsu)  Thu 8 Apr 04 11:37

 Okay.  What I am saying is the following.  For any given pair of entangled
 particles, you will have a roiling cloud going one way, and a roiling cloud
 going the other way.  For any given roiling cloud, we can choose one of the
 eight possibilities above as to what happens when it hits the measuring
 apparatus at A.  Conservation of angular momentum says that if we choose,
 say:
 
 spin up-1 | spin dn-2 | spin dn-3
 
 we then have to choose, for the roiling cloud heading towards B:
 
 spin dn-1 | spin up-2 | spin up-3
 
 because whenever we see spin up-1 at A we always get spin dn-1 at B, and
 so forth.

science.552.1162: "Quantum mechanics is where quantity becomes quality," says (jax)  Thu 8 Apr 04 11:42

 Um, I think so, only, you don't get to measure all three at once,
 right? You get to choose, like, spin-1 at A and spin-1 at B, or
 spin-1 at A and spin-2 at B, right?
 

science.552.1163: Pseud Impaired (mitsu)  Thu 8 Apr 04 11:53

 You're beginning to see the crux of the matter, grasshopper.
 
 But for the sake of argument let's just stick with what you've said yes to
 already and follow the consequences of that through, which is that we
 can answer these three questions for a given roiling cloud in a manner which
 is independent of what the other observer (at B) decides to measure and
 is entirely determined by the state of the roiling cloud and the orientation
 of the apparatus.
 
 There are really only two fundamentally distinct possibilities.  One
 possibility is that you have a line which is the same for all three
 cases, i.e., up-1, up-2, up-3, or dn-1, dn-2, dn-3.  If one of these
 lines is the case for a given particle, we have to choose the opposite
 corresponding line:
 
 up-1, up-2, up-3 at A : dn-1, dn-2, dn-3 at B
 
 In this case we have a situation where 0% of the time you get corrresponding
 observations given two random but different orientations of your instruments
 at A and B.
 
 The other case is where one of the measurements is different, i.e.,
 
 up-1, dn-2, up-3 at A : dn-1, up-2, dn-3 at B
 
 All the other cases are just permutations or inversions of the above
 case.

science.552.1164: "Quantum mechanics is where quantity becomes quality," says (jax)  Thu 8 Apr 04 11:56

 You're saying B-2 is the same angle as A-2, etc., right?

science.552.1165: Pseud Impaired (mitsu)  Thu 8 Apr 04 11:57

 Now let's see what the statistics look like for that case.
 
 If it's
 
 up-1, dn-2, up-3 at A : dn-1, up-2, dn-3 at B
 
 Suppose we choose to measure at A in orientation 1, and at B in orientation
 2.  We will then have a "match" --- we get up-1 at A and up-2 at B (we're
 saying "up-1" and "up-2" match just for the sake of argument).
 
 Similarly for all the other possible combinations of apparatus orientations,
 we have 4 matches, and 2 non-matches.
 
 I.e., if you randomly pick an orientation at A and B that are different, and
 you have roiling clouds with the above lines, you will have a "match" 4
 times and a "non-match" 2 times.
 
 Since there are six such combinations, that means that 4 out of 6 times you
 will have a "match" --- i.e., 2/3rds of the time.

science.552.1166: Pseud Impaired (mitsu)  Thu 8 Apr 04 11:58

 Slippage.  Yes, B-2 is the same angle as A-2, but all we have to know for
 the sake of argument is that whatever the angles, B-2 and A-2 will always
 show the opposite measurements for a given pair of entangled particles in
 our experiment.

science.552.1167: "Quantum mechanics is where quantity becomes quality," says (jax)  Thu 8 Apr 04 12:07

 Um .. yes, but how is the fact that you can create a truth table
 enumerating all the possibilities, a truth table that exhibits on
 paper the 2/3 ratio of match to non-match, predictive of what you will
 actually find in measurement? It sounds like building a paper
 model and expecting reality to match it.

science.552.1168: Pseud Impaired (mitsu)  Thu 8 Apr 04 12:24

 The table depends only on one assumption, which you agreed to above:
 
 The measurement of a given roiling cloud depends only on the roiling cloud
 and the orientation of the measuring apparatus.
 
 The 2/3rds maximum statistics follows logically from that one assumption,
 as I demonstrated.  So, the question is, what is it about that assumption
 that you want to retract?  (We're getting very close to the main point.)

science.552.1169: "Quantum mechanics is where quantity becomes quality," says (jax)  Thu 8 Apr 04 12:25

 Okay, stipulated. Go on.

science.552.1170: Pseud Impaired (mitsu)  Thu 8 Apr 04 14:05

 What this means is that if the roiling clouds are of the first type
 (all the same, up-1, up-2, and up3, or dn-1, dn-2, and dn-3) then we will
 get 0% matches no matter what orientation of the measuring apparatus you
 choose (1, 2 and 3 are all opposite).
 
 In the case where one of the three is different from the others (say, up-1,
 dn-2, and up-3), you will get matches 2/3rds of the time for random
 orientations of the apparatus that are different (A-1 and B-2, or A-3 and
 B-1, or whatever).
 
 This reasoning means that in your roiling cloud universe, the MOST we can
 expect the two instruments to "match" (as defined above) when they are
 oriented at different angles is 2/3rds of the time.
 
 But (and now we can finally cue the Twilight Zone music) what we actually
 observe is that for two randomly oriented instruments whose angles differ by
 120 degrees, we actually see the same measurement 3/4ths of the time, or 75
 percent.
 
 In other words, starting from the assumption:
 
 The measurement of a roiling cloud depends only on the intricate internal
 structure of the roiling cloud and the orientation of the measuring
 instrument.
 
 we must conclude:
 
 The most one can expect randomly-oriented instruments at A and B that have
 different orientations (selecting between one of the three possibilites)
 to "match" is 2/3rds of the time.
 
 But in nature, we observe them matching 3/4ths of the time.
 
 Thus: there must be something wrong with the initial assumption.
 
 The various interpretations of QM are different ways of dealing with
 that initial assumption.

science.552.1171: Pseud Impaired (mitsu)  Thu 8 Apr 04 14:07

 That is, the different interpretations of QM attack different aspects of
 what might be wrong with the initial assumption.

science.552.1172: "Quantum mechanics is where quantity becomes quality," says (jax)  Thu 8 Apr 04 16:50

 Suppose the "we must conclude" is wrong. Suppose we don't have
 to conclude that from all the other truths you have expressed.

science.552.1173: Pseud Impaired (mitsu)  Thu 8 Apr 04 17:06

 I broke the proof down into little steps, each of which is so small that you
 agreed with them as I stated them, one by one.  Although it's true that the
 chain of reasoning is long enough that you might not be able to intuitively
 see the end from the beginning, if you don't accept the conclusion but do
 accept each step in the proof, then you have to tell me what specific step
 you don't, in retrospect, buy.
 
 The steps, to recap:
 
 Measurements are determined by the roiling cloud and the state of the
 measurement apparatus.
 
 This means, for a given cloud, you can write down what the measurement would
 be if the apparatus was in position 1, position 2, or position 3, for that
 cloud.
 
 We know that for two entangled clouds, measurement at A along 1 is always
 the opposite of measurement at B along 1, and so forth.  This is empirically
 verified and predicted by conservation of angular momentum.
 
 This means for the particle approaching A, the three measurements A1, A2,
 and A3 must be the opposite of the measurements B1, B2, and B3.
 
 For a given pair of entangled clouds, we can write down the measurements we
 expect to see at A and B given an apparatus angled along 1, 2, or 3.
 
 There are only two distinct possibilties for those measurements.  Either
 they're all the same (up, up, up) and (down, down, down) or one is
 different from the other two (up, down, up) and (down, up, down).
 
 In the former case the non-coinciding matches are 0%.
 
 In the latter case the non-coinciding matches are 2/3rds.
 
 But in nature non-coinciding matches is actually 3/4ths.
 
 Now, where in this chain of reasoning is the problem?
 
 I will say this: you were on the right track when you said that in reality,
 we can only measure the particles in one specific set of orientations, not
 all three.

to be continued ...


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