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2016-12-31
Happy Unspooky New Year
Did you know that many non-Christians celebrate New Year? Of course for them, and for many Christians also, it is only a happy calender event, and usually only "westernized" people really care about it. Still, it is another international aspect of a secularization process that started a very long time ago. We are very far from Anno Domini, or the Year of our Lord. But when have people ever rejected an opportunity to party? After all, they still celebrate their own religious events, including their own New Year, very often in a very different way. More traditional.
Anyway, 

Happy New Year.

Spooky!
The issue of two particles communicating with each other faster than light has divided great minds like Einstein and Bohr. It is also the most spectacular proof that Nature cannot be understood with common sense. Two particles that seem to communicate with each other beyond space and time! That is the stuff of legends and myths, and still, it looks like an undeniable scientific truth confirmed again and again by countless experiments.
I will make use of Tim Maudlin's "Quantum Non-Locality and Relativity: Metaphysical Intimations of Modern Physics", 2002 in the description of the problem.
This is how I understand it:
Two photons are created simultaneously by whatever process, going in opposite directions. They are indistinguishable from other random photons, even though they seem strangely connected. Whenever one passes a polarization filer, so does the other, and both are absorbed in the same way.
This is where we have to be extra vigilant because, just as by Feynman, sometimes we are dealing with individual photons, and other times with a whole group of them. The latter is the case when we try to find regularities in the way photons pass or are absorbed by a second filter. There is an equation that explains, or at least predicts the quantity or the probability, it does not matter in this case, of light transmitted by the second filter when both filters are misaligned by an angle α.

This is where the spookiness starts

According to legend, when a filter with a certain value is applied to one photon (A), the other photon (B) reacts as if the filter had been applied to it also and reacts accordingly. Therefore if still another filter is applied to photon B the result is the same as if two filters had been applied successively.

This mode of presentation, which Maudlin also uses, just as Anton Zeilinger does in this video, is I think one of the main reasons why the problem has never been solved. As such, the explanation given is wrong because the analysis is applicable only to an average and not to individual photons.
There is a simple reason for this: a photon may or may not pass a first filter. It has a 50% chance to do that. The same way, not all photons will pass the second filter, but in large numbers they follow the equation cos²α. Also, statistical correlations only make sense when many elements are involved, otherwise we would be dealing with a deterministic system.
What Zeilinger and many others do is jump, illegitimately, from statistical regularities to deterministic relations, like one die giving four each time the first die does so.

Allow me to reformulate the problem:
When two photons are considered, and a filter is applied to one group of photons, and another filter applied to the second group of photons, and then the general results are analyzed statistically, then it looks like both filters have been applied successively to only one of the group of photons. The same equation, cos²α, is applicable to the end result.

Back to the Hitachi experiment. Would it have made any difference if the electrons which passed slit #2 would have been sent to Teneriffe or Timbuktu first, and only later compared to the pattern created by the electrons of slit #1? The "interference pattern" would certainly not have been immediately obvious, but a subsequent analysis would have brought it to the fore sooner or later.
We can therefore, most probably, eliminate the factor "communication at a distance" as superfluous. We do not need it to explain the phenomena at hand.

This is in fact what is happening with the entanglement experiment: a source of light is split into two beams and the result when both slits are open is different from when one or the other is closed.
Even more than in the original experiment, the results given by a simple group of photons only make sense when put side by side with those of the other group. That is the only way statistical correlations can be discovered. It would be therefore meaningless to say that a photon reacts as if the same filter has been applied to it as to the other photon. The same way, it would not make sense either for a whole group unless it is compared with another group under the same controllable conditions.

In other words, in the end, the entanglement experiment is just a version of the two-slit experiment, and must be judged by the same criteria. Comparing the results given by each group would be the same as comparing the pattern given by each slit apart, and then together.

Once we have arrived at this conclusion, the spookiness seems to slowly dissolve. It does not matter where the partial results have been sent to, only that they are back and set side by side for us to analyze. And then it becomes less strange that the behavior of the second group looks like it has been at least partially defined by the first one. The entanglement is certainly happening, but it is an entanglement of data that are looked at with statistical glasses.
The interference patterns showed by the two-slit experiment take here the form of a photon whose behavior seems determined by the other photon miles away.
I therefore dare claim that the so-called entanglement is an optical and statistical phenomenon, just like it is the case with the classical two-slit experiment.


2017-01-02
Happy Unspooky New Year
The Mach–Zehnder Interferometer or Scoobi doo Science

"Quantum Physics A First Encounter INTERFERENCE, ENTANGLEMENT, AND REALITY", 2006 by Valerio Scarani has a foreword by none other than Alain Aspect whose experiments at the start of the 80's are considered groundbreaking, even if they were not the first to deal with non-locality.
Scarani's book is very well written and agreeably clear in comparison to most books on the subject. But even even he cannot escape the strangeness of the concepts of entanglement and non-locality. We must therefore forgive him if he, very soon, maybe too fast, adopts the mystical style which is representative of anyone writing about quantum theory.
Still, his presentation is certainly a relief for people who, like me, are easily put off by complex formulas, and I hope I will be able to convey in words what he did so well with very simple drawings and short explanations.
We are dealing with a specific version of the Michelson Interferometer, so let me explain why first this post has not been placed in the corresponding thread. We are here less interested in interference phenomena than in that of entanglement and locality. The question whether all those concepts really can be distinguished from each other is certainly legitimate, but I would prefer to postpone the discussion to a later time when I will be able to show more clearly the lines that bind them.

The Mach–Zehnder Interferometer is explained in four easy drawings which I cannot reproduce and which I will describe as faithfully as I can.

Fig.1. represents the basic element, or rather compound, out of which any interferometer is built. A photon meeting a beam splitter which is a special kind of mirror that lets more or less 50% of the light through and reflects the other 50%. Since photons are an all or nothing kind of guys, that means that half of them will be allowed to pass while the other half will see the door closed before their nose. Those that pass will be welcomed by detector or box T, for Terrific or Transmitted, while the unlucky others will be gathered in the R detector/box for Rejected, or more nicely, Reflected.

Fig.2 is a slight complication of the first setup. Instead of two boxes, T and R, we get an extra beam splitter between each box and the photon that has been respectively Transmitted or Reflected. Which means that we have now a grand total of four detectors or boxes, two on each side representing the four possibilities:
Transmitted-Transmitted (TT)
Transmitted-Reflected (TR)
Reflected-Reflected (RR)
Reflected-Transmitted(RT)
While in the elementary setup each detector welcomed 50% of the participants, these four detectors have to be satisfied with only 25% each. The upshot being that such a result is not surprising at all, but is what we would expect in a rational world. After all, the interferometer still has only two arms, and each arm is getting no more than half of the total of photons.

This changes radically with the following setup, so please fasten your seat belt as we are about to crash.

Fig.1.3 As always we have photons meeting a beam splitter and being divided among two arms, T and R. What is new is that on each arm "a perfect mirror" has been placed that reflects the photons to one single beam splitter. For those who can not consult the original text, imagine that the beam splitter receives light from above, and from the left. A photon coming from above will be either transmitted straight downward to TT, or reflected to TR. The photon coming from the left can also either be reflected downward, turning TT into TT/RR, or transmitted to RT, where it joins the TR photons.
Again, thanks to the mirrors, we are able to use only two detectors instead of the four we would have normally needed.

And here is the incomprehensible result: instead of the expected 50-50 distribution, 100% of the photons end up in the RT/TR box, and none in RR/TT box!
Before you break your head on this mystery, let us look at a following setup

Fig.1.4 is exactly the same as 1.3 except that one arm has been made longer with the help of more mirrors. The results may seem even stranger than by 1.3, I personally find them rather comforting. They somehow restore my confidence in the rationality of physical processes.
While with 1.3, where both arms were of equal length, one box/detector remained empty, by changing the length of one arm we get more and more photons in the TT/RR box, until in the end they are all there, and the TR/RT box stays empty!
Why should I rejoice? Well, remember what Feynman said about reflection and the strange cycle it showed from 0 to 16%? This way I have the impression that Nature is very consequent, which gives me hope that her behavior is predictable and can be expressed in something better than mystical probabilities. Please do not misunderstand me. There is nothing mystical about probabilities. We need them anytime our knowledge is insufficient, which is most of the time. But the idea that Nature itself is bound by these probabilities is, in my eyes, a metaphysical bridge too far. Let other scientists believe what they want.

Here again, I have no idea why the length of one of the arms can change the ratio of photons in each box, but I find it reassuring that we do not even need to look for hidden variables. It is right there in front of our nose: changing the length of one arm changes the ratio between both detectors! What more do you need to convince you that we are dealing with physical processes that are in principle knowable? That causality has not been superseded?


2017-01-02
Happy Unspooky New Year
When Logic abandons you, get a dog

I have of course tried to find a logical answer to the puzzle posed by the Mach–Zehnder Interferometer, but each principle that I though of turned out to be incompatible with the experimental results. And since I have no reason to deny their validity and conspiracy theories have never been my thing I simply had to admit that my rationality had met an unsurmountable wall.
It might be interesting for the reader to get a sample of this fight against don Quichottean windmills.

The problem of course is the passage from 1.2 to 1.3. How is it possible that two detectors which are expected to retain 50% each of the input show such a lopsided result, 100-0?
I will not try to retrace the many hours of bewilderment and the many false starts, instead I will present a much more favorable image of my ratiocinations.
Fig.1.3 is in fact the combination of two 1.2 setups. Instead of having two isolated beams each travel through a beam splitter and be divided in a T and R group, photons have first to choose an affiliation (T or R) and then go through the screening process again. So how can four boxes be brought down to two?
We know that in 1.2 every photon has the possibility to choose out of two detectors, and since there are now only two, each arm will contribute to both T and R, two separate detectors or boxes. But in the combined setting, 1.3, these two separate boxes have been thrown together and a new box, TT/RR has been created. The problem is that there are no TT or RR photons in 1.2, since only the final reaction is significant: a photon is either Transmitted or reflected, which means that there is no difference between T, RT and TT on one hand, or R, TR and RR on the other. They all should therefore end up in two different groups. 
Which is not the case, since in 1.3, TT and RR are in one box, while TR and TR are in the other, and no sign of simply T or simply R.

The decomposition of 1.3 in two 1.2's seems therefore fallacious since it does not correspond to what is really happening in 1.3.
Could we find a better description explaining the passage from 1.2 to 1.3?
I am afraid I could not find one, and although that might say more about me than about the problem itself, it seems to me that this failure cannot be without its significance: we cannot judge the results given by 1.3 on the basis of what a combination of 1.2's would have given us. 1.3 has its own rationality and its own rules.
I also thought that the presence of mirrors changed the whole situation and that their role should be analyzed carefully. I still think so and have even thought of an analogy, that of the flip-over sport swimmers make at the end of the track. We are speaking of optical phenomena, so it is not strange to think that mirrors, optical instruments par excellence, would have an influence on the whole. But that is how far I could get and I gladly leave the empirical research to others better equipped for it.
The only thing I know for sure is that the boxes TT/RR and TR/RT do not correspond to what we would expect to get if we combined two 1.2's, so it is not wholly surprising that the final results are not what we exactly expected.
It would be therefore probably essential to determine the exact relation between 1.2 and 1.3, and try and understand the logic behind the transformation of one into the other. Maybe even before the investigation in the role of the length of each arm in an interferometer.

These are some of the reasons why I was a little bit disappointed, if not entirely surprised, by Scarani's haste in introducing the wave and interference theory as an explanation of the Mach–Zehnder Interferometer puzzle. There is so much yet we do not understand of light, and grasping at familiar straws is detrimental to science in the long run.

2017-01-03
Happy Unspooky New Year
Don't drop the soap!
As Zetie, Adams and Tocknell said in their short article "How does a Mach–Zehnder interferometer work?" published in 2000: "the key to the problem lies in what happens to a photon approaching the beamsplitter from behind."
You have to take into consideration the side from which the photon is entering the beam splitter, and, doing that the authors can explain the 100-0 ratio between both reflectors perfectly. It is simply a matter of wave length, reflection and path length. The equation itself needs not worry us, only the result counts, and it is completely in favor of the wave theory.
There is only one very happy cloud at the horizon: no common showers allowed! As Scarini puts it: "we definitely sent one particle after the other so it is impossible that, through an unfortunate coincidence, two or more particles encountered each other at the second beam splitter and that the output was dictated by an unwanted collision." (p.8)
Which means that whatever wave length, path length or any other property might distinguish one photon from the other, they should all be detected once they leave the second splitter in any direction.
We are therefore still in need of an explanation, and the blind application of mathematical tools assuming the validity of wave theory is of no help at all.


2017-01-04
Happy Unspooky New Year
The Disentanglement of Entanglement

In a previous post I argued for a rational approach of the problem posed by Fig.1.3, but then I left myself exposed to the objection that such an approach was impossible because as soon as we approached the apparatus and tried to take specific measurements the situation changed radically: "We must conclude that each particle is ‘informed’ about all of the paths that it could take..."
 Scarani then continues on the same page:
"if we know the path followed by each particle, then at detection half the particles are found at TT or RR, the other half at RT or TR, whatever the difference in length of the two paths. To put it plainly, if we try to know by which path the particle is traveling, we completely lose the surprising effects of apparatus 3 – the particles behave according to our intuitive prediction." (p.9)
This is the famous quantum philosophy in action: simply looking at an experiment changes the behavior of particles. It is like they can feel us looking at them and that makes them adapt their behavior accordingly. The pre-Islamic poet seems to have described them perfectly: if we want them straight, they are straight, and if we want them crooked, they are crooked. What more can you wish for?
Let's analyze the situation very critically.

First we have to deal with the apparent fact that looking at an experiment or performing measurements on it make particles behave according to our intuition. Is that so?
Let us hear Scarini out, and we will use the old-fashioned police method we all know from the movies, we will make him repeat the same statements ad nauseam in the hope that he trips himself. And aren't we lucky, he does just that the second time he has to repeat himself already: "if we know the path followed by each particle, then at detection half the particles are found at TT or RR, the other half at RT or TR". What could that possibly mean?
The only place where it would make sense to put extra detectors would be between both beam splitters in Fig.1.3. It would not help very much to put them after the second splitter since we already have detectors A and B there, and putting them before the first beam splitter would be a joke.
So, what is the affirmation really worth? We have learned that extra detectors before the second beam splitter would assure us of a 50-50 distribution between both detectors, which is exactly what our intuition was hopelessly shouting in our ear all this time.
That certainly sounds good, does it not? And then we realize that we now know as little as we did before we placed the extra detectors! We still cannot exclude the possibility that all the photons will end up in one detector or the other in a 100-0 ratio! Why? Because it is still possible that all photons coming from R will become RT, and all coming from T will become TR. We have no guarantee that some, or half of them, will end up in TT/RR as our intuition so strongly suggests.
And that is all what the so-called explanation of the return of the photon Jedi's really is. We want to believe that when we are looking at the experiment we are back on familiar ground and we are eager enough to fill up the blanks left by the image presented to us by Scarini and other proponents of quantum theory.
As I had argued before, Fig.1.3 follows its own logic, different of that of 1.1 and 1.2 which are much closer to our intuition and experience.
So, in summary, looking at the particles does not change anything in their behavior, and we certainly cannot conclude that they somehow know in advance which paths are available to them, or that they can communicate with each other beyond the boundaries of space and time.

This brings us to the second part of the problem: what do the photons do exactly when or after they arrive at the second splitter? Well, that is no mystery at all! They either all congregate at a single detector, or divide themselves up in two groups whose size depends on the length difference of one arm relative to the other.
Let us imagine that the mirror, or something in the configuration of 1.3, turns the probabilities in certainties and that anything that comes out of T ends up in RT or TR, and that the same cause makes all R photons end up also in the same detector. Probabilities only make sense when we are unable to calculate causal effects because of the number of elements involved, or because of our lack of knowledge.
Unless somebody can reenact Bell's achievement of excluding the possibility of hidden variables, there is no reason not to believe in such a possibility. Especially since it is something purely empirical instead of metaphysical.
Once we have accepted such a scenario it becomes very easy to imagine one or more causes to the fluctuation of the results bringing about a total turn around of the ratios between both detectors.
This demands a change of mentality among scientists, but maybe it won't be so hard as asking them to believe in "spooky actions at a distance".

[By the way, here is a variant of 1.3.
Have the photon traverse two splitters on the horizontal line and be reflected downward by a perfect mirror at the end, and again horizontally by a second mirror, but in the opposite direction to where a detector is placed, directly under the first beam splitter.
Again, starting with the first beam splitter, we go down this time through another beam splitter before hitting the same detector.
We still need one detector, which we will position practically at the center, at the crossing line of the middle splitters respectively on the horizontal and the vertical line. This second detector will be our TR/RR detector, while the previous one will correspond to RT/TT.
Notice how, with the same starting position, one beam splitter, we end up with different boxes. TT and RR are no more in the same box but are divided among both detectors, as are TR and RT.
Logically this variant looks equivalent to 1.3, the question is, did we change the labels only, or are the paths really different?]


2017-01-07
Happy Unspooky New Year
The Disappearance of Interference Patterns
Fig.1.3 might help us find a very simple explanation, while the use of a screen might in fact hide what is really happening.
Take the traditional two-split experiment where light is said to go randomly through one of two slits to fall on the screen and create interference patterns. How could we compare such an experiment with fig.1.3 where obviously two detectors, comparable to two screens, are used?
I think that this interpretation is not exactly right. Just as in the traditional experiment, Fig.1.3 presents only one screen, the second beam splitter. The two detectors can be considered as specific locations on the screen. If you want to consider each detector as its own screen, then you have to get rid of the beam splitter, which would turn 1.3 into 1.1, the primary element with which all interferometers are constructed.
It becomes then wholly understandable how interfering with one of the slits makes interference patterns disappear. If observing what comes out of one path comes down to intercepting the photon on that path, then no interference pattern will show on the screen since it needs both inputs.

The question now is, is it possible to know where each photon came from?
Yes, if Zetie&al are right in their analysis. It should be possible to know how long the path of each photon was because of the thickness of the beam splitters, and depending on whether the photon had to cross this width once, twice, or not all because it got reflected from the first surface.
Since these measurements would take place after the second beam splitter, they should not change eventual interference patterns.
Until now, starting, with Einstein and Bohr, all efforts at analyzing the path, momentum, spin, or whatever, was directed at the slits themselves. Once the particles have hit the screen or detectors, then I fear that the information is irremediably lost. This information can be retrieved only at the last moment, after the particles have cleared the last obstacle. Which would seem to make perfect sense to me.
Another possibility is measuring whatever you want at the exit of both slits and reconstructing the interference patterns on the basis of the results. Surely someone should be able to write such an app?
Remark that in both cases the measurements only make sense if the particles have cleared the last obstacle before the screen.

Light or Photons?
Obviously, measuring a particle will most probably change its state, which would seem to confirm Bohr and Heisenberg's conceptions. But then, since when is science concerned with the fate of a single particle or even an individual  macroscopic object? It is true that when analyzing the behavior of one object, be it microscopic or macroscopic, a researcher will have to choose which factors to take into consideration. A biologist who would get a unique sample could not be reasonably asked to perform all kinds of tests on that sample, especially if said tests are destructive. His first concern would be then to grow enough duplicates and perform different tests on each individual sample.
Likewise, we cannot expect from physicists that they calculate all aspects of the behavior of a particle by using a single isolated photon or electron. We have to allow them a large enough sample if we want them to do their work properly.
This requirement of a large test population is certainly not unique to quantum theory, and should therefore not be used as an argument in its favor.

2017-01-07
Happy Unspooky New Year
Determinism and Probabilities: From Quantum Theory to Trump
They all had it wrong, those statistical researchers and modern Cassandra's. Trump will be president in two weeks, and the world is still turning, the rich getting richer and the poor poorer. How is that possible?
Well, a voter's motives are a complex ensemble of abstract ideas and emotional preferences, and to sum them all up in a single action will always be challenge, even without taking into account the changing circumstances in which the voting takes place. That certainly does not mean that social statistics cannot unveil trends and make predictions possible. It does put a limit to the accuracy of these predictions. For instance, apparently economic welfare goes along with diminished "fertility" in the form of less children. That is something that seems to be universal, at least in modern societies. In earlier times wealth would probably show an increase of population because of a decrease in children mortality due to undernourishment and related diseases. Something that can alas all too easily be shown in regions like the Sahel.
Sociology can therefore say many things about groups of individuals, but the more specific it makes its targets, the more uncertain its predictions.
Is it that much different for chemists, biologists and physicists, or is it maybe only a matter of degrees?
Ikea would probably test a cupboard, if they test at all, by having machines open and close the doors and drawers repeatedly for days, weeks, or if necessary, for months on a row. That does not tell us of course anything about the durability of the next best cupboard, which could last as long as a few months, weeks, days more or less than the first. But that is precise enough not only for Ikea, but for all of us. It wouldn't be reasonable to demand more.
What is then the difference between a cupboard and a voter? Statistics do not care about individuals, and that is why they can never predict the durability of a single cupboard or the voting behavior of a single voter. All they can say is that if all individuals behave like the one(s) tested, a certain result can be expected.

Einstein-Bohr: Love-Fifteen
["Can Quantum-Mechanical Description of Physical Reality be Considered Complete' ?", by Einstein, Podolsy and Rosen (EPR), and the reply with the same title by Niels Bohr, both published in 1935]
What is really striking in EPR's definition of reality is that it is a laboratory reality, and not what laymen mean with this term, the vagueness of the latter being certainly one distinguishing aspect. Take for instance this affirmation:

"If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity." (original emphasis)

"without in any way disturbing a system", why should that be important in defining reality? In fact, I would say that the opposite is true of everyday reality. It is that which hinders you in your wishes and desires. If you cannot perform an action without disturbing the system then you can be certain that there is something "real" countering it.
The above affirmation would certainly make sense if the authors intended to distinguish theories and measurements which are somehow linked with reality, from those that are pure imagination, but the idea that they can this way decide of what is real and and what is not is somewhat pretentious. This metaphysical arrogance is clearly expressed in the following: "Regarded not as a necessary, but merely as a sufficient, condition of reality, this criterion is in agreement with classical as well as quantum-mechanical ideas of reality." The criterion in question, no disturbance of the system observed, is  based on nothing else but "results of experiment and measurements". 
In that, Einstein and Bohr are in complete agreement, they are both dealing with lab-reality: If the state of the object is changed by your measurement, then the property measured cannot be considered as real.
This conception, not to say metaphysical bias, is obvious in what EPR as well as Bohr consider as a "physically observable quantity".
I will avoid the use of meaningful mathematical formulas for two reasons, the first being that I really do not wish to make a fool of myself. The second reason is more substantial. Scientists who read those papers will very often be influenced by the mathematical correctness of the argumentation and more easily agree with the conclusion if they can detect no mathematical error, forgetting that it is not a mathematical but a metaphysical problem.
EPR wants to distinguish the momentum of a particle from its coordinate, and with the help of a number of equations, decide whether any or both these properties can be considered as physically real.
The application of the rules leads to the following conclusion: momentum is real, coordinate is not. "In accordance with quantum mechanics we can only say that the relative probability that a measurement of the coordinate will give [some] result [r]." Coordinate cannot be predicted, only directly measured. Only, since such a measurement would change the state the particle is in, we have to conclude that "when the momentum of a particle is known, its coordinate has no physical reality". (original emphasis)
More generally, instead of momentum and coordinate, this logic is applicable to any so-called non-commutable factors, that is factors A and B for which A times B is different than B times A.
EPR had previously made another astounding metaphysical claim: "every element of the physical reality must have a counter part in the physical theory We shall call this the condition of completeness."
Well, then is it is very simple, there are no physical theories. After all, which theory could claim that it contains a counterpart for "each element of the physical reality"?

Einstein makes it very easy for Bohr to counter his arguments, even if Bohr had apparently to stay awake for it quite a few nights.
Bohr's argument is very simple: there is no way of measuring momentum and coordinate without influencing the state of the particle. And I wholeheartedly agree with him. The same way Ikea cannot test a cupboard without destroying it, and Ford test their tires without having worn a few of them to the thread.
The idea therefore that matter beyond a certain size can only be known in probabilistic terms is certainly correct, but only half of the truth. Macroscopic objects can also be known only in a probabilistic, statistical way, so whatever Bohr has to say about the quantum level is in principle applicable to the macroscopic level. And since this "uncertainty" does not prevent us from planning actions in the (near) future and making predictions which very often come out, then there is no reason why quantum science would do any worse, or any better.
Einstein's view was too simplistic, while Bohr was too full of his importance to realize that his science was really nothing new. Epistemologically speaking.
Interchangeability of Particles
Objects which are considered as being identical are expected to behave the same way. If we apply this principle to particles then there is no reason why we should not be able to determine exactly not only the path but also the momentum, the location or what not from a (generic) photon in an interferometer or two-slit experiment.
All we need to do is put a detector which would be at the same time an emitter. While the incoming photon is being analyzed, and identical photon would then be emitted at the same angle to finish the trajectory to the screen.
That would of course not work with experiments demanding "live" reactions.
More importantly, by defining the terms under which two particles can be considered as interchangeable, the gap between so-called quantum and macroscopic processes would be made much smaller, if not completely bridged.



2017-01-08
Happy Unspooky New Year
Que dirait Dirac? Hot Pursuit
A highly dangerous criminal, armed and dangerous, has fled into a deserted mall going through the main entrance. After a main hall,  there comes a T-crossing, one side going straight east, the other down south. It does not really matter which one you take, since after a 90° turn, you come into a long hall which ends with another T-crossing, one leading to the south exit, the other to the east exit. The police is left with a dilemma. They do not know when the suspect went into the wall or how fast he is, and they do not have enough people or time to cover both exits.
Dirac, asked as an expert consultant to give an advice to the police in this matter, could only repeat what he had said in his bestseller "The Principles of Quantum Mechanics", (1930, 1935, 1947, 1958!): do not go into the mall at any cost! By doing so, you will make the criminal take one specific path without any way of knowing which one. As long as you remain outside of the mall, the suspect will be in a state of superposition, and therefore present on both paths. Which means that the police can just wait for him at any one of both exits where he cannot miss to reappear. When the sheriff objected that there was no way to know which exit to choose, Dirac sneered and reminded him that quantum science was not for the ordinary man and it would not make any sense to him anyway if he, Dirac, explained it to him. "So just pick an exit, any one, and be done with it!"
The suspect is still running.

2017-01-09
Happy Unspooky New Year
The Disentanglement of Entanglement (2)
Shaoul Ezekiel is really a font of information. I particularly like his demonstration of how easy it is to corrupt polarization of a beam of light. It is exactly what we needed to understand why changing the length of a path changes the ratio of particles registered by both detectors. Once again, we have no need of spooky or mystical explanations as to how a particle knows which path it can take, and whether the length of an arm has changed and by how much. Polarization gets corrupted, and what are beam splitters but polarization filters? What we need now is an explanation of this "corruption". Maybe we could ask the Untouchables?

2017-01-10
Happy Unspooky New Year
Fresnel or the End of Wave Theory

George: you mean particle theory.
me: nope.
George (mumbling): I need another host.
me: what's that?
George: nothing. You may proceed. I'm gonna watch Back to the Future... To get my sanity back.
You (falsely enthusiast): great! How about some popcorn?
George (grunts): I'd rather have chocolate. Lots of it!
You (sincere): I thought you'd never ask! What kind of porn do you like?
George (indifferent): lesbian.
You (grinning): cool! Can we watch some after the movie?
George (somber): sure, as long as I don't have to listen to Me.

[I don't know where they get their ideas from. I never watch porn.]

In the second volume of his oeuvres completes , par.12, Fresnel describes an alternative method of showing interference fringes by two beams of light coming from a single source. Instead of two pinholes or slits, he uses two mirrors which are placed close to each other in such a way that the bright source can be seen on both. I have never seen it mentioned again by any other author I consulted. Every time interference fringes are discussed, it seems obvious that they have to somehow originate in a version of the two-slit experiment as first described by Young. Except for the fact that Young did not describe slits as much as he described the role of both sides of a light beam being interrupted by an opaque thin object like a hair or a thread.
Fresnel's alternative method is interesting for the simple reason that there are no shadows or slits involved in the creation of these interference fringes. Which means that he cannot use Newton's failure to see that shadows do not have straight edges, but are crisscrossed by almost imperceptible light bands, as an argument in favor of the wave theory of light. At least, not in this context. Fresnel only needed a "loupe", a magnifying glass held close to his eye as an anachronistic Sherlock Holmes, to get the fringes projected on his retina.
The problem with such a setup is that it suspiciously resembles the familiar subtractive model of colors whereby the combination of different (secondary) colors give rise to other (primary) colors, and also to black, instead of white, as is the case with the additive circle.
Whether black can be considered as the result of the absorption of all colors, or that of destructive interference, sounds almost scholastic in its subtlety.
But then, even before the advent of lasers, Fresnel, just like Young, emphasized the need of using a coherent source, as monochromatic as possible, to show interference patterns. Otherwise, instead of dark spaces between the fringes, colored spots would be shown.
In other words, a color circle would be highly unsuited to show interference patterns and the black in the center can best be interpreted as the result of absorption and not destructive interference.
This, added to the fact that empty spaces seem simply to take on the color of the background, be it white, black or any other color, makes their interpretation as the result of destructive interference very implausible.
Apparently, neither the wave theory nor Newton's analysis can give a satisfying account of the so-called interference fringes.


2017-01-11
Happy Unspooky New Year
Huygens revisited
I find Huygens' idea of (secondary) waves a very powerful one, even if his model of light does not really convince me. Somehow it seems to explain important facts about light, how it can go around corners without losing its main, straight direction, and also meet other waves when particles going in straight lines would simply ignore each other.
Even if one does not buy into the destructive interference story, some explanation is needed as to how light seems able to do much more than beams of particles can account for.
There is a very familiar property of beams of light which seems to be very often ignored. Light might travel in straight lines, but it certainly does not travel in straightforward lines. In fact, we know light either as an ever expanding sphere of brightness, like a sun or a bulb,  or as an expanding cone of light, as when it comes out of a flash light.
My metaphor of an infinite number of images had already given me a clue as to the importance of the width of a beam in conveying an image through space. My example of the street lamp and how it appeared each time to move with the position of a pinhole, is I think another clue.
Information contained in a small beam of light will still be there when this beam of light gets wider and wider, and vice versa. Also, it seems like rays have a tendency to push each other out of the way, and claim as much space as possible for themselves. That would explain how rays which have to go through a very narrow pinhole again create a cone of light as soon as they leave the hole. How can they do that?
You would expect rays that enter a pinhole obliquely to follow their course in a straight line, creating a narrow beam of light entering also obliquely the dark chamber. How could they possibly, as particles, change direction and act as is they were originating from a source of light situated at the mouth of the pinhole? Especially since there are also examples of light rays entering a space obliquely.

Light rays get compressed when entering a narrower space, and expand as soon as they can. In the second half of Goethe's video we see that light beams from an arrow formed of lighted lamps all go through the same hole, each one, including the first, filling it. They all accommodate each other to go through the opening and then start to expand as soon as they have passed through.

Huygens's genius was to recognize that the model of projectiles was not adequate, that the behavior of light looked indeed more like that of a wave. But he did not think the concept through and got carried away, just like Young, Fresnel and others, by easy analogies.

The first thing we have to explain is how a single source of light can become two distinct sources each following its own paths and creating together the interference patterns.
First thing first, the duplication of the light source. Imagine one source of light behind the middle part separating two holes or two slits, all at the same level. The light will propagate in the direction of the wall, some rays being stopped by it, others will be let through by the slits.
This is a crucial moment and the way we describe the events will determine the kind of theories we will be able to build.
We can think of the light constituted of rays that move in straight lines in every direction. In this case, the only rays that will be able to pass through the slits will be oblique rays, and there is no reason for them to change direction once they have crossed the slits. This way we would get two isolated fields brightly lit at each extremity of the screen put a distance away from the slits, and there will therefore be no interference phenomena at all. 
This is obviously wrong, so we have to abandon the idea of light rays.
Does that mean we have to abandon also the idea of light as made of particles? That is the jump that Huygens did, later followed by everyone, because it seemed the most straightforward, and therefore logical solution.
We cannot answer this question yet, first we have to know what happens to the light between the source and the slits.
The wave theory sounds very plausible. A big wave is split into two smaller ones, and these two waves fill up the space after the slits in the direction of the screen, with crests and troughs interfering sometimes constructively, other times destructively. There is no doubt that the wave theory offers a very plausible model of the behavior of light.
Is there an alternative?
Let us take our inspiration from the wave concept and apply it to particles. Let us say the light source starts as a single point, which then divides itself into 3, 5, 7, 9.... All the while going forward. Arrived at the left slit be elements 13, 14, 15, 16, 17. Let us rename them as elements 1, 2, 3 ,4 ,5. These five elements will be able to expand more quickly now that they are not hindered by the original outer limits, covering over half of the width of the panel separating them from the other slit, where the same process takes place. Even when added together, the elements in both slits will have much more space to expand in than they would have had if they had remained a part of the original light source. If they keep the same division rate, the distance between them will be relatively greater. Wherever we put the screen, we will see blobs of light that were in fact destined to break up in smaller units until each one was composed of a single photon. What the wave theory considers as locations of destructive interference would simply be the empty spaces between blobs created by each successive division.
Also, we must realize that the empty spaces are never completely empty, especially when two light beams are interacting with each other. In fact, what are considered places of destructive interference are probably the locations where fewer photons have landed, coming from a single beam.
This process of quasi-cellular division should not be considered as something mysterious. A ball of light will emit a condensed cloud of elements in all directions, and the distance between the elements of that cloud, or field if you prefer, will become larger and larger. 

A proper understanding of the behavior of particles should make the concepts of field and wave superfluous, even though many, if not most, of their effects would have to be retained.


2017-01-11
Happy Unspooky New Year
Huygens revisited (2)
Can my model also explain Huygens' Principle? 
I see only one possibility for this to be possible, and that is to negate the equation one electron one photon, the physical equivalent of the sacred democratic principle. I had already argued that many more people, and devices, can register the presence of light than theoretically possible by the emission of a limited number of photons. The idea that we can understand light by following the path of a single photon, which is at the basis of the concept of an optical ray, is I think a formidable obstacle to a real understanding of light. What wave theory considers as interference of a wave with itself should be seen as the interaction of many particles.

Also a problematic issue is how come, depending on the positions, relative to each other, of the slit and the light source, we see sometimes oblique rays, other times horizontal ones?
But then, wave theory has the same problem. The example of the arrow in Light Darkness&Colours - Goethe's Theory, is very significant. We could rotate the image 90° counter clockwise and look at both lines horizontally to make it easier for us to analyze. It will still be obvious that each image of a lamp is created because only the rays having a certain direction have been let through the hole. Again, please do not forget that this is a difficulty faced by wave theory as well. All lamps forming the arrow are identical, so why is it that they all send their image in a different direction, making it possible for them, each time, to go through the pinhole?
Let us then replace the lamps with flashlights, or directional light sources. How would then the image of the arrow look like?

This is I think a moment where the weaknesses or ray optics become evident. Only the flashlights more or less placed in front of the slit would see their beams reflected on the screen through the slit.
That does certainly not mean that only those lights would be visible to an observer standing at the same level as the screen. In our rotated, horizontal, view, this observer would only need to move along the screen to see each lamp forming the arrow. Just like we would see them by looking left and right, up and down, when our eye is held against the pinhole.

This asks of us a new definition of light. We need at least to make the distinction between illuminated objects and their visibility.

Take the rays of light entering the pinhole. They can be described in terms of ray optics as a band of light traveling in an (oblique) straight line from the source, through the slit, all the way to the screen. Just like we can see the end of the tunnel, or the artist under a spotlight, we can see them from different angles without becoming ourselves illuminated.
We could also see, from this side of the pinhole, the band of light produced by a flashlight on the other side, whose rays did not enter our side at all.

The question now is: does light have a direction? I know this sounds rather silly to anyone who has ever hold a flashlight in his hand. The nature of the source will determine how light will propagate in space. At least, so it seems. But then the beam of a flashlight is probably nothing else but a slice of the bright ball a small sun would show, just like a laser light would be nothing else but a slice of the flashlight beam. Light does not suddenly behave differently with those three kinds of sources. We may reasonably assume that the same laws are applicable to all three situations.
Also, when you enter a beam of light all distinctions between the different sources would vanish.

We can now, hopefully, better appreciate the meaning of the question: does light have a direction?
Look again at the beam entering a dark room through a small hole. It certainly looks like directional rays to me, so why do I keep claiming that they are not?
Imagine the dark room fully lit because the hole is so large it hardly stops any light from entering. And now make this hole smaller and smaller. Are you coercing the light rays in a specific direction, or do they "instinctively" know if they can bend enough to pass through the hole? Or, more simply, were they already headed in that direction and did not need to do anything to be allowed through the hole? But then, how many directions are there for photons to follow? However you move the hole, there will always be rays that go through it. Are these, at least partially, the same rays? And, if that is the case, how can all these directions not collide with each other?

Here is a simpler alternative.

Take the cone of light formed by a flashlight and direct it towards a wall a little further away. Now close two dividing panels so as to leave a very narrow beam of light between both spaces. My claim is that the directionality of the light has not changed, that therefore polarization filters do not do what we think they do. What happens is somehow comparable to coloring in a dark color, let us say black, the space behind the dividing panels, except for a small band where light is still being reflected.
It might look to us like photons are moving in this specific direction, while in fact they simply represent the elements in the atmosphere that are receiving light, while others are not.
The question whether something is moving from one element of matter to the other, and what that something is, is a question I have no answer to.
What seems obvious to me is that all elements within the bright parts of the cone will be affected. These bright parts can be considered as a grid whose cells become larger with distance, since at least two of the sides are growing apart.
A slit would therefore function as a polarization filter by preventing light from reaching most of the grid, except for a small band.
In fact, we might as well consider the field of light as a static phenomenon, which gets affected by the placing of opaque or transparent objects, filters, slits, diaphragms and openings.
We can therefore never change the direction of light except through reflecting surfaces. For the rest, we only decide which part of space will or will not receive light.

This brings us to another fundamental principle of ray optics: the reversal of the image whereby what is up in reality appears down in the image, and left appear right, and vice versa. How can one explain that if photons are not following ray trajectories?

Let me first direct your attention you to a fundamental discrepancy that has seemingly always been ignored. Every illuminated object is assumed to reflect light in all directions, which makes it possible for mirrors to reflect an object "normally", and not upside down. An object is therefore emitting its "normal" image as well as its reversed or upside down image all the time. How come we only see one of them at any time?
Imagine now a large tv screen with only one pixel lit, the one on the left (or right) upper corner, and a mirror covering the whole of the opposing wall. Again, we put a dividing panel with a hole in it.
Before we close the dividing panel we must ask ourselves where the lit pixel will be reflected on the mirror.
This is not as simple as it sounds. Just like we would be able to see the pixel wherever we are standing against the opposite wall, the mirror on it will reflect an image of the pixel to our eyes wherever we stand.
But once the panel is closed completely, and a small hole in it is opened, then the situation changes radically. We won't be able to see the reflection of the pixel everywhere on the mirror, even if it will always be visible to us at an angle or another. In fact, just like ray optics predicts, the only reflection will be at the opposite lower corner of the real pixel.
We are facing now quite a dilemma. Ray optics predicts a reversal of the image because of the crossing of the rays, but if there are no rays, how can the reversal, and we know it happens, happen?
Let us consider again the example of the arrow in the video, and look at the moment where the first lamp was lit. What would have happened if, instead of turning the other lamps on, we had moved the hole up or down?
It is reasonable to say that we would have gotten each time the reflection of the lamp at the corresponding place on the screen. It would have been the reflection of the same lamp and there is no reason to assume that the image would have been suddenly reversed just by placing the dividing panel or moving the hole.
Imagine now a second pixel turned on in the opposite corner and on the opposite side, and also having another color than the first one. What will you see in the mirror? I am sure that it would be possible somehow to catch a combined image, and color, of both pixels, just as it would be possible to see both colors separately just by shifting one's position very slightly.

The difficulties we are having with the analysis of the behavior of light stems, I think, for a great part from the illusion that we are dealing with simple, indivisible quantities. We see a pixel as one, as we see its reflection on the mirror, and the idea that the same location could also contain the reflection of another object is hard to accept. Unless we seek our hail in mysterious concepts like superposition, attributing to a single element the magical ability of being two things at the same time.
In the case of pixels and their reflections, it would be I think more plausible to admit that our vision, and optical devices, are limited in their resolution, and that what we see as a single surface reflecting a single image, could be a very complex space harboring many images.
Going back to the image of the arrow and its reflection through a pinhole, then we can say that the only image still available to the lamp is on the opposite side and corner of the dark room. That must be the reason why the larger the pinhole, the less sharp the image is. Too many reflections at the same locations.

It is important to realize that conceiving the light field as stationary is just a figure of speech. Somehow light has be continuously brought in, and that is why we can still have visible images of dark scenes from a camera if the exposure time is long enough.
Also, the distance between the hole and the wall on which images are projected is of course very important. Other possible reflections that would create even more blur end up luckily before or after the projection surface. Focus is, as everybody knows, a simple way of cleaning up an image of unwanted reflections. What we must realize if that a picture out of focus is not (simply) a technical defect. It shows that an object does not emit a single reflection of itself, but infinitely many. 

As you see, by abandoning the concept of wave as well as that of ray we open up many new paths in the inquiry about the nature of light. Probably too many for a single individual to walk them all.


2017-01-12
Happy Unspooky New Year
Huygens revisited (3)
Let me first mention a serious flaw also in my own analysis, one which I already mentioned in passing and which no other theory can explain either.
I have no idea how to explain that objects reflect their image only upside down, except in a mirror. More precisely, why only upside down images appear in pinhole darkrooms and on photo negatives (and none in mirrors)?
It would seem to me that there where an upside image is possible, a normal one should be also. How come we do not see that? What are we all missing?
You can build a very simple diagram with a program like Paint
First you need a vertical line somewhere in the middle of the screen, with a slit in it. Then draw a triangle with its top up on the left side, preferably not in front of the slit.
You can now draw two sets of lines. The first set is parallel and shows a simple translation of the triangle from one side to the other. The upper line will pass close to the upper part of the slit, and the lower line to the lower part. At the end we will have an identical image of the object.
The second set will show the familiar drawing of crossing rays creating an upside down image on the other side.
What is important is that both images are possible.
Of course, when using a converging lens only the second, classical, case will be possible, but what about a naked pinhole?
There does not seem to be any rational solution to this puzzle, only strange ones like all rays emitted by an object somehow have to say together, or some other mystical explanation.

Until we change the given of the problem. Both models assume that the image of the object nicely aligns its rays in such a way that they cross the slit in the same or exactly in the inverse order, top to top (or bottom) and bottom to bottom (or top). Such a view gives us indeed only two solutions, a translation or an inversion, and we are back to our dilemma.
It becomes very different when we make all points of the object pass either close to the upper or, alternatively, the lower side of the slit. Then, even if all lines seem to cross at the same point, they all end up at a different location, in an inverse order.
Apparently, just like by the use of a lens, rays cross each other and swap positions, only the location of the crossing is different. This would also explain why a small hole gives sharper images than a larger one.

But doesn't that mean that light does have a direction? Absolutely, we can simply direct our flashlight to wherever we want. In this sense, the beam has a direction. That does not mean that individual particles also do, except as part of the beam. Here again we can consider the light shining in space as a grid of stationary particles.

One thing this analysis still does not explain yet, is where the other images have disappeared. I surmise it will have something to do with focal length, and the relative distance of all the factors involved. I will just have to admit my ignorance even while expressing my conviction that rational, and empirically supported, explanations can be found.

Ray Optics revisited
I would like to present an alternative explanation of what happens when rays go through a converging lens. It consists in considering the crossing point as a slit, which would explain why in both cases the image is reversed. Ray optics describes this point mathematically, as an abstract point, which we know is empirically untenable. By considering it as a slit we can more easily look for empirical explanations as to what is happening in this portion of space.


2017-01-12
Happy Unspooky New Year
Que dirait Dirac (2): We are the Bohr, resistance is futile

Here are some quotes from section 2. The polarization of photons, itself part of the first chapter The principle of Superposition .
"Questions about what decides whether the photon is to go through or not and how it changes its direction of polarization when it does go through cannot be investigated by experiment and should be regarded as outside the domain of science." [may I call that obscurantist?]

"It is supposed that a photon polarized obliquely to the optic axis may be regarded as being partly in the state of polarization parallel to the axis and partly in the state of polarization perpendicular to the axis." 

"When we make the photon meet a tourmaline crystal, we are subjecting it to an observation. We are observing whether it is polarized parallel or perpendicular to the optic axis. The effect of making this observation is to force the photon entirely into the state of parallel or entirely into the state of perpendicular polarization.

Before all that, Dirac had declared: "It is known experimentally that when plane-polarized light is used for ejecting photo-electrons, there is a preferential direction for the electron emission."

What if, as I have argued, photons, whatever they are, do not have any direction? Imagine again the lit space as a grid with growing cells. Whatever obstacle is put in the path of the light, it will only stop a part of it, and only for some time or distance.
Think now of a polarization filter that only lets vertical light through. What does it really mean when particles have not direction to select them by?
We can imagine vertical slits, or on the contrary, horizontal thin wires to let only "vertical" photons. Since the grid cells are expanding, this filter will only work for short distances, as proven by Ezekiel. Moreover, because light is not really moving as much as matter is reacting to whatever causes it, also particles which would be considered "horizontal" would very soon start to react, contributing to the "corruption" of polarization.
Which means that we do not have to assume a mystical superposition of states anymore. Particles which are stopped at one moment, are free to pass at the other. And that has nothing to do with us observing them and making them leave their blessed state of superposition.

I honestly cannot believe that people took Bohr and his friends seriously for so long. But then, who knows? Maybe magic ain't dead!
As Ramzi Suleiman said in a private correspondence "Einstein was the first to convince physicists that our intuition and logic are not to be trusted. Quantum theorists went [much further] in their fantasies."
https://www.researchgate.net/publication/312154856_Information_Relativity:_The_Special_and_General_Theory


2017-01-16
Happy Unspooky New Year
"The issue of two particles communicating with each other faster than light has divided great minds like Einstein and Bohr. It is also the most spectacular proof that Nature cannot be understood with common sense."

Just wanted to disagree. Common sense suggests that extension is an appearance, not a metaphysical reality, and that 'all is one', so nonlocal correlations can be expected.  

2017-01-16
Happy Unspooky New Year
Common sense?

https://briankoberlein.com/wp-content/uploads/nYuzAo4-300x168@2x.jpg

That is from Real and Unreal, and the author does seem to agree with you.



2017-01-17
Happy Unspooky New Year
Upside down, round and round
Why don't we ever see objects upside down, except in a camera obscura? Does that have to do with the presence, or absence, of a lens?
The fact that our eyes are lenses does not seem to play any role, since we can experience both situations.
It would seem that the way a mirror functions is the key to this mystery, even though we will have to explain why our eyes only see one kind of image, even in a camera obscura where, theoretically, we also should be able to see the world in its normal position.
It looks like there is no difference, as far as our eyes are concerned, between an object or its mirror image. They both project their reverse image on our retina.
The fact that this would seem only possible if the image is formed by rays not crossing each other at the focal point, but going from one point on the object to a corresponding point on the mirror, does not change anything for how we view objects and mirror images. Another possibility is that the image we see on the mirror is in fact projected upside down on our retina! Just like the real object.
The question now is, why do we see images projected on the wall of a camera obscura upside down? That seems to mean that the way objects are projected on a wall or mirror, depend on the presence or absence of a slit. But then, objects which are at the same level as the opening should be projected in a mirror-image way. Why doesn't that happen?
Maybe we should question the assumption that rays on the optical axis are propagated without any change or refraction. After all, the center of an object will have also to be divided between an upper half and a lower half on the retina. There is therefore no central line that would somehow be neutral. However close two vertical points will be to each other, one will be projected upward, and the other downward, in the reverse of their natural order.
Another mistake is to consider the mirror image as a real object. We see the tree straight up in the mirror exactly because it is reflected upside down on the mirror. If we turned around and looked at the tree, it would be reflected on our retina just the way it had just been on the mirror.
While if the tree is projected on a wall instead, it will also be upside down, and its projection on our retina will be straight up, making us see it upside down. 
I know. I'm starting to have a headache too.
We have to remember only one thing. A mirror works like our retina, any image projected on it would be like an image projected directly on our retina (minus the left-right reversal, or whatever it is).
It would be vain to treat such a mirror image like a projection on the wall, since we cannot move without changing it, while the projection would remain the same, except for minor changes of perspective.

The mystery of light has turned into the mystery of mirrors.
The idea that a mirror image is, just like the retinal image, upside down, is in fact not only plausible but also necessary. Imagine you have a mirror with borders of different colors. The borders will appear upside down on your retina, just like the image of the tree on your retina. But if the image of the tree on the mirror did not also appear upside down on the mirror, but straight up, then it would look like the mirror itself has been rotated upside down, the upper border becoming the lower one, and vice versa. In fact, it also explains how the image of a tree in a mirror does not appear upside down on a photograph. 
In conclusion, objects are always reflected the same way, and that has apparently more to do with how light propagates than with how lenses, or our eyes, work.
Capisce? I'm not sure I do. Even if that makes what happens in a pinhole camera, for an instance, an arrow of light that slowly is formed upside down, look less mysterious. 
The subject certainly deserves more time and attention