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Wednesday, August 22, 2018
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HERE IS A MAKE-BELIEVE STORY THAT I MADE UP TO HELP A NON-MATHEMATICALLY INCLINED FRIEND OF MINE TO GRASP WHAT HEISENBERG‘s UNCERTAINTY MEANS IN THE QUANTUM WORLD — SORT-OF, ANYWAY . . .

Imagine meeting a person from a different, far away place – and in that different, far away place, people get first names and last names, just like us

BUT – each person from this far away place gets a set of multiple first names, and multiple last names; E.g., the person can be [George, Martin, Louis, Roger] + [Smith, Edwards, Ortiz, Russo]. Also, every second or so, the combination changes, more or less randomly. We can’t know why right now — maybe it’s because their brains evolved differently than ours, maybe it’s because of cultural differences, could be a lot of things. But for now, we just need to accept that there’s something different about “how they do names” in this far-off land.

(If you describe these people using “quantum physics language”, you would say that their first and last names are different from ours because they are quantum super-positions)

AND ONE MORE FUNDAMENTAL CONDITION – the stranger can only concentrate his mind on one part of the name at a time; either first or last. Let’s say it takes the stranger 2 seconds to go from a First Name observation to a Last Name Observation in his head: I.e., First name . . . then 2 seconds, tick tick tick . . . then Last name. So you ask – tell me your first and last names, please; and the person from afar answers, Louis (2 seconds) Ortiz. You ask again – and this time it’s Roger (2 seconds) Edwards. Etc.

Because of the way that this person’s brain is set up, i.e. as an addition of two separate names (first and last) that change independently, there is an observation delay between the two. The stranger cannot just directly observe and then tell you exactly what both names are at any instant — he or she was just not set up that way! (Although the stranger can have a hunch about what his or her full name is at a particular moment, as we will discuss soon). This stranger does not do what we can do, i.e. just memorize two names which almost never change (OK, women used to adopt their husband’s last name, but that social custom may be slowly fading away).

Curious person that you are, you want to know more about how the name thing works for this stranger from afar — so you ask the person if they can tell you their first name every 1 second, and they say yes, fine. They can answer faster because they keep looking at the same thing in their mind, they don’t have to change their mental view from First Name to Last Name, which takes longer (thus accounting for the 2 second delay between First and Last Names).

So, you say, please tell me your First Name over the next 5 seconds: Louis, George, Louis, Martin, Roger. Try again: Martin, George, Louis, Roger, Martin. One more time: Martin, Martin, George, Martin, George. (don’t worry, Louis will have his day in subsequent samples!)

You input the various names you get from the stranger into a randomness analysis program, and it tells you that the name pattern over time is most likely random, there is no relationship between one name and the next name in time.

You then make the same request of the stranger from afar with regard to Last Name. First try: Ortiz, Smith, Smith, Russo, Ortiz. Second try: Edwards, Russo, Edwards, Ortiz, Smith. Same thing, random selections every second. Being good with statistics, you ALSO check about “cross-correlation” — is there any relationship between what the Last Name will be following a particular First Name. But once again, you come up with a likely “random walk”, no indication of correlation or relationship.

AND THEN IT HITS YOU !!! When you ask the person their First and Last name in sequence, the answer you get is not their “real” full name at any particular moment! Not even for a micro-second !! You JUST CANNOT know their real FULL name at any instant !!!!

Why not? Well, based on what you heard from the stranger about how he figures out what his names are, it seems clear that by the time you get the Last Name (2 seconds after you get the First), the First Name has changed at least twice !!! And the Last Name has also changed at least twice over those same 2 seconds – so you DON’T KNOW what the Last Name was when you were told the First Name. (And don’t know the “real” First Name when the Last Name is spoken).

For this person from afar, as with us, their First Name and Last Name serve different functions. There is some reason why in that far off place, people get separate First and Last Names. But the strange feature of their Name, i.e. that both Names change every second, together with the third feature, that the person has a mental observation delay between “Name realizations”, make it impossible for anyone to be absolutely certain about First and Last Names at any one instant.

In theory, you could imagine that in this far-off land, the people came with minds that merge First and Last name into a big mental list of every combination of first and last name (George Smith, Martin Smith, Louis Smith, Roger Smith, George Edwards, Martin Edwards, Roger Edwards, etc.), and this person from afar could constantly select his name randomly from this list-in-the-head, and thus observe both at the same instant.

But in that case – that would be equivalent to having only one type of name, doing only one thing. If you want the two names to mean or signal different things (or if you want them to be determined by different processes, e.g. say there were 8 First Names that are randomly determined according to one probability distribution, and 12 Last Names determined randomly through a different probability distribution), then you inherently must separately measure the two names. Given that, the time delay situation between mental name observation makes it inherently impossible to know what the FULL name is at any instant !!! You can know the First name; or you can decide to know the Last name – but NEVER the true Full Name with absolute certainty at a particular instant.

Now in the large scale world, the “classical” world – it’s as if we amalgamate a big population of these persons from afar; we deal with big populations. Classical world does does not focus on only one or two particular strangers. Usually, these individual people from afar have probability distributions determining their randomly selected First and Last names – let’s say that Martin is at the peak of the probability wave for First Name. So Martin is the most common First Name; and let’s say that Smith is the most common outcome for the Last Name probability curve.

In that case, the grouped name outcomes for all the individuals in the population are still random, because the next outcome of any one person is not influenced by what the last outcome was (and we further assume that each person is independent, there is no cross-person name correlation). BUT, because of the curved probability distributions in all of the individuals, one name can still come out more often than others over time, i.e. over many observations. And likewise, some names can very seldom come out, some are fairly common — but one name is the one that most frequently shows up due to the probability curve inside all of the individuals.

So, when we deal with a big population of these individuals, each having a similar set of possible First Names and Last Names, and each having the same probability distributions for First Name and for Last Name . . . . to deal with this, we take a vote. We find out which First Name wins the vote, and which Last Name wins the vote. And because of the law of large numbers, about 99.99% of the time when we take a vote, we get Martin as the winner in the First Name vote, and Smith as the winner in the Last Name vote. So, we reliably call this population “Martin Smith”. It doesn’t seem to change from vote to vote, so we conclude that we CAN reliably know both the First and Last Name of our huge city of people. Remember once again, we in “Classic Land” are concerned with the CITY, not with each of the millions or billions of individuals with changing first and last names. So it appears at our “classical level” that we CAN SIMULTANEOUSLY KNOW the First and Last Name of the CITY.

And that’s sort-of why we don’t concern ourselves with Heisenberg Uncertainty in Classic Physics or observations in the Human-scale world.

BUT WAIT, ACTUALLY IT’S NOT THAT SIMPLE — my story and the explanations within it may been somewhat “misleading” on the matter of the known versus unknown name for any individual. My example would have you believe that when you ask the stranger from afar his First Name and then his Last Name, his First Name changes by the time the stranger answers what he currently observes his Last Name to be. But it really does exist, even if not observed (akin to the saying that the tree really does falls in the forest even if no one perceives it).

For example, when you ask First Name of the person from afar, he says “Louis”; then you ask Last Name, and he says “Ortiz”. I told you just now that by the time the stranger examines his mind and speaks out his Last Name, his First Name has changed, perhaps to “Martin” — but you cannot know what the First Name has changed to by the time that you find out the Last Name. His mind is set up to answer one name question at a time, and only one name question. SO, there is an “Uncertainty Problem”, seemingly.

OK, let me admit something — this is misleading. I believe that most physicists would say that when the Last Name is spoken, the First Name has reverted to a “Superposition” state comprised of the probabilities of 4 potential names. And vice versa — when First Name is spoken, the Last Name is still a “probability cloud” i.e. superposition, where the actual name remains undefined. I led you to believe that both Names actually exist at any point in time, although they constantly and randomly change and cannot always be observed. That is NOT what most scientists would say.

HOWEVER, there ARE a few who MIGHT take this interpretation — this interpretation requires “HIDDEN VARIABLES“. David Bohm was famous for proposing this interpretation, based on non-local influences (scientists have proven that LOCAL influences cannot drive hidden quantum variables, but they haven’t yet ruled out non-local “spooky action from afar”, akin to quantum entanglement). HOWEVER, as you probably know, most scientists still go with the Copenhagen Interpretation . . . i.e., that until you measure a superpositioned state, it remains in a cloud, as something not “real” in our daily sense.

Because of the relationship between the position and momentum / wavelength waves in a photon, you can only accurately measure and thus “fully flatten” one of the two waves at a time (“flattening” is really more like turning a spread-out, bell-like wave curve into a spike); when you flatten one completely, the other one stays fuzzy, i.e. spread out. If you TRY To measure both at the same time, you will get a mixed result in terms of accuracy/certainty — both waves will shrink, the superposition will become limited (maybe the possible names will narrow down to two instead of four), but the FN / LN outcomes could still be “wrong” (better said, when observed together they are both subject to some level of inherent uncertainty — it’s hard to say just what is “right” and “wrong” in a situation like this, it gets very philosophical!).

And there is another detail that I missed in my story, although I could tack on the following addendum to my tale of the stranger with the superpositioned names, so as to illuminate what I missed (and also explain what I just said about how the unmeasured Name does not actually exist, but remains as a “spooky” superposition until actually measured — just as Schrodinger’s Cat is both dead and alive until you open the box!).

So, in fact, you CAN get an answer on what the First and Last Names are at the same time from the stranger — BUT, the answers are not certain to be “accurate”! E.g., say that the stranger could remember what his various FN and LN outcomes were for the past hour; if you get him to give you his best guess regarding both his LN and FN in the present moment (when he has not had enough time to accurately check FN and LN individually — he’s just giving his “hunch”), he might say “Martin Russo”. You could then ask him a few minutes later what he did or how he felt during the moments when he was Martin Russo; and he will tell you very sincerely, “oh that was wrong, I have not been a Martin over the past few minutes” (alternatively, he could say that Russo has not come up as his Last Name during this time). But there are other times when you do this and the stranger affirms that his initial “hunch” about his Full Name was right.

So, the overall accuracy of a “joint answer” under Heisenberg Uncertainty is better than a random guess, but less than 100% certain. If you ask for only one name, you get 100% accuracy on one, and you are left to randomly guess about the other at that instant. But if you get a “measurement” regarding both names at the same instant, you get something like 50% certainty on both FN and LN (not exactly, the equations for this are complex). It’s better than random guesses, but still subject to some uncertainty, as can be proven over repeated trials.

WELL . . . hopefully that gives you a “rough feel” for the weirdness of quantum particles and their “mechanics”. The only way to really know what Heisenberg’s theory means is to devote many years of your life to learning and understanding complex, abstract mathematical ideas and techniques, and how they apply to what quantum physicists have thought and determined from a wide variety of experiments over time. But a rough analogy like mine can at least make the interested non-scientist realize that this stuff is not as weird and mystical as some people make quantum physics out to be. Things on the level of tiny particles are definitely different! But as in our world, there are still rules that they play by, even if there are also a lot of actions or movements that can’t be explained (unless the “hidden non-local variable” approach somehow turns out to be true).

Heisenberg’s principle is in effect another rule by which the uncertainty of the quantum world plays. As with the stranger and his many changing names, there are things about quantum world that are much like the “classical world” that we live in, and yet some things that go very differently.

Can there be a social lesson in all of this? To me, this is another way of saying that just because your group or society thinks about things one way, doesn’t mean that there aren’t other ways that also work in other situations. I’m surprised that no clever author has tried yet to do with quantum physics what Edwin Abbott tried to do with basic geometrical math in the novel “Flatland“.

Flatland is an imaginative short novel about living, conscious beings whose bodies are geometric shapes (squares, circles, triangles, hexagons, etc.) living in a 2-dimensional world. It was written way back in 1884. Flatland is considered to be a work of “mathematical fiction”, which is a very small genre. Most books in this category are stories involving human mathematicians; very few if any have non-human mathematical objects as the main characters, as in Flatland.

The geometric denizens of Flatland are social beings, and they have a way to perceive each other and to socially interact. As with humans in 3D world (or “sphere world” as Abbott called it), they also have their prejudices and social hang-ups, just like the Victorian society that Abbott came from. Perfect circles were presumed to be perfect; for everyone else, i.e. those having flat sides, the more sides you have the better. Triangles were the lowest shape (only 3 sides), and women weren’t even shapes! They were simply lines.

The shape and line people in Flatland were obviously not the most open-minded creatures out there. The narrator, a square, had a dream about another realm called “Lineland”, where every being was simply a 1-dimensional line (male or female). The narrator dreamt that was able to get in touch with the king of Lineland, but could not convince him that more than one dimension was possible (and almost got killed in the process). After that dream, a sphere from 3 dimension land somehow got into Flatland and appeared before the square. It took a while, but said 3D sphere managed to convince the 2D square that another dimension was out there. The square has his epiphany, and conveys this info to Flatland’s leaders. The are convinced, but they see 3D thinking as a danger to the state, and prohibit anyone from preaching about extra dimensions.

Abbot meant this book to be a social critique of the closed-mindedness of Victorian England. So I wonder if an imaginative author could write a modern story about quantum particle beings, and use them as a way to reflect on our current social problems and controversies. Yes, I wonder what a writer could do with Heisenberg’s uncertainty? (You have just read how I tried to fictionalize it.) I.e. with the constantly changing position and energy that particles experience, along with their changing waveshapes as a result of on-going interactions with other surrounding particles and their field-waves. How would this author imagine a world of field-particle complementarity (aka “wave particle duality”)?

And so much more in this strange, and yet in some ways recognizable world . . . what about the entanglement and loss of entanglement of particles? What about the fact that dark matter doesn’t want to interact with most other matter and energy (aside from the mysterious gravity particle and field)? What about the rare and mysterious weak-force bosons? And the dangers of meeting up with one of your own anti-particles? And quarks, which dance freely around each other exchanging gluons, but can’t wander too far away from each-other (the only way to separate them is to use so much force that a new partner quark is created)? And virtual particles, which continually appear from nothing and quickly vanish? What if all of these critters had a mind and a voice – what would they say and think in their various interactions? What would their society be like? What would they realize, and what would they miss? Could they tell us anything about ourselves and our social world, just as Abbott’s Flatland shapes once did?

I hope there is a literature major-turned-physics grad student out there who might be up to this task! A web search didn’t turn up anything remotely like a quantum version of Flatland; I could not find an imaginary story of a society of sentient quantum beings. It’s a book waiting to be written – if someone could actually get their head wrapped around all of this! I hope that my own story of the “stranger from afar” with the changing names will provide some inspiration for a 21st Century sequel to Flatland.

(FOOTNOTE: There was something of a Flatland sequel in the 2001 book “Flatterland“, where Vikki the Line from Flatland is given a tour of a variety of wacky hyper-dimensional geometries by a “Space Hopper”; quantum reality is touched on during this tour. But there is no time for Vikki to dwell on the creatures living in the curved, hyper-dimensional spaces that Hopper takes her to, and how they imagine their reality. I feel that we need to ponder what a quantum social order would wind up believing!).

◊   posted by Jim G @ 7:23 am      
 
 


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