Brett Rants

The Quantum Universe Explained

So That Even Someone Like You Can Understand It

Though, not without a long aside into the world of the Maybe Monad, which maybe (get it) is a bit... um, superfluous.



Determinism means that something is computable (i.e. Determinable), stochastic means random, unpredictable, or probablistically based, I probably will discuss this image in depth later down the page, so best to wait until that happens prior to asking/answering too many questions


See? Simple...

Let's Start With Some Basic Information Theory

Information is data. It is something that a human knows (and/or something a human believes that they know, as plenty of humans hold plenty of incorrect beliefs, as humans are want to do) and which (so, my definition has two parts; one of which being that data) can be communicated to another human being (which is to say, I am excluding that which is ineffable from my discussion). Thus, data includes all human created artefacts, including words, text, music, sound, images, graphs, figures, movies and so on.

All such artefacts (and in fact, everything in nature) can be digitized. Everything on The Internet has been digitized. So, that covers almost everything on the list right there. And for the remainder, one can create an arbitrary long string of zeros and ones which encodes the state (velocity, motion, direction, and so on and so forth, et al, including position, charge, and spin, as needed and ad nauseam) of any and all sub-atomic particles which comprise the artefact in question.

Thus to the extent something can be knowable, it can be encoded as zeroes and ones.

Unfortunately, not everything is knowable.


The Limits of Knowledge

At some point in the slicing and dicing of The Universe, one invariably (yes, invariably) reaches a point where further information is unobtainable.

Usually, this point is reached when the limits of measurement and recording are reached. Scales are only so accurate. At some level of enlargement, photos get fuzzy. And sound recordings only have so much fidelity.

At which point, the string of zeroes and ones in the data stream start to include unknowns: 0100?1??001???...

The question marks (in the preceding data stream) indicate unknowns. And in the Classical View of Things, every last question mark is the result of human error and limitation. However, in the Quantum Mechanic View of Things, at some point of fidelity (say, when looking at the shower of quarks, which results when a boson particle is hit with a semi-polarized field of modularized gamma-energy... or some such nonsense) the question marks are an inherent part of reality.

Classical Universe: question marks exist because humans are, well, human. The ? is in point of fact either a zero or a one, but which one is not known by the human observer.

Quantum Universe: question marks exist because that's the way it is. It's not so much that God doesn't know whether the data point is a zero or a one, as God simply hasn't yet decided which one it is to be: i.e. The Universe is a work in progress.

Or to put it more succinctly, it is convenient to use question marks alongside zeroes and ones when encoding The Universe.


Monads Are So Simple As To Be Trivial

Much is made of Monads in the world of Functional Programming. Monads have been likened unto burritos... likely, by someone who was hungry and suffering from malnutrition at the time, as Monads are nothing like Burritos.

Monads are, in fact, quite simple.

A Monad is a Singleton Set (i.e. {*}) whose only possible operation is The Identity Function (i.e. ), which is a fancy-smancy mathematical way of saying 'A Monad is a Monad is a Monad' and/or 'A Monad Maps to itself and nothing else.'

If x is a Monad, then the only mathematical operation available to x is f(x) and f(x)=x.

As a sidebar, this is of interest to Programmers, as it allows non-state-changing side-effects like printing to screen.

def print_monad(x):
    print x
    return x

def display_monad(x):
    display x
    return x

Now, the above are not really Monads, as they have side-effects (print and display, respectively). But as state doesn't change (i.e. the output is the same as the input and no variable has been changed on the sly), nobody really cares. Or to be more accurate, the folks who care about Monads don't so much care about print or display, as they care about the state of x (and all the other variables in the program) remaining unchanged by the operation.


The Maybe Monad: One Monad To Rule Them All

OK. Sure. Monads are simple. They're basically dots (a point of datum) with a single arrow that points back to itself (welcome to the exacting world of Abstract Algebra). But Maybe Monads are a whole different ball of wax. And they, oddly enough, are almost exactly like burritos.

Ha-Ha!

Just kidding.

Maybe Monads aren't much more complicated than any other type of Monad.

Stated simply, a Maybe Monad might have a value and it might not (hence, the maybe part). But once a Maybe Monad has a value (if ever it does), that value will never change (like, never-ever-ever).


FINAL_GRADE(at_semester_start) = unknown
FINAL_GRARD(after_grades_post) = A+

A Binary Maybe Monad
    returns 0 if 0
    returns 1 if 1
    returns 0, 1, or ? if ? 
Note: The return value for ? is not randomly decided. Rather, the return value for ? is chosen from the set {0, 1, ?) according to predetermined rules based on the type of Maybe Monad being utilized.

In my experience (limited as it may be), Maybe Monads are invariable used to store the value of a variable which may or may not be known. And hence, Maybe Monads are perfect for forward looking statements whose values will not change once they are, in point of fact, known.

If there is a conceptual trick to the Maybe Monad, it is in realizing that mathematicians cheat left and right... only, they don't call it cheating. Sure, there is a difference between a ? and a 0 or a 1. But once the Maybe Monad resolves to either a 0 or a 1, the value never changes. So really, another way of looking at the ? in a Maybe Monad is that there are two types of ? (?→0 & ?→1) and until the ? resolves, we don't know which one we are talking about... not just yet, anyhow.


Unfortunately, There Ain't No Maybe About It

So, any bit of information (say, the composition of a Universe) can be reduced to a string of zeroes and ones.
    1010 0011 1100 0000...
That is, of course, assuming one knows all there is to know about said Universe. Otherwise, there will be unknowns.
    ?010 0011 1100 00?0...
Perhaps, a lot of unknowns...
    ???? 0??1 1??0 ????...
Perhaps, mostly unknowns...
    ???? ???? ???1 ????...
Classical Mechanics views those unknowns as relating to the limits of the human condition: that with enough knowledge each and every ? would reduce to either a 0 or a 1.

Quantum Mechanics doesn't so much disagree with that whole Limits of Human Observation Thing as add in the additional caveat that some unknowns cannot be known no matter what one does, that some ? are simply ? and always will be, not because of human limitations, but because that's The Nature of The Universe.

In short, The Universe Thinks In Unknowns.

It's not a limitation.

It is what is.

{And yes, even ???? 0??1 1??0 ???? can be encoded (just like everything else) in binary simply by replacing each 0 with 00, each 1 with 11, and each ? with 01 or 10.

Also, there's no real reason to believe The Universe thinks in Binary. It more likely thinks in Quark, Muon, and so on, if you know what I mean, which the longer I write seems less and less likely.}

And now that I look things over, I think that brings us right back up to the top of the page.


Let Us Begin Anew




The Same Image as Tops The Page


Remember This?

The Classical Universe

In a Classical Universe, The Universe knows itself. There are no unknowns. There exists absolute knowledge about position and momentum. And since there are deterministic (i.e. absolutely predictable) rules about how The Universe functions, the future is knowable (to anyone with sufficient knowledge, say an omniscient being).

In the above, the vertical red line is the here and now with the red disk being its view in cross-section. The shapes are arbitrary and of little importance. Though, you know, they make sense to me.

The black lines radiating away (and/or projecting) from the red disk (fore and aft) represent a future (and/or past) that is predictable, absolutely knowable (once again, to any omniscient being), and set in stone. Personally, I like to think of The Deterministic Universe as Crystalline. But that's just me.

To the standard view (aka interpretation), I would just throw out (i.e. add) these additional ideas.

First, knowable state does not imply knowable or predictable rules. I mean, one of the reasons Quantum Mechanics came about was because of the unpredictability of The Universe. So, even if the current state of The Universe is knowable, that by itself does not prove pre-determinism... even if that is the Classical Paradigm.

Secondly, even if The Rules of The Universe are completely predictable, that does not imply the past is knowable, only the future. Suffice to say that many mathematical operations are uni-directional and provide little information about their inputs. If f(x,y)=42, one knows The Answer, but little has been revealed about the inputs x and y (or the way the function actually works). More concretely, when two bodies collide, while it is true that momentum is conserved, the final state reveals little about (or at least, it does not contain complete information regarding) the pre-impact motion of the initial bodies (on account of any individual momentums being added together, a process which cancels out opposing forces: e.g. 1++1-=0).

But for the most, these last two points are throwaway asides. In the Classical Model, The Universe is Known.


The Quantum Universe

Conversely, in a Quantum Universe, not much is known, at all.

Sure, we have the same red disc. But it is a disc full of holes... or as I like to think of it, it's a disc on fire.

And as to the future, it is an unknown. Sure, we could have a future as indicated by the black disc, somewhere on the Deterministic Line... or anywhere else within the bounds of the solid blue lines, which define the edges of Probable Reality. But absolutely (that is to say, with any degree of precision), the future is unknown and unknowable.

And for the most, the past suffers from the same indeterministic (as in, not deterministic, better known as stochastic) fate.

Essentially, the present is not knowable, as even The Universe does not know what it is about. So, good luck knowing either the past or the future.

And like I said, when it comes to The Quantum Universe, I've come to think of it as a disc on fire, burning as it turns, with no past to call its own nor any future to make its home.

It simply is an Eternally Burning Flame.

And truthfully, I wonder if there is much more to it than that.

{In other words, if one were to make a copy of a Quantum Universe (not sure how one does this), the unresolved unknowns remain unknown (even to The Universe itself), so they would be free to resolve differently in each individual copy of a Quantum Universe. While in a Classical Universe, each copy would forever after remain identical.

Classical Universe = Copy of Classical Universe

Quantum Universe ≠ Copy of Quantum Universe

Ah, I Maybe Should Have Said This First

This is the part of the essay (or should that be web-page) in which I wonder if I haven't gone astray. I mean, that was a pretty long foray into Monads. And is it just me or do Monads seem to be quite beside the point? Also, I'm not exactly an expert on Quantum Theory. I have no doctorate. And as it happens, this post is primarily the result of awakening the other day and for whatever reason thinking (and/or musing) for an hour or two about Quantum Mechanics. So, like, I might as well be saying this post is based upon a dream.

Here.

Let's start over.

Want to know what I really know about Quantum Mechanics?

It's simple.

According to Quantum Mechanics:
And having utilized a bullet point list, you just know I'm getting serious... now.

Of course, I'm not so serious (nor ever will I be) that I won't start another bullet list (like, right away) to illustrate some of the conceptual problems with the aforementioned bullet point list.
So as far as I am concerned, there really is no reason to believe The Universe obeys Quantum Mechanics. All effects can easily by explained (as I just have) as being by-products of the human condition.

Thus, Quantum Mechanics may not be so much inherent to The Universe as inherent to its occupants.

This may not seem like a fine-line distinction. But it is. It's the difference between truth and folly.

But then (quite ironically), it likely makes little difference... at least, for one such as me.


Ignorance Is Bliss
and/or
What You Don't Know Can't Hurt You

You will never know Truth. I mean, I might. Heck, I probably do. But you? You will (most definitely) never know Truth. You will forever flounder around in the dark. Oh, you might die. You might even get into Heaven. But is it The Real Heaven? Or that Fake Heaven where they put folks like you? You won't know. You can't know. And you never will.

That's the place (A Mathematical Purgatory, if you will) in which I find myself when it comes to Quantum Mechanics... or did.

It was always, "Is this real or not? This can't possibly be the way The Universe Works. I just doesn't make any sense."

And then one day, I just stopped caring. I was like "Whatever." And it wasn't even a strongly emphasized Whatever! laced with emotional overtones. I didn't say "Whatever!!!" throwing an exclamation mark (or two or three) at the end for emphasis. I was just, like, "Whatever."

Mathematician do that a lot (say, 'Whatever!' and/or throw their hands up into the air in disgust and despair) as they come to learn (from reading proof after proof which does the same) that any model which meets the prescribed restraints is good enough. If it works, it works. And Quantum Mechanics works... mostly because it allows us (that being the cool kids and myself, and you too, if you want to join us) to use Quantum Mathematics.

And Quantum Mathematics is just plain cool... because it ain't got hardly any rules.

Yeah, baby! We use stochastic Mathematical Principles. And that Deterministic (1+1=2) Math Crap just doesn't cut it with us.

But as I think I covered that particular subject (The stochastic Mathematical Principles that all the cool kids are using) in my previous post on Quantum Computers (some time back), I think I'll end the discussion on that particular topic right about here and simply say:
The Universe IS (and since I made that not only bold but underlined it as well, using all caps to boot, there is absolutely no point in arguing the point) a disc (please see The Disc World Anthology by What's His Name for a complete discussion on the subject) fated to Burn Eternal (in High Quality Flame, no less), making me wonder (at the very end, right here, in fact) if I'm not really in Hell (condemned to suffer in my own lunacy for Crimes Against Nature and Mathematical Heresy, as must all who read my words). Still, one might as well make the most of it while we are here.
Sorry, I got carried away with the asides there.

Suffice to say, The Universe is what it is and any Mathematics that comes close to modelling it is good enough (at least, until further information comes along), so don't worry your pretty little head about it.

{Prior to dismissing my cavalier attitude, one might wish to consider Dark Matter and Dark Energy: constructs whose sole justification can be found in the insanely vast divergence between the values predicted by theory and those actually observed. Dark Whatevers are very much a case of Fake It Until You Make It.}



Questions!
Questions!
Questions!


[[? ? ? ? ? ? ?]     [[? ? ? ? ? ? ?]
 [? ? ? ? ? ? ?]      [? ? ? ? ? ? ?]
 [? ? ? ? ? ? ?]      [? ? ? ? 1 ? ?]
 [? ? ? ? ? ? ?]      [? ? ? ? ? ? ?]
 [? ? 0 ? ? ? ?]      [? ? ? ? ? ? ?]
 [? ? ? ? ? ? ?]      [? ? ? ? ? ? ?]
  [? ? ? ? ? ? ?]]     [? ? ? ? ? ? ?]]

Now that we all know Quantum Mathematics is just a game, the question becomes where do we go from here? What might the Advanced Rules look like?

Topology

Given that there exists a minimum constraint on both Space and Time, I wonder the geometric shape of this minimal construct. My guess would be some sort of Four-Dimensional Sphere. But it doesn't have to be. Of even more interest is how the individual pieces fit together. Personally, I visualize it as a Graph (of the type consisting of Nodes and Edges). But I haven't the slightest idea how many Edges go with each Node, how they fit together, or whether the whole is dynamic or static. See? Lots of questions.

Ideal Data Structure

The Universe, likely, does not think in the same terms as humans. But given that it does, what would be the simplest most concise Data Structure in which to organize Quantum Data. Given the Space-Time Graph discussed above, filling the Nodes with mass and so forth makes sense. But since the average Space-Time Coordinate is likely devoid of information (basically, I'm calling The Universe stupid at this point), I think a Sparse Matrix would be more appropriate. The two arrays that start this section are conceptual representations of this last idea. Though in truth, every zero or one would have to be replaced by a nested array or two. But that really is a minor point... and/or jumping far beyond the scope of this paper.

The Unknown

Given that most of the (theoretical) information in The Universe cannot be retrieved, I wonder if that doesn't imply it's not there at all. Well, it does, as that's the whole reason I discussed the Maybe Monad. But what I really mean is I wonder if the Maybe Monads themselves are not implied and are artefacts of the mathematics being used rather than The Universe being studied. Eh, I've probably covered this already, as my mind sort of loops around going back to what I have already covered (i.e. the difference between Classical and Quantum Mechanics). Anyway, the base realization is the existence of the possibility (so, I don't really see how I could qualify that any more) that there exists (which there most certainly does by current Quantum Theory) a local maxima of information. Hence, Sparse Matrixes. But given a local maxima, who is to say there is not a local minima? And by combining the two, I think one (maybe you, but probably not me) could come up with some sort of Sub-Quantum Classical Theory or Sub-Quantum Quantum Theory in which the Quantum Effects we see are artefacts of lower lever processes. Eh, suffice to say, we do not know that beyond which we know. And as such, any theory which groups the unknowns (as say Quantum Theory is reported to do) may be of service.


In Short, What Can Be Known About The Unknown?

  1. What's the minimal theoretical observation?
    • It can't possibly be a single bit.
    • So, what is it?
  2. What is the distribution of information?
    • Is there a local maximum of information?
    • Is The Universe mostly composed of unknowns that even The Universe does not know?
  3. For that matter, are any and all unknowns simply an artefact, in that, what there is of The Universe is completely knowable and what's seemingly an unknown is simply something that is not there?
  4. And finally, are humans Strange Attractors for Information?
    • Likely not.
    • But wouldn't it be cool if we were?
      • And really. If not Strange Attractors for Information, perhaps we are (or at least, I am a) Strange Attractor(s) for Misinformation.
And with that, I have covered much more than I had originally set out to do, which was merely to annotate an image (as posted once again below) as quickly and expeditiously as possible.



The Same Image as Tops The Page


I really should lay off the Hard Dru--... er, I mean, the Hot Chocolate. I think its having a deleterious effect on my cognitive ruminations and ability to focus.



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