Quantum III: On Terrible Jokes and Cosmic Terrors

This is the third of three posts on quantum mechanics. See the first and second here and here, respectively.

I absolutely hate science “jokes”. I utterly, completely, despise them. Sure, they’re not all bad—but the overwhelming amount of them live in a weird space where the entirety of the punchline relies on a sense of smug self-satisfaction for knowing what the joke is referencing, making these jokes a great litmus test for finding out which of your friends is a pretentious tool that wouldn’t know comedy if it broke into their house and took their kids for ransom. To give you an example of this kind of crime against laughter, here’s a classic joke of this type (where I mean “classic” in the sense that the Hindenburg disaster is a “classic”):

Werner Heisenberg gets pulled over while driving. A cop comes over and asks, “Do you know how fast you were going?”

Heisenberg replies, “No, but I know exactly where I am”.

This joke is about as funny as dialysis. Medgar Evers may have said that you can’t kill an idea, but when it comes to this joke, God help me I can try. If the only way to get rid of the concept of this joke was to go back in time and prevent cars from ever existing, I’d get my jogging playlist ready in record time. This is a science joke in the sense that an Aston Martin made entirely out of compacted coffee grounds is a coffee machine.

But I digress; the point of this blog is not to point out bad jokes, but to explain what they’re referencing. And now that we’ve managed to get through the key conceptual hoops of quantum mechanics and what it can/can’t do in the previous entries, we’re in a good position to address this!

Let’s do a quick recap of what we’ve figured out so far:

  1. The universe doesn’t determine outcomes precisely, so the laws of quantum mechanics deal only with the probabilities of things happening.
  2. The way those probabilities change with time is -very- weird, to the point where we can’t describe this change using the typical method we’d use for probabilities in a non-quantum world. This is what causes quantum objects to be “glitchy” until you interact with them.

So really, the only thing keeping quantum mechanics from being a boring old theory about statistics like how you lose money in a casino is how those probabilities are changing over time! The question du jour is then obvious; what’s causing those probabilities to change over time?

Well, it turns out the core of what causes all of the weirdness in quantum mechanics is at the very heart of physics: energy! And, because it’s so important to the quantum world, let’s digress a little bit to talk about what we mean by energy. For the purposes of this entry, energy is just a number that depends on two things; how the object in question is moving, and how it interacts with everything else around it. As a result, energy depends on things like where other things are relative to the object, and how the object itself moving.

As it turns out, energy is incredibly important in quantum mechanics because an object not having a specific energy is precisely what causes all of its probabilities to change over time. And if the probabilities don’t change over time, then there’s no difference between the behavior of a quantum pencil and its classical, statistical, brother (boring!). Hence, the universe often not assigning specific energies to quantum objects is where all the properly crazy quantum stuff comes from.

Let’s take a look at one way this tidbit triggers a weirdness cascade throughout the rest of quantum physics by delving into an example. Consider a quantum teapot, zipping through a completely empty universe. In this situation, if we knew the energy of the teapot precisely, then we would know its speed as well; in an empty universe, the energy of this teapot is exclusively dependent on its speed and vice-versa. In addition—if you trust my previous statements—then the probabilities of the teapot’s observable properties shouldn’t change with time. If the teapot had, say, a 50% chance of being in position A when we measured its energy, then it should retain that probability for the rest of time.

But how could it? Remember, even though we might not where the teapot is, we know where it can be, and we know that it has to be moving with a specific speed that we can discern. So if we also knew that the teapot was in the neighborhood of position A, we know that it would have to eventually move away from the neighborhood of position A, and the probability of it still being in position A would now have changed with time, contradicting our previous statement!

Teapot 1

And no matter how much you play around with the information you have about where the teapot can be, there’d only be one scenario in which this wouldn’t be a paradox: if the teapot had the same probability of being everywhere, in which case the concept of position doesn’t have any meaning at all. It would become some kind of cosmic entity, omnipresent, eerily lurking in a “glitch” state, steadily moving through a desolate universe of itself where movement has no purpose.

Teapot 2

Scary, right? Welcome to quantum mechanics. This innate relationship between the nature of position and velocity, combined with velocity’s connection to energy and energy’s connection to changing probabilities, are what leads to that “Heisenberg uncertainty principle” hoopla everyone keeps talking about when they try to explain the punchline of their unfunny jokes to you. And trust me, all the other weird stuff you hear about in quantum mechanics pops out of similar thought experiments to this; marrying this little energy-time change connection with other boring classical physics results, such as velocity being the rate of change of position in the example above.

With this in mind, I’ll discuss just one more quick example. The central tenet of all physics (and you definitely don’t want to mess with that) says that the energy of an object which isn’t exchanging energy with some other object is constant in time—energy can’t just spontaneously appear or disappear. This naturally implies that, once we know the energy of a single isolated object, it can’t change from that value the next time we measure it. As you can see from the previous example, this puts a lot of restrictions on how such an object can behave—and in more realistic and restrictive situations than the empty universe above, only specific energy values yield probabilities that are consistent with the extra restrictions imposed by the environment. And as you can probably surmise, this means you very often can’t find an object to have just any arbitrary energy after interacting with it, only specific values of it; this is the historical hallmark and experimental mine canary of quantum mechanics.

That’s enough for now! I’ll conclude this entry by providing you with a science joke of my own:

Werner Heisenberg gets pulled over while driving. A cop comes over and asks, “Do you know how fast you were going?”

Heisenberg replies, “Now I do.”

He vanishes into thin air. The world feels changed; the colors off, the hues subdued.

The officer stares blankly into the empty seat. A nylon face forms in the seat upholstery; it whispers a single phrase.

“I am arriving.”

The officer begins to form the concept of fear. He vanishes before being able to do so.

Heisenberg has become the demiurge—he shapes and reshapes the universe as he sees fit. Stars die and are reborn in instants. Comets pulse in green and red as fractal Bauhaus palaces made of solid xenon crystals shatter and reform in the region once occupied by Saturn’s rings.

The Earth and its inhabitants fluctuate chaotically in the same manner; an irradiated wasteland consumed by eldritch nightmares one second, a savannah of polygons dotted with wireframe people the next. They are none the wiser to their predicament, their collective consciousness a fleeting mayfly. They are beyond hope now—they are beyond most things.

Ohm resists.

Quantum II: On G̴̡̕͝l̷̛̀͝i̧̧t̶̡̕҉͞c̀̕h̨̛̀͟e̸̶̡̕ş̴͡͏͞

This is the second of three entries on quantum mechanics. Read the first here.

Now that I’ve spent some time talking about how other people get quantum mechanics wrong, it’s about time I get my own chance to screw it up. Following the set of arbitrary rules I laid out in my last quantum mechanics entry, I’m going to start by listing some things you cannot do with quantum mechanics:

  • You cannot influence the universe by thinking about something.
  • You do not have a chance of spontaneously teleporting to Mars.
  • Your ex does not have a chance of spontaneously teleporting to Mars.
  • You cannot travel into alternate universes.
  • You cannot travel faster than light.

This can all be summarized by stating:

  • You cannot do anything impossible in “normal” physics using quantum physics.*

If you retain anything from reading this post, let it be this! Also, see that asterisk? I did say before that I’d alert you whenever I said something that is debatable, and that’s what I’m doing there. But fear not, I’ll explain it all in fine print at the end of my third QM entry; ignore it for now.

Anyways, given that little postulate stated above, you may ask what the difference between quantum physics and normal physics is. Well, back in the Renaissance, the prevailing notion was that the universe was like a complex mechanical computer; that given the state of the universe as it is now, the laws of physics would procedurally generate every future state without any ambiguity. Another way to describe this is that you could always predict everything that’s going to happen in the future if you knew everything about the universe right now. However, the basis for quantum mechanics is that this is false and you should feel bad for thinking that!

The basis of quantum mechanics is that the laws of physics are fundamentally incomplete. For certain situations, the laws of physics don’t say what should happen specifically, only what can and can’t happen. An intuitive example of this is standing a normal pencil on the pointy end; after letting it go, it will inevitably fall down, but there’s no obvious preference of direction in which it will fall down to. What Renaissance physicists would counter with is that knowledge of the pencil tip shape at the microscopic level and the motion of the air molecules in your room will always tell you how the pencil will fall down—and that is absolutely true, with the caveat that it is functionally impossible to obtain that information.

Pencil

The real problem appears when you go down to the smallest scales of the universe, to a single isolated particle (or a few); there’s no hidden features there, no “tip shapes” or other properties to rely on when the laws of physics don’t explicitly tell you what’s going to happen. Of course, there are no subatomic pencils, but there are multiple processes in the quantum world (mostly involving radioactive decay) that preserve that feature of not having a precise or well-defined outcome.

This leads to two critical questions, the first being pragmatic and the second philosophical:

  1. What do these objects do when the laws of physics don’t determine their specific future?
  2. What do these objects become when the laws of physics don’t determine their specific future?

The answer to the first question, which may or may not be intuitive, is that they’ll do one of the things the laws of physics say they can do! Our quantum pencil will fall in one direction sometimes and another direction sometimesand the best we can do is quantify those probabilities using experiments, develop some physical laws for those probabilities based on our data, and that’s that.

If you think about it, there isn’t really anything quantum-y about that at all. This is exactly the way we’d try to describe the physics of our normal pencil falling down; setting it up to fall down a bunch of times and recording the different outcomes to guess the probabilities of it going one way or the other. This is so ubiquitous in the world of science that it is its own long-standing field of physics: in short, bo-ring!

Where things get spooky is when discussing the answer to the second question I presented above. See, for normal objects, not measuring what state they’re in doesn’t affect anything about the probabilities in which you can find them. When the normal pencil falls down and you’re not around to check on it, you can still say it fell down to some specific position; you just don’t know which until you check. For a quantum pencil, this can’t be true!

This is due to the fact that, for objects with no specific future defined by the laws of physics, the probabilities of its possible outcomes can affect each other. This is completely insane! For a quantum pencil, the fact that it could fall to the right can affect its probability of falling in every other direction*. As a result, the chances that a quantum object will behave one way or another can be affected by when and how you interact with the object as you check its status! (The precise way in which those probabilities affect each other is so tricky that they not only needed to describe it indirectly by instead describing a related quantity, but they also had to use imaginary numbers to be able to describe that.)

For this reason, we can’t really say the quantum pencil exists in the same way a classical one does before you interact with it. In fact, it is literally impossible to comprehend it traditionally since it violates one of the three classic laws of thought! For the purposes of our brain, when the quantum pencil falls down and you’re not around to measure it, it’s in some weird glitch state until you interact with it, where you’ll find the quantum pencil fell down either to the left or right just like the normal one would.

Pencil 5

To illustrate this difference from a philosophical point of view, let’s say that I was an amoral psychotic and decided to link the life or death of a cat to the direction in which a normal pencil is falling down. If the pencil falls to the left, the cat lives, while if the pencil falls to the right, the cat dies. I, meanwhile, am getting some coffee as this insane little experiment is going on.

At some point while the barista is preparing my ristretto, the normal pencil falls down and the cat either lives or dies, and will remain in that state as I go check on what happened with hot coffee in hand. Nothing weird here (other than the part where cats are dying).

Pencil 2

Now we replace the normal pencil with a quantum one and observe that, because the life and death of the cat depend on the state of the pencil, the cat gets put into a glitch state too after the quantum pencil falls down! As a result, I can’t really say anything about whether or not the cat is alive or dead until I go check on it. (This is a very famous thought experiment). Also worth mentioning is that in normal physics, this linking of statistical outcomes between pencil and cat has a name, but in quantum mechanics they call it something fancier even though it’s functionally the same thing.

Pencil 3

If we want to make things really interesting, we can extend this experiment a little bit. Let’s say that, when I look at the cat post-pencil drop, I have an emotional reaction that differs based on what state I find the cat in. If it’s alive, I’m happy, and if it’s dead, I’m sad. Now let’s get a bit meta and say that some AI that can detect emotions is experimenting on me experimenting on cats, and that it was installing some Windows update until after I see the outcome of my experiment. In that situation, from the point of view of the computer, both the cat and me are going to be in a glitch state until it checks what emotion I’m feeling; even though I am clearly seeing the cat as being either alive or dead!

Pencil 4

This means the strange glitchiness is totally dependent on frame of reference and independent of whether or not something “conscious” is measuring things! This isn’t the first time we’ve run into this craziness, but it does have a lot of philosophical juice in QM that people love to spend hours debating on (presumably while getting high on something). As a result, and this is a thing a lot of people get wrong, human consciousness does not affect quantum mechanics.

Alright! That’s enough for one quantum entry. In the next one, I’ll discuss some more cute examples of counter-intuitive behavior in QM and keep trying to stay on my mission of making quantum boring again. Wish me luck!

Quantum I: On Being a Former Crackpot

This is the first of three entries on quantum mechanics.

I have been trying for quite a while now to write something on quantum mechanics, but QM is a notoriously difficult thing to deal with in pop-sci. There is perhaps no more misinterpreted field of physics than quantum physics, and any informal talk of the interesting things that quantum mechanics can do will inevitably lead to comments or questions involving things like parallel universes, teleportation, the nature of consciousness, and so on. Unfortunately, these questions tend to be less about learning quantum mechanics and more about reinforcing misguided opinions about what people already think quantum mechanics is. As a result, for my first QM entry, I’m going to do something a bit peculiar and talk about the difficulties of writing about quantum mechanics rather than write about quantum mechanics itself. (Meta, I know!)

You see, quantum mechanics, thanks to its esoteric charm and strange predictions, serves as a magnet for all sorts of kooks and cranks who are raring to tell you that all your problems can be fixed with a quick dose of quantum snake oil. The reason they get away with this is two-fold:

  1. Most science advocates have marketed quantum mechanics as an exotic otherworldly concept where “impossible” things happen.
  2. All simplified descriptions of quantum mechanics are bound to be missing something essential.

The first is a regrettable but expected consequence of trying to get people engaged with physics. Just like everyone going into acting dreams of being the next big Hollywood star, most would-be physicists started getting into the field because they thought they’d figure out the secret to time travel/teleportation/etc. and saw quantum mechanics as their “in”. (This sometimes being because a book by [insert pop-sci author of choice] talked about things that sounded like that).

The problem with this is generated by those who decided not to continue their interest in quantum mechanics through formal study, and proceeded to take all the fanciful metaphors and simplified explanations in these books literally. Then they see someone famous tell them that they can improve their life through some weird mystical quantum nonsense, conclude it matches more or less what they read in those pop-sci books, and get reeled right in.

I am intimately familiar with the allure of this quantum quackery because I was one of the suckers who fell for it! In fact, the entire reason I got into physics in the first place was because, when in high school, I watched a “documentary” on quantum physics by what I later learned was an insane cult whose leader believes she can psychically channel a Lemurian warlord from 33,000 BC. (I’m not kidding.) It was only after I had made several science teachers worried about my opinions and took a proper look at quantum mechanics that I realized how much of a moron I had been. I still remember the look* on my physics teacher’s face when I told him that people can control the molecular structure of water with their thoughts.

*It was a liberal mix of Vietnam war flashback thousand-yard stare and that face you make when you find your dog took a dump on your carpet.

In fact, why don’t you take a look for yourself! Watch Academy Award-winner Marlee Matlin really earn her paycheck by listening to a Liza Minnelli lookalike tell her about how saying nice things to water can make it “better” (and also through getting hit on by who I can only describe as the used car salesman version of Cipher from The Matrix).

Seriously, the only thing that could have made that guy creepier is if he pulled out a ticket wheel and offered her a VIP pass to climb Mt. Baldy. But I digress.

It’s worth noting that the reason I got suckered into believing this garbage is precisely because nothing that anyone said in this fake documentary sounded at odds with what I had read in pop-sci books. In fact, every single book talked about what QM could do and no one talked about what it couldn’t do. So I’ll jot that down as one of my tenets for my following entries on QM; explicitly lay out what quantum mechanics can’t do.

The second item on my list is a more fundamental result of the difference between the language of mathematics and conventional spoken/written language. Just like there are certain words in other languages that are untranslatable to English (saudade, hygge), most of physics is not fully translatable into any verbal language. The most we can get away with, as is the case with the words above, is to try and give our best attempt at nice albeit incomplete explanations of it. If that wasn’t the case, why would we even bother putting up with math at all? Physicists could just learn everything we needed to know through blog posts like this one instead of expensive math-laden textbooks! And like the meal descriptions at your local dodgy Chinese buffet, when things are hard to translate, you usually wind up getting at least a little bit of nonsense.

Bad_Translation_2

The people who tend to succumb to this the most are philosopher types who want to associate the concept of quantum mechanics to some particular metaphysical or philosophical viewpoint. And that’s totally fine! In fact, all of science was originally conceived for this particular purpose; that’s why it used to be called “natural philosophy”. But the necessity of learning the mathematics that QM is written in to make that sort of argument is paramount. For example, I once had a discussion with a philosophy student that went something like this:

  • My work is on relating quantum mechanics to philosophical principle x/y/z.
  • Wow, you should find a way to argue it using the mathematical formulation of QM!
  • Well, I’m not really interested in learning the mathematics.
  • Then you’re not a good philosopher.

Prickly, I know, but trying to argue philosophical viewpoints in QM without using the math is like getting an orchestra to play Strauss’s Also sprach Zarathustra by humming what they should play to them without any sheet music. It is, although theoretically possible, hilariously time-consuming, and almost certainly going to sound like this.

Does that mean that all pop-sci descriptions of QM are useless? Of course not! But what it does mean is that all pop-sci descriptions of QM are going to be incomplete, and the best that us pop-sci writers can do is to point out those missing pieces in our write-ups. So let me put that down as my second tenet: I am going to tell you what parts of QM I haven’t explained or don’t fit my analogies. Essentially, if you can’t spot the mistakes in your pop-sci explanation of quantum mechanics, the mistake is that you’re explaining it.

In short, what the next two entries will represent is not an attempt at describing quantum mechanics correctly, since doing that is impossible without talking about Hilbert spaces and probability amplitudes and whatever. What it is is an attempt at explaining quantum mechanics as best as I can while following the two little rules I set up for myself:

  1. Explain what quantum mechanics can’t do.
  2. Explain what’s missing from my pop-sci description of quantum mechanics.

It turns out that, once you establish one or two mind-boggling things, everything else is fairly obvious! In fact, if after reading these entries you come away with the idea that quantum mechanics is boring, I will have been doing my job.