What are the origins of the Heisenberg Uncertainty Principle? Is there any way to cheat it? What does this all have to do with waves? I discuss these questions and more in today’s Ask a Spaceman!
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I want you to imagine standing on a beach, watching the waves just roll on in. Why? Well, one. Because I could really use a beach vacation. And I hope you take me with you in this imagined world of ours and so we can enjoy it together. And two. It's a metaphor, but but not really a metaphor, because it's a real thing in and of itself. But it will also help us understand something that we can't imagine when we're standing around and watching waves roll in on the beach. So does that count as a half metaphor or I I'm not exactly, But it doesn't matter anyway. You're on the beach. It's a gorgeous day out. It's sunny and warm. Like I said, you're watching these waves roll in. You can hear it. Maybe there's a seagull or two. you got a drink in your hand. You The sun is beating down on it is just amazing. And because you're you and this is my metaphor, you decide to run a little physics measurement. You know, I'm I'm the one in charge of this fantasy. All right, so we're just gonna go with it. It's part it's part of the deal.
You get to go on a beach vacation, but you have to do some physics experiments. You decide you want to measure the wavelength of the waves. Wave length if you think of a wave, this Rolly upy downy thing and I'll describe waves in a little bit more detail in a little bit. But generally waves are these upy Downey things, and the distance between any two upy parts is the wavelength or the distance between any two downy parts is the waves repeat themselves, and then the distance a wave has to go before it repeats itself is the wavelength, and you're gonna measure the wavelength of these ocean waves washing onto the shore. To do this, you're gonna stand right on the shore, and you're gonna watch as the waves roll over you so the water might start at ankle deep, and then you'll watch it rise up to your thighs and then back down to your ankles. You know, like like waves tend to do, and it'll just keep going over and over and over again. So to measure the wavelength, you just need to watch the water go up and down on your legs for a while, and and so you can mark when it reaches like the highest point on your leg and then weigh it a little bit and then it will come back.
And then that gives you some sense of the wavelength and some measurement. But how long of time do you need in order to make this measurement? Well, let's say Let's say it takes 30 seconds for a wave to wash over you and then be replaced by a new one. So ideally, you would want at least 30 seconds so you could watch one whole wash of the waves come by. And if you had, like, 3000 seconds and you could watch wave after wave after wave, you could take measurement after measurement after measurement. You get super precise on this, but you don't need 30 seconds, right? As long as you can capture most of the wave and you generally know how waves behave because physics, Then you can reconstruct it and make a pretty solid guess as to the wavelength. Like if you watched it for 29 seconds, you're like, OK, I think I know when that crest of the wave is gonna come, and so you can use that to measure the wavelength. But imagine I only give you one second to watch the wins. Just one second. Just 1 1000. That's it, that's all.
You get to watch these waves, too. That's hardly any time. You basically have no idea what the wavelength is because you haven't sampled. You haven't studied the wavelength, the wave itself long enough in order to get a measurement of its wavelength. So it could be in that one second. You could have measured a very, very, very short wave and just happened to catch most of it. Or it could be a really, really, really long wave. And you've only measured a tiny fraction of it in that one second you you don't have enough information. But what if I gave you 10 seconds or 20 seconds? The more time I gave you, the better picture you would have of the waves behavior and then the more accurately you would be able to know the wavelength. There's a trade off there. The faster you take your measurement, the less you know of the wavelength, and the longer you take your measurements. The more you know of the wavelength, the more precise you are in your timing. The more narrow your window of observations, the less precise you are in the actual measurement.
Vice versa. And if you knew the mathematics of waves and you start noodling around with the mathematics and the equations, you could probably build some sort of relationship. Like, say, I don't know the uncertainty in your measurement time or the duration of the measurement time is related to the uncertainty in the wavelength calculation and vice versa. And unfortunately you can't have both. You can't have a super short measurement that happens as quickly as you want at the same time that you have an ultra precise measurement of the wavelength itself. So your measurement time, the amount of time you take to do the measurement, can be super duper, duper short. You can do it in a microsecond, but that's not gonna tell you anything about the wave itself, and vice versa if you take a really long time. If you take 10 hours to make this measurement, then your precision on the measurement of the wavelength increases Congratulations. You've just encountered your very own uncertainty principle. And we're talking today not just about any uncertainty principle, but the uncertainty principle, the Heisenberg uncertainty principle, which I have totally seen written as HUP or hup, which I just have an instinctual rejection of that acronym.
I don't know if it's just a personal taste thing. It's just when I see hop written on a page I I twi my eyelid twitches and I cringe a little and there's this muscle in my neck That's it's just not it. I don't like it. So today, and it just looks lazy. And today we're not gonna be lazy, and we're gonna call it the uncertainty principle. We're gonna use its full name out of principle. Was that a lame enough joke? If not, you can contribute to Patreon. That's patreon dot com slash PM, because your contributions get this show to be funnier, and that's worth it for everyone. So just like five bucks a month can make this show funnier for everyone, because then I can afford better jokes. I have to go in the bargain bin for jokes Here, folks. That's patreon dot com slash PM Suter. You also get access to ad free versions of the show, which is pretty cool. But mostly you're supporting science and better jokes. Anyway, the reason I did the whole watching the waves on the beach thing was a so we could get a little mental break, because I think we could all use it. And B, perhaps the most important thing that I want to communicate in this episode is that the uncertainty principle.
Yes, the uncertainty principle isn't special. It isn't unique. It isn't weird. It isn't crazy. And it's not just about quantum mechanics. Uncertainty principles come up in all sorts of physics and especially the physics of waves. And if you walked into this episode about quantum mechanics not expecting a lengthy discussion of waves and said, Well, then I'm I'm sorry, but this is just the way it is. If we want to talk about the uncertainty principle, we gotta talk about waves. And so let's talk about waves. Waves carry momentum and energy from one place to another. That's what they do. They're like a repeated pattern that is capable of transmitting energy and momentum from one place to another. If the sun sends light waves to you, it carries energy and momentum from the sun to your face. If I speak into this microphone, I am emitting sound waves. These sound waves carry the energy and momentum from my throat to the microphone.
Pick up and then eventually a speaker makes sound waves that you eventually hear. That's what waves do. Waves transmit energy and momentum. There are all sorts of waves out there. There are sound waves. There are light waves. There are water waves, but all waves involve some sort of displacement, which is the fancy physics term for wiggling around. So, for example, sound waves are what happens when air molecules start wiggling around and through their wiggling around. They transmit energy and momentum. So I breathe through my throat. My voice box vibrates, does its biological thing. It pushes on some air molecules. They push their neighbors. Then they push their neighbors. They neighbors, neighbors, neighbors, neighbors. This wave propagates out and people can hear me. Water waves. Same deal. You you know a hurricane happens in the central Atlantic. It pushes on that water. It creates a wave. The wave transmits that energy and momentum out to the shore. We have a few handy properties. We can use to describe waves.
Waves are pretty cool. There's an amplitude like how strong the wave is. There's a wavelength, the distance from crest to crest or trough to trough. There is a frequency, which is how quickly these crests come by you. All of these quantities are connected with a wave's energy and momentum. Momentum is gonna be a very important thing here. And if you have any idea already what the Heisenberg uncertainty principle is, you know that momentum is going to enter into this story. Waves are capable of not just transmitting energy, but also momentum. They can literally push things like If you stand in water at the edge of the ocean, waves can literally push you over. If I shouted at you loud enough, presumably I could also push you over with sound waves. Light waves are capable of pushing things. They carry momentum. It's not incredibly strong, but it's not zero either. So they count. Waves carry momentum, and the properties of the waves, like the wave length or the amplitude, tell us about the waves, energy and momentum.
So all of this is very neat, but also kind of boring. So let's make it a little more interesting. Let's do another experiment. We're we're still on the beach. No way am I leaving the beach yet. But last time we found that we have an uncertainty principle relating to the time it took to measure a wave's wavelength and how accurately we knew that wavelength. So now, instead time, let's look at space. I'd say. Now you're looking out over the ocean and you see this perfect picture, perfect set of waves. I mean, it's gorgeous. There's a crest of water like this line of water, all lined up perfectly parallel to the shore and then behind that, there's a dip. And then there's another rise behind that, with another crest perfectly parallel. And then another dip and then another rise. And on so and so on. Stretching from one end of the beach to the other, stretching all the way out to the rise and, like you couldn't draw a better set of waves, is just absolutely perfect. Where everything seems uniform, everything's in lockstep.
There is line of crest, wave crest, and then behind that is another line. Behind that is another line, and they're all equally spaced. And it's gorgeous. You're looking at something that physicists enjoy calling a plane. Wave it. They say that because it's pretty plain and boring hearts. That's another pun. I'm sorry a plane wave is PL a at. Yeah, never mind. I just can't help myself. So anyway, a plane wave. It's super easy to measure the wavelength of that plane wave that's stretching back to Horizon. All the wave crests are the same distance from the ones behind them, so you can just measure them like you can just stand there and break out your ruler and measure wave, crest to wave, crest and boom. That's the wavelength. It's as accurate as the ruler you brought with you to the beach for some reason, probably because you're like doing physic experiments on the beach. But here's another question like you got that way of, like, super easy boom, Where is the wave? Seriously, where is it like, if I was standing next to you and I asked you, where is the plane wave? You would look at me and then look at the wave and then look at me and look at the ocean and you just kind of shrug and gesture all around you say it's it's kind.
It's just over there, like Look, you can look to the left. It's all the way down there. You can look to the right. It's all the way down there. You can look all the way out to the rise, and it's way back there like the wave is just here. It's all over the place. It's one big wave. It's not like they're there. I can't point to it with my finger, but I can gesture. It's all it's everywhere. It's one big wave. Please note in your notebooks. If you're keeping notes for a plain wave, you could easily measure the wavelength. But you had a difficult time pinning down its position. So let's switch to a different kind of wave. A pulse? Yeah, like a pulse like poop I. I don't know. That's my best impersonation of a pulse we've we've all encountered pulse A wave pulses before. It's just a poop like I don't I don't know how else to describe it. It's a pulse. It's It's like a wave that looks more like a packet like there's nothing, And then there's something, and then it's gone again. We encounter these kinds of pulses all the time, and they sure are waves. I mean, they're wiggling and they're carrying energy and momentum, so that fits all the criteria of a wave.
I thought about continuing our beach metaphor because it's so lovely out there. But an example of a pulse of water waves is a tsunami, and that just didn't sound as much fun anymore. But if you want to pretend we're having this deep physics discussion as a giant pulse of water comes to destroy us, be my guest. So let's just make it a little bit more abstract, so we don't have to stare a tsunami in the face. We're just gonna talk about pulses, wave pulses. A pulse is super duper easy to locate in space is right there. Like if if you wanted to point in the tsunami wave coming in that wave pulse, You say it's right there, Paul, Come on, like don't you see it? And shouldn't we get to higher ground? If you see a wave pulse on a slinky, you can just point to it. It's moving, so you have to keep track of it. But it's like right there you can follow it. It's very, very easy to locate in space. You don't even need to gesture. You can just point. But what's the wavelength of the pulse? The wavelength of the pulse? That's a little bit trickier, because the pulse just has one shape, you know, it starts from nothing, and then it rises up to a peak and then shrinks back down to nothing.
And since wavelength means the distance from crest to crest and there's only one crest, the notion kind of breaks down. But when you dig into a wave pulse, you find out that it's actually made of lots of little waves, all working together to make the pulse happen. Some of these waves have long wavelengths. Some have short wavelengths, some have in between wavelengths and combined. Together, they all add up to make the pulse happen. So they combine together at the center of the pulse to make that big pulse, and then they cancel each other out at the edges of the pulse to make it go away. So that's how you, uh, how that that's how we understand a wave pulse is. It's actually made of lots and lots of little waves with all sorts of wavelengths. So for a pulse, we have the opposite problem. As for a plane wave, we know its location very well. It's right there, but we don't know its wavelength very well. So look at this tradeoff for a plane wave. We know its wavelength very well, but not its position.
And it's opposite for a pulse. There's this tradeoff between position and wavelength. Have I mentioned yet that the wavelength of a wave is related to its momentum? So when I say that there's an uncertainty relationship between position and wavelength, I'm really saying that there's an uncertainty relationship between a wave's position and its momentum. If there ever was an opportunity for a dramatic pause, this is it. Dramatic pause over before I continue, though I want to tell you about our good friends at the great courses. Plus, we all love learning stuff. I love learning stuff so much that is, one of my favorite parts of doing this show is all the cool stuff that I get to learn and then tell you about it. And the great courses plus gives us that form fuzz feeling in our hearts of learning. something cool every single day like this course, mind blowing science. It's created in partnership with Scientific American, and they explore so many cool topics like the first monster black holes, which we've talked about in this show, and the enduring appeal of Tic tac toe, which we have not but is also equally fascinating.
I want you to try the great courses, plus you get unlimited streaming access. You can learn virtually anything, and it's all thoroughly vetted. Fact based. It's real deal stuff. So you're learning stuff, and it's actual real information, which is kind of hard to come by online. I want you to go out and learn. Go forth, learn cool things, have a good time with the great courses. Plus, you get an entire month of unlimited access for free, but you need to go to special URL. It's the great courses plus dot com slash spaceman. That's right. The great courses plus dot com slash spaceman. Now, where were we? Let's take all this language about waves and uncertainties and go quantum. Here's the deal, and here's why. I'm talking about waves so much to talk about the Heisenberg uncertainty principle because this is where the language of uncertainty first came into quantum mechanics. It came in through the language of waves.
Once we realized that everything is a wave. No, really everything. Everything that you see, everything that you touch, everything that you hear, everything that you sense everything that you are made of is a wave. This is one of the big insights of quantum mechanics. You can't. You don't have these two separate worlds where there's particles over here with particle like properties and waves over here with wavelike properties. It turns out everybody shares something of everything. We call this the wave particle duality where you can, like, shoot a beam of electrons and pass it through some double slit experiments, and you get wavelike interactions between them, which which doesn't seem right. But it's the way the universe is. It turns out, everything just has wave properties it. The universe is not cleanly separated into particles and waves. It all mixes around big old stew. OK, fine. You can point to an electron and say, Dude, it's totally a wave, or at least partly a wave or a wave, depending on when and how you ask it.
But as some wavelike properties. But what is it, A wave of? In quantum mechanics, the wavy nature of reality describes the probability of where I might find a particle the next time I go looking for it. So when I say an electron has wavelike properties, it does have a wave associated with it. This wave tells me where the electron might be the next time I go looking for it. Remember, in quantum mechanics, you're never exactly sure where stuff is until you actually perform the experiment, the wave tells me where I can expect to find it. So places of high amplitude are the places of high likelihood of finding the particle and places of low amplitude are where I don't expect to find a particle the next time I go looking for it. And depending on the physical situation, you can change the wavelike nature of every particle, and that will change where you expect to find the particles. It turns out that an electron floating around or or zooming around If you prefer, however you imagine the subatomic world, it's up to you.
In the world of quantum mechanics, it looks like a wave pulse, just like our horrible tsunami wave analogy. If I shoot an electron at you, the probability wave associated with that electron looks like a pulse. It starts from nothing, and then there's a whole bunch of something, and then it's gone again. It's telling you like, Yeah, you're likely to find the electron like right there as it's moving around. But that wave pulse just like a wave pulse of water waves or sound waves is actually made of lots of tiny little waves that all conspire together to make that pulse happen. And just like the wave pulse of water, we can pin down its position. But we can't pin down its momentum. An electron traveling you can tell very precisely where it is, but you have a hard time telling where it's going, and this is something cool. You know what happens to pulses of water waves as they travel, They spread out because a pulse is made of lots of little different waves with all sorts of different wavelengths, and they all conspire together to make that pulse happen.
That alliance doesn't last for long because all these little waves, with all the different wavelengths, travel at their own speeds, and so slowly over time, these independent waves that go to make the pulse happen start to disagree. They're like some want to go fast and some want to go slow, and some are just fine the way it is, and and they start to argue a bit, and so the pulse widens out. That's what happens if you make a pulse of water waves. You can watch it slowly spread out, just like a pulse of water waves. You can have a pulse of probability waves, a pulse of matter, waves associated with every particle. And it means when you shoot an electron, it starts out highly localized in space. But you're not exactly sure where it's going. And as it travels, that pulse widens. The pulse, remember, tells you where you can expect to find the electron, which means as the electron travels, it gets harder and harder to pin down its location.
And that's a real thing that we can measure. And we have measured a consequence of the wave nature of particles. The wave nature of reality act like waves in any other situation, particles that travel you have a harder and harder time pinning down where they are as they move so right away, with a simple situation of just one ordinary lonely electron doing whatever it wants to do. We see a relationship between the knowledge of its position and the knowledge of its momentum. The more you know about one, the less you know about the other and it gets worse. Consider a slightly more elevated situation. Say electrons in an atom, right? All you know, when you go to measure electrons in an atom and do experiments is their energy level, right, because either you shoot light at an atom and then it makes the electrons excited and go up to higher energy levels. Or they emit light and the electrons drop down to lower energy levels. We call these energy levels orbitals, by the way.
That's all. You know, when you go to study an atom and an electron, you're like, OK, it's at this energy level. That's pretty much it. You don't know as much about its position or or momentum, so your picture of an atom is all wrong. If you happen to have a mental picture that involves an atomic nucleus, and then there are all these electrons spinning around them like planets around the sun. Except the orbits are all skewed like That's so wrong. And I can't believe that somehow became the symbol for all of science. Is this out of date? Incorrect false picture of what an atom really looks like. Atoms don't look like that. Atoms don't look like a little nucleus with these electrons spinning around them like planets orbiting a sun. That's not how it works. Instead, electrons in an atom are fuzzy. You don't know where they are until you look now, they are somewhat constrained because they are bounded to the atom.
But when you go looking, if you wanna know Hey, where exactly is that electron? How fast is it orbiting? Was it doing? You don't know until you go specifically looking for it. And then you just get a probability of where it might be the first person to point all this out with that. That just because you know, an electrons energy level in an atom doesn't mean you know as much about the atom as you hoped you would. The first person to point this out was Doctor Quantum himself himself, Werner Heisenberg, a character who will feature prominently if I ever get around to that series on quantum mechanics. I've been promising for half a decade now, but for now it'll just have to do. He realized that something funky was going on because of the wave nature of matter. So he saw in the development of quantum mechanics, he saw this. Hey, everything's a wave. And then, hey, because of this, maybe we don't know everything there is to know about observations like when we make an observation or a measurement of these electrons and these particles, Maybe we don't learn everything we thought we did because of this wave nature and anything with a wave of nature.
You run into these fundamental limits, and he first tried, tried deriving this and explaining this fundamental uncertainty relation. Given a simple measurement set up, let's say, let's say you have an electron sitting around minding its own business in your mission, should you choose to accept it is to measure the position and momentum of the electron as best you can. OK, in order to do that, you're gonna take a picture of it, right? You're gonna you have a beam of light that you're gonna shoot at the electron, it will bounce off of the electron and into your eyeball. And that will tell you where the electron is, what it's doing, where it's going, what its relationship status is. Just everything. But what kind of light do you use in this little electron microscope? One option is to use really high frequency light that will give you tons of precision because the wavelength of the light is super small and so you'll shoot it at the electron. You'll miss Miss Miss Miss Miss Miss Boom, and they'll hit the electron and then bounce up into your eye. And you're like, Boom, that's exactly where it is. I know it is because of that short wavelength. I'm really good at finding that electron.
But that high frequency light will have a lot of energy, and it will kick the electron right in the butt, something fierce instead of flying, ruining your knowledge of its momentum. OK, so maybe instead of high frequency light, you use like low frequency beam of light. And so instead of smacking the electron, you just kind of rub up against it suggestively like you just pour these low frequency, low energy radiation in, and they they brush up the against the electron, then they kind of make their way to you. And you're like, OK, OK, you barely budge the electron because you're not shooting it with high energy stuff, so you know its momentum really well, because, you know you haven't kicked it around, but that long wavelength, right, really only gives you a fuzzy picture of its position. The result is you can't have both as much as you would like. There's a fundamental limit if you multiply your knowledge of the position by the knowledge of the uncertainty, that multiplication, that new quantity can't be any smaller than Plank's constant Divided by four pi.
Why playing Wisconsin Y four. Pi Different episode That's the minimum. Your uncertainty of that situation can't get any smaller than that. That product has to be larger than that number. Now that number is very, very small, which means in macroscopic situations you don't really encounter it, but it comes about from the wave nature of matter, just like your uncertainty about waves in the microscopic world come about through their own wave nature. Yes, waves have a wave of nature, but this seems like in the way Heisenberg introduced it in the way it's introduced and talked about, like how I literally just talked about it. It seems like this is just a fuzzy measurement thing, not a real quantum thing that's baked into reality itself. It feels like we should be able to be clever enough to beat it like OK, Heisenberg's idea for, like shooting light electrons. Maybe we have a better way and we can get both very precise position and very precise momentum and that we're just missing something in all this quantum mechanics.
This was Einstein's big objection to quantum mechanics, one of them, which I've talked about before, and it turns out this really is baked in. This is not I wanna repeat this over and over. The Heisenberg uncertainty principle is not due to some sort of observer effect, where, in order to see something and measure it, you need to interact with it. And that leads to some uncertain. No, no, no, no. I don't want you to think of that. It's very tempting to think of it that way, but I want you to not fall into temptation. This uncertainty this relationship between the uncertainty and position and momentum is baked into reality itself. It is fundamental. You cannot ever design a clever enough experiment to get around it. You cannot outwit nature because this is how nature works. And to dig into that, we need to talk a little bit more about quantum mechanics because there's more than one way to skin a Schrodinger's cat. And the way of nature of matter isn't the only picture of the quantum world available to us.
I know, I know. I need to do the series on quantum mechanics. OK, it's coming one of these decades. A lot of quantum mechanics. You can describe it using this particle wave duality thing. There's another picture of the quantum world, which isn't really a picture at all. It's just a set of complicated math equations and relationships. We call it Matrix Mechanics because it's math based on matrices, and if you don't know what a matrix is, then don't worry about it because it doesn't really matter. It's just another mathematical construct. And approach to quantum mechanics is perfectly compatible, proven compatible with all the wave particle picture, Schrodinger Probability, all that kind of stuff. It's just a different mathematical formalism that makes a lot of calculations easier. The wave picture is very intuitive. Well, as intuitive as quantum mechanics can be, because we have so many wonderful analogies to the world of waves in our macroscopic existence, like that's how we arrived. That's how Heisenberg arrived at The uncertainty principle was by drawing analogies to what happens to real life waves that we can stare at.
But the Matrix picture of quantum mechanics turns out to be much more useful and powerful. It's actually the daily driver for the typical quantum mechanic, Uh, but it has no visual analogies. It's just a bunch of math. Hence, if you've wondered about all these various interpretations of quantum mechanics, that's why, because we're just left with a bunch of math equations that work with no mental picture to back it up in the Matrix mechanics version of quantum mechanics is absolutely crystal clear. The the uncertainty principle isn't just a failure of our ability to make measurements. It's not a matter of failing to outwit and outsmart nature. It just is. The Heisenberg uncertainty principle is baked into the math of quantum mechanics as a fundamental notion of reality in the famous Heisenberg uncertainty principle isn't the only uncertainty principle out there. It can happen all the time. There's an uncertainty principle related to knowledge of energy and the amount of time you take for that measurement. There's an uncertainty principle between energy and position.
There's an uncertainty principle between different components of angular momentum, like angular momentum in one direction and angular momentum in another direction. There's a fundamental limit to what you can know in the Matrix language of quantum mechanics, and I know I'm going off the deep end here, but that's where the uncertainty principle is. So hold on to your swimsuits. For every system, there are a list of things that you can possibly observe, right If you've got some system, some particle, some atom, some whatever, you're just studying something. There's a list of things that you can measure a position, momentum, energy, color, cheesiness. You know the list goes on. These are called observables because they well, they're observable. And the process of making an observation of taking a measurement is to find out information about one of those observables. So, like, uh, one observable is position now I'm going to make a experiment to measure the position of these particles, and once I do, I have acquired information about their position.
I have acquired information about this observable. Sometimes when you make a measurement on one observable, you automatically get information about some other observables like like If you measure position in one direction, you usually or you can set up your experiment to automatically get information about position in another direction. So ya like. That's fine. Sometimes these observables work together, where information about one gives you information about other things, but sometimes they don't. Sometimes when you make a measurement or an observation about one observable, you don't learn anything else. It tells you nothing. It is silent. It is ignorant about other observables, and anytime that happens, an uncertainty principle comes into play. I like to think of it like a budget. Say I want to learn about a system I've only got so much money to spend, and every dollar that I spend gives me some information.
Sometimes there's like a buy one. Get one deal, I can spend $1 on one observable, and I also get information about another observable. There's a free giveaway. You buy a cat, you get a litter box for free. But sometimes you spend a dollar on an observable, and that's all you get. You get that one dollar's worth of that one observable, and and you don't get anything else like you bought a loaf of bread. It doesn't come with free milk. You just get the loaf of bread, and any time that happens, when you spend your observational dollars, eventually you're gonna run out of money and you can decide where you want to spend this budget. Do I wanna spend $5 on position and $5 on momentum today? Do I want to spend $10 on position and $10 on momentum? Well, I'm sorry you can't do that because that broke your budget. You can spend $9 on position and one a momentum. One on momentum and nine on position. 50 50 all in on position. No, absolutely nothing about momentum.
That's fine. You. But that's your budget. The Heisenberg uncertainty principle is a budget. It tells you the maximum amount of money you can spend on observations, and you just can't go over your budget. There's no credit card here. Heisenberg is a cash only kind of guy. He gave you 10 bucks and you've got to spend it now. Sometimes you can wisely spend your dollars and get some more information for your budget. Like OK, I'll spend $1 on this observable, and I also get some information about other observables. But sometimes you don't. And when that happens, your budget comes into play and you're stuck. We first noticed this uncertainty principle because of all the matter wave probability business. But it really goes much, much deeper. Uncertainty is the rule in quantum mechanics. The subatomic world and our knowledge of the subatomic world is fundamentally limited.
You cannot know the position and momentum of a particle simultaneously to as arbitrarily high position as you want. You don't have the budget for it. There has to be a tradeoff. This limits fundamentally our knowledge of the quantum world, and there is no way around this. It is so much bigger than just position and momentum. That's just the prime example, the first one we thought of by analogy, with all the waves, Really, what it's telling us is that it's impossible to know everything there is about quantum systems. That is why Einstein ended up hating quantum mechanics because it seems like it shouldn't be. You shouldn't be allowed to do this. It feels like we're clever. Come on. We have, like, space ships and stuff. We can't figure out a way to measure position momentum as accurately as one. No, we can't because nature won't let us. That's the way it is. And so when I end every show with you know, see you next time for more complete knowledge of time and space, I really mean complete knowledge of time and space, subject to uncertainty.
Principles. Thank you to Mark MA B and Dean B for the questions that led to today's episode and thank you to patreon, especially my top patreon contributors. Patreon dot com slash PM Sutter. It's Matthew K, Justin Z, Justin G, Kevin Duncan, M Corey D, Barbara K, Dude Robert M, Nate H and F Chris Cameron, NAA Aarones, Tom B, Scott M and Rob H. It is their contributions and everyone else that is keeping this show alive. And I truly, truly do appreciate it that I am certain about, and you can keep asking those questions go to ask us spaceman dot com. Ask spaceman at gmail dot com. Hashtag Ask us spaceman at Palma Sutter on all social channels. Go read my book. How to Die in Space. It's fun. Go leave a review on iTunes or Spotify. I really do appreciate it. Tell your friends and just be curious, you know, subject to certain quantum mechanical limits. And I'll see you next time for more complete knowledge of time and space, subject to uncertainty principles.
I'm not going to say that every time. But today I think it's fair. The United States Border Patrol has exciting and rewarding career opportunities with the nation's largest law enforcement organization. Earn great pay, outstanding federal benefits and up to $20,000 in recruitment incentives. Learn more online at CBP dot gov slash career slash USB P