Daniel and Jorge Explain the UniverseDaniel and Jorge explore whether basic rules of our Universe are broken at the quantum scale.
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Uh? Not worried, but I try to do as much of it as possible. Oh.
Is that because you're very environmentally responsible?
Nu, it's because I try to do this little exercise as possible.
You're such an adult.
Hey, I'm doing it for the planet, not just for me.
Well on behalf of planet Earth. We're all very grateful for your lazy attitude.
Oh thanks, My body is also very grateful, although maybe not in the long term. Hi am Jorhemer, cartoonists and the author of Oliver's Great Big Universe. Hi.
I'm Daniel. I'm a high energy particle physicist, but I don't often feel very high energy or high. There were times in my life when that was more true than Yeah.
I seem to remember those times. Yeah, But isn't it high a relative term at least in physics? Like how high is high energy? Can't you always go higher in energy?
You can always go higher in energy and what people called high energy fifty years ago we now call nuclear physics. So doesn't even.
Qualify what it's not low energy, It.
Doesn't even qualify as low energy physics.
I guess nobody wants to be called a low energy physicist.
Yeah, would you want to be called a low energy cartoonist?
Well, I am, and if you call me that it would be accurate. But I guess you can call me that, why not?
Yeah? Sure? Well, high energy really means highest energy. And as we keep pushing the boundaries of what we can achieve, then yesterday's high energy collider is today's nuclear physics.
Hmm, sounds like a good slogan for the LGC. Yesterday's high energy is now today's nuclear energy. But anyways, welcome to our podcast Daniel and Jorge Explain the Universe, a production of iHeartRadio.
In which we use all of our energy to help you understand the nature of the universe. We tear things apart, we peer inside. We try to understand at a microscopic level, how does everything work? Is there a story we can tell about what's happening to the littlest bits in the universe and how it comes together? To explain our reality.
That's right. We like to exp or the high energies, the low energies, and all the energies in between that there are in this universe to discover, to explore, to learn about, and to blow your mind with.
And energy is a really central concept in physics and in people's understanding of physics. We'd like to think about things in terms of energy, little quantum fields vibrating with energy, energy being passed between particles, energy used to create particles. In some sense, physics is a study of.
Energy, and one that requires some amount of energy to explore, right. I mean, you can't just do physics from your couch, can you.
I don't know if it takes more energy to do physics or cartooning, but you can sort of lie in your couch and just think about the universe, you know, the way the great theorists and the Greeks have done. But absolutely to do experiments to explore the universe, to investigate it deeply, you need to poke it, you need to probe it, you need to interact with it, and that does take some energy.
Well, I feel like energy is kind of a topic that it's a word you learn as a kid, and that everybody has heard of this word, and we all use it every day in our everyday lives. But to actually define energy is kind of tricky, isn't it, Not just from a physics point of view, but also if you ask somebody what energy is, you don't get an easy answer.
Yeah, energy is a very loaded term, right. We have a sense of like feeling like you have low energy in the morning, or running out of energy to do some chores or something. But it's one of these words that physics that's redefined have a specific meaning, a very crisp idea for what energy means. The way we also have like meanings for force and work and other words that we also use in everyday English without as precise definitions.
Right.
But even those the simple terms have been changing in physics over time, Right, Like the word the idea for force has changed with quantum mechanics, hasn't it? Like it used to be an invisible force that we feel towards the Earth or the sun, But now they're talking that maybe it's like a particle or something, it's an exchange of particles.
Yeah, the mechanism that explains it is definitely different. I think the concept of force is a change in momentum of something. Something in exchange of momentum essentially has been pretty constant since Newton. Yeah, these things definitely can change. And you know, for example, we've redefined gravity to not even be a force. So what gets counted as a force and what doesn't and how that all works definitely changes. And we like to dig into these basic principles and say, like, what does this really mean? Where does it come from? Do the universe have to be this way? Is energy essential to the universe? And one of the ways that we do that is by noticing what the universe respects, like what doesn't change in the universe, what's constant, what's conserved. That gives you a clue about sort of what's important to the underlying machinery of the universe.
Right, You kind of want to know what the rules of the universe are, or what the principles of the universe are by which it lets things happen in it, right exactly.
And one of the deepest rules that people imagine the universe follows is conservation of energy. That energy is somehow immutable, that it can slosh between different kinds of energy kinetic to potential to mass, to velocity to whatever. But the energy has to go somewhere and has to come from somewhere. That it's a basic component of the universe itself.
Yeah, it's a very fundamental rule that people seem to learn about even in high school physics. But is it actually true? Does it always happen in this universe or does it get broken at some levels, like the quantum levels? And so to the end the podcast, we'll be asking the question does quantum mechanics conserve energy? Now, when you say quantum mechanics, do you mean like the field or the people who study quantum.
Mechanics the mechanics of quantum physics.
Yeah, can you be a quantum mechanic like a car mechanic, but at the quantum level.
Yeah, bring your fields in. They need some new parts. We'll order them.
That's right, Your quantum carburetor needs to be swapped out exactly.
You know.
In this case, we're talking about the rules of the smallest bits in the universe, the tiniest little things, the electrons, the positrons of photons, all the smallest stuff in the universe seems to operate on different rules than the bigger stuff in the universe. Baseballs and basketballs and rocks and stuff that we're familiar with. And so while we're taught that energy is concerned very generally, we're interested in whether that's always true, and whether it's true at the smallest scale.
Yeah, so this is a big question. Does quantum mechanics conserve energy? And so, as usually, we were wondering how many people out there had thought about this question, whether this is a rule that can be broken at the quantum level, or whether the whole universe follows it.
Thanks very much to everybody who answers these questions. If you would like to receive a regular dose of tough physics questions in your inbox, right to me too, questions at Danielandhorge dot com, and I will send them to you.
Well, regular dose. Now, do these doses make you high in physics?
These are microdoses, so yeah, oh, I see right, it's more of a low key high. They're not supposed to blow your mind. They're just supposed to color your experience of the universe a little bit.
I see, it's more of a nuclear hut exactly.
It's not a high energy dose.
Well, think about it for a second. Do you think quantum mechanics conserves energy. Here's what people had to say.
I think so, or at least the rate of decay is so minute that we are not currently able to detect it on a cosmological scale.
I think quantum mechanics conserves energy. I feel like it would be big news if we found the law of conservation of energy to be violated, though maybe it has been and I just haven't seen that news. But the notion of quantum fluctuations seems like it would violate that law. Though I don't really understand quantum fluctuations.
I'm assuming it doesn't just because I remember listening to your podcast on how energy actually isn't conserved in the universe. So I'm assuming that quantum mechanics follows that as well. But I don't actually know.
I'm not sure about this question. And like conserve in what like in your book frequently asked questions about the universe, you did say, like there's like a quantum foam, and like when the universe is expanding, it's just connecting to more quantum particles. I guess, so I'm gonna say I don't know, because if you mean in the universe, like not the growing section then no. But if you even include all the other disconnected quantum phoam, then I'm not sure.
All right. People are on the fence about this. Some people say it does, some people say they don't think so, well, they're not sure.
Yeah, I was really surprised by this. I was expecting people to rush to the defense of conservation of energy and say it's a fundamental law of the universe.
Maybe it's because we've had whole episodes where we say that then she's not conserving the universe. That maybe influence the answers here.
Oh my gosh, people actually listening and absorbing the content.
Amazing, amazing, they're learning. Well, it's great that they are listening to us. And because we have talked about this idea of conservation of energy in the universe, and we've talked about how it's not actually conserved in the universe as a whole.
Right, that's right, And that was in the context of sort of general relativity, thinking about the universe as it expands and as space is changing, how we define energy in that context, and that sort of blows a lot of people's minds to understand that energy might not be conserved in the universe. At the biggest scales, you know, when you zoom all the way out and think about how the universe is expanding and what happens to stuff inside of it.
Right, because in the other episode we talked about how the universe is expanding due to dark energy, and basically like there's more space being created all the time out of nothing, which means that energy sort of being added to the universe, created in the universe out of nothing.
Right, Yeah, that's right. And your comment out of nothing, I think says a lot. You know, it implies that energy needs to come from somewhere, and so when you say energy is created, you have to give some explanation for where it comes from, even if you're saying out of nothing. But this tells us that energy isn't something fundamental to the universe. That it can go up and it can go down, like lots of things in the universe, like the number of people in swimming pools, is not a constant number of the universe. It can go up and it can go down.
How do you know, Are you sure I'm.
In the middle of an extensive worldwide experiment to measure the number of people.
A moment, Yes, Oh, you thought you were going to.
Challenge me on that and call me out. But actually I've been doing this in preparation for five years just to make that casual comment.
You know, somehow I don't believe you.
Then await from my paper in Nature. Okay, it's coming out soon, I promise.
Sure. Let's see the draft. Read me a poll paragraph from the draft right now.
Oh, I can't disembargo it because it's too high profile. I see I signed an NDA. What am I going to No, obviously I have not done that experiment.
A nuclear disclosure agreement, which means it's really low.
But clearly there are things in the universe that do change things that are not fundamental to the universe, while there are other things that are fundamental, like momentum. We think momentum is conserved in the universe, and that comes from a really deep symmetry about space and time that the experiments you do anywhere in the universe should give you the same answer. That doesn't matter where you put your origin in space. The rules of physics don't care. And that gives you directly, as a consequence of Nuther's theorem, momentum conservation. But energy is not in that same category, and energy can go down and it can go up. Like when the universe expands, you get in new space, and that space comes with energy. But also energy gets decreased because as space expands, it reddens the wavelengths of all the photons inside of it. Take for example, the cosmic microwave background radiation from the early universe. When it was created, it was very high energy. That plasma was super dup or hot. It was thousands of degrees. But it's been stretched out by the expansion of the universe to very long wavelengths and now it's like three degrees. Calvin, where do that energy go? It didn't go anywhere, it's just gone.
Well, it's not gone, it's just gonna spread out, is it.
No, there's less energy in those photons. Those photons have gone from high energy to low energy.
Because they got stretched out.
But the total energy is also different. It's not just the energy density.
But they're longer now, the photos are longer. Yeah, so isn't that where the energy went.
The energy of those photons is less. They're also longer, but the energy of those photons is less. If you stretch space, the photons get redder, which means they have less energy.
Well, I guess this is what I mean. Because the idea of energy, the concept of energy can really vary into a lot of these arguments about whether it can be conserved or not. I feel like maybe they depend on a good definition of energy, and so maybe for folks we should talk about what energy actually is. How do physicists define it?
Yeah, I wish I knew what energy was.
Wait, what.
Energy is a really slippery topic. It's something we've been struggling with over the last few decades to really define. We have some very crisp but unsatisfying definitions of energy. You know, in some cases you can say energy is the thing that's conserved over time, you know, so you can define it to be something that's conserved. Really, I think a better way to define energy is to talk about like the forms it can take. You know, Like there's kinetic energy, which means energy of motion. Something is moving that has energy. There's potential energy, the energy of configuration. Like a book is sitting on a shelf, there's energy stored in that. You know, it takes energy to put the book on the shelf. Mass, for example, is a representation of internal stored energy. Put a bunch of photons into a box, they have energy. That box now has more mass. All these are different ways you can calculate energy, and if you add them all up, you get the total energy. And so that's sort of how we define energy. But you know it's a little hand wavy.
Wait. Wait, wait, so I was right earlier when I said that we I don't really know what energy kind of is, but you made it seem like we did.
No, we don't really know what energy is in the broadest sense, but we can define something, say this is what we call energy. I don't know if it really captures our full experience of energy, but yeah, we can write down a formula for what energy is.
But I guess the question is what did those things have in common? And why do you use the same word for all of them? The kinetic energy, potential, energy, you know, energy of mass. Why do you use the same word for all of those things?
Yeah, great question, And the reason is that in classical mechanics, at least you know, things moving around at our scale at or fairly low speeds, we notice that they can turn back and forth into each other. Like you take that book on the shelf, it has potential energy and no kinetic energy. You push it off the shelf. Now it's speeding up towards the ground. It's losing potential energy and gaining kinetic energy. So we notice that these things can turn into each other, and therefore we group them together into one big category. We notice that, at least in classical mechanics, the total the sum of them all, does stay constant. The like if you're out of all the potential energy and all the kinetic energy at one moment, you do it again later you find you get the same answer.
And how does that relate to the energy of a phototon, which you mentioned earlier.
So now we're departing classical mechanics a little bit. We're talking about a quantum object, but we can still think about the energy of a photon. A photon has kinetic energy because it's in motion, it's always in motion. It has only kinetic energy. So photons definitely have energy.
Well, it seems like maybe the common factor is the idea of motion, like things moving have energy to them, and things that can move in the future or can cost things to move, or like the potential to cost something to move is what maybe you would call energy.
Maybe I think that puts kinetic energy in a more primary position than potential energy, which I'm not sure is justified. I think there really are at its core two different kinds of energy there stored energy, potential energy and kinetic energy. I'm not sure which one would be more fundamental.
And so are those the only two kinds of energy? So you have in classical physics kinetic and potential.
Yeah, those are the two forms. People might think, what about mass? What is mass? Is that kinetic energy or potential energy? It's sort of a special case. It's just sort of a label we give some kinds of energy if they're stored internally, Like if you have gluons inside a proton, they have a bunch of kinetic energy they're zooming around. They also have potential energy of their bonds. All that energy is inside the proton, so we call that mass. So mass is sort of a label we give to some energy, but it's not on the same level as like kinetic and potential it's not its own kind of energy.
So then if an eight year old asked you, hey, doctor Whitson, what is energy? What would you answer?
I would say, I've had this nightmare scenario many times and I have no idea how to respond.
You would their face, Ah, run away? No, seriously, like, what would you say, you have to say something, what would you say, I'll get you started. It's a quantity that.
I'd say. Energy is something that makes things move, but it's also something you can store. That's my best shot.
It's almost like a liquid or something.
You know, for a long time people did imagine that energy in the form of heat, was a liquid that flowed between things. But it's not a physical quantity in itself. It's a description of the physical state of other quantities. Like a liquid can have energy, but so consolids. It's not like when energy flows from one thing to another, there's some physical substance that moves between it. It changes the state of those objects.
Well, I guess I'm a little surprised you're having so much trouble just defining energy, which is pretty interesting. But as you said, I think one thing that we do sort of know about it is that in some cases it's conserved and maybe in some cases it's not so. Well, let's dig into the question and when it's conserved, is it conserved at the quantum level or is it not so let's dig into that, but first let's take a quick break.
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All right, we are mustering up the energy to talk about something that apparently physicists can't define. Energy, such a basic word that even little kids use, everyone uses in their daily lives. But it seems, Daniel, that it's something physicists can't really define very well. Maybe only mathematically you can define it. Is that kind of the case.
Yeah, And as you'll see when we get into the quantum system, this is going to be even trickier. And physicists disagree about how to define energy and whether we can even define it In terms of quantum systems.
Well, it seems like we don't even need to get through the already don't know how to define it exactly.
And that's why I want to be upfront about how complicated and confusing this topic is, even in the easy case, because when we get to the hard case, it's going to get even trickier. So I did my best to give you, like my understanding of energy, but if you look at the official definition of energy, I find it's even less satisfying. Like if you just google energy and you ask Wikipedia or chat GPT, like, what is energy?
Well, it's you know, legit sources, legit sources.
They say energy is the quantitative property that is transferred to a body, and that doesn't really even tell you what it is. It's like, okay, well it can move from one thing to another, but what is it? Man? It doesn't really answer that question.
Well, that's kind of what I meant before, is that it's a quantity. Is basically kind of the only way you physicis know how to define it, right. It's a quantity. It's something that you can measure that can be a lot or a little, which you seem to be able to measure about things, and that sometimes seems to be conserved.
So mathematically we can write down a formula that defines it, and then it's defined in terms of things we can measure, like velocity and position and stuff like this. And it turns out that if you're write it in certain ways, then that number doesn't change. The internal values can slash back and forth, but the total doesn't change. That's sort of like the crispest most mathematical definition. But I think what we're proving forward is like what does it mean philosophically? Like what are the implications of that? And that's much trickier.
Well, you seem to not want to give primacy to kinetic energy, but in a way, that's kind of like our most direct experience of energy, which is motion, right, Like if something has a lot of energy to either moving fast, or it's hot or it's exploding. For us, in our experience of the universe, energy is basically things moving fast or things that can make things move fast.
Yeah, if you're talking about the experience of it, then you more directly experience motion than stored energy. It's energy you don't really experience when it's stored because it's just being stored. It's when it's transformed into kinetic energy that you're experiencing it, Like if you zap yourself on a battery, it's the motion of those electrons being transformed from the potential into their kinetic energy that's zapping you.
All right. So then you said that sometimes it's conserved and sometimes it's not. So when is energy conserved in a classical way?
In classical sense, energy is only conserved when space time is not curved and when space time is not changing. So if space time is fixed, like you have flat space time, meaning you shoot two photons and they stay parallel to each other, then you can expect energy to be conserved. But if that space is changing, like it's expanding the way our universe is, then the general relativity energy is not conserved. Even more generally, anytime you have curved space in general relativity, you do not have conservation of energy. So, for example, black holes colliding do not conserve energy.
Wait, what what do you mean.
Black holes collide? You have the collision of two quare curved bits of space, and what comes out of that is not the sum of what goes into that. You're not guaranteed that in general relativity, but is.
In space always curved like uncurving space around me, and yet I don't seem to have infinite energy.
That's right, you do not have infinite energy, and you are curving space around you. But the total amount of energy in the system changes in time in general relativity, and it gets really fuzzy and weird because general relativity is really hard to think about. In some reference frames. According to generalativity, energy is conserved and others it's not. Depends sort of on how you're looking at things.
Okay, it sort of sounds like you're saying like, if you don't think about general relativity, then you can assume that energy is being conserved. If you assume that there's general relativity and things are being space is being bent like around black holes or the expansion of the universe, then you can't assume that energy is being conserved.
As long as we're above the quantum level.
Right, So it's mostly like whether or not you ignore the bending of space time exactly.
If you can ignore the bending or expansion of space, then classically you can think of energy as conserved.
Right, And so we talked about that the universe is expanding, and so therefore, energy is not being conserved. And we talked about two black holes colliding. Energy is not being conserved there. So now the question of the episode is when you get down to the quantum level, is energy still conserved even though maybe there's no space time bending at the quantum level. If you assume there's no bending at the quantum level, does energy get conserved?
Yeah, and we have to assume there's no space time bending at the quantum level because we don't know how to do quantum mechanics when space is curved and you have gravity, and gravity for particles is something we don't understand. So let's assume space is totally flat and we have objects, you know, like baseballs and rocks for which we think energy is conserved, and then zoomed down to the quantum level and try to understand when you have photons and electrons instead of rocks and baseballs, is energy still conserved? And really the deep question is like is energy conservation something that's through and through the universe at every scale or is this something that emerges only at the scale we experience it out of something that operates totally differently, because remember, quantum mechanics breaks all the rules of classical physics. It says things don't actually have well defined positions and locations, and lots of the things that emerge at our level are not true at the quantum level. So it's not guaranteed that everything about our experience will be translated down to the quantum level.
All right, So then let's answer the question, does quantum mechanics can serve energy or not?
So the short answer is we don't know.
Surprise, surprise, but let's talk about it anyways.
The slightly less short answer is, it depends on what you think is happening at the quantum level, mostly about what happens when you try to measure energy.
What do you mean? So I guess because it's quantum mechanics, you have to measure things. That's very importing quantum mechanics. So you're saying, we have to answer this question with this idea in mind.
Yeah, exactly. So let's start off the easy case without measurements and have a picture in our minds or what's happening. You know, Quantum mechanics tells us that there are probabilities for various things to happen, and we can calculate those probabilities using the rules of quantum mechanics, and those probabilities propagate. You have two electrons heading towards each other, they might scatter off each other and go that way, they might pass right through each other. All those probabilities are sort of live until somebody actually asks the question and makes a measurement using a classical object and you know, tries to take a picture of it. Until then sort of have all the possibilities live. So that's quantum mechanics without measurement, you know, that's what we're imagining is happening when we're not looking. And in that scenario we can ask, well, is energy conserved? Like when all those probabilities are slashing around, the electrons are maybe bouncing off each other and maybe not, is energy conserved there? And already we kind of run into trouble because we don't really know how to define energy here. Like what if you have a quantum system and has a few different possible states, a low energy state and a high energy state. How do you define the energy of it? Is it like the weighted average of the probabilities of the various is it something else? I've had conversations with a bunch of physicists this week to try to sort out what people think energy is. And some people say, you can't define energy in that context, and other people say, no, it's definitely the weighted average of the various probabilities.
Right, I think, meaning maybe for people who are not super familiar with quantum mechanics. So in quantum mechanics, particles and things like that aren't just in one state, like a baseball sitting on your table. It's like it's doing multiple things at the same time. It's here, it's a little bit there, it's moving in this direction a little bit, but it's also has the probability to be moving in this other direction. And so you're saying that maybe one way to measure its energy, or to think about its energy is like, if it has a fifty percent probability of going this way, then you take that energy and multiply by a half. And if it has a certain probility that it's moving this way with that velocity, like a twenty five percent probability, then you maybe multiply that energy by a quarter, and then you would add it all up and maybe that would kind of give you an average of its energy.
Yeah, exactly. Like, if it has a fifty percent chance of having twenty five jewels of energy in a fifty percent chance of having seventy five jewels, then you say, well, I'm going to average those two. I'm gonna say its energy is fifty jewels because on average that's what it has. And here allowing the particle to still have both probabilities to say, oh, maybe it's in the lower energy state, maybe it's in the higher energy state.
Right, it's in a superposition, it's with alive and dead. Then you said, some of your physicist friends said, you can't do that, like that's not even that doesn't make sense.
Yeah, and they say you can't do that because you can't measure that. Right, you never measure the fifty. Like if you went and asked the question, all right, we have the particle in this state, go measure the energy. You're gonna get twenty five or you're gonna get seventy five. You're never going to get the average. It's like saying the average number of children in the US is two point four, but nobody actually has two point four children, right, And so in the same way, you'll never see this particle have that energy so in what sense is that the energy of the particle. That's sort of the complaint.
That's kind of a fundamental problem with quantum mechanics. Like it's you know, the cat is alive and dead. Obviously the cat can't be alive if you see the caddies can't be both. But in a quantum sense it is both.
In a quantum sense, it is both. In quantum sense, we need a new idea for what these things mean, Like what does position mean in a quantum sense? Well, you know, for a particle that you haven't measured, it's not really well defined. There's only a probability where is the particle Actually, well, it's not anywhere. Actually, So these concepts that are so important to us at the macroscopic scale have to take different meanings. We have to do this like philosophical extrapolation. And this is a problem with energy. For example, say we have the particle and has two different possibilities, the twenty five jewel and the seventy five jewel. Then you go and you measure and it turns out it has seventy five jewels. Well, if a minute ago you said it had fifty jewels, because that was the average now you've measured it and you said you have seventy five jewels. Where did that twenty five jewels come from?
Right?
And so boom right there, you have a violation of conservation of energy if that's how you define energy before you measure it.
Wait, say it again. It is energy suddenly appear.
So if you start out with a particle we were just talking about, it has a fifty percent chance so having twenty five jewels, and a fifty percent chance of having seventy five jewels. So we say, okay, we define the energy of it to be fifty jewels because that's the average. Now you go and you measure it, and you measure it to have seventy five jewels for example, Then according to our definition of energy, it's gone from having fifty jewels to having seventy five jewels, And so where did that energy come from?
It didn't come from anywhere. It just said before it was a guess about what its energy was. It was kind of like the expectations of it or the average of what we think its energy was. But then the second instance is what we measured its energy. So they shouldn't be a surprise if it's more or less should it.
So you're saying those are really two different things. One is an actual energy because you've measured it. The other is just some estimation of what we might measure, but not really the energy.
Well, and it is in the quantum sense, right, like it's alive and it's dead before I look at the cat in the box and then I wanted to open the box. It's alive with it. It's not like the cat suddenly came back to life.
And I think this comes down to a question of like interpretation. You know, what is happening there? It does the particle secretly already have seventy five jewels and now we're measuring it and discovering it. You know, is the uncertainty there or reflection of our lack of knowledge about something that's actually already determined, or something that really isn't determined until we measure it. The particle really is in a superposition of those two states. If it really isn't determined until we measure it, then we do have to kind of ask, like, where does the energy come from when the universe decides to make that seventy five jewel particle instead of the twenty five jewel particle.
Well, I guess in the same way that you can ask if you find that the cat is alive, how did the cat come alive? It was if it was alive and dead before you open the box.
Right, But the difference between the two states of the cat doesn't violate the conservation of energy, which we thought was maybe a fundamental rule in the universe. That violates the conservation of the number of dead cats, which nobody really thinks it's.
A conservation I hope not well or well. And this says that we think that it's impossible for a cat to go from being dead to being alive. Right.
I think if we're going to make the analogy to the shortening your cat experiment, and then you want to ask the question, is the cat alive before it's measured? And the answer I think a lot of people would give is it's neither alive nor dead. It has the probability of being both. And then to extrapolate that philosophically back to our particle, you'd say, well, the particle doesn't really have twenty five or seventy five jewels, It just has a probability of being both. And energy is not really well defined. So I think one answer there is to say, well, energy is not really defined without measurements, so you can't answer this question, and the others to say, no, that's the definition of energy, and there is violation of conservation of energy. So you either have to give up an understanding of what energy means for quantum particles or you have to give up energy conservation.
All right, So it seems like the moment you measure a quantum particle is super important because it's so fuzzy before you measure it, and it's so crisp after you measure it, and so you kind of fall into a trap to try to compare the energy before that moment and after that moment. You know, you could interpret it as saying that energy is not conserved, or you could interpret it saying, well, you know, there's no definition of energy before you measure it, and so therefore don't even worry about energy classivation exactly.
But there's really important loophole that we're overlooking here, and that's the measurement itself. Some people argue that energy isn't conserved, that this extra energy must come from the measurement, that we're only violating conservation of energy because we're not including the full system. Right, energy is only conserved inside a closed system where you don't have energy transfer anyway. Right, Like energy is not conserved for a battery. As you use it, it's energy is decreasing. But if you include where that energy is going, usually it is concerned. So some people argue, ah, what about the measurement. In order to measure something, you have to like poke it, you have to interact with it. Maybe you're adding that energy when you're making that measurement and things do balance out in the end.
Wait, what that was very confusing. Can you give me an example.
So let's say you want to measure this particle and you want to say it doesn't have seventy five jewels or twenty five jewels. How do you measure things about a quantum particles? You have to balance another quantum particle off of them. So shoot this electron with a photon, then measure where that photon goes and use that to detect what the energy of your particle was. Well, now you're shooting your electron with a photon, which is going to change its energy. And so people argue, when you're doing this, the energy that gives that electron. Seventy five jewels comes from that photon somehow.
But then wouldn't you measure that the overall energy went down because you would measure the photon after it hits the electron, and you would see that it was had less energy exactly.
So this is the game people try to play in order to recover conservation of energy for quantum mechanics. They say, this argument is flawed because you're not taking into account the energy of the measurement. So there's a whole cottage industry and a bunch of paper. It's recently about whether it's possible to recover it using the measurement or whether that's a red herring.
Well, the whole thing could be a red herring, right, Like it could be that it just doesn't make sense to talk about energy before the measurement.
It could be, and that actually depends also on your interpretation of quantum mechanics. We're talking right now in the Copenhagen interpretation, which has this whole idea that there's a superposition and when you make a measurement it collapses to one of those options. That's just one view of quantum mechanics, and our argument about the energy non conservation depends on that view. It turns out in other views of quantum mechanics they tell a whole different story.
All right, well, let's get into what these other views of quantum mechanics are and what they say about the conservation of cat energy or not. So let's dig into that. But first, let's take another quick break.
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Terms apply. All right, we're talking about energy, whether it's conserved in the universe, is it conserved at the quantum level? And I think we've established that it's a minefield of confusion for everybody. Some people might say, does it even make sense to talk about energy before you measure something? And you know, it doesn't make sense to talk about whether the cat is alive or dead before you open the box. And some people might say that it does kind of matter, right, or that if you discovered the cat to be a liver before or after, maybe you killed the cat when you open the box. That's kind of what you're saying exactly.
And it's amazing to me that this is a topic of recent discussion. This is not like something that Boor and Heisenberg argued about and figured it out in nineteen thirty seven their papers about this. Like last year, you know, people are still debating what energy even means in quantum mechanics, like sort this out. Folks had to for one hundred years. You think that would be enough time to figure out basic stuff about quantum mechanics.
Yeah, can't you just run an experiment to figure this out? Like if measuring an electron somehow adds energy to it or creates energy, can't you just measure that? Can you just design an experiment where you shoot a photon ad an electron.
So people are trying to design experiments and the crucial thing is designing an experiment where you think the measurement will not influence the energy of the system. That's the goal, because then you can have an internal system and an external system, and you can isolate it and say this is the whole system. So you want to try to separate your measuring device from the energy of the system.
Wait, wait, do you mean like they're trying to come up with how to measure something without measuring it.
Well, they want to measure it without changing its energy, So they want a energy independent measuring system.
But I guess if you shoot a photon a an electron, don't you know how much energy the photon has when you shot it, so that you can take it into account later when it comes out? Like, why is this problem so hard?
Well, every quantum object has an uncertainty to it, So you shoot a photon at it, you try to generate photons with specific energy, but those photons will also have an uncertainty to them, and that uncertainty propagates through your whole experiment. So what you want to try to do is set up a scenario where the uncertainty you're adding by your measurement is smaller than the difference in the energy between the two states of the thing that you're measuring. So you want to like try to use or something really low energy to measure a really big difference.
I guess it's kind of like, you know, you're trying to figure out if the cat is alive or dead in the box, and you're setting in a cat to do it, but it turns out that the scientist cat is also a quantum object, so it could also be a live or dead, in which case you don't really know the scientist cat is killing the other cat exactly.
So what you want to do is try to send in like a tiny miniature kitten that you can argue is going to not influence whether your cat is alive or dead as much as.
Possible, or that you know for sure if it's a live or dead.
Or the uncertainty on it is smaller than the uncertainty on the thing you're trying to measure. So people come up with these crazy clever experiments where you try to use really low energy device measure a very high energy difference in the possible states of the object. So the thing you're measuring is not influencing the state enough to change the answer.
Oh, I see, Yeah, like you said, you want to send in a scientist kitty whose state. Whether the kitty is a lib deat is not really going to influence whether the big cat is a libradat exactly.
And so there's these folks that come up with this really clever experiment where you take a box and you put low energy photons inside of it, and under some almost magic like wave mechanics mathematics, there's a place in the box where the photon wavelengths add up in a special way to wiggle at a really high energy. So waves can add up and they can cancel each other out. This is constructive and destructive interference, where it turns out if you put a bunch of low energy photons into a box, there's one portion of the box where they're wiggling really really fast where all those photons added up kind of make a higher energy photon than the sum of all the energy of the photons you put in. And they came up with this way to try to reflect that one part of the photon out of the box by slipping a mirror in really quick. And so it's sort of like putting a few low energy photons in a box and then getting out a really high energy photon. So this is the experiment they proposed would prove violation or conservation of energy and quantum mechanics. But there's a lot of controversy about what this experiment might mean and whether you could actually do it.
Oh, I see, because if you measure a really big photon coming out of this corner of the box, you have to wonder where that energy came from.
Yeah, how did the universe make this high energy photon out of just a few very low energy photons? Where did it come from? Just like the example we were talking about before, how did the particle get seventy five GeV when the expected value of the energy was fifty Where did that energy come from? And you can only really ask that question where did it come from if you believe it should come from somewhere, which implies that it's conserved, that it has to come from somewhere, that it's like flows around in this limited amount. But if energy is not conserved, it can just like go up or down, like the number of dead cats in the unit. Then that's not really a problem.
But couldn't you say that the energy of that right photon in the corner came from the little photons or would it come out with a much bigger energy than the if you add up the little smaller photons.
Yeah, in this case, the energy is much bigger than the sum of the energies of all the photons you put in, So you can't explain it by just like having added up those photons. It's a really cool experiment. It's called super oscillation if you want to check out more details about it.
Well, but then you said that this is all just a base on one interpretation of quantum mechanics. What did the other interpretations say or how can they help us?
Yeah, because a big part of the issue is what happens when you make a measurement. Right, if you go from a state that has on average fifty jewels of energy and you make a measurement, how do you end up in one of those states? And where does that energy come from? And other interpretations of quantum mechanics tell a very different story about what's happening there. For example, the Many Worlds or ever ready in quantum mechanics says that there is no collapse of the wave function. That if you have a superposition of two possibilities that cas alive or the particle has twenty five or seventy five jewels of energy that when you make a measurement, the universe just branches. Now there's one branch that has one option and another branch that has the other option. And so in that sense, if you're like averaging over the branches, nothing has really changed. You know, the total energy in the universe hasn't changed. One individual branch might see seventy five jewels, so they might think they're seeing violation of conservation of energy, but averaged over all the branches, including the ones that don't see, nothing has really changed. There's still just a distribution of different energies.
I feel like you just skipped over a humong this concept, which is just throwing the multiverse. Yes, exactly, in the multiverse quantum multiverse. So you're saying, like, one way to interpret quantum mechanics is that things don't collapse. You know, if something if the cat is alive and dead, it means that there's a universe where the cat is alive and there's a universe where it's dead, and so overall energy is still conserved. That's kind of the idea.
Yeah, energy is just unevenly distributed among those quantum multiverses. One of them it's more, another one gets less. Overall, it all balances out across the multiverse, but in an individual universe, an observer does see a violation of energy. So that's a pretty different story than what's being told by the Copenhagen group.
Let me see if I get this, so, like, I have the cat in the box, and I open the box and I find that the cat is alive, and I think, oh my god, this is a violation of cat aliveness in the universe because before the cat was only fifty percent alive and now it's fully alive.
Sure.
Yeah, And you're saying, if you think that the actually there's a multiverse, is a quantum multiverse, then there's no real violation because if you consider my universe where the cat is alive, and your universe where the cat is dead, then it makes sense for me to see that the cat is alive, and it makes sense for you to see that the cat is dead. There's no violation here.
Yeah, because across the quantum multiverse it's still fifty percent alive and fifty percent dead.
But in the single universe version of quantum mechanics, the cat aliveness went up from one half to one if I see that the cat is.
Alive exactly so in the collapse theory where measuring it forces the universe to choose one of these branches instead of maintaining all of them, then somehow the number of live cats in the universe goes up from half to one, violating the well known principle of the number of living cats in the universe.
Yeah, or people in swimming pools, which I'm going to wait for that paper from me. Okay, hold your breas, yeah under the pool, yes, Okay. So then I feel like maybe I wonder, like you're saying, if we require energy to be conserved in the universe for real, for sure, then maybe I wonder if that's proof that the multiverse exists, because that's the only way this is going to work.
Right, That's a cool perspective I hadn't thought of. Yeah, I suppose if you define energy that way as across the multiverse and you insist that it's conserved, then Copenhagen interpretation of quantum mechanics does violate that. But that's not something you can test, right. You can never access these other brand inches of the multiverse. You can ever know if they exist and if other people are measuring other things. Then you we can only ever access our branch.
We think, maybe, right, maybe you can this. I think we've talked about this before and in our books, like you could maybe discover something about the mathematics of our universe that maybe points to the necessity of other universes.
No, we definitely argue in our book that it might be that the only consistent explanation of the universe is the multiverse. So you can prove the multiverse exists without ever experimentally verifying it, though that takes a lot of confidence to say that there's no other explanation out there.
That would take a high amount of confidence, not a nuclear amount of confidence.
So extrapoling in that argument, if you can somehow prove that a complete theory of the universe has to satisfy conservation of energy at the quantum level, then yeah, that might require the existence of the multiverse. But I don't know how you would prove that requirement because energy is not even necessarily well defined at the quantum level.
I wonder if that means that some of the other places that we've seen energy conservation being violated, like the expansion of the universe. I wonder if that can mean that, you know, as our universe expands and gains energy, maybe there's another universe out there losing energy and being compressed.
It's a great question and one of the reasons I really like this question zooming down to the microscopic scale and trying to understand what is conservation of energy there is because we're really interested in what it means at our scale, Like where does energy come from? Why is it conserved for us? Is it because it's required at the quantum level, or is it because it emerges somehow? And so yeah, maybe energy non conservation in general relativity could eventually be derived from some deep quantum gravity, some explanation of the nature of space time at the quantum level that has these consequences at our scale or at the scale of the whole universe. So that would be really fascinating.
Yeah, or maybe vice versa, right, Like, if you prove energy conservation at the grand level, it must might have some consequences about you know, what we think is happening at the quantum level.
It could be though sometimes conservation laws cannot be exact. They can just emerge, so they don't have to always hold true at the quantum level to hold true at the classical level. But there are some things that are true at the quantum level, Like we think conservation momentum is rock solid at the quantum level, and the reason we have it at our level is because everything is made out of these quantum bits which follow these rules. So we don't know basically whether conservation of energy is exact the way conservation momentum is because it comes out of the quantum level, or if it's something that emerges somehow when you get classical physics.
I guess maybe your people in a pool experiment is going to conclusively prove that.
Then give me one hundred years. It's going to take a lot of data.
What you Why do you need five years to do this?
Oh man? Because the IRB, you know, you're doing experiments on people. You got to sign the papers. It's the whole thing.
I see. Yeah, And then there's a pool, so the forms get wet. It's all a big mess. What does this have more implications for our understanding of quantum game tax or understanding of energy conservation in the universe.
I think it has consequences for our understanding of what energy is. As we drill down to see what the universe really is like at the microscopic scale, we learn about things that turn out to just be features of our existence. They're not generally true at every level of the universe, you know, like there's no equivalent to ice cream at the quantum level, for example, there's no equivalent to cats. Those things only exist at our level. And so I love that as we keep looking deeper into the universe, we discover things about our experience that turn out to just be part of our experience. They're not generally true about the universe, like our sun is unusual, and maybe our planet is weird, maybe our way of life is weird. And the same way, we discover that the way we experience the universe and the things we think are fundamental about it actually aren't. To me, that's really cool and it opens up questions about like other conservation laws, are other things that we thought were hard and fast and true about the universe actually just sort of like emergent approximate things, and at a quantum level they're not preserved. That would be kind of scary.
Well for me, I'm getting the sense that maybe, like even if we do discover that energy is conserved or not in our universe. That wouldn't maybe really tell us what the real truth is because we wouldn't have access to maybe the multiverse in other universes, which would maybe cancel out what we think is the rule of the universe.
Yeah, that's right. We could see what we think is energy non conservation, but in a bigger picture it all balances out, and so we might never really know these answers.
Well, I'll just take comfort in the fact that even if I don't exercise today, maybe there's a quantum whohe in another universe who is doing double the exercise for the tour that both us and in some way you can say that I exercised today.
Yeah, that's true, and that quantum whoorge will live longer than you, and on average, you know, some fraction across the uterus will be alive or not.
Yeah, there you go. There you go, playing with some kittens and counting people in a swimming pool. All right, Well, we hope you enjoyed the Thanks for joining us, See you next time.
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