Something Deeply Hidden | Sean Carroll | Talks at Google

Thank you, it's great to be here at Google. I have used your service on the Internet and yes, I want to talk about quantum mechanics and I guess I know there are some experts in the audience. I suppose there are many complete ones. Non-experts, but probably even the most well-rounded non-experts, have heard the phrase quantum mechanics and know that there are many books on quantum mechanics and why you need another book on quantum mechanics and I think the answer is that I don't like any of the other books, especially because what they tend to do is emphasize how difficult it is to make sense of quantum mechanics, how surprising and spooky and mysterious it is, and I admit that there are things about quantum mechanics that are difficult to understand, but I don't think that there is nothing intrinsically unintelligible about it, so the message of my book is that you can understand quantum mechanics, not that you can't, of course, I am against my esteemed predecessor. at Caltech Richard Fineman who believes I can I think I can safely say that no one understands quantum mechanics and I know what he means, you know he's not wrong, we, quantum mechanics, for those of you who don't know, is this theory wonderfully successful that we developed. mainly during the first quarter of the 20th century, that's supposed to apply to everything in the universe, but it really becomes manifest and necessary when we look at microscopic things, when we look at electrons or atoms or things on a very, very small scale and we can use this theory for With extraordinary precision we can make predictions that have been tested to twelve decimal places of precision.

Quantum mechanics is absolutely necessary to understand why the Sun shines or how transistors work or why this table is solid. Well, why does Fineman say this? Because although we can use quantum mechanics to make predictions if you ask physicists, but they don't know what's really happening and that's okay, it's okay not to know things, but when you don't know what you should try to do is learn how to figure it out and how Field physics has decided not to do that, instead taking the people who are trying to understand quantum mechanics at the deepest level and treating them like the superstars and the most important people in the field, kick them out of the field, have decided that in trying to understand quantum mechanics at a deep level it is not our job as physicists it is just to make predictions I think this is bad the analogy I like to use is with Aesop's fable of the fox and the grapes if you remember this one, the fox sees the grapes and I would like to eat these wonderful juicy grapes and jumps but he can't reach the grapes the fox can't reach the grapes then the fox says you know what I never really wanted those grapes anyway they were probably sour the fox represents to physicists and grapes represent the understanding of quantum mechanics.

We used to try very hard to understand quantum mechanics and subsequently we stopped and I think it was a mistake, so let me tell you how we got to quantum mechanics. This is a false version of the story, but it gives you an idea, so in 1909 we had this picture of the atom, which is the same cartoon that you will always see when people talk about atoms. I think it's literally the logo of the Atomic Energy Commission or the Nuclear Regulatory Commission. There is a core in the middle. The atom we now know is full of protons and neutrons and there are electrons orbiting the atom.

Well, the problem is that although this is consistent with some data, it cannot be true as a final answer, at least by the standards of classical Newtonian mechanics because these electrons spinning in orbits should emit electromagnetic waves when you take a charged particle as a electron and you shake it in any way, it has an electric field that radiates in all directions, so when you move the electron, the field adjusts and when you move it up and down, the field waves and we see those of that's where the light we're seeing now is coming from vibrating electrons so these electrons moving in circles should be emitting light and that means they should be losing energy and they should be spiraling into the nucleus of the atom and you can calculate what How fast should that happen, it's about 10 to minus 11 seconds, which is a very short period of time, in other words, according to the rules of classical mechanics. applied to Rutherford's model of the atom, all matter should be dramatically unstable, you and the chair you are sitting in at this table and the earth itself should collapse to one point in a tiny fraction of a second, that prediction does not fit the data, so we need to do

something

better.

There are a lot of ideas discussed around what we eventually find: don't think of the electron as a point particle in an orbit, think of the electron as a particular wave, we call this a wave function, which is the most boring name and Uninspiring for the most important thing in all of physics, the wave function, is the idea that, instead of being in an orbit around the nucleus of the atom, think of the electron as being described by a wave that extends around the atom. and just like a violin string that is plucked in different ways you know that a string that is tied at both ends has an open frequency as I assume that is the fundamental frequency at which it can vibrate and then there are overtone harmonics in which can vibrate in different ways, the point is that there is a discrete set of different shapes that can vibrate in the same way, if you think of the electron as a wave instead of a particle, there is a discrete set of shapes that that wave can have in the atom and there is a minimum energy form, so instead of just spiraling towards the center of the nucleus, the electron goes to its minimum energy configuration, which is still extended, it is the form in the top left here, spherically symmetrical, these other shapes are higher energy versions of the electron wave function and then it just stays there forever and if you remember, high school chemistry was tortured by images of electrons doing these things and the various orbitals they could be in, so this became a way of thinking about why matter is stable, an even better match.

Years later, Erwin Schrodinger came up with an equation for how these electron wave functions of these orbitals actually behaved, and I'm giving you the details of Schrodinger's equation because I know everyone wants to go out and solve it and has time on their hands. There are people here at Google. who spent a lot of time solving this equation on quantum computers and you don't need to know the details of the Schrodinger equation if you are not an expert in quantum mechanics, what you need to know is that there is an equation, so physicists love equations for good reasons is because you can start from the original idea that the electron is a wave around the atom and now you can apply it widely, you can apply it to any other circumstance, you can take the wave function doing anything and you can let it evolve, you can solve this equation in words, Schrodinger's equation says that any wave can be decomposed into different energy parts and each energy part evolves at a separate rate, so the energy of the waves is proportional to the speed at which it evolves, that It is the Schrodinger equation. everything and therefore this equation that you still know, suggested in 1926, is still correct, as far as everyone knows, it is one of the fundamental rules of nature, so you might think that we are triumphant that quantum mechanics is basically finished, that we know now the electrons.

They are not particles, they are waves this is the equation they obey that is what you want in a good physical theory an understanding of what nature is and what equation it obeys the problem is the data does not stop there so this is a small image wonder of a piece of uranium in a cloud chamber, then a cloud chamber has some pressurized gas that when a charged particle moves through the gas, it ionizes the particles around it and creates a little track, so if you have a piece of uranium is radioactive, it will actually emit electrons and alpha particles and things like that and you can use the Schrodinger equation to say well, what does the wave function of the emitted electron look like?

The answer is that it looks like a spherical wave. in all directions more or less equally, there are details, but that's the basic story, but then you look at it and you never see an electron coming out in all directions equally. What you see in this image are trajectories of straight lines, as if the electron were a particle again. What's up with that? We have not yet answered this question. What's up with that? This is the sad part of the modern understanding of quantum mechanics. So what people said was, "Look, it looks like the way electrons behave in their wave functions is different when you." You don't look at them like when they're in the nucleus around the nucleus of an atom versus when you look at them like when they're in the bubble chamber or the cloud chamber.

Okay, surely that can't be the final answer, but what was the strategy adopted by physicists in the 1920s is yes, that is the final answer, so they invented an idea called wave function collapse. They said that safe wave functions for electrons or whatever obey the Schrodinger equation when you're not looking at them, but when you measure a quantum mechanical system, its wave function changes suddenly and unpredictably and instead of predicting exactly what is going to happen, you can predict the probability of different things happening and the probability is greater where the wave function was greatest and after you measurement you have It happened that the wave function changes were located where you observed them, for which on the left here you have a picture of a wave function that could be fully extended for an electron.

Imagine measuring the position of the electron, its wave function collapses somewhere and if you look at it again immediately, you will see it in the same place, so this is the attempt to understand why electrons are all spread out in wave functions when you don't look at them, but they look like particles when you look at them. Because the act of measurement is

something

special, it actually does something to the particle in a particular way, so this is what is not called the textbook or the Copenhagen interpretation of quantum mechanics. This is what we teach our college students.

I'm not going to reveal the truth. I know this is what we really tell our kids, it's what they told me. The rules of quantum mechanics, according to this way of thinking, come in two groups. There is a set of rules for when you are not observing the system. Those rules say that the electron is described by wave functions or any quantum system, there is a wave function and that wave function obeys the Schrodinger equation and that is exactly in parallel with the rules of classical mechanics in mechanics. classically there is a system and it obeys some equations and that's it, that's all the rules in quantum mechanics you have those rules, but then there are additional rules for what happens when you measure, look at or observe the system.

You can only measure certain things when you do, the wave function collapses and the best you can do is predict the probability of a certain collapse that is the Copenhagen interpretation this is clearly unacceptable as a fundamental theory of nature. I mean, what are you talking about? You know it's okay to make predictions and build things, but it's clearly not the final answer. This was the point of discussion in the famous Bohr Einstein Debates in the 1920s and 1930s Niels Bohr was one of the founders and proponents of the Copenhagen interpretation. Einstein said: look, it's fine as far as it goes, but clearly it hasn't gone far enough, we have to look deeper, hence the title of my book. there's something

deeply

hidden

, there's something else going on that we haven't explained yet and Bohr and his friends said no, no, it's okay, don't worry about it and his friends were born totally won the PR battle, but I think Einstein in reality was In this particular dispute, let me mention two reasons why the Copenhagen interpretation alone cannot be the correct final answer.

There is what we could call the problem of reality. We started by saying that electrons should be considered as wave functions, but what is it? The wave function really is the wave function, a complete description of nature, in other words, is there an isomorphism between the mathematical formalism of a wave function and what makes reality or is it part of nature but not nature? whole part, maybe there are other variables in there, that's what Einstein himself thought there was a wave function, but there were also particles, so the wave function described what happened when you didn't look at them, but when you measure something you see the real particle and in the modern version they are called

hidden

. variable theories, Bohemian mechanics is the most famous version, but perhaps the wave function does not represent reality in any way.wave function the cat in the observer.

I should really put all the rest of the universe to be strictly correct, so here is all the rest of the universe, it's usually in this The context called environment, so I made a picture of the grass, but actually what you should think about is the light coming from these bulbs with the air in the room like all things, all the degrees of that were not explicitly recorded. which collide with us all the time but we don't know where each individual photon is long before we open the box in the box there are photons, there are air molecules etc., they will interact with the kacct and they will interact with the cat differently depending on whether the cat is awake or asleep because the cat is in different places in the box, so a photon will hit it or not depending on whether the cat is awake or asleep, so the environment becomes entangled with the cat long before open the box and finally you open the box and you say what you call what you're doing is called measurement, but actually you're getting tangled up with the two different quantum states that were always there now, why?

It matters, it looks a lot like this equation at the bottom is very similar to the equation we had before, what matters is that these two different states of the environment, well, they put it this way: the environment is doing two things different and separated in the two parts of the wave function, the part where the Quetzal wakes up and the part where the cat sleeps. The technical term is that these two environmental states are orthogonal to each other. You can prove mathematically that this will happen very, very quickly and what that means is that the two separate terms in this equation evolve separately obey their own equations of motion if something happens in one part of that sum of two terms, it doesn't affect anything that happen in the other term, so it always says that this is the prediction of the Schrodinger equation and it is correct, believe it, this is the final answer that I haven't realized is that you are asking why I don't feel like I'm in a superposition the answer is because now there are two of you there is one of you who saw the awake cat and one of you who saw the sleeping cat it's like these two different parts of the superposition describe different worlds so the crucial part here is that never puts the worlds in the usual interpretation.

I'm not really giving away a surprise here, it's sometimes called multiple worlds. interpretation of quantum mechanics, he never called it, that name was invented only in 1970 by Bryce, namely the point is that if you just have the Schrodinger equation, you just follow what it does, the worlds look like that or not, they always were there, only points. Discovering what they naturally come to be, the decoherence process separates the wave function into distinct branches that no longer interact with each other, so they are, for all intents and purposes, separate worlds. Now there are a lot of questions you can ask about the interpretation of many worlds. many of them are easier to answer some are difficult many of them are difficult to be honest, but I'm not going to go into all of them.

I just want to give you an idea of ​​how we answered them, so one question is how many worlds there are, we don't know, that's the short answer, we don't even know if the number of worlds is finite or infinite, well the direct and simple answer is that there are infinitely many worlds. is what he himself would have believed at the time Technical level for those of you who know a little about quantum mechanics the question is what is the dimensionality of the Hilbert space the space of all possible wave functions for simple systems like an electron in non-relativistic quantum mechanics or a quantum field theory Hilbert space is almost always infinite dimensional and therefore, for all intents and purposes, there are an infinite number of worlds, but we don't know this for sure and people like me think that quantum gravity implies that Hilbert space is actually finite dimensional, so maybe there is only one finite dimension. finite number of worlds, but even if it's a finite number, it's a really big number, so instead of thinking about division, wave function branching happens in special events where you work hard to make it happen , it happens all the time, there are radioactives. disintegrates in your body about 5000 times a second and each one of them duplicates the universe, so instead of thinking about a special event that divides the universe, there is a constant hiss as the universe subdivides and that is the way to think about it.

It's not a doubling of the world with twice the energy and everything there is a certain amount of world missing from the equations and it's subdividing and differentiating as time goes on, think of the world as dividing, not like it's being divided. copying in a way now there are some objections that I think I can easily answer one is that there are too many universes sorry I don't like this it's not a very scientifically respectable concern but you know I get it the problem is you know there's enough stuff going on in a universe, doesn't it seem like an ontological extravagance to add all these extra things?

The answer to this is that once you believe in quantum mechanics, the potential for all these worlds was always there. Once you believe that electrons can be in superpositions, you should believe. that people can be in superpositions and worlds can be in superpositions Hilbert space is the name we give to the space of all possible wave functions is no larger in many worlds than in Copenhagen or the quantum mechanics interpretation of anyone else is simply that at many worlds the wave function is wherever it is in Hilbert space, so this might be an objection to quantum mechanics, but it is not an objection to many worlds per se.

The second question is how can this theory be tested? All these other worlds that I can't interact with, don't that violate the spirit of science? Should I be able to test my predictions well? There's a longer conversation here, but let's appeal to Karl Popper, the philosopher who said that a good scientific theory must be falsifiable, of course, every scientific theory makes some predictions that cannot be tested. The question is: is there any event, any experiment that you can imagine that could give you answers that would make you reject the theory and remember everything? This is the claim that wave functions exist and they obey the Schrodinger equation, that's the world, so this is the most falsifiable theory ever invented.

All you have to do is find variables other than the wave function or find the wave function by doing something other than obeying Schrodinger. equation and there are experiments underway to do exactly these things. Karl Popper himself was a great admirer of Everett's interpretation and thought the Copenhagen interpretation was a philosophical monstrosity, so in terms of testability, Everett is as good as the anyone else's interpretation of quantum mechanics now. So, I think those are the easy-to-answer objects. There are two other questions that are more difficult. I'm going to do just a minute with one of them and then a couple of minutes with the other.

The first difficult question is where does the probability come from? As an empirical matter, when we make measurements on quantum systems, it is certainly true that the best we can do is predict the probability of certain measurement results, and in Copenhagen that is because we included a postulate in the theory that says that there is a rule of probability, okay? As long as all the postulates are that there is a wave function that obeys the Schrodinger equation, there is no mention of probability. In fact, the Schrodinger equation is one hundred percent deterministic. If I know the wave function at a given time, I can predict it at any time. another time there is nothing probabilistic about dynamics, so how does probability come in?

What do we know about quantum mechanics from experience? The answer is this idea of ​​self-localization of uncertainty. In fact, you can know everything there is to know about the wave function and there is still something you don't know. which is where you are inside the wave function, so let's go back to the cat and the observer after the decoherence occurred, but before the observer knows which branch of the wave function there, the decoherence happens very, very quickly, Typical time scales are less than ten seconds minus twenty. in a large macroscopic system that you are not trying to protect, so before the observer opens the box, a decoherence occurred in the wave function that branched, so there are already two branches of the wave function, the branch of the awake cat and the branch of the sleeping cat, but because the observer did not look, there are two copies of the observer that are exactly identical to each other because the observer has not opened the box.

If you ask the observer which branch you are on, awake cat or sleeping cat, they don't know that they are identical, so even though they know the entire wave function of the universe, they don't know which branch they are on, that is an uncertainty of self-localization and one can ask, given some reasonable assumptions, whether there is an exceptionally rational way of assigning credence as probabilities to being in one. branch or another and you do the calculations and the answer is yes and you guess what is exactly the same postulate that you had in the Copenhagen interpretation, the probability is given by the wave function squared, so it is very natural that the probability arises .

Although the underlying dynamics are completely deterministic, now the most difficult question is how do we relate Eveready in quantum mechanics to the classical world that we see of tables and chairs, and for me it is difficult to understand this because most of my fellow physicists do not even They think this is a problem. I think it's the most difficult problem and we should all think about it, but you know, we all grow up we tend to think about the world classically, so we look around us and see that there are cats there. there are trees, there are people, those are the starting point when we start when we try to describe the world, so when even professional physicists make quantum mechanical models of the reality of spins, materials or particles, they start with some classical description and then They quantify it.

So you start with some classical stuff and then there are rules that they teach you in graduate school or undergraduate education to turn that into a good quantum theory and at the end of the day you have a wave function that mathematically is a vector that lives in the Hilbert space. living in this giant dimensional vector space presumably that's cheating, presumably nature doesn't start with a classical theory to quantize it. Nature doesn't need that nature it's just quantum mechanics from the beginning, so in a sense you should start with wave function thinking. as a vector in some abstract Hilbert space and deriving the rest of the world, that's how nature actually works, which turns out to be really very difficult and is more difficult in many worlds than in other approaches to quantum mechanics and other approaches to the quantum. mechanics, whether it's Copenhagen or hidden variables or whatever, they introduce some features of the classical world into the definition of the theory even though there are many worlds when it comes to assumptions when it comes to pieces of the theory itself.

Everett is the leanest. and the baddest wave functions in the Schrodinger equation and that's it. Any other approach to quantum mechanics adds extra things and those extra things give you insight into why the world seems classical in a certain way. In Everett you have to work harder. Why does the world seem classical? Classical is a perfectly good question, so keep that question in mind, why does the world look classical? There is another question we have, which is quantum gravity. I'm sure you may have heard of it depending on what corners you're on. Keeping in mind that we still don't have a good quantum theory of gravity, we can follow this procedure that I mentioned here and it works for all forces in nature and every piece of matter in nature, except gravity, for electromagnetism, for nuclear, the particles we know about leptons and quarks, etc., you start with a classical theory, you quantify it, you get a reasonable answer for gravity.

The best classical theory we have is Einstein's general theory of relativity and his point is that gravity is a feature of spacetime. itself, that is, it is the curvature of space-time, curves and warps of space-time in response to matter and energy, and we experience that curvature as the force of gravity, so it has a perfectly good classical theory , we can put it in our black box and we can quantify it and we have a terrible mess, it doesn't work, we still haven't successfully taken classical general relativity and applied the usual quantification rules successfully, that's why people are driven to consider alternatives such as string theory or loop quantum gravity, etc.

They have made some progress, but none of them.time? Is there a notion of running out of space on some of the returning branches? and hitting each other, it absolutely is, so if there are a finite number of possible branches and branches occur all the time, mathematical theorems tell us that we are going to run out of branches, happily we are not close to doing that and how do we do that? would see. is simply the approach to thermal equilibrium within any branch, what happens is that all branches become indistinguishable from each other because Equity Briam looks the same no matter where you started well, so in some very real sense, once that happens , it's not so much about the branches. reject together since there is no difference between the different branches there is no obvious way to divide the University of branches at all why can you say with such confidence that we were not close to that because it does not seem like thermal equilibrium?

I mean, happily there are still stars shining in the sky, so anything else I can sign books if we have a few minutes left, but yeah, this is a different style of question, but I think quantum mechanics has a reputation for being a very arcane and yet I think that the kind of thinking that is suitable for theoretical physics is probably quite widespread and common and I think this mainly because I am a software engineer because I find myself at home reading and listening to theoretical physics books and things that You know, bad theories. It smells bad in the same way that bad software smells bad, so if this is really the biggest problem you know in science, possibly how can we have a radical change that allows you to meet ordinary old people who Do you like to think this way to do something about it? and it's not just like increasing the number of nuts, yeah, you know, I mean, it's a good question and it would be easy to joke about it, but it's hard to give the right answer, you know, here's the good news, you know, of course, quantum mechanics.

It involves mathematics, complex analysis, linear algebra, etc., but it's not that difficult, and also these types of questions, these fundamentals of physics, mathematics are not the obstacle, you know, it's really like it's undergraduate mathematics and you can obtain it as a professional theorist. physicist in field theory or string theory or whatever in mathematics becomes more and more difficult, but none of that is really relevant here, honestly, so I think that if you are an honest self-taught person and who likes to study quantum mechanics from a textbook and learn enough Thinking

deeply

about the fundamentals of physics questions is very doable.

I mean, one of the two best books on the foundations of physics is David Albert's book, Quantum Mechanics and Experience, and David Wallace's book, The Emerging Multiverse, and they're both pretty accessible. to people who like matrices in calculus, so I would say, "read them, take them seriously, and see what you have to do." I was just going to make an observation: I enjoy a podcast that

talks

about a lot of these things called mindscape, yes. I have a strange cast somehow. I didn't mention that. Thank you. Thank you. Your $5 is in the mail. Subscribe to my podcast.

Sometimes I talk about quantum mechanics, but other times I talk about music or movies or whatever we're going to talk about that day, so it's a fun mental escape. Thank you very much for inviting you.