Aristotle argued almost 2,400 years ago that a perfect vacuum could never exist. Today, the concept of nothingness figures at least implicitly into almost every theory of modern physics. In this episode closing out season 2 of “The Joy of Why,” the theoretical physicist Isabel Garcia Garcia of New York University and the Institute for Advanced Study talks with host Steven Strogatz about the impact of quantum mechanics on the definition of a “true vacuum,” the possibility of false vacuums, how the concept of vacuum energy relates to the cosmological constant, and how her studies of the vacuum could help to resolve frustrating puzzles in string theory and cosmology.

“The Joy of Why” will return with new episodes in early 2024.

Listen on Apple Podcasts, Spotify, Google Podcasts, Stitcher, TuneIn or your favorite podcasting app, or you can stream it from Quanta.

Transcript

Steven Strogatz (00:03): I’m Steve Strogatz, and this is “The Joy of Why,” a podcast from Quanta Magazine that takes you into some of the biggest unanswered questions in math and science today. In this episode, we’re going to ask: Does nothingness exist?

(00:17) Philosophers and scientists have long debated whether nothingness is even possible. Aristotle, for instance, argued that a perfect vacuum could never exist because, if it did, objects moving through it wouldn’t encounter any resistance and hence could travel infinitely fast. And 2,000 years later, when the boy genius Blaise Pascal proposed that it might be possible to create a vacuum by sucking all the air out of a closed container, René Descartes shot back, “It seems to me that the young man who wrote this booklet has a little too much emptiness in his head.”

(00:51) Still, to most of us, the idea of a vacuum sounds reasonable. If you take a container, seal it tight, and somehow remove everything inside, well, it sure seems like there could be nothing left in there. But can we really call it nothing? After all, there could still be energy inside or perhaps subatomic matter and particles that we just can’t see. In modern physics, this idea of nothingness has been making a comeback. In fact, it turns out to be the basis of every theory of something. Nothing nowadays is something.

(01:25) Are you confused yet? Well, here to help us sort all this out is Isabel Garcia Garcia. She’s a theoretical physicist currently at both New York University and the Institute for Advanced Study. She’s looked at everything from the bubble of nothing to the interplay between particle physics and gravity. Isabel, thanks so much for joining us today to tell us a little something about nothing.

Isabel Garcia Garcia (01:48): Thank you for having me.

Strogatz (01:49): Oh, well, it’s a great pleasure to have a chance to meet you and chat with you. So why don’t we begin, just to make sure we’re on the same page, with the basics of what do we mean by a vacuum? Is there one definition that we could all agree on?

Garcia Garcia (02:03): Nowadays in the context of a theory of quantum mechanics, or quantum field theory more generally, very intuitively what we mean is literally what is left when we remove everything that can be removed. There’s some idea that, as you were describing earlier, you know, if we take this room and we take all the people out and all the furniture out, then we take all the air out — all the little molecules and atoms that make the air out — then something like that would be the vacuum. So that notion of, you know, removing everything we can until we can no longer remove anything else, that can be made more precise, again in the context of quantum theory. And that state that is left is what we call the vacuum. And sort of by definition, everything that exists, exists on top of this bedrock that is the vacuum.

Strogatz (02:51): So if we can remove everything, what’s left, I guess, is nothing. That is the vacuum. You spoke about removing matter, like removing the furniture — I like that image — the furniture, the people, the atoms. Before we get to quantum theory, so if we’re just speaking of a classical vacuum, I understand that there could be different notions, like an electromagnetic vacuum or a gravitational vacuum?

Garcia Garcia (03:17): That’s basically just a statement about what particles you actually are getting rid of. If you make an electromagnetic vacuum, you’re sort of just assuming that, you know, you’ve removed all the photons in a certain region, perhaps in a cavity. And you make it free of any type of photons in this way. You can take that farther in the context of classical physics and say we’re just going to remove everything. And what is left over, we will call the “absolute vacuum.” And so in the context of, you know, classical physics, that is a notion that makes sense. And that state that we are left with, which is completely empty, no particles are in there. And in particular, it contains no energy. There would be sort of like complete stillness, if you wish, in this vacuum. So there is a picture that in classical physics, that’s how you would think of the vacuum, and it makes intuitive sense from our daily experience of classical dynamics.

Strogatz (04:10): Right. So it doesn’t seem that super problematic, I mean, except for what Aristotle was complaining about, but that was a long time ago. But still, within classical physics, it does seem like there’s nothing in principle that outlaws — if I understand you right — nothing outlaws a vacuum classically. How does this idea change, though, let’s say when we get to the old quantum mechanics of, I don’t know, the 1920s or something like that? Is there a vacuum in that kind of quantum theory?

Garcia Garcia (04:36): This classical idea of the vacuum we were discussing made complete sense, made a lot of sense, sort of pre-20th century. With the discovery of quantum mechanics, a lot of things changed. One of the things that changed is the fact that in words, we can say that in quantum mechanics, there is no such thing as complete stillness. You may have heard of something called the Heisenberg uncertainty principle, which is one of the bedrocks of quantum mechanics. This tells us, in particular, that the uncertainty in the position of a quantum particle multiplied by the uncertainty in its momentum — sort of the measure of like how fast this is moving — that quantity, that product has to be larger than what is known as Planck’s constant over 2 pi, okay? So it cannot be zero, it has to be larger than a certain quantity.

(05:26) One of the most striking implications of this, that has no analog in classical physics, is that a quantum particle can never be, sort of, exactly at complete rest. So, you can imagine a pendulum going back and forth. And in a classical physics mindset, you can imagine the pendulum being sort of like at rest, just hanging down vertically. When that happens, that pendulum has zero kinetic energy. It’s not moving anywhere, and it has zero potential energy because it’s, you know, at the minimum of that gravitational potential.

(05:57) If we take into account the physics of quantum mechanics and we consider the quantum version of that pendulum, it turns out that that state of stillness is never achievable. Heisenberg’s uncertainty principle tells us that if we try to localize the quantum particle at the very bottom of the pendulum, then the uncertainty in its momentum and its velocity needs to be large. So, there will be some average motion of this particle around this minimum. Conversely, if we try to make the motion, the momentum of the particle, very tiny, its position will fluctuate a lot. So it will be displaced on average by a large amount from the minimum. So you either have some large amount of kinetic energy or some large amount of potential energy.

(06:44) So there is no winning, so to speak. You cannot make the state of this quantum pendulum be at this complete still state of, like, zero energy in the way you can do it in classical mechanics. So you can already see that, you know, in quantum mechanics, this notion of stillness, of zero energy, of like absolutely nothing is happening doesn’t quite make sense. And this goes by the name of what is called the zero-point energy of quantum systems. There is some minimal amount of energy that it is possible to reduce the energy of a quantum system down to, and the number is not zero.

Strogatz (07:15): It’s so interesting, that was a beautiful explanation. Just let me underline something that you didn’t mention. But I think, if my understanding is right, you will agree. That this is not something having to do with temperature. People might have learned at some point in school that at absolute zero, all motion stops. What about that in this context?

Garcia Garcia (07:34): That is a classical notion. So, of course, you know, at finite temperatures, things are in motion due to thermal fluctuations, etc. This is something that is true even at zero temperature, that is where quantum mechanics — all the effects are sort of dominated by quantum physics. It is in this context that this zero-point energy is real.

Strogatz (07:52): It is just such an amazing thing, like so many things in quantum mechanics, that are, as we always say, counterintuitive or bizarre because we ourselves are macroscopic. We’re not — well, we do have daily experience with it because, in fact, I am talking to you right now using probably semiconductor chips that are based on quantum mechanics. But we’re not thinking of it like that. It just seems hard to believe that there’s no such thing as absolute stillness anymore. So, why is that relevant? You are talking about a particle can’t be totally still, but can we also apply the uncertainty principle to a field?

Garcia Garcia (08:24): Yeah, indeed. So, once we move from quantum mechanics to quantum field theory, the main entities that we use in quantum field theory to describe our universe and quantum field theory in general are fields. They are no longer particles. And we understand particles as excitations of these fields, OK? So you can think of a field in very rudimentary terms. One of these tiny simple harmonic oscillators, sort of like this tiny pendulum, existing at every point in space. So, when you think about it, you can ask the question: “Well, you know, I can define a quantum field theory as some vacuum state where a number of fields are defined on and are propagating on, and the excitations of the fields will be my particles.”

(09:10) But we can ask, well, even in the absence of any actual excitations, any actual particles, what is the energy of the ground state of the system? What is the energy of this vacuum where the field exists? And because the energy of each of these tiny quantum mechanical pendulum, you know, is a finite number, is this zero-point energy, and because the field is a collection of an infinite number of these pendulums, if you do the calculation in quantum field theory, the answer comes out to be infinite. So, quantum field theory at first seems to be telling you that, actually, the vacuum energy density is in fact an infinite number.

Strogatz (09:49): Yeah, OK.

Garcia Garcia (09:51): Which is something that, you know, doesn’t make a lot of sense, but it’s something that shows up already at the level of undergraduate physics. And so, how do we deal with this puzzle? This is something that bothered the early practitioners of quantum field theory a great amount. And in typical physics style, what we do is we hide it under the rug until we have something better, something better to say. And that’s because, in the context of quantum field theory — what I mean by that is, before we introduced gravity into the description of nature — in the context of quantum field theory we cannot actually measure the absolute value of the energy of the vacuum. All we can hope to measure experimentally, all that is physical are differences in energies between different states. So we can measure energies relative to the energy of the vacuum. So in some sense, what we sort of do in a very handwavy manner is that we subtract infinity, and we are left with, sort of like, some finite quantity that tells us, you know, how much energy a certain state has on top of the vacuum. That’s sort of like the physicist’s way, in the quantum field theory, of ignoring this puzzle.

Strogatz (10:58): OK, that’s interesting. Let me see if I got that. I mean, I’m used to the idea from the physics that I took that changes in energy are the things… This comes up in electricity and magnetism in the first course, that we talk about a potential relative to ground, you know, or something like that.

Garcia Garcia (11:14): Precisely.

Strogatz (11:14): So, differences in energy, that’s a common idea, and that you can sort of set the zero for the energy anywhere you want back in this classical setting. But it’s interesting what you said earlier. So you say when we think of a quantum field, it’s like think of a harmonic oscillator at every point, and they’re all jiggling with their zero-point energy. And so the idea that, like, I have absolute nothingness, which would correspond to a field equaling zero everywhere, that’s just not achievable because the zero can’t stay zero because its associated momentum will be big. And so everything is fluctuating. Even emptiness is fluctuating.

Garcia Garcia (11:50): Absolutely.

Strogatz: OK. But you say when you try to add up the total amount of energy associated with all that jiggling, that’s what comes out infinite?

Garcia Garcia (11:58): Yeah. So, naively, the answer would be the energy of the vacuum is actually infinite, which, again, is something that in quantum field theory, we cannot really make sense of. But in a sense, you know, it doesn’t really matter because that is a quantity that we can never measure directly. We can only measure sort of, you know, differences in energy relative to the vacuum energy. So, we sort of like handwavingly sweep it under the rug in this way.

(12:21) So that would raise a question even in quantum field theory: Are we even sure that the vacuum has that energy? Is there such a thing as the vacuum energy? And how can we be sure? Like, how can we experimentally verify that concept? In the spirit that it is only differences in energy that you can measure, Hendrik Casimir proposed in, sort of, mid-20th century, an idea to verify that concept of vacuum energy by disturbing the vacuum and measuring the change in the vacuum energy itself.

Strogatz (12:56): You’re thinking the same way I’m thinking. I was going to ask you next about the Casimir effect. So, let me just be quiet and let you tell us about the Casimir effect.

Garcia Garcia (13:04): Yeah, so there is some energy intrinsic to the vacuum of a quantum theory. If we disturb that vacuum, that vacuum will respond in a way that its vacuum energy will also change. So, if we can measure that change in vacuum energy as a result of some disturbance, that is the way of experimentally verifying that that concept, the idea of the vacuum being the sort of jiggling, non-still entity, we can experimentally verify that idea. Hendrik Casimir proposed an experiment to measure a change in the vacuum energy. The idea was to start with an electromagnetic vacuum. So in the lab, engineer some kind of cavity where you take out all the photons. So you really take every single individual photon out of a certain cavity, there is sort of like quote-unquote “nothing” in there. Then, you disturb the vacuum by placing two parallel, ideally perfectly conducting plates of material. By perfectly conducting we mean that all the electric charges, the electrons, etc., in the surface are free to move. And therefore, they are free to adjust to the presence of any electromagnetic field that may exist. OK?

Strogatz: Yup.

Garcia Garcia (14:13): Now, in the lab, we can sort of engineer a situation where we move the relative distance between those two plates. So, if the world was a classical world, having those two plates move around relative to each other in an otherwise empty electromagnetic cavity would have no effect. If you try to measure the force that these plates are being subjected to or you try to measure any kind of pressure or any other properties, like, literally nothing will happen to the system. Now, in the framework of quantum mechanics, even though we have taken all the particles out of this cavity, the electromagnetic field will be fluctuating inside the cavity. And the fact that we’ve placed two conducting plates inside the cavity will affect the nature and the properties of those quantum fluctuations. And as we move those plates relative to each other, that changes the properties of those quantum fluctuations, OK? And that changes as well that energy of the vacuum of the system.

(15:12) Now, in physics, a change in energy as we change distance, that is what goes by the name of a force. So, a prediction of the existence of this vacuum energy is that as we move these plates, these plates will experience a force on them, OK? A pressure, as a result of this change in vacuum energy. And that is exactly what was experimentally verified in the lab. It was found that these conducting plates experienced a pressure on them that is attractive. And the magnitude of that pressure was actually found to be consistent with the calculation from the quantum theory. That experiment was done a few years later in 1997.

Strogatz (15:54): It’s just great. To make sure I have it, I think I got it from what you said, that it’s not like these are capacitor plates with charge on them. It’s not that they’re pulling on each other, or they’re feeling some electromagnetic force like we do in that first electromagnetism course I mentioned. These are uncharged plates. And yet, because of these quantum fluctuations, they do experience, well, we nowadays call it the Casimir force.

Garcia Garcia (16:22): Yes. Because of the quantum fluctuations of the electromagnetic field in the region, the charges that exist on these plates, even if they are overall uncharged, they do respond to these fluctuations. And that’s sort of what we can measure in the lab. And the relevant quantity is this pressure that these plates experience.

Strogatz (16:39): Now I take it that this is only really detectable if the plates are close enough together.

Garcia Garcia (16:44): That’s right. The plates need to be very close together. In order for us to see this effect. The pressure that acts on the plates is inversely proportional to the fourth power of the distance between the plates. So you win a lot by making these plates very close to each other. And you know, you very quickly make this effect too tiny to be detectable, if you pull them apart.

Strogatz (17:05): I see. Oh, the fourth power, you say inverse fourth power?

Garcia Garcia: That’s right.

Strogatz (17:08): Huh. Oh, that’s interesting. I’m not used to seeing inverse fourth powers. The famously, you know, gravity’s, right, inverse square in classical theory. Dipoles would be inverse cube. Inverse fourth power is interesting. Oh, I did actually want to go backwards just for one minute. Because I’m so amazed at this idea of the infinite energy of the vacuum being predicted. Does that have anything to do with space itself being assumed infinite in extent? Or even in a finite region of space, would we still have infinite energy according to this prediction?

Garcia Garcia (17:39): That is a great question. And it has to do, to some extent, with both. But actually even in a finite volume, you will have this prediction. The reason is that in principle, you know, those quantum fluctuations in the context of quantum field theory can have arbitrarily large amounts of energy. And sort of, that is what at the end of the day kind up gives us this quote-unquote “infinities.”

(18:00) Now, quantum field theory is not a complete description of nature. It misses a very important piece, which is gravitational interactions. And we know that, through our daily experience and for thousands of years, we’ve known that gravity is obviously a very important part in the description of nature. So really, we have to go beyond quantum field theory into what is called quantum gravity — a theory that combines both the theory of general relativity that explains gravity at the classical level with quantum mechanics. And first of all, it is in that jump from quantum field theory to gravity that the vacuum energy stops being sort of an unphysical quantity that we can only measure other energies relative to, but it has absolute meaning. And it has absolute meaning because in the context of a gravitational theory, energy is something that gravitates. It’s not only mass, but as we learn from Einstein, energy also gravitates and that means that it can bend the fabric of space-time. Also reacts to the presence of energy and in particular, it will also react to the presence of a vacuum energy.

(19:04) Now, if the actual value of the vacuum energy was infinite, that would curve space-time so strongly that it would reduce it just to a point of no size, OK? Which is obviously not the case.

Strogatz: Thank you!

Garcia Garcia (19:20): So we know that indeed, you know, the vacuum energy is not infinite. And in fact, we know from experimental observations of how fast our universe is expanding, we know that the universe is expanding in a way that is accelerated, so it expands ever faster. That tells us that experimentally, the vacuum energy density of our universe is a positive quantity. And its magnitude is extremely tiny. OK?

(19:46) And I mean extremely tiny compared to any other energy scales that are relevant to the description of physics that we know of. So just to give you some numbers, the value of the vacuum energy that we can infer from experiments — via, again, the expansion of the universe — is of order between 0.1 and 1 millielectron-volts. That is an extremely small number. It is many orders of magnitude smaller than even the mass of the electron. Even smaller than the mass of the proton. Well below other scales, like the scale of QCD, the scale of the electroweak interactions. And way, way, way below the largest scales of all that we think is relevant for the description of nature, which is the Planck scale. So that is a number we know is a fact of nature. We know from experimental observations that the vacuum energy density is not zero, but it’s in fact extremely tiny.

Strogatz (20:42): I hear people sometimes talking about 10 raised to the 120th power. Are you telling me that the vacuum energy compared to the Planck energy, is that the factor we’re talking about now?

Garcia Garcia (20:54): Yes.

Strogatz: 10 to the minus 120, or something like that?

Garcia Garcia (20:57): Yeah. So when people talk about this 10¹²⁰ number, that is the ratio in what is called energy densities. So if I take the Planck scale, which is 10¹⁸, roughly gigaelectron-volts, divided by the number I’ve just told you, you know, roughly tend to like one millielectron-volt, And I raise that ratio to the power of four. That’s where this number 10¹²⁰ comes about.

Strogatz (21:23): Uh huh. Raising to the fourth power, why? Because of four dimensions in space-time?

Garcia Garcia (21:27): Yeah, four space-time dimensions, that’s what we mean by a vacuum energy density.

Strogatz (21:30): OK.

Garcia Garcia (21:31): Yeah. So that’s where the fourth power comes about. And when we try to calculate in the context of a quantum theory, dynamical contributions from all the fields we have around to this vacuum energy — where we actually calculate this energy density in quantum field theory, we find that the vacuum energy is infinite — that can be refined. And in fact, in a true theory, where there’s some maximum energy that we can prove that our little pendulum can sort of like move at, the answer is not actually infinite. It comes out to be finite. But in all ways we know of how to do that calculation, the answer that we find comes out to be naively way too big.

(22:10) So for example, even in the context of the Standard Model of particle physics, we have a ton of particles and fields around. You can actually just calculate with pen and paper what will be the contribution of fluctuations of those fields to the energy density of the vacuum. And it comes out to be something proportional to sort of the relevant scale in the problem to the fourth power. So the electron will contribute to the vacuum energy as the mass of the electron to the fourth. But even that is many, many orders of magnitude than what we have found observationally. So there is this puzzle by the name of the cosmological constant problem, which is that the actual measured value of the vacuum energy density is way smaller than all the other relevant energy scales that we know exist in nature. And our calculational frameworks to kind of make sense of that discrepancy are not giving us an answer.

Strogatz (23:04): Hmm. Let’s pause there to let, sort of, soak in that, because our show is about big unanswered questions in math and science. And it sounds like you’ve just put your finger on one of them. So the cosmological constant, the smallness of it, is one of the giant mysteries in physics today, if I’m hearing you right.

Garcia Garcia (23:22): That’s right. So the cosmological constant is precisely what we mean when we say the energy density of the vacuum. And the fact that observationally we see it to be so small compared to all the other relevant energy scales that we know of in nature, it remains the most conceptually puzzling problem in particle physics.

Strogatz (23:42): Could you summarize, then, why is the vacuum so important for physicists to study?

Garcia Garcia (23:47): In a sense, the vacuum is sort of like the starting point of any theory. It is part of the definition of where your theory is. You define your vacuum state as the thing where nothing can be removed from it. In technical terms, we sometimes say like the vacuum cannot be annihilated, there’s nothing left to be removed. And on top of that, you build everything else. So the properties of these vacuum states influence the properties of everything else that you’re going to build on top of it. They influence the properties of your theory, at any other energy scale. So it’s sort of like the pillars of the rest of your theory that you’re going to use to describe nature.

Strogatz (24:24): So is this issue with the cosmological constant being so small, is that the main problem that the vacuum poses? Or is there some other big problem that we should be discussing as well?

Garcia Garcia (24:34): There are various puzzles about the vacuum that the universe finds itself in. The fact that the vacuum energy density the cosmological constant has, this very tiny value is certainly one of the most puzzling. And quantitatively this number 10¹²⁰ just makes it clear that the magnitude of it is beyond anything that we can even conceive. So it is one of the most serious problems. But it is by no means the only mystery of our vacuum. There are other properties of our vacuum that are also somewhat mysterious. And the origin of them, we don’t understand.

Strogatz (25:09): You’re definitely giving me the feeling that there is a lot to still be discovered in physics. That there are a lot of very serious problems with the Standard Model and with our current understanding. And I guess this is the consensus view that more or less all physicists studying fundamental questions like the ones you work on, would agree. There’s a lot to…

(25:30) OK, so let’s start talking about some of your work. I wonder if we should begin with talking about things like vacuum decay, the idea of true vacuum, false vacuum. Can we start there? Would that be a good place to start?

Garcia Garcia (25:40): Yeah. So again, in the framework of classical physics, there is only such a thing as “the” vacuum. If you’re stuck in this state that has zero energy and there’s no other way — like this is the state that minimizes the energy and anywhere you go from there, the energy of your state increases. Basically, you will be stuck there effectively forever.

(26:03) Now, that is something that is no longer true in the context of quantum mechanics. And that is where this idea of sort of like tunneling and vacuum decay first makes an appearance. So you can imagine you’re in a system where you’re at the vacuum with some potential, you sort of like remove everything you could possibly remove. And you are in this state that has a certain vacuum energy. So that is what we call your vacuum. But it could be that there is some other region of parameter space in your theory where it turns out, you can also remove things in a somewhat different way, and the energy of that vacuum is actually even smaller.

(26:43) Now, in classical physics, you can actually not really go from one to the other while conserving energy as a whole. But in quantum mechanics, you can. You can just tunnel from the vacuum that has a slightly larger energy to this other vacuum, which colloquially we will refer to as a true vacuum, that has an even smaller, somewhat smaller vacuum energy. And we call it a true vacuum because, you know, if you start in some false vacuum that has some somewhat bigger vacuum energy, if you wait long enough, the quantum mechanical probability that you actually sort of tunnel yourself to this other lower energy vacuum, that probability will become more than one. And eventually, you just have to wait long enough, that’s where you will end up.

Strogatz (27:24): Just to make sure that we all have the right kind of picture in our head. This idea that there’s a non-unique vacuum, you could speak of two different — I assume more than two, probably, but at least two: a false and true vacuum. In terms of tunneling, and so on, maybe you could give us a classical picture where we think of a landscape with a well, and then a hump, and then a deeper well, and you know, like that. Can you describe that kind of idea?

Garcia Garcia (27:50): Yeah. Before we jump into that, let me perhaps give you an example that may be more familiar to us in the context of thermal physics. So we are used to, for example, somewhat similar events, when we, for example, you know, if you put a pot of water in the stove, you heat it up, eventually, you will have bubbles appearing in the water that contain vapor and then the water will evaporate in this way, right? So, in some sense, your system, which in this case is the water, sort of like your universe is the water, has transitioned into this other state, which at high temperatures is the preferred state, which is vapor, right, like gas. So that happens as a result of thermal fluctuations, not as a result of quantum mechanical fluctuations. But basically, even at zero temperature, quantum mechanics has a way of giving rise to processes like that, where a system that is not in its preferred state can actually sort of tunnel quantum mechanically by nucleating sort of, like, bubbles of this new vacuum into this new state, which will be the true vacuum.

Strogatz (28:55): That’s very helpful. That’s interesting. I didn’t have that picture in my head. But I like that, especially with the word “nucleate.” Because I’m aware of, in the case of thermal physics, that you can have a liquid that doesn’t want to be a liquid anymore. It wants to be…

Garcia Garcia (29:07): Right. So it’s stuck in the false vacuum.

Strogatz (29:10): OK, it’s stuck. And then it needs a nucleation event to trigger it. That’s these bubbles that we need to talk about, like the expanding bubble of nothing. Kind of, except in this thermal setting, not the quantum setting.

Garcia Garcia (29:22): Yeah. So it’s sort of an analogy but the dynamics of it, sort of the picture you should have in mind of like the system is in some state with a certain energy and then it has to cross this energy barrier in order to be able to put itself at this lower vacuum. In the case of thermal physics, it happens as a result of thermal fluctuations that allow you to sort of jump over the hump. In the case of quantum mechanics, quantum mechanics has a way of allowing you to just tunnel through the hump and into the close vacuum.

Strogatz (29:48): Wow. So now why don’t we start talking about extra dimensions, because you earlier alluded to the idea that until we include gravity into this story, you really shouldn’t be thinking about the vacuum in modern physics without including gravity. We need gravity to be part of the story.

Garcia Garcia (30:04): Yeah, gravity is an essential ingredient in making sense of all of these concepts. What the vacuum of theory is, in particular what a vacuum energy is, conceptually also what its quantitative effects are. So gravity is definitely an important piece.

Strogatz (30:16): So then should we talk about ideas of string theory and extra dimensions? I’ll let you take the lead on what concepts do we need to know first.

Garcia Garcia (30:24): As it is well known, the leading theory, and in fact the only theory that we know of that sort of successfully makes sense of quantum mechanics and general relativity together, is string theory. And it is a property of a string theory that the theory can only be consistently defined in a space-time that has dimensions more than four. Things can vary a little bit, but typically string theory has to be formulated in 10 space-time dimensions.

(30:52) Now, that is weird because obviously in our experience in daily life, we know that we live in a universe where space-time is four-dimensional. We have three dimensions in space plus time, so that makes our space-time four-dimensional. So, what happens with these extra six spatial dimensions that string theory comes with? And the answer is that for any successful description of nature, those additional dimensions of space need to be what we call compactified. So, by compactified, we just mean it’s a fancy way of saying that those extra dimensions have to be super, super tiny. So tiny that not only we don’t see them, we cannot experience them in our daily life. They are sort of like completely hidden from our view, from our experience.

Strogatz (31:46): Well, OK, where to go next?

Garcia Garcia (31:48): So, let me say a bit more. Yeah, let me say a bit more. Experimentalists, in different ways, look for extra dimensions. So far, we haven’t found evidence that there are any, but it is a logical possibility that there could be more spatial dimensions in our universe than the ones we observed. And moreover, it is a feature of this theory of quantum gravity, the only theory of quantum gravity we have which is string theory. And so if these extra dimensions exist, they need to be compactified. So very tiny.

(32:16) And that, by the way, is another property of the vacuum in which we live. So there could have been, and there probably are in a general theory, other vacua where those extra dimensions maybe were infinite in extent. They were uncompactified, like the ones we experience. It has to be that a property of our vacuum is that all of those extra dimensions are compactified. Now, if you start with a theory, like string theory that has 6 extra dimensions. And on all of those different dimensions, there are a lot of other fields beyond the ones we have in the Standard Model where these fields propagate. As we compactify the theory from these 10 dimensions to our four-dimensional space-time, it turns out that there are very many ways in which you can do this. The number of combinations in which you can compactify things and, you know, fields can behave in these as you compactify down to 4D is something that grows very fast. This leads to this picture that was made more precise in the early 2000s by Raphael Bousso and Joe Polchinski that string theory comes with this vast landscape of four-dimensional possible vacua that arise as a result of all of those possible ways you can bring string theory down to four dimensions.

Strogatz (33:37): And so these are all conceivable universes, I guess, that are consistent with string theory. It’s just that we happen to — I mean, assuming the theory is correct, we live in one of them locally, I guess, is that right?

Garcia Garcia (33:51): That will be the idea. In principle, instead of predicting a single theory of nature, which is, you know, something that looks like our universe, string theory would seem to predict something like this vast landscape of possibilities of universes, the vast majority of which look nothing like our universe.

Strogatz (34:09): And so your own work: Is it that some of these theories are unstable?

Garcia Garcia (34:13): Yeah. So, I want to emphasize that the discovery, if I can put it this way, sort of like a theoretical discovery, rather, of the string theory landscape, it was a big shock, I would say, for the theoretical physics community. And it really was like a tour de force, I think it really changed the perspective on what we actually expect from string theory for a lot of people. And in many ways, it’s very troubling. It’s sort of like we have a theory that predicts nothing, because it predicts everything.

(34:39) So how do we choose? Like, how can we explain the features of the universe that we live in? Like, why do we live in one particular vacuum and not the other? When you have 10⁵⁰⁰ possibilities that seems like a very hard ask.

(34:53) Prior to the discovery of the string landscape, we couldn’t explain the size of the cosmological constant and people tried to find arguments as to why it could have that size. And sort of a famous argument by the late Nobel Prize winner Steve Weinberg that you may have heard of by the name of the anthropic argument goes as follows: If the cosmological constant had been any other value, a universe like ours, where galaxies exist and people like us exist, and where people like us can do physics, and actually, you know, build telescopes and make these observations that allow us to measure the vacuum energy and therefore argue about it, that universe could not have existed if the vacuum energy would have been anything other than roughly the value we’ve observed.

(35:37) Like, for example, if the number was a lot bigger, the universe would be expanding a lot faster, in a way that would have precluded, for example, galaxies to form and planets to form, etc. So he made this anthropic argument that has something to it on the one hand. But at the same time, it makes a lot of physicists very uncomfortable because we want a theory of the universe, and we don’t like to have to refer to ourselves, put ourselves, humans, in the middle of some kind of big argument as to why things have to be this way. Right? It feels, it feels backwards, it feels like, like physics should go beyond this. Like, we have this idea that, you know, we are not special, like our place in the universe is not special in any way. So why do we have to refer to our own existence to explain this observation?

(36:22) And then the discovery of the string landscape actually made that anthropic argument more precise, because actually, now, there is a landscape of vacua, where you can imagine scanning the value of, like, the cosmological constant and sort of making the arguments more precise and saying, “Well, there are actually all of these other possibilities where a universe like ours doesn’t exist. So it must be that we live in the one where a universe like ours is possible.” There are people in our field that are at peace with the idea that may be our only way to understand the size of the cosmological constant. But a lot of people also feel very uneasy.

(36:59) And I think — I’m certainly one of those people, in that I feel like this is telling us that we’re actually missing something conceptual about the whole picture. And so, you know, one possible way out of having to make these anthropic arguments but that still kind of can coexist with the existence of a string theory landscape is, if, in fact, many of those other vacua are actually not fit for not only life like ours but, like, anything. Any life.

(37:09) So that’s where the importance of understanding the stability of all of those different vacua comes in. If many of those other vacua are so short-lived, that only exist for a very small amount of time — so you know, an amount of time that is smaller than the current age of our universe — then those would not be allowed vacua for us to exist on.

Strogatz (37:54): Right, that sounds like a very plausible kind of criterion to think about, of these 10⁵⁰⁰ possibilities, which ones… Not so much that they’re hospitable to life, as you say, but just hospitable to anything, to having any kind of structures or anything in them other than just… Is that the point? That universes that can sustain anything, as opposed to just like immediately collapsing into vacuums with nothing in them?

Garcia Garcia (38:20): Yes. So there are different types of instabilities that these vacua can be susceptible to. You know, they can go from the current vacuum into like some other vacuum that looks similar, but a little bit different from the previous one. But then there is this remarkable possibility that was discovered by [Edward] Witten in the early ’80s, that in theories that have extra dimensions, a vacuum could actually decay to something that is true nothing. And by true nothing, we actually mean, a region where not even space-time is defined. Like, even space-time ceases to exist in that vacuum. So that would be a candidate for a true nothing in the context of, you know, quantum theory.

Strogatz (39:04): Wow, should I be picturing sort of a hole? Like this is the end of space-time or something on the other side?

Garcia Garcia (39:09): Yes. Let me explain first the simplest example in which such a dramatic possibility could take place. These types of instabilities can only occur in theories that contain extra dimensions. And as we discussed earlier, those extra dimensions have to be compactified. So we can imagine a four-dimensional universe with a fifth dimension that is, perhaps you know, a tiny circle. A bubble of nothing could nucleate in this four-dimensional vacuum and it would look very much like a spherical bubble inside of which nothing exists, the space-time no longer exists. So in a somewhat rigorous way, the surface of this bubble is the end of space-time. So this bubble sort of would nucleate. And then it would start expanding very quickly, very quickly approaching the speed of light. And eventually, as far as we can tell, you just completely eat the whole universe.

Strogatz (40:05): And this is something that you and your colleagues calculated in a fairly recent paper,

Garcia Garcia (40:10): Right. So Witten discovered this instability in the early ’80s. And he calculated the probability of that process happening, depending on the size of the extra dimension. What I did with my collaborators, Patrick Draper and Ben Lillard, we actually asked the question of, in more realistic theories where that extra dimension is dynamically stabilized, were there other fields responsible for the size of that extra dimension? It looks naively like that would make it very hard in practice for that type of instability to still be relevant. So we asked the question of, in a realistic model, in a realistic situation, how likely is this to happen? Or is this sort of like just a mathematical observation that cannot actually happen in a physical theory? And what we realized is that, in fact, this class of instabilities are more robust than was previously believed. They can actually exist under a more general set of circumstances than what was done previously.

Strogatz (41:10): And is the condition that the curled-up dimensions are like your tiny circle that’s added to space-time at every point? What, those circles have to be below some size threshold? Is that the idea, or above, or how does that work?

Garcia Garcia (41:23): Yeah, so the rates of nucleation dominantly depends on the size of the extra dimensions. So if extra dimensions are too large, it becomes too difficult for this process to take place. But that was already known. But moreover, the details of whatever sector is responsible for these extra dimensions being compactified? Under general assumptions, those details are largely irrelevant. So we also determine under what circumstances the dynamics of the sector that sort of determines the size of those extra dimensions can shut off this type of instability and under what circumstances it remains a viable way in which a universe could destroy itself.

(41:23) For us, that was a way of starting to explore in a general four-dimensional landscape of vacua, trying to quantify whether some of these other vacua could actually be sensitive to this decay into a bubble of nothing, as opposed to decay into other, more reasonable final states.

Strogatz (42:25): And so the big game that you’re trying to address here, just to go back to that point about the anthropic principle and the Weinberg argument, is that this kind of work — not to say your work exactly — but the spirit of your work may be a way out of these anthropic arguments for answering this great mystery.

Garcia Garcia (42:43): Precisely. Precisely.

Strogatz (42:45): The vacuum energy’s smallness.

Garcia Garcia (42:47): Indeed, it would be a way of sort of like, still taking that concept of a huge landscape of vacua that is predicted by a theory of quantum gravity, like a string theory, but being able to sort of select the vacuum that actually hosts our universe in a way that does not necessitate these anthropic selection arguments that are so, kind of, in a sense, unlike physics in many ways.

Strogatz (43:13): Exactly. Well, this has really been fun, Isabel. Thank you. We’ve been talking with theoretical physicist Isabel Garcia Garcia. Thanks again so much for shedding some light on nothingness.

Garcia Garcia (43:24): Thank you for having me.

Announcer (43:25): Space travel depends on clever math. Find unexplored solar systems in Quanta Magazine’s new daily math game, Hyperjumps. Hyperjumps challenges you to find simple number combinations to get your rocket from one exoplanet to the next. Spoiler alert: There’s always more than one way to win. Test your astral arithmetic at hyperjumps.quantamagazine.org.

Strogatz (43:54): “The Joy of Why” is a podcast from Quanta Magazine, an editorially independent publication supported by the Simons Foundation. Funding decisions by the Simons Foundation have no influence on the selection of topics, guests or other editorial decisions in this podcast or in Quanta Magazine. “The Joy of Why” is produced by Susan Valot and Polly Stryker. Our editors are John Rennie and Thomas Lin, with support by Matt Carlstrom, Annie Melchor and Zack Savitsky [as well as Nona McKenna and Saugat Bolakhe]. Our theme music was composed by Richie Johnson. Julian Lin came up with the podcast name. The episode art is by Peter Greenwood and our logo is by Jaki King. Special thanks to Burt Odom-Reed at the Cornell Broadcast Studios. I’m your host, Steve Strogatz. If you have any questions or comments for us, please email us at [email protected] Thanks for listening.

“The Joy of Why” will return with a new season in early 2024.