This lecture on the Multiverse is about as speculative as it gets. I remember Alex Filippenko sympathizing with the audience during his course's lecture on the subject, saying he knows this topic sounds way out there, but no one really understands it. Sean Carroll approaches it more seriously, perhaps less sympathetically, but more importantly he clearly lays out the various schools of thought.
Combining the two previous complex lectures sounds daunting. Inflation and string theory do not predict dark matter or dark energy, but there are important implications, especially for dark energy. The problem with the vacuum energy value seeming so non-natural leads us to try some king of recalibration. The Quintessence and gravity modifications seem like more natural values, but have experimental problems.
The compactification of the many dimensions of string theory leads to phase changes. But the Cosmological Constant problem creates 10E+500 of phases, or different possible vacuum energies.
The Anthropic Principle deals with the values that allow us to exist, whatever the definition of us may be. That leads to an environmental selection of values we can choose from. The tautology that the universe must have certain values for us to be able to be here observing it is balanced by the predictions we can make of the ensemble of the so many things we see.
Saying that our universe is homogeneous can sound very parochial from our limited point of view, or very parsimonious from our knowledge of the universe. We are limited in observing our universe by the CMB, so cannot be sure of either statement. We must allow for both to be true and make predictions. The Multiverse of string theory allows such sort of abstract experiments. The vacuum energy is just one of many parameters where the whole set of possibilities is called the landscape.
The curled up dimensions discussed earlier could unwind themselves into a small unique set of possibilities. Inflation has the flux of virtual particles where one patch could become dominated by dark energy and accelerate by inflation. Once again there are 10E+500 possible ways this could happen.
Sean carefully admits how this kind of talk can sound illegitimate and non-scientific. But considering such an ensemble with all its possibilities, natural and non-natural, may allow us to see if we ourselves are actually rare or common. Finding which versions of quantum theory or string theory values could work for various part of the multiverse is legitimate.
Within the ensemble there will be selection effects making some parts inhospitable for any observers to exist. But what are the observers? Are we defining them to our own bias? Consider a part of the multiverse where a heavier proton decays into a lighter neutron. This neutron world would be very different to us without chemistry or observers. But we can't know for sure that this is the case. Neutron molecules could form for all we know.
We should care about these scenarios after considering that the vacuum energy of our universe should be at the Planck scale, 10 to the 120 times larger in value than we observe today. Yet if it were that large, we would not be around to even consider it. Not even one proton would be able to exist. If it were 10 to the 120 times less in value than today, the universe would have collapsed long ago.
So if the vacuum energy is small enough for our existence, we either had to get lucky or we just happened to get lucky. The latter could be due to some dynamic mechanism making the vacuum energy low according to some physical law, or just due to the vacuum energy just being a random number. This randomness is possible, but unsatisfying. Sean gives an example for the former, were we just got lucky. A planet with an atmosphere that never allowed scientists to see the sky, has them trying to understand the temperature. They reason that there are just so many other planets out there, that some will have a nice temperature. Objectors say that sounds just too philosophical.
Think of that atmosphere as our CMB. The vacuum energy equals its value due to some equation or it's an environmental variable that is different from place to place. The latter is then a selection effect, not a law of physics.
Therefore we can try to make predictions about the ensemble. Steven Weinberg did such a thing in the 1980s by saying the Cosmological Constant should be roughly +/- 10 times the current matter density. We've now found that value to be 2 or 3 times, so he was right. Can we predict things like masses of particles or the amount of dark matter? More dark matter implies more structure in the universe to make galaxies. But Sean sees this as a stretch, more of a postdiction than a prediction. Environmental selection is also not a constraint, like the axion versus supersymmetric form of dark matter.
There is a divide between those who think the Multiverse can be used as a vacuum energy experiment, or that the whole idea is just plain crazy! The latter is then again divided into the grumpy old men objectors and the non-grumpy old men objectors.
Sean takes the former less seriously. They say the Multiverse is not scientific and no predictions are really recalibrating nature. Sean sees this an unconvincing and that science is possible. Look at how we dealt with the unnatural horizon and flatness problems by finding how inflation made them natural. The vacuum energy may make more sense in a Multiverse, that would lead to better understanding of the science.
Sean takes the non-grumpy objectors more seriously. Some say there will not be any important and detailed predictions that come from study of the Multiverse. Sean points out that the Steven Weinberg Nobel Prize might be used to refute this argument. But did he really just get lucky? Weinberg's Multiverse was the same as our universe in every respect except the vacuum energy. He derived his prediction of vacuum energy roughly equaling matter density, only from that difference.
But that is not what the Multiverse tells us to do. Everything changes from place to place, the dark energy, the perturbations, etc. So the Weinberg example was a less strong prediction. A true prediction would not be as precise as Weinberg's makes it seem to be. A typical observer in the infinite Multiverse would be nowhere near to such an answer. We need much better models of inflation or string theory, and if not, then we never will be able to make true predictions.
Imagine an infinite number of observers seeing X, while a greater number of infinite observers see Y. Is X or Y necessarily right? Back to earth, Sean agrees this is all extremely speculative, but it might turn out to be right.
The real lesson is that there is no convincing value of vacuum energy. That drives us to environmental selection and the Multiverse is the best we can think of right now. It could be the right answer.
The worst anthropic version we could think, is that the universe is arranged as we demand it to be. We should keep an open mind as our data lets us focus more and more on a correct version.
In this lecture we're going to get the payoff from the previous two, on inflation and string theory. Talking about string theory, we realized that we would like it to be the case, that namely what we think of as the unique string theory that lives in higher numbers of dimensions, predicts things like dark energy and dark matter composition. Yet this doesn't quite turn out to be true. String theory predicts too many things and as far as we can tell, it's compatible with all sorts of different possibilities.
Nevertheless it has an impact on how we think about dark matter, and especially about dark energy. So in this lecture we'll talk about how ideas from string theory and inflation, change our notion of what constitutes a natural vale for the vacuum energy. Remember that after we talked about dark energy existing, and going through all the different possibilities for what it might be, the possibilities of quintessence ad changing gravity were interesting yet ran into problems with experiments.
The possibility that it is vacuum energy, an absolutely constant amount of energy in every cm³ of space, didn't run into any problems with experiments, yet seemed very unnatural. The value the vacuum energy would have to have is just so very different from the value it seems to actually have in our universe. So string theory has the chance to recalibrate our notion of what it means for a number to be natural, and that is the long precess we'll go through in this lecture.
So the punchline is that string theory says there can be many different phases. All the different ways there are of taking the extra dimensions of string theory, and all the different branes and other things it predicts, and compactifying them down to get a four dimensional spacetime like the one in which we live, can correspond at low-energies to different phases of spacetime.
Just as water can come in different phases, liquid (water), solid (ice), and gas (water vapor), it's the same underlying thing. It's not like there are three different theories for each. It's the same stuff, manifesting itself in different forms. Likewise with string theory, it's saying there are perhaps 10 to the 500th power of different phases for spacetime. All these different ways in which the fundamental vibrational modes of the string can show up as particles, as numbers of particles, and as the vacuum energy.
The vacuum energy is going to be a number that changes from phase to phase, from compactification to compactification, so will take on all sorts of different values that total some 10 to the 500th power! Within that ensemble, we're going to get a lot of different possibilities, and one might just be the one in which we live.
This idea is sometimes called the anthropic principle. The idea that we're picking out, among a huge ensemble of possibilities, those which allow us to exist. The reason why that's a sticky situation is because we don't know what "us" means in that sentence. What kind of definition do we have for what counts as intelligent life?
So we're not going to go into any of those issues in any detail, but we'll rather think of it as environmental selection. It's not a surprise that if you live in a universe or set of universes in which conditions can be very different, that we're going to observe those conditions that are hospitable to us living there. That is just a tautology, and is not surprising.
The interesting part is when we go from the tautology to using it to make predictions. Within this ensemble, what is likely for us to observe? we might be able to change our notion of what you would expect ahead of time, by realizing we live in an ensemble of many possible universes, rather than in one unique thing.
So we live in a universe that we can't see in its entirety. The observable part is defined by a horizon. We send back light rays into the past, and because the speed of light is finite, those rays hit the boundary of the Big Bang at a finite distance. There's almost certainly parts of our universe which we can't see because they're simply too far away. That is not a surprising claim or controversial in any way. We can certainly see out to the CMB, and if we're trying to be clever about it and learn how to use neutrinos or something like that, we can push that back a little further. Yet there's still a very clear demarcation past which we can't possibly see, given to us by the Big Bang itself.
So what is beyond that part that we can see? The part we can see, seems to be homogeneous and isotropic. Not only is the configuration of stuff more or less the same, the same density of stuff from place to place, but it seems from our observations that the laws of physics are the same. It's not true that the charge of the electron is a different value in one part of the universe than any other. As far as we can tell, they're the same everywhere.
So is it possible that you can just extend that understanding infinitely far? Is it conceivable that we live in a universe where conditions really are the same everywhere, even outside what we see? The answer is absolutely yes. There's no reason we can give, either logically or within the laws of physics as we currently understand them, against the idea that the universe is truly the same everywhere, even for outside of what we observe. Yet by exactly the same criteria, there's no reason we can currently give to say the universe is the same everywhere. It is absolutely just as reasonable to say the universe is very different outside.
On the one hand you might say that it's very parochial, very anthropocentric of us to take out local universe and extend it all over the place. On the other hand you might say that it's not very parsimonious to have a universe that is wildly different. We have a universe which looks very nice as it is, why not just take the simplest possibility and extend it all over the place? The point is that we can't answer this question, just by pure thought.
So when we're in a situation like that, what we have to do is allow for both possibilities. We don't need to make a decision, but we're going to ask what happens if the different things are possibly true. So for this lecture we'll ask what happens if there are different regions of the universe, where conditions are very different?
So we're going to call this the multiverse, yet not in any metaphysical sense. It's not like there are different universes that are separate from each other by some profound difference. They're just different regions of space, into which we cannot get. That's an interesting thing to think about as a possibility, but it's string theory and inflation that takes this possibility and makes it very tangible.
In other words, string theory plus inflation gives us a set of ideas from which we can talk about the possibility of a multiverse in a scientific way. It is string theory that allows space to take on different conditions. Not just different densities, but different phases. So the different ways we have of taking the extra dimensions of space in string theory, and curling them up, give us different low-energy physics.
In our current world we seem to have four dimensions of spacetime, with three of them as large dimensions of space. We also have the standard model of particle physics, which is characterized by a set of particles and numbers. So we day we have certain fermions, bosons, interactions relating the particles, and parameters like charge, mass, and so forth. One of those parameters is the vacuum energy.
So when string theorists realized there was more than one way to compactify the extra dimensions, they saw there was going to be a huge number of ways. Something like 10 to the 500th power, is the current best guess. They've given the name "the landscape" to this set of possibilities. So the string theory landscape is something we can think of as like some jagged landscape here on earth, and every little minimum, every little local valley is a different place you can live. Different valleys of course are going to have different local conditions, temperatures, densities, heights, etc.
So that's an analogy to what we have in string theory, where there are different ways to curl up the extra dimensions. Yet perhaps not in an infinite number of ways, so perhaps it's not "anything goes." Yet that number of different ways is still very large, 1 followed by 500 zeroes in huge indeed.
Now we're very far from being certain that this is actually true or not. Currently our best understanding of string theory says there are perhaps 10 to the 500th power, different ways to curl-up the extra dimensions. However it's certainly conceivable the current state of the art just isn't good enough to say that for sure. In other words it's possible that once we understand string theory better, we'll come to understand that even though you can curl-up things in different ways, they don't stay curled-up like that. You might curl-up the extra dimensions in a certain configuration, but they quickly unwind into a different one.
It is therefor still quite possible that once we understand string theory better than we do today, we will narrow it down to a very small, perhaps even unique set of possibilities. That is a goal to keep in mind if it's true, but the current best-guess on the basis of what we seem to understand right now, is that these different phases of string theory really are stable and really can exist in principle.
So what inflation does is take phases of string theory that can exist in principle, and gives them a way to actually exist in practice. What inflation says is that at very early times in the history of the universe, we don't know exactly what was happening, but perhaps there were chaotic fluctuations. Different conditions were going on all over the place, there were very high temperatures, very large fluctuations from place to place.
In some tiny little patch of that initially chaotic system, you got a domination by something like dark energy. Some inflaton field with an approximately constant ρ, which caused that little patch to accelerate, to expand to a huge size. Eventually the energy within the inflaton reheated into matter and radiation, so we see what we see today.
So if you take the idea of inflation and combine it with the theory of 10 to the 500th power different possible stable final states for the compactified dimensions of string theory, you get a way to make those possibilities real. By starting inflation in slightly different conditions, by allowing inflation to go on in slightly different ways, you can have different trajectories, all of which populate anyone of the 10 to the 500 different valleys in the landscape.
In other words, we're imagining a multiverse that starts out in some chaotic condition, and then through inflation happening in different parts, different, ways, using different physics, we get a final condition in which you get huge bubbles of universe, all of which could be in any one of the 10 to the 500 different phases of string theory.
Clearly there are a lot of details to be filled in when we talk about something like that. Right now there's a lot of hand waving involved, and we don't know the correct picture. Yet that kind of picture is perfectly plausible. It might very well be, according to what we understand right now, that the universe we observe is a tiny infinitesimal fraction of everything there is. It is arguable that this is the lesson of Copernicus. If you're not putting us at the center of the universe, you shouldn't assume that the conditions we observe, are the same that obtain all over the universe.
So one thing we'll talk about is whether or not this is legitimate or OK to talk about regions of the universe which we cannot see? People will say that if you can't observe these different regions of the universe, they have no affect on local physics, no affect on what is going on in our region of the universe, and they never will, therefor talking about them isn't even science. So who cares about whether or not they're there?
Well the reason why we'd possible care, and we'll talk about this in more detail later, is because living in our ensemble changes our notion of what is natural. If you only live in a unique universe, then you might guess that the constants of nature will naturally take on the values that would seem easy to us if everything was of order one, if there were no large differences between the different numbers that you saw. Yet if you live in an ensemble, then every possibility happens, even some extremely rare ones.
If one of these extremely rare possibilities is somehow more hospitable for us to live in there, then we should not be surprised if we live in one of the rare possibilities. It would be very natural for us to live in a universe in which the parameters of nature, somehow didn't seem natural. That's why it's worth thinking about this possibility that we live in an ensemble, a multiverse of different phases of string theory.
Other people will say in a related way that it's not a scientific theory if it doesn't make scientific predictions. We should point out that the multiverse is not strictly speaking, a theory. The multiverse if it's there, is a prediction of a theory, the theory of strong theory combined with inflation. Now that's not a very exact theory right now. We don't understand either inflation nor string theory, well enough to tell us precisely what the predictions are. Yet the goal of this kind of way of thinking, is the following.
Someday we'll be able to do experiments that will convince us that a certain theory of quantum gravity is correct. Hopefully we'll be able to narrow down on the basis of data, on the basis of experiments, which version of string theory or quantum gravity, if any, correctly describes our world. We will within those experimental constraints, be able to say that the following fields can act like inflatons, so can make the universe expand.
In other words on the basis of data, we will build a framework that makes a specific prediction for what the multiverse should be like. Within that prediction, you can begin to make sense of questions like what should people observe who live in that ensemble? So even though the prediction of the multiverse is itself not testable, it might be an airtight prediction of a model that had other testable predictions. That may or may not be a Utopian goal, but that is the kind of thing we are shooting for when we think about these ideas in the back of our head.
OK, so now the philosophy is a little bit out of the way, so lets try to talk about putting this to work. What if we really do live in a multiverse. What if there really is an ensemble of different places that we don't observe where conditions are very different? Well it goes without saying that within that ensemble of different possibilities, there will be very strong selection effects when you ask what is observed by a typical member of that ensemble?
We imagine, roughly speaking, that some of these places in the multiverse are very inhospitable. We just can't live there. So it is not surprising that no one is observing them, if observers cannot exist. Now we admit that there's a very big question here of what is an observer? What is somehow what people call a conscious person, or some intelligent scientist who can live, if the laws of physics are very different? You could ask very detailed questions about this.
For example, imagine a universe that is almost exactly like our own, yet in which the proton was a little bit heavier than the neutron. We talked about this when discussing the standard model of particle physics. What would happen is, a proton would then decay into a neutron, since heavier particles decay into light ones. So instead of a world made of atoms, where you had atomic nuclei surrounded by electrons, you have a world made of neutrons. It should be clear that such a world would be very different from a world in which we live. You can't have chemistry in a world made of neutrons.
You might therefor ask, can such a world have intelligent observers? Some people think they know the answer to that question, yet Sean does not think that he knows the answer! He could hypothetically perceive that neutrons could get together, making little nuclei made of 1, 2, or 3 neutrons. Then these nuclei could even get together to make neutron molecules which could build up into neutron amino acids. He truly doesn't know whether or not there is sufficient room for complexity in a universe made almost all of neutrons, to support intelligent life.
Therefor he doesn't care, and he won't talk about any predictions we could make at a very quantitative level, that say if we increase the mass of the proton by 10%, then life cannot exist. We're going to keep an open mind about that, and stick to things which we think every reasonable person would agree on, do say something about whether conscious observers can exist.
In particular, we're going to talk about the vacuum energy! This is one thing we think has a very unnatural value. If it is the dark energy, the vacuum energy is 10 to the -120 times what we thought would have been its natural value. That seems preposterously finely tuned from the point of view of ordinary particle physics. If everything were natural in the standard model, the vacuum energy would be at the Planck scale, at 10 to the 120 times bigger than it is today.
However, nobody Sean has ever met, claims that life could exist if the vacuum energy were that big. If it were that large and positive, the acceleration of space would make it absolutely impossible to form planets, or for that matter, individual atoms! You couldn't even make a proton in the universe where the vacuum energy was the Plank scale, and everything would be ripped apart very quickly. You'd be left with an empty universe almost instantaneously, so there's no room to form life in such a universe.
If the vacuum energy had the magnitude of the Planck scale and were negative, it would make the universe re-collapse in one Planck time, much too small of a timescale to have any realistic or interesting particle physics, and much less to actually form life. In other words, when it comes to the cosmological constant, we have a very strange situation. The cosmological constant is just a different word for the vacuum energy, and it should be at the Planck scale, so that's its natural value. Yet if it had its natural value, we would not be here to talk about it!
So on the one hand, it's not surprising at all that the cosmological constant doesn't have its natural value. It can't have its natural value, or we wouldn't be here thinking about it. The question is why do we live in a universe in which the vacuum energy, the cosmological constant, is small enough to allow us to be here?
There are basically two different possibilities. One is that we just got lucky. In other words, there is no reason why the vacuum energy is small enough to allow for the existence of life. It just happened to be that value. Within that possibility of the "just got lucky" idea, there are two sub-possibilities. One says we truly just got lucky, so it's not only that the vacuum energy is small, but it's just a random number. There's no dynamical, physical explanation for why it's small, it was just randomly chosen and happily turned out 10 to the -120 what it should have been, therefor we can exist.
That is an absolutely possible theory of the value of the cosmological constant. Sean can't tell us that theory is wrong, but for obvious reasons it's kind of unsatisfying. It would be a truly lucky roll of the dice for us, for the vacuum energy to be that small. The other possibility within the idea that we just got lucky, is that there is a dynamical mechanism. The thing that we got lucky about is not that the cosmological constant is a random number that is small, but that the cosmological constant is small because there is some physics that we haven't yet figured out that makes it small. We're lucky for the existence of that physics, not for the random throw of the dice that made the vacuum energy very small. Yet right now, we don't know what that physics is. We're just guessing at it. Many people are hopeful that we'll find it at some point, but we just don't know.
The other possibility within that "we just got lucky" that the cosmological constant is small, is that we had to get lucky in the sense that the cosmological constant is not a once and for all constant of nature. It's an environmental variable that takes different values from different places. If the cosmological constant takes different values in different regions of the multiverse and in some of those regions it's small enough that life can exist, then it's not a surprise. Then it's not that we got lucky that we exist in those regions.
Let's get an example. Imagine that an analogy of astronomers who lived on a planet, where the atmosphere was opaque and could never see the sky. On this planet the temperature was very mild and never changed. It was 70 degrees everyday, but you couldn't see anything besides the clouds overhead. In such a universe, in such a hypothetical situation, what would the scientists who live on that planet try to do? They would try to understand the temperature that was on their planet. They would ask if there were laws of physics that predicted the temperature would always be 70, and we could be here?
Well other physicists on that planet would say, "my idea is that there are also other planets, and the temperature is very different there." Yet there are just so many planets, that life is going to arise on those planets where the temperature is nice. Others will say, Oh come on, that's just philosophy not science, we can;t see these planets so how can you be talking about that?"
Our current situation is actually much like that. Just like there are clouds in the sky of this hypothetical planet, we have a horizon given by the CMB, past which we can't see! Maybe there are other regions of the universe out there, where conditions are very different. The fundamental question before us now is, if the vacuum energy is a once and for all constant of nature, for which there should be some equation that predicts its value, or is it an environmental variable? Is it different from place to place, and therefor chosen by a selection effect, rather than a deep law of physics?
So if we're going to decide between those possibilities, it would be nice to take this idea that there really is an ensemble of different possibilities, and actually use it to make some sort of predictions. So not just to use it to make us feel good about the value of the vacuum energy, but to actually do something precise with it. We'll want to consider the entire ensemble and ask what a typical observer living in that ensemble of multiverse, actually observe?
So this very exercise was undertaken in the 1980s, by Steven Weinberg, a well-known physicist who won the Nobel Prize for his work on the standard model of particle physics with the W and Z bosons. Well he says that we can actually attach numbers to this statement, that if the cosmological constant were large and positive, it would rip things apart. It it were large and negative, it would make the universe re-collapse. He did a little calculation and argued that the typical value of the vacuum energy that would be observed by a conscious observer, was something like 10 times as big as the matter density.
He means that the vacuum energy could be anywhere from -10 times the matter density, to +10 times the matter density. So you pick a random number between -10 and +10. A typical number would between these would not be 10 to the -5 power! It's going to be on the order of 1, like +3, -5, or something like that.
So in 1988, Weinberg made this prediction that someday we'd observe a non-zero cosmological constant. This was a prediction he made before we went out and found it. So then 10 years later, we did find it, and in fact it was consistent with his prediction. The vacuum energy we think we have observed, is 2 or 3 times the matter density. That is consistent with being between -10 and +10. Not only is it between there, but it's kind of a typical number you'd expect it to be if you picked a random number between -10 and +10.
So what does that mean? It means that you can predict something, or at least you can try. So you might want to try and predict other things, such as the masses of the elementary particles, the mass of the electrons, the quarks, and so forth. Even better, you'd like to predict something we haven't yet observed, to make sure we're still on the right track. The problem is the environmental selection that says we can only exist where conditions allow for us to exist, isn't a very strong constraint on things we haven't yet observed.
What is the dark matter? Is it a WIMP, is it the LSP, or is it the axion? The environmental selection principle doesn't tell us which one. We can exist just as well, with both axionic dark matter or supersymmetric dark matter. You could even ask how much dark matter should there be? Some brave souls have tried to argue that the environmental selection principle, predicts that there should be dark matter. The reason why is because the more dark matter you have, the more structure you form in the universe, the more galaxies, and therefor the more observers. To Sean personally, this seems like a bit of a stretch. It seems more like a postdiction than a prediction. We already know that is dark matter there, we're trying to justify it after the fact.
Yet he thinks that for vacuum energy, there is some possibility of something going on there. We don't know exactly what will go on, we don't yet know how to predict things we haven't observed, but it's still interesting to try and push our current knowledge of how the ensemble would work, past what we get.
Nevertheless, let's give equal time to the objections to this way of thinking. We should say that currently within the physics community, there is a sharp divide. There is a set of people who take very seriously the idea of the multiverse as an explanation for the observed vacuum energy, and an equal number or larger, who think it to e completely crazy! So we'll give the arguments from people who think that even talking about this is not what we should be doing.
There's two basic kinds of objections to talk about the multiverse. One is what we'll call the grumpy old man objections, and the other are what we'll call the sensible objections. The former are the ones that just say, "Doing stuff like this isn't science, as you could never observe the stuff out there, so you're giving up on our attempts to understand the universe based on evidence, observations, and experiment!"
These are un-convinving to Sean as reason to not think about the multiverse. First, because it might be like that. It might be the case that outside what we can observe, the universe takes on very different conditions. Whether or not we can observe them, it might be the truth, and ultimately our goal is to get at the truth, by what ever method we can. If the way we get there is by naturalness arguments, rather than direct experiment, then that's what we have to live with.
The second is that the multiverse is not, as we said, a theory that makes strong predictions. It's a prediction of a theory that we can use to recalibrate our notions of naturalness. The point is that when we look at naturalness, when we look at quantities we measure in nature and say, "That one doesn't look right, it looks unusual to us," we're taking that as a clue. We're saying that we really don't understand the final laws of physics, but we're trying.
Sometimes the way we're moving toward the final laws is to do an experiment that gives us more information. Yet other times, the way that we move toward a better understanding of the final laws of physics, is to look at unnatural features of our current understanding. For example, that's what happened with the horizon and flatness problem in inflation. We thought there was a good understanding of how the early universe behaved, but w didn't know why. Thinking about the reasons why the universe would be nearly flat and homogeneous, led us to inflation. Thinking about the value of the vacuum energy, might very well make more sense in the context of a multiverse, that might lead to a better understanding of other things.
The non-grumpy objections Sean takes more seriously. There's a set of objections to thinking about the multiverse that we think are quite reasonable, and we should take seriously. So basically what these objections are saying is that even if, in principle, we do live in a multiverse with various things going on, as a matter of practice it is impossible to extract from that any detailed predictions.
Against this, you could say, "Well, Steven Weinberg who won the Nobel Prize, made a detailed prediction, what about that?" Yet there's a good objection to the fact that Weinberg made a prediction and sort of got lucky. The point is that he made a very specific calculation that did the following things. He said what if we had an ensemble of the multiverse, in which conditions in all the different parts were exactly the same as they are here, except for the cosmological constant? He only allowed the vacuum energy to change, and he derived the prediction of the vacuum energy that could be pretty close to the matter density.
Yet that's not what the actual multiverse situation tells us to do. It says that from place to place, everything changes. Not just the vacuum energy, but the set of particles we have, the way that inflation works, and so forth. If you are allowed to change not only the value of the vacuum energy, but other quantities like the value of the dark energy, or the amplitude of the initial density perturbations, you would make a much less strong prediction. The true multiverse prediction for the value of the cosmological constant, is not nearly as precise as Weinberg's calculation makes it seem to be.
So the truth is, we just don't understand the multiverse well enough right now, to make detailed predictions using it. What we're doing is saying that there's this set of universes, this set of places in the universe where conditions are different. There could be an infinite number of such places, and an infinite number of observers in every one of those places. We're trying to say, "What does a typical observer in that ensemble actually observe?"
The state of the art is right now, nowhere near being able to answer that question. It may be because we don't understand inflation and string theory very well, or it may be because we never will! That there isn't any right answer to this question. If there are a infinite number of observers who observe this, and an even larger infinite number who observe something else, how are we possibly to say which is more likely for us to be there?
So this is all speculation at this point in time. Yet the reason why it's worth going over is that it's speculation that might turn out to be right. The real lesson is that we don't have any convincing theory of the vacuum energy, and we're driven to the environmental selection in the multiverse as the best we can think of right now. It might turn out to be right, the worst version of the anthropic principle would be to think that the universe arranges itself into the way that you think it should be. What we should do is keep an open mind about all the possibilities as we get more and more data to help us zoom in on which one is ultimately correct.
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