And so what we've shown is with these four derivative theories, the same is true. That you can pick a subspace, you have to pick a subspace, and that on that subspace all inner products are positive. The only problem is that that subspace only includes the vacuum.
Okay, that sounds like a huge problem. No, I mean, depends what you want to do with it. If you wanted to describe particles, you would say it's a terrible problem, I can't describe particles because they all come along with these negative probabilities.
But if what I want to do is to describe the energy of the vacuum, I'm completely happy. I say, okay, I throw in these dimension zero fields, they contribute to the energy of the vacuum, but they don't allow any particles. And what we found is if you add 36 of them, they fix the vacuum of the standard model, but you do not have any extra particles.
In fact, they do more than this, because they give you a possible way of building the Higgs field out of these dimension zero fields. And that's very tantalizing, because that might end up solving the hierarchy problem. Oh, wow.
Okay, so let's keep an accounting right now of all the problems that this solves. So one is the vacuum catastrophe, another is the hierarchy problem, another is three generations of matter which we haven't gotten to, but we will. Another is the singularity problem of the Big Bang.
Right, and the density perturbations on large scales. So we see the density. And dark matter.
And dark matter. And dark energy. So what we claim is that everything can be fit into this framework.
So what's left? Well, this is possibly a unified theory of everything, without any new particles or forces. So that's why we're excited.
It's a very radical alternative approach. In some ways it's not so radical, in some ways it's much less radical. Correct.
That's exactly how we feel about it. Because of the culture of physics today, it's now radical to be not radical. Exactly.
You said it perfectly. So we're very surprised by this, but there's a huge sociological issue, which is that people have been playing with supersymmetry and string theory and extra dimensions for decades. And inflation for decades.
And so there are multiple models, 99% of people in the field are publishing papers in these frameworks. As I say, there has not been a single, you know, what drives me is there's not been a single precise observational prediction to be confirmed, which has been confirmed in any of these cases. And that's what led me to profoundly doubt this methodology.
So I said, okay, I'm going to adopt the opposite methodology. I'm just going to refuse to add anything extra. And ask, what is the least I can add to the standard model, the very, very least, which will allow me to address the primordial fluctuations, the vacuum energy, the number of generations.
And we stumbled on these 36 crazy fields, which seem to cancel out the problems. And I should say, when we first introduced them, it was just the numerology. With 36 of these weird fields, we could cancel a vacuum energy and fix these symmetries.
And I should emphasize only it's kind of very lowest order approximation in the calculation. It remains to be seen when you do it in more detail. And that's challenging and we have to do it.
But it's a first hint, it's really, I can't claim it's done and dusted, you know, far from it. It's a first hint. But with those very same fields, we then calculated what density perturbations should we see in the sky come out of the Big Bang, you know, what perturbations came out of the Big Bang.
And that matches what we see numerically. So those same fields, these weird dimension-zero fields, explain why the fluctuations in the early universe were scale-invariant. And they also explain quantitatively this small tilt.
We got much more than we bargained for. We never expected those numbers to come out. Again, I have to say, we've made assumptions along the way, always, we have always made what seemed to us the simplest assumptions, and those simplest assumptions led to the right numbers.
Okay, so now we have to justify those assumptions, and so on and so forth. But we are in the situation, I think, where we have a framework on our hands, which might just explain everything. Now let me ask you a sociological question.
So do you think that theoretical physicists today, the majority of them, actually care about the nature of the universe? Or do you feel like they more care that they uncover the theory? In other words, do they disagree with your theory, or doesn't even get to that point because they're unwilling to listen?
Even though you say, look, I have the answers to the questions that you're searching for. It's a mixture. A large number of referees, for example, of our papers, clearly haven't read them.
They look at the paper, and this goes for grant applications too, I submitted a big grant application based on all this. The feedback I got was very disappointing, because people were basically saying, where's the inflation? Where's the stuff I'm used to?
It doesn't seem to be there. Or they were just saying, you know, four derivative theory, clearly nonsense, and they weren't willing to engage. So that has been, I think, most of the response has been a bit like that.
Not really taking it seriously yet. I can't entirely blame them, because what we've done is preliminary. We've made various assumptions and simplifying assumptions.
It's very much a first step. And yeah, they can sit back and just wait. That's perfectly reasonable.
I would say it's quite disappointing that string theorists, who are using many similar criteria to what we use, are just so much embedded within 11 dimensions or 10 dimensions that they won't engage with realistic cosmology. Most of them won't. A few exceptions will.
The very best string theorists, in fact, do engage. For example, I was at a workshop recently with Ashok Sen, who's a very, very original string theorist and has had great insights from string theory, but is not at all a sort of closed-minded. So he would certainly jump if he saw a framework that was just as powerful as string theory, but involved much fewer assumptions.
And he engaged very much, and he was very interested, and so on. So we've had some positive responses, usually from the best people. There's a large number of people who more or less follow the fashion, and they have not engaged yet, though I am getting lots of invitations to get talks.
So I think it just behoves us to give lots of talks, explain, not to go away, and answer as many questions as we can answer. On the whole, I'm optimistic that eventually people will, if this framework is right, people will definitely start to see it. The most convincing thing in the end is an observational signature.
If we have a signature, which no one else has, and it's seen, then I think people will start migrating to our theory. So there is one, which is very interesting. It's to do with neutrinos.
So there's pretty good evidence that right-handed neutrinos do exist. In the minimal standard model, and that's no supersymmetry, just as usually taught in quantum field theory courses, the minimal standard model has only left-handed neutrinos. But every other particle, electrons, quarks, have both left- and right-handed.
So all the fermions come in left- and right-handed versions, but neutrinos don't in the minimal standard model. However, we know the minimal standard model is wrong, because when we observe the light neutrinos, they have small masses. And so these mass differences have been measured in the light neutrinos.
And the simplest explanation for those neutrino masses are that actually there are right-handed neutrinos, which are very heavy, and so when a left-handed neutrino is traveling along, it can oscillate into a right-handed neutrino, a virtual right-handed neutrino, for a short interval of time, and then that right-handed guy decays back into a left-handed neutrino. So this neutrino mixing is called the seesaw mechanism, because the heavier you make the right-handed guy, the smaller the effective mass of the left-handed guy. So this seesaw model was known since the 70s, it's very beautiful.
If you say the right-handed ones are pretty heavy, bigger than about 10 to the 10 GeV, you know, 10 billion GeV, so impossible to make in a particle accelerator, that's enough to explain the light neutrino masses. And indeed, in our framework, with these 36 dimension zero fields, we find we are forced to have three generations of particles, exactly as we see, in order for these, for the vacuum energy and the anomalies in scale invariance to be true, for it to cancel, we have to also have three generations of particles, just like we see, and each generation must have a right-handed neutrino. So we have three generations of particles, each one has a right-handed neutrino, that automatically gives the left-handed neutrinos a small mass.
Now you can say, what's the dark matter? How does the dark matter fit into this picture? And it turns out that one of these three right-handed neutrinos is the perfect dark matter candidate, because right-handed neutrinos are not allowed to couple to the force-carrying particles, the strong, weak, or electromagnetic forces.
Right-handed neutrinos are completely neutral. And so one of them could easily be the dark matter. So in fact, this is the way we originally came to this whole idea, is we realized, hey, wait a minute, there's an obvious candidate for the dark matter, it's a right-handed neutrino.
And then we asked, how do you predict the abundance of a particle which doesn't couple to any other particle in the standard model? Because you see, if a right-handed neutrino is the dark matter, it must be stable, which means it cannot decay into other particles, which means that actually it couples to nothing in the standard model, it only couples to gravity. So how do you predict its abundance?
And we found by considering this two-sided universe with the CPT symmetric boundary condition, we could then calculate the abundance of right-handed neutrinos. And we found that the number came out about right, that we could get the right dark matter density from right-handed neutrinos by actually calculating how many of them are produced simply due to the expansion of the universe in this double picture. So now, if one of them is stable, it's easily the simplest candidate for the dark matter.
I don't think anybody questions that. And I would say, therefore, it's the first thing to go after. If it's stable, how do you go after it if it doesn't couple to any other particle in the standard model?
Well, you go after it indirectly, because you say the left-handed neutrinos are not allowed to couple to it either. Because if they did couple, then it would decay into them. So you've got to switch off that coupling of left-handed neutrino into right-handed neutrino for this one right-handed neutrino that's the dark matter.
You must switch off that coupling. That means that one of the left-handed neutrinos is exactly massless. So the signature of this dark matter candidate is that the lightest neutrino must be massless.
The amazing thing is that in the next three to five years, we're going to have very precise measurements of the lightest neutrino mass. If you enjoyed this TOE clipping, then the full video is linked in the description. You should also sign up for TOEmail, which is again in the description and the pinned comment.
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