0:00 I’d like to talk about causality. So you have a phrase that there are “dueling arrows of causality.” That could be yours or your collaborator Menezes. What did you mean by that, that there are dueling arrows of causality? So this is what I referred to earlier in this, that when you do this theory with four derivatives—any theory with four derivatives—you give up some portion of the usual axiomatic field theories. And it seems that at least with path-integral quantization followed the usual pathway, that what you get is you’re giving up some aspects of causality.
0:50 And that aspect is the following. There is an arrow of causality that’s built into our theories, and that’s contained in the factors of $i$ in the quantization procedure. If you do path integrals, it’s $e^{iS}$. If you chose $e^{-iS}$, you would actually have the exact same theory but just a different arrow of causality. Things in positive time would influence things later in negative time. Basically, time reversal changes $i$ to $-i$. Time reversal is anti-unitary.
1:40 And so if you take $e^{iS}$ and do time reversal on it, you get a time-reversed theory that’s exactly the same. And the nature of the theories with higher derivatives is that you get a massless, in the case of gravity, a light particle with the usual arrow of causality and a very heavy particle with the opposite arrow of causality. So if you produce this guy, if you come in with positive energy, it propagates not forward in time like it normally does, but normally it propagates backwards in time for a short period of time. It decays; you then get normal particles out,
2:27 but you had a short period of time where this thing propagated with a different direction in time. It takes a while to wrap your head around, but at least I’ve come to peace with it. Why does it take some time to wrap your head around? Well, so we’re used to the idea that particles can propagate to the left, particles can propagate to the right when they’re carrying positive energy. However, the standard theory is if you have a positive energy particle, that only propagates in one direction in time; propagating in the backwards direction in time doesn’t normally occur. And that is because we use $e^{iS}$ as the
3:26 path integral. It’s equivalently if you do commutators with $i\hbar$ as opposed to $-i\hbar$. And so we’re not used to seeing, in this case, when you decompose the interactions, you get the light particle with $e^{iS}$ and the heavy particle—the ghost particle—with $e^{-iS}$. And let me make a caveat just to be honest: the theory that has this seems to work. We’ve been able to do one-loop calculations in it. I think it’s still not clear how one does higher-loop calculations, and we don’t know for sure that it works at all orders,
4:11 which is one reason for exploring lattice calculations. And so I shouldn’t say that it’s known to be without flaws, but it’s known at some order in perturbation theory. Does the S-matrix assume causality? So the S-matrix defines a transition from stable states in the past to stable states in the future. Right. Well, if light cones are somehow fuzzy, then that’s what I’m wondering is what would be considered “in” versus “out.” How do you define the S-matrix? So in this case, all these heavy particles that have the funny propagation are unstable. And
5:02 so they don’t live in the distant past or the distant future when you do define an S-matrix. They just live in its intermediate states. So you go through a region. So you imagine doing a scatter and you take usual particles in. You scatter them. Some have resonances that go to heavy particles that are normal particles. Some have these funny ones that propagate backwards for a short period of time. But then you end up with all your normal particles in the future. So the proof of unitarity that Gabriel and I did, it makes an important feature that only normal particles live in the distant past and the distant future for the S-matrix.
5:50 Does this mean there is something non-local occurring at the Big Bang? I don’t know how to answer that. I mean, I don’t know the answer. We are trying to look at some of the implications for the early universe, but it’s not really clear how one defines the start of the universe in any theory. You know, we could describe it accurately after a certain phase where the physics that we know kicks in, but I don’t know what starts the universe. You told Quanta Magazine that you’re not convinced that quadratic gravity is the final theory. Right. But that’s much like the Standard Model in the sense that I also don’t—the
6:37 Standard Model I don’t expect to be the final theory. In the case of quadratic gravity, it feels to me like the Standard Model. It feels like it’s a renormalizable quantum theory that would kick in at some scales, much maybe the scale of inflation. And for those scales, it would be a perfectly fine theory. But at that level, we have the Standard Model which has three separate theories involved. We have a renormalizable theory of gravity. That doesn’t feel like the final theory to me. It feels like something else is going to explain
7:25 the origin of all of these theories. And so I expect, or I would naturally expect, that there is some deeper theory that explains the Standard Model and gravity both. String theory is a possibility. That’s perfectly fine, but it could be something else. I’m actually a champion of a crazier theory, which is Holger Nielsen. Holger Nielsen had this crazy idea that at very high energies, everything happens. So basically, you can imagine everything you can imagine happening. He calls it
8:10 “random dynamics.” And that the reason why at low energies you only see certain theories is that some theories are protected and are able to have massless fermions, massless gauge bosons. So gauge symmetry and chirality protect fields from generating masses. So gauge bosons, it’s probably well-known. Chirality is probably less well-known than for fermions. If you have chiral fermions, you have a left field by itself; it can’t have a mass. And so his argument was that the reason we see at low energies the Standard Model with chiral
8:57 fermions and gauge fields is that they’re the only ones that are protected at low energies from generating large masses. And therefore you get $U(1)$, $SU(2)$, $SU(3)$. And by the same logic, you could get a gravity theory that is protected by general covariance from having larger masses. And so this is sort of the “anti-unification.” Instead of unifying, you have everything happening at high energies, but only some things living to low energies. I just like it as an idea. Okay, this is super interesting, because you’re so conservative in terms of you don’t want to posit more than necessary, but then over here you’re extremely attracted to something that is quite zany.
9:46 Well, this is a bit, yeah, it’s a bit contrary, and I have to say it’s, if you search yourself for biases, one of the biases of the field is that things unify. And we don’t really have any evidence for that. There’s no evidence for gauge unification at all. People normally talk about unifying electricity and magnetism, but that’s not really two gauge theories. What you’ve done is you’ve identified the single gauge theory that describes both of those phenomena, $U(1)$.
10:34 And the electroweak unification isn’t really unification. You started out with E and M and a weak theory, and you’ve explained it by having two theories that mix, $SU(2) \times U(1)$. They’re not unified, they’re just mixing. So we’ve never really seen unification. So the idea of unification could just totally be a bias. It could be that the theory as we go up in energies is $U(1)$, $SU(2)$, $SU(3)$, $SU(4)$, $SU(5)$, $SU(6)$, $SU(7)$, or something else as you go up. It doesn’t have to ever come together into a unified theory, a unified gauge theory.
11:21 Yes. Okay. So, at first, when you were saying that there hasn’t been unification, you qualify that with “gauge unification.” Because the standard folklore that people hear is, well, there was the heavens and the earth and Newton unified that with gravity. Then there was space and time and then Einstein unified that with spacetime. And then there was electromagnetism or electricity and magnetism; they unified and so forth. Yeah, but those are just identifying the appropriate interactions. It’s not a unification
12:13 of any interactions. You know, E and M—electricity and magnetism—look like different phenomena, but we’ve actually, Maxwell, you find out that it’s really the same underlying theory, just one theory. So, if you want to use the word unify, it’s okay, but it’s not unification in the sense that the particle physics field assumes is going to happen at high energies. We assume that we’re going to merge into some $SU(5)$ or $SO(10)$ or $E8 \times E8$ or some unified theory with more degrees of freedom, but which has a higher symmetry than what we have at
13:02 the moment. That’s a beautiful idea. It’s a great idea. I’m not saying it’s wrong. I’m just wondering if that’s a preconception that keeps us from seeing other options. Hi, everyone. Hope you’re enjoying today’s episode. If you’re hungry for deeper dives into physics, AI, consciousness, philosophy, along with my personal reflections, you’ll find it all on my Substack. Subscribers get first access to new episodes, new posts as well, behind the scenes insights, and the chance to be a part of a thriving community of like-minded pilgrimers. By joining, you’ll directly be supporting my work and helping keep these conversations at the cutting edge. So click the link on screen here,
13:49 hit subscribe, and let’s keep pushing the boundaries of knowledge together. Thank you and enjoy the show. Just so you know, if you’re listening, it’s curtjaimungal.org.
