Theories of Everything with Curt Jaimungal - Dirac's 90-Year-Old "Mistake" Unifies All of Physics

Episode Date: July 29, 2025

As a listener of TOE you can get a special 20% off discount to The Economist and all it has to offer! Visit https://www.economist.com/toe In this episode, I speak with Professor Felix Finster, a radical thinker reimagining the foundations of physics. We explore his theory of causal fermion systems, where reality emerges from quantum correlations—without assuming spacetime or geometry. From the Dirac sea to quantum gravity, this conversation challenges familiar concepts and offers a glimpse into where the next physics revolution might begin. Join My New Substack (Personal Writings): https://curtjaimungal.substack.com Listen on Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e Timestamps: 00:00 Introduction 03:12 The Origins of Causal Fermion Systems 06:55 Engaging with Alternative Theories in Physics 15:22 The Standard View of Causation 18:21 Classical, Quantum, and Pre-Quantum 23:06 How Spacetime Emerges from Disconnected Points 29:49 Recovering Lorentz Signature Without Assumptions 31:48 Recovering the Born Rule from First Principles 39:39 The Measurement Problem 46:20 Bounds on CSL Parameters 49:45 The Dynamics of Spacetime 57:47 Collaboration with Yao and Reflections on the Theory 1:03:13 A Quantum Gravity Theory Without Supersymmetry 1:05:28 The Dirac Sea 1:11:40 Addressing Infinite Energy in Semi-Classical Gravity 1:13:09 Octonions in the Vacuum Structure 1:17:32 Chirality and the Action Principle 1:20:33 Baryogenesis and Why Matter Exists 1:35:10 Rethinking the Strong CP and Hierarchy Problems 1:38:43 Recognition, Collaboration, and Growing Attention 1:54:00 Mathematical Criteria vs. Experimental Tests 2:01:02 Advice for Young Researchers Links Mentioned: - Felix's Papers: https://scholar.google.com/citations?user=F7ppNroAAAAJ - Felix's Bio: https://www.uni-regensburg.de/mathematik/mathematik-1/startseite/index.html - Causal Fermion Systems [Paper]: https://arxiv.org/pdf/2405.19254 - Linear Dynamics of Wave Functions [Paper]: https://arxiv.org/pdf/2101.08673 - The Principle of the Fermionic Projector [Book]: https://www.amazon.com/Principle-Fermionic-Projector-Advanced-Mathematics/dp/0821839748 - Baryogensis for Causal Fermion Systems [Paper]: https://arxiv.org/pdf/2111.05556 - Holographic Mixing [Paper]: https://arxiv.org/pdf/2410.18045 - Standard Model Physics from an Algebra? [Paper]: https://arxiv.org/pdf/1611.09182 - Barry Loewer & Eddy Chen [TOE]: https://youtu.be/xZnafO__IZ0 - Fay Dowker [TOE]: https://youtu.be/PgYHEPCLVas - String Theory Iceberg [TOE]: https://youtu.be/X4PdPnQuwjY - David Kaiser [TOE]: https://youtu.be/_yebLXsIdwo - Ruth Kastner [TOE]: https://youtu.be/-BsHh3_vCMQ - Amanda Gefter [TOE]: https://youtu.be/yABPvDJ6Zgs - Jacob Barandes [TOE]: https://youtu.be/7oWip00iXbo - Eva Miranda [TOE]: https://youtu.be/6XyMepn-AZo - Emily Adlam [TOE]: https://youtu.be/6I2OhmVWLMs - Scott Aaronson & Jacob Barandes [TOE]: https://youtu.be/5rbC3XZr9-c SUPPORT: - Become a YouTube Member (Early Access Videos): https://www.youtube.com/channel/UCdWIQh9DGG6uhJk8eyIFl1w/join - Support me on Patreon: https://patreon.com/curtjaimungal - Support me on Crypto: https://commerce.coinbase.com/checkout/de803625-87d3-4300-ab6d-85d4258834a9 - Support me on PayPal: https://www.paypal.com/donate?hosted_button_id=XUBHNMFXUX5S4 SOCIALS: - Twitter: https://twitter.com/TOEwithCurt - Discord Invite: https://discord.com/invite/kBcnfNVwqs Guests do not pay to appear. Theories of Everything receives revenue solely from viewer donations, platform ads, and clearly labelled sponsors; no guest or associated entity has ever given compensation, directly or through intermediaries. #science Learn more about your ad choices. Visit megaphone.fm/adchoices

I was no longer happy because I understood what was going on, but I didn't have the feeling that what we did was really describing nature. It seemed somewhat artificial. Then there's the issue that it's not clear what quantum gravity actually is. Professor Felix Finster has spent over 30 years rethinking the fundamental units of physics. His theory, Causal Fermion Systems, begins with the concept from Dirac that negative energy states aren't these mathematical artifacts we thought they were, but instead form an actual real sea, underlying reality. From

this foundation Finster constructs space-time as correlations between wave functions spread across discrete points. There's no pre-existing geometry. There's no assumed metric. There's just abstract operators and a variational principle. Interestingly, from this austere beginning, you actually get general relativity. And the standard model emerging. What's more, there are three generations.

Correct gauge groups, matter versus antimatter asymmetry, which is why you're here today to watch this, the measurement problem collapses, and even chirality breaking is predicted. correct gauge groups, matter versus antimatter asymmetry, which is why you're here today to watch this, the measurement problem collapses, and even chirality breaking is predicted. A true candidate for a theory of everything. My name's Kurt J. Mungle, and on this channel,

I investigate theories of everything, or of reality, with rigor, using my background in mathematical physics. Today's conversation demonstrates how mathematical precision and physical insight can rebuild your understanding of nature. A special thank you to our advertising sponsor, The Economist. I thought The Economist was just something CEOs read to stay up to date on world trends, and that's true, but that's not only true. What I've found more than useful is their coverage of math, of physics, of philosophy, of AI, especially how something's perceived by countries and how it impacts markets. Among weekly global affairs magazines, The Economist is praised for its

nonpartisan reporting and being fact driven. This is something that's extremely important to me. It's something I appreciate. I personally love their coverage of other topics that aren't just news-based as well. For instance, the Economist had an interview with some of the people behind DeepSeek, the week DeepSeek launched. No one else had that. The Economist also has this fantastic article on the recent DESI dark energy data, and it surpasses, in my opinion, Scientific American's coverage. If you're passionate about expanding your knowledge and gaining a deeper understanding of the forces that shape our world, then I highly recommend subscribing to The

Economist. It's an investment into your intellectual growth. One that you won't regret. I don't regret it. As a listener of Toe, you get a special 35% discount off the annual subscription. This is a new discount exclusive in podcast form to this channel and it's unprecedented. Now you can enjoy The Economist and all it has to offer for less. Head over to their website, www.economist.com slash toto to get started. That's T-O-E. Make sure to use that link. That's economist.com slash T-O-E to get that discount. Thanks for tuning in, and now back to the exploration of the mysteries of the universe with Felix Finster. Professor, you spent three decades developing a theory, which we'll get to in detail, which

turns vanilla physics upside down into, I don't know, bubble gum flavor. So you start with abstract operators instead of starting with space type. I want you to talk about the history of how this came to you, but also why there is resistance and there is, or at least was, a good reason for that resistance. It's not as if it's just arbitrary animosity from your colleagues. arbitrary animosity from your colleagues? Yes, I mean, I mean, it all started when I was a physics student in the third year of my studies and I heard a lecture on quantum field theory. And back then I was very enthusiastic about physics. I mean, I liked all these concepts, also like math as well, I should say.

But then in this quantum field theory course, I was no longer happy because, I mean, I understood what was going on, but I didn't have the feeling that I really, that what we did was really describing nature. It seemed somewhat artificial. It was also maybe too computational, but the underlying concepts were no longer so clear. And then I was kind of unhappy about this. And this is when I kind of started thinking about kind of alternatives. Could one not do this better? Of course, in a quite naive way, I mean, as probably most or many young students do when they learn a subject.

I mean, also a part of the learning process is of course that you ask the question, why is it done the way it is presented in the lecture? Or can one not do it in a different way? And this is then when kind of a few first ideas came up that I thought, well, maybe we should do it like that. Why shouldn't it be better to proceed somewhat differently? And this was all quite vague at the time. But I was kind of persistent and pursued these ideas a little bit.

And also tried to talk to physicists, something like the professors in my lecture, for example. And back then I felt some resistance, as we already mentioned. And this is partly because it was, as I said, the concepts were kind of vague. It was not so clear where this was leading to. And of course, this is also nothing you can expect. I mean, if someone just comes up with a vague idea, I mean, you can't expect him to present a full theory yet. And then the resistance, I didn't really quite understand why. I mean, my naive expectation was that, say, also, I mean, now I'm professor myself, so I suppose like a young student came to my office and told me, look, I mean, I have these

ideas and he has a few computations, what do you think? Then actually, I think I would be happy and I would try to understand what he or she is trying to do and try to support him or her. I mean, I think this is the ideal or reaction and also the reaction I was hoping for. And still I don't fully understand why the reaction was different. I think it was partly maybe it was what I did was a bit too mathematical. Also of course all everybody's busy so people have a lot of other things to do and then if someone comes and you don't understand right away what he wants to do, then maybe you don't want to go into this further or

deeper. I'm not quite sure. Do you buy the busyness argument? What I mean to say is that it's in part a physicist's job to understand, maybe all parts, but in large part a physicist's job to understand nature. And in understanding nature, it would be great if one understood the alternative approaches. Alternative is even a dirty word in some circles in theoretical physics. But anyhow, do you buy this busyness argument or do you see this, no, this is maybe you should set aside one day a month to look over alternative theories or what have you? Well, I think I understand this argument party.

Of course, everybody's really busy and I was a young student. And maybe part of the problem is that people don't take young students seriously. I mean, if I had been a professor already back then, I'm sure that would, they would have taken me more seriously. Right. Yeah. And yeah. So is that why you got pushed into the math department?

Because you wanted to solidify your ideas or was there something else? Well, I mean, I was already studying both at the same time, I mean, in parallel. But I liked, I found, well, at the beginning, I liked physics much more. I saw that math more as a tool, like a more computational tool. Of course, you need to know math to do physics, but the interest for math in itself, so in the mathematical structures and the theory behind it, I mean, this came when I studied. And then at the same time that math became more interesting, physics became less satisfying. And this is then why at some point I decided, well, then let's move to math. In fact, I mean, in the end, I also got the master's degree in physics or in the end,

I finished with both degrees. But this was simply because I had already taken so many physics courses that it didn't take much additional effort to also get the master's in physics. But I mean, there was really a change. I said, okay, I want to continue in mathematics. And also because somehow I felt the math community bit opener, more tolerant, more, well, maybe they appreciate the work more of other people. More tolerant?

Yeah, more tolerant. More tolerant? Yeah, more tolerant, yes, because in mathematics, as long as you do interesting mathematics, so this means there are interesting structures, some kind of deep results, you prove something, it is all mathematically rigorous, then this is appreciated by the community. And in physics, some of these, of course, the standard in physics is you want to describe nature, which is of course more difficult. I mean, if someone young starts with, has some alternative ideas and then the physicists tell him, well, I mean, before we start talking about your theory, you

should basically reproduce all known physical results and you should get some new predictions. And once you have that, then you can come back and talk to me. Then of course, I mean, this is far too early. I mean, you can't expect from a young people to accomplish that. And this is why then simply the communication with physicists was much more difficult. And which of the mainline approaches to a theory of everything or quantum gravity reproduces all of known physics and also makes testable predictions?

You mean so which of the known approaches to speak I like best? Many times when someone's coming up with an alternative approach like yourself or Faye Dahlker, they get told, hey, if you can't reproduce the standard model and three generations and the masses or what have you, then don't talk to me. But then that person themselves are working on a theory which can't reproduce the standard model, or it just has the hopes of it and they don't know the specific initial configuration that will lead to it. Or it has a variety of testable predictions, some of which have just not come true. Like if that critique is being thrown to you, then which of the mainline approaches satisfy these hurdles? Well, to me, of course, I mean, now we are 30 years later.

I mean, I developed my ideas much further. And now I can say, I mean, that this theory of causal fermion system really gives in certain limiting cases, the well-established physical theories back. So you get like the standard model on the level of classical field theory, you get quantum field theory, and you also get classical relativity. So this is what you get in limiting cases. And to me, this is also like one of the basic requirements. If someone claims it should be a theory of everything, maybe I should say in general, I don't like this notion theory of everything too much,

because it pretends that this is a theory which can really explain everything. And there is no such theory yet. I think what is important, what I would say more of, for example, causal fermion systems, that it's like a promising candidate for a theory of everything. So this means that it has the potential of really describing physics on the fundamental level. And in order to be able to claim that, you have to get the well-known theories in certain limiting cases. And this is what we have so far. And yeah, I don't think that there are many other approaches right now which achieve the same.

Of course, there are a few and there are many who claim that. Of course, it's also, well, it would be long discussion to say like which theory gives what precisely and so on. But I mean, to me, unfortunately, there are not too many alternative theories around. Why do you say unfortunately? Well, I think it would be good for the field of physics in general or this whatever fundamental physics to have different competing theories around, which ideally make different predictions so that you, with experiments who can falsify or verify things, this would be good.

And this would also be like a healthy kind of environment, healthy situation. And unfortunately, this is not how it is. I mean, of course there are theories like string theory, which kind of dominates the field. And then there are a couple of alternative approaches as quantum gravity, which just describes quantized gravity, but it's not a theory of everything in the sense that it doesn't describe the whole whatever, not all the other interactions as well. And, but what I, what is missing somehow is that these different approaches really compete with each other and also in this way communicate with each other, interact with each other.

And this is partly because there's not much experimental evidence right now. In other words, there are no experimental results to be explained which could be tested. So this is why the field is a little bit, well, remote, detached from experiments, let's say like that, which is also from my point of view, not the way it should be in physics. But anyhow, this is how things are right now. should be in physics, but anyhow, this is how things are right now. Do you see that there is a lack of experiments? Because there are unknowns like dark matter anomalies, like the G2 experiment with the muon.

So aren't there still phenomenon to be explained? No, sure. This is true. I mean, there are, I think there are quite a number of things which are unknown. quite a number of things which are unknown. But often the problem is that there are different possible explanations. So these are not phenomena where I could say well I do one simple experiment and then I can decide which theory is right or wrong. But the phenomena are typically very complicated. There are many different effects which come into play at the same time. And therefore it is difficult to find really clear answers. And also, I mean, the standard model of, of parliamentary particle physics, for example, works excellent.

I mean, it really makes many predictions. I mean, there are not many deviations. Now we're going to get to your theory, but prior to doing so, it has the word causal in it a couple of times. So there's causal fermion systems, causal actions. There's a causal structure, but that's there in ordinary GR. So why are you obsessed with causation? What is the standard view of causation?

What's meant by causation as well? Yeah, I mean, by causation, usually people mean that the past determines the future. So in simple terms, suppose you know the physical system at an initial time, then you can also in principle compute what happens later. So in other words, the past can affect the future, but not the other way around. And of course, this is like a basic, I mean, fact of physics or what we experience in daily life that there's something like causality, time passes to the future. And then the question is like, well of course how does this come about

and also how is this to be described on which level of physics should this come up? And well there are for example this causal set approach, then we say, well, this is my starting point. I just start with a set of space time points and there are causal relations between them. This is not the way it is done with causal ferment system. So the idea is more you start with other structures and one sets up physical equations.

Maybe I can explain this a bit more in detail later. And as a consequence causal relations come up or are generated or emerge, however you want to call it. And the reason why it's called causal Fermat systems because this causal structure kind of plays a central role also in how these equations are formulated. So, I mean, these equations, as I said, I mean, they don't pre-assume a causal structure, but they kind of generate a causal structure. And also in a way that space time points which have spatial, with space like distance, do

not interact with each other. A bit like generalizing the usual concept that no information can be transmitted faster than with the speed of light. A similar concept is also built into this causal action principle or into the basic fundamental equations. So there's another approach called Adler's trace dynamics. I'm not sure how familiar you are with it. I have a question for you about how your approach differs. No, sure.

I mean, in fact, I'm familiar with it. In fact, right now we are writing kind of comparison paper together with Claudio Paganini and Jinda Singh and Shane, in fact, and Farnsworth as well, where we want to, where we compare the causal action principle with trace dynamics and with non-commutative geometry. Because from the kind of analytic point aside, they are kind of, they are close relations, so at least one can compare this nicely. One of the differences is that trace dynamics is so-called pre-quantum, whatever that means, whereas yours is quantum from the get-go.

So I want you to explain those terms because the audience may be wondering, well, what is quantum number one? Number two, what is classical as distinct from quantum? And then number three, what the heck is pre-quantum? Okay, good question. I mean, this is pre-quantum in this atlas trace dynamics. So one starts with a certain action formed of traces. And the idea is then that, I mean, an important, maybe I should have said this before, for quantum theory, it's important that you have non-commuting operators which satisfy certain commutation relations.

I mean, the simplest example is this position momentum commutation relations, this Heisenberg commutation relations. So this is something one wants to have in order to be able to speak of quantum theory. And in Adler's trace dynamics, one has some non-commuting objects right from the beginning, so some operators. And then the idea is that kind of in the statistical kind of thermodynamic, or if you take in the statistical mean, well, it's a bit oversimplified now, but I mean, just trying to convey the idea. I mean, if you take a statistical ensemble, then these canonical computation relations

come up using the law of large numbers. So this is like what is meant by pre-quantum and then quantum theory arises from there. And this causal fermion system approach approach it's a bit different. I mean we also have like non-commuting operators but and also we get this canonical commutation relations at some point but what is more important is the concept of having wave functions in space-time. So I mean to me like also the feature of quantum theory is that you have a wave function. I mean, probably most people are familiar with the Schrödinger wave function or the Schrödinger, which describes the Schrödinger cat.

We have this superposition principle for wave functions. So this is also an important feature of quantum theory. And such wave functions, this is built in this called a Fermat system approach right from the beginning. So you have these wave functions and you have operators which are non-commuting and then there's this specific action principle, the so-called causal action principle, which in such a way or has the feature that this causal structure then emerges. Now why do you say that the wave function lives in space-time instead of in configuration

space? Well, because let's put it like that. I mean, right at the beginning, we start just with points, a set of points. And this will later be the space-time points. But a priori, I mean, if you just take a set of points, you can't talk this big of space-time yet. So there's no topology currently? Yeah, topology depends.

I mean, let's say, suppose we just take a finite number of points for simplicity. I mean, then there's no topological structure. And also what is missing is something like an order relation, causal relations between the points. So therefore, if you just have a set of points, I wouldn't call that a space time. So space time is additional structures. And then the structure we start from our wave functions which are kind of spread out. So this means you can evaluate it at these individual

points. And then this causal action principle brings these wave functions into specific configurations and kind of optimal configurations. So you minimize a certain functional. And as a consequence, these wave functions also induce additional structures on the space-time points. So in this way, the space-time one can then speak of space-like and time-like separated points. One can speak of future and past and causal relations and so on. And then once you have all these additional structures, then you have something what I

would call a space time. Hi, Kurt here. If you're enjoying this conversation, please take a second to like and to share this video with someone who may appreciate it. It actually makes a difference in getting these ideas out there. Subscribe, of course. Thank you. Okay. So let's slow this down.

You start with a set of points. These are just like powder that are disconnected. And then you have a wave function. You said that the wave function spreads out. Now spreads out meaning what? That one wave function can encompass more than one. So it's not just one wave function. It's a whole family of wave functions.

And each wave function is, I mean, out of this wave function means that at each point, it takes values in a kind of vector space. I hope it doesn't get too technical. Maybe I should expand it a little better. I mean, at each space time point, there is like a vector space attached. So the so-called spin space. So it's a bit, I mean, for people who are familiar with a vector bundle, it's a bit a similar structure. So we have like base points. So these are just these finite number of space time points. And then at each

space time point, you have a vector space attached. And now these wave functions are just And now these wave functions are just vectors in the Hilbert space, which, and out of them, you can also construct something like a section in the bundle. So this means at each point you get a vector in the corresponding spin space. This is then a wave function. And now we don't have just one of them, we have a collection of many of those. Okay, so quick question here. So at some point we're going to get to how you get the standard model gauge group, but just because you get a gauge group that comes out, it needs to also come out to get a G

bundle structure, not just a gauge group and maybe it's associated bundles and so on for spinners. So do you get all of that structure coming out as well? Yes. So this comes out, but it kind of in different, like at different stages on a different level. So I mean, right now we are at the most fundamental level. So we just have these space time points at each space time point, we have a spin

space attached and this spin space also comes with an inner product. So this means there's something like a scalar product, but which is indefinite. So we have an indefinite inner product space attached to each space time point. And then there's a kind of group of unitary transformations acting on this spin space at each point. And this is kind of the, well, the source of local gauge invariance. So there's kind of a freedom to transform these spinors, if you like, at each space-time point. And if you then move up to a bit higher level to get like effective theory, if you take many wave functions and many space-time points and take certain limiting situations, then this freedom

to transform the wave function at individual space time points then gives rise to local gauge freedom, local gauge transformations, similar to what you have in the standard model. So space time is just a web of correlations of these many bodies? In the end, this is how you can see it. I mean, I mean, there's still the notion of space-time points, but then these different space-time points are, the relations between the space-time points are induced by these wave functions. And in the end, you have like a web of correlations between all these space-time points. And this is what really makes up the space- time as we know it or as we experience it.

Now how do you get Einstein's equations out of this or the action that minimizes the Ritchie scalar? Yeah okay I mean this is of course quite a long path so but of course I can summarize it a bit I mean right now we are on this level of you have these individual space time points. Now, what is really like the crucial point that although you don't have many structures at this stage, that this is enough to formulate physical equations. And this is done with this causal action principle. This is a certain functional which now depends on this family of wave functions which is non-negative so you can minimize it. So now one minimizes this functional by varying all these wave functions and then once you have an optimal

configuration, a minimizer, then they are also corresponding Euler-Lagrange equations. And from the procedure here is reminiscent of what one does in classical field theory. You also have like an action functional, an action minimizing this action gives Euler-Lagrange equations, which are then the equations of motion. So it's inspired by that. But the mathematical structure of this action principle is very different. So it's not like a standard Lagrangian because simply because on the level of this space time points, you can't do all these usual things. You can't just take derivatives. You don't know what a field is and so on. So we really have to formulate it in a different language with different objects.

Good. And then in this way, one gets kind of the theory, the kind of abstract fundamental theory. And from the mathematical point of view, this is all nice. I mean, this is all consistent. You know that there exist minimizers, you do all the Lagrange equations are well defined and so on. But the question then of course is like, what does it, how can you describe a really physical space time in this setting and what do you get in the end?

What does this causal action principle tell you about the dynamics of the resulting system. And in order to answer these questions, it's important that minimizers can be obtained starting from flat spacetime. So if now I start from the other side, I just take, okay, let's take our standard four-dimensional Minkowski spacetime. And then I consider in this space time wave functions, which satisfy the Dirac equation. And then I build a certain family of such wave functions. Then one sees that they really form a minimizer of the causal action principle. So this means I have a specific solution of these Euler-Lagrange equations, which just describe empty space, just a non-interacting Minkowski space. And this is of course a key point.

Also it was of course one of the key requirements for coming up with the causal action principle. The way I came up with a specific form is because I wanted Minkowski space to be a minimizer in a certain sense, in a well-defined sense. Where I'm confused is that I don't see how in this causal fermion system, how do you recover the Lorentz signature without imposing it? It seems to me to be sneaking in via just whatever you posit as the action. Well, not quite. sneaking in via just whatever you posit as the action? Well, not quite. I mean, what is true is that on this fundamental level, there is no

Lorentzian metric, also there does, there's no manifold structure. I mean, the space time points do not need to form say a four-dimensional smooth manifold, so there is no continuum space time in general. There's also no Lorentzian metric. continuum space-time in general, there's also no Lorentzian metric, but there are other structures which also correspond to the causal structure. I mean this is why it's called causal action principle and so on. So in other words you have this kind of web of correlations as we called it earlier between the space-time points. This also gives rise to causal structure. And now what happens now if you take this example of Minkowski space and then you construct the causal fermion system out of that you do not only get a minimizer of

the causal action principle but you also see that these different causal structures coincide. So this means that the causal structures of the causal fermion system, then agree with the standard causal structure in Minkowski space. So therefore one can say that this usual causal structures of classical space-time, Minkowski space, Lorentzian space-time, they kind of are generalized in this causal fermion system approach. And okay, yes. So therefore, it's not that I'm sneaking in the causal structure, it's more that I recover

it to see then later, okay, now this complicated web of correlations and the causal structure coming from there then agrees in the example with which is something I'm already familiar with. So the standard causal structure of Mikovsky space. Do you recover the Born rule or do you grant it initially? The reason I ask this is because from my understanding of your work, there's this absolute square of the wave function, so the side bar squared that you use to probe space time. But this to me assumes the Born rule already. And so I was just curious about it. Okay, sure, sure.

I mean, then maybe I answer this first. I mean, I would still like to come back to your original question with how do you get the Einstein equations? I mean, I can of course then come back to that. I mean, concerning the Born rule, I mean, you let me answer it like that. I mean, the Born rule means, okay, you make measurements and then the wave function determines or the wave absolute square of the wave functions tells you about the probabilities of things happening. And in order to make sense of that, I mean, the first thing one needs is something like a conserved

scalar product. I mean, you want to take a measurement in quantum mechanics means you want to take expectation values. You have a certain observable and operator on the Hilbert space and you want to take an expectation value and then this tells you what the mean average outcome of the experiment is. So the first thing is you need something like a scalar product. And there is like a scalar product on the fundamental level of a causal firmament system because we start with the Hilbert space. But this is not enough.

What you need is a scalar product in space. So I mean, typically a measurement takes place at a certain time. And then at this time you need to have a scalar product, which is typically the integral or the wave function squared or something like that. And the nice thing is that in this caudal fermen system approach, that is also of course a similar structure, the so-called commutator in our product, which can be formulated in terms of surface layer intervals. So the idea is, I mean, we have this space-time, which doesn't even need to be continuous space-time,

it could be discrete, but now you want to have some evaluate something at a fixed time. So what does this at all mean? And the way this is made precise is that you split up space-time into the past and the future of something you consider as the time you are interested in. So instead of considering a cushy surface of equal time, you consider its past and its future, which has the advantage that it works, for example, also in discrete cases, where it's not so clear what the Cauchy surface itself is. And then, okay, but maybe it gets a bit technical. So the important point is that there is now a so-called surface layer interval. So you can think of this as a kind of something which is smeared out in time and is like a scalar product on the wave functions, which is then time

independent. So we have to say, okay, I have something like, for example, I take a normalized vector at the initial time, let it evolve, but then at a later time, it is still a normalized vector. And the norm is now something which is kind of smeared out in time a little bit. In order to compute this, we have to integrate our space and also over a thin, tiny time strap. So, this is how this works.

So, in this way, one has like a conserved scalar product. And this is good because then you can say, well, the integrand of this scalar product, this is then my probability density. And the total probability is equal to one because the state is normalized even at a later time. So we have something like whatever conservation of current conservation, the total probability is conserved. And then you can also compute then what is the probability of a particle to be in a certain spatial region at a certain time. Okay, and then so therefore, first of all, the mathematical setup allows you to formulate the Born rule. Now the question, of course course is does it really hold? So I mean why do you know that these expectation values of operators really correspond to the

probabilities of the outcome of experiments? So this is kind of the physical essence of the Born Rule. Why does this hold? And this is something we worked on quite recently. I mean, I worked on the paper last, well, maybe about one year ago together with Claudio Paganini and Johannes Kleiner. So to form up students postdocs of mine. In fact, Claudio Paganini is still working in my group. And there we showed that first of all, this bone rule re-holds and also it gives an explanation for why the wave function collapses in the measurement process.

Okay. I'd like to get to that. Firstly, you never have to apologize. No guest has to apologize on this channel for being technical. The audience loves the technicalities and that's in large part what separates this channel from others. Okay, then I'm glad to hear that. Of course, still I'm hesitating. I mean, let me just... But still I don't know if the audience is familiar with the measurement pros, with the measurement problem in quantum mechanics. Okay, so why don't you outline the measurement problem? But also, I'm still confused as to how you get the squares, the psi square instead of

some other nonlinear term like psi cubed or psi fourth or what have you. Explain that to me. Yeah, okay, good question. I mean, this is because this conserved quantity you get involves this kind of sesquilinear in the wave function. This is what you get from is kind of sesquilinear in the wave function. This is what you get from the mathematics. And well, of course, ultimately it has to do with the fact that I start with the Hilbert space in the first place.

I mean, I start with the Hilbert space. I mean, one of the basic ingredients of a quantum thermos is the Hilbert space where you have a scalar product already. And then this scalar product can later be represented in space time with the surface layer integrals, but the fact that it's still sesquilinear comes from the original Hilbert space scalar product. But still it's kind of interesting that all these conservation laws and so on fit together, I mean, this kind of, well, it gave me like a kind of confidence that we are on the right track.

I mean, that what we are doing really makes sense because somehow you see that the structures you get is really what you need to formulate physics and so on. Sorry, you say we here. What year was this and who is the we that you're referring to? Yeah, okay. Good question. I mean, this commutator inner product, this is maybe 10 years old. So I mean, this is in the paper together with Niki Kamran and Marco Oppio.

So Marco Oppio was a former postdoc of mine who unfortunately dropped out of academia a few years ago. Niki Kamran is a collaborator of mine and we've worked together since, well, more than 25 years. So he's a regular visitor also here in Regensburg and also I visited, he's in Montreal at McGill University, also visit him there often. And so, I mean, we worked together since many years. And, well, I mean, the, as I said, I mean, so this commutator in our product is not so old,

maybe 10 years old. You have another book that's like almost 20 years old, The Principle of Fermionic Projector, Projections, if I'm not mistaken. I've been studying you for quite some time now, so I'm getting many of these ideas mixed up. And I know that we have to get to the dynamics of space-time as well as the measurement problem. Why don't we get there? Okay, fine. So maybe just summarize the measurement problems. I mean, if one does a measurement in quantum mechanics, then this also changes the system. I mean, and then mathematically one computes the expectation value with respect to

an observable. And this tells me about the expected outcome of the measurement. And as a result of the measurement, the Hilbert space vector ends up in an eigenstate of the measurement apparatus. state of the measurement apparatus. So this means depending on what you measure, also the system changes and the state vector ends up in the corresponding eigenspace of the observable. And this is something which doesn't have a good explanation within quantum mechanics. I mean, the Copenhagen, the standard Copenhagen interpretation of quantum mechanics, this is one of the postulates. But this is nothing which is explained intrinsically from the equations of quantum mechanics. It's nothing you can derive from the Schrödinger equation.

In fact, it is something extra. So this means also this means when you do a measurement, something happens which cannot be explained within the theory. And this is not a fully convincing. I mean, this is not convincing. And of course, this has puzzled physicists for many years and there are different approaches to explain that. And now this causal ferment system approach also provides an answer, but in this case

it is really a consequence of the dynamics as described by the causal ferment system. So you don't need to put this, people call this collapse of the wave function or reduction of the state vector so that the wave function kind of changes in the measurement process. And this is something which can explain from the equations coming out of the causal action principle. So this is something we just wrote last summer, so this is really fairly recent. And this also answers the question with the Born Rule, which kind of started our discussion here. I recall your solution to the measurement problem has to do with noise. Yes, exactly.

So okay, I see. So you looked at the paper in more detail. So the way it works more is as follows. I do my homework. Okay, so let me try to explain this. I mean, so we have this Euler-Lagrange equation of the causal action principle. So these are kind of the fundamental equations. And then, of course, as a mathematician, we want to know how do the solutions look like. And I spent quite a lot of time analyzing the solutions of the Euler-Lagrange equation

and of the linearized feet equations, or this linearized version of these Euler-Lagrange equations. I studied this in detail. And it turns out that there are many more solutions as you would expect from other physical equations. For example, you get the Maxwell solutions of Maxwell equations, like say, plane electromagnetic waves. So these are specific solutions, but there are many more. And then the question is, what do all these additional fields do and how can you describe them?

And our approach is to describe them stochastically. So this means we say, well, we don't know how all these fields look like. And the reason that we don't know how they look like also has to do, we don't really know what the microscopic structure of space-time is. We just know how space-time looks macroscopically, but we don't really know what's going on,

on very small scales. And these kind of fluctuations on small scales, they can also be described by these linearized solutions. So this is why we take the point of view where we have all these many, this multitude of fields, which we assume to be non-zero, and we describe them in a stochastic way. And they couple to matter. So suppose you have an electron sitting here, then all these fields couple to this electron and also have an effect on the dynamics, on the time evolution of this wave function.

And this is then something we studied in detail. And it turns out that one gets a connection to collapse models, which are already around. I mean, there's this particularly CSL model, continuous spontaneous localization model. So it has kind of similar features what we get here. And in this model, one considers the Schrödinger equation plus a stochastic term plus a nonlinear term. So it's important to have these two types of correction terms.

And now our stochastic terms, this comes from this background, which we describe stochastically as I just tried to explain. And the nonlinear term comes from the fact that the causal action itself is nonlinear. So the resulting equations are nonlinear equations. So therefore we have all the ingredients right there and we saw, okay, it really gives rise to such a collapse model. And I should also mention that it's not exactly the CSL model, the model we get is somewhat different, which has to do with the fact that everything is kind of non-local in time. I mean, I also already explained this surface layer integral where everything is

kind of integrated over a small time strip. There's something similar in the equations as well. Things are kind of smeared out in time. And this gives like an additional feature of the model, which also seems quite important and interesting. So the way that you get it is via reproducing the CSL model. Yes. Right. OK, now just for people who are interested in different

interpretations of quantum mechanics, I'll place a link on screen here because I have a substack where I go through the top 10 most popular interpretations, even though they should in some ways be called different theories of quantum mechanics as they differ in their predictions and the CSL is one that differs. So if my memory serves me correctly, there are two parameters at least in the CSL model. One that has to do with the localization length and also a collapse rate. So do you have bounds on those? Yeah, okay. I mean, there are some of that.

Right, there are two parameters in this CSL model which can be tested experimentally. And there are also tests going on right now. I mean, people are measuring these parameters or in fact, right now one gets bounds for these parameters. So the parameters can only be in certain ranges. And then there's another, I mean, the effect which is, I mean, which puts the best bounds on these parameters is a heating effect. So, I mean, well, if you think you have an electron sitting there and then it's surrounded by kind of background fields. One effect is that the electron starts wiggling.

So, it did say energy from this from this environment, it's transferred to the electron. And this is then something one could measure. So, I mean, more specifically, I mean, this is done in this, for example, in this Gran Sasso tunnel in Italy, where they also do neutrino experiments. So you are in the middle of a tunnel under big mountains, so they're surrounded by rocks. So this means there is not much radiation. And then we just have a probe sitting there. And then the, if you believe in the CSL model, then there is still some

heating taking place, which means that this probe then emits photons just spontaneously, which you could then measure. photons just spontaneously, which you could then measure. So this means one just puts a probe there, one puts kind of detectors around it to measure like photons of different energies, and then you try to find something. And this puts bounds on these parameters. And well, now an interesting feature is that for our model, this is something we are working out right now.

I don't know if you want to mention this in the video already or not, because the paper is not finished yet. I mean, right now, yes, we are maybe let's write it like that. Let's say like that. I mean, right now we are analyzing if our model also gives rise to heating. I see. These are preliminary results. You're verifying them. So, I mean, it seems that our model does not necessarily give rise to heating. So this means that these experiments should not be, I mean, these experiments do not really test our model.

But as I said, this is preliminary. Maybe you should even cut this out as you like. So my understanding is that the CSL also has some violations of conservation of energy. And I'm not sure if yours would also. Exactly. This is basically this heating, what I said, is also a violation of energy conservation because in the electron, if it gets hotter, it gets the energy increases. And this is something we are looking at right now and it seems that in our model, energy

is conserved. Interesting. I have a slew of questions that I'll get to more of them at some point. now and it seems that in our model energy is conserved. Hmm, interesting. I have a slew of questions that I'll get to more of them at some point. We should get to the dynamics of space-time. Yeah, okay, fine. Maybe we should come back to your question. How do you get the Einstein equations, for example?

I mean, what I explained already is that we get Minkowski space as a minimizer of the causal action principle. So this means we can describe a non-interacting space-time. Of course this is boring, but this is kind of an important starting point because now we can put in a dynamics to the system so we can for example introduce electromagnetic fields, introduce additional particles, anti-particles, gravitational fields and so on. So we can consider any space-time no matter it doesn't need to satisfy the usual physical equations. We can just take our space-time and add additional stuff. And then we can ask the question does this new space-time still satisfy

the Euler-Lagrange equations or not? And the answer is in general not. I mean, if you start perturbing the system, the equations will be violated. But then it turns out that if you consider specific perturbations, then the Euler-Lagrange equations are again satisfied. So in other words, these are the perturbations which are allowed physically. And then it turns out that in certain limiting cases you see for example if you

introduce particles, antiparticles and a Maxwell field then the Euler Lagrange equations of the causal action will be satisfied if and only if the coupled Einstein Dirac equations are satisfied. No, not Dirac, sorry, Dirac Maxwell, of course. So if like the electromagnetic field satisfies the Maxwell equations and if the electrons satisfy the Dirac equation. So in other words, you get the dynamics of the usual physical dynamics back. Hmm. So this is why, I mean, this is how, this is what we call the continuum limit. So on this continuum limit, one gets back the physical equations on the level of classical interaction.

So we have a classical electromagnetic field coupled to the system of electrons. And with gravity, it works similarly. So we also get then the coupled Einstein, now really Einstein-Iraq equations, if we introduce a metric and then ask the question for which metrics are the Euler-Lagrange equations of the causal action satisfied. Okay.

So if you can get the Einstein field equations from this approach, and also space-time itself is just via this emergent web of correlations. I don't even know if we want to use the word emergent, but you get the idea. I imagine that these are fighting words at a general relativity conference. So what is the technical pushback you receive when you present this to relativists? Yeah, okay, good question. back you receive when you present this to relativists? Yeah, okay.

Good question. I mean, with relativists, in fact, I don't, I mean, they don't object to what I'm doing. I mean, typically like relativists, they are interested in class, I mean, I'm talking about, let's say, classical relativists. I mean, I know them quite well because I also worked on classical relativity for quite some time. I mean, the classical relativists, the starting point typically is the Einstein equations. So we write down the Einstein equation, we have some meta distribution and now we want to find solutions, we want to analyze solutions, analyze the dynamics and so on.

And then this is a problem mainly of solving PDE. So it's like a partial differential equation problem. And many people are mathematicians like me. I mean, they delve into the analysis of these equations. And, but they often don't really care where the equations come from. I mean, it's just where this Einstein formulated the Einstein-Fied equation, and I want to analyze those equations. Right, right.

So therefore, I mean, I have good contacts with many of these people and I know them quite well, but typically when I then start talking about causal firmament system, then they say, okay, fine. I mean, if you are interested in that and go ahead, but I mean, I'm more conservative. I just want to stick to the equations I'm familiar with, and I just want to work on the Einstein field equations. So this is my typical reaction I see from this community. And of course, I mean, I understand this well.

I mean, for me, one reason why I moved away from this kind of analysis of PDEs is that I'm really interested in doing new physics. I want to do something which has the potential of going beyond the standard physical theories. And of course, this is what I pursued this causal fermen system approach. And then there are other people to address. I mean, for example, I could talk to quantum gravity people. And I mean, they are of course more interested in whatever the what is the quantum nature of space time or with these causal set people, what is the structure of space on some small scales and so on. But this is a somewhat different community. These are more like physicists working on gravity.

Well, in the meantime, also have quite good relations with them. I mean, for example, I mean, we have a guy quite, from my perspective, big conference here in Regensburg. So with about like 80 to 100 people. And also this year in October. And there will be people from different communities, I mean, from quantum gravity, from the dynamical triangulations, from also geometers and people who do quantum information and so on. I mean, the goal is, of course, to see where the connections are. Do we have similar interests? Are there methods which apply to different approaches and so on? So my goal would really be to bring these different communities closer together. And also in a way where some, as I said, I mean, I have

nothing against competition and also, I mean, I have nothing against competition. And also, I mean, there should be different competing theories and we should be able to compare them. So I'm not saying that I want to bring people together and we are all our best friends. I mean, this is also maybe not the goal. The goal is more that people talk to each other and that they say, well, you argue productively here and the other one is better there. And then in this way, everything evolves in a way where hopefully or eventually, I mean, some progress takes place, right? And often the problem is that these, there are different communities and they, but there is often not too much interaction.

In particular between mathematicians and physicists, because they speak somewhat different languages. Other mathematicians say, I have already interesting problems to work on. Why should I be interested in other problems and so on? And so therefore, I think what one should try is to overcome this so that really people who don't know each other yet, that they sit together, discuss problems and hopefully then come up with interesting new ideas and new concepts. In any case, I mean, this is the motivation for our conference in October. Let's see how it will work.

So there are different fields in fundamental physics and they don't interact, they're the free fields. Well, of course, maybe I mean, I'm maybe oversimplifying. I mean, also, I mean, in physics, there are many different communities. So what I'm saying is just, of course, the people I know is already a small subset of people. And I was just making a joke. Okay.

So speaking of fields, by the way, you've collaborated with Xing Tong Yao. So Yao for people who have heard that name, but they're not quite sure where they're in string theory are Calabi Yao manifold. And it just has that name because there was a conjecture which was proved by Yao from Calabi. So you've collaborated with Yao directly. Yes. Has he ever pulled you aside and talked to you about this saying this is your ideas are insane or they're genius or they're foolish? Yeah, of course. Yeah, sure. Of course I talked with him. I mean, I was his post-doc, I should say.

I mean, like after getting my PhD, I was thinking of where should I, I wanted to go abroad, where should I go? And then my master advisor, diploma advisor. And then I was very happy and lucky to be a postdoc there. And back then, so this was from 96 to 98, I mean, this causal firm system approach was still in a very early stage. And I mentioned this a little bit, but just on the side. And I, back then, I thought what I should do also in order to have a career, to have a chance and to stay in science, I should establish myself in mathematics. And of course, being in Xing Tung Xiao's group was the ideal, I mean, environment for doing that. So this means I basically also put this caudal ferment system aside and I worked on problems

which Xing Tung Yao gave me. So this was more like PDEs, hyperbolic PDEs. And I also started working together with Joel Smoller from the University of Michigan back then. And so this means when I was a postdoc, I talked with Yao a lot also about string theory. I mean, already back then I told him that I was critical of string theory. Of course he disagreed. I mean, he always had the opinion. I mean, of course he said there's interesting math going on in string theory.

Right. No doubt about that. And of course, like Xing T. Right. No doubt about that. And of course, like Xing Tung Yao was heavily involved in that. And then he said, well, whether this is physics or not, this is a different questions, which I am not the person to tell, so to speak, but of course he was also proud that the physicists were using his concept and his Calabi-Yau manifolds and so on.

So this was when I was a postdoc. And then I kept visiting Yau quite often, regularly at the beginning and then no longer so often because I didn't travel so much anymore due to family obligations and so on. And then I visited him again for a longer period, 10 years ago, nine, nine and 10 years ago. So I was at Tabart for two months. And then I also gave talks in his seminar. I mean, he has a student seminar with all his graduate students and also a few post-hours, quite many people.

And I gave a series of talks there. And then, of course, I also asked Yao on his opinion and he liked it. I mean, he didn't have any direct objections. And well, but also at the same time, I felt that he was also not fully convinced, let's put it like that. But also that's maybe not nothing I could expect. I can't expect him to say, well, I worked on string theory for many years, but now I work on causal ferment systems. This is nothing I could have expected.

Of course. So therefore, I got positive feedback by him and also was encouraged to proceed with that. And also concerning publication of papers, for example, I mean, Yao is also editor of many journals and he was also quite supportive of this approach. Although, as I said, it's not his approach. And strictly speaking, it's maybe a bit of competition to string theory and what he's working on, but he doesn't see it like that. And also he's not, well, some way he generally speaking, he's a very, first of all, very

knowledgeable of course, but also very open-minded person. So, I mean, as long as, I mean, so this was very positive. Oh, great. But as I said, I mean, he didn't really fully support it. I think he's still a bit skeptical of the approach, which is fine. personal reflections, you'll find it all on my sub stack. 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 pilgrimrs. 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, hit subscribe, and let's keep pushing the boundaries of knowledge together. Thank you 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 C-U-R-T-J-A-I-M-U-N-G-A-L.org, curtjymongle.org. Now your approach also doesn't have supersymmetry, correct? Yes. Now that's also fighting words for quantum gravity conferences. Yes, I mean, that's somehow the reason is that, I mean, supersymmetry is like a symmetry between fermions and bosons. So, I mean, like fermionic matter, this is electrons, quarks, I mean, all the matter

is made of fermions and bosons describe the interactions between fermions, so like whatever photons, quarks and so on. You know, supersymmetry is a symmetry which transforms fermions into bosons and vice versa. And this concept does not fit into the causal fermion system picture, because this is why it's called causal fermion system. So to me, the basic constituents of which make up space-time and give the space-time structure are the fermions or the fermionic wave functions, whereas the bosons just come up as an effective description of the interactions of all these fermions. So to me there's really a fundamental difference between a fermion of a boson and this is why this doesn't fit together, doesn't fit to supersymmetry. Good, I mean somehow concerning experiments it seems that,

I mean I'm not an expert on experiments, but from what I heard it seems that supersymmetry has pretty much been ruled out. So therefore somehow I'm on the... So this is of course good for causal ferment systems, so to speak, but I mean, I don't want to... Whatever. As I said, I'm also not so familiar with the experimental... With the status of experiments. Suppose that at some point supersymmetric partners of particles were found, then this would mean that this causal experiment system approach would have to be modified considerably. Right. I wouldn't say that supersymmetry has been ruled out by experiments. I would just say that we now have experimental bounds on the masses.

Yeah, okay, sure. So let's put it like that. So far no supersymmetric partners have been found. So tell me about the Dirac sea. Okay, so this is a, I didn't mention this yet, but somehow in the discussion already it was kind of in the background, so to speak. So if I describe the Minkowski space, so just a vacuum as a causal fermion system, the way this is done is that one considers a family of wave function, namely those which describe the Dirac sea. Now, what is the Dirac sea? So I mean, the Dirac equation formulated by Dirac has solutions of positive and of negative

energy. And of course this was noticed right away by Dirac and then people asked the question what should wave function of negative energy be? This doesn't make physical sense. And then Dirac came up with a solution, which he called Dirac C. And his proposal is that in the vacuum, all these negative energy solutions are filled. So this means they are all filled by, I mean, this is all in the one particle description, I should say.

I mean, you have this kind of a family of one particle wave function and all the negative energy states are occupied. And if all these negative energy states are occupied, this means, like in view of this Pauli exclusion principle, if you bring in additional particles, they can no longer occupy these negative energy states. They are already, everything is filled already. So therefore these additional states have to occupy positive energy states. These are then the electrons.

So this electron has positive energy. And then what you can also do, you can take one of the states of negative energy and bring it to a state of positive energy. And in this way, then you get an electron, a state of positive energy. And it is also a hole in this sea. And a hole in the sea is just, you have to change the sign of everything. It's a bit like an air bubble if you are under the water. So this hole in the sea then has positive energy because it's in a hole. It's a hole in a sea of negative energy.

So it appears as something which has positive energy and it has the opposite charge. And this is then the positron. So the positron also has positive energy, but it has the opposite charge as the electron. So this is the idea, the picture of Dirac, which on one side was very successful because it predicted antimatter, which was also found shortly after. But on the other hand, it was criticized by physicists and also by mathematicians because it was, didn't seem a well-defined concept. If you really take it seriously, this means that if you're just in the empty

space, there are many, many wave functions or many, many particles flying around which all have negative energy. Well, even worse than many, it's uncountably many. Exactly, infinitely many. So therefore, if you compute, for example, what is the energy density of this Dirac sea, it is infinite, infinite and negative. And the charge density is also infinite. So therefore, you get infinities right away.

Okay, so why is Felix, like many people are bringing something back, like blue jeans are coming back. Why is Felix bringing the diraxi back? Yes, I mean, first of all, I mean, this also comes back to how all this started. I mean, also already when I was a young student, I somehow liked this idea of this Dirac sea because it naturally explained why particles and anti-particles are there. And this is something you can observe. So, I mean, and then in the standard quantum theory lectures, I mean, you do some

mathematical constructions and then essentially the Dirac sea is gone, which is not what I wanted to do. I mean, my idea was really maybe we should take this picture by Dirac seriously, so there really is this sea of infinitely many particles flying around in the vacuum. But then of course if you want to take it seriously then you have also to address the criticism. So you have to say, well, how do you deal with this infinite energy density and this infinite charge density? And then so my naive idea was, well, maybe one should simply formulate different equations which do not have this problem.

In other words, just writing down these Maxwell equations and on the right side you put the charge density is maybe too naive because this charge density is infinite. And the same with the Einstein equation, just taking the Einstein tensor is, and then you put the energy momentum tensor of the whole Dirac sea, this makes no sense. Right. So this is why the idea very early on is that this was in the 1980, 1988 or something like that. Not quite 19, say 1990.

Sure. So the idea was then to formulate different equations which do not suffer from this problem. This is exactly what led to the cause-lection principle in the end. This is designed in such a way that this diraxy drops out. This means this naively computed infinite energy density no longer appears in the equation. This is something which is just gone. The same with the infinite charge This means this infinite, naively computed infinite energy density no longer appears in the equation. This is something which is just gone. And the same with the infinite charge density.

So therefore, in this way, I could kind of revive this original Dirac's picture without running into the usual problems. In semi-classical gravity, there's a problem with an infinite negative energy. I don't understand. If you're recovering GR, I imagine you're going to use a semi-classical equation at some point. So where's this infinite energy going in the equations? Yeah, I mean, I do get this semi-classical Einstein equations, but I do not simply take

this naive energy momentum tensor. So instead what I do is, I mean, I say this if I'm in the vacuum, so then I have this Dirac's, but this is a minimizer of the Causs-Lexon principle. So the Euler-Lagrange equations are satisfied. In other words, I have the Einstein equation with zero right side. And then if I introduce additional particles, so I produce holes in the Dirac sea, these deviations from this Dirac sea configuration, this is the only thing that comes up in the equations. So therefore I get kind of the energy momentum, the kind of semi-classical energy momentum tensor, but only for the deviation from the Dirac's. In other words, the Dirac's is kind of the optimal configuration, the ideal meta configuration, so to speak, which you don't see in the equations.

And only the deviations of that, kind of the fact that you don't have a perfect fermionic configuration, this is what comes up as meta sources in the equations. Tell me why octonions come out of your vacuum structure. So I was watching your OSMU lecture, which I'll place on screen, and you mentioned Tejinder Singh. So Tejinder deserves plenty of credit because there are fascinating lectures in that whole series. I think it was like a year long. Coalfury is there as well. So, I want you to tell us what are Octonions, why did they come out?

Are they forced? Why not the next one, which is the Sedions or the Sed-Sedenions? I always mispronounce that. Right, right. Or the split Octonions or what have you. And does this connect to Cole Fury's work? So there are a variety of questions there. Yeah, sure.

I mean, this is in fact, I got involved in this or interested in this fairly recently. I mean, so Tejinder Singh visited me in Regensburg when was it? I think three years ago in summer. And then we started discussing and then he got me interested in octonions. Of course he has his own octonionic standard model theory. And we discussed and I wanted to try to, we try to kind of match things together to see to try to, we try to kind of match things together to see how the structures in his approach in causal firmament system fit together. Yes.

And we noticed that to some extent this works. And, but I mean, there are still many things unclear or to be studied further, let's put it like that. So maybe the basic starting point is, and this is if you would now want to really describe the whole standard model as a call with the causal ferment system. So you want to have, you need to want to have new genomes, quarks, you want to have all the gauge interactions of the standard model, then the starting point for the causal ferment system is always you have to say what is the, how does the vacuum state look like? And the vacuum state that looks is formed of such dirac seas as we just discussed, but

now you have to take many of them, namely one for each type of particle. And then in the end, what this leads to is you have to take seven identical copies of diraxes, in fact of what we call sectors. Each sector contains three diraxes to account for the three generations of elementary particles. So we take seven of such sectors, which are identical. And then there's an eight one, which is different. This is the one which describes quarks. And it's different because there's a, we have to assume that there's a left-right asymmetry. So the chiral symmetry is broken in this sector. Good. And then we have like these eight sectors in total. And then the

starting point with this is if you want to get a connection to octonions then the octonions also can be represented by eight cross eight matrices. So they act naturally on these eight sectors. And then the question is well why eight? And do these algebraic structures of the octonians really reflect certain properties of the causal action and the causal lagrangian and so on? And so this is something we discussed quite in detail. And then in the meantime, well, I also visited the Jinda once together with Jose Isidro in Valencia. And then they also came here last year in summer.

I should say they will also be in October at this conference, which I mentioned earlier. So we want to discuss all this further. And the general goal is to understand, at least I mean from my my perspective to understand how all these algebraic structures like octonions and also, I mean, there are other like exceptional Jordan algebras and other algebraic structures. How they, first of all, how do they come into play if you describe these causal fermions systems? And in particular, how do they connect to the

structure of the causal lagrangian and the causal action principle. Did I hear you say chirality, that you have an explanation for chirality? Well maybe explanation is not the right word, I would say. I mean, let's say, I mean, we, so we, to describe the vacuum, we work with the direct particles in order to build up these diraxes. And the direct particle always has a left and the right-handed component. So therefore there is a chirality there already. And now we need to assume this is really an input. I mean, there's no explanation for that right now that this neutrino sector breaks the chiral symmetry.

But we don't have to be very specific. For example, one possibility is that one of the three neutrino generations appears only as a left-handed particle. There's no right-handed counterpart, but there are other possibilities as well. So we don't need to be very specific, but there needs, there must be some left-right asymmetry. And only if this is imposed, then we get the correct gauge groups of the standard model and the correct couplings and the mixing matrices and all of that.

So you get mass differences between the neutrinos? Because in order for there to be neutrino oscillations, you require mass differences, no? Yeah, okay, yeah, exactly. So I mean, the precise statement is that at least one of the neutrino generations must be massive, so they can't all be massless, and that there should be a left-right asymmetry. So this is all we need. And also like a massive node, massive neutrinos are also needed in order to get so that the

vacuum is a minimizer of the causal action. I mean, this is what I said at the beginning. I mean, we have this, this vacuum state should always be a solution of the physical equations. And if you just work only with massless neutrinos, this doesn't work. So somehow it's necessary that at least one of the neutrinos is massive. But as I said, I mean, we don't get, I mean, let's put it like that. I mean, if we suppose we do not put in a chiral asymmetry, then we get different gauge groups, different couplings and everything changes. I see.

So in other words, the statement is like, if you want to have the interactions of the standard model, then in the nogino sector, there must necessarily be a left-right asymmetry. Interesting. So you don't derive chirality. You have to assume it. Once you assume it, you get the standard model gauge group? Yes. So some of chirality is built into the vacuum, how our vacuum looks like.

I mean, as I said, as soon as you work with the rock spinners, I mean, there's this left and right components, you can write it as a pair of wild spinners and you have chirality right away. Now there's many different tributaries that we can go down. So one of them is about baryogenesis, which is just this large unsolved problem in cosmology. Why are we here? Why aren't we just a sea of photons or something else?

So please explain what baryogenesis is and what is the mechanism from which it emerges in your theory? Okay, I'm happy that you ask that. Well, I mean, first of all, baryogenesis in general, the question is, why is there more matter than antimatter? I mean, if you look out in the stars, I mean, they are all formed of matter. I mean, you can produce antimatter in the lab and also some cosmic radiation, there's also some antimatter there, but still

there's a large abundance of matter compared to antimatter. And the question is, how does this, why? What is the reason for that? And most physicists believe that right after the question is, how does this, why, what is the reason for that? And most physicists believe that right after the Big Bang, there was a symmetry between matter and time matter. In other words, in my picture, I mean, you had this completely filled Dirac seas, so you have neither matter nor anti-matter. And then the Dirac equation explains pair creation. I mean, as I indicated earlier, you take out a state from the sea and you bring it into a state of positive energy. This

creates pairs, but there is no way you could create matter without creating antimatter. So then the question is why, how did this matter-antimasymmetry, how does this come up? So did this emerge, I mean, was this created dynamically? This is what most people believe in. And then how? And as I said, the Dirac equation by itself cannot explain that. Well, and then our mechanism, I mean, there are explanations which work, use quantum feed theory concepts. And so I would say there are already possible explanations for bariogenesis, but there is no consensus on what the correct mechanism should be. And causal ferment system now gives a different proposal for bariogenesis. And the idea is, at least on a non-technical level, I mean, it's quite simple.

I mean, as I said, I mean, we take this d-RUXY picture seriously. So this means at the beginning, we have, suppose we have a completely filled Dirac's. Now the system evolves. I'm really thinking of evolving starting from the big bang. So right after the big bang, you have this completely filled Dirac's. Now the system evolves in time and then there's inflation and structure formation. I mean, many different things happen. And the ideas as a consequence of that, at a later point, you need fewer states to form

the Dirac sea. And then there are states left over, so to speak, and they then occupy positive energy solutions and this is the matter we observe. So this is the whatever simple intuitive idea behind this. Now if you want to describe this more concretely, then one has to derive corrections to the Dirac equation. I mean, as I said, I mentioned earlier, the Dirac equation allows for pair creation, but it does not allow for the creation of particles without antiparticles. So therefore we have to go beyond the Dirac equation.

And this is something we can do because we have this causal action principle and the corresponding Lagrange equations. So what we do is that we derive corrections to the Dirac equation coming from this Corlection principle. And then these corrections, they allow for bariogenesis and this is then what we analyze. And this is, I realized I started this with Claudio Paganini, I went to this postdoc of mine, who I mentioned earlier. In fact, he had the idea. I mean, we had here summer school, when was it? 2018, I think. Yes, I mean, and then he was one of the participants of the summer school. And after the summer school, he told me, well, have you thought about bariogenesis? And then this is how we started thinking about that. And so, and more recently, I also worked this out together with a graduate student of mine, so Marco

van den Belcerano. So this means we worked this out also on a technical level. So mathematically, it's kind of clear what, how to, how this mechanism works. And there is something called the Sakharov conditions. I'm unsure. Are you accepting the Sakharov conditions? Yeah, because it requires a C and a CP violation. I don't know where the CP violation would enter in your formalism. Yeah, this is also something we, yeah, good question.

I mean, this is also something we analyzed in our paper. And it seems that our mechanism is compatible with this Sakharov criteria. Uh-huh. So the next step for us is to work this out more quantitatively. So, and what we need is, I mean, what is, how did, how was the metric in the early universe, for example, and then once we have the metric, the early universe, for example? And then once we have the metric, depending on time, then we can compute, at least in

principle, I mean the rate of bariogenesis. So this is something I would like to do in the near future. So I talked with a few physicists already. And well, it's not quite so easy, first of all, to find a common language. And also, well, in cosmology, there are many unknowns, right? Who knows how the metric looked like right after the Big Bang? I mean, this is nothing we can observe directly. So this is why there are, of course, there are models, but they are quite sophisticated,

they involve many parameters. And this is why we are still trying to get into this. Of course, there are models, but they are quite sophisticated, they involve many parameters. This is why we are still trying to get into this. Hopefully, we can really compute how big is our bariogenesis rate and does it match up with observations? How does it relate to other bariogenesis mechanisms and so on. Now your causal action has only a single parameter that's free, the kappa parameter. Is this supposed to somehow give rise to the 25 or so different parameters in the standard model as well as this bariogenesis factor?

Or does that come from the configuration of the Dirac C? Like is it somewhere else? Yeah, okay, they are good, good question. I mean, of course, of course, I mean, you're right. I mean, on the fundamental level in this course selection, there is just one parameter kappa because all the others who can kind of scale away. I mean, there's just one scale-free parameter and this parameter kind of tells you about, it's related to kind of the ratio of the Planck length to

the Compton length. I mean, this is a very small dimensionless parameter and this parameter is determined by kappa and vice versa. Good. And then of course, if you have one parameter, you would say, well, great. This means I just have one parameter. I can compute all the other parameters on physics. Unfortunately, this is not how it is, at least not at the moment, because, well, we have to model the vacuum configuration.

So we have to say, what is, how does the vacuum configuration looks like? And then we have to say, well, there are different diraxies and then three parameters come into play. First of all, each diraxy comes with a mass. So then you have like three masses and we have the three neutrino masses as additional free parameters. And then there are, at least at the moment, parameters which come from the fact that we need to regularize the system. I mean this is also something I should maybe I should have mentioned. I mean this caudal-ferment system approach.

The idea is that, well first of all we have the our space-time continuum description. This is something which should not hold on all length scales. If you suppose you zoomed into tiny length, at some point you see that space-time is discrete, for example. So there's a certain minimal length scale which comes into play, which you can think of as the Planck length. And then this is typically put in by regularizing the system. So you smear out all the objects on a certain length scale, which we call epsilon, and which you can think of as the Planck length.

And then only this regularized object are the physical objects. And of course, we don't know how space-time looks like on the Planck scale. So therefore this regularization procedure also involves a number of free parameters. And in fact at the moment quite many. I mean simply because we don't really we don't know how space time looks like on the Planck scale. This is the basic shortcoming here. So therefore then we have to describe this effectively and in a way, which again involves a number of three parameters. So Felix, I have to ask what's left then, because you have the standard

model gauge group, which comes out. You have no necessary supersymmetry. In fact, it would be detrimental to your model, maybe even fatally. So you have a potential measurement problem solution. You have chirality, three generations, which we didn't get to, but we can save that for another time. And you have a single parameter, which it's not quite correct to just say there's only a single modifiable parameter in your.

There is an action, but not in your whole theory. But anyhow, so what's left in matter, anti-matter symmetry? Like if it solves all of these issues, then why aren't more people taking it seriously? Well, I hope I agree with you that more people should take it seriously. No, no, so I think this comes if time evolves. I mean, it simply takes time for people to recognize the approach and also to catch up and also understand. I mean, this is all the mathematics is not so easy.

So this is nothing you can, I mean, you have to learn it first. It takes time to do that and so on. But overall, I'm optimistic. And I should say, I mean, there's two, from my point of view, there's a lot to be done. I mean, what we have right now is that just we see it, as I said, it's a, to me, it's a promising candidate for unified theory, say theory of everything, as you would probably say, in the sense that you get, in the limiting cases, you get the known physical theories back. And this is already, I mean, this took a lot of time to work out. And as I said, this was the criticism right at the beginning.

When I was a young student and I talked to physics professors, they told me, well, before you come talk to me, I mean, you should really reproduce all the known physical results. And when I can say that now more than 30 years later, I'm in a position where I could really talk to this. So why don't you? Well, I guess they are no longer around. I guess they are all retired by now. But I mean, of course, in a more general sense, I mean, I think now is really the time to talk to the physics community again. And the goal is really to address, but to go beyond the well-established theories and to see if we can get, can do more, get any, of course, ideally

get predictions, is there something we can explain and there are first steps already. I mean, we have this like a collapse mechanism, we have this bariogenesis, but there are many more things we would like to do. So therefore to me this is just the starting point. And of course, yeah, I mean, and one thing I think which is missing, the first question is for me, if you ask me what I should spend my time on. I think what I should do is try to develop the mathematical setting further to a point where it is easier to use for other people. So in other words, I should develop it to a point where I can say, look, I mean, similar to Feynman rules I mean they are this is how to compute things and then people can just say okay I take these rules and

then I can compute things and see if I get reasonable but this is not so easy I mean right now the mathematics I think this is also partly why people are a bit hesitant to to work on this it's that the mathematics is rather involved. And of course, for mathematicians like me, maybe this is not so much for the problem, but I mean, for a typical physicist who doesn't have this kind of deep or long mathematical training, it is not so easy to compute things. And I think this is some, this is where I should really try to improve the situation by simplifying things. And I see, in fact, I'm doing this already. For example, I mean, one of our PhD students, I mean, Patrick Fisher, I mean, he's working on us on a framework where you

can really do these computations more systematically. You do not only get the field equations as I did already, but you can also compute corrections systematically. And then hopefully these are then corrections which could be measured and so on. So I mean, to me, there's a lot to be done. I mean, first of all, me personally, in any case, but also I mean, for physics, for physicists who want to work in this area, I think there are many interesting problems around. And also, I think now is the time where one can really tackle things. I mean, let's say 20 years ago, there were too many open questions, the concepts were not yet clear enough.

In other words, it was not clear what to do. But in the meantime, since the mathematical setup is worked out, one can restart and look at specific problems phenomena and work them out one by one. Are there any problems that you think are actually not problems in physics? So for instance, the strong CP problem in your model, you think it doesn't arise or the hierarchy problem. I'm not sure. I mean, good question. I mean, I also don't want to make any bold claims here. So maybe I would. Well, I can give you an example, a quite elementary example.

So a problem in physics could be why don't we observe supersymmetry at the LHC or what have you. Okay, but in your theory, that wouldn't even be a problem because it doesn't assume supersymmetry to begin with. So that's like an elementary case. So what I'm asking is there are a list of problems like 100 problems in physics that there's somewhat of a consensus on. What I want to know is are there any of these problems that are considered fundamental that you think they're not even problems? Not that you've solved it, it's just that this isn't even a problem. We put it here and we think it's a problem, but it's not.

Yeah, okay. I mean, it depends always. I think it's not that the problem simply disappears, but I mean, you could say that maybe some problems are no longer fundamental problems. I mean, for example, if you think of all these divergences in quantum field theory, these divergences disappear once you regularize the system. And in the causal fermet system approach, there is a way that you can formulate the equations kind of intrinsically in the regularized setting. So therefore you can take the point of view where the regularized objects, these are really the physical objects and in this way there are no divergences anymore. So therefore on the fundamental level these divergences don't cause any problems anymore.

On the other hand, if you now really want to compute things, and then this whole renormalization procedure is still of importance. In other words, the fact that the Planck scale is much smaller than the length scale of typical physics is something you still need to take into account in your computations. So therefore, even if you think there is a fundamental length scale epsilon and we know how to describe this mathematically and so on, it is still a valid point or interesting question or also a difficult problem to understand what happens if in my, say, perturbative description, if I let epsilon go to zero. So therefore this issue of renormalization is not resolved. But these divergences are no longer fundamental problem.

I see. You see, I mean, of course, this is not nothing, say, a hardcore physicist, nothing I can, I know that I can't convince a hardcore physicist by that because he will say, well, in the end you do the same computation as we do, you haven't solved anything. And I agree with that point of view. But conceptually there's a difference because you don't need to worry about these infinities anymore because you say, well, I know that for very small scales, space-time has a, say,

discrete structure or granular structure. And I know how the equations look like there intrinsically without referring to space-time continuum anymore. So therefore this is a conceptual step forward, which also solves the underlying problem to some extent. This year, 2025 does seem to be a breakout year for your theory, because it was covered by Sabine Haassenfelder recently, so there's a plethora of attention now. And then there was the Tejinder, which was last year, the Osmo conference.

And then there's an upcoming conference that you're working on. Well, what I want to know is your wife has followed you working on this theory for decades, for longer than many people's careers. How does she feel watching you as now attention is finally being thrown at you? Well, in fact, I think my wife doesn't really care. I think my wife is no mathematician or physicist. I mean, she has a different profession.

She's like a speech therapist. So this means also that we don't really talk much about math and physics. Same with my wife, actually. Yeah, because I guess otherwise I would always just continue talking about math and physics at home. So I mean, the way, typically when I get home, of course, I tell her, I mean, what happened at work, but nothing specifically math physics oriented. I see. And, and well, I mean, to me also, I think now is the right time to kind of propagate

the approach. So I'm happy also that it's covered by you and by Sabine Hossenfelder and by Shane and other people that we have this conference and so on. Because I think now it's the time where hopefully the approach becomes more popular and also people take it more seriously and hopefully young people start working on this approach. I would be happy if this happened. And also, as I said, where kind of critical discussions take place.

I mean, so taking seriously by other communities doesn't mean that they necessarily like my approach. I mean, I would be happy if someone comes and says, well, there's whatever. I see these problems. How can you tackle them? Or don't you think our approach is better in this respect? I mean, I would be happy to enter this discussion. Yes.

Now, do you feel like causal fermion systems in the beginning wasn't allowed a seat at the table? One, because it was too immature, it wasn't rigorous, it didn't reproduce the standard model or GR or what have you. So that's one reason why it wasn't allowed a seat at the table. Do you think that's a valid criteria? What criteria do you think should allow someone or some theory a seat at the table? Yeah, good question. I think generally speaking, I mean, it would be good if there were more

approaches on the table. And this also means that young people who typically come up with new ideas, they should be given the opportunity to really do what they are interested in without being criticized right from the beginning. I mean, for me, it was quite a hard time. And I was also kind of lucky by going to math and then going back to physics that I made a career despite following my own ideas. Generally speaking, I mean, like if someone has a new ideas are not really, I mean, not welcome in science. In science or in physics or in a particular subset of physics? Let's say in physics. I mean, I don't want to speak in science. In science or in physics or in a particular subset of physics? Let's say in physics.

I mean, I don't want to speak about science. I want to be precise. No, no, sure. Also, I don't want to make too bold claims. I mean, in physics, it is definitely true. Well, in math also, to some extent, I'll just speak. I mean, if you want to make a career in science, what you typically do or the best strategy is that you enter one of the well-established fields and try to establish yourself by working on problems which your teacher gives you and

which other people are interested in. And this way then you are in a community and the community, the people in the community support themselves or support each other and also help each other getting positions and so on. I mean, this is how it is in science, or at least, I mean, in math and physics, and I guess in other fields it will be similar. So in other words, there's a lot of sociology involved. There's a certain community of people who know each other and so on. Now if someone comes with a new idea, he typically doesn't belong to any of these groups

and these groups are typically skeptical. So this means you are basically, there's nobody who supports you. And this is from my point of view, a big problem because it leads to the fact that kind of well-established theories self-propagate, so to speak. I mean, so, I mean, the young people again work on the same problems their teachers work on, at least, I mean, maybe exaggerating a bit. So basically, I mean, there are really new developments. People who have new ideas don't get a chance in the system. And I find this a big problem. And maybe in physics it's a bit more than in math, because as I said, mathematicians are more tolerant. This is also smaller groups, because in mathematicians, well, partly because in mathematics, the topics are even more specialized. So this means that people who understand certain problems are just small groups.

Whereas in physics, there's often like, and there's this string theory community, and then there's the loop community and so on. And if someone doesn't belong to one of these communities, it is very hard. And this is a problem. And I said I was really lucky because I was kind of naive as a young student. I didn't know all that. I just tried to do what I was interested in. And I was lucky that it worked out nevertheless. But I mean, I had quite a hard time and I would hope that young people now would have it easier.

So I'd like to linger on this as I'm terribly interested in the health or the unhealthiness of most fields in science, but in particular of fundamental physics or high energy physics. So what is the reason for this issue? Is it that there's the dominance of certain approaches and that prevents exploration of alternative ideas? Or is it publish or perish culture and it incentivizes incremental changes on toy models as some people claim, or maybe publish or perish is not so much of a problem. What do you attribute this issue to? Well, good question. I mean, if you think this publish and perish attitude is part of the problem. So this means that young people are under pressure to write many papers.

And of course, it is easier to write a paper on a well-established field than if you do something new. And part of the problem is also kind of the sociology of science. And in particular, I mean, I should be careful saying that, but I think this is part of the problem is that kind of the well-established people in science or typically like older people, well, I'm also getting older, maybe I should try not to speak of myself. So in the case of the well-established people, I mean, of course they have been working on a specific set of problems for a long time. And as a consequence, you have a specific mindset.

And maybe it is normal if, if, if you get older, I mean, that, uh, what you are interested in, I mean, you are interested in, you are not as broadly interested when you get older, typically than a, than a young person. person. Well, and then what happens is that the decisions in science, like who gets a position, I mean, who is hired at a university and so on, I mean, the decisions are typically taken by the older generation, of course, because these are the influential people and so on. And often they want that their own work continues, which is also understandable. I mean, if you say suppose there's a problem we have been working on for 20 years and you couldn't solve it. And then you want someone of the new generation to continue working on that. And if someone has a result in this direction, of course, you find this highly interesting. And as a consequence, I mean, what typically happens is that kind of the influential people, they support people who work on related problems.

So therefore, this is what I mean by sociology and also maybe this is natural. I mean, this is how humans are. I mean, that this hierarchical system so that influential scientists decide on the future of science is not working in the ideal way. I'm not claiming that I know how to do it better. I mean, as I said, maybe this is a general problem or this is how humans are, but I see that this is a problem. I do want to delineate here because it's important to me that we don't say that this is a problem

in science as such when it's actually a problem in not even in physics, but a specific subfield in physics, namely high energy physics or what have you, because I don't want people taking away science is broken or academia is full of charlatans or what have you. I want to make this problem extremely clear. I agree. So, I mean, maybe I shouldn't have, what I'm saying here is not on science in general. I mean, there's not much I can say. I mean, I can only tell you what I'm saying is just on say mathematics, where I know the situation quite well. Where as I said, it's a bit better for my impression than what it is in physics. And physics, of course, are also just theoretical physics, high energy physics.

I mean, the topics I'm a bit familiar with and where I know the leading people. Yes. Now is another issue just that physics has become too divorced from experiment? Because even if that's the issue, how do you fix that without blaming either the experimentalists or the theoreticians, but also they don't have the universe to guide them, so you could also blame the universe. Like what is the issue and how does one solve that? Good question.

I mean, well, I think there is a problem that in blood, parts of theoretical physics are no longer connected to experiments anymore, because I mean, this is how it used to be, and this is also how it should be. I mean, if people come up with a new theory, it can be tested and it's right or wrong. And then maybe this theory was not right. And someone else comes up with a new idea, which is again tested. I mean, it's basically like this continuous testing is kind of important. Yes. And if this no longer takes place, then you need some other criteria to decide which theory is good, which direction should be supported, where should the money go and so on. So then you start using other criteria and then it gets a bit problematic.

Because if you could then what do you do instead? I mean, then people say, well, my you use beauty in physics or they use, it's not so clear certain concepts, which people like. And then also a lot of belief comes into play. I believe in strings, I do not believe in strings and so on. And then, and then the whole field gets a bit, from my point of view, a bit weird because it's not so clear what are the criteria anymore by which you decide on, well, in the end, it really decide on who of the young people gets a chance to continue in science and who

does not. Yeah. So part of why I'm trying to be extremely clear is that even if this is a problem with something broader than just a specific subfield of physics, it's not clear to me that that's a unique problem that characterizes just that system, but systems in general. So for instance, if you had a conference, whether it's a scientific conference of mathematical physics or what have you, or sociological or social science or psychology, would you host

someone whose theories you believe are completely flat out wrong? I don't know what I would do. I'm curious what you would do. And the same obviously goes with hiring, but I'm just speaking about a conference for now. Well, it depends. I mean, well, of course we had to ask ourselves this question as well. I mean, like, who do we invite, for example, to our conference in October?

Well, I think one should try to be not prejudiced. I mean, if there's a theory and it has been clearly ruled out by experiments, of course, I wouldn't take it seriously anymore. Apart from that, I would be open. And I would also take as criteria, I mean, do the other theories also take us seriously? I mean, other words, I mean, if there's no point in inviting someone if I know right from the beginning that he doesn't want to talk to us. I mean, I'm exaggerating a bit. I mean, maybe just coming back to your point like with experiments, I think like physics, I mean, one has to really be careful in distinguishing different communities. For example, I mean, also in contact also with experimentalists, for example, what I mentioned to you with this measurement, collapse measurements, for example. And this community there is very open and they

are not dogmatic. So they just say, okay, this is what we measure and can you explain it or not? What are your predictions? What is it what we should measure? In other words, they are really, this is how it should be. So they are not prejudiced. They just want to get input for the experiments. And as I said, I mean, this was a very kind of a good experience. And I guess it is like that in, I think as soon as you are connected to experiments, this is how it is. So, I mean, this problem I mentioned earlier is mainly then in the parts of theoretical physics, which are not connected to experiments. And I should say, I mean, as a mathematician in mathematics, it's different anyhow.

I mean, we don't have experiments, of course, in math. Right. But then there are other criteria, for example, is it mathematically deep? Do we get connections between different mindsets, between different theoretical setups and so on? In other words, there are also kind of not really clear. I mean, of course, it's all a bit subjective, but at least there are kind of common set of criteria, more or less common criteria by which you can judge if this is good mathematics or not. Now a quick technical question, and then I want to get to the last question, which will

be about advice to young people. But prior to that, I forgot to ask you about the graviton. Is there a graviton in your model? Okay, good question. I mean, like what we have right now is, first of all, we get classical gravity. And I should also point out also on the nonlinear level, just because like Sabine Hossenfelder, I mean, she kind of criticized that we only get it on the linearized level, which is not quite true. I mean, so basically what we do is we choose kind of Gaussian coordinates to draw our computations

and then we just do linear computation, this is correct. But since the whole setup is the Fiery-Morphism invariant or compatible with the equivalence principle, it is clear that the equations of gravity which we get must be tensor equations. So in other words, you get the Einstein equations with the Einstein tensor up to corrections. And then these corrections must again be in terms of the curvature tensor, higher order in curvature. So this is what we get on the classical level. Now concerning your the

graviton, I mean you of course you refer now to quantum gravity what happens there and this is I it's not clear I don't have a clear picture here. What we did recently the paper which did recently, the paper which we wrote last year is that we showed that one gets QED, so quantum electrodynamics in a limiting case. So in other words, one really gets second quantized bosonic fields in this causal fermion system set up, and this also comes up naturally. And this procedure works in principle and one has to be careful here. I mean, so in principle one can do similar computations or use similar arguments for the gravitational field. And therefore, I mean, one would guess, well, then what you get is a quantized gravitational field. This is then quantum gravity.

However, I'm very careful with this claim, first of all, because what does it mean in principle? I mean, there are still many things to be done and we want to do this step by step. And once we have done it, then I would say we also get quantum gravity. And then there's the issue that it's not clear what quantum gravity actually is. I mean, it's a non-renormalizable field theory. So therefore, as a quantum field theory, it is not properly defined. So it's not clear what it really is.

Would these extra corrections to the Einstein field equations help or hinder in the renormalization? Well, I think this, you mean this nonlinear terms, I think it's not clear why they should help, let's put it like that. So I think like this problems of quantizing gravity is still there. However, I mean, one should keep in mind we are working in this continuum limit now. There's still, we have the picture behind it. If you go to very small distances, the structure of space-time changes anyhow. And then, and taking this into account, we are in a well-defined setting.

In other words, we have equations which describe gravity even on the Planck scale. So there's no problem with the mathematical equations there. And this is what I would call quantum gravity. But it's not quantum geometry, whatever. I mean, so there are kind of quantum structures on the, on, even on the Planck scale, which are described by the causal action principle. This is what I would call quantum gravity. But you see now the problem or the question is, is this the same as what loop quantum gravity people do? And this is far from obvious because they kind of start from the other side. They start from classical gravity and quantize that.

And you see, I mean, it's to me, it is not so clear what is the right mathematical formulation of quantum gravity. And my personal opinion would be, well, causal, the causal action principle, this is the right description of what quantum gravity is. But then I would have to convince other people of that. And I guess we are not yet there that people agree on my point of view. Right. Okay. Maybe just concerning quantum gravity to me, like the key question is, I mean, there are

also experiments carried out where you want to see quantum gravity effects. And I think this is really the, to me, this is the crucial question. Maybe the question is, suppose you take, you take a system involving many atoms, so which is relatively heavy. So that also the gravitational force plays a role. And then you take an entangled state formed of these, so that was an entangled many-body state, which interacts gravitationally. And then the crucial question is, I mean, is gravity classical or quantum? And this can then be decided. The question is like if gravity is purely classical then decoherence effects come into play and you can't really form a superposition of these states. On the other

hand if gravity is also quantum theory then you can just form superpositions of such kind of mesoscopic quantum systems. And this is something, I mean, I think these experiments are, I mean, they are working on that. I think this hopefully will see results in the next few years, which can really then answer the question, is gravity on the fundamental level classical or quantum? And there my personal opinion would be, I guess it's quantum. But this doesn't really answer the question what quantum theory, what quantum gravity really is, because then you have to be more specific.

What is the mathematical description of all of that? And there, there are many different ideas and approaches. And as I said, I mean, there's no consensus. Professor, when people ask you for advice, like what would you have told yourself when you were younger, if you had access to your brain now, or what have you, does that advice differ depending on if it's a graduate student versus a postdoc or do you have general advice? Well, it's difficult to give advice because I think the situation is not easy for young people. I mean, it wasn't easy for me either.

I think it was also difficult back then. But generally speaking, I mean, if you want to do something new, you have new ideas. It's very, I mean, it takes a lot of time, a lot of persistence to really put them through because you have to basically like, well, it's not that new ideas are appreciated immediately at the beginning. It's really like more an uphill battle where you have to try to convince people of that for a long time until finally you get some recognition. And I should say I'm still in the process of doing that. I mean, of course, situation is much better than 30 years ago, but still, I mean, we are a small community and we have to try to convince

other people of our approach. And of course, trying to convince, there's nothing bad with that. And also I like doing that. But I mean, when I was younger, it was really more, really like a, it was not so easy to survive in the scientific world, so to speak. And therefore, my advice for young people is mixed. I mean, first of all, I mean, the first advice is you should do what you really like to do and what you love to do.

Because in particular, if you think of the fact it's a long struggle, it only makes sense to do that if this is really what you want to do. I mean, you need to be dedicated to it, you need to be willing to invest a lot of time and energy into this. And this only makes sense if you are 100% convinced that this is really what you want to do. And also this is something I also say for example to my master graduate students and so on. Because sometimes there's a tendency, well, I mean, there are some topics that are fashionable, maybe I should better do that because this improves my chances to make a good scientific career. And then my advice is, also my experience is, I mean, if you really want to do that, then definitely then you should go ahead and do whatever big data, AI, whatever is interesting.

It's a big topic right now because this definitely helps for your career. But if you do this just because you think that it improves your chances on the scientific job market, then you should better not do it because then you won't, basically your motivation will go down at some point. As I said, I mean, I don't have a clear advice. I generally speak, I mean, everyone has to find his own way, which is not his or her Sure, so her path, which is not easy. And yes, but I mean, still, but I think what one needs in any case is be more persistent. I see from young people, they often they give up too early. I think they have promising ideas. Then they start to, it's talking to professors and then they get discouraged and then they say, well,

fine, then I simply stop doing that. I do something completely different. And this is of course, this is a pity often because in any case, what my advice for young people is, well, you should really, first of all, try to find out what we want to do and then pursue this with a certain persistent which goes over a certain time, say a few years even, before taking a decision whether you want to continue doing that or not. Professor, thank you so much for spending over two hours with me.

Okay, so thanks Kurt for everything. I hope this was fun. It was fun. It's fine. It's more than fine. And I hope to speak with you again. As I said, thanks a lot for everything Kurt. I'm really happy and grateful that you do that.

Of course. Thank you. Great. Bye bye. Thanks so much. Thank you. Bye bye Kurt. Hi there. Thank you. Bye-bye, Kurt. week, you get brand new episodes ahead of time, you also get bonus written content exclusively

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