Physicist: "It Was Hiding in Plain Sight"

The missing mass that we've defined as the art matter problem isn't missing. It's the rest of the visible universe and it's been hiding in plain sight. It's been there all along. Is the graviton then composite or fundamental? It's neither. It doesn't exist. Man, talk about fighting words. Nature will keep you honest. >> This is the legendary Professor Philip Mannheim, and today I'm excited to bring You his first ever podcast. He's been working on a theory which solves dark matter and quantum gravity simultaneously for literally decades. You start out with the standard theory. It doesn't work

for galaxies, so you invent dark matter. It doesn't work for cosmology. You invent dark energy. It doesn't work for quantum theory, so you invent string theory. I haven't done that. I've just taken the theory and I've solved it. On this channel, I, Kurt Jaungle, interview researchers regarding their theories of reality with rigor and technical depth. Today, what the professor argues is that we've been wrong about dark matter. We also have no big bang in the universe. According to his theory, add further speculations on what collapses the wave function is a particle that we don't see.

It's one of the most startling discoveries in human history. I I I can't describe it any other way. >> Welcome to the story of conformal gravity. Professor, what precisely is Einstein's theory of gravity? Oh, well, I have to give you a somewhat extensive answer to that. Um Einstein in the early 20th century developed what's called the special theory of relativity and he was dealing with a problem and the problem was there was there was Newton's laws of motion and there were the Maxwell equations of electromagnetism and they had different symmetries and What Einstein realized was

there had to be a universal symmetry which we now call Lorent invariance which meant modifying Newton's law and that you can see this very simply. If you take Newton's law, it just says u you you you apply a force, you get an acceleration. Keep on applying the force, the acceleration will get bigger and bigger and bigger and eventually you'll be able to go faster than the speed of light. And so something had to change if you Were not going to be able to go faster than the speed of light. So what he did was he

came up with special relativity and in a sense this just generalized Galileo's object and Newton's first first law of motion that uh there's no force fell for uniform velocity and Einstein made it for uniform covariant velocity and so he finishes up with a theory in which observers can move with arbitrary speeds but uniformly up to the speed of eyes and the physics must be The same. Now missing from that were two things. One was well what the observer is not required to only go at uniform velocity. The observer is allowed to accelerate and there was

another theory of Newton's called Newton's law of gravity which did not obey the relativity principle. So he had he had two problems that he had to solve and it turns out that the solution to those two problems are different even though we usually look at Einstein gravity as a Package and that the first issue was um well suppose you take Newton's second law of motion force is equal to mass times acceleration and you rotate the system then you generate a new term and M was very concerned about that new term and he said, "Well, maybe

it's fixed by an interaction with the distant stars." But what was really happening was that Newton's law of motion as just written by Newton and it starts out force is equal to mass times acceleration, but Then is generalized to special relativity still was not invariant under under an arbitrary change in the coordinates. So if the observer chose to rotate, the physics should not change, but the equation changed. And Einstein found a way of writing down a more general form of Newton's second law of motion so that it would not change when the observer changed um

changed um his speed or or rotated and that one is what we call the geodeic and let me write it State it down m d2x lambda da squ that's the generalization to special relativity of of Newton's law of motion plus gamma lambda mu dx mu d to dx mu new d to equals 0 where gamma lambda mu is the first derivative of the metric. It's called the connection and that equation is a general coordinate vector and so if you make a transformation that equation will transform and will remain zero. Now it has two features. It's

a sum of Two terms. The acceleration the d2x lambda d to squ and the gamma lambda mu new dx mu da to dx new da neither term is separately a general coordinate vector. In other words both of them will transform but the combination of them with the unique weight is plus the connection not plus twice the connection >> the unique weight will remain invariant. And so that answers the question of how do you write Newton's law of motion in An accelerating coordinate system. Now at this stage it's still got nothing to do with gravity and

it's and it's and this is still true in flat space and we do it all the time when we change from cartisian coordinates to polar coordinates that suddenly doesn't make spaceime curved. So this is simply a property of coordinates. But Einstein then discovered something quite remarkable. Two things that are absolutely Remarkable. One is if he could get gravity to come out of the connection term, then because they had the same weight, you would get two forms of the equivalence principle that the inertial mass is equal to the gravitational mass. Namely, it's m times that whole

function d2x lambda da squ plus gamma lambda mu da dx mu da and so on. So that would guarantee you that the m that appears with the acceleration which is called the inertial mass and the m that appears With what's going to be the gravity the connection would be the gravitational mass and they would have to be equal because if they were not equal that's that quantity would not be a general coordinate vector. So it has very unique weights. He also noticed at least I think he did. I don't know if I said so was

that if you take the connection at any given point you can make a coordinate transformation that would make it zero at a point >> at one at any at any given point but it would not be zero at the next point but at any given point you could make it zero. And if that were the gravitational field, then you have shown that it's equivalent to an acceleration at that point. And that was that's what we call the equivalence principle. The equivalence of gravity and acceleration. Now the question is when is it real? If you can

move it away, how how do you know if it's real? And if you read the Relativity textbook of Adler, Bazan and Shifa, they say, well, you might be able to transform so that you have a rotating flywheel, but a rotating flywheel certainly does a lot of damage, >> right? So then the question is when is it real and when is it and when is it just an artifact of making a transformation? And the answer is but you can't change the second derivative. The connection is the first derivative of the metric, but making the change in

The first derivative doesn't change the second derivative. So you can't get rid of that as well. And the second derivative gives you the reman tensor. And so the reman tensor by definition of a tensor, if it's non zero, there is no coordinate transformation that can make it zero. And therefore what Einstein realized was that if gravity was described by the reman tensor then you would have a general coordinate Invariant description of gravity. So from looking at the geodeic alone you learn the metric is the gravitational field. the metric couples in a general coordinate invariant way

and that when the geometry is not flat namely when the reman tensor is non zero then you have an an an effect that we call gravity okay now all of that is intrinsic to Einstein's program and any in my opinion any theory of gravity must contain all of those Ingredients. However, what that does not tell you is what is the gravitational field. You now know that the connection depends on the metric. You know that the remanensor depends on the metric, but you don't know what the reman tensor is. So, you need an equation to fix

the reman tensor. And then you will be able to solve the theory, get the gravitational field, and then you'll be able to determine the Response of a particle to a gravitational field. So that those are the steps you need. So how does Einstein fix an equation that's going to tell him what the metric is? The discovery that the metric is the gravitational field, in my opinion, is one of the most startling discoveries in human history. I mean, I I I can't describe it any other way. I mean I I was used to writing down the

line element dword is at mu dx mu dx mu is is the the s word And he turns at mu which is 1 one one minus one he turns it into gravity I I mean I've known this for many many years and I'm still startled that he was able to do that but it doesn't tell you what the metric is and he then does the following he says well I want to I've now answered Question a namely how do we describe physics in an accelerating coordinate system? But what do I do about Newton's law of

gravity? Well, if you write down Newton's law of gravity, You write down the pluson equation deli equals row and it's a second derivative. And the rement tensor is also a second derivative of um of the metric. So if the metric is the gravitational field, it's very natural to generalize Newton's the pluson equation to an accelerating coordinate system by using what are called the Einstein equations which are based on the Richie tensor and the Richie scaler using the Einstein tensor. So it's it's what you would do if you Wanted to ask the question which is what

I believe Einstein asked. What does Newton's law of gravity namely the um quason's law look like in an accelerating coordinate system? >> Einstein works that through comes up with the Einstein equations and they give him two things. They give him one is Newton's law and they give the v^2 over c^² correction and then that is tested in the perihelion of mercury and in the gravitational bending of light. However, it's phen I hate to say this. It's phenomenology because he starts out with del^ squ= row and works his way up to general relativity. But why would

he choose where did del square fals row come from? Only only from it only from the experience that we previously had of of new newton's law of gravity. So it's not deriving Newton's law of gravity. It's actually finding a generalization of it which would hold in an accelerating Coordinate system and um that was that was the steps those were the steps he took. >> Now just a moment I have a quick question. Okay. So what's wrong with already knowing where you want to end up and then thinking okay I need to make my theory such

that in some appropriate limit I need to end there. That actually sounds like good physics cuz it's like we know this guy works approximately for the majority of cases. Yes, >> we should get there. >> Okay. What I'm saying is it's on a different conceptual footing than the equivalence principle. General coordinate invariance. The metric is the gravitational field. The reman tensor when it's non zero means there is a gravitational field. All of that is generic. the Einstein equations are specific and they're constructed to do a specific Thing which you're absolutely right at that time that

was the specific thing he wanted to do. There's no no question about that. However, we run into a problem and the problem is that people look at the Einstein theory as a package. Namely, they don't distinguish between accelerating observers and gravitational field. And they are different because even if there's no gravity, you can accelerate in the presence of an Electromagnetic field. And in fact, electromagnetic fields cause accelerations. So they all have they all have to work. Um so he picks on the second order equation because that was the one that was there. And when it

works, everybody said the theory of gravity is solved. But what I'm trying to show you is that there was a flaw. not necessarily a super flaw, but there was a step in the reasoning that wasn't as secure as Everything else. Now, what have we done when he does this? We call what he did general relativity, but that's not fair and that's not a fair description because special relativity means invariance under Lorent transformations. It doesn't mean any specific equation of motion. So general relativity should mean invariance under general coordinate invariance with the metric being the gravitational

field. That's what it should mean. It should not mean and the gravitational field obeys the Einstein equations. But because he did the two at once and because it worked, everybody takes the view that that that you have you can't touch anything. Now let me show you immediately where it can go wrong. And the question is where did we get pluson's law from? Well, Newton gives us a 1 / r potential and delt fi is is row. The solution is 1 / r. Well, suppose I gave you del 4i= row. A fourth order derivative equation. The

solution is a 1 / r plus an r. If I give you del 6fi equals row, I get a 1 / r, an r, and an r cubed. In other words, Newton's law of motion 1 / r is not uniquely tied to the second order plus equation. But all those other terms, the ones that grow like r or grow like r cubed, aren't important for the solar system because the solar system was still very Short distance. So those terms could always have been there. And you wouldn't know from looking at the solar system, >> right?

It's when we go to galaxies and we jump up by a factor of a thousand that all of a sudden the question is does Newton's law of gravity continue to hold untouched or is there something else going on which we usually call dark matter? We meet dark matter in the regime where we did not derive the Einstein equations In the first place. Namely, it was geared to the solar system. But what Einstein does by generalizing it to the Einstein equations, it then becomes the Einstein equations on every scale and not just on the solar system.

Now this objection was raised by Edington in about 1920. He pointed out he said look you can get the Einstein equations by varying what's called the Einstein Hilbert action which is just the Richie Scaler. He says well you can also get them from varying the Richie scaler squared but you get these extra terms. So you there was nothing unique about the second order Passon equation and I've been arguing for a long time now that if you want to make the claim that the universe is full to the brim with dark matter you have to find

some fundamental principle that would tell you why you should be using the second Order parson equation and that's the challenge and so that's that that's that's where That's where I think there's a difficulty in the theory. I'm not saying that the universe isn't full of dark matter. I mean, that doesn't follow from what I've said so far. Um, but nonetheless, uh, there is this loophole in the way that Einstein gravity is constructed. So it's it's a theory which tells you um I have a very specific equation of motion And that's the one that you use

and that's the one that gives you Newton's Newton's law. But what I'm arguing is Newton's law was built into it. It it's it's output if you had some other reason to use the to use the Einstein equations. But as long as the way Einstein built it up as far as I can see is it's Newton's law of twasson's law and Newton's law were input. Now can we change the Einstein equations? Well of course everybody but everybody including Einstein changed the Einstein equations by adding on a cosmological constant. So from the very beginning Einstein was saying

well it's the the theory is not unique. I can add on extra terms. The one he added on was the um cosmological constant which has had one of the most checkered histories of anything in physics. But the fact that he was able to do it meant that what he was working with was not unique. >> Right? If it were unique then you either Would be able to add it or not. You would know. But he didn't. He because it because the Einstein equations were not unique that left open the possibility of adding on a constant

lambda which is the cosmological constant that Einstein himself did or adding on the Richie scaler squared which is what Edington did. So there's a lack of uniqueness and if my view is that we have to resolve this lack of uniqueness one way Or the other and that will tell us whether we should be living in a universe with dark matter and dark energy and so on. Okay. Now so that's Einstein gravity. Now at the same time people started to think about the quantum version of Einstein gravity and here the interesting thing is Einstein is responsible

basically for quantum theory and for gravity and yet when you put them together you run into trouble. >> It's it's very ironic. >> So what is called quantum gravity does not mean find me a theory of a a quantum theory of gravity. It's finally a theory of gravity whose low energy limit is is Einstein. I remember the doubt before I launched this podcast. What if no one shows up? Starting anything legitimate and seriously feels like a huge leap. And Shopify is who I trust. It powers millions of businesses from Mattel to Gym Shark to people

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jitter, they're definitely worth a try. New customers get 15% off with the code TOE at takeulttra.com. That's take ultra.com using code TOE and tell them we sent you. >> So it's find me a quantum theory of Einstein gravity but not find me a theory of gravity. And the difference between those two is something like gravity has this set of features. One of them being general coariance. Another One being we're going to get to this richy flatness at say the solar system level. Another one being that you want it to follows geodessics and so forth. And

you could also have that it follows Einstein's equations, but Einstein's equations don't follow from this feature list. That's right. They're they're independent of that list. Yes. Got it. Exactly. That That's very good. So, as far as I can see, there is a lack of uniqueness in the Theory of gravity as it's formulated. And when people talk about quantum gravity, they mean we already know the classical theory of gravity and therefore we will try to find a quantum theory that will have that as its classical limit. Now we've done that with electromagnetism. Electromagnetism is is a

very unusual theory because in the following sense is Maxwell writes Down the Maxwell equations. Maxwell doesn't know anything about relativity but he writes down the Maxwell equations. Einstein comes along introduces special relativity and the Maxwell equations don't change. Then Einstein use introduces general coordinate invariance and the Maxwell equations still don't change and then quantum field theory comes along and the Maxwell equations still don't change. >> Mhm. I mean the most amazing thing is that when people write down quantum electronics they write down the actual action using quantum fields but how can they do that because

I Maxwell didn't derive it for quantum fields the answer is the quantum electronamics theory happens to be reormalizable and therefore the output classical fields which are really matrix elements of the quantum operators will obey the Same equations. So if we wanted to to discover a theory of quantum gravity, we would try to mimic what we we've already successfully done in quantum electronamics and we would look for a theory whose matrix elements, gravitational fields whose matrix elements would behave as the the classical theory that we'd like it to behave as. So we're we're sort of not

doing things the right way. And the reason I say that is historically we started out with classical physics and then got to quantum physics. But we now know that's the wrong way to go. I mean we always say that classical classical physics is the limit h bar goes to zero where h is plag's constant. But h bar never goes to zero. It's what it is. You no there's no mechanism to switch it off. What there is is a way to get interference so that You get you get classical you get classical results but nothing to

do with letting h bar go to zero. So the question that I started to think about was well in order to get a proper quantum theory of gravity we need to know what classical limit we're aiming for. >> Yes. Okay. Whereas have done something completely different. They say we already know the classical limit and we're going to try To work work it through. And well, they haven't they haven't succeeded is the best way to say it. And but I I certainly don't say that they've not invested an incredible amount of thought into it. Let me

see if I got this straight. There's a symmetry which we're going to get to called conformal symmetry which you say and your colleagues that you and your collaborators I mean >> yes >> will solve the issues of dark matter and dark energy twinly as well as QG quantum quantum gravity >> yes >> and that it's not so unnatural so some people may look at that and say it's contrived but you say no no no let's run a thought experiment let's imagine Einstein didn't happen but quantum theory developed and you have Q of QED QCD and

so forth And then you think okay I don't have this classical gravity Doesn't exist in this thought experiment. You have a wish list as I mentioned a feature list of what I want gravity to have features I want gravity to have general coariance etc etc. But you don't have Einstein's field equations. >> Yes. What would be natural to you knowing quantum theory would be to write down a a renormalizable yes field equation set of field equations and something that is Thrown out called the vile curvature in for Einstein is something that you say maybe we

we don't need to throw it out and if we included it >> yes >> then we not only have this conformal symmetry but we have reormalizability we have all the best of scenarios which also happens as a consequence we're not even trying it also explains dark matter and dark energy. >> Yes. >> So, is that roughly correct? >> Yes, it it's roughly correct. And you you had John Donahghue on your your program at one time. John and I have both agreed on the following that if quantum field theory had been developed before Einstein gravity, we

would not have gone to that particular theory. We would have looked for a reormalizable field theory from the very beginning because SU3 cross SU2 cross U1 the strong electromagnetic and weak Interactions are reormalizable theories. So we have to ask why are they reormalizable theories and we already know that Einstein is the Einstein theory is not reormalizable and the huge efforts in loop quantum gravity in string theory and so on have been to try to make it into a consistent quantum theory and that's an a very an extensive and very committed exercise that those people have

done But what I ask is well can I find a reormalizable Theory of gravity? Now what makes quantum electronamics reormalizable? Well the answer is it has a dimensionless coupling constant whereas Einstein gravity is not reormalizable because it has a dimensionful uh coupling constant. Now we've already measured met that with the weak interaction. The for fermy fermy wrote down the for fermy interaction with g fermy that was dimensionful and the Theory was not reormalizable but we discovered we could rewrite it as a gauge theory and so we found in the end that there was a different

formulation of the quantum theory that would get us back to the for fermy interaction at at low momenta momenta much less than the mass of the w or the z bzon so that's suggesting to us that we shouldn't be looking at Einstein gravity as um the way we have been we should only be looking to see what we get at in in a Low energy limit. So that was so the first question was why is quantum electronamics reormalizable and the answer is because it's got a dimensionless coupling constant but I could have given you a

maxual action which would be instead of it being f mu f mu it could have been f mu box f munu where box is the second derivative that's just as good electronamics there's nothing wrong with it it's covariant it obeys special relativity But it's not reormalizable. And the reason it's not reormalizable but by adding in the dell squ you have to add in something else a coupling constant which has a dimension because the whole thing has to have the action still has to have dimension four. So why would we not use del square f mu

newu del squ f mu for for for electromagnetism? And you say it's not reormalizable. And I say well um you have to decide whether Einstein's lack Of reormalizability would also exclude it. If you want to exclude fu new del^ squ f mu new because it's not reormalizable then you should exclude Einstein gravity as well. So you have a conundrum. So instead what I realized was that anything other than f mu squar would not be conformal invariant and conformal invariance and in it simply says it says you take a triangle and you stretch it up then

all the angles remain the same but if you have a Little weight hanging on one of the arms then as you stretch it up that arm will sag and so if you have masses you lose the conformal symmetry. So when Vile introduced this and it was very soon after after Einstein about 1918 or so the problem with it was well things do have mass but we learned much much later in the 1960s with with the development of of Goldstone Bzons that mass can come in the back door. It it can come in through The vacuum.

It's not a property of the operators or the equations of motion. is a property of the states that you calculate the operators in. So it's possible now that we know about spontaneous breakdown it's possible to go back and say well now we can have a universe which has a conformal limit. You see and so if you do that you then explain why quantum electronamics is reormalizable after all. Now when you do it for gravity as as you noticed you're led to fourth order equations of motion the reason being is each the the reman tensor is

two derivatives of the metric reman tensor squar is four derivatives of the metric. The action is integral d4x and therefore the coefficient is is dimensionless. Now you can have global scale invariance which just means you have rich square richy tensor squared and reman tensor Squ or you can have local conformal invariance namely that you do this locally at every given point of the spaceime >> then you're led to a unique action which is the square of the vile tensor and the vile tensor is approximately the traceless piece of the reman tensor and so you could

have this theory which would be based on the vile tensor and it leads up to fourth order equations and I started to think about that that theory Because conformal symmetry would be pointing me in the same direction that it's pointing me in SU3 cross SU2 cross U1. So that would make gravity as close as possible to the standard theory. Um people that I spoke to all told me the same thing and that was that this theory had states of negative norm namely ghost states. It was not unitary. It's not physical and it can't be allowed.

Uh I knew that I didn't quite know what to do about it. But about I'd been Working on something else. I've been working in particle physics. I'm not I'm not a relativist. I'm not an astrophysicist. I'm a train I'm a particle physicist and I did my first posttock in Brussels with Robert Brout and France Anglair and they had they were manybody theorists and their ideas on on what we now call the brow the Anglere Higs mechanism came about because they knew about Anderson's mechanism for for making photons massive In in a superconductor. And at the

same time renormalization group ideas were just coming in to into condensed matter through the work of of Wilson and Kadanov and so on and it was gradually being transcribed into uh into particle physics. And so I had this training in reormalization group and from there from Brussels I I came to the institute for advanced study in Princeton and at that point I asked the following question at the phase transition the whole the whole System is correlated into long range order and that's a scale symmetry you have correlation lengths that extend the full length of the

crystal and that's the scale invariance but the order parameter is zero. the there's no magnetization. The magnetization only comes when you go below the critical point. But at the critical point, which is what the condensed matter people were doing, you had exactly um scale symmetry. So I Started to ask the question, well, could I get scale symmetry as a way of generating masses? Namely, not looking at a system at the critical point, but looking at a a system at t equals z. And I found a dynamical way to do that in which I had a

conformal symmetry that was restored because I was at what's called a fix point namely that the coupling constant obeyed very spee operator and when its dimension And it's typically it is dimensions three cuz It's three halves for each spinner. When it dimension drops to two then the theory becomes so infrared divergent that it spontaneously breaks and you get long range order. And so I had by that point I had understood that there was a way to get mass generation in a theory with no mass scales. Hm. So I then pressed on and I I worked

on Grand Unified theories and so on. And in the late 1980s I got a Uh national um Academy of Sciences National Research Council fellowship to the Godard Space Flight Center in in Maryland branch of NASA in Maryland for for a year. I went there and I started to collaborate with a person called Deeos Kazanist. Now Deeos was an astrophysicist which I was not and he also knew relativity which was very helpful. He had originally been a student of Dave ShraMM at Chicago um Enrico Fermy Institute got a position at NASA and he had actually discovered

inflation before goth. um he had written a paper that if the universe went through a desitter phase then there would be no horizon problem. Now it's very interesting that I mentioned Anglair and browse they at the same time working with Edgar Gunig had also shown that if the universe went through a desitter phase there wouldn't be a horizon problem. Alan Guth's work Came a little bit later, but what he showed was that yes, you also solve the flatness problem, which by the way, dark energy has unsolved, but we'll get back to that a bit later

perhaps. Um, sorry, just a moment. In order to make this more comprehensible to people, they may be confused at what is renormalization exactly. So, can we give a a quick threeminut crash course on reenormalization, reenormalization group, >> okay, >> which is not precisely the same thing. And then also conformal symmetry as distinct from just mere scale invariance. >> Okay. All right. Um reormalization is you're faced with the following issue. You write down a theory, you take the free theory, you quantize it, you get an infinite number of modes because a field is described at every

single point of the spaceime. It's it's not Described on a line. It's all over. And therefore in momentum space that means an infinite number of modes. And then when you start to interact switch on an interaction and you interact then you can excite every one of these modes and that's an that's an that's an infinite effect because you're swimming over an infinite number of modes and that's bad news. However, in a reormalizable theory, you can redefine the parameters that are Already in the lrangeian to make the reormalized charge the reormalized mass in such a way

that you can cancel those infinities. Now, in Einstein gravity that doesn't work. You can cancel the infinity first order, but then it comes back in second order and you you can never catch up because it's not a reormalizable theory. But reormalizable means that the theory can handle its infinite modes that you put into it By quantizing the theory that you that you can do summations over modes in such a way that you can still get finite answers. I subscribe to the economist. Their science and their AI coverage is among the best I found anywhere. And

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and their AI reporting regularly surprises me with how deep it goes. And they're Also of course known for global affairs, both political and economic reporting. They are top tier. And interestingly and flatteringly, TOE is one of the only podcasts that The Economist partners with. So as a listener, you get an exclusive 35% off. That's not a deal that they have just anywhere. Head to economist.com/toe to subscribe. That's economist.com/toe for 35% off. Now, Fineman said it was a dopey procedure and and there's some Ancient views, not ancient, but 100-year-old views from direct and he said that

he didn't he saw it as sweeping infinities under the rug. But it's much more rigorous than that. It's become much more rigorous since the 80s. So, do you also view it as a trick? >> Okay. Um, I I I don't view it as a trick, but if we could get that trick to work for gravity, I think everyone would be happy. Um, I I certainly don't think it was a Trick. Um, DRA actually tried to deal with this infinity problem by introducing an indefinite metric. And I'll I'll come back to that when we talk about

PT symmetry. Perfect. So there actually is a solution to that problem. Um PI picked up on it as well. And in fact that's how PI got to the pi villow regulator which is 1 over k^ 2 - m^ 2us 1 over k^ 2 - m prime^ 2. So it's a difference of two propagators and pi villow is able to do this reormalization While while preserving gauge invariance. >> Right? But then you've got that minus sign which we'll have to deal with and there's a lot of story a whole story in that. >> It's like whack-a-ole.

Like you solve one problem and then some others creep up and you just have to whack them down and something else pops up. >> Okay. With with the best will in the world I would say that dark matter, dark energy, string theory, super symmetry, Extra dimensions, anthropic principle is doing exactly what you just said. >> Okay. So now conformal symmetry means ah okay conformal symmetry it goes like this. you can make uh the Lorent group has six generators, three boosts and three rotations and the prankare group adds in four translations. So that 6 + 4

is 10. You could also make a dilitation which is just a one-time stretching which gets you to 11. But then there's another four transformations you can Make which are called special conformal transformations which involve reciprocals of of the coordinates and those 15 objects close on a group and that group is the conformal group and it's the full symmetry of the ly cone. Right? In other words, you can see why if the light cone says ds^2 is equal to zero, then 25 ds^2 is also equal to zero. So what you finish up with is the light

cone has more symmetry than lorent and pankor. However, standard gravity is based on making local lorren transformations and local um pankorank translations. but not on making the conformal transformations local. That's what Vile does. Uh we'll get back to that. So the so reormalization is a procedure which will work and it's fully legitimate and people have proven Rigorous results about whether a theory is reormalizable or not. Um what I've described for you a moment ago is exactly how SU2 crossu1 got off the ground. It was you replace the germy by the exchange of a gauge bzon.

You made the gauge bzon massive by the angller brow higs mechanism and then you had to show that the radiative corrections the the reormalization loops are under control and they were and that's that's why we Think the theory is correct and it's been tested. So it it it's hard to see why it would be wrong. So that so that's renormalization. Now the next question was well when you do reormalization you have to introduce a scale which is a cutoff because you've got this infinite number of modes and then you introduce what's called a counter term

which depends on the cutff in the opposite way. So it cancels it and a Reormalizable theory says you can get away with a finite number of counter terms and always get rid of this lambda. But the lamb intrinsically breaks the scale because it has a scale. And therefore you had a different question which was well I've got a lander in first order, a lander in second order, a lander all the way out to every order. Can they organize themselves in such a way that that they all cancel each other? And you can see the following.

Let's suppose I have a term that goes like e to the minus lambda. >> Mhm. >> It's 1 minus plus lambda^ 2 / 2 minus lambda cubed over 3 where all those terms have unique coefficients. And if everything works out and all the coefficients come out the way I just described, then that entire sum which looks like it's violently divergent will go like e to the minus lambda and Therefore vanish when lambda goes to infinity. That happens when you have a what's called a reormalization group fix point. Namely, it's it turns out that it controls

all of the radiative corrections. Each one of those terms that lambda lambda square, they're all quantum loops and they're called radiative corrections. They're all controlled in such a way that the sum of them is well behaved and in a in a Crystal at this critical point you ask the following question. You have a you have a high temperature ferroagnet and you lower the temperature. How does it know it's supposed to go into into into a ferroagnetic phase? How does it know it's supposed to produce an order parameter? And that is you need a cooperation of

all of the modes of the theory into what's called long range order. >> Yes. >> So, and what made people like Wilson really excited was that you could get long range order from short-range forces that you did not need long range forces to get long range order. And that's and the best example of that was the icing model. And so you have this long range symmetry which is a conformal symmetry which occurs if you have if you're at a fixed point of the reormalization group. Now there are two options for this fixed point. One is

that it's the physical Coupling constant and that that's an idea that goes back to Galman and low in quantum electronamics and the other is that you go that you asmtote to that value and that's that's Wilson's point Wilson's point was the the zero of what's called the beta function doesn't have to be it doesn't doesn't have to be the physical coupling constant it can be but it it didn't have to be and then People discovered that if this funny beta function which usually goes like This instead went turned down then the theory becomes what's called

asmtotically free and that that was a bombshell that was the the work of of Dave Pollitzer Frank Wilch and David Gross and when they discovered that nonabelian gauge theories were asmtotically free and at the same time Huft and Fel and Velman had shown that nonabelian gates theories were reormalizable which was not known at the time and then Weineberg Salam and Glacia Had been promoting weak interactions based on these nonabelian gauge theories and then everything came in the neutral currents came in the the W and the Z bzons came in and a few years ago the

Higs bzon came in so everything everything comes in and it then looks very much as though um the the fundamental theory of nature at at least for 3 + 2 + 1 is strong electromagnetic and weak is uh reormalizable gauge theories. So at this point and they're all reormalizable because they're conformal invariant except there's one snag in the standard theory and that is that we write down this funny double well potential and the double well potential you can write it as lambda ph 4 minus mu^2 f^ 2 and the minus mu^2 has a scale otherwise

the potential would wouldn't wouldn't go up and come down again. So In the standard theory of introducing the double well potential you break the scale invariance in the lrangeian and there's no scale invariance however what I had been doing in dynamical symmetry breaking with sib replacing the scalar field then there is scale invariance and it's broken in the vacuum so I had a different way of approaching things and as far as I can see conformal symmetry can only be relevant in the Real world under two circumstances. one that we are at a reormalization group fixed

point so that all those lambda lambda squares are all organized themselves and two that there is no fundamental scalar field there's no elementary scalar field that it must be a dynamical bound state and I've written papers saying the diagnostic that we need to identify is can we tell if the higs bzon the 125 5G that we've discovered is it in the Elementary lrangeian or is it a dam dynamical dam state? >> In other words, is the Higs composite? >> Yes. Is it composite? So if it's com if it's elementary and it goes into the fundamental

theory, then you no longer have scaling variance because of the minus mu^2. >> So you need mass to be dynamically generated. Yes. And if the hicks was composite, it would have this dynamical generated mass which would have Conformal invariance. They follow all the they follow together. Yes. Now if the Higs is elementary and it's in the the lrangeian then it's the god particle because it gives mass to everything. If on the other hand it's dynamical then the vacuum is the god vacuum because the vacuum gives mass to everything. And so and what's the what's the

benefit of having a dynamical scalar field? The Benefit is that you no longer have to deal with the hierarchy problem. You see the hierarchy problem says the following that when you calculate the self energy of a scalar field it can emit well we say it couples to the firmians so emits a firmian and absorbs a firmion and that gives a quadratic divergent energy and we have to reormalize it down. Now you could have said, "Oh, but that also happens for photons." But photons has gauge invariance and that protects you And the scalar field doesn't have

any any invariance. And so you've you have no real way of making its mass um come all the way down to 125 GV. There was a mechanism that was specified to do that which is called super symmetry. But we now know from the LHC not having super having found any super particles. We know that even if super symmetry exists, there are no super symmetry particles in the same mass region as as the Higs Bzon that could solve this hierarchy problem. So the failure of the LHC to find super symmetry is actually a serious challenge for

the standard SU3 cross SU2 cross U1 theory. Now scale and variance could be global or local. You could change the scale globally just over the whole system or you could point by point. >> When it's local, it's called conformal symmetry. So that's the background that I was working in on considering conformal symmetry as playing a role in mass generation in elementary particle Physics namely in SU3 cross SU2 cross U1. Um and I showed that if you do that then you get dynamical goldstone bzon uh massless particle and you get a dynamical hig bzon with the

mass and that's I've suggested that that should be um the the true hicks. Now when I got to NASA and I started to collaborate with Deos Kazanis, this was in the 1980s, we started to think about the question Of the cosmological constant. Because when if you think of this double well potential, the difference between the the upper maximum and the lower minimum, that's the energy of the vacuum and that that is the cosmological constant. So when you have spontaneous breakdown, you produce a cosmological constant even if you didn't have one to begin with. In phase

transitions, that just says you get you you release free energy when you make the phase Transition. And so there's this energy that's suddenly appearing. And no matter what theory of gravity you have, we do know that as the universe cools down, it does go through the electroeak phase transition. And that's at least at a TEV and a TEV is 10^ the 15° and so a black body would be t 4 would be 10^ the 60. And so we know that we release a cosmological constant which is at least 60 orders of magnitude bigger than the

data could possibly Support. So that's the cosmological constant problem. And super symmetry had this wonderful idea. You have a contribution from a firmian and contribution from a Bzon. Because of Fermy statistics, the firm loop has an extra minus sign and they cancel. And so super symmetry became extremely fashionable because it could do that. It could it could control the vacuum energy. It could control the Higs energy. It became An ingredient for getting string theory down from 26 dimensions to 10 dimensions. So it becomes the super string theory. And of course, super particles would be an

ideal candidate for dark matter. So it covers an enormous set of issues in particle physics. However, it still needs to be found and that's not happened. So super symmetry has the problem that it only controls the cosmological Constant if the super symmetry is exact. Namely, the mass here and the mass there cancel. >> Mhm. They can't cancel because we know the super particles which we haven't found must be at least a teev in mass and therefore they don't cancel and therefore the broken super symmetry gives you a very big cosmological constant and so super symmetry

which was a good idea in order to control the energy of The vacuum really doesn't do it. Okay. So Deos Kazanos and I was thinking about this in the 1980s. This is long before the accelerating universe. That didn't occur till 1998. And we were looking for a mechanism to control the cosmological constant. And I realized that there was another symmetry beyond super symmetry which is conformal symmetry because if it's exact, remember the the the angles remain the same when you scale Everything up. And so we started to think about the idea that gravity might have

a conformal symmetry. And we realize immediately that the action would have to be the square of the vile tensor. It would lead us to fourth order equations of motion. And so we started to work on that. And of course I was fully aware and my colleagues were constantly telling me uh don't work on this theory Because it has a ghost. It's not a unitary theory. And I didn't know enough to be able to refute them. But I said, "Never mind. Let's see if nature likes the theory cuz if it does, nature will know how to

solve the ghost problem even if I don't know how to solve it." So that was my strategy. So we write down this C² theory. This is 1987 1988. The equations of motion of fourth order derivative equations. They're absolutely grotesque. In those days, there was no software package that you could just open up and say, "Give me the vial tensor." >> Right? >> So, we had to write our own software package from scratch. We used a program called Maxima, which I don't think exists anymore. Um, and it took us four months, four months just to get

the equations correct. Now, you can see that Deeos and I really Believe this. >> Mhm. >> We were going to invest four months. And we didn't even know it was going to be four. We didn't know it'd be four months. It could have been more. And we didn't even know we'd succeed. But we did succeed. And we got the equations exactly. And it only took us one afternoon to solve them. And when we solve for the geometry outside of a static spherically symmetric source, we Got a one over r potential which we were very very

excited about because our problem had been from the beginning if we write down a theory which doesn't contain the Einstein Hilbert action because G Newton has a scale. How do we get one over R? And so we we said well at least let's try to see if we can get one over R. And we did and we got the one over r. But because it was a high derivative theory, there were other solutions. And the Second solution that we got was a linear potential. And we just looked at it and we nearly we almost fell

through the floor because we realized if the one over r is falling and the linear potential is rising, the average is flat. >> Mhm. And we had the opportunity to explain flat rotation curves. Now you might think linear potentials are bad news. But the they're the good news in the following sense. If the total Velocity is flat is constant and the Newton piece is falling, which is Kepler, then the piece that's missing must be rising. The piece that's missing isn't flat. the piece that's missing is rising because it's the rising plus the falling which makes

the flat. And so we had a chance to get the linear potential. Um we then realized and and we said this in the paper we wrote in the astrophysical journal when We got the solution we said well if linear potentials are important then the objects on the other side of the universe are putting out their own linear potentials and they must be affecting local dynamics. And that's max principle, >> right? And so we finished up reinccorporating max principle into gravity. It's not there in Einstein because Einstein's geometry is asmtotically flat. So in the end it

Doesn't satisfy Max principle. But here the geometry is not asmtotically flat and it does. And so the Max principle in our view is there's an interaction between the local and the global physics. Now, let me ask you a quick question. >> Sure. >> Durk also had a large number hypothesis which also connected the global to the local. >> Yes. >> And I'm curious if if your work validates his or if it's orthogonal to it. >> I I'm not I don't know enough to be able to answer that. I'm sorry. Um it's really a question of

why G Newton should be so much smaller than let's say the electric charge. If you have two two objects together a meter apart, the electric force between them is 40 orders of magnitude bigger than the gravitational force. And Draq was trying To explain that. I have not been able to do that any more than Einstein does it because Einstein just says you stick G Newton into the equations of motion. It doesn't tell you what G Newton to use. You just use the one that Caendish had. >> Yes. >> But but you've assumed the answer in

a sense. I I I recognize that question. and I haven't uh been I haven't thought about it. >> Ah okay. So what was the next thing that You did? >> The next thing we did and it's also in this paper we wrote back in in the late 1980s. We asked well we live in an expanding universe but when we do um galactic rotation curves we're looking at the behavior of an of a particle moving inside a galaxy. So it's in the rest frame of the galaxy. So we asked, what would the expanding universe look like

to someone who who's in the rest frame Of a galaxy? And we worked it through and the answer was a universal linear potential. And so we came up with two linear potentials. One that was local that we've recovered from the local source and the other one of which was global which was coming from the rest of the universe. It took me seven years to untangle those two objects because they were both linear potentials. But let's go back First of all to our our solution that for a static spherically symmetric source you get a 1 /

r and an r. Well, I said to you right at the beginning that's what you get with del 4i equals row. Uh-huh. You see, so the natural pluson equation in this theory is the fourth order pluson equation, not the second order plus equation. And we still get the same geometry as Einstein for the solar system. So let's let's just go back to the solar System. Uh what what do we need of a physical theory? Well, we say we want to recover Einstein, but we don't. Well, we'd like to. What we need to discover is the

Einstein solutions in the region where they've been tested. And what's been tested in the in in the solar system is that the geometry outside the sun is rich flat. So we don't actually test Einstein's equations. We test the solutions to Einstein's equations. >> Yes. Exactly. You because Richie flat is A solution is the immediate exterior solution to Einstein. We do test it in the inside when we do cosmology because we're inside the universe. But as far as the solar system, we're just testing outside outside of U Einstein. So what we're actually doing is not pluson.

It's a little plus equation. It's del square equals 0. But that equation doesn't make any sense unless you have a way to get the coefficient of the 1 / r related to properties of the interior. So we do Indirectly test Einstein. We know that it's Richie flat which said it's the the the metric is one over a constant over r but that constant you can only get by solving the Einstein equations in the interior of the source and then balancing them at the uh at at the surface but that only gives you that the coefficient

is the integral of row the density over the source. It's one particular moment of the source and you can't from measuring the moment Determine the integrant. If you wanted to get the integrant, you'd have to know all the moments, but we only get one. So, so there's that's another another flaw in the standard discussion is that um the geometry outside of the sun is Richie flat and Richie flat is a solution to conformal gravity. Now conformal gravity is based on derivatives of the richy tens of vanishing. So if the richy tensor vanishes then its derivative

does as well and therefore you'll always get back to Einstein's solution. But the derivative can vanish without the richy tens of vanishing and so you get extra solutions like the linear one. >> Mhm. So physics that's demanded of what we know of the solar system is only that we have to recover the solutions to Einstein gravity in the region where they've been tested. If we get the equations then of course we'll get the solutions for free but we don't need the equations. Can we get those same solutions with a different set of equations? And the

answer is yes. You could go to fourth order theory, but then you will get different solutions when you go to larger distance. And so where where Deeos and I finished, we realized that we had found a solution to the cosmological constant By a symmetry which gave us a chance to get a solution to the dark matter problem. And then we have to do fits to rotation curves. And that took me a long time. And gradually it emerged I I did most of the work with my one-time student James O'Brien. It emerged in the end that

the two linear potentials were both playing a role, the interior one and the exterior one. And there was a competition between them because they Were pushing in opposite directions. And what we found was that we could fit 138 galaxies, that was how many we were known at the time, rotation curves, using just that universal linear potential coming from cosmology and the universal linear potential coming from uh the local source. And we need a few more things, but we needed a one more universal parameter coming from clusters of galaxies. Um, and we could fit 138 galaxies

with Those fixed parameters, the same parameters for every galaxy. Dark matter needs two two parameters per galactic halo. And so it needs 276 more parameters. Fair. And so we could so easily have failed but it turns out that it that it works. Now at the same time I was making a slightly different track and that was well I showed you that when we change the vacuum which we have to in order to generate masses then we get a mass scale But then I'm going to get a cosmological constant and that's true. I will get a

cosmological con I'll induce one by dynamics. Now how is it controlled? Well, the answer is in the conformal theory, the trace of the energy momentum tensor is zero. And therefore, the trace is controlled in such a way that the cosmological constant that's induced cannot be any bigger or any smaller than everything Else anything else in in the energy momentum tensor. In the standard theory, that's called the cosmic coincidence. Namely, a mega lamb's 7, a mega matter is.3. So, they're they're the same today. But the point here, >> Right. Right. Right? It's it's a natural occurrence.

Now, there was one piece of the story that I left out, and that was that in order to get the cosmology to look what it looks like in the rest Frame of the galaxy, I needed the cosmology to have negative curvature. And then the linear potential would be the square root of minus the curvature. But the curvature of cosmology is going to be uh something like the Hubble scale. And therefore this extra linear potential was naturally a cosmological scale. I didn't have to force it. Now in the cosmology you have the background and you have

fluctuations. The fluctuations I showed produced a quadratic potential but again universal because it got nothing to do with the local source. And so when I finish up, I have a local 1 / r that didn't go away. A local linear coming from inside the source, a global linear, and a global quadratic coming from the cosmology and the fluctuations in the cosmology. >> Mhm. For >> and I do three or 4 thousand data Points. >> Wow. Now, why the heck does this work? Why does it work? Um if you look at the ro if you look

at the galaxies and you look at v ^2 over c ^2 r that's the that's an inverse length and you just look what that value is for the whole 138 galaxies and all of them are coming out to be of the order of 10 the minus30 inverse cm which is approximately the inverse of the Hubble radius written on the data. Nothing to do with me. It It's there. Now, you may have heard of a theory called Mond. That's Mond. That's Mons a Z. That's why it works because a Z does set the scale of all

these galaxies. You've had John Muffett on this program. His theory log, same story. He has that universal acceleration. So there's a universal acceleration in the data and it has nothing to do with me, has nothing to do with Mgrim, has nothing to Do with Moffett. It's it's just there. So if it's Lambda CDM, Lambda CDM has to explain why there's that universal acceleration, you see. So where do I finish? Where I finish is I've got 138 galaxies. Um, I can fit all of them using the luminous matter alone, no dark matter. And I've replaced dark

matter by the rest of the universe, the cosmology and the fluctuations in the cosmology. So I say the missing mass that we've defined As the original dark matter problem isn't missing. It's the rest of the visible universe. And it's been hiding in plain sight. It's been there all along. You just didn't want to do it because you were hung up on one over r. You see, the problem with one over r is if it's really true and it's one over r on all scales. If you have a problem here, you can only solve the problem

by putting matter where the where the problem is Because it's it's still local. Whereas if the linear potential, you could put matter outside and and and it it can do the job. And so that as far as I can see that solves the dark matter problem in galaxies. Kurt here. Note that if you'd rather listen to toe, we're on Spotify, iTunes, everywhere with a podcast catcher. You can just search my name or theories of everything. And also remember to hit subscribe. >> Now your colleagues who are telling you, hey, you shouldn't pursue this. There is

a fatal error, namely negative norms and ghosts and so forth. >> Yes. Did they prior to them telling you this, did they already know about all the issues that it could potentially solve? So suppose it solves six of the major issues, but it has this other problem. No. >> Did they know about that or did they just say it has this other problem? >> I I would say I would say that it's possible that people realize that conformal symmetry would control the cosmological constant, but they never pursued it because of the the ghost issue. So

all of all of these things I found after the fact just because I I I knew enough about conformal symmetry that I wanted to apply conformal symmetry to gravity. Now I did something else and that was if I have a space of negative curvature. It Acts like a con a concave lens. A convex lens will pull the light in. A concave lens causes light to diverge. >> Mh. And so if the universe has negative curvature, photons are given a push by the geometry and that's the accelerating universe. >> And so as soon as I heard

about the accelerating universe, I realized that I'd written a paper in 1992 which had all this in it, but I had never pursued it. And in 1998, as soon as it came out, I immediately wrote a paper to show that I can fit the accelerating universe data without any fine-tuning that the cosmo I told told you the cosmological constant was under control. But it's more if the curvature is negative because omega lambda plus omega m plus omega k is one. If omega k is positive then omega lambda has to be less than one because it

had to be one minus something. Therefore what I had already Realized was the deceleration parameter had to lie between 0 and minus one. No choice couldn't be anywhere else. If it's anywhere else then the theory is wrong. So I worked it through. I got an expression for the luminosity distance versus red shift. I applied it to the accelerating universe data and it lies right on top of the data with the deceleration parameter emerging at the one free parameter in the theory as minus.37 Right between 0 and minus one. Uhhuh. And that and then of course

in this theory there's no finetuning. So the universe always accelerates. It doesn't just accelerate very late. And so at higher and higher red shift, this theory is going to depart from standard theory. >> Interesting. >> And what I've been doing so far is well, I've got the background. I've got the accelerating universe, but what about The fluctuations? And is it really true that I can accelerate all the way back to last scattering? And I've had a set of very good students uh Matthew Phelps Sanka Amora Singh Tananiel Lee and currently my latest student Daniel Norman

and I have been working on the fluctuations and you are fully justified in holding up on saying this is great until we were to until we can fit fit the fluctuations. I don't know we will but we're working very hard on it. Um nature may be kind. Nature may nature may be not kind. All I can tell you is Einstein uh once said and we we always quote him rafin is got uh subtle is the lord but he went on to say arbashef but he's not vicious you see so I think maybe maybe the I've

gone a long way so maybe all all the other pieces will fall in but nonetheless that's So I've handled two separate problems the cosmological constant problem and the dogmatter problem. Now let me just state there's a lot of question now about land the CDM itself and my view is if lander CDM is wrong at some point it's going to start failing to fit data and we've seen a little bit of this at the moment but not enough we've seen the Hubble tension namely >> using the land CDM for for the plank Fluctuation data gives us

a value of the Hubble parameter which is about 68 km/s per mega parc whereas the usual sephiid cosmic distance ladder gives us 73 and that's a quite a serious uh difference it's not much as I'm not in the standard camp I don't believe it's big enough to say it doesn't work however the other issue that's emerging and this is coming from Daisy Desi is that it looks like dark energy you might depend on red shift that it changes with with Cosmological epoch. Now if that were to be the case that would be an absolute catastrophe

for the standard theory because the fact that you would then not make dark energy a cosmological constant does not mean that the cosmological constant problem has gone away. That was there from that's always been there from the very beginning. Why isn't it 10 to the 60? Is it plank scale 10 120? That hasn't gone away. >> It's made worse. >> Yeah, it's made wor in other words, a red shift dependent uh dark energy is is really bad news for the cosmological constant problem, but we'll have to see how how that plays out. So, there's something

else your theory solves, or I wouldn't call it a problem per se, but it's more like a question. If I recall correctly, it's the size of galaxies. >> Yes. Okay. So it turns out that I've got A linear potential and a quadratic potential. They have opposite sign. So if the quadratic potential gets too big, the distance gets too big, the quadratic potential becomes negative. But that's velocity squared and velocity can't be complex. Therefore, galaxies have to have a finite size. Now to understand this, a one over r potential, whatever else you want to say about

it, it never cuts off. It doesn't matter how far away you are from the source, there's always going to be um there's always going to be a bound state possibility. But this is giving an actual reason for why galaxies have a finite scale. Now, since you asked me about this, let me go back and uh discuss what what what happened with James O'Brien. >> Oh, and you should know that I have the ability at any point if you wanted to show something on screen. You don't have To pull it up on your computer now, but

I can show it for the audience. So, I can show finite size length in the in the galaxies. I can show curves that you said that your your model was able to fit the 130 or what have you. So, anytime you just let me know and it's on screen. >> Okay. Um well you can show some rotation curves of ours if you want. What had happened was this and this was James O'Brien's uh PhD thesis with me. Um when I had first applied this linear potential to galaxies, there were only 11 galaxies that were known

that whose rotation curves were well enough studied that you could actually do modeling with them. And while I said that the linear and the the falling and the rising would balance as you go out to larger distance the linear tens linear must win and therefore eventually the rotation curves that are flat have to turn up. Now you should also know that for dwarf galaxies they already are rising. It's the bright spirals that are delayed from rising because the Newton term is so big because it's a big luminous galaxy. >> So I expected to see this

rise and James I said James go ahead and find some galaxies for me and we'll see what they look like. And he found me 138 galaxies. I mean the data for them. I I didn't Even know they existed but he he found them all. And we apply the theory and it doesn't work. It doesn't work because the rise is not there in the data. At the point where I expected the the everything would rise, it doesn't rise. And I realized we went through the data and we found there were 200 points where my theory said

it should rise and it didn't rise. >> That sounds bad. >> Yes. And then now you're going to hear something quite remarkable. I still had one extra term in the theory. That's all the quadratic term, >> but it's one term with one number and it's universal. >> Uhhuh. >> So I realized what that one term can cut down one rise. But it turns out it cut down the entire 200. >> Yes. Gez. In one number, we got 200 points that were rising and they all they all curve down. And if they keep on curving then

that's what you said before that eventually uh the galaxy would have to end. >> That is quite remarkable. So what occurred to you both when when you were able to fit how many 138 you said or 200 with one parameter? >> It was 138 galaxies 200 data points were in the um the awkward region. Well we we Just realized it was correct. we realized that there was something going on in galaxies that was being missed in Lambda CDM. Now, it may not be that conformal gravity is the answer, but what I've been saying all along

is here's this formula with with the linear term, the two linear terms, and the quadratic term. If you think that lambda CDM is the answer, then derive it in lambda CDM Because it fits the data points. that that's that was what I would ask my colleagues to do. Um but that's not happened. Now Mgrim and John Moffett all of us have been saying look we have these theories they're the universal acceleration parameters. If you don't like them derive them in in your theory. It's not you shouldn't you shouldn't say what we're doing is wrong. You

have to say that's up to data. and data is saying that there's there's a structure That's that's currently being missed. Okay. Now, by this point, I began to think this theory is on the right track. It's reormalizable. It resolves dark matter. It resolves dark energy. And standing in the way of just one question, the ghost problem. >> Right. Remind me the year at this point. Uh this was the year the the year was 2008 and I'll tell you what happened. >> Bender is coming. >> Yes. I um had always felt that nature Knew how to

handle this problem even if I didn't. And I went to a conference. I've known Carl for many many years. And he talked about the Lee model. The Lee model was introduced by TD Lee in the 1950s and what it did this was the early days of reormalization. It allowed you to calculate the reormalized coupling constant in a closed form analytically which was very very powerful. But as you move the parameters all of a sudden you discovered that there was a region where You suddenly got negative norms. And so this was a problem that Powley and

Chileen and Lee and Heisenberg had all worried about but had never come up with a solution. Um I had actually looked at this problem when I was in graduate school. Um there was a theorem called the Heisenberg nonlinear spinner theory which preceded everything because this was still in the 50s and it had an indefinite metric. Uhhuh. >> And Heisenberg sort of said, well, you Know, this this solves the scale invariance problem of the theory, but it it really was was still a problem. And Carl had realized that when you move the dra the reormalized coupling

constant to a certain value and you got this negative norm. At the same time, the bur coupling constant became complex and the theory was no longer hermission. And so everything that you've done was presupposing That you had a hermission theory. And Carl had realized have to give you a little bit of background. In 1998 or so, Carl and his former student Stefan Bcher had been looking at the Hamiltonian P^2 + iX cubed with an I with a complex I. So the potential is complex. You would swear that the that it must have complex icon values.

You you would absolutely bet any money that it has complex icon values. Except It doesn't. All of its icon values are real. And Stefan and Carl showed that using WKB approximation. And then a few years later, Dory Dunning and Teo proved it as a rigorous theorem that all the values of P^2 + IX cub are real. Now Carl had realized that that's a theory where you have a PT symmetry. Parity sends x cub to minus x cubed and time reversal sends i to minus i. So ix cubed is pt symmetric. Now Vner in 1960 when

he introduced time reversal had said the following the shreddinger equation is iid dt. So if I let t go to minus t I won't keep the shreddinger equation unless I let at the same time i go to minus i. So I need an operator that will complex conjugate numbers not complex conjugate functions because we do that all the time when you take the emission conjugate but you have to conjugate you have to conjugate numbers And that's called antilinear and what Vner had shown that if you had an anti-linear symmetry then the anti-linear operator will conjugate

E into E star because it's a complex cont and that means that for every E there should be an igon value E And so you had two possibilities. E equals E star. So the energies are real. >> Mhm. >> Or the energies are in complex conjugate pairs. And so once you have PT symmetry then you have the possibility of real values and the P ^2 + IX cubed has that symmetry and that's why it values are real. So when I got interested in this program when Cole gave this talk he said that when he uses

the PT theory which means the following. How do you you construct a norm a probability? Usually you say you take the cat and direct tells you take the hermission conjugate of the cat The bra and the bra ket is the probability. That's not the most general what realized is if the Hamiltonian is not her mission you take the pt conjugate of the k and that norm is positive. And so when people said that they had a negative norm theory, what they meant was the direct formula for this for the scalar product for the inner product,

the direct formula was was was giving You the negative answer, not the theory. You're in the wrong Hilbert space. The Hilbert space is dictated. If the Hamiltonian is not hermission, then you have to use the PT conjugate. I'll come back to this in a minute. For relativistic, you have to use CPT. >> Right? We'll get we'll get to that in a moment. So when Carl did that for the Lee model, all of a sudden the ghost disappeared and it was a perfectly consistent Theory. So, I had I hadn't known Carl since forever, but we were

at a conference together and he talked about this and he gave a it was in in in Florida at Fort Lauderdale run by the University of Miami and he talked about this and I said to him, Carl, you have a theory with a that you have a way to get rid of a ghost and I have a theory with a ghost. Let's get together. So, Carl was at the time was uh was in In Los Alamos for the year. So I went to Los Alamos and we sat down and we solved that problem in three

days. In three days we we we figured out the whole thing. Now of course maybe 3 days but we both came with with 20 years of prior experience. >> Of course. >> Yes. But in 3 days we'd realized that conformal gravity was a PT theory and not a hermission theory. And then there was no ghost. Now The thing that made this work was that going back to what I said about quantum electronamics, everyone had always taken it as a given that whatever the quantum theory of gravity was, the Hamiltonian would be hermission. But it never

needed to be hermission. Her mission is is is too strong a requirement. Now when I started to work with Carl I real I realized the following. I knew a little I knew a little bit about this very little but I knew from my days as a student that if a Hamiltonian is her mission the values are real but I also knew that that's only one way. >> Right. Right. You can have something that's real that's not her mission. Right. >> Yes. >> When you say her mission do you mean Self adjoin in its more general

form? >> Yes. self her mission in the 19th century understanding of second order differential equations that you can get rid of surface terms I see and that's exactly that's how Dak arrived at hermission quantum mechanics in the first place and because he he copied what people already knew from from the 19th century so you can it's true and you you said it if the Hamiltonian is not mission it does not follow that the iggon values are not real. So I started to think about this and I said well if hermaticity is sufficient to give a

real value what's the necessary condition so you open a linear algebra book and you won't find it and the reason is it's not a linear condition it's an anti-linear condition the theory Has to have an anti-linear symmetry and that's the necessary condition for real values. And so what this meant was and why I think people have never been able to make Einstein gravity into a quantum theory is beyond the issue of reormalizability. They're insisting that the Hamiltonian be hermission because it always has been hermission and in the fourth order theory it isn't. But it has

an anti-linear symmetry and that's that's the second flaw. It doesn't mean that therefore the Hamiltonian is not hermission. But what I'm saying is by restricting to her mission Hamiltonians you would you're looking at too narrow a problem because you you it was obvious that the metric the classical metric is real and therefore the Hamilton must be hermission but it doesn't have to be hermission for the metric to be real. It Only has to have an anti-linear symmetry. Okay, so we worked that through and we published a paper in physical review letters and what we basically

had shown was that the 1 / k^ 2 - 1 over k^ 2 - m^ 2 propagator was reormalizable and unitary because you were in it looked like you see when I when I write to you a propagator 1 over k^ 2 - 1 k² - m^ 2 terms cancelling each other. You see the Big advantage is they both go like 1 over k^ squ but with the minus sign the net effect is one over k to the 4 and so for very high momenta the one that we needed the cutoff because we've got all

these modes now you don't have the now you don't have to worry because now you've got reormalizability and when you had John Donahue on your program that's what he was talking about was second plus fourth the one of a k square comes from the second and the Other one comes from the fourth order and from second plus fourth you have a reormalizable theory gravity. But if you look at the propagator, you've got the 1 over k^ 2 and the other one has a minus1 over k^ 2us m^2. So if you just take the normal vacuum

t5 vacuum for the propagator and put in intermediate states, you'd put the sum n bra minus the sum mc bra. You put it in and you get that propagator and you've got states of negative null And the theory is not unitary. However, you can't do that. You can't look at a C number propagator and tell me the Hbert space. If you know the Hbert space, you can get the matrix elements, but you can't from the matrix elements get the Hbert space. And what Carl and I showed in that theory was that when you thought you

were writing those sum on nn minus sum on mm equals 1, you had presupposed that those states were normalizable. If they were, then that would be correct. And what we had showed, and this grew out of work that I'd done a little bit earlier with Aaron Davidson, who was another longtime collaborator of mine, he was at Bengorian University. um we had shown that the states were not normalizable and therefore the whole discussion of ghosts you were in the wrong hilbert space. Now does this also work in QFT? So I imagine this works in QM but

is This >> Lawrence >> yes of course I mean what Carl and I did initially was we did it for quantum mechanics. I I long since generalized it to quantum field theory. Yes. But it's the exactly the same story. Now, we discovered that the solution to the ghost problem was not that we got rid of the ghost, we never got rid of the ghost. We just showed that the reasoning that caused you to think there was a Ghost was not valid. Right. Right. Right. I mean, everybody that was trying to get rid of ghost was

adding on terms that would cancel something, but you never needed to do that because it was never the reasoning was wrong. And what of course how does it work is instead of having vacuum T55 vacuum the left vacuum has to be the PT conjugate of the right vacuum and not the hermission conjugate and then when you put in intermediate states it's no longer modulus squared And therefore you can get a minus sign I mean that that's those are the details but the basic point was and the thing that saves the theory is that the states

were not normalizable Now Carl had developed a whole apparatus for dealing with non-normalizable states. Namely, there was a way to continue them into the complex plane. So if you had think that something that went like e to the plus x^2 on the real axis, it went like e to the minus x^2 on The imaginary axis. And so this theory lives on the imaginary axis. And of course if people were trying to do quantum gravity with everything living on the real axis and that's in my opinion why they couldn't succeed. So so that was the so

that was the first side of the story was was the PT. Now the second side of the story and I realized this as soon as I got to know about PT was that there was a connection to CPT And the CPT goes the following. The Lorent group breaks up into four units, four regions. There's the one with the real the real coordinates. Then there's the one which is related by par, one which is related by time reversal and one which is related by par times time reversal which is PT. Now parity reverses the spatial piece.

Time reversal reverses the time piece. So PT reverses all four components of X mu and that's Lorent. That's consistent with Lorent. And so what you discover is that there's an extension of the Lorent group which involves a PT transformation into this other region where X mu is replaced by minus X mu. And that turns out to be the covering group of the Lorent group. And so if you have that as a symmetry then Carl said look PT is natural. It's related to the lorren group. Hermiticity is a is an artificial requirement on on a function.

It's a Mathematical requirement. Symmetry of the Lorren group is a physical requirement. >> So you get vile spinners out of this. >> Not yet almost. So that's PT. Now you do it for so you did it for coordinates. Now you do it for firmians. So I did it for firmians didn't work. The reason is for firmians p is gamma 0 and t is gamma 1 gamma 3 but gamma 0 gamma 1 gamma 3 is not a lorent is is not a lorren invariant. You have to Multiply by gamma 2. Gamma 0 gamma 1 gamma 3

gamma 2 is commonly called gamma 5 is a lorren invariant. But gamma 2 is charge conjugation. So for firmians that transformation is CPT, not PT. And so what I'd realized was was that CPT symmetry was intricately connected to the complex Lorent group. And so if the universe is complex Lorent invariant, then CPT Can follow. And then if C is conserved then you're back down to PT which is what you get for the non-relativistic case. However, that's not the whole story. And the reason is if I write down something like cyosi which is a lorren scala,

it's a CP CPT invariant but it's now got a coefficient. How do I make the the the coefficient is going to be conjugated by by time reversal? So it may not be real. So can I make the coefficient real? And the answer is yes. If I impose probability conservation and so I replace the entire discussion of CPT theorem by complex Lorent invariance plus probability conservation gives me CPT. Now any non-relativistic theory that descends from uh relativity would automatically have probability conservation And if you have a non-ermission Hamiltonian you need to have the CPT conjugate be

the bra not the hermission conjugate and then probabilities conserved. So the key feature and I think this is what people have missed. The key feature of quantum mechanics is not hermiticity is probability conservation. Hermiticity implies probability conservation but probability conservation does not imply hermiticity Any more than herity implies reality but reality of values doesn't imply hermiticity. So probability conservation is in my opinion the most important feature of the theory and that's that's how the PT works. Okay. Now, as soon as I started to work with Carl, we solved the problem of the ghost and now

I can tell you why it's guaranteed that this is the solution. You take the firm and you couple it to geometry Through the spin connection, which is how we describe a propagation of um spin a half particles in a gravitational field. You take the action pi bar i gamma mu d mu plus capital gamma mu pi that's the coupling of a direct firm to the spin connection and you do the path integral over s and si bar you get the c^ 2 action you've integrated out the firmians the Only thing that's left is the metric

and the metric appears as c^ squ why is it c^ squ because the drag action was conformal invariant with the spin connection. So it was already conformal and therefore you automatically get um the ced action. So now you you've only got two argument. There's only two things you can say either the we know the standard theory doesn't have a ghost. Therefore it could the the Gravity theory could not have one if it's induced by integrating out the firmians. But if it did, then the entire SU3 cross SU2 cross UU1 would collapse when it's coupled to

gravity. So you've only got two choices. Either there's no ghost or SU3 cross SU2 cross U1 is wrong. And there's no reason for a ghost because you're starting out in the theory which are ghost free the standard model and you just integrate out the Firmians. So in the end there could never have been a ghost in the first place. But how do you show that there's no ghost? You've got to construct the Hilbert space and get the um and get the bras. The bras are called the dual space. And the whole point of these theories

is that the dual space does not have to be the hermission conjugate of the of the of the cats. There's physics is richer than that. Quantum mechanics is richer than that. And that I think is what Carl has really established is quantum mechanics does not require the dual space to be the hermission conjugate the same the same way that Draq originally introduced it. It's a richer theory and it's that richer theory which works in the fourth order case. Okay. Now when I did this I realized that VNA has said there's an E and there's an

E star. Therefore I now have a way to describe decays because if the energy is complex then it's E it's E plus I gamma and then E to the I * E plus I gamma gives you E to the gamma T which um which can decay. So for the first time in my career, I had a way of describing decays. But you paid a price. You needed both of them. You needed that one that grows because it's a complex conjugate pair. One grows like e to the gamma t and the other grow falls like e

to the minus gamma t. And when you combine them, the gamas cancel because you get prob you've got to get probability conservation because that went into the CPT theorem. And therefore each mode the growing mode cancels the decaying mode and vice versa. So let's let's see how that works. We go back to Rutherford. Rutherford discussed radioactive decay. And you you ask well it's e to the minus Gamma t. You measure the gamma and you measure the half-life. And that's how we get we we do half- livives of materials. And that looks like it's not unitary

because emission Hamiltonians don't have complex values. So that doesn't look like it could possibly be unitary. So what's going on? Well, it's decaying into something. And the decay products are building up. As the population of the state that's decaying declines, the population of the States that it's growing going into increases. So one decay is e to the minus gamma t and the other one is e to the plus gamma t and the total population remains fixed. So what you really have to do when you do decays is you've got to include the decay products and

then you have and then you have CPT symmetry. Okay. Now I wrote a paper in 2018 in JF A. I was discussing all of this and I Said that if I have um with if I have an e to the minus gamma t then vner tells us that there's a time delay h bar over gamma which is just the uncertainty principle. So when a particle travels by a square well it's it's delayed for a while before it's released that's and that's called the bright vignner formulation of of resonance formation. So the physics is the wave

is held for a while and then it escapes the Well and then it continues on and it's held for a time har over gamma time delay. But I said, "But there's another one with a minus gamma, and that gives a time advance, a negative time delay, and they're both operative." And then I saw an an article in a strange place, the BBC, of work by someone else on that was on your program, a Fry Steinberg, who had Said that when you excite an atom into the first excited state, it's supposed to decay with a rate

h bar over gamma where gamma is the radiative width of the upper level. But he said it doesn't. It decays right away. And I wrote a paper which said that the reason it's decaying right away is because the time delay is canceled by a time advance. And so the net effect is you have a line width but you have a time you have a Time for the transition which is not given by h bar over the line width. It's given by h bar over the energy difference between the first excited first and the excited state.

The ground state and the excited state. And so when I wrote that paper, I began to have some confidence that the correct way of describing decays is by having both the both modes at once because that's What PT symmetry requires. If if I may, let me tell you everything that I've told you in in in this interview has solved problems that occurred to me when I was a graduate student. >> Yes. Yes. And when I was a graduate student, I was being taught the grand laws of physics. We used a textbook by Messier uh which

was excellent textbook. I I've used it when I teach it when I teach quantum Mechanics. I had an excellent set of teachers Carl Levenson, Harry Lipkin, Eagle Tali, Amister Shalit. Um and I learned a lot of quantum mechanics from them. But I also as I was listening to them uh some things didn't sound right and I identified four different things well four and a half different things that didn't sound right. I'll tell you the half in a moment. The half was a discussion of the Heisenberg nonlinear Theory with its indefinite metric which I I've told

you how to resolve that through the work with with Bender. Um but the four things the first one was I said the following the Hamiltonian generates time translations parity generates space reflections time translations and space reflections commute. Doesn't matter which sequence you do them because they're acting on different things. >> Mhm. >> And therefore the Hamiltonian must commute with par. You see? And of course we knew that the weak interaction violated par. And I was told that there was an answer to that question which was originally suggested. TD Lee had thought about this and he

said yes but when par acts on a left-handed neutrino it doesn't go anywhere because there's no right-handed neutrino and therefore the HP commutator isn't defined by the States. And I had two objections to that. One was who said there's no right-handed nutrino? We just hadn't found one as as of the time that the time that parity violation was discovered. And the second was there was there's a lambda baron which decays into a proton plus pi minus and it's parity violating and it doesn't involve nutrinos. So why should parity be violated in processes that don't involve

neutrinos? So I was puzzled by that but I didn't know the answer. What did he say when you said that to him? >> Well, that was Well, I wasn't talking to TD Lee. I was just talking to my my professors at the Viceman. Oh, >> I see. >> And um well, they they agreed that there was an issue, but I I didn't know how to what to do about that. When I started to work on dynamical symmetry breaking, it occurred to me that par could be Spontaneously broken, namely in the vacuum, not in the lrange.

But to do that, I'd have to change SU2 left cross U right cross U1 to SU2 left cross SU2 right cross U1. Make it chyro. And the only way I can make it chyal would be if there were right-handed neutrinos and right-handed currents. So now I have to spontaneously break it down to SU2 left cross U1. But it turns out that there was a way to do it and that is when you do the durac Mass it's sy which links the right-handed firm with the left-handed firm. When you look at a myeronomass it's transpose CI

with C is charge conjugation and that mixes right with right or left with left. So if the right-handed neutrinos got a myeronomass, you would break the right-handed sector, the right-handed nutrinos would become Very heavy. The right-handed currents in the SU2 right would become heavy and you'd be down down to SU2 left cross one and then you could do the standard thing. So I realized that par is probably a good symmetry in the real world and there's another reason for doing this and that is if we take the strong interaction is QCD QCD has a global

chyal symmetry and some of it is gauged and becomes the weak interaction But that made no sense to me. If you're going to gauge any of it, you'd have to gauge all of it. And therefore, for me, the weak interaction is the gauge of the strong interaction chyro symmetry. But that requires right-handed nutrinos exist. So the my my original concern was well par would take left-handed to right-handed. I said yes, but par gets broken even though that the right-handed Nutrinos are the mechanism for breaking the par. And so everything ties together. Now it turns out

that there's some evidence for this now because we have we found that the neutrinos that we see in nutrino oscillations are massive. Now the reason they're massive is if the two any states that are degenerate then any linear combination of them is is still degenerate. Therefore the only way you can get nutrino oscillations is if they're non- degenerate. And therefore at least one of them has to be massive if there's an oscillation. How would you make them be such small masses? Well, there's something called the seesaw mechanism which is a feed down from grand unified

theories through the right-handed nutrinos. So the these very light particles get the square of the direct mass divided by the myeronomass of the right-handed neutrino. So right-handed nutrinos now are very much in vogue. Okay. So that Was the first issue. The second issue was something very strange that I could not understand. The d the laurent group has firm the lens group is the fundamental group of nature. Its firmians are reducible into a right-handed vileon and a left-handed vilemion. >> So the direct firmian which contains both of them is reducible under the lorren group. And I

could not understand How could the Lorent group which is the fundamental group of nature be reducible under the spin when the spin of half is the fundamental building block of nature. It didn't make any sense to me that something was wrong. But I as a grad student I didn't know what what else to do. So I I left it there. >> Oh wait just a moment. I'm not understanding the problem. Tell me the problem as you saw it as a grad student. Okay. The problem was the left and the Right-handed firmians are independent representations of

the Lorren group. They're not connected. No Lorent transformation can take you from one to the other. >> Mhm. >> So if you try to build a theory on left-handed firmians or a theory on right-handed firmians, those are disconnected theories as far as Lorren is concerned. But Lorren is the Fundamental group of the universe at least was thought to be at that time. And therefore I would have expected that the firmians if they're the building blocks would have been connected by some transformation. >> Okay, except I didn't know anything about what it might be. When I

started to work on conformal symmetry, I realized I told you the conformal group has these four five extra operators beyond the quenom Pankor. Those five transformations mix the right and the left-handed firmians. In other words, the direct firmian four component and four cross four * 4 is 15 + one and we've got six lorren four translations one one dilitation and four conformal is 15. The draq spinner is the fundamental representation of the of the conformal group and therefore the conformal group which I've been using for gravity already I discussed that the conformal group must be

the fundamental theory of the universe and it's the symmetry of the light cone. why I don't like super symmetry is super symmetry is not the symmetry of the light cone and that's why I didn't like it but conformal symmetry is the symmetry of of a light cone and therefore furians have to be four components and then there have to be right-handed neutrinos The neutrino could suddenly not be two component anymore question about right-handed nutrinos going way back to when I was in grad school gets resolved by the conformal true because it says right-handed nutrinos must

exist. >> Now, if we're permitting right-handed nutrinos, then how's that not a candidate for dark matter? Because you're already excluding dark matter or salt dark matter. >> Oh, >> with a parameter. >> So, where are these right-handed nutrinos then? >> Well, okay. For the for the moment, uh they're out of reach. Um I'm sorry to have to say this and I'm I'm really very disappointed. um and that is I haven't yet come up with a theory that would give me an upper bound on the right-handed neutrino mass. I've only got lower bounds and Those lower

bounds are not achievable at the large collider and so that problem still is still open. I don't know. um right-handed neutrinos as a candidate for dark matter would have to have a much much smaller mass. They'd have to have maybe a KV mass or so on. But >> can I ask you a silly question? >> Sure. >> Of course. >> If the Higs is composite, >> yes. >> Do you believe the graviton then is also composite or is fundamental? >> It's neither. It doesn't exist. >> Man, talk about fighting words. Yes, going back to this

conformal theory, when you quantize it, you find something very very strange and that is it's a fourth order theory. So you would say I'm going to have to have two gravitons Because I' I've double the number of degrees of freedom. But there's a theorem due to Weineberg which says that if you have a spin 2 particle, it must couple through the Einstein tensor and therefore I can't I can't have I can't have that that occur. But there's a there's an escape clause and the escape clause is it requires that the the metric of that Hilbert

space be positive definite. >> Now we said a moment ago, oh but I just Showed you it wasn't negative definite. What I didn't tell you because it was unrelated at the time, it turns out that I get zero norm. And so what happens is the graviton becomes a zero norm state, not a positive norm state. And so you have gravitational radiation because it's a it's a coariant metric theory. But when you quantize the gravitational radiation, you don't get a particle. But even though we always did that with Photons because that presupposed that you had a

Hilbert space of positive definite a positive definite norm and Carl and I wrote a paper to show that in these fourth order theories you can actually get zero norm photo gravitons and so the result of that is that they're not observable. Now I'm going to say something which you should never quote me on. Well I've written it so I'll say it. It's possible that the collapse of the wave function is due to The emission of the zero norm gravitton that we don't connect that we don't uh observe. But um that's about as far as I've

gone on. >> Well, on that question, >> this is interesting. I'm going to get you to go a tad further. >> Yes. >> Because there are two other theorizers that I see you be extremely close to. One is Tur Rock/Lam Boil which I'm going To just place as one theorizer and then the other is >> Roger Penrose. So taking the symmetries of the Ly cone extremely seriously also reminds me of Twister theory and then the love for conformal symmetry and his conformal cyclic cosmology is it also has a rhyme there. Now you saying that gravity

make me connected to collapse also has a rhyme with Roger. >> Yes, of course. And there are so many other rhymes with Turac boil and that Whole research program as well. So I'm wondering what is the relationship between these two broader research programs? I I have visited Neil and Leam in Edinburgh few summers ago and what they're doing is they have a CPT invariant universe which has the universe that we have and then there's a mirror there's a mirror reflection of it and that can get rid of the big bang singularity and that's exactly what

Roger Penrose is doing as Well because he has he has a cyclic universe and when I first started working on conform form of gravity I realized that it had a cyclic solution you see and that would have been the case if the curvature were positive but when I finally showed that the curvature was negative it's a theory which never has a singularity and the way the theory solves the fatness problem is by never being singular And so I mean roughly the following you write down a dot^2 + k is equal to row is the freerman

equation uh row goes like 1 / a to the 4 1 / a the 4 blows up when a is zero a dot blows up when a is zero and k is irrelevant and that's the flatness problem so to get around that Allan goth puts has an exponential growth before then but what I do is I say ah yes but you've got the wrong equation it's a dot square plus k Is equal to minus row and then there's no singularity and So then you've got one universe that lives forever with no big bang. And that

means that in the early universe the the radius is finite. So that's a little bit different from what Penrose and and Tur Rock and Boiler do lean boy are doing. >> So there's no period of inflation. >> Uh no because you you never needed it because the uni if you look at the Integral of dt over a of t and you take t a of t is t to the n. If n is less than 1, then the integral of dt / t is t is finite and that's the horizon. If you do dt /t,

you get log t, which blows up at t equals z. If you do dt over e to the ht, it also blows up. It it also it also has no horizon. So you will get a horizon for any theory for which the expansion radius is t to a power greater or equal To one and exponential is certainly in that category. So you don't need to be exponential to solve the horizon problem and you don't need inflation inflation to solve the uh the flatness problem. Now I said before that inflation in the end doesn't solve the

flattening problem because what it shows is that omega m plus omega k plus omega lambda is one that omega k is suppressed by this exponential expansion in the early Universe. So you get that omega m plus omega lambda is one. Fine. However before you had lambda you had omega m equals 1. And therefore you had a prediction that the that the crit that the matter density of the universe was critical. The critical density being it equal to one. But when you have omega m plus omega lambda equals 1, you've now got a real problem because

omega m a mega m is redshifting. Omega lambda is Not. And they have to add up to one today. So this the.3 and the 7. So somebody had to adjust the very early universe 10 billion years ago. So that land such that the matter density would fall in such a way that it would just be catching up with that land would just catch up with it today. So you still got a finetuning problem which is called the cosmic coincidence problem. But inflation was introduced to get rid of finetuning And yet you still have a new

you've solved the fin. So what was thought when the accelerating universe was was first observed, which was 28 years ago, it was thought that something would happen before inflation, which would be related to quantum gravity that would lock you into those values so that it would take 10 billion years before a mega lander could could build up to one. And so people looked to string theory to um to see if they could solve that problem. Can you show that there's a string theory very early universe pre-inflation which will lock you into the right values of

omega m and omega lambda. Now of course that hasn't happened. Um people always say that string theory can't be falsified at ordinary temp at ordinary energies. You have to go to plank scale Energies. But that's not true. We know that omega lander is 7. We know it's not 10^ the 120. Therefore, string theory has to explain why it's 7 otherwise it falsified. If string theory could come up with a number for a mega lambda and it turned out not to be 7, then then string theory is falsified and and that's at ordinary energies. So that's

that's the challenge for string theory is to explain why it's not 10 to The 120. And for the moment it looks like the more natural thing to occur in in string theory is anti-deitter not ditter which would make a mealander negative. Now the there are that's not the only thing that can happen but overwhelmingly it looks like you get a mealander negative. And so that problem uh is still there. There's still a fine-tuning problem in in inflation even without string theory. And Despite everything, omega m equals.3, omega lambda equals 7 really works remarkably well for

the fluctuations. And so if I'm going to be able to get anywhere, I've got to I've got to recover those results. Otherwise, um otherwise I have a theory of nothing, not a theory of everything. Even with everything else I've done um with the dark energy, with the dark matter, with with the um w with with with the quantum gravity, with the with The PT theory, with all of that, I still have this problem of the fluctu I still have to solve the fluctuation. It's not it's not it's not that I can't it's not that I've

calculated them and it didn't work. I I just have this problem that I have to do the calculation and that that's where I am at the moment. So, I've told you about two things that bothered me in grad school. the commutation of the Hamiltonian with par and the issue of the direct firm being Reducible under the lorren group getting me to look for group and right-handed neutrinos but there were two other things that bothered me what are they >> okay we were we were told about the CPT theorem and we were told that it was

a great success because it predicted that the K plus lifetime and the K minus lifetime were equal which they are so particle and antiparticle have the same lifetime which is a consequence of CPT. The only problem that I had with that was that the proof of CPT theorem required that the Hamiltonian be hermission and therefore neither the K plus nor the K minus would decay in the first place. So it just did not make sense to me that you could apply a theorem that you only establish for hermission Hamiltonians that you could apply it to

decays. Now there was a related problem which is the fourth one which is we learned very Early on that when you look at scattering in the scattering amplitude you find a cross-section which peaks when delta is pi by2 when the phase shift is pi by2 and you fit it with a bright vignner you continue the bright vignner into the complex plane and you get a pole and you identify that pole with a particle and how do we the particle data tables contained lots of resonances that have been observed by seeing peaks in the Cross-section. Now

the problem is you can't have an isolated complex value. You either have none or you have them in complex conjugate pairs because of CPT >> because because of CPT symmetry. So first of all I proved CPT theorem without heraticity only using probability conservation and then I saw that I needed a complex conjugate pair of solutions And then they would be they could be iggon states of the scattering Hamiltonian and now you will immediately ask me well don't I then get two resonances well the answer is no and it's Going back to what we said before,

it's 1 / e - e1 - i gamma 1 minus 1 / e minus e1 + i gamma 1. That's the propagator. And there's a minus sign in the middle. And when you add those two together, you Just get one resonance where e when e is equal to e1. But if you added them together, you get more you get something totally different. So, it's the relative minus sign that gives you unarity. Except everybody tells you the minus sign means it's a ghost, but Carl and I had shown it wasn't a ghost in the first place.

So now we can put in the relative minus sign. And that's the Hamilton that's exactly the propagator that Dra was Using to try to get to get physics without dead wood. I think it was he was trying to get better behave behavior asmtoically. And um uh Lean Wick did the same thing. And so what Carl and I were able to show was that even with the relative minus sign, you still have unitarity. And you have to have it because I'm getting the complex conjugate pair because of probability conservation. And so if I have probability conservation,

I must get unitarity because that's what unarity is. It says uh you have time independent evolution. Um, so all all of those things hang together. Um, so then I I came up with something very surprising and I only released this very very recently. I now go I went to the square well and I plotted that propagator that I just gave You 1 / E minus E1US I gamma minus 1 / E minus E1 plus I gamma. took the modulus squared to get the cross-section. I plotted the cross-section and it's a bell shape. Okay, >> which

is a re which is a resonance and it's an exact resonance and you can fit it with a bright vignner but you have to fit it with a bright vignner with a different gamma with a different width and that's not the right width and That's what people have been doing and they've been fitting they've been fitting it with it with with this width um using the bright vignner and I'm saying is that that's not correct because the bright vignner was never was never an state of the Hamiltonian and you can see it in the following

way. You take the square well. It's got a real potential. So you write down the sh the the value equation determinant of H minus lambda I equals Z. H is real if the potential is real. So that's a real equation. Real equations only have two kinds of solutions. Real or complex conjugate pairs. Therefore there must be complex conjugate pairs. And they must combine the way I just described with the relative sign in a way that still preserves probability conservation and give you a normal bell-shaped cross-section. And that's and that's that's then a real Life elementary

particle. And so what you have is you send in a wave you send and you get scattering of of two particles and then the the Hamilton the cross-section grows like e to the plus gamma gets to the peak and then it falls like e to the minus gamma. So you need both effects to produce the one peak and that's basically the same thing that I was describing about a frame Steinberg's uh experiment. It's the same idea. The time the time delay and the time advance Organ cancel each other. >> Have you spoken to Steinberg? >>

Uh no no not not not yet not not as of yet. Um so that's so you can see that things that I was worried about in graduate school um I I discovered that that there were actual answers to them which were not the answers that could be given at the time and that they've really tied in w with everything that I've been doing and I've really followed my nose in a way. Um I wanted to get Control of the conform of the cosmological constant. I went to conformal symmetry. I solved the theory. I found I

could get rid of dark matter. I applied it to the accelerating universe. I found that I could um I I I could fit it without fine-tuning. I applied it to the early universe and found that I had no horizonal flatness problem. And then when I quantized it, I found that it was a PT theory, Which again I didn't know at the time I started working on it. And all of this is just it's sort of flowed automatically from from one step to the next. Do you have any idea as to how the Higs acquires its

dynamical mass? >> Oh yes. Um okay. When you look at electronamics with uh a fixed point then you get scale invariance with anomalous dimensions. And so the firm propagator scales as p ^ 2 to a power. That's what anomalous Dimensions mean. You get scale in variance with a with a power. If that power is negative, then you can show that the bare mass is zero. That's the same condition. But as you make the power more negative, you make the theory more convergent in the ultraviolet, but you at the same time make it more divergent in

the infrared. And when it comes down by one whole unit, the infrared divergences become so Severe that they force you into a different Hilbert space and that's that's the mechanism and then the electron mass is dynamical. So if you like when I first started thinking about this you know there's this idea that goes back to point of how do you stabilize an elect um an electron if it's if its energy if MC² is E^2 over R namely if itself energy is entire mass and point introduced the point array stresses Those stresses are coming from the

vacuum so in a sense this This dynamical theory that I described to you is really a theory of of point stresses and then and then and then the mass the massive electron is stabilized. Now what about when it comes to dark matter the evidence for it isn't just rotation curves >> of course. Of course >> so what about say collisions galaxy Collisions or >> okay >> other structure formations or cluster dynamics etc or lensing? Okay, the fluctuation theory that I'm working on will address the anisotropy in the CMBB and will address a large scale structure.

Whether it'll do it correctly remains to be seen. However, the issue of gravitational lensing is much more subtle. You see, you just take the lensing formula in a standard textbook Like like Weineberg's book that presupposes that the light is coming in from an asmtotically flat geometry because that's a standard Schwarz geometric. Now if I have a linear potential light is not coming in from an asmtoically flat geometry and the whole calculation has to be revised and there's a spirited discussion in the literature as to what is the correct gravitational lensing formula Um when you have

a non-asintoic geometry. Now you might say, "Oh, but what about the sun? How how do how do we get gravitational bending by the sun?" And the answer is we never measure gravitational bending by the sun. What we do is we measure the light without the sun and then 6 months later the light passes the sun. We're measuring the difference. >> Uhhuh. And in the difference the background drops out. So we're not measuring the trajectory of a photon as it goes by the sun. We're measuring the change in the trajectory as it goes by the sun.

Those sounds the same. Can you tease out the difference for me, please? Okay. The calculation of the bending of light by the sun is the bending in the local geometry. And it's you're doing two measurements. One with the sun in the way and the other with the sun not in the way. And you're measuring the difference. >> Mhm. >> The difference. It didn't matter what was going on away from the sun. That's the same in both cases. So it drops out in the difference. So the bending by the sun is a difference experiment. Lensing by

a galaxy due to a distant quaison the light coming by. It's it's you're seeing the entire trajectory. >> Okay? >> In other words, you can't do the experiment with the with with the Cluster of galaxies out of the way. So it's not a difference and that's why it's that's that's why it's different and that's why it's become so so very complicated. Um, and I'm I'm fully aware of that. Uh, yes, there's there's many more things I I I still have to do. Let me ask you to wrap up a personal question if you don't mind.

>> Sure. >> I'm sure as you're developing this Theory, as you've have developed this along with your collaborators over the past couple decades. >> Yeah. >> That you've encountered criticisms of various sorts. Like you mentioned a ghost and what about this and what about that and what about like some that I've thrown at you today. But I'm also curious if you've received more than just criticism, more like derision that what are you doing? You're a fool for Working on this. This is obviously down the wrong path or something like that. >> Well, maybe. >> Well,

I don't know if I'll even put this part in, but I noticed from running this channel that people who have their own theory, they tend to look down at other theories. It's not just mere critique at at some sort of scientific level. >> Yes, I I get a lot of resistance. Let me put it this way. Everything I've written Eventually gets published, but it puts a demand on my nervous system to get it published. You see, I mean, in bad enough that I'm working on an alternate gravity theory, but I've also given up hermiticity. So,

so I'm getting I'm getting a I'm I'm getting flack from every direction. But the one thing that saves me is tenure. Tenure allows you to work on any problem you want. Yeah. But I I've only I've followed this theory because in I tried To describe it to you in this interview. I've just followed the steps one after the other and that's where it's led me. It's not that I've I've never invented anything. I've I've just taken the theory and solved it to see what it looks like. And I mean, I can tell you now, but

these some of these things take years to figure through, but once you figure out it's very simple to to describe it, but it's I've not gone off in different directions. And Look, I mean, you start out with the standard theory. It doesn't work for galaxies, so you invent dark matter. It doesn't work for cosmology. You invent dark energy. It doesn't work for quantum theory, so you invent string theory. But you keep on patching it up. I haven't done that. I've just taken the theory and I've solved it. And and it'll take me wherever it'll take

me. And I have no no control over that. And then I I fit data. I mean, I shouldn't be fitting all This data if I'm so completely on on the wrong track. The reason I laughed is just because I thought you were going to say, "What saved me, Kurt?" And you were going to say something ethereal, and you're going to say, "The Dax's confidence saved me," or "The Llassian saved me over the pluson." Yeah. >> Or, "My wife saved me." Or something like that. Then he says something extremely practical. >> That's not true. >> Tenure.

>> That's not so true. Tenure is is the thing. I mean, it's >> it gives you the freedom to work on things that your colleagues don't approve of. Whereas if you're not tenured and you're seeking tenure, you have to work on mainstream physics. You you will never get hired if you don't work on mainstream physics. But Once you get hired, once you get tenure, you're free to work on non- mainstream physics. Now, I would not choose to work on non- mainstream physics if I didn't think the mainstream physics was I wouldn't choose to work on

non- mainstream physics. I didn't think the mainstream physics were getting nowhere. I mean, you know, you you have the dark matter problem, the dark energy problem, the quantum gravity problem, and you just you proceed as as though you can Ignore them. And I don't understand I I don't understand why people would do that. But I'll I'll tell you I I'll tell you the difficulty that I have and it's this. I gave a talk once. I I give talks to to community groups. I get gave a talk to a middle school some middle school children and

I asked them who knows the name of a scientist. Every hand shot up and they all said Einstein. And then I said who knows the name of Another scientist? Total silence. And that's that's the danger of of challenging Einstein. >> But I'm not challenging him. I'm I'm taking what he's done and I'm looking at where there are issues that could still be addressed. I don't mind if you don't like what I've done, but you've still got to address the issues I've raised. Professor, what advice do you have for students who are watching? >> Uh, Well,

don't trust experts. You know, Vner was once asked, "What's the definition of an expert?" And he said, "It's the person who's made the most mistakes in the field." And I think that's true. I mean, physics is we we make mistakes. And and don't be worried if you make mistakes. Trust your own judgment. Uh I also tell everybody um don't work on conformal gravity until you get Tenure. >> I think that's the that's the more practical advice there. again, >> practical advice. But the um by the way, I say that a bit cheekily. I do hope

people look into your theory and I'm going to place many of your papers on screen and in the description so the researchers who are watching can inform themselves. >> Yes. Okay. Um what I wanted to say was while we have this grand dark matter Edifice there's an undercurrent of dissatisfaction with it. I mean it's it's been going on now for 40 years and they they keep on not finding anything and uh you know nobody's given up yet. I mean there are no there are no time limits in physics. It may take a hundred years to

find it. you know that's the way the physics works but nonetheless I Think that people are dissatisfied but not ready to not ready to jump and if and if this goes on um I mean John Mford and myself um Monty Mgram are uh you know we're we're really out in left field and uh whether people would ever join bonus remains to be seen. But we're fairly it's not just that we're against dark matter. We have developed theories to deal with the absence of dark and that's the that's it's not just Words. I mean and you

know the standard people have have really got to come up with with with one of these formulas either the MOG or myself or the man formula and derive it from lander CDM. You can't just say that, you know, what we're doing is nonsense. I'm saying fine, but the data don't think so. And you know, physics, maybe I can give another answer to you. In the end, physics is an experimental science. And I've always said that the number of Wonderful mathematical theories exceeds the number of physically relevant theories by n minus one. So don't be too

seduced by the mathematics. You've got to keep data in mind. I I when I did my PhD, I did did it with um phenomenologist named Oria or it was a vitamin institute in Israel and that's what I learned from him. Always keep an eye on data. Nature will tell you what to do. It's you you should not you can't proceed Without nature. Let let me explain. You take the rotation group and and it's designed for integer spin. Well, it has half in half integer spin representations, but that doesn't mean they exist. They may exist, they

may not exist. The rotation group alone will not force them to exist. Uhhuh. You see what does force them to exist by the way is the conformal group. Uh because then four component firmians Becomes the fundamental representation. So mathematics will take you so far and that's that's the language of physics. That's that's what we do. But you've always we should never lose sight of data. And that's what I tell my students is never lose sight of data. Nature will keep you nature will keep you honest. >> Professor, thank you for spending so so much time

with me. >> And I hope you enjoyed it and I know the audience enjoyed it. >> It was and is an honor. Thank you. Thank you very much for inviting me and uh for giving me an a chance to explain what I'm doing. It's basically my entire career. I've been doing this since since 1972. Hi there, Kurt here. If you'd like more content from Theories of Everything and the very best listening experience, then be sure to check out my Substack at Curtjongle.org. Some of the top perks are that every week you get brand new episodes

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