STFC-RAL-CR03 R61: Thank you very much for joining me.
STFC-RAL-CR03 R61: Very nice to be back at, Rutherford Appleton Laboratory again after 20 years or so.
STFC-RAL-CR03 R61: It's great to see a couple of familiar faces, and a bunch of new ones as well, so thanks for everyone coming. I've got a good postdoc, spent about 10 years all together.
STFC-RAL-CR03 R61: I was working in experiments, and so I'll explain a bit about how I transitioned to working to this more, theoretical project, as I go along. I shall explain the title before I start. So the question mark on unification is partly because everybody thinks it's an important question. You can always just clear the world as a series of models.
STFC-RAL-CR03 R61: that we apply to different aspects. I think we've seen experiments.
STFC-RAL-CR03 R61: Others believe that it should be some unified theory, an all-embracing description of all about personal observations. Also, if you believe, in some form, you need to be taking this question, what is it apply to? What does it mean?
STFC-RAL-CR03 R61: And then whether it's possible or not, if you've done something simple, it's going to be too complicated, something beyond us. Second part of the title, what's got a kind of double meaning. It's kind of my answer to the first part, in that it is a matter of time, it's suggested something simple, something attainable, and the key will be
STFC-RAL-CR03 R61: Something in the nature of time itself will be the key to this kind of,
STFC-RAL-CR03 R61: communication, program I'll describe. So, during the talk, I was trying to make this case, rather than building
STFC-RAL-CR03 R61: Unification, based on a particular form of matter. We're actually learning the space, but focus on the form of time instead.
STFC-RAL-CR03 R61: So let me just, first of all say what I mean by the invitation to get everyone on the same page. So I'm thinking of something that's quite simple, something unique, could be a simple entity or concept, or math structure. If it is a simple, entity or concept that you have, because of description to develop into a form, theory.
STFC-RAL-CR03 R61: Unless the boundaries as an infrastructure to be able to account for
STFC-RAL-CR03 R61: I'm thinking three generations of electrons and quarks with the gauge structure, and ideally, ventral masses and couplings.
STFC-RAL-CR03 R61: 20 or 35 parameters we measure.
STFC-RAL-CR03 R61: External model and neutrino acid remixing as well.
STFC-RAL-CR03 R61: And also account for unifying quantum theory gravity. It's a unified framework that works for gravity and quantum theory.
STFC-RAL-CR03 R61: And ideally, we'd like to incorporate something about cosmology to account velocity observations, so some dark sets and dark matter, dark energy.
STFC-RAL-CR03 R61: And the universe, and maybe put it all together in kind of a big picture.
STFC-RAL-CR03 R61: with, questions of the origins in general coming before the Big Bang.
STFC-RAL-CR03 R61: So people often work on these three things independently.
STFC-RAL-CR03 R61: And there can be unification programs, which are based more on just the unified series, for example, or just amalgamating quantum series of gravity, or even a unified dark sector. But if we're looking for an overall unified program.
STFC-RAL-CR03 R61: There are also questions in each of these things we might want to understand better, like, for example, the, things of neutrino sector in the model, or problems in quantum mechanics, like the measurement problem, or making singularities.
STFC-RAL-CR03 R61: And especially things like tensions and cosmological models. There are things in these existing, areas that we'd like to understand more. And one area which, like, to me, is kind of neglected in these kind of outlines of what we're looking for is unification, is kind of the nature of, unification itself.
STFC-RAL-CR03 R61: Kind of questioning the foundations of unification, how we go about constructing a symmetry, while the table just applies similar kind of ideas, like supersymmetry and retrspatial dimensions.
STFC-RAL-CR03 R61: So this slide was intended to kind of, transit to an outline of the talk, which kind of more or less does, but I won't talk about all of these things in the context of this new approach. But I will talk a lot about using time, rather than matter.
STFC-RAL-CR03 R61: or space, like, heterdimensional space, it's a basic entity. And this takes a mathematical form of generalizing property.
STFC-RAL-CR03 R61: I'll describe how it very directly connects the same mathematical structures, which are very unsuitable to describing some of the model-like structures.
STFC-RAL-CR03 R61: I'll then lead up to, introducing how it connects with a framework for unifying content theory with gravity. I won't go into detail on that in this talk, and I'll also lead up to describing
STFC-RAL-CR03 R61: And briefly describe how it,
STFC-RAL-CR03 R61: These two actually candidates for dark matter and dark energy, and early universe, structure formation, and basically when I get there, I'll kind of…
STFC-RAL-CR03 R61: Get to the, end of the summary.
STFC-RAL-CR03 R61: And so I'll mainly talk about the first point, at the top, and I'll keep coming back to this basic idea.
STFC-RAL-CR03 R61: And then I'll link it menu with standard models, and with cosmology, and then a few things about, quantum gravity.
STFC-RAL-CR03 R61: As well in between. And I will keep coming back to the basic idea, but let me just introduce this basic idea, and I'll take a kind of, historical run-up to this idea. In terms of relations between space, time, and matter, in theories that we're familiar with.
STFC-RAL-CR03 R61: So going back to classical physics, we complete, absolute time and space as two independent things, like stage, on which we include matter. In case of classical physics, in terms of particles, comparable, I mean, solid barriers. And then the special relativity.
STFC-RAL-CR03 R61: introduces property time, where these are now… these are the general finite kind of intervals of space and time, and they come together in this quadratic form with a red symmetry, which leaves invariant, property time from the left-hand side.
STFC-RAL-CR03 R61: So now we have the spacetime formula, and in this, arena.
STFC-RAL-CR03 R61: Matter can be particles and fields. In fact, special relativity in 1905 was motivated as a more consistent framework for Maxwell's equations which transformed in a covariant manner between different, advanced frames.
STFC-RAL-CR03 R61: Now, speaking with this,
STFC-RAL-CR03 R61: this, this Lorentz form for, proper time. In general relativity, this now only applies at the local level. So in general relativity, in the larger space-time, there's a curved spacetime structure, so locally, we still have this, four-dimensional space-time Lorentz form.
STFC-RAL-CR03 R61: And that is still in the form of articles and, fields. And then going to extraspatial dimensions, and these additional components right here onto the right-hand side.
STFC-RAL-CR03 R61: And the idea is that, in this automatic spacetime form, now the Lorentz symmetry is extended to some sort of n-dimensional spacetime, so the SO1, and this here is an n-dimensional spacetime symmetry. The idea of having extra spatial dimensions
STFC-RAL-CR03 R61: is that matter will somehow be associated with these extra components, or their symmetries, or the metric geometry. Somehow these extra components will give us the source of matter in this original report of spacetime.
STFC-RAL-CR03 R61: Now, going from spatial relativity… relativity to extraspatial dimensions.
STFC-RAL-CR03 R61: The Lorentz metric, and I'll often write this expression here for profit time in the summary form using this Lorentz metric down here. They go into extraspatial dimensions rather than summing over 4 components, and now some over n components, so the metric is kind of extended out.
STFC-RAL-CR03 R61: So briefly, the idea of generalizing proper time
STFC-RAL-CR03 R61: is not to take this, quadratic form with extra components, but rather to generalize further and go to a power of P. It's not just quadratic, but qubit, quartic, higher order forms.
STFC-RAL-CR03 R61: This will be our generalized form for proper time.
STFC-RAL-CR03 R61: These alpha coefficients are just generalizing these metric plus and minus ones and zeros, but now it's in a general non-combatic form, and we're, again, summing over n components, but now, as I say, going to a power of P.
STFC-RAL-CR03 R61: And, this will have a larger symmetry. It won't be a Lorentz-type symmetry, it'll be a larger symmetry, but it will still embed four-dimensional space-time Lorentz symmetry, so we'll still be able to pull out a four-dimensional local space-time part.
STFC-RAL-CR03 R61: Now, not as added to our extraspatial dimensions, but as a kind of a factor in what this turn up here. So there'd be this quadrificial spacetime box, the quadratic part, would be multiplied by some other delta X's that make this up to a piece order.
STFC-RAL-CR03 R61: polynomial, and there'll be the extra bits, the further connect with all the parts that make up this whole expression here. So we're still pulling out the point range of spacetime.
STFC-RAL-CR03 R61: But the extra components now, make up the basis for matter, have this different kind of form. So we're going beyond four-dimensional spacetime, but unlike actual spatial dimensions, we're allowing for us beyond just quadratic order.
STFC-RAL-CR03 R61: When we pull out the Lorentz symmetry, this will break the symmetry, the full symmetry down to the Lorentz, and this will leave behind any internal gauge symmetry for the theory of the physics. Okay, so let me just simplify this slide, and let me just say a little bit about how and why, as an experimentalist, I started to think about this.
STFC-RAL-CR03 R61: So, when you're an experimentalist, you hear quite a lot… from the 90s, you heard a lot about series of extraspatial dimensions, and we know about Cluser-Kline theory with five-dimensional space-time.
STFC-RAL-CR03 R61: And then we also care about spend theory, which works in 10 or 11 or 26 dimensions, but when you're a naive experimentist thinking about this, you think, why would you have 10 or 11, 26? If you're going to add it to the spatial dimensions, why do you stop?
STFC-RAL-CR03 R61: why not keep adding them until you have an infinite number? So that was the original kind of thought on this.
STFC-RAL-CR03 R61: And any kind of infinity is quite the dizzying thought. So if you imagine one spatial dimension, you've got the right angles, and then a third, and you can't picture a fourth, but you get the idea, you've got right angles again. You can keep going in your mind, having all these extra spatial dimensions, but…
STFC-RAL-CR03 R61: trying to conceivable infinity, it's like traveling in a rocket infinite distance across space. You can imagine going beyond the solar system, beyond the galaxy, the edge of the visible universe, but going at an infinite distance, even when you've gone
STFC-RAL-CR03 R61: A million times.
STFC-RAL-CR03 R61: further than the visible universe, having got started and going to infinity. And here, in adding on extra spatial dimensions, you're adding infinity, but this list would go on across the screen to infinity. However, in the case of adding extra spatial dimensions, when this thing
STFC-RAL-CR03 R61: n goes to infinity, this is still a symmetry. There's a symmetry because it leaves this little thing on the left-hand side invariant. So this thing is still invariant, even when you go to a very large number of spatial
STFC-RAL-CR03 R61: dimensions. So the same way in our four-dimensional space-time, we're drifting through our four-dimensional space-time. The time we measure is just this time on the left-hand side, this thing that clocks measure is proper time, time experience. So even in an infinite-dimensional space.
STFC-RAL-CR03 R61: despite this busy and prospecting of all these extra dimensions, you can somehow hang onto this idea of proper time. This is just a real number.
STFC-RAL-CR03 R61: to clinging onto this real number. We can add it, as we do, say, in Newtonian physics, where we just add it as an absolute parameter, but we're only writing it in a quadratic form in relativity, which is kind of a strange thing to do at the time already, to write it in a quadratic form. But it's just a real number, so we can write it as a cubic or a quarter, any one we want to, as we do down here.
STFC-RAL-CR03 R61: On the right-hand side, there's no reason why matter should be quadratic, because if nothing quadratic about matter, that is free to have any kind of mathematical structure here. The only problem that needs to be quadratic is the space turns up. We can still pull that out.
STFC-RAL-CR03 R61: So that's the kind of argument
STFC-RAL-CR03 R61: for losing this unnecessarily, restrictive assumption of linear quantifiable form in spatial dimensions. This is possibly a bit unfamiliar. On the next slide, I'll give an example of a cubic form for profit time, and I'll say how very directly
STFC-RAL-CR03 R61: When you drop this assumption and go to this higher order form, it's just directly leads to structures which resemble standard model type structures.
STFC-RAL-CR03 R61: Okay, so let me just, summarize a little bit this. So basically, we think of going from classical physics to special relativity when an equal sign
STFC-RAL-CR03 R61: in equations of physics can carry a lot of weight sometimes. And really, when we think of this in relativity, we might think of it as going from right to left, because we know about coordinates already, and you put them together in the left-hand side. Here, prior to this thought about infinite dimensional space-time clinging onto this on the left-hand side, we're focusing more
STFC-RAL-CR03 R61: I'm thinking of this as an expression for this time interval, so we're going all the other way from left to right, thinking as an expression for time.
STFC-RAL-CR03 R61: So just to summarize this, in classical physics, space, time, and matter are three independent things.
STFC-RAL-CR03 R61: Special relativity, spacetime is now lumped together to unify in the consciously spacetime matter, particles, and fields in that space-time. In neuronativity, in the extended spacetime, we've got, Einstein-Built equation, which links to space-time geometry with dependence and matter. So you already have this kind of overlap between spacetime and matter.
STFC-RAL-CR03 R61: And the space-time geometry is now describing the gravitational field.
STFC-RAL-CR03 R61: So the motivation originally for Pluser Collide was that if space-time geometry is describing a gravitational field, if we generalize that geometry, maybe we can incorporate the magnetic field. The ultimate aim, extraspatial dimension, is to incorporate ZASTA into our space-time structure.
STFC-RAL-CR03 R61: And this final step here is to not stop space-time, but to shift focus the left-hand side and to start with time.
STFC-RAL-CR03 R61: So we're dragging out the current space and matter out of time, getting this more unifying kind of picture. There's a kind of a progression here.
STFC-RAL-CR03 R61: There's a further step along this trajectory. So we're kind of examining this motivation. We don't need a hydraptic form for matter when we go… when we're all making our space-time form.
STFC-RAL-CR03 R61: As I've tried to argue, simply more unique, more unifying. It's more conservative, starting with time. It's something we're very familiar with, it's very fundamental in physics. All the equations of physics require engine time parameter to do dynamics.
STFC-RAL-CR03 R61: It's also more direct. The direct symmetry breaking properties will give us the properties of physics.
STFC-RAL-CR03 R61: So, it's possibly the simplest unifying relation between space, time, and matter. This is the kind of starting kind of motivation for looking at this approach. So, let me describe
STFC-RAL-CR03 R61: Yes, how we get to, say, a quadratic… say, a cubic form from a quadratic form.
STFC-RAL-CR03 R61: Right, so we want to get to something higher order powers for, probably time from this quadratic structure. So, the next two slides are possibly the most technical mathematically, but they're not needed in detail for the rest of the talk. I just want to show a little bit about how to build a theory from this structure.
STFC-RAL-CR03 R61: In this quadratic form, In a well-known way, can be written as a determinant of a 2x2 matrix.
STFC-RAL-CR03 R61: to these, 2x3 constant submission matrices. If you write out the determinant, you get this quadratic form here, and the right symmetry is now replaced by… well, it becomes this,
STFC-RAL-CR03 R61: 2x2 unit determinate convex matrices are multiplying to this matrix in a certain way that preserves the determinant. So once we've got a determinant form.
STFC-RAL-CR03 R61: I can recognize that 2x2 determinant embeds in a 3x3
STFC-RAL-CR03 R61: It makes it so that, in a very, kind of, standard way.
STFC-RAL-CR03 R61: I can embed the 2x2 part in the top here, and now in the 3x3 form, cubic form for proper time, these are now matrices of 3x3 complex emission matrices, and it simply goes from SL2C to SL3C. And when we write out,
STFC-RAL-CR03 R61: a kind of standard co-factor expansion of a 3x3 matrix. For example, get the determinant of this top part multiplied by this delta X8 here, and then we get these other cross terms, which are the other kind of parts of the cofactor expansion.
STFC-RAL-CR03 R61: The way I've written this is what I have on the first 30th slide. We're having generalized property type in general, we're pulling out a quadratic part here, four-dimensional spacetime.
STFC-RAL-CR03 R61: I did now a factor in one term given this single quantitative delta X8, and the various of the,
STFC-RAL-CR03 R61: cross terms at the end. This is an example of how we can pull out a quadratic form of spacetime, say, a cubic form. And the question will be, we're using this coordinator part here as our spacetime, and these extra bits would be matter, and what are these kind of matter components look like? So in this case.
STFC-RAL-CR03 R61: They start off with 9 components, which is full symmetry. When we pull out four of them for our external spacetime, this will break the symmetry, and we find that we get an SL2 symmetry, which is just our red symmetry we started with, and we now pull out an internal leftover part, which is a U1 symmetry, just find it in the mathematics.
STFC-RAL-CR03 R61: So if we look at this, this cubic form, this block form like this.
STFC-RAL-CR03 R61: So these are these delta X4 external components. This is a two-component complex, like,
STFC-RAL-CR03 R61: geometric vector over complex numbers is this side, now delta X8. And these will be our, kind of, basis for matter. These are the kind of extra bits that we shave off in pulling out our, kind of, four-dimensional spacetime part. If you look at how these things transform under this broken symmetry.
STFC-RAL-CR03 R61: And this is the original, kind of, external vector. Delta X80 is just a neutral scalar, and this doublet here, this psi.
STFC-RAL-CR03 R61: comes in here. This transforms as a left or right-handed bioscinner of unit charge. This is always already a little bit encouraging in terms of standard model structures, because if you look at the standard model, we do have things that transform under electromagnetic or hypercharged U1-type symmetries, and we get Dirac spinners of,
STFC-RAL-CR03 R61: large leptons and quarks, which are made up of left and right particles. So we already get at least a tiny piece, and a non-like structure when we do this kind of cubic mineralization a couple of times.
STFC-RAL-CR03 R61: The question will be that when we go to hire, more components.
STFC-RAL-CR03 R61: higher order forms for proper time, will this start to look more like the standard model, or less like the standard model? So I'll show the same table in a couple of slides' time for a 56-component form, rather than a 9-component form for proper time, and the question will be whether it starts to look more like a standard model. How to get these 56 components
STFC-RAL-CR03 R61: It's quite technical, but I'll summarize it here. So… We've got problem.
STFC-RAL-CR03 R61: We went from 2x2 matrix to 3x3. We can also augment complex numbers by replacing them with, optolians, and don't worry if you're not familiar with these, I'll just briefly say they're a direct generalization of complex numbers with seven imaginary units, so a complex number is a real and imaginary part.
STFC-RAL-CR03 R61: Returnians, which might be familiar, have 3 imaginary units, and Nocturnians have 7 imaginary units.
STFC-RAL-CR03 R61: And these don't have too many applications in physics, which is why they might not be quite so familiar.
STFC-RAL-CR03 R61: But they do still have a norm that you can define under by multiplying one into its conjugate, which is where you negate all the imaginary parts and have an inverse.
STFC-RAL-CR03 R61: And this, this norm is, is,
STFC-RAL-CR03 R61: observed by multiplication, as it is for complex numbers, which means you can describe symmetry transformations with these Octonians. You have to be careful, though, because in general, they're not associative. So when you multiply a string of them together, it matters where you put the brackets.
STFC-RAL-CR03 R61: This is unlike, for example, a matrix algebra, where you can… you could re-bracket things in different ways.
STFC-RAL-CR03 R61: But even despite small associativity, you can still form this determinant structure for a cubic form for proper time, and have this SL3O, now, SL3O action on them. And it turned out that this symmetry is equivalent to E6, and this E6
STFC-RAL-CR03 R61: is one of what's called the five exceptional lead groups. So this, this gives us a collection of these six.
STFC-RAL-CR03 R61: Again, don't worry about the technicalities, I'll summarize why this is relevant in a moment.
STFC-RAL-CR03 R61: It turns out, another step up in technicality, that this E6 symmetry, or this cubic form for proper time, embeds directly in an E7 symmetry acting on a 56, this is the 56 I mentioned earlier, on the quartic form for proper time in this thing called the Freuden participle system, which is just the technical name.
STFC-RAL-CR03 R61: But this, this object, which now includes two copies of this 3x3 Optonian emission agencies, and a couple of other real components.
STFC-RAL-CR03 R61: The point I want to make is that by using this generalization from quadratic to cubic and quartic proper time, we get this direct connection with exceptional lead groups here, E6 and E7. There's been no
STFC-RAL-CR03 R61: It's the 70s that, if you look at ground unified theories, starting with SU5 in 1974, SO10, there are also models in the 1970s with E6 and E7 out for E8. But it's well known that E6 and E7, E8 have well-known connecting with Sandra model.
STFC-RAL-CR03 R61: from the signature-breaking structures, as do the Octonians in more recent studies. So this mathematical structure generalizing proper time directly connects the mathematical structures which are known to the Octonians.
STFC-RAL-CR03 R61: A slight difference is, for Grand Unified Series, they're just internal cinches only, whereas here we're pulling out filler ed scripts, we've also got the… the sensory bracing pattern is different.
STFC-RAL-CR03 R61: But still, you might expect to see something that resembles a standard model. So I'm basically just going to show you the result now, what happens for E7. So on the previous slide, I showed it for this 9-component form, where these two components here transformed as a vial, spinner.
STFC-RAL-CR03 R61: The question is now, we're now augmenting this to these 56 components, what does it look like under the symmetry break?
STFC-RAL-CR03 R61: Another note, but this quartic form for proper time on these 56 components.
STFC-RAL-CR03 R61: We're going to again pull out just our four constraints from external space-time. Now we find, as well as the Lorentz symmetry, we've also got, as well as our U1 internal symmetry, we've also pulled out an SU3 symmetry.
STFC-RAL-CR03 R61: When we look at how these 56 components collectively transform under this broken symmetry, we get a table that looks like this. This is our original four components, this is our external vector.
STFC-RAL-CR03 R61: But over the other… out of the other 52 components, we find that there are Iraq-like, spinners transforming as singlets and triplets into the SU3, and writing down charge magnitude, we get this, charge… fractional charge structure like this. So if we're looking for structures that look like standard models, we see a resemblance here
STFC-RAL-CR03 R61: with electron-like and de-quark-like structures, written in U-quarks and, neutrinos in inverted commas, because they don't have the right moment spin structure. But this table is very rich in kind of model-like structure. We get things like SU3,
STFC-RAL-CR03 R61: Thinglets and triplets and factorial charges for these reds and spin structures.
STFC-RAL-CR03 R61: And there are also details of electroweak symmetry breaking that are written in this table. So, these components here behave a lot like Higgs components if you take the scale and magnitude of the external flow vector.
STFC-RAL-CR03 R61: And that's because if we cover up… if we cover up this range, and don't ignore it for a moment, we can construct something like a brand unified theory, just based on the internal symmetry part, and there we can add to this SU3, kind of internal SU2 plus U1,
STFC-RAL-CR03 R61: And if we look at the kind of electroweak symmetry breaking that's implied by this, then it turns out that these components behave a little bit like, the Hinks in a fandom model, to break the symmetry down to this U1 that we see here. But we can't do this at the same time as having Lorentz symmetry. Things are kind of scrunched up.
STFC-RAL-CR03 R61: a little bit too tightly, but that's not really the point. The point is that,
STFC-RAL-CR03 R61: These symmetry breaking structures are extremely rich in Standard Model-like structures, coming directly from generalizing proper time through to this quarticope.
STFC-RAL-CR03 R61: order.
STFC-RAL-CR03 R61: So this is incomplete, and there are disturbances, but these things do come out very directly, much more so than with exospatial dimensions.
STFC-RAL-CR03 R61: So, we need to go to a higher order for generalized copper time.
STFC-RAL-CR03 R61: And in particular, we really need,
STFC-RAL-CR03 R61: These false winter structures are fully electroweak theory and three generations, and this leads to a prediction that something like E8 has the largest exceptional lead group on at least a quintic form, possibly of optic form, for the source on the model. So, that's a kind of prediction of the theory.
STFC-RAL-CR03 R61: Just to mention that, possible complaints about this are that this isn't exactly one generation, it doesn't quite work. But I would say that if there is a fuller symmetry that gives you the full three-generation picture, you fall out a fraction of it. You don't necessarily expect to find one pristine generation. The one thing, and there's no such thing as a pristine generation.
STFC-RAL-CR03 R61: In nature, because of mixing between the neutrinos and between the quarks, so… Pulling out one to…
STFC-RAL-CR03 R61: action of this. You would expect to find some model structures, but not pristine generation, so this is quite… I think this is a problem, this doesn't look exactly like one generation. Another thing is that E8 doesn't work when you do the basic,
STFC-RAL-CR03 R61: the group analysis, but this is a kind of Octonian construction, which has its non-associative property. And the third possible complaint is that we're putting them together in a unifying symmetry with the Lorentz group.
STFC-RAL-CR03 R61: Now, if you put your Lorentz group and gauge groups together in a larger group and call out a symmetry of your physics, then by the common Mandela theorem, you get trivial Staff emergencies, and that's really what we see. But here, we're starting with the larger symmetry, and we have to break this symmetry, absolutely, to pull out our quadimetric spacetime. It's the broken structure.
STFC-RAL-CR03 R61: which is the century of the physics. I've written these just for… Completeness in slides,
STFC-RAL-CR03 R61: these three points. Just mention that for E8, yes,
STFC-RAL-CR03 R61: when you understand the group theory, thing, then there's, an associativity axiom for your group composition, which is not satisfied by the Optonians. This is why Optonians can give you non-sided representations, and an E8 is a complicated structure, even without doing this. Recently, my former Rutherford and Oxford colleagues,
STFC-RAL-CR03 R61: Ben and Claire have been doing some work on an E8 structure. It's a very complicated business, trying to find this E8 optic structure. It's a bit like a kind of a giant Rubik's Cube-type puzzle, because it's not just you can build this thing up in stages, it's both algebraic facets that all have to come together at the same time.
STFC-RAL-CR03 R61: I'm very pleased somebody's working under that. But yeah, so that's the kind of… but the difficulties of this, I think, makes the first… what to me is the first prediction of the theory non-trivial, and that is that there is some kind of Octonian-based E8 symmetry to complete the, the Spartan model scope check.
STFC-RAL-CR03 R61: Physics predictions are a bit harder to come by for the Beyond the standard model, because you really need to see each… what I should mention is that most theories have a Beyond Standard Model prediction, usually by adding something on to the standard model, and taking the standard model as existing, and then adding on some fields, and so on. Here we're trying to build things up from the most elementary level.
STFC-RAL-CR03 R61: and reconstruct the standard model, and then, in turn, see what comes out beyond that. So, but we can look ahead to see where that Beyond Standard Model Physics might be.
STFC-RAL-CR03 R61: Certainly E8 would be big enough for there to be new gauge symmetries, or new states in the symmetry breaking, but already an E7 is a basis for left-right asymmetry. I'll explain kind of a cartoon form in these slides.
STFC-RAL-CR03 R61: So, E7… so E6 is only 27 components. It's even more squashed up than the E7.
STFC-RAL-CR03 R61: So, one of the big puzzles with E6 was that the place where you'd like to put the neutrinos in the components was the same place where you'd like to put the Higgs, the big puzzled for a while. Then you go into E7,
STFC-RAL-CR03 R61: This had the same 27 components, but also its complex conjugate, and that introduces left- and right-handed
STFC-RAL-CR03 R61: left and right-handed sectors, that opened up this thing into two separate sectors, so it priced apart this neutrino sector and the Higgs sector. And because the Higgs is associated with these external components, which we now have to insert either in the left or the right-handed sector, this breaks the left-right symmetry at this external level.
STFC-RAL-CR03 R61: So, the Higgs seems to be sitting there where you'd want to put the right-handed neutrino, which suggests that in projecting for what this E8 structure would look like, and
STFC-RAL-CR03 R61: It'll still have the Higgs somewhere in the right-handed neutrino sector. So there's a very strong suggestion here that the Higgs is going to be somehow a composite of right-handed neutrino states. I've drawn this in a deliberately kind of seesaw kind of fashion, with the Higgs kind of weighing down.
STFC-RAL-CR03 R61: on the right-hand neutrino side. So this was written in a paper a few years ago, comparing some models with two writing neutrinos. So, in principle, in those principles.
STFC-RAL-CR03 R61: This strongly suggests that the theory would only have two right in the neutrinos, and then the Higgs kind of somehow being composite of the third.
STFC-RAL-CR03 R61: So that's the area where new physics is quite likely coming from this, this approach. Okay, so let me move on a little bit. So this was about to send a model. How does gravity fit in with this?
STFC-RAL-CR03 R61: So, normally, in general relativity, we start off with, flat spacetime, and then we use this general metric structure to describe the gravitational field in the original spacetime. But we still have locally inertial reference frames, so there's the red symmetric here.
STFC-RAL-CR03 R61: So on the other side of this, this new theory, generalizing proper time, but it does so at the local level, and these are kind of complementary generalizations, globally or locally, but they still…
STFC-RAL-CR03 R61: idea of leaving proper time invariant is central to the theory. Here it's on the general coordinate transformations, and here it's on the general transformations of these… or local central transformations of these components.
STFC-RAL-CR03 R61: Where we pull out the Lorentz symmetry, the local,
STFC-RAL-CR03 R61: local inertial reference frame, and that leaves these residual components, which would be aromatic components, in spacetime. So, in the 1930s.
STFC-RAL-CR03 R61: I so famously expressed dissatisfaction with the field equation.
STFC-RAL-CR03 R61: Relating the geometry of a spacetime, which is this eigosine tensor, which is a function of derivatives in the metric, equating it with the energy-momentum tensor, same-time marble, the differential geometry on this side is perfectly known, whereas on the right-hand side.
STFC-RAL-CR03 R61: engine momentum is like a phenomenological model that we put in there to model what we know about Rapid. It was kind of dissatisfying. So his motivation for unified field theory was to try to incorporate the wood on the right-hand side by augmenting the geometry, in particular this metric tensor on the, on the left-hand side.
STFC-RAL-CR03 R61: The approach I have here is not to augment this geometry, but to augment this geometry, just the local geometry, and use these components as the basis for the kind of instrument on the right-hand side.
STFC-RAL-CR03 R61: There's a natural progression here from time as a linear thing to a quadratic form. It needs to be quadratic to include spacetime, because space… spatial geometry has a quadratic form, and then onto higher-order forms to include spacetime and also mass.
STFC-RAL-CR03 R61: And again, you can drop this assumption of being quadratic, because there's nothing quadratic about incorporating structures that matter. This is a kind of an aside.
STFC-RAL-CR03 R61: When you look at the standard model symmetry breaking structures here, as I mentioned, these external components are closely connected with the Higgs through the scalar field here. We can rearrange this equation
STFC-RAL-CR03 R61: And so the proper time has it scaling in these local corners because of this kind of, the fact that this is embedded in this larger structure. So we try to write this, geometry as close as we can
STFC-RAL-CR03 R61: And we have to keep that space type, then we get this small kind of perturbation.
STFC-RAL-CR03 R61: basically means that we can write it as a flat spacetime, but it's scaled by what we call this Higsby amount, this scaling of this four-dimensional space-time part.
STFC-RAL-CR03 R61: some variations of what we're calling the Higgs field, it's going to directly warp the local space-time geometry.
STFC-RAL-CR03 R61: And these are local, time dilation effects. So the Higgs is directly connected through the Einstein,
STFC-RAL-CR03 R61: Hence, so now with this warping of the geometry. And we're reading the Eisenh equation from left to right as being
STFC-RAL-CR03 R61: This is a property of matter that the spacetime is occurring.
STFC-RAL-CR03 R61: So that any kind of field that interacts with these external space-time Higgs components will perturb the geometry. There's a direct link here between the notion of mass and general relativity, which is connected to space-time, curvature, spacetime warping, and the Higgs field and standard model, but they're normally two separate things.
STFC-RAL-CR03 R61: Okay, just one side. So this fits in very well with general relativity. We can just kind of implant this graph, this locally here, but we're trying to build the theory here just from the basis in, time.
STFC-RAL-CR03 R61: So the question is, if we're starting with timing as a basic entity, how can we build a general relativistic framework, rather than just kind of wrapping it in locally? And this is the next kind of argument I'll try to make.
STFC-RAL-CR03 R61: It's kind of a pivotal point of the theory. So normally we express time just as this linear thing, where we add it in terms of intervals of time together, and these fit together in the real line, and we can put them anywhere in the real line. This is the way we normally think of time adding intervals together. But because we're thinking now that this is an expression for an interval of time.
STFC-RAL-CR03 R61: We can also write it as a quadratic form like this, over these four kind of intervals at time.
STFC-RAL-CR03 R61: And the point being that we are reading this as an expression for proper time, so we're pulling out these components from our interval of time.
STFC-RAL-CR03 R61: And because of this arithmetic quadratic structure, this has a geometric interpretation of former three-dimensional space. So we're kind of pulling out this form of three-dimensional space from the left-hand side, from our interval of time. And if we take the full four-dimensional inspection.
STFC-RAL-CR03 R61: This describes a four-dimensional space-time element, and that's because the Lorentz symmetries of this thing
STFC-RAL-CR03 R61: applying to these coordinates, passive coordinate transformations map out a light tone geometry. We can also think of this as active, Lorent transformations, that map out this kind of hyperbolic rotations for proper time in the forward, light cone.
STFC-RAL-CR03 R61: So this quadratic structure here, because of this minus sign, it preserves this causal structure of time, but we also pull out a spatial structure at the same time. So the point is that, when we have this, simple linear thing, these simple intervals here fit together in the line. When we go to this quadratic form over four components, these things
STFC-RAL-CR03 R61: fit together, in an patch of R4, so we can either think of that as,
STFC-RAL-CR03 R61: In the same way that these coordinate intervals here all fit together in the same line, we can think of each of these delta X's fitting together in their own kind of coordinate axis, and this element here can now be anywhere along this line. Similarly, along the other axes, we can think of this as being anywhere along
STFC-RAL-CR03 R61: this coordinate line. So these fit together in R4, and more generally, we can think of this as describing geometric elements of a local four-dimensional spacetime.
STFC-RAL-CR03 R61: which naturally fit together in this four-dimensional space-time structure, which is taken to a continuum limit. So, our flow of time itself, by taking out these local quadratic structure, can be expressed kind of intrinsically in four-dimensional spacetime form.
STFC-RAL-CR03 R61: which preserves its causal properties between events throughout. So, the pivotal argument here is that you can use this arithmetic substructure of time, which is just implicit in the nature of the continuum.
STFC-RAL-CR03 R61: To express time itself in a geometric form in which it flows, rather than kind of adding time to the geometry somehow.
STFC-RAL-CR03 R61: So any trajectory through this, this space-time now will satisfy this local, local form.
STFC-RAL-CR03 R61: So, this can be taken to an extended, region of arbitrary size.
STFC-RAL-CR03 R61: allowed to pull forward from space, time, the universe, any size we want it to be. And the point being is that the thing we normally think of as time, perhaps, as just these world lines, are really just elements within this overall structure. The whole thing is a temporal structure.
STFC-RAL-CR03 R61: And it contains, kind of, all, like, these are things that we, normally associate with tunnel. The whole thing is, kind of, I mean.
STFC-RAL-CR03 R61: Things like causal set theory also recognize this central causal property of spacetime. It's a central feature of what spacetime is.
STFC-RAL-CR03 R61: Now, because we're writing this as an expression for our proper time interval at the beginning, we can directly, generalize this now to generalize problem time, still pull out our spacetime part, but then locally we have these extra parts which we're taking as our matter content, and we follow those mathematical rules.
STFC-RAL-CR03 R61: to those E6 and E7 symmetries is directly linked to some of the model-like structures. But what we have now
STFC-RAL-CR03 R61: And then there's a quantum spacetime full of these kind of, this physics. So what we have is we've constructed this full quantum spacetime block, we've built it out of our elements of time, so it contains an everywhere
STFC-RAL-CR03 R61: flow of time underlying the evolution of the matter state. So the analogy is… so we're building this four-dimensional space-time block by pulling these cognitive time out of our flow of respect.
STFC-RAL-CR03 R61: By pulling out the geometry of space out of these components of time.
STFC-RAL-CR03 R61: So what we're kind of marrying together these kind of dynamic elements of flowing time with a block structure of the fundamental spacetime. There's a kind of analogy with a rivet here, where
STFC-RAL-CR03 R61: when you look at a river, you just see a solid block that doesn't sort of move, it's always there in the same kind of geological feature, but it's always flowing, it's containing the water. It's going to… it's dynamic, but it's also static. It's a bit similar, we're building now four-dimensional space-time out of the flow of time, essentially. And,
STFC-RAL-CR03 R61: Well, this is his key observation, is that the block is associated with no solution to no relativity.
STFC-RAL-CR03 R61: Whereas the dynamic flowing aspects are more to do with, evolution of states and quantum theory. This is one argument why this framework provides a useful setting for the problem of unifying gravity with quantum theory, because we're unifying together a block four-dimensional space-time structure, this underlying flow as well. Now, I'm not going to talk about
STFC-RAL-CR03 R61: I'm not going to talk about… there's this whole branch of the theory which deals with trying to amalgate in a relatively quantum theory. I'll just say, the approach taking is here is to take… normally people try to take quantum theory as a given thing and try to quantize gravity or quantize spacetime in some way.
STFC-RAL-CR03 R61: assume that there is quantum gravity, a quantization of gravity. Here, we're doing the opposite. The strategy is to take in relativity quite literally as one spacetime, and we're trying to, reformulate quantum theory within that.
STFC-RAL-CR03 R61: setting. So, I'm not going to go into the technicalities, I'll just mention it briefly in the next slides, but rather, I'll contrast this… this local construction with local elements. I'll make the contrast and make the point with theory of extraspatient dimensions.
STFC-RAL-CR03 R61: So, from four-dimensional space-time with general relativity.
STFC-RAL-CR03 R61: The usual approach with extraspatial dimensions is to construct a high-dimensional global space-time structure.
STFC-RAL-CR03 R61: So this is some complicated thing, it's hard to kind of picture, but it's… so it's this metric here that's basically, the gravitational field, which is kind of generalized in this high-dimensional spacetime form, and then we compactified spacetime. So there might be one extra compactified dimension, like Cusman Klein, in a five-dimensional spacetime.
STFC-RAL-CR03 R61: Or in string theory, it might be some more complicated idea of manifold type thing, something like that.
STFC-RAL-CR03 R61: That's the general strategy of retrospatial dimensions. Here, by contrast, we're coming in at this purely local level, pulling out our local inertial frame, this Lorentz metric here, and we're generalizing these components to a higher order for the proper time, pubic appropriate time.
STFC-RAL-CR03 R61: So this will be, yeah, powers P greater than 2, as well as more than four spacetime components. The rate of symmetry is augmented to this higher symmetry here, which is then broken.
STFC-RAL-CR03 R61: When we pull out the local events part, which kind of leaves a kind of residual gauge theory part, a gauge symmetry part, which would be the source of our local gauge symmetries of the theory.
STFC-RAL-CR03 R61: And all the residual matter components, so the residual components of this I'm pulling out fundamental spacetime part, they'll give us our matter components transforming under this broken symmetry.
STFC-RAL-CR03 R61: So these are alternative means of identifying matter by generalizing the metric. So extraspatial dimensions, we go to this high-dimensional space-time and then compact it by down. Here, we come straight in at the local level.
STFC-RAL-CR03 R61: And just analyze this local form and take off the extra components as our form of matter. So just as a comment, whenever the spatial dimension started with collusion and climb.
STFC-RAL-CR03 R61: over years ago, people were trying to unify the gravitational field with a classical electromagnetic field, an extended thing. So it kind of made sense to come in at this global structure, because you're looking… these are field components, and you want field components that describe your maximum field.
STFC-RAL-CR03 R61: Now, in particle physics, we're really modesting it in local particle interactions, local symmetry properties. We do think about, well, the local structure of matter, the local structure of,
STFC-RAL-CR03 R61: particles. So, whereas in extraspatial dimensions, this is a very indirect way of going to a high dimensional space and then compacted by now, it's a local structure. Here we just start as a local structure, and we stay there.
STFC-RAL-CR03 R61: to get these kind of properties and matter. So it's a more direct way of getting to these local matter properties. And we then build up this photon of spacetime from the local elements, and that geometry will depend upon the nature of these residual gauge symmetries and residual residual components. So we're building up the geometry
STFC-RAL-CR03 R61: the Einstein tensor as a function of matter fields and gauge fields, and that, again, will define our energy dimension on the right-hand side, reading this equation more from right to left. So, in contrast to extraspatial dimensions.
STFC-RAL-CR03 R61: We begin with a global spacetime and compactify down.
STFC-RAL-CR03 R61: There's typically a huge ambiguity in meter types, depending on how you form these claviar menopause and catapactified down. So you might end up with a rather bad form of uniqueness, have to appeal to some kind of multiverse or anthropic principle or something like that.
STFC-RAL-CR03 R61: Here, we get the matter locally, and this matter looks a lot like the standard model when we do these kind of symmetry-breaking structures for E6 and E7.
STFC-RAL-CR03 R61: And then we build up this unemployment response, so our ambiguity comes in.
STFC-RAL-CR03 R61: And there's a vast degeneracy of matter contributions. So the matter types are fixed by the symmetry breaking. The actual components of which matter fields we use and how they interact together, there is an ambiguity in that. But that's, in the theory, taken to underline the independence and quantum theory.
STFC-RAL-CR03 R61: So, in this equation here, general relativity comes in as the overall equation, as I build equation, and locally.
STFC-RAL-CR03 R61: Quantum theory comes in from the degeneracy of the matter fields underlying the same geometry. That's the idea, building up this theory that's building quantum theory and gravity together. So, in principle, that's a good form of uniqueness, because we have to account for different things in quantum theory. As a final topic.
STFC-RAL-CR03 R61: I'll quickly describe… oh, that's the paper. Yeah, it's all written up, but all of these things I've talked about are written up in the papers on the paper.
STFC-RAL-CR03 R61: As a final topic, just describe how this theory also contained a dark set.
STFC-RAL-CR03 R61: To get there, I'll make a more direct comparison
STFC-RAL-CR03 R61: Again, with this approach of matrix facial dimensions, comparing it with, type… this approach theorizing proper time at the local level, doing head-to-head, more, closer… close head-to-head comparison.
STFC-RAL-CR03 R61: There's extraspatial dimensions by looking at what happens to extraspatial dimensions falling right at the local level. So we can do the same thing in extraspatial dimensions coming at the local level.
STFC-RAL-CR03 R61: Where we extend out the spacetime form of this, quadratic form from the time interval here.
STFC-RAL-CR03 R61: Rather than extending the proper time itself. So what I mentioned before is that if we go to P both and two powers, and this is what leads to, say, for example, this vortic form.
STFC-RAL-CR03 R61: over 56 components, which had this E7 symmetry, which we broke down, and it had all these kind of standard model properties, electro-peak symmetry radiating type properties, and the prediction of going on to the 8 to get the full sunder model. So that's what happens when we generalize proper time. But we could do a parallel analysis with extraspatial dimensions.
STFC-RAL-CR03 R61: at the local level, which is just in those quadratic form, but we can still do the same local symmetry breaking kind of thing. So what happens in this case?
STFC-RAL-CR03 R61: So, say, rather than breaking an E7 symmetry, we're breaking this larger event symmetry. If we do the symmetry breaking, we pull out our external four-vector part here.
STFC-RAL-CR03 R61: And the residual part is now a scalar field transforming under this, residual rotation symmetry here. So the point being that if you do the simplest possible thing, the extraspatial dimensions.
STFC-RAL-CR03 R61: this looks like nothing whatsoever like the standard model, it's just… it's just getting scalar particles, you don't get spin states, you don't get things like these gauge groups for SU3 or U1, you just get an SOM, so nothing at all like the standard model.
STFC-RAL-CR03 R61: So that's why generalizing public time is far, far better suited to some of model-like structures. But at the same time.
STFC-RAL-CR03 R61: In a way, we got to this form here by augmenting this four-dimensional space-time form, and this is a kind of a special case for generalizing proper time.
STFC-RAL-CR03 R61: So why can't we do… we're just… this is done last proper time, because we're adding on components, it's not shitting to the four-dimensional,
STFC-RAL-CR03 R61: the case. So yes, this is a problem derives in proper time. So what is the physics of this? Well, here, the internal gauge symmetry
STFC-RAL-CR03 R61: It's just in parallel with the Saint-Amond kind of gauge symmetries, so it's hidden from the San Damon sector. We've got these two independent gauge sectors, so there's no… there's no gauge interactions between this matter and this matter. This forms a natural candidate, I call it dark quarks here, you know, they're scalars, but this forms a natural candidate for a kind of hidden QCD
STFC-RAL-CR03 R61: Non-compact, sorry, compact, non-abilion gauge route.
STFC-RAL-CR03 R61: So there are many models about, hidden QCD-type dark matter, which can form, kind of, blue ball or dark headline-type states, and in fact, it forms a candidate for self-interacting dark matter, because there's some interaction between… between these states.
STFC-RAL-CR03 R61: So these are kind of, dark, but because they have the same basis in the same four-dimensional space-time, there is a gravitational interaction between them. So there is a gravitational interaction between these two sectors, which might mix a natural dark matter kind of depth. There's a possibility of a Higgs portal.
STFC-RAL-CR03 R61: Since the Higgs is closely connected to these particles, but the theory's not well enough developed for that. So this just raises the question of how many other ways might there be to generalize point of time?
STFC-RAL-CR03 R61: And I'll mention, finally, one last topic of physics, one other possible sector.
STFC-RAL-CR03 R61: So to get to this E7, what I did right at the beginning of the talk was to go from this, this,
STFC-RAL-CR03 R61: to go from this quadratic structure, to a 3x3 matrix structure, and then we produced the octonials to get this 27-component form with an E6 symmetry, and then we extended that over to an E7, quartic form, and did a symmetry-breaking structure to get out into some monolites, which was out of the first part of the tour. But what we could have done
STFC-RAL-CR03 R61: as a form of generalized proper time, but we could have, when we went to a 3x3 matrix, we could have just gone to a 4x4 matrix. This gives us an alternative quartic form for generalizing proper time. There's no reason to stop there. We could go to a 5x5 matrix, 3xp matrix in general. This is another sector for generalizing proper time, and what does this look like?
STFC-RAL-CR03 R61: So it's just a general topic of time. So we can do the same symmetry breaking trick here, where we pull out our external four-dimensional space-time and ask what the matter particles look like now. So again, we've got this independent, internal gauge symmetry from our standard model kind of visible sector over here.
STFC-RAL-CR03 R61: And the question is, what are the properties of this kind of… this kind of gaze sector? So I'm just going to pull out… pull out this table on the next slide and say a little bit about it.
STFC-RAL-CR03 R61: So the new feature that occurs for this sector of generalizing public time is that this gauge group here, which I initially thought was problematic, because it's what's called a non-compact gauge group, it's not like an ISSO or SU gauge group, the standard model.
STFC-RAL-CR03 R61: It contains, well, it's a non-compact gauge, which means it contains
STFC-RAL-CR03 R61: in the quantum theory, you'll have negative energy kinetic energy states, as well as positive energy, which is normally a worrying thing. Can anything interact with a negative energy state would just be crazy out of the vacuum, and it would be very unstable.
STFC-RAL-CR03 R61: So about 5 years ago, I was holding a few, cosmology conferences, online.
STFC-RAL-CR03 R61: And there was a talk on dark energy, and one slide on something called phantom Dark Energy.
STFC-RAL-CR03 R61: And there was negative kinetic energy came up on the screen, and it comes to the scalar model, so there are actually dark energy models that use negative kinetic energy.
STFC-RAL-CR03 R61: And, people worry about it a little bit in phantom models, because if you've got these negative energy scalar states here.
STFC-RAL-CR03 R61: they can always interact by gravitons and, generate, kind of, standard model states out of the vacuum, so the whole thing would just, like, slow and go mad, unless you can somehow suppress this. I briefly mentioned it in the theory that
STFC-RAL-CR03 R61: talking about here, when we unify gravity with quantum theory, gravity is a classical theory.
STFC-RAL-CR03 R61: So, in principle, this diagram does not exist for these negative energy states, but there is an equivalent diagram, which is these self-interactions
STFC-RAL-CR03 R61: And this non-obedient gauge theory, so you could create this negative and positive, gauge boson receptor out of the vacuum. So at first sight, this looks quite bad.
STFC-RAL-CR03 R61: So then, actually, this would just fill the vacuum, and they'd also annihilate each other, so you can create this kind of stable equilibrium. And by doing a kind of parallel analysis of Plant and dark energy models, which are scalar models, you can follow what happens
STFC-RAL-CR03 R61: to the energy density and the pressure density, and there's a complete, symmetry between the positive and the negative energy contributions. So, in principle, the energy density of this thing is zero, the pressure is zero on all microscopic scales, so we just won't know it. So this room could be formed as kind of vacuum, positive and negative gauge bosons in this dark sector.
STFC-RAL-CR03 R61: There's no interaction other than gravitational with us, and it's gravitationally negligible because it sort of just cancels out. Apart from the fact that there are also these kind of, matter states down this side here. So these introduce an asymmetric perturbation, and in principle, you can now be a vacuum equation
STFC-RAL-CR03 R61: Which will give you a,
STFC-RAL-CR03 R61: something like a cosmological constant, something like a dark energy expansion. So I won't go through the details, but I'll just kind of flash up. If you look at the general properties that you look for in dark energy, then qualitatively, this is kind of uniform in space and time.
STFC-RAL-CR03 R61: So as the universe expands, it's still being created out of the vacuum, so it, filled the universe as it expands, and we've got a source of negative pressure from these negative energy, contributions. There's a source of ultra-low,
STFC-RAL-CR03 R61: energy density, coming from this kind of, cancellation and site perturbation, and in principle, although it's not clear it would be stable and dark, because it may only be a gravitational interaction comes from a fundamental theory. So it's a possibility of a possible dark energy candidate, and there is a kind of possible way of testing this.
STFC-RAL-CR03 R61: Eventually. Again, this comes from those cosmology conferences on Zoom a few years ago, and a lot of talk about using the,
STFC-RAL-CR03 R61: Structure of the early universe.
STFC-RAL-CR03 R61: as a possible source of structure formation in the galaxy. So here, if these processes are happening with plus or minus energy creation in the early universe, this will lead to, local energy fluctuations, which, if they are kind of
STFC-RAL-CR03 R61: Expanded by some kind of dark, inflation source.
STFC-RAL-CR03 R61: These could be frozen into the space-time geometry and seed, kind of, formation of galaxies later on. This is a standard idea that something in the physics of the very own universe could have seeded, kind of, galactic formations later on.
STFC-RAL-CR03 R61: This is a transition to, kind of, dark matter states. So this is called something like the Cosmological Collider Cosmological bootstrap. So, bootstrap means that you're using
STFC-RAL-CR03 R61: Constraints of the early universe, symmetries that kind of constrain what the physics can look like.
STFC-RAL-CR03 R61: Collider, because in principle, at the very early universe, you're getting to very high energies, so you can reach higher energies than in particle physics. This is a bit of a nostalgia. There's an event from 30 years ago when I was at SLD. Right in the middle is the,
STFC-RAL-CR03 R61: SLD vertex detector, which was constructed here at Rutherford Lab 30-odd years ago.
STFC-RAL-CR03 R61: But then that's a different clock. Here, I'm trying to say that in these kind of processes, the E plus and minus clouds are going to quarks. You have this kind of gluons and quarks being produced, these kind of stringy-like structures.
STFC-RAL-CR03 R61: If this is going on in the early universe, we've got this positive energy, gauge bosons and positive energy core-height particles coming out, whereas negative energy.
STFC-RAL-CR03 R61: So is this just happening in the very early universe, and then gets stretched out.
STFC-RAL-CR03 R61: This, in principle, could see things like cosmic wall or cosmic bone structures, and there's also a signature coming from negative energy kind of production, which could be said to be boys. But my point is that when people look at these cosmological collider and bootstrap kind of approaches.
STFC-RAL-CR03 R61: usually the physics is very different to this, so because the physics signature is quite different, in principle, this is a way something like this might be tested. So I'm going to head towards summing up now, and I'm going to get there
STFC-RAL-CR03 R61: by a kind of a short story, from Heisenberg.
STFC-RAL-CR03 R61: I read this in this small volume from A Life of Physics, and it's pre-printed lectures. This is a lecture that Heisenberg gave in the late 60s in Italy at a conference on contemporary physics about his life in physics. And at the end of his lecture, he described a story from his childhood.
STFC-RAL-CR03 R61: Where he was building a box.
STFC-RAL-CR03 R61: Nope.
STFC-RAL-CR03 R61: Heisenberg's box is not for accommodating Schrodinger's cottage, you might think. We were building it to kind of put books and things in, so it's probably the early 1910s. And as he describes making this box, he got to put the lid on, and he took the first nail, and he just…
STFC-RAL-CR03 R61: Crash the nail in really hard.
STFC-RAL-CR03 R61: And when he bashed his nail in, he was kind of disappointed that on all the banging, it kind of become displaced.
STFC-RAL-CR03 R61: From where it was supposed to be, and everyone had this kind of experience at some point. So as Heisenberg tells the story, his grandfather, who was a handicraftsman, was watching on. He said, no, you don't do it like that, take that nail out. What you should do is get all the nails together, and cut them all in a little bit, and then when you've got everything quite secure, then you should stop crashing things in.
STFC-RAL-CR03 R61: Probably when you've got everything nicely lined up. This, of course, is his analogy for his approach to physics, and it's a warning about running in too quickly with kind of rigorous mathematicus. When you try too much of a rigorous mathematical message, you get too attached to those, points of mathematics rather than the physics.
STFC-RAL-CR03 R61: I should have the whole picture in mind before you fix this, you know, it's too firmly mathematics.
STFC-RAL-CR03 R61: So, of course, you do need the rigorous mathematics, but the point is that by solving big puzzles in mathematics, it's great for mathematics, doesn't necessarily mean you're solving problems in physics. It's just about getting the physics picture in place, and then kind of working out the details through that rigorous mathematics.
STFC-RAL-CR03 R61: So, in the modern day.
STFC-RAL-CR03 R61: yeah, five theory is a bit like this, with the right kind of conceptual foundations, issues with the standard model, there's issues of quantum gravity, and then issues in cosmology, and we want all of these things to kind of come together, basically, and then kind of theory. So, to properly sum up, we've got… I mean, just to sum up. So,
STFC-RAL-CR03 R61: So did this approach to analyze proper time works very well, and I think, the kind of take-home message here is probably, I think it does work well for the people. The main obstacle is that we normally
STFC-RAL-CR03 R61: We think we can't possibly build a theory constructing the whole world out of time. It's just too simple, and it doesn't have enough structure in time to build this thing. But on the other side of this obstacle, it's kind of obvious that time provides a natural unifying basis, because, well, I mean, everything happens in time. There's something kind of…
STFC-RAL-CR03 R61: universal about time. I mean, everything happens in time. If you can find a way of constructing a theory out of time, then it's automatically just a very unifying approach. There's a kind of changing worldview, it's kind of a big changing worldview.
STFC-RAL-CR03 R61: Just this, A lot of people,
STFC-RAL-CR03 R61: quotes this from Einstein, that everything should be made as simple as possible, but not simpler. So, there is this general feeling in physics that, because it's much quoted, that people are looking for a very simple theory, a very simple idea.
STFC-RAL-CR03 R61: So here, the trick is to see how it's possible to construct a theory just some time. So I'm just going to go through, summarize this, just this argument for how you can build a theory from time. This is a kind of a take-home message maybe to think about. And the barrier is that we normally think of time
STFC-RAL-CR03 R61: There's a one-dimensional line in space.
STFC-RAL-CR03 R61: Alright, that's lying in space-time.
STFC-RAL-CR03 R61: I would say there's nothing in the world that really corresponds to the same line that sort of follows around. It's not really what time is. Well, if we're just taking time as a continuum, then there says nothing about spatial extension whatsoever.
STFC-RAL-CR03 R61: So we have to forget about time reslying space, and seeds sound a bit like the seeds, three-dimensional space, but intrinsically for what it is, without anything missing. The way I sometimes think about this is like listening to a flow of a piece of music in a dark place, or where you're not thinking about space. Just this sense of a flow in time.
STFC-RAL-CR03 R61: Well, we can describe this flow mathematically by the real numbers, and the key point is that real numbers, we can't just add them and subtract them, but we can also multiply them, divide them, take roots, and so on. So if we're treating time as a continuum, and the real numbers have these properties, then it means that time itself has these intrinsic properties. This is the key point.
STFC-RAL-CR03 R61: Absolutely, if we can write.
STFC-RAL-CR03 R61: We can write time as just adding together, just using this plus and minus prophecy, the way we usually think of time, but we can also… and they do fit together, we normally think of the continuum of time.
STFC-RAL-CR03 R61: But we can also express a real interval using these other properties of the real numbers. In, for example, this quadratic form like this, and we can pull out the structure of space from this structure of time.
STFC-RAL-CR03 R61: which has a geometric interpretation, the whole thing having an interpretation for this minor sign, having a causal kind of light kind of structure. In the same way that these simple elements here fit together in a line when we think of time, these quadratic elements, because of this geometric interpretation.
STFC-RAL-CR03 R61: These fit together in a four-dimensional space-time world.
STFC-RAL-CR03 R61: Basically, we're taken to a continuum of networks.
STFC-RAL-CR03 R61: to have this local-like kind of structure, local reference frame, like general relativity. So…
STFC-RAL-CR03 R61: The idea is that the alphabetic subtractor type contains a different form from which it flows. This is a final slide. So we can then construct this extended bottom of the space type just out of this flow of time. So there's two stages to get here. One is to forget time… forget of time as being alive, just think of it as a continuum, like, listen to the piece of music.
STFC-RAL-CR03 R61: And then recognizing this internal structure of time, which has this geometric interpretation. So the whole thing is a temporal structure, and it contains these kind of
STFC-RAL-CR03 R61: At these worldlines.
STFC-RAL-CR03 R61: But the point is that, and we're reading this from left to right, so there's even an argument here that the reason why the world is relativistic is because we're starting with time, and we're kind of pulling the currents of space out of this continuum of time, is what links space and time together in the space-time form.
STFC-RAL-CR03 R61: And if we're pulling these components out of this flow of time, we can also extend this to,
STFC-RAL-CR03 R61: High-dimensional forms, which is how we get these structures of matter coming out here.
STFC-RAL-CR03 R61: So this gives us our… and that's matter content in the space-time. It's changing perspective in time being something like a world bin, or whatever it is, or parameter in the world, so the world being something in time. Now, to sort of get matter and space out of time.
STFC-RAL-CR03 R61: may sound a bit strange, because time and matter are strange at… time and space and matter are different things, but already in relativity, for 100 years, we mix up matters… we mix up time and space components in relativity, and in theory, directs spatial dimensions, we mix up space and matter.
STFC-RAL-CR03 R61: So, we already have theories which mix up time and matter and space components, so all that's involved here is a rewiring of the interplay between time and space and matter in a manner which is more streamlined, and by construction, more,
STFC-RAL-CR03 R61: more unifying, and it sounds like we're doing a lot by trying to pull space and matter out of just a time. Well, the whole point of unification is to get as much as possible out of as little as possible. We can argue as far as you can go, trying to pull out a really unifying kind of picture.
STFC-RAL-CR03 R61: And, through this construction, you unify together this block and dynamically. It provides this kind of basis for quantum gravity, as I briefly mentioned, by looking at degeneracy of components in this construction.
STFC-RAL-CR03 R61: And when you actually look at the matter content, when we take this in a nice one topic time, and you break it over fundamental spacetime, there is a sector which is richer than the model, and it leads to a prediction this structure gets fall through the diagnosis on the model, but there are also these other sectors
STFC-RAL-CR03 R61: which have properties like, compact gauge groups for dark matter, and also this negative energy contribution, a bit like phantom dark energy, as a vacuum dark energy state, or dark energy. And it all comes together under one unifying
STFC-RAL-CR03 R61: equation, one simple equation. It's another feature sometimes sought for, unification. Also.
STFC-RAL-CR03 R61: I think quite often, when you're breaking down matter, we can get more at the matter from, say, visible matter to microscopic matter to molecular or atomic matter. And as far as… you can always say, what is that made out of? You get it at a smaller level. Here, we're starting simply with time.
STFC-RAL-CR03 R61: And you might say, well, what's time laid out? We can't really break up time any further. It's precisely by recognizing this intrinsic arithmetic kind of substructure. We're already decomposing time itself. It's by decomposing time.
STFC-RAL-CR03 R61: We pull out this space and magic thing. So by getting down to the simplest level, and already decomposing it, we're getting down to some kind of bedrock level.
STFC-RAL-CR03 R61: the bare bones of what we could build a theory out of. So, again, maybe, as you might seek for unification, it's getting down to some real, sort of, bedrock level.
STFC-RAL-CR03 R61: And, of course, it might sound implausible, but by its very implausibility, it's also very constraining what it can do. So it's quite striking that when you do drag out properties of matter in spacetime from this, it actually hits these three targets for unification in terms of standard model-like structures.
STFC-RAL-CR03 R61: modern gravity in dark sectors fairly well. So I think if anybody
STFC-RAL-CR03 R61: sort of experimentalist or theory interested in unification, because of the general, kind of, motivation for this in general terms, and how well it hits the targets for unification, I think it's worth considering something like this approach, economies in proper time, or something quite similar to that. So yeah, thanks very much for…
STFC-RAL-CR03 R61: Thank you very much, David.
STFC-RAL-CR03 R61: Yes.
STFC-RAL-CR03 R61: We have time for questions, Adam.
STFC-RAL-CR03 R61: I mean, I've loved the idea, since I heard you first say it, about 15 years ago. I find it interesting when you were saying about the maths, the physics and the maths, and where they…
STFC-RAL-CR03 R61: they come together. Because what… I feel like your basic point is we should look at the structure of the continuum.
STFC-RAL-CR03 R61: Or the source of the structure of reality. Like, so, I love that you're sort of starting with physics end, like.
STFC-RAL-CR03 R61: So you think, coming at it from what is… because, you know, like, the continuum has, like.
STFC-RAL-CR03 R61: points in it that I think could be rich for your quantization, like the rationals, for example, are a special set of points in the continuum. That's almost like a quantization of the continuum. Yeah.
STFC-RAL-CR03 R61: I think the way we often introduce the real numbers as a continuum, we often get this, we learn about integers first, in steps, and then we learn about some rational numbers.
STFC-RAL-CR03 R61: And then we realized that when you try to say, like, like Cyrus, when you try to draw a triangle with
STFC-RAL-CR03 R61: what's the length of the hypotenuse? It's square root of 2? And you can't write that as a fraction anymore, so you need something else. And so often, often the real numbers are introduced as kind of filling in the gaps kind of thing, of fractions and sort of rational numbers. In my view, that's the wrong way of looking at the real continuum.
STFC-RAL-CR03 R61: the continuum was an extent in itself, and there are, I think, some mathematical definitions of the continuum directly, and they could…
STFC-RAL-CR03 R61: A continuum isn't really made out of points, made out of the continuum. The smallest
STFC-RAL-CR03 R61: no matter how far down you go, you still have… Yeah. So, when you say about quantization, my view is
STFC-RAL-CR03 R61: on that, and I haven't even talked about some of those here, is that because it's such a simple idea, so, so, it's so constraining.
STFC-RAL-CR03 R61: that…
STFC-RAL-CR03 R61: quantization type is going to come out from those constraints, ultimately. Yeah, exactly. I don't think you should be quantizing something. You should be having quantisation. I think it's something that's a very, very constrained way of, kind of, building stuff. Yeah. On the points thing, I kind of think that the continuum is pristine. Those are, like, dividing points. They're not, like, what the continuum's made up of, but they're points where it can be divided.
STFC-RAL-CR03 R61: Yeah, I mean, you can introduce points, yeah, but I don't… yeah, I mean…
STFC-RAL-CR03 R61: there are different ways of looking at it, but I don't personally… I used to think of the beginning of the main output points, but it is, but then you get all this kind of… I mean, these kind of levels of infinity and stuff, yeah, kind of…
STFC-RAL-CR03 R61: Yeah, but I think that's it, it's going to continue. The way it's used in practice and all that.
STFC-RAL-CR03 R61: Ever since, like, Newtonian mechanics, I mean, you always use calculus, and that kind of element of the dutinium, being able to use differential calculus to do dynamics, and using different equations, Maxim's equations.
STFC-RAL-CR03 R61: All of these things use the continuum. It's that property of the continuum. So that's why it's kind of a quite conservative theory, before we're using the continuum property at times, but rather than using it as an independent variable and differentiating things with respect to that continuous variable, we're using the fact that we can decompose this continuum itself.
STFC-RAL-CR03 R61: the right structures that matter. Yeah, and that's what the thing I found fascinating from the start, is that just from that simple thing, you end up with structures that
STFC-RAL-CR03 R61: That's not the way I got into it. I mean, I was thinking of all these conceptual relations between baseline and matter, but… because…
STFC-RAL-CR03 R61: Once you get this equation, then…
STFC-RAL-CR03 R61: Talk about the Bacchanites, talking about the Syria after that.
STFC-RAL-CR03 R61: And it's quite… it is quite… I mean, I think the sticking point is so counterintuitive that we can get so much out of it. So little, but that is the point of communication.
STFC-RAL-CR03 R61: Yeah, I didn't really get the idea until 5 years after the first talk I sat down in yours, so… One thing that really helped me is to realize that,
STFC-RAL-CR03 R61: how energy relates, because, like, energy is the noisy charge of time. Energy as being the noisy charge of time, right? So, if…
STFC-RAL-CR03 R61: me and someone else, are measuring time slightly differently because of the coefficients we've got. We're, you know, we see energy differently, and there's no symmetry there, and that's why, you know, if I run into them, it hurts.
STFC-RAL-CR03 R61: Because we're measuring time differently, so therefore our energies are asymmetric. That was when it clicked.
STFC-RAL-CR03 R61: You said this is the most general form you can write? Oh, yeah, yes, it's quite… I mean…
STFC-RAL-CR03 R61: Yeah, I mean, certainly depending on taking these alpha coefficients right down to the,
STFC-RAL-CR03 R61: zeros across the minus 1 to generalization of this scope. And that's because, yeah, well, I suppose originally I was thinking of writing it… if you write it explicitly, there aren't any kind of
STFC-RAL-CR03 R61: characteristics, which aren't, sort of, invented, if you like. It was just an arithmetic expression without any other coefficients in there. When you've got, kind of,
STFC-RAL-CR03 R61: permutation over different possible indices and so on, but when you write it in short form, these could be various, sort of, each day numbers and so on. But, yeah, I mean, the question… I have not, classified
STFC-RAL-CR03 R61: how many possible ways it is explicitly possible to be composed. I mean, I know that there are at least these three possible ways, for example.
STFC-RAL-CR03 R61: So, I don't know how many systematically thought of that, how many others there are. And there are various other kind of caveats here. So, for example, I imagine this is like a compact age group you get from SON groups for dark matter, but you could, you could make this, also the generalization to having
STFC-RAL-CR03 R61: What, in the context of extra, kind of, spatial dimensions would be extra time dynamics would also have a non-compact
STFC-RAL-CR03 R61: component, so you could end up having, like, a dark energy sector in here as well, because it could… so both of these sectors, in fact, could contain what I like a compact gauge, at least a non-compact gauge. That's what I meant a little bit, I said, about dark matter and dark energy interacting, because it might actually both contain dark and dark energy. So yeah, so…
STFC-RAL-CR03 R61: There are barriers of the United States, I haven't
STFC-RAL-CR03 R61: The reason I want to stand out would be
STFC-RAL-CR03 R61: ones that came up, you know.
STFC-RAL-CR03 R61: But it is, yeah, I mean, to me, it's quite striking that it is very restrictive what you can do, but yeah, these viewpoints on the model.
STFC-RAL-CR03 R61: like structures, and these do have qualitative features that you look for in dark matter and dark energy. And then, in that kind of chronological pie chart of visible matter, dark matter, dark energy, we see these three sectors very differently. These three phenomenologically completely different things, the fact that they all come out
STFC-RAL-CR03 R61: The sectors of this thing is quite frightful to me, because I'm working at this moment.
STFC-RAL-CR03 R61: Certainly, the point is here that
STFC-RAL-CR03 R61: This doesn't just provide a framework in which you can hang this thing on, which is often the case in the translation I mentioned, if you have an extra fields or super symmetry, etc. In that framework of translation over the sphere, everything is coming directly out of the theory.
STFC-RAL-CR03 R61: If that's what taught me, I've wanted to see
STFC-RAL-CR03 R61: it's possible to derive, you know, content theory and this quantum gravity context, rather than just quantizing things, just to… since it's the first scope of this, to see what comes out. As I mentioned relativity, time it comes out. This would be dragging spatial components out of time, consistent with causality.
STFC-RAL-CR03 R61: what links time-space together in relativity, so I try to get as much out as we can, rather than sort of putting anything really by hand, sort of.
STFC-RAL-CR03 R61: I mean, I think it's already almost time. It's almost time, yeah. So we can continue discussions or launch. We can, join or manage. We are going, David.
STFC-RAL-CR03 R61: So we… close the seminar now. Thanks, everyone.
STFC-RAL-CR03 R61: Oh, I hope so, yeah, but I thought it was the most cricket game. I think that's it.
STFC-RAL-CR03 R61: Yeah, yeah. Yes, and it wasn't too technical. There were…
STFC-RAL-CR03 R61: quite a bit of equations, but I think you did a very… Yeah, it's very… I think you were just intend to assist with every line of equations, so while talking, you made explanation.
STFC-RAL-CR03 R61: Yes. Whereas our explanation, if you're changing the past aspects of it, it sort of breaks. So this is why I love…
STFC-RAL-CR03 R61: days, I think, is… is… you can't change anything, you're just saying, what's the structure? An infinitesimal piece of fun.
STFC-RAL-CR03 R61: We don't put anything else at the moment.
STFC-RAL-CR03 R61: What was the…