Jorge Pullin: Okay? So our speaker today is Salator. Privacy will speak about light con thermodynamics.
Salvatore RIBISI: So thank you for the invitation. I'm very happy of being
Salvatore RIBISI: here like talking to the the same, or the being following the most. At the beginning of my career.
Salvatore RIBISI: So now, services have been.
Salvatore RIBISI: how catching the interest of many researchers in the
Salvatore RIBISI: in the last years and today. So I will
Salvatore RIBISI: try to briefly review the the properties of maybe the simplest
Salvatore RIBISI: of the no surfaces we can think about, which are light consuming Gowski spacetime.
Salvatore RIBISI: So in this talk I will talk about the thermodynamic properties of light guns.
Salvatore RIBISI: And so why can we? Why do live contactable dynamic properties?
Salvatore RIBISI: So the answer comes from the fact that light comes in or be Mikoskey space types are conformal, killing horizon.
Salvatore RIBISI: What does it mean? So we have the conformal group which is isomorphic to SO. 5, one.
Salvatore RIBISI: and then it generator. Psi. Of this group
Salvatore RIBISI: defines a conforming field, such that when we do, the derivative of the nintoskee matrix
Salvatore RIBISI: through the side through any of the generator.
Salvatore RIBISI: then what will. The result is proportional to the Nico schematic itself
Salvatore RIBISI: with side being a scalar. So we have a function
Salvatore RIBISI: which you can compute.
Salvatore RIBISI: and this is the result for any of the 15 generators of the Conforma group.
Salvatore RIBISI: Then we focus on the spherically symmetric ones. And then we only have 3. We only have 3 generators left.
Salvatore RIBISI: which are the D, lato vector field
Salvatore RIBISI: time translations and one of the special performance transformations.
Salvatore RIBISI: Therefore, the most general conformance radius conformachine Fielding, because his facetime is given by a linear combination of these 3 vector, fields.
Salvatore RIBISI: And so here you have the simple form written in terms of not coordinate. So you is the usual advanced time and either retired time.
Salvatore RIBISI: Okay, so
Salvatore RIBISI: with.
Salvatore RIBISI: we want to study to to get to the point. When we find Blackton, we want to study the
Salvatore RIBISI: council structure or given by
Salvatore RIBISI: this family of conformal cleaning fields.
Salvatore RIBISI: So we, we compute its norm. It's very easy to do.
Salvatore RIBISI: And we see that it's given by the product
Salvatore RIBISI: of these 2 polynomial of degree. 2.
Salvatore RIBISI: So,
Salvatore RIBISI: We see that the normal vanishes
Salvatore RIBISI: at the root of these 2 polynomial meals.
Salvatore RIBISI: so which are given by this to find to
Salvatore RIBISI: past the future light comes
Salvatore RIBISI: u equals to u plus minus, which is the root of this polynomial and the same routes apply for this polynomial.
Salvatore RIBISI: and, moreover, the there is a sphere
Salvatore RIBISI: in which both polynomial, at which both polynomials vanish.
Salvatore RIBISI: which, given by the intersection of U equal u minus and v equal to e plus. So this is a sphere which is given which is at a given
Salvatore RIBISI: model, given time and at the given radius, which depends on the
Salvatore RIBISI: under their say, intersection of the divide goes. So we put now all this information
Salvatore RIBISI: in a space time diagram.
Salvatore RIBISI: So here.
Salvatore RIBISI: yeah, we have Minkowski space time
Salvatore RIBISI: and with the integral lines.
Salvatore RIBISI: oh, of Xai. But this family of conformity fields.
Salvatore RIBISI: So you see that site defines to conform a killing horizons at the past and future lightcoms of these 2 events.
Salvatore RIBISI: or plus and or minus
Salvatore RIBISI: each horizon, as a constant, conformal, invariant surface gravity defined via the gradient of
Salvatore RIBISI: of the norm of sites, Esther.
Salvatore RIBISI: and then we come at the first analogy with black holes, which are, which is, that events is pastime.
Salvatore RIBISI: are separated as in spherical, each aspherical charge, black codes. So here you will have that region to
Salvatore RIBISI: where the confirm activity field
Salvatore RIBISI: is like. Like.
Salvatore RIBISI: You will let the analogus of the outer region of a black hole.
Salvatore RIBISI: and this would be the outside, out the horizon horizon.
Salvatore RIBISI: and here, on the future light, colourful plans, you will have the inner horizon.
Salvatore RIBISI: another
Salvatore RIBISI: announce with the alright with the horizons of black hole horizons, is that the topology is the same.
Salvatore RIBISI: namely, s. 2 cross r. So a sphere
Salvatore RIBISI: cross R,
Salvatore RIBISI: so this diagram also exists
Salvatore RIBISI: in the, as also an extreme alversion, which is when
Salvatore RIBISI: or plus, coincides
Salvatore RIBISI: with or minus.
Salvatore RIBISI: And so region one
Salvatore RIBISI: shrinks to 0,
Salvatore RIBISI: and we only have region 2, and this region
Salvatore RIBISI: above and below, and the conforming field is time, like everywhere, but
Salvatore RIBISI: on the future path, light on where it's
Salvatore RIBISI: whether it's now
Salvatore RIBISI: and the surface gravity will be 0.
Salvatore RIBISI: Okay, starting from
Salvatore RIBISI: this fact. So I think from
Salvatore RIBISI: this is from these properties.
Salvatore RIBISI: the ransom tires
Salvatore RIBISI: found the so-called laws of light con thermodynamics.
Salvatore RIBISI: So the 0 slope is that the surface gravity is indeed constant
Salvatore RIBISI: on the conformal killing horizon.
Salvatore RIBISI: Then there is the first load, which is very many results that
Salvatore RIBISI: under conformal environment matter, perturbation. So if you perturbed
Salvatore RIBISI: the Minkowski metric with conformal environment, you end up with a balance flow
Salvatore RIBISI: which you can find here. So
Salvatore RIBISI: all the quantities appear in the balance through our conformal environment.
Salvatore RIBISI: But we have to be careful with the, with their interpretation. So we already saw what's Kappa?
Salvatore RIBISI: Which in this formula is the equivalent of the temperature.
Salvatore RIBISI: and is the charge associated with the with the scope for marketing field.
Salvatore RIBISI: and the area is a conformal, invariant generalization of the area that takes into account the fact that the area of the horizon
Salvatore RIBISI: would also increase without any matter perturbation.
Salvatore RIBISI: So this is the remote result.
Salvatore RIBISI: They find a second law that Gsa's that states that
Salvatore RIBISI: this area can only increase.
Salvatore RIBISI: and as a third law defined that.
Salvatore RIBISI: The extreme version of the
Salvatore RIBISI: of the diagrams of the 3 month conform opportunities
Salvatore RIBISI: have vanishing temperature.
Salvatore RIBISI: as we already said.
Salvatore RIBISI: as well as vanishing entropy.
Salvatore RIBISI: Okay? Because also the area of the my 4 kit sphere in that case would be
Salvatore RIBISI: will be 0.
Salvatore RIBISI: Okay, so far, so good. So this is.
Salvatore RIBISI: if you want, like the
Salvatore RIBISI: the setting of light or thermodynamics.
Salvatore RIBISI: But
Salvatore RIBISI: we have this analogy, they in their work. They also find the the meaning
Salvatore RIBISI: of the temperature in in some circumstances, what we, what I want to show
Salvatore RIBISI: is that you can actually find, decompose the
Salvatore RIBISI: they might. Let me then go ski vacuum
Salvatore RIBISI: in terms of particles associated to this conforming field.
Salvatore RIBISI: and the the temperature that we find
Salvatore RIBISI: is indeed related to this the composition.
Salvatore RIBISI: So let's
Salvatore RIBISI: clarify some points first.
Salvatore RIBISI: So the integral lines of psi. So the trajectory of
Salvatore RIBISI: date, the site of the I mean of
Salvatore RIBISI: sign you, if you want.
Salvatore RIBISI: corresponds to observers accelerating readily with a constant acceleration which is not given by by Kappa.
Salvatore RIBISI: but is, I mean which, but it's still proportional to it. And here you are
Salvatore RIBISI: the concept of proportionality.
Salvatore RIBISI: however, the temperature measured by a non-devite detector will not be the temperature we are mentioning here, but the usual A over to buy.
Salvatore RIBISI: And this is due to the fact that under the detector breaks conformal environment, so you you can try to model a scale environment detector.
Salvatore RIBISI: The the text, the temperature Kappa. But we believe that the interest of this decomposition relies rather on global features
Salvatore RIBISI: of the volume, then to local measurements.
Salvatore RIBISI: So
Salvatore RIBISI: and that'd be the same.
Salvatore RIBISI: Let's start showing the the our
Salvatore RIBISI: and the results of our work and the path
Salvatore RIBISI: that leads to it. So please, if you ever have any doubts, feel free to interrupt me, because I think all the steps are easy.
Salvatore RIBISI: But if for any reason
Salvatore RIBISI: you you missed one, which probably means that I haven't been clear enough.
Salvatore RIBISI: It's better for everybody than if you stop me
Salvatore RIBISI: so.
Ivan Agullo: So, Salvatore. Yes, just a clarification. You have 1 one such the composition for each choice of raviol conformal killing Baker Field right.
Salvatore RIBISI: With patient
Salvatore RIBISI: so that the composition
Salvatore RIBISI: it's as if in the
Salvatore RIBISI: I will. Didn't say
Salvatore RIBISI: I mean, it's for Evan is
Salvatore RIBISI: family of radiant conformity. I understand one such the composition
Salvatore RIBISI: for every
Salvatore RIBISI: given family of conformal candidates, so I have a family given by some parameters.
Salvatore RIBISI: so every parameter, like a choice of parameter, gives
Salvatore RIBISI: alike that our big rise to this light comes to Disco for marketing horizons.
Salvatore RIBISI: and then you can make the composition.
Salvatore RIBISI: But I mean.
Ivan Agullo: Of param of parameters will will shift the position of this horizons right.
Salvatore RIBISI: Yeah, yes. Let's.
Ivan Agullo: So, so thank you.
Salvatore RIBISI: Thank for the question, Ivan, So
Salvatore RIBISI: the first step to write the Mikosky vacuum as a proposition of particle sets associated to site. We want. We need to characterize positive frequency solutions of the client or delegation with respect to inertial time on a light theme.
Salvatore RIBISI: So to do that we start by solving the simplest equation in the history of Ifgs, which is
Salvatore RIBISI: the scalar field, the question for a massless scalar field.
Salvatore RIBISI: So we do that
Salvatore RIBISI: we know, we can decompose the solution in terms of harmonics
Salvatore RIBISI: spherical harmonics, spherical harmonics, and already a part.
Salvatore RIBISI: We solve the equation. So the language of the question becomes an equation for its radial part.
Salvatore RIBISI: which is solved by the hysterical business functions.
Salvatore RIBISI: So
Salvatore RIBISI: we now we find that we loop
Salvatore RIBISI: for a surface
Salvatore RIBISI: where the decomposition will be made, and we notice that since we are dealing with a non object.
Salvatore RIBISI: the solutions are completely characterizing the union of the past
Salvatore RIBISI: and future light, Tom, which is the red surface you can see
Salvatore RIBISI: in this diagram. So we evaluate now our solutions in this surface.
Salvatore RIBISI: So this surface is given by U. Equal RH.
Salvatore RIBISI: For the future, light on and vehicle our age
Salvatore RIBISI: in the in the past light on. So we replace this.
Salvatore RIBISI: We replace these quantities in the solution, and we noticed that now the solution splits in 2 parts.
Salvatore RIBISI: one which is defined.
Salvatore RIBISI: or V bigger than RH.
Salvatore RIBISI: And one which is defined
Salvatore RIBISI: for you smaller than our age, which is the past license.
Salvatore RIBISI: So
Salvatore RIBISI: this solution, this whole solution, then, can be written in terms of a single variable which covers the whole real line.
Salvatore RIBISI: A.
Salvatore RIBISI: So
Salvatore RIBISI: this a
Salvatore RIBISI: in this case, in terms of the single variable spanning from minus infinity to plus infinity
Salvatore RIBISI: solutions of the Glen Gordon equation. Take this forward
Salvatore RIBISI: or day.
Salvatore RIBISI: 5. First of all is analytic.
Salvatore RIBISI: since it's the product of analytic function. And now the question is.
Salvatore RIBISI: what? How do we correct? How do we characterize
Salvatore RIBISI: positive omega solutions?
Salvatore RIBISI: 200 equation. Again, we have to look now where this this function really solution is bounded
Salvatore RIBISI: to, since they is, it is analytic to see where it is bounded. We have to do the expansion for large set.
Salvatore RIBISI: We do it, and very good. So this is the the form of depression which you could probably expect.
Salvatore RIBISI: and the solution from this solution you see that it is bounded. Once you look at it in the complex plane.
Salvatore RIBISI: for in the for negative imaginary part of that.
Salvatore RIBISI: so to to resume this result.
Salvatore RIBISI: positive frequency solutions are analytic functions of that bounded in the lower half complex plane.
Salvatore RIBISI: Imaginary part of that
Salvatore RIBISI: is more than 0.
Salvatore RIBISI: So very good.
Salvatore RIBISI: This is more the same result that you would get by starting solution on a on a plane.
Salvatore RIBISI: But okay, we. It was necessary to see if everything will be the same for the the composition on a light phone.
Salvatore RIBISI: Now that
Salvatore RIBISI: a this has been done.
Salvatore RIBISI: we want to characterize positive frequency solutions associated to Xi.
Salvatore RIBISI: So
Salvatore RIBISI: we take account. Ordinary transformation, as you will usually do if you look in the for ringler.
Salvatore RIBISI: for the vendor decomposition.
Salvatore RIBISI: and under this coordinate transformation the Minkowski metric.
Salvatore RIBISI: So this coordinate transformation is valid in the region, too.
Salvatore RIBISI: and the Minkowski metric appears as a conformal factor, which depends on this style and row variable
Salvatore RIBISI: times this metric.
Salvatore RIBISI: So you immediately notice that the
Salvatore RIBISI: conformal metric
Salvatore RIBISI: is independent of Tao.
Salvatore RIBISI: and so the only part of the measuring which depends on Tao is the conformal factor.
Salvatore RIBISI: and therefore then the Tao is
Salvatore RIBISI: I go for marketing field of the schematic. No surprises. Then the towel is actually our signing.
Salvatore RIBISI: So
Salvatore RIBISI: we want to study.
Salvatore RIBISI: then the solutions which are related
Salvatore RIBISI: with the solution. With respect to Dow.
Salvatore RIBISI: and to do this we use properties
Salvatore RIBISI: of of the sort of fields.
Salvatore RIBISI: and I mean that we? We look at the way they scale under coordinate under conformal transformations. So you know how the metric transformed.
Salvatore RIBISI: and we also know how solutions of the conformally mapped.
Salvatore RIBISI: a Klein Gordon equation.
Salvatore RIBISI: our transform.
Salvatore RIBISI: And we can use this one, because, of course, we are in Minkowski. So the the rich scalar is 0.
Salvatore RIBISI: So the solution
Salvatore RIBISI: on the on, the in the conformal metric. Again, take this form, so we can again decompose, because of spherical symmetry into spherical harmonics
Salvatore RIBISI: and and impose this time dependence. And then it became becomes again
Salvatore RIBISI: the clergonal equation becomes again an equation for the radial part.
Salvatore RIBISI: We solve it, and we get this equation, let us first lose
Salvatore RIBISI: might seem hard to to solve.
Salvatore RIBISI: but
Salvatore RIBISI: we were interested
Salvatore RIBISI: interested into evaluating the solution near this boundary.
Salvatore RIBISI: and so near this boundary
Salvatore RIBISI: row. If you look at the coordinate Transformation row goes to infinity.
Salvatore RIBISI: therefore this effective potential vanishes
Salvatore RIBISI: and and the radial solution becomes trivial, become trivial, trivial, exponential.
Salvatore RIBISI: and this is the form of the of the
Salvatore RIBISI: of the solution of the equation.
Salvatore RIBISI: So now we have to bring this solution
Salvatore RIBISI: on the again in the middle schematic through a conformal transformation.
Salvatore RIBISI: And this is our view. So here we used the the inverse transformation between
Salvatore RIBISI: Tau, raw, variable, and D and R.
Salvatore RIBISI: So
Salvatore RIBISI: phi. 2 is a solution with respect
Salvatore RIBISI: to the toxi
Salvatore RIBISI: in Region 2,
Salvatore RIBISI: we can do the similar
Salvatore RIBISI: work to for for one. And so we get the solutions here.
Salvatore RIBISI: and the solution in region, too. Very good.
Salvatore RIBISI: What we want to do like the reason we did that is because we want to find.
Salvatore RIBISI: A combination of these 2
Salvatore RIBISI: of these 2 solutions
Salvatore RIBISI: that, is positive frequency with respect to inversion. Time
Salvatore RIBISI: to do that, we start by. Take this complex function.
Salvatore RIBISI: F. Omega, that you see really looks very much like
Salvatore RIBISI: 5, 2.
Salvatore RIBISI: And we evaluate
Salvatore RIBISI: in the lower half complex plane. So you see that
Salvatore RIBISI: the only problems of this function are in the real line.
Salvatore RIBISI: So everything is well behaving on the.
Salvatore RIBISI: on the lower health complex plane.
Salvatore RIBISI: And so we evaluate this function close to the
Salvatore RIBISI: close, to the real line. So
Salvatore RIBISI: for
Salvatore RIBISI: of course, for Z, for x, for for the real part of Z,
Salvatore RIBISI: which is the right interval so bigger than our H smaller than minus our H.
Salvatore RIBISI: There is no problem. You immediately see that it coincides with i. 2.
Salvatore RIBISI: We have to do a bit of complex analysis to check
Salvatore RIBISI: what happens when we evaluate it in in between minus our age and our age.
Salvatore RIBISI: So
Salvatore RIBISI: you you start by evaluating it at this point. You do all the computation by
Salvatore RIBISI: by me
Salvatore RIBISI: doing the right rotation in the
Salvatore RIBISI: in the complex plane. You get the wrong sign, you redo the computation, and you finally get this result, which is that
Salvatore RIBISI: F.
Salvatore RIBISI: Omega. So this positive frequency solution with respect to inertial time, when evaluated between minus RH. And RH.
Salvatore RIBISI: Gives you an exponential factor. Times a negative frequency solution. With respect to the
Salvatore RIBISI: A
Salvatore RIBISI: with respect to Xi in region one.
Salvatore RIBISI: You can do the same by defining a solution which looks like
Salvatore RIBISI: Taiwan.
Salvatore RIBISI: And so what you get
Salvatore RIBISI: is that FW.
Salvatore RIBISI: And that W. Prime
Salvatore RIBISI: are analytic and bounded in the lower half plane in terms of the Mikos people routine. Thus they are positive frequency solution.
Salvatore RIBISI: So at this point
Salvatore RIBISI: you can make the usual, the composition you you are used to since
Salvatore RIBISI: Aru. So you you see that
Salvatore RIBISI: you can take the Annihilator and Creator operators associated to 5, 2 and 5, one.
Salvatore RIBISI: and you know that they once applied on the Nikosi volume, they they give you 0,
Salvatore RIBISI: and by recurrence you can find that that
Salvatore RIBISI: that then the the Minkowski Vacuum appears as appropriate state of
Salvatore RIBISI: of the sum, I mean, of the and then you get the third mistake
Salvatore RIBISI: of particles
Salvatore RIBISI: belonging to region one
Salvatore RIBISI: and belonging to Region 2.
Salvatore RIBISI: So
Salvatore RIBISI: so far.
Salvatore RIBISI: There is a subtlety that I have not. That which
Salvatore RIBISI: which is the fact that
Salvatore RIBISI: what I have actually done is that the composition in the regions that you see in red and in blue.
Salvatore RIBISI: in my, in my spacetime diagram?
Salvatore RIBISI: So actually, you have particles here. So in the past horizon of Region 2, and the past horizon of region 3.
Salvatore RIBISI: Associated 2 particles in the future horizon of region one.
Salvatore RIBISI: So this
Salvatore RIBISI: should be the actual decomposition.
Salvatore RIBISI: But
Salvatore RIBISI: we can make an identification which can be done explicitly
Salvatore RIBISI: of the Hilbert spaces
Salvatore RIBISI: in this surface in the past of Region 3.
Salvatore RIBISI: And in the future horizon.
Salvatore RIBISI: Or we can do
Salvatore RIBISI: through this identification by studying, studying the solution in the 2 boundaries.
Salvatore RIBISI: Then we we get the results when I show them the mode.
Salvatore RIBISI: Okay.
Salvatore RIBISI: so what are the
Salvatore RIBISI: perspectives on this work like, what are we thinking about
Salvatore RIBISI: when studying this problem
Salvatore RIBISI: well, and
Salvatore RIBISI: there are several. So the most immediate one
Salvatore RIBISI: comes from the fact that the laws of light control thermodynamics
Salvatore RIBISI: can be extended to any conformally flat space time.
Salvatore RIBISI: and there are some. There is a list of space. That's where we know thermal properties of one
Salvatore RIBISI: quantization with respect to the other.
Salvatore RIBISI: and we can expect there to take me to get to have a similar decomposition of one budget with respect to particle belonging to different quantizations.
Salvatore RIBISI: Then there is another perspective, which is probably, I mean
Salvatore RIBISI: more. I don't know.
Salvatore RIBISI: More involved
Salvatore RIBISI: comes from the fact that the temperature and the entropy of conformal horizons
Salvatore RIBISI: have been used by these authors to get wide transverse gravity using local thermodynamic approach. So they they argue that if you use.
Salvatore RIBISI: and actually the low customeratic approach.
Salvatore RIBISI: instead of getting
Salvatore RIBISI: general relativity. What you actually get is a live transverse gravity.
Salvatore RIBISI: which is generalization of unimodularity.
Salvatore RIBISI: They evoke some mechanism which has been already managed by Paris, Sebastian, New York, and work non-conformal bar matter
Salvatore RIBISI: will be in that case the source for the cosmological constant.
Salvatore RIBISI: So my idea is that quantifying kind of quote unquote. The violation
Salvatore RIBISI: light, conform thermodynamics by this nonconformal matter may give insights of this object, so maybe we can give
Salvatore RIBISI: quantification of
Salvatore RIBISI: a
Salvatore RIBISI: if like. If there is an actual link between the
Salvatore RIBISI: speculation that have been done in this paper.
Salvatore RIBISI: and the mechanism which is being started by
Salvatore RIBISI: these are all source.
Salvatore RIBISI: But as that can be working.
Salvatore RIBISI: another interesting perspective, in my point of view.
Salvatore RIBISI: comes from the study of moving mirrors, which is usually done in one plus one dimensions. So there are several reasons, of course, why it's done in one plus one dimension. One is that that
Salvatore RIBISI: and the
Salvatore RIBISI: the trajectories of moving plane gives
Salvatore RIBISI: gives like our like radiation and
Salvatore RIBISI: bring their own. Servers
Salvatore RIBISI: are, are not spherically symmetric. So one side
Salvatore RIBISI: of the problem comes from the non spherical symmetricity. If you want of
Salvatore RIBISI: of ringer observers of 5 min of ringer observers. So in this case, I think that this different decomposition, which is spherically symmetric, might help
Salvatore RIBISI: building some models of
Salvatore RIBISI: of spherical is in metric.
Salvatore RIBISI: me worse, and trying to build some unitary model where you can start with the
Salvatore RIBISI: their, their, their effects and their properties.
Salvatore RIBISI: On the other hand, another reason, of course, is that one plus one dimensional conformatory theory is easier way, more easier way, easier than
Salvatore RIBISI: the 3 plus one dimensional. And okay for this complication. They I don't have any help to be like this is
Salvatore RIBISI: this, of course, a fact.
Salvatore RIBISI: But I hope that the previous problem is can be.
Salvatore RIBISI: can still be overcome by this by this analysis.
Salvatore RIBISI: So there is also some work
Salvatore RIBISI: by some collaborators where they show that where they find this conformal temperature
Salvatore RIBISI: in the in the context of conformal quantum mechanics.
Salvatore RIBISI: And yeah, I'm also interested to see it
Salvatore RIBISI: like, what is the direct link from
Salvatore RIBISI: quantum mechanics to
Salvatore RIBISI: to to
Salvatore RIBISI: I mean for dimension of one to fifth theory. And if there is a way to to explain this relation? Directly, because I mean events the same, they find the same temperature.
Salvatore RIBISI: and that's similar, the composition. So I want to see what are the limits of this
Salvatore RIBISI: of the of their analysis. And what are the the nice properties? Instead?
Salvatore RIBISI: I didn't get into the hand, I promise. So they come with the perspective. So in another one comes from the area of measurements. In point of view, theory, where
Salvatore RIBISI: the algebra of observables related to apparatuses
Salvatore RIBISI: has come back support in the regional space, and we share the same features as total diamonds.
Salvatore RIBISI: So I again.
Salvatore RIBISI: I wonder if studying the the problem of measurements by
Salvatore RIBISI: in in Nikosi space, and by different apparatuses
Salvatore RIBISI: can make use of these results like, if there is, there is some link.
Salvatore RIBISI: And then the last question I have like. I wonder how angular momentum will will enter this game, because
Salvatore RIBISI: there are insights here and there that
Salvatore RIBISI: there is a way to define a charge associated to angular momentum in this case. But of course, there are also complications given by extremality and
Salvatore RIBISI: and rotating space times which
Salvatore RIBISI: can be non-trivial, for in the case of Mikos in in the in the case of light comes.
Salvatore RIBISI: So I wonder if there is a way to to study this problem
Salvatore RIBISI: like accurately, but like finding some results with, but
Salvatore RIBISI: without getting too much in trouble. And that's it, I guess. So thank you for the attention
Salvatore RIBISI: I'm open to questions.
Hal Haggard: Thank you so much. Savatory.
Hal Haggard: Lee. Please go ahead.
Lee Smolin: Yes, can you summarize your work?
Lee Smolin: In a way the result is very simple. Tell me if I'm right, if you have an an ingoing.
Lee Smolin: but
Lee Smolin: near scry minus.
Lee Smolin: and then you can find a new continuation of the wave function without singularity into an outgoing particle near Scribe, plus by making use of these identifications
Lee Smolin: is that the interpretation of your result.
Salvatore RIBISI: It.
Salvatore RIBISI: Hurricane! Can you repeat? I'm not sure I'm getting the.
Lee Smolin: If if I take them in going.
Lee Smolin: aren't
Lee Smolin: near sky minus.
Lee Smolin: it's non singular region one I can transform and follow the wave function to a non singular outgoing quantum near spy plus
Lee Smolin: is that, yeah?
Lee Smolin: So that is, gives us a kind of definition of a quantum field theory
Lee Smolin: involving both the region ingoing and the region outgoing, which is non singular.
Lee Smolin: I think that that's that's a good. If I'm correct, that's a very interesting. Please help.
Salvatore RIBISI: Yeah, okay.
Salvatore RIBISI: I think.
Lee Smolin: In. In other words, if I had a regular.
Lee Smolin: a, a normal solution, which was singular in the region one, I wouldn't see that I could get this way. I can take a pure state incoming, you know
Lee Smolin: the pastor region one and 2,
Lee Smolin: and continue it to an outgoing quanta.
Lee Smolin: which is non singular.
Salvatore RIBISI: Right? Okay.
Lee Smolin: 5 plots.
Lee Smolin: So that gives you a non singular definition
Lee Smolin: of a quantum field theory.
Salvatore RIBISI: So having a a quanta which is non, which is non singular here in region one.
Lee Smolin: Can join to Aquanta, which was non singular.
Lee Smolin: falling in near sky, minus.
Salvatore RIBISI: Right. Yes.
Salvatore RIBISI: it will give you a non singularity.
Lee Smolin: And so this gives you a definition
Lee Smolin: of the states of a quantum field theory, which is time asymmetric.
Lee Smolin: but which is non singular.
Lee Smolin: I may be just wrong. Could somebody correct me if I am?
Lee Smolin: But that's what I think you're you're saying here in this blue region.
Salvatore RIBISI: Yeah, but I I'm I'm not sure I follow. What is the
Salvatore RIBISI: singular part.
Lee Smolin: Well, there is no single.
Salvatore RIBISI: Alright. Okay. Yeah. Yes.
Lee Smolin: That's important.
Salvatore RIBISI: Yes, yes.
Hal Haggard: You, Jen. You had a question also. If you wanna respond to Lee's request, feel free as well.
Lee Smolin: Yes, please.
Eugenio Bianchi: No, not really. I don't. I'm
Eugenio Bianchi: don't have anything to add, though. I I I can go ahead and ask. Yeah, I saw a lot of real stuff. Okay?
Salvatore RIBISI: Yeah. Yes. Please.
Eugenio Bianchi: Salad. A very nice talk. I I have 2 questions one on
Eugenio Bianchi: So conformal symmetry plays a central role here in the mathematics. I want to understand. What is your perspective on the physics? Do you need conformal symmetry to speak about thermodynamics? If your scalar field does a mass? What is the point that you would make.
Salvatore RIBISI: So if my color field doesn't mass.
Salvatore RIBISI: I am.
Salvatore RIBISI: There must be some. That's where I was
Salvatore RIBISI: kind of mentioning here. There must be a violation of something.
Salvatore RIBISI: but this violation can be quantified.
Salvatore RIBISI: So the point is that
Salvatore RIBISI: I don't think this pleating will be as easy in the case of
Salvatore RIBISI: non-form matter.
Salvatore RIBISI: I don't know conformally invariant field theory, but I think we can get.
Salvatore RIBISI: and we could get an insight of what's going on
Salvatore RIBISI: by looking at the
Salvatore RIBISI: at the lowest. So
Salvatore RIBISI: by looking at, I think the from these lows we can see, we can see. I mean by starting it.
Salvatore RIBISI: We might see, like what happens once the conformal environment is broken.
Salvatore RIBISI: We can quantify, and we might get.
Salvatore RIBISI: I don't know. Like the we can see
Salvatore RIBISI: how thermodynamics will get modified.
Salvatore RIBISI: But
Salvatore RIBISI: what I'm
Salvatore RIBISI: quite sure about is that
Salvatore RIBISI: it cannot be the same like if you you wouldn't type. The thermodynamics wouldn't be exactly the same.
Salvatore RIBISI: But you. So you will have a trace part coming from here from
Salvatore RIBISI: from the mass. This end.
IEM-CSIC: Put a lot of attention to it, but I feel like.
Salvatore RIBISI: Okay? And so yeah, I think you will have another term
Salvatore RIBISI: quantifying this
Salvatore RIBISI: violation
Salvatore RIBISI: of conformal environments. So I don't know if I'm answering, but it's like this is.
Salvatore RIBISI: what do you think about it?
Eugenio Bianchi: Yeah, that that's and the second question I had is, if you had thought about looking at the general boundary in this situation together with Harle and Carlo. We had considered this diamonds and affiliation of the diamond
Eugenio Bianchi: and the fact that you can identify the fact that the region is mixed by looking at that foliation, that lens shape general boundary. This is something you can do both if you are conformal symmetry, if you don't have conformal symmetry.
Eugenio Bianchi: but for conformal symmetry. Clearly
Eugenio Bianchi: you can do more. Have you? Have you looked at that.
Salvatore RIBISI: And no, I mean I I I think I see what works you're talking about. But
Salvatore RIBISI: no, I don't. I haven't looked about the this
Salvatore RIBISI: results like, what are the
Salvatore RIBISI: you mean? The timel properties by looking so instead of getting the whole Nikkowski only getting the only studying the the diamond. That's what your
Salvatore RIBISI: so Justin, you.
Eugenio Bianchi: Can consider a foliation inside the diamond as fluation. It is adapted to the coordinates that you've introduced. Yeah.
Salvatore RIBISI: Okay, no, I haven't.
Salvatore RIBISI: I haven't started yet, please.
Salvatore RIBISI: This situation.
Salvatore RIBISI: Thanks for the remark.
Eugenio Bianchi: Okay. Thank you.
Hal Haggard: We have a question in the chat which I'll read out. But if the questioner would like to to follow up, please feel free. So they ask.
Hal Haggard: why do you? Why does your surface have the interpretation of temperature?
Hal Haggard: Is it different from the killing one? Does this interpretation make sense.
Salvatore RIBISI: Okay, so first of all.
Salvatore RIBISI: is a.
Salvatore RIBISI: so the difference with the killing one is that
Salvatore RIBISI: in this case, I mean, if I understand correctly the question, I would say, like, in this case, we don't have a Canadian field. We have something which is different, like which is not.
Salvatore RIBISI: which is useful if you want more, general Buddy. So yeah, it's not like a healthcare field. So we have to find
Salvatore RIBISI: a more general definition.
Salvatore RIBISI: And the definition, of course, will be, then the properties will be weaker than those of an actual clean field.
Salvatore RIBISI: But okay, if you look, want to see the interpretation.
Salvatore RIBISI: the first interpretation comes from. This comes from the fact that
Salvatore RIBISI: if you do the matter per, if you do matter perturbations, you do get a balance lower. This temperature
Salvatore RIBISI: appears.
Salvatore RIBISI: and then again,
Salvatore RIBISI: a different thing. Another interpretation come from the fact that if someone really, for some reasons
Salvatore RIBISI: you want to decompose them for ski vacuum
Salvatore RIBISI: in terms of particles associated to these 2 different regions. So space time.
Salvatore RIBISI: you do you see that this temperature appears
Salvatore RIBISI: then? And this is like the second answer I will give
Salvatore RIBISI: while staying inside Minkowski. Space time. Then, for the third answer I will go. I will leave.
Salvatore RIBISI: Nikos is past time, and I will go to the real of conformally related geometries.
Salvatore RIBISI: And then there there is a set of conformal transform of Y transformations
Salvatore RIBISI: of the the Minkowski metric.
Salvatore RIBISI: where this conformal student field becomes an actual killing field.
Salvatore RIBISI: and then, in that case
Salvatore RIBISI: the interpretation is the usual one, because the light guns are mapped
Salvatore RIBISI: to actual killing horizons, and the temperature will be the temperature
Salvatore RIBISI: measured by any
Salvatore RIBISI: extension. You know. Stationary observers following that orbit
Salvatore RIBISI: will be similar to the same interpretation of
Salvatore RIBISI: hawking temperature for
Salvatore RIBISI: for for an event horizon. If you want.
Hal Haggard: They, they thank you.
Hal Haggard: Are there other questions or comments?
Hal Haggard: I have one, but it's one of these slightly unfair ones, because I'm going to ask if you know a reference. Have you seen this work of
Hal Haggard: of Zurich and Catherine Zurich and Eric Verlinde, where they're proposing that the thermodynamics of this variety that you're talking about.
Hal Haggard: Might be measurable in gravitational wave interferometry.
Salvatore RIBISI: You know the answer is very simple. No, I haven't tried.
Hal Haggard: Okay, it's fine. I I.
Salvatore RIBISI: Definitely, a reference.
Hal Haggard: Yeah, that's fine. I'll send it along to you. I'm very. They're they're proposing that we actually might measure these these fluctuations of space time, and that that would indicate quanta.
Hal Haggard: And I'm very curious, you know. I I'm curious whether what we all think of that as a community.
Salvatore RIBISI: Okay.
Hal Haggard: Eric Longin was next, and then Lee.
Erlangen: Yeah. Hi, this is Hannah speaking. Can you hear me?
Hal Haggard: Yes.
Salvatore RIBISI: Hey? Yes.
Erlangen: Great thanks for the nice talk I just wanted to say, and I think you mentioned this, but I wanted to understand it better. I wanted to say that this situation reminds me of the quantum queue theory for an accelerated observer in the wind language.
Erlangen: and in particular also to what is called in this quantum field theory, algebraic quantum field theory, community that these are double week month theorem, which says that in this sort of double which you have.
Erlangen: I believe you have exactly this, this kind of thermal structure for the for the state that you have there. In this, I mean, they formulated very differently. But but I think it boils down to something like something like your this, this equation that you had. Just now this blue equation where you have the tool, this this thermal factor, and then a tensor product of the left and right States.
Erlangen: And I wanted to know if you have any comment on this. If this is the same, if yours is sort of a generalization to an arbitrary
Erlangen: conformal.
Erlangen: conformally flat space times of this.
Salvatore RIBISI: Yeah. So so first of all, I mean, I know the but I I think you didn't mention the cable theorem. It was an older theorem.
Salvatore RIBISI: So I know that in the case of a call of a bifurcation surface you're right. There is then the
Salvatore RIBISI: the decomposition or vacuum. I mean that they
Salvatore RIBISI: you can see a thermal vacuum.
Salvatore RIBISI: I mean, given, there is a global vacuum which appears
Salvatore RIBISI: paramount in the in the 2 wedges. So so in this case it's it's not a killing. It's not a bifurcation.
Salvatore RIBISI: It's I mean that
Salvatore RIBISI: it's a conformal bifurcating surface.
Salvatore RIBISI: So the difference is that here you don't have a skinny field. You have a conformal kingy field.
Salvatore RIBISI: and yes, and you are. So this is as in the in the Arv case. What's I think it's not obvious, but maybe
Salvatore RIBISI: I'm wrong. But
Salvatore RIBISI: I when I looked at it, it didn't seem obvious, is that you can always
Salvatore RIBISI: that the fact that it appears thermal. I agree. The the fact that you can always decompose it explicitly
Salvatore RIBISI: seems to me I think it's
Salvatore RIBISI: slightly less trivial, but the the full decomposition.
Lee Smolin: Shouldn't reiterate.
Salvatore RIBISI: But yeah, for it was for Kimville.
Salvatore RIBISI: is they? I mean, that's what happens with with the reindeer kidney field in.
Erlangen: Yeah.
Salvatore RIBISI: There, I don't know. Thanks.
Erlangen: Okay? So so it's a different
Erlangen: different different feel right? Different length.
Erlangen: Hey? Thank you.
Salvatore RIBISI: As you do.
Hal Haggard: Lee, did you want to go ahead with your comment?
Lee Smolin: Well, I think I'm hardly the person to express the view of the field.
Lee Smolin: but I do, repeating one of the older members. I do recall that there was a very similar discussion.
Lee Smolin: maybe 2030 years ago, by people criticizing the Fermi Lab group.
Lee Smolin: who, if I remember right, made the same proposal, and it was pointed out by Giovanni Milliona, Camellia
Lee Smolin: and other people that they were basically
Lee Smolin: the tab
Lee Smolin: getting rid of the
Lee Smolin: of the phase that makes the vacuum coherent and replacing it by a thermometer
Lee Smolin: and vacuum, which is.
Lee Smolin: if we're conservative members of the field, is neither right thing to do.
Lee Smolin: You can always make more particles appear by putting in a thermal path in the vacuum.
Hal Haggard: Thanks, Lee.
Hal Haggard: other questions or comments.
Hal Haggard: I'm going to take the luxury of a few minutes just because we have a little extra time. So do. If you're thinking of something, it's it's feel free.
Salvatore RIBISI: I think I mean I'm fine.
Hal Haggard: Okay. Wonderful.
Salvatore RIBISI: Thanks for the yeah. Thanks for the questions. It was very nice and nice discussion.
Hal Haggard: Good.
Hal Haggard: Thank you, everyone, and we'll see you soon.