Norbert Bodendorfer: Hello i'm back.
Norbert Bodendorfer: i'm very sorry for this my Internet connection failed.
Norbert Bodendorfer: Can you hear me now.
Jorge Pullin: yeah I think zoom in general fail because it kicked me off i'm just putting me back.
Please come.
Jorge Pullin: seamlessly keep kept on recording.
Norbert Bodendorfer: So just let me know when I should continue, and also what was the last thing that I said.
Jorge Pullin: Just just you can continue and.
Jorge Pullin: I got kicked out, so I don't know.
What happened later.
Jorge Pullin: Okay.
Norbert Bodendorfer: Good so let me continue, then yes, we read you sure, so what I was saying before, when I was saying, the word.
Norbert Bodendorfer: Is not share sorry.
Norbert Bodendorfer: Okay, so.
Norbert Bodendorfer: What I was mentioning before, is that we cannot read off or gravitational read normalized hamiltonian so we have a fundamental hamiltonian that is the one in representation and J equal to one half, where we have.
Norbert Bodendorfer: Most fine grained view on our system we keeping track of all possible volume mind states and the course version we now get by computing the.
Norbert Bodendorfer: By just taking the generators here in a larger representation and this gives us this operator down here yeah and the difference now is that.
Norbert Bodendorfer: We again have a sign time sign structure, but the volume now has corrections that depends on this realization scale che we are at yeah and, if you take James one half they just drop all of them drop out here, as you see, and then this last line also become zero if you sent Jacob one half.
Norbert Bodendorfer: And this line here produces this volume yeah So what we see is that this reorganization room floor so keeping track of less volumes or course grading wise together.
Norbert Bodendorfer: That produces small volume corrections like this in particular produces large, small volume corrections because they grow with the amount of course gaining that you do.
Norbert Bodendorfer: Also, what we can note here is that this hamiltonian has again.
Norbert Bodendorfer: is again build from this se one one operators in a representation.
Norbert Bodendorfer: Which means that it will preserve.
Norbert Bodendorfer: These.
Norbert Bodendorfer: Sub spaces, that we have drawn here yeah so it of course preserve the sub spaces, which are considered as those spaces, where you have to renew ominous theory.
Okay.
Norbert Bodendorfer: So now we will discuss this operator, a little more later, when we talk about what lessons should be drawn.
Norbert Bodendorfer: From this calculation here.
Norbert Bodendorfer: But before we do that we can try now to estimate how big the error is that you're doing if you're neglecting such effects.
Norbert Bodendorfer: And this is what will be done in this section here we're just on the error estimation.
Norbert Bodendorfer: So we're not doing a computation we are, we are just come to compute the cosmological evolution of such a system, this is the standard accuracy computation.
Norbert Bodendorfer: We you start with some States, you know that that redefined far away from the quantum regime say.
Norbert Bodendorfer: And then you evolve them, and when you get close to the big bang singularity that you would have classically, then you get something like a big bounce and your system is perfectly regular during that bounce.
Norbert Bodendorfer: The question is now how do we set the rationalization scale here yeah So what should this.
Norbert Bodendorfer: scale jb.
Norbert Bodendorfer: And now, if you have some bouncing a cosmology then at the time of the bounce the volume is the smallest, so this is just how the balance works.
Norbert Bodendorfer: And when you go back to our core screening picture we have this many hidden workspaces and when we are at the balance or volume is the smallest and.
Norbert Bodendorfer: Then the we want the some of the volumes here and not to be smaller than the smallest volume, because then wouldn't you go description or sister yeah so this puts now a restriction on the amount of kind of find draining or refining that we can do yeah because, if we have a certain.
Norbert Bodendorfer: minimum volume or.
Norbert Bodendorfer: We have a certain volume at the balance, then we cannot put too many of these cells.
Norbert Bodendorfer: There, because the cells each come with a minimum of volume and we cannot exceed the volume at the balance.
Norbert Bodendorfer: yeah so the most fine grained version of this computation we can do is if we have the minimum volume or the volume gap in each of the cells at the bounce yeah So this is the most extreme find raining that we can do for our computation.
Norbert Bodendorfer: And that is also then what we take as an rg scale, so we would like to take the.
Norbert Bodendorfer: volume that we have at the balance in one cell at as an rg or this kind of the rg scale and we now do computation for or we do with the standard accuracy computation where we compute the cosmological evolution and we want to track the density at the bounce.
Abhay Vasant Ashtekar: So can I just ask a quick quick question since the judicial cell was any way an arbitrator So could I not just say that the traditional cell is the one that the volume of the traditional sales solid the bonds, is in fact the minimum value so in some sense I mean it.
Norbert Bodendorfer: So that is what actually yeah.
Norbert Bodendorfer: So this is.
Norbert Bodendorfer: yeah this is how you would intuitively think about the most fine grained version of your theory.
Abhay Vasant Ashtekar: So that's compatible with what you're doing is that right.
Norbert Bodendorfer: yeah that's exactly what i'm doing.
Abhay Vasant Ashtekar: Good Thank you yes.
Norbert Bodendorfer: yeah so now you want to do this computation that we just discussed and you can do it in such a way that in each of the cells.
Norbert Bodendorfer: You have this G which one half representation to the most fine grained representation or you could do it in such a way that you have a higher representation in each of the cells.
Norbert Bodendorfer: But then also what you mean by minimum volume gets changed now, so you could do this computation even if you already did some.
Norbert Bodendorfer: sort of course training here, along the lines that we discussed before and it's still the same computation so this jake.
Norbert Bodendorfer: will enter, but as I just said what we've learned is that during the bounce in one cell, we have the minimum possible volume for the representation that we're working with at the moment.
Norbert Bodendorfer: And the result of the computation is not giving here, so we first compute the expectation value of the hamiltonian.
Norbert Bodendorfer: And we compute that in one of these per room of coherent states, and then it turns out that from these you know labels there's just one number alpha that is real number.
Norbert Bodendorfer: ranging between zero and one is important, and this value of this morning comes out as one of our alpha times some prefect are dependent on Jay.
Norbert Bodendorfer: yeah again has to be multiplied by Jay because it is an extensive quantity and it's one this one of alpha is this function, depending on the spinners that you.
Norbert Bodendorfer: know you also compute the volume at the bounce time, so you can compute what is the balance time there by minimizing the volume and then computing this object here.
Norbert Bodendorfer: And you find this Islam that Jay so against gates lecture because its extensive and then it has this dependence on the spinners.
Norbert Bodendorfer: And this is a function, you can check this is always bigger equal than tool which is good, because then the reside here is bigger than to them the J, which is just the volume gap in the representation of working in yeah.
Norbert Bodendorfer: And now you can divide the tool and you get what you would typically call the density at the bounce now, this is the metric energy density at the bounce.
Norbert Bodendorfer: And this is famously a bounded quantity and groupon cosmology and what you find is it gives you this expression here.
Norbert Bodendorfer: And this now is smaller equal than one or two number squared and if you ever did these computations with this polarized hamiltonian.
Norbert Bodendorfer: Then you know that this one over to Lambda squared, this is what the effect of classical computation would give you yeah so the effect of classical computation gives you a.
Norbert Bodendorfer: upper limit on this density, at which real quantum states can bounce and here we see that a real quantum states have a smaller or equal bounce density, which is then again what we would expect.
Okay.
Norbert Bodendorfer: But now what we do, we visualize the result of this computation in a diagram and here we plot on the first access this parameter alpha that labels how the physical result is.
Norbert Bodendorfer: And what we plot now is in blue we plot, the volume at the bounce and we normalize it by the minimum volume that we have an all representation.
Norbert Bodendorfer: So that the smallest possible value that blue line can take us one because of its normalization here, so it goes to one as alpha goes to one.
Norbert Bodendorfer: And here in real units that volume would be too long the J and all the bounce density for alpha equal to one is one over for Lambda squared in real units or normalized with the critical effective density one half now.
Norbert Bodendorfer: And now, as you decrease alpha towards zero, you will find that the volume at the bounce becomes large.
Norbert Bodendorfer: So, as you go here, the volume at the balance becomes large and diverse as you go to alpha equal to zero, and at the same time, the density at the bones increases and goes, all the way to one yeah it goes to the critical effective density.
Norbert Bodendorfer: And this statement, you know as saying that if you have very large quantum numbers and, in this case, meaning of volume that is very large throughout the complete evolution in particular at the balance.
Norbert Bodendorfer: Then you work physics is faithfully described by the classical effective equations yeah and then also the bounce density goes to the density up rife with effective equations.
Norbert Bodendorfer: But now for us in this course training point of view as said we would like to have the true physical description, to be the most fine grained one.
Norbert Bodendorfer: Meaning that from the true physical description, you get this one of a for Lambda squared bounce density.
Norbert Bodendorfer: And you would also get that for one more for Lambda squared bounce density, if you would act with a renewal as tema tuning on the properly renominated states where the large trace states.
Norbert Bodendorfer: And, whereas if you act with the fundamental hamiltonian on the States with large J then you're in this effective equation regime and you obtain this bonds density.
Norbert Bodendorfer: So in this simple toy model that we're doing here for this observable off the bounce density you get a factor of two difference if you neglect every normalization.
simone: So you know.
simone: i've lost something.
simone: Because alpha is just the part of the label of the credence to the birth of the speed or which you said you take the same in the small scale, or in the large scale coarse grain or finer picture.
Norbert Bodendorfer: So, so what.
simone: Why is now.
Norbert Bodendorfer: Yes, so what other determines is on.
Norbert Bodendorfer: Is kind of on which magnetic quantum numbers here coherent status peaked.
simone: Sure, yes.
Norbert Bodendorfer: And what you see here, if you take alpha one now, then this becomes a tool.
Norbert Bodendorfer: This becomes two and then your volume at the balance is to Lambda Jane So this is the minimum volume so then.
Norbert Bodendorfer: If you take alpha equal to one then your coherence status peak completely on the lowest possible volume styling state yeah so you can set is exactly the lowest volume mind state.
simone: yeah okay.
Norbert Bodendorfer: yeah whereas if you take alpha going to zero, then you can check.
Norbert Bodendorfer: This volume becomes very large so your coherence date will repeat on very large volumes.
simone: No, no, no that's fine but, but you said that in the finer picture, or in the course picture the label of the golden state is the same, so they we normalize or no normalized as as they have the same out, for this is what i'm not understand the.
Norbert Bodendorfer: essence, so they have the same alpha what I was trying to say here is that the computation here, you can do for any J so.
Norbert Bodendorfer: think you already read normalized your system that for some level J, so you already coarse grained some fine representations into one box, then you can sit with this computation.
Norbert Bodendorfer: But then the volumes that are supposed to be small other volumes that are close to the volume gap in the renewal unless representation in and the volume get becomes larger so that alpha tells you how close to the volume gap, you are.
Norbert Bodendorfer: yeah in the volume get is different in different representations.
Norbert Bodendorfer: Because in a higher representation to course many, many volumes together, so your volume gap has to increase.
Abhay Vasant Ashtekar: Can I ask kind of a related but there's like different mission at a fundamental level you we all, we agreed that.
Abhay Vasant Ashtekar: I mean that is natural to say that that the bounce there is only kind of the initial set is chosen, so that the bounce the volume is the minimum possible right so with the with the yeah.
Abhay Vasant Ashtekar: So, then, I just have a value for the role there Why am I robots, why is it robots running, is what I don't understand because.
Abhay Vasant Ashtekar: We believe that.
Abhay Vasant Ashtekar: Yes, fundamental answer is just fix right.
Norbert Bodendorfer: Yes, so rebounds depends on the volume that you have at the bounce.
Abhay Vasant Ashtekar: Right and we agree that we.
Abhay Vasant Ashtekar: Choose it we choose a fuel cells, so is that the volume of the bombs is the minimum possible right in there.
Norbert Bodendorfer: So, you know that is what you would ideally do so this is this is this end of this picture so to the minimum possible, then you read this end, but you may also.
Abhay Vasant Ashtekar: choose a while it.
Norbert Bodendorfer: Is and then you go towards this.
Norbert Bodendorfer: Effective equation limited.
Abhay Vasant Ashtekar: But, but I mean you know there's also the.
Abhay Vasant Ashtekar: From the accuracy hamiltonian whatnot can also opt in.
Abhay Vasant Ashtekar: I mean, of course, one can also opt in the lower bound of that hamiltonian.
Abhay Vasant Ashtekar: Right image don't operate without going into the effective theory.
Norbert Bodendorfer: Yes, exactly.
Abhay Vasant Ashtekar: And, and the point was that that lower bound is extremely close to what happens for a very sharply big states, yes, which is which up like the aquarian state, so therefore I would be at the right hand side of your graph right.
Norbert Bodendorfer: You know, for, for the very sharply peak states that you're referring to your at the left hand side because they have a very large volume at the bounce.
Norbert Bodendorfer: Usually choose your state, so that they still have a large volume at the balance.
Abhay Vasant Ashtekar: I think, maybe we.
Norbert Bodendorfer: Thought as all of these states, you have a large volume when you're far away from the bounce.
Norbert Bodendorfer: Of the relevant question is, what is the value of the volume at the bounce.
Right.
Abhay Vasant Ashtekar: Okay i'm getting with everything but there's still some disconnect but maybe we should just.
Norbert Bodendorfer: Okay, let me, maybe this clarifies it so.
Norbert Bodendorfer: This picture is not surprising to a QC practitioners because they're the similar statement would be that small volumes bounce with less than critical density, so this is an observation that has been made before yeah and some limit using coherence states and also in America right like.
Abhay Vasant Ashtekar: But Okay, I think we should I mean i'm Am I getting I just various results, I see, but I did they don't connect for me, but I think I should just talk to you so let's just go.
Norbert Bodendorfer: yeah so then.
Norbert Bodendorfer: i'm about done, I just want to mention, where I think, or what lesson I think should be drawn from this computation here.
Norbert Bodendorfer: So, first the technical lessons and the technical lessons that I see is that.
Norbert Bodendorfer: small volume corrections are amplified by the rg flow So if you compute some sort of energy flow, we should expect that small volume corrections are amplified and, in particular, we see here that, if we normalize a state to escape J, then the corrections are also off the scale J so here.
Norbert Bodendorfer: This operator here is sensitive to this correction when the volume is of scale to Lambda J.
Norbert Bodendorfer: yeah so this means if you're going to microscopic scales or by going to microscopic scale, you cannot get rid of small volume corrections now, because if you're going to microscopic scale are using quantum states that are peaked at microscopic skates, then you need to use the.
Norbert Bodendorfer: Properly or anomalous tenant Union.
Norbert Bodendorfer: And that contains terms that have a small volume corrections that are sensitive at those gates.
Norbert Bodendorfer: And somewhat surprising to me, even if your fundamental hamiltonian does not seem to feature any small volume corrections yeah like we remember me Tony here did, then these small volume corrections can be generated by the article.
Norbert Bodendorfer: So you should expect to have them.
Norbert Bodendorfer: and also what we just saw the rg flow is most pronounced when course screening from smallest to intermediate spins yeah so.
Norbert Bodendorfer: For example, if you look at this red line down here if you increase your spins from the smallest possible wants to two times the smallest possible ones.
Norbert Bodendorfer: You almost make all of your arrow at this point yeah So if you go to say five or so, then, then you know you like 99% of your error is already made if you're using spins at the order of five or so.
Norbert Bodendorfer: yeah, and this means that you cannot get away by using what someone would call intermediate spins, so there are spins they're not very large but also not very small, so this is also something that does not work.
Norbert Bodendorfer: Okay, so, then what is the relevance of these computations and clearly this is a very simple time model with very strong assumptions and those assumptions need to be lifted.
Norbert Bodendorfer: In a future computations but as far as what i'm thinking is that you cannot expect that such effects would go away, as you make your system more complicated so use our G flow can only become more complicated, as you make your system more complicated yeah.
Norbert Bodendorfer: And then the effect that we saw here is this effect of using many small spins instead of few large bits.
Norbert Bodendorfer: So then similar rg effects should be expected in the following types of computations.
Norbert Bodendorfer: So, for example, if you compute your effective dynamics, by taking the expectation value of some hamiltonian in some set of States, those are typically coherence states and typically pete.
Norbert Bodendorfer: On our spins and then this large spin is important here, so there you would expect that the small spin answers different getting the results derived here.
Norbert Bodendorfer: The same is true if you take a large spin boundary state in spin for models and then the important word is again non renominated spend for models, because if you would take renomination into account as we did in this time order.
Norbert Bodendorfer: Then, of course, the large and small spin answers are the same yeah.
Norbert Bodendorfer: So here for this point i've shown you the computation only in the canonical quantization in this talk, but we have transferred everything also to work here in state path integral.
Norbert Bodendorfer: we're at the same result happens and if you're interested in that there are extra slides, but they did not fit in the regular talk.
Norbert Bodendorfer: And also these things will be taken into account when you do a little condo cosmology.
Norbert Bodendorfer: And there again large quantum numbers correspond to taking the volume at the bands that we large, and this is something that is often done to get rid of small volume effects that you have in several of the htc hamiltonian.
OK.
Norbert Bodendorfer: And now to collect this in one a catchy statement.
Norbert Bodendorfer: So I would say that why large spin loop quantum gravity seems to lead to a discrete version of GR so this seems to be well established in all of these approaches here.
Norbert Bodendorfer: This is a different limit than the continuum limit, so the limit of many small spins and now the important takeaway from this calculation is that the quantum effects of different.
Norbert Bodendorfer: yeah So if you would work in this type of computation you may still say that.
Norbert Bodendorfer: While you get discrete you are at some scale and then, if you work above that scale then you're still fine, but now this calculation tells you that you should not expect to get the same quantum effects in that.
Norbert Bodendorfer: Calculation here, but if you don't get the same quantum effects, then it's questionable.
Norbert Bodendorfer: Why you do this calculation because you're interested in the quantum effects of the continuum theory and not the quantum effects of some other limit, which is some discrete GR limit that is disconnected from this continual theory.
Okay.
Norbert Bodendorfer: So then, there are some conclusions which I just mentioned, in part, so just two things I won't mention.
Norbert Bodendorfer: there's a square and say path integral on the extra slides if you're interested.
Norbert Bodendorfer: And one thing that is, I think, important here is that the result that we did right here it's not surprising by itself, because it's very well known that.
Norbert Bodendorfer: hamiltonian re normalize haga what was somewhat surprising is that you can do everything erotically here.
Norbert Bodendorfer: And you can do that because you strongly use this Su and group structure, which relates this course training in the simpler cosmological systems to a changing representations in a group theory Okay, so thank you very much.
Jorge Pullin: or any questions.
Abhay Vasant Ashtekar: So could you go back to two slides.
Abhay Vasant Ashtekar: Right, so I think you're saying that the this small i'm still confused.
Abhay Vasant Ashtekar: about the I mean it's almost everything I understand, but then there's some disconnect for me so are you saying that if I in fact I did what I what we agreed that we might do, which is to take us fuel cells, so that it's walling to the minimum possible at the moms and then we go on.
Abhay Vasant Ashtekar: Then, in that case, are you saying that there there's going to be a major deviation.
Abhay Vasant Ashtekar: Some.
Norbert Bodendorfer: classical music.
Abhay Vasant Ashtekar: Because of large volumes, because we are course grading on a more and more towards grading.
Norbert Bodendorfer: So so sorry I didn't get this part of the question so it's a major deviation where.
Abhay Vasant Ashtekar: Again, so that all the J corrections right.
Abhay Vasant Ashtekar: And so, as a university evolves I mean you know, presumably Jay becomes larger and larger right.
Norbert Bodendorfer: I know, so I mean Jay is Jay is fixed once and for all ah.
Norbert Bodendorfer: yeah so Jay just tells you how many of these small cells, you have coarse grained so what you're asking is when when are these corrections important the.
Norbert Bodendorfer: corrections are important.
Norbert Bodendorfer: When the volume is close to the minimum volume to the volume gap because here's essentially the volume get squared.
Norbert Bodendorfer: Roughly the volume get squared was written here, so these corrections I important close to the bounce.
Norbert Bodendorfer: And what they do is they modify in this example the bounce density, if you compute the expectation that you have the volume and the result looks exactly like that, for the effective equations just with a difference that the bounce density gets cut in half.
Norbert Bodendorfer: yeah and.
Abhay Vasant Ashtekar: As soon as it may, stop even with respect to the the what was called as the minimum energy density.
Abhay Vasant Ashtekar: By the.
Abhay Vasant Ashtekar: Day just take the expertise and value of the operator.
Abhay Vasant Ashtekar: In any State you want.
Abhay Vasant Ashtekar: The list of the density operator in any state you want yeah so the last part right so.
Abhay Vasant Ashtekar: i'm not sure about factors have to.
Abhay Vasant Ashtekar: I think the ltc result is that these robots minimum is one apple to Lambda squared in your case.
Norbert Bodendorfer: Exactly yes yeah okay.
Abhay Vasant Ashtekar: Okay, so so that is the result, and that is the I mean coming from the.
Abhay Vasant Ashtekar: The lower bound to the angle of the density operator me that what you what you wrote down yes.
Norbert Bodendorfer: Yes, yes, so this is the, this is the upper bound of the density operator.
Norbert Bodendorfer: For some of the upper bound, that you can arrive in.
Norbert Bodendorfer: Africa with which you sing yeah and.
Abhay Vasant Ashtekar: And then, then the statement is that so, in what so i'm not understanding when the middle line is coming up.
Abhay Vasant Ashtekar: So the statement is our bounces really operating in the complete condom domain and then the the energy density maximum it is upon one upon to Lambda squared but you're saying something like if I look at re normalized something, then.
Abhay Vasant Ashtekar: This happens, but at the box itself Why am I read normalizing anything I should.
Norbert Bodendorfer: Okay, so maybe, let me make the statement again, and let me try to strip it of all technical complication so you want a true physical description of your system.
Norbert Bodendorfer: Where the volume at the balance will be the minimum possible volume right yeah and that computation you're doing, and that is this right hand limit here good now this just the result, and now you may also do a computation where the volume at the bones is large.
Norbert Bodendorfer: And this is this limit here okay yeah and then there's anything in between.
Norbert Bodendorfer: And this is just the result yeah and Now the question is, what is the physically correct computation.
Norbert Bodendorfer: Very good, so you know, there is also this is the interpretation question that you know need to answer for this picture here.
Norbert Bodendorfer: And what I would like to say is the physically correct computation is this one here, where you keep track of you know, as many as much of the fine grain structure as possible.
Norbert Bodendorfer: So in some sense quantum numbers are small in the quantum regime.
Abhay Vasant Ashtekar: Okay, I think okay.
Norbert Bodendorfer: And then you and you can do the computation now with this re normalized thing, the question is, you know if you want to describe this universe, which is built from this many smaller quantum numbers.
Norbert Bodendorfer: In terms of one single large quantum number, then you can do that, but if you want to do that, you need to use the renewal as tember 20th and then, if you use the renewal SME to infer that you still get this answer here yeah because.
Norbert Bodendorfer: In terms of the you can use the normalized hamiltonian and then your volume gap in this higher representation is now a larger volume gap yeah so you're still in this machine here.
Abhay Vasant Ashtekar: No, but what what I don't understand is that is in standard Lucas molly there's also a result which says that the the minimum eigenvalue the hamiltonian.
Abhay Vasant Ashtekar: That insecure operator is one upon to Lambda squared, as you just told me that is a convention.
Norbert Bodendorfer: yeah not maximum.
Abhay Vasant Ashtekar: Maximum of is is one upon to Lambda squared right, yes, but you're saying that the correct answer so you're saying that the maximum value is not attained at the mouse.
Norbert Bodendorfer: Now so So yes, exactly, so the calculation you're referring to is what is given any possible type of quantum state that you can use.
Norbert Bodendorfer: What is the correct what is the upper limit of this bounce density, and that is this one here and we completely agree about that, but the question is whether the suitable states, which you know suitable physical states.
Norbert Bodendorfer: You know satisfy that bound okay okay yeah and they don't like it.
Norbert Bodendorfer: As much repeat on large volumes at the bounce satisfy that bound, but states which are peaked on smaller volumes don't Okay, thank you.
Abhay Vasant Ashtekar: Thank you for the explanation I think anything, no, no i'm getting yeah okay.
Alejandro PEREZ: And I kind of asked the question.
Alejandro PEREZ: Okay sorry I missed the first part of your talk and i'm sorry I couldn't be there in wilmington this question might be a stupid question having to do with the fact that I didn't hear a piece.
Alejandro PEREZ: You use it is used to the language of randomization but the system here has finally many degrees of freedom what you're not, I mean the system is always something we find communities, a film is it correct to say that what you what you're doing is you know.
Alejandro PEREZ: Adding the connection between the this quantum cosmology mall description and the full theory and it is there in this connection to the full theory that you have this course raining taking place, so to say.
Norbert Bodendorfer: Yes, that is correct, so let me go to this picture, make it quick, so what i'm discussing so far is kind of this picture here you agree with me right, yes, but in the full theory that is this picture.
Norbert Bodendorfer: yeah so you know you have many vertices that are coarse grained into one vertex yeah and.
Norbert Bodendorfer: And that here happens with a finite number of degrees of freedoms, and that would also happen with a finite number of degrees of freedom from the full theory, if you consider that there's a gap in the volume.
Alejandro PEREZ: Losing user or when you do that well here, you always have the same news so it's a.
Alejandro PEREZ: it's an allegory of course raining or something like that, I mean it's not we call screening is.
Norbert Bodendorfer: It is course when you because you're keeping track of less and less degrees of freedom so here you're keeping track only of the global degrees of freedom seekers of the some of the volumes.
Norbert Bodendorfer: As well as you system, you have only one or two days a film that that's all always exactly and that's that's why you need to patch many of them together to talk about corresponding here yeah so in each of the cells, you have one set of these degrees of freedom.
Norbert Bodendorfer: So your sub do you typically introducing.
Alejandro PEREZ: yourself not.
Norbert Bodendorfer: In any medical screening or.
Alejandro PEREZ: Am I confused, I mean you, you don't have this cells, the cells appear only in your book your book notes in your notes to to justify one or another hamiltonian in theory that has only two degrees of freedom or one degree of freedom.
Norbert Bodendorfer: So if you I mean we can discuss it with this picture here, so there is a version of Luke quantum gravity.
Norbert Bodendorfer: That gives you a copy of the new quantum cosmology have a space for every vertex yes, and in this formulation.
Norbert Bodendorfer: You can track the volume of a box with one vertex or you can track the volume of a box, with four vertices or you know any number of them and, within that theory which is equivalent to considering copies of the htc habit space patch together so many copies of them, we asked this question.
Norbert Bodendorfer: So it is what you would typically think from a course training course grading question in full of gravity, so you do something like a block spin transformation that groups many vertices into one.
Abhay Vasant Ashtekar: Okay, thank you, so I mean another way, but let me see if I if I election and Norbert book is basically patient, I mean another way is another way to say this is really that you're looking at it.
Abhay Vasant Ashtekar: And then there is not a microstructure and a lot of.
Abhay Vasant Ashtekar: degrees of freedom but it's only when you call is green I mean as.
Abhay Vasant Ashtekar: When Alex was probably not there.
Abhay Vasant Ashtekar: Is that on the right hand side you got many more observable on the on the left hand side is, and so, when your course grading you're basically tracing or all those observers.
Norbert Bodendorfer: Yes, i'm.
Abhay Vasant Ashtekar: Sorry operating.
Abhay Vasant Ashtekar: So it's definitely got a few observers, and this, this is really the the tracing operation that is happening up here in the in you're.
Abhay Vasant Ashtekar: going from right to left left left hand corner, and that is why he went on the left hand side you've got only a few degrees of freedom really those few degrees of freedom are being regarded as being what is left over after you are average or after your coarse grain or already.
Abhay Vasant Ashtekar: Yes, so so therefore so analysis which I mean Alex was saying that the only two degrees a fair idea is that there are only two degrees of freedom because you are kind of Christ or all kinds of other things.
Yes.
Abhay Vasant Ashtekar: Is that okay Alex are you not happy.
I am still confused.
Alejandro PEREZ: Because on the right on the right, instead of a single be, for instance, in principle, is what you're saying about you would have more than one be.
Alejandro PEREZ: Right, I mean there's more than one means one there are local leaders of freedoms that you don't have on the on the left.
Abhay Vasant Ashtekar: Right.
Abhay Vasant Ashtekar: I mean, I think.
Abhay Vasant Ashtekar: In the degrees of freedom is really in terms of.
Abhay Vasant Ashtekar: Observers exactly so on the left hand side both obviously as observers have been I mean you're taking space and you're just stressed, or those observable.
Abhay Vasant Ashtekar: And this is exactly what.
Alejandro PEREZ: Normal is doing, but.
Abhay Vasant Ashtekar: that's what I believe and that's why i'm checking with him and he agreed.
Alejandro PEREZ: you're imposing some how these things fluctuate together, so to say, I mean you imposing the homogeneity or.
Norbert Bodendorfer: They they fluctuate independently yeah so what i'm proposing is that the quantum state here, and all of these vertices the same quantum state and once I perform in measurement.
Norbert Bodendorfer: You know i'm not projecting on the same volume it stayed in each of these cells yeah so, for example, if I want to get volume 10 here, I could have one plus one plus one plus seven, but I could also have two plus two, plus two, plus four.
Norbert Bodendorfer: yeah so I need to sum of all of those sub possibilities and some of all of their you know probabilities to get there to get the probability to get say volume 10 on this side.
Abhay Vasant Ashtekar: What else I could just add a footnote and see elected, this is something that is bothering you.
Abhay Vasant Ashtekar: may be bothered that in any of either the small cells on the right hand side you're still using kind of accuracy to kind of intimate space yeah.
Abhay Vasant Ashtekar: Maybe that is what it's about, and so the idea here is that well, strictly speaking, you know you at any time you, you are to go at some sufficiently small scale.
Abhay Vasant Ashtekar: The homogeneity is assumption is okay.
Abhay Vasant Ashtekar: And at that scale, then you know I can use the QC hilbert space.
Abhay Vasant Ashtekar: But of course on a larger scale.
Abhay Vasant Ashtekar: they'll QC thing really comes because i'm averaging out.
Abhay Vasant Ashtekar: it's a bit like what people might say classic classic classic and exit that in classically everything is complicated because of non linearity is.
Abhay Vasant Ashtekar: In here that everything is easy because of me condom theories linear they will say that well yeah you know little patches maybe universe is homogeneous.
Abhay Vasant Ashtekar: patches fit together and then you know what happens to that's why this you know more unique is.
Abhay Vasant Ashtekar: How do we leverage to get the the the freedmen equation that's the kind of question, people are asking.
Abhay Vasant Ashtekar: And you have nobody saying that well in this little patch go to sufficient, the small patch so that it is actually you know well approximated.
Abhay Vasant Ashtekar: That in that time, the number of degrees of freedom is very small, and I just to whatever it is, and then, and therefore I got.
Abhay Vasant Ashtekar: Now, if I look at, but I got many, many of those patches and therefore I got many, many observers of the type that normal normal just mentioned, which when coarse grained use me the left hand side.
Abhay Vasant Ashtekar: Is that a fair description normally.
Norbert Bodendorfer: I wouldn't have stated.
Norbert Bodendorfer: Everything like that, I mean for me, really.
Norbert Bodendorfer: More important picture than this is this picture here, so I will say there's a toy model which where we have you know we have finals orbits that are looking like spin it works, but in this theory every vertex is an htc have a space, so these pictures are equivalent and.
Abhay Vasant Ashtekar: yeah i'm saying the same thing that thing that they feel that in the TT the the the sale is equal to ucl but space is physically transforming to say that well in that patch I am I can take it to be homogeneous in that batch.
Abhay Vasant Ashtekar: i'm not saying it's one to one i'm just saying.
Norbert Bodendorfer: I would put less emphasis on you know this cosmological assumptions that the universe is homogeneous on smaller large scales for me, this is just a toy model for course training.
Abhay Vasant Ashtekar: Right i'm just giving a motivation for that type time or one might say, why are we using the storm at all right physically yeah.
Abhay Vasant Ashtekar: Maybe you don't want to say that there is any physical justification for the time or and then what i'm saying is not relevant.
Norbert Bodendorfer: i'm aware that the simplification zero so strong that we should be careful, talking about this being physically justified, but I think it's justified to look at this effect of course grading small spins to large since.
Abhay Vasant Ashtekar: Okay i'll try to give you motivation, but you're saying that you don't want that, I mean it's two to three people motivation okay.
Jonathan Engle: I wanted to ask just one question.
Jonathan Engle: Normal what value should J have if i'm going to do calculations and make predictions to compare with the cmt, for example.
Norbert Bodendorfer: The smallest possible.
Jonathan Engle: Really, the smallest possible because it as small as possible is the smallest number of.
Jonathan Engle: These these exact cells, I mean those would be the smallest cells right, but when you're doing prevention.
Norbert Bodendorfer: Maybe, let me try to rephrase your question to understand what the question is asking so i'm.
Norbert Bodendorfer: Not rephrasing the question, so you know when you do a computation you should use many small quantum numbers, this is what I would say.
Abhay Vasant Ashtekar: I think the confusion is coming, because I, because I had the same confusion, I mean Jay I mean when you when I got a whole bunch of such cells Jesus kept fixed, but then you got no time Jay where is the number of cells right.
Norbert Bodendorfer: and
Abhay Vasant Ashtekar: And so I think many of us thought that end time Jay oh Jay but that's not so I think that Jonathan the statement would be anytime Jay is very large right.
Abhay Vasant Ashtekar: Maybe, your question is how many central I be using.
Jonathan Engle: yeah or if the number of cells is relevant for actually making predictions.
Norbert Bodendorfer: So the correct, I mean the the correct statement would be that you should use a quantum state that contains many small quantum numbers.
Norbert Bodendorfer: Yes, and then you may compute with a quantum state by keeping track of all of those quantum numbers and acting with the true fundamental hamiltonian all those quantum numbers.
Norbert Bodendorfer: Or you make coarse grained those quantum numbers in a few large quantum numbers and act with the denominator tended to me that, by definition, gives the same answer so it doesn't matter where they use one of the other description.
Norbert Bodendorfer: But what do you should not do is, you should act with the fundamental hamiltonian on a large quantum number state, because then you can read normalized only the state, but not the operator.
Jonathan Engle: I see Okay, thank you.
Any other questions.
Abhay Vasant Ashtekar: So would this procedure, give you the same thing as I mean i'm not asking for him i'm just asking for exploitation will this procedure, give you kind of filter in space times results or is something that I use corrections in your view.
Norbert Bodendorfer: I have no idea what will happen once you go beyond this symmetry assumptions yeah so we know that there are you know these results that point towards signature change and everything we may lose Romanian structure.
Abhay Vasant Ashtekar: No, no they're talking about it cmdr.
Abhay Vasant Ashtekar: In the cmt yeah.
Abhay Vasant Ashtekar: So in the cmt era that we're going to get you know this is continuation of jonathan's question.
Abhay Vasant Ashtekar: Okay, that that that if you do it what you would like to say correctly.
Abhay Vasant Ashtekar: and am I going to meet.
Abhay Vasant Ashtekar: His expectation that.
Abhay Vasant Ashtekar: So now.
Abhay Vasant Ashtekar: The person agrees with the conductivity in space time or is the expectation that that description is.
Norbert Bodendorfer: In short, the expectation would be it agrees with what is typically happening in a QC just the bounce density changes yeah so what you would need to do now, you would need to study how.
Norbert Bodendorfer: You know fluctuations propagate on that background, and you would need to do some version of the computation that.
Abhay Vasant Ashtekar: You would.
Norbert Bodendorfer: Other people were doing.
Norbert Bodendorfer: For some time now, and now, one would think whether something goes wrong, because you use in any small quantum numbers here but i'm.
Norbert Bodendorfer: not really sure about that, but but probably not so, probably in the production in the approximations that are usually done and the way the competitions are usually done it should just change the bounce density, but that is just I guess right now.
Jonathan Engle: Any other questions, I want to ask one more question, so I by mentioned something interesting that.
Jonathan Engle: Of course, the homogeneity is really only approximately true when you go to a certain length scale and at that link scale, you would expect the volume of the universe, to be much more than the minimal volume so then wouldn't you so i'm not quite sure if if this does that perhaps throw.
Jonathan Engle: throw a difficulty into into this argument that you should be assuming that the the fundamental theory has has.
Norbert Bodendorfer: No, I mean the the argument was stay the same, and the expectation stays the same that you know even at scale, so the universe is homogeneous once you look closely enough, you will not find.
Norbert Bodendorfer: You know, a discrete structure far away from the Planck scale.
Norbert Bodendorfer: yeah so the universe is still given by a quantum state that has many small volumes and therefore the dynamics also reflect that and the arguments would still apply the computation would of course be much more difficult, and you could not use this group theoretic arguments.
Jonathan Engle: Well, what I mean is that, so if we if we.
Jonathan Engle: If we take the smallest sell to be the salvage that's large enough such that we have approximate to my engine at the volume that cell is going to be much larger than.
Jonathan Engle: The lowest allowed volume in the representation so so i'm not sure if that.
Jonathan Engle: To what you're arguing is that one should always take the the State that has the the smallest allowed volume at the bounce.
Norbert Bodendorfer: What i'm saying is that if you work with a cell that is always at a large volume or so, then you should use the newtonian which has been normalized to that scale.
Norbert Bodendorfer: And that keeps track of the effects that the cell is actually made up of many small volumes.
Jonathan Engle: But this normalization procedure that you're using assumes homogeneity on all of the smaller scales and so we're saying that this is, this is a scale that's the smallest scale on which there's imaginary so you wouldn't be able to apply this.
Jonathan Engle: This normalization procedure in order to get to that scale this.
Norbert Bodendorfer: I would not be I mean I would not be able to apply this precise computation, but the question is not whether you expect that the computation that takes care of the fact that you know, things are not exactly homogeneous would give you a different result, whether that is a reasonable expectation.
Jonathan Engle: I think it would, because when you don't have a margin at then you're not forced to have all of these minimal volumes over the whole region that gives you a large minimum volume.
Norbert Bodendorfer: So it could give you a slightly you know the result could be different, the precise function for but.
Norbert Bodendorfer: The relevant question is whether you expect once you introduce in homogeneity if this effect that the small spin physics is different from the large been physics is wiped out, and that is not a reasonable assumption.
Norbert Bodendorfer: yeah so you expect that things are still different they're clearly more complicated, but you don't expect that is effect disappears.
Norbert Bodendorfer: And that's that's the main message you should not trust rocks then computation if you don't renominate you hamiltonian.
Abhay Vasant Ashtekar: This one comment that quick formula, how to make orange Jonathan maybe it's useful maybe it's not it is that you know it's very surprising, but it is true that if you take the smallest sell at the bombs.
Abhay Vasant Ashtekar: And follow its evolution of you know, using some standard and facially model model, like the starbucks key model then.
Abhay Vasant Ashtekar: i'm not just talking in the background, because it's all has to do the backgrounds and not with perturbations So if you take the smallest possible volume at the the QC says right and.
Abhay Vasant Ashtekar: And then.
Abhay Vasant Ashtekar: And then see it's a really.
Abhay Vasant Ashtekar: Really.
Abhay Vasant Ashtekar: The entire observable universe, and at the same time.
Abhay Vasant Ashtekar: Because yeah there's also confusion, a little bit I mean it's not then the confusion of presentation, but when we think about it, because here.
Abhay Vasant Ashtekar: What has been kept fixed is not the physical volume right, I mean is the traditional wall is the is a goal moving volume that is getting getting a keeping that is being kept fixed.
Abhay Vasant Ashtekar: So I think if you look at in terms of physical volume, then it is very surprising, but it's true that that in this standard models and so on, that that people use starbucks inflation that the entire observable universe is really coming from.
Abhay Vasant Ashtekar: The expansion of the minimum sell X.
Abhay Vasant Ashtekar: Since out the entire observable universe, today I say okay.
Abhay Vasant Ashtekar: Which is shocking but it's true.
questions.
Okay let's thank the speaker again.