Conformal Spacetime Geometry and a New Cosmology — Q&A

0:00 Thank you, Professor Penrose. I like very much this feature of the conformal cyclic universe, and I think that it's very important to, one of the most important things to understand here is what is the entropy of the gravitational field in this case. So your proposal is that is the number of the volume, but here I have to ask you to be more precise because I am a bit confused because in general relativity is the volume respect to which observer. And also I have a further question because I mean I would like to have an entropy that comes from the microscopic degrees of freedom. Well, you certainly need for a precise notion of entropy in the gravitational field. And this is something very lacking, really. You would need to know what macroscopic parameters are, you need the phase space, you need to know what macroscopic parameters are you're concerned with. I'm really talking in a very kind of global or hand-waving nature, where it's clear that it is gravity that's concerned, because it's the clumping which takes place and it's the which gives you the big increase in entropy. And so, in detail, yes, it would be very much, it would be a good thing to have a better theory of what the gravitational energy is. And I used to worry about this for long, and I more or less gave up worrying about it, to think that, well, you know, there's a huge effect here, even if we don't know precisely how to assign entropy to the gravitational field. At least, if we just talk in general terms, there's a huge effect, which is, I take your point, it would be a very good thing to have a much better notion of the gravitation fluid than we have at the moment. So in this picture, the idea is that the entropy is lower, lowest, when the space is homogenous and desipropical? Yes, that's right. So the unit, you see there's a sort of, so much discussion in cosmology of the Friedman-Robertson-Walker models and inflation is all discussed in that background you see. But that's begging the question because it's the very fact that you're using the Friedman etc. etc. models is forcing the entropy to be ridiculously small compared with what it might be. But really to understand that properly you would need exactly what you're asking about

2:30 as a better description of entropy in the gravitational context. when you have a transition from one eon to the next I understand that the conformal structure is preserved but you have a change in the conformal factor and I have two questions I have not understood what will determine this change and the second is that global or local does it depend on space I'm afraid I wouldn't get to this is why I was rather racing over the point. But the idea is, let me just describe it in general terms. The idea is that you have an arbitrary, pretty arbitrary conformal factor which is only constrained initially in to say that infinity is smooth and the other way around, that the Big Bang is smooth. But now you can ask for the equations that preserve the trace of the Ritchie tensor. Now the trace of the Ritchie tensor in the time of regime is where I'm supposing that there's nothing of relevance from massive particles. Now, that's a question you might ask more about. But let's suppose that we can ignore massive particles. Then this means that the trace is entirely cosmological constant. So then you look for the equations which take you from one such metric to another, and you have something like the Calabi equation which tells you the different conformal factors that will enable you to do this and this is a second order differential equation and so you have basically two things to fix at the crossover so you've got to find two things to fix which fix that metric and that's the tricky point because either the things that you want to fix are automatically something or you can't make them do what so you're constrained and so the condition that I settle on and I think is the most likely one to be correct is to say that this thing here this pi thing here is zero to third order and this is a big constraint on this thing and I think it's just right to fix it but there is a good question there about whether this is right so my conjecture here is that to say this is zero to third order, I should say it's pi pi minus this thing here in the bracket,

5:00 that the norm of this thing, three times the norm minus lambda, is zero to third order. And you see this expression comes in into this mu, which is the rest mass that it grows automatically. And if this is zero to third order, it balances these things and makes it, it keeps it zero for as long as possible. And that's my conjecture. Would you say that this one form is related to what is called a veil vector in veil theory? I don't know. I don't think I said that, but maybe there is something. It's not a veil geometry here. Yes, yes, I know, but when you have conformal invariance, then you have a veil vector on which cures. Yes, that's true. Let me think about that. I'm not sure if it's connected with that. It's a thing which is quite a natural expression. Now, apart from a sign change, because this omega really becomes the negative of that one, it's completely smooth as you go from one side to the other, and keeping that smooth is part of the condition. But also keeping the zero to high order, or keeping this norm equal to around 0 and 3 to high order is what I'm saying is the condition. Thank you. Thank you. Okay. Thank you very much.