Okay, yeah, I just, Jim asked me to say a few words about an alternate derivation of a mock effect equation just from standard general relativity. And you might have seen us here on the first night. So it took a stab at the same thing. And so we, I think, reconciled between Martin and I are understanding. And we understand what Jim did. And what Jim did is basically legitimate, but more seat of the pants. So I think we wanted to show explicitly that it is in general relativity. So, okay, this board's cleaner. So I just wanted to summarize real quick what Jim did, what I did, what Martin did, and not bother you with the algebra. I do have a write up that I can get, I gave a few of you, Jim has it, you know, a few of you have it, so if you want to see the algebra. But, but basically with these mock equations, we sort of write Newton's law, D squared phi equals 4 pi g rho. So that's Newton's law so far. And then the mock effect, we get stuff like D rho DT squared. And then I'll put a twittle, I'm not sure on the sign, D squared rho DT squared. And is that about it? Something like that. I might be missing C squareds to make the units work. So fundamentally, Jim has come up with this observation that in general relativity, you get an effective source term to the standard gravitational field. And it doesn't depend on the gravitational constant. So the gravitational constant is a small number. So that's why we need a Jupiter mass, you know, to make, if we say plausibly, a wormhole black hole. Because the gravitational constant is so small. The significance of these terms is they don't have this small term. And in fact, I would say these are scale free. And it's sort of weird. And we've talked about this. So that's why these can be large. So that's the mock effect stuff. Now, you have in your quick study a summary of Jim's derivation. So you can follow through and I pulled it from Jim's book and, you know, pulled it from the dozens of pages where it spread throughout, condensed it down, summarized his assumptions. And every little step is basically correct. But if you say step back and say in general relativity, how would I do this textbook style, that's I think what Martin and I tried to do to get this field equation. So my approach was to start with the linear and Martin's approach. The linear field equations, and in fact, I will just write it again here since we've seen it yesterday. Okay. E equals pi g rho c to the fourth. Actually, whoops, this is a tensor. So what there's a standard in all the relativity textbooks, you linearize the Einstein equations to get the Newtonian limit. You also linearize to get gravitational radiation. So linearization is standard stuff. It's in all the textbooks. And I also wrote down the linear equation. What I did though is, so I'll just put an L here. What I did is take the linear equation which looks like this. Yeah, I'm sorry. Dill squared phi. So we got that piece. That's no problem. C squared d squared phi dt squared. I realize I'm writing it a slant. Sorry about that. E equals rho c squared. So this is the linearized field equation, more or less, in broad outline. But it doesn't look like this. And so the trick that Martin and I both said is, what if I just do something sensible with this term and try and convert it? So I put lance plus Martin here. So we both start from this. So my idea was to say, to eliminate this term, I'm going to use the geodesic equation. And you guys saw that yesterday in my talk. And what it does, the geodesic equation, has interesting properties. It relates the change in the energy of a body to the change in the energy of the gravitational field, dt phi. So I use this. I take the second derivative of this, plug it in here, and I get a Mach effect type equation. It doesn't have the exact same terms as gyms, but it has the one that he keeps to build all his equipment with. So it seems to correspond where it matters, doesn't correspond where it doesn't appear to matter. Martin's approach, for his second equation, he said, I'm going to put, use the Newtonian result phi equals gm over r, and take time derivatives of that. And he plugs it in here, and he gets something that has these scale-free Mach effect terms. So I think we all sort of are pretty much convinced. I would say maybe a consensus of this meeting, if it didn't exist before, is that the field equation, the Mach effect field equation with the scale-free stuff is in general relativity. No doubt about it. But the gym doesn't stop here. He goes on and does engineering. And he makes an assumption about what d row dt means. And that's what I call gyms' fourth onsatz in his derivation. That's where I think, again, Martin and I, we're talking, we're not quite sure. Probably gym made it this far and got it right. This part is probably right too, and we're just trying to catch up. But this is where things stand. Simple enough? I just want to mention that that's the old way. And now the new way that we have Rosé O'Dalham is, is to start with the mass equation. We have d2, n dt squared, and dn dt, all squared, all in one term with logarithm. And we're actually using that, which is directly from the field equation. And we're not making the assumptions that we did before. So now we have a much, much better force equation, and that's what we're going to use for the future. What's your second equation, so to speak? It's just a mass equation, but the masses that you get directly from that equation. So it's a density. But this is the field equation. You need one more, I think. You need one more. What? Do you want one more to get? I drive from the co-variant equation. I've said it was this like it would hear. It says it's row, and then these are the d row terms. We put some more involved row d row, and then that's the mass equation. So I'm getting light down directly from a whole lot of field equation. It's not in a field equation. It's not a mass equation then. No problem, yeah. There's no mass equation there. That's all right. So I think we're solving the mass equation now. We're not making any assumptions about what the row is in terms of the voltage, or any of that stuff. What's the mass equation? It's the one under the board. It's this. It's this. So the delta m over volume is 1 over 4 pi g. So you put all that lot into a turn like this, and you call that delta row. And then this is mass over volume. Mass over volume. But the end. Yeah. And t is the times the d and dt. That's just the definitions. I just wonder, you guys, you don't use linear field theory. I don't think so. I'm using the full scale covariance form of the whole market theory. I've had a space and then I get that to the future equation. My hypothesis is the field equation is not enough in relativity. You need one more. Why don't you need anything more in mind? Yeah. There's nothing more to add. So yeah, I'd be that's the same approximation to it. The whole logic thing gives it to you exactly with no approximations in full covariant form. So is that a good spot to leave it, Jim? Yes. Thank you. Library. It's coming. Thank you. Thank you.