Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Yes this is also invariant under group theory. The invariant I mentioned before the Woldline is [math]ds^2=x^2+y^2^z^2[/math] for example this is the worldline (particle path) that all observers can agree upon. For the Schwartzchild its a different worldline of your lightcones. An invariant quantity can also apply in conservation laws. Torque being constant in conservation of angular momentum. It is an unchanging quantity for the equation being described. In group certain mappings are invariant while others will change. This stuff takes years to learn all the ins and outs. Are you against getting a good GR textbook to start with? I could recommend my favourites. Lets start with the above equation. That is Galiliean relativity. In that form Pythagorous is true [math]a^2+b^2=c^2[/math] in group and QFt this is the Cauchy inequality and triangle inequality. The Kronecker [math]\partial^i_j[/math] where i,j are unitary vectors (always equal unit coordinate unit on s graph) identifies this particular geometric graph. If I go to relativistic speeds this graph skews along the x coordinate plane (length contraction) that is skew assymetric. I only need 1 additional variable to account for this skew (gamna) or some use beta. Now GR takes this further, it goes into curvilenear coordinates. It will use k for curvature. The Levi- Cevitta uses two vectors in freefall and a third to map the change in parallel transport (k) be careful this letter can have different meanings in different metrics. now in tensor notation a pure field will always have either upper or lower indices. A mixed field can be 1 upper and 1 lower. The upper indices are contravariant while the lower covariant. These tells us what rotations we must perform at a given time. They are not values they are tensor operators. They do not sum up under algebra. The first indice symbol [math]\mathbb{T}_\mu\nu}[/math] [math]\mu[/math] is the row operator while [math]\nu[/math] is the column operator. Don't confuse the above with stress tensor it is any tensor. Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Vmedvil Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Yes this is also invariant under group theory. The invariant I mentioned before the Woldline is [math]ds^2=x^2+y^2^z^2[/math] for example this is the worldline (particle path) that all observers can agree upon. For the Schwartzchild its a different worldline of your lightcones. An invariant quantity can also apply in conservation laws. Torque being constant in conservation of angular momentum. It is an unchanging quantity for the equation being described. In group certain mappings are invariant while others will change. This stuff takes years to learn all the ins and outs. Are you against getting a good GR textbook to start with? I could recommend my favourites.Different invariant and that is still SR and yes, it is invariant for time, which i still Special Relativity a single transformation not all transformation like a morphic group. The Equation you are looking for which was typed wrong is in this section 4-D Spacetime titled "Null Geodesic"https://en.wikipedia.org/wiki/Special_relativity Edited December 31, 2017 by Vmedvil Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Yes I was giving a basic example (Euclid). Those equations are your parts to use. Every group including QM will use those parts (partial integrals.) You should be able to greatly simplify your equation by using parts by integration. You only need one set of tensors for geometry regardless if your using QFT, QM Dirac etc. You should never need repeated instances in the same equation. Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Vmedvil Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Yes I was giving a basic example (Euclid) What does that equation say? Answer me this does it use that invariant Version of SR? Now, do you see why it was me laughing? What is (d2 /∇2) - (Cdt)2 Edited December 31, 2017 by Vmedvil Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Read my last post. the equation you have is not fully reduced not by a long shot. Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Do you want the actual equation for harmonic geometry? It is incredibly simple. It also includes GR. Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Vmedvil Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Do you want the actual equation for harmonic geometry? It is incredibly simple. It also includes GR. This is a Quaternion look that up. I just called that to give it a less long name. Edited December 20, 2017 by Vmedvil Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Oh please look up what a quaternions means by math definition. Don't make the mistake of thinking you know than I do. Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Vmedvil Posted December 20, 2017 Report Share Posted December 20, 2017 Ya, I would but I happen to know what I am talking about. Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Great so why didn't you do the parts by integration throughout your entire equation under those basis? Too lazy?? or couldn't google how to? Why do you think I mentioned it idiot. You also need the inner product and the outer product to complete it Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Vmedvil Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Great so why didn't you do the parts by integration throughout your entire equation under those basis? Too lazy?? or couldn't google how to? Why do you think I mentioned it idiot. You also need the inner product and the outer product to complete itIt doesn't happen on the right side of the equation Del "∇" was solved for. Edited December 20, 2017 by Vmedvil Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) then its useless except in one form of geometry and not any of the others Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Vmedvil Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) then its uselessFalse, you don't know what it was solved with. Automorphic Qauternion different rules, I will dicuss this with you tomorrow. Edited December 20, 2017 by Vmedvil Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Don't bother. I don't waste my time on fools that don't ven know what quaternion is that claims they do. Your equation above does not follow the Quaternion rules under summation.Provide the Slerp, and squad in quaternion form if you think you can for a spherical cubic interpolation or even the spherical linear interpolation. ( I expect to see the functionals).You haven't shown an understanding of calculus above so don"t try to BS me first off Quaternions is non commutative. Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) You so full of crud it's not even funny anymore Seriously why would you have [math]E^2_{relativistic}-E^2_{rest][/math] Couldn't figure out how to use the energy momentum equation?[math]e^2=(pc^2)+(m_oc^2)^2[/math] I'm not wasting more time on this garbage Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Shustaire Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Don't bother replying I'm not coming back to a site that allows this garbage. Edited December 20, 2017 by Shustaire Quote Link to comment Share on other sites More sharing options...
Vmedvil Posted December 20, 2017 Report Share Posted December 20, 2017 (edited) Don't bother replying I'm not coming back to a site that allows this garbage. That is that equation reverse solved for p , Mo = Erest/C2 Keep throw stuff out there maybe you will into a part that doesn't show a utter lack of algebra interpolation skills. Edited December 20, 2017 by Vmedvil Quote Link to comment Share on other sites More sharing options...
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