Timeline for Differences in Quantum Field Theory in 4 Spatial Dimensions
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11 at 17:35 | comment | added | controlgroup | Let us continue this discussion in chat. | |
| Sep 11 at 17:27 | comment | added | Gray Sheep | There is even some experimental rule for that, $0.4+0.3*2^n$ AU. It does not match for MErcury (only if $n=-infty$), neither for Pluto, but it is a close match for the others. I really can not understand why is it so f...g hard to understand in it. And yes, yes, yes, there is f...ly no reason to close out 3+ D only because some equations match well only in 3D. That is all. "there is no stable orbit in 3+ D" is the largest bullshit well known in physics, that is all! | |
| Sep 11 at 17:23 | comment | added | Gray Sheep | Orbital radius grows exponentially with the number of the planet. There is the third column, check the numbers. After you have understood that it is close to an exponentially growing series, I think we could happily talk. | |
| Sep 11 at 17:21 | comment | added | controlgroup | You mean that the orbital radius grows exponentially with distance; yes, that is true. But it is also a fact that there aren’t closed orbits for systems with forces proportional to $r^x$ for $x\neq 1$ or $-2$. | |
| Sep 11 at 17:20 | comment | added | Gray Sheep | No, it grows roughly exponentially, like here can you see: web.njit.edu/~gary/202/Lecture7.html Table in the middle, third column. Another important thing, they are mostly circular and co-planar. Neither of the rules are exact but odds is that it is the result of some self-regulating mechanism. | |
| Sep 11 at 17:17 | comment | added | controlgroup | The planetary orbital radius remains constant without external influence, as is the case for all eight planets of the Solar system. Eccentric orbits are also perfectly stable. It is also the case that closed orbits do not exist in higher-dimensional gravity that disobeys $F\propto r^{-2}$; this has been rigorously proven. @GraySheep | |
| Sep 11 at 17:09 | comment | added | Gray Sheep | Exponentially growing radius: in many-body systems with a big central body, long term state is that planetary orbital radius grow roughly exponentially and they are roughly circular. Like in the solar system. I have heard this "no stable orbit" thing so many times, and I am so sorry but it looks so strongly as the school example of a factoid! | |
| Sep 11 at 17:05 | comment | added | Gray Sheep | Sorry but that is not true. A circular orbit can exist in any dimensions. One can calculate the radius by an elemental, not even differential equation: centripetal force should equal gravity, done. I think the reality behind this statement is that there are practically no elliptical orbits, there are elliptic-like orbits with a very strong precession. | |
| Sep 11 at 16:59 | comment | added | controlgroup | The issue is that there do not exist any closed orbits in $F\propto r^{-3}$ systems, so climates on planets wouldn’t be nearly as stable as they are in 3+1D. I’m not sure what you mean by exponentially growing radius; that would just mean spiraling towards infinity which still kills everything on the planet. | |
| Sep 11 at 16:52 | comment | added | Gray Sheep | My reasoning is analogic to the micro-world. I do not see, how would an $\frac{|r|}{r^4}$ potential well make things so bad, if our current $\frac{|r|}{r^3}$-related potential wells, the question is in most practical problems: do we have an energy for an ionization or not. Yes, of course, chemistry would be really, really different - already electromagnetism would be likely very different, imagine for example that Faraday tensor would be 5x5 instead 4x4. Maybe we would have a third field beside electric and magnetic field. | |
| Sep 11 at 16:52 | comment | added | Gray Sheep | I do not think that this orbit stability problem would be such a high issue. My reasoning is that long-term orbital perturbations can cause also major effects even in our 3D, and the result is that the stable planetary orbits regulate themselves into roughly circular and exponentially growing radius. I am nearly sure in a very similar result also in more spatial dimensions. | |
| Sep 9 at 13:01 | history | answered | controlgroup | CC BY-SA 4.0 |