Timeline for What would the periodic table of a 4-Dimensional universe look like?
Current License: CC BY-SA 4.0
25 events
| when toggle format | what | by | license | comment | |
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| Mar 30 at 17:23 | comment | added | Nanite | I believe $l_1 = l_2$ is required for spherical harmonics (and $l_1 \neq l_2$ is only possible for rigid rotators) -- see physics.stackexchange.com/questions/800776/… . | |
| Feb 5, 2023 at 22:26 | comment | added | NoLongerBreathedIn | A clearer clarification: There is 1 s orbital. There are 10 p orbitals; three of them are left-handed $(1,0)$, three right-handed $(0,1)$, and four ambidextrous $(\frac12,\frac12)$. There are 35 d orbitals: five $(2,0)$, eight $(\frac32,\frac12)$, nine $(1,1)$, eight $(\frac12,\frac32)$, and five $(0,2)$. And so on. Yes, this does make my previous comment wrong; it should be 1, 11, 46. I missed the $(2,0)$ and $(0,2)$ cases before. | |
| Feb 5, 2023 at 3:56 | comment | added | NoLongerBreathedIn | The correct restrictions on $l$ are not obvious, but I think they are as follows: $l_1+l_2<n$, $l_1$ and $l_2$ must either be both integers or both nonintegers. The second restriction is absolutely required to be a representation of $SO(4)$, but the first I'm not sure about (though it is definitely correct on the diagonal). So the first levels would have a spatial orbital count of 1, 11, 36. | |
| Dec 18, 2022 at 15:04 | comment | added | riemannium | Very stupid question: how the counting changes if instead of 4 space-like dimensions we get $2n$ or $2n+1$ space-like dimensions, for n integer greater than 2. What would be the analogue of the octet and 18-electron rules in these universes? | |
| Jun 17, 2021 at 1:30 | comment | added | praosylen | I've attempted to do that calculation before, at least for the radial degree of freedom, but I'm unsure if my calculations are correct. What they seem to indicate is that there are no bound states around a four-dimensional 1/r^2 potential, because every would-be eigenstate of the Hamiltonian with negative energy either diverges for small r or for large r, to the point of being un-normalizable. I've encountered papers before that claim no bound states exist, but I've never seen anything other than "standard methods" cited, so while my conclusion is correct my explanation for why may not be. | |
| Mar 26, 2021 at 15:02 | comment | added | wilsonw | I am not sure if it's relevant, but I think you can solve Schroedinger or Dirac's equation in 4 dimensions. | |
| Aug 9, 2019 at 1:16 | history | bounty ended | HDE 226868♦ | ||
| Aug 2, 2019 at 16:48 | history | edited | celtschk | CC BY-SA 4.0 |
Fixed 3D rotation group (and an unrelated typo)
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| Aug 2, 2019 at 16:45 | comment | added | celtschk | @elduderino: Yes, should definitely be SO(3). Fixed. Thank you. | |
| Aug 2, 2019 at 16:12 | comment | added | el duderino | "The corresponding rotation group is known as 𝑆𝑂(4) (as opposed to 𝑆𝑈(3) for 3D space)." Most of this is a bit beyond my comprehension level, but as a small nitpick: shouldn't that be SO(3) instead of SU(3)? The unitary group contains complex matrices so applying those to $\mathbb{R}^3$ would result in some unphysical rotations. | |
| S Sep 23, 2015 at 19:53 | history | suggested | user1717828 | CC BY-SA 3.0 |
fixed divergence equation since I guess nobody else read it
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| Sep 23, 2015 at 17:40 | review | Suggested edits | |||
| S Sep 23, 2015 at 19:53 | |||||
| S Sep 22, 2015 at 3:12 | history | suggested | nitsua60 | CC BY-SA 3.0 |
completely separate -> distinguishable; I hope it doesn't seem trivial, but "distinguishable" is really the QM-important term here
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| Sep 22, 2015 at 2:40 | review | Suggested edits | |||
| S Sep 22, 2015 at 3:12 | |||||
| Sep 21, 2015 at 23:07 | comment | added | HDE 226868♦ | @LorenPechtel I believe you're right about that, under normal circumstances (I don't want to rule out weird setups that I haven't though of yet). I'll most likely add that to my answer, or at least a mention of that. | |
| Sep 21, 2015 at 23:05 | comment | added | Loren Pechtel | My understanding is that you can't have a stable orbit in a 4D world. In a classical world that would play havoc with the electron shells but in a QM world I'm utterly unqualified to address what might happen. | |
| Sep 16, 2015 at 10:06 | comment | added | Youstay Igo | @Seth & Burki: Do you guys really thought you could understand 4D particles while living in a 3D world? I don't think atoms (as we know them) would really exist as such in a 4D world. The primary structures of matter would be far far more complex. | |
| Jun 12, 2015 at 12:44 | comment | added | Arpith | So...... could we still have a 2-D periodic table that we could write on paper and mug up atomic numbers from before exams? | |
| Jun 12, 2015 at 8:12 | comment | added | Burki | wow... and... what does that mean? | |
| Jun 12, 2015 at 6:53 | history | edited | JDługosz | CC BY-SA 3.0 |
edited body
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| Jun 12, 2015 at 6:19 | comment | added | JDługosz | Would fermions exist? Would there be more ways that "spin and statistics" work out? | |
| Mar 27, 2015 at 12:08 | history | edited | celtschk | CC BY-SA 3.0 |
added an important fact that was missing originally
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| Mar 27, 2015 at 2:23 | comment | added | Monty Wild♦ | From my reading on this subject, I thought that the number of electrons in each shell was 2 x Floor([Dimensions]/2) x ([0-based shell number] x ([Dimensions] -1) +1), so in 3D, S=2, P=6, D=10 & F=14, while in 4D S=4, P=16, D=28 & F=40. | |
| Mar 27, 2015 at 1:26 | comment | added | Seth | Wow. You could have just made all that up and I'd be none the wiser. | |
| Mar 27, 2015 at 0:51 | history | answered | celtschk | CC BY-SA 3.0 |