Timeline for (Co)homology of the universe
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 4, 2012 at 7:36 | comment | added | Ron Maimon | @ChrisGerig: Ok, but I see now why you said what you said, and I agree with you regarding the content. I wasn't right in laying all the repulsion to Pauli, there's a part that's nuclear repulsion once the electron shells overlap, and this is a tradeoff. You could have made the argument explicit, though, rather than relying on authority. | |
| Dec 4, 2012 at 7:23 | comment | added | Chris Gerig | I agree, and is rigorously proven by Dyson-Lenard, that what makes matter hard is Pauli-exclusion (plus Uncertainty Principle). I hope we can now leave this to rest. | |
| Dec 4, 2012 at 7:17 | comment | added | Ron Maimon | I think I gave your argument too little credit--- I see now where you are coming from--- the near surface forces are a mix of exclusion and nuclear repulsion, and the exclusion is only for keeping the bulk phase stable, while the repulsion can dominate the touching force, for example if the spins on the surface electrons are anti-aligned. But in this case, you tend to shear off the electrons from one solid in chemical bonds to the other. Maybe I should update the answer to that "what makes matter hard" question (although it is important to say that it's exclusion that sets matter's scale). | |
| Dec 4, 2012 at 7:15 | comment | added | Ron Maimon | @ChrisGerig: The electromagnetic part is net attractive even when you are close, so long as you don't have overlap. I see your point now--- consider the opposite e-spins hydrogen, which becomes a molecule, and then the electrostatic repulsion of the nuclei keeps it from collapsing, even though there is no electron exclusion, and it can be a d-2 atom with bosonic nuclei. The electrostatic repulsion is important in cases where you have molecular bonding, to understand why the nuclei don't come closer then they do. But it's still the issue of fermionicity at core, bosonic electrons will clump up. | |
| Dec 4, 2012 at 7:00 | comment | added | Chris Gerig | Last post: that's clearly not what I meant... "far" relative to distance between electrons/nuclei. $F_{Pauli}$ is for the stability of matter (which you mistakenly confuse with the interaction between matter). As for the on-topic issue, I don't care about you now starting to define the terms, I care about how they are thrown into the post and intermixed with every other word... this is what I call gibberish. | |
| Dec 4, 2012 at 5:52 | comment | added | Ron Maimon | Also, F_EM is purely attractive at distances greater than touching, it's Van-Der-Waals force. | |
| Dec 4, 2012 at 5:52 | comment | added | Ron Maimon | There is no excess complications--- string theory allows for nontrivial topology, and you have to argue why it's not disallowed by causality, since wormholes are disallowed. a periodic identification is not disallowed (if it is spacelike), a topology like a Calabi Yau is not disallowed, and an orbifold is not disallowed, even though they are complicated topologically. This is also where homology links to actual physics, since the Euler characteristic is the generation number. I don't know how to make it less wordy, because these are wordy concepts, not math-y concepts. | |
| Dec 4, 2012 at 5:48 | comment | added | Ron Maimon | @ChrisGerig: A "patch" is a region inside a cosmological horizon--- it's a standard cosmology term. The "FRW phase" is when the universe is expanding, i.e. not inflation and not 100 billion years from now when it's dominated by cosmological constant again. The normal expansion allows new stuff to come in from the boundary as new stuff gets visible, and one has to consider if this new stuff can be a handle. It can be an orbifold, or a black hole, why not a handle? The reason is that wormholes are incompatible with causality (this is the boosting argument, also found elsewhere here). | |
| Dec 4, 2012 at 5:20 | comment | added | Chris Gerig | But no real disrespect, I just prefer less over-complications and excessive rambling of physics words. Your explanation can be more clear cut than what it is, and a bunch of things can be dropped completely without impacting the intent. | |
| Dec 3, 2012 at 20:01 | comment | added | Chris Gerig | To your first comment, that's it, that's all your post really says (the universe is contractible), but drawn out in gibberish. And as to your second comment, no we do not know that the universe is contractible. | |
| Dec 3, 2012 at 19:55 | comment | added | Ron Maimon | @ChrisGerig: When you say "we are unsure of the topology", you are referring to two things: 1. there is some question of whether the observable universe has identifications inside the cosmological horizon, but it probably doesn't, since we would see it in WMAP 2. we don't know the topology of the unobservable universe and we never will. I am adressing point 1 by assuming the experimental data is conclusive (which it nearly is), and point 2 by rejecting the idea that the universe extends past the cosmological horizon. | |
| Dec 3, 2012 at 19:53 | comment | added | Ron Maimon | @ChrisGerig: There are no symbols, but there is math. If you consider the universe a 3-disk bounded by the cosmological horizon, then topologically it's a manifold with boundary, and it is deformation retractable to a point (ignoring other boundaries, like black holes on the interior), so it's homology is trivial. This is a (simple) theorem: a space which deformation retracts to a point has trivial homology. The case when you have black holes in the interior introduces nonretractable 2-cycles, it's the 3-disk with punctures topologically, and the dimension of H2 is the number of BHs. | |
| Dec 3, 2012 at 12:43 | comment | added | Chris Gerig | The whole layout, there is no real math here, you just go off and indirectly make some implications. In particular, to this day we are unsure of the topology of the universe, so I'm not sure you can suggest its noncompact dimensions are Euclidean space. | |
| Dec 3, 2012 at 2:59 | comment | added | Ron Maimon | @ChrisGerig: That's very strange--- I understand this stuff completely, and usually people have no trouble following what I write (at least, I think they don't, from comments). What is un-understandable about it? Can you quote, so I can make it clearer? I don't find it written in a hard to understand way when I reread it. What confused you here? | |
| Dec 3, 2012 at 1:58 | comment | added | Chris Gerig | I'm guessing it's because your explanation is un-understandable. It literally comes across as gibberish with just physics-words thrown in. I have no clue why the OP accepted your response. | |
| Dec 2, 2012 at 20:37 | comment | added | Ron Maimon | Was the downvote because I didn't include black holes? Yes, these do give a second homology, but I didn't think that was the spirit of the question, because it's kind of trivial. | |
| Dec 2, 2012 at 20:37 | history | edited | Ron Maimon | CC BY-SA 3.0 |
include black holes
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| Dec 1, 2012 at 22:39 | vote | accept | Espen Nielsen | ||
| Dec 1, 2012 at 22:29 | history | answered | Ron Maimon | CC BY-SA 3.0 |