Wikipedia:Reference desk/Archives/Science/2018 September 4

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September 4

Nodes of atomic orbitals

When dealing with atomic orbitals, we say they have nodes where the wave function's value (and hence the probability density) is zero. Some nodes occur at particular angles (relative to an arbitrary origin) and are known as angular nodes, and some occur at particular radii from the nucleus and are known as radial nodes. The number of radial nodes for a given orbital is given by the relationship n-l-1 where n is the principle quantum number and l is the orbital angular momentum quantum number. Now, all orbitals have a node at the nucleus itself except for s orbitals (l=0). It stands to reason that this node must be a radial node, because it occurs at all angles, but only at the particular radius of zero. But the 3d orbital has quantum numbers n=3 and l=2, so it should have no radial nodes. I can confirm that it does have a node at the nucleus by looking at its radial wave function which shows it approaching zero at the origin as opposed to the s orbitals which do not. So I have a contradiction. Either the 3d orbital does have a radial node, or the node found at the nucleus for orbitals where l>0 is not a radial node, though I don't see how it is an angular node either...maybe it's a special type of node? 202.155.85.18 (talk) 02:51, 4 September 2018 (UTC)

Atomic orbital is our main article. Your

${\text{radial nodes}}=n-l-1$

formula is off by one for all p and d orbitals (even for 2p, n=2 and l=1 so 2-1-1=0 but your radial wave function diagram has zero amplitude at r=0) so it is definitely something special about the center vs r>0 nodes.

What is the origin of your formula? Not that I dispute it (it's easy to find in many college-level texts), but there may be an explanation in the surrounding prose. For example, [1] says: " The ‘-1’ portion accounts for the node that exists at the ends. (A half of one node exists at one end and since there are two ends, there’s a total of one node located at the ends.)" Look at the shape of the s with a maximum at r=0 vs others having a standard (amplitude=0) node at the center (as you notice, it's unusual). So the idea of a node possibly not actually existing there in the same way could mean that the –1 term is not correct in the other context (or is mis-explained in one vs the other).

The formula is from my inorganic chemistry text. They seem to be treating these "nuclear" nodes as a kind of special node, distinct from radial nodes. Fair enough. The rest is making sense to me now. I have another question though: the text also gives this relationship between the number of peaks in the radial distribution function that just seems totally wrong. A 1s orbital's RDF would have no peaks if this relationship were true, but on the very next page they give the radial distribution function of a 1s orbital with 1 peak. The relationship also fails for other orbitals' RDFs which don't display the predicted number of peaks. 202.155.85.18 (talk) 04:34, 4 September 2018 (UTC)

Other refs call the r=0 of s an "antinode", and looking at our Node (physics) article, this appears to be a good description for a "free boundary" due to the nature of the system rather than a zero amplitude. So if that counts as a node, then every calculation by the formula is off by one (1s has 1 node—the antinode) and the "–1" term is simply a bogus/fudge-factor to account for imprecise or incompletely explained other terminology. DMacks (talk) 04:26, 4 September 2018 (UTC)

My text uses the term "anti-node" to refer to anywhere there isn't a node. So in that case, the nucleus is an anti-node in the case of s orbitals, but a node in the case of all other orbitals. 202.155.85.18 (talk) 04:41, 4 September 2018 (UTC)

Have a look at Commons:Hydrogen_orbitals_3D. The complex solutions are the ones that really let you see what is going on; add complex solutions with opposite m numbers to get a real solution with nodes on the x and y axes. Looking at the pictures, you can see the argument that the node "occurs at all angles" is flawed. For the m=0 solution, you should see there are two nodes that have the cross section of an "X of revolution" passing through the center ... I suppose I can't call them "planes", but they're not radial. For the m=2 and m=-2 case, add them up and you'll see the genuine planes that are apparent at Commons:Hydrogen orbitals 3D real for most of the d orbitals. Yeah, the 5th d orbital is different in a sense from the others, yet it has something of the same idea. Wnt (talk) 16:21, 8 September 2018 (UTC)

Gravity

Something about Einstein's theory of gravity never sounded right. Warping space time? But if time is just a series of events, and space is the absence of matter, how can it be warped by a physical object? There's nothing to warp in the first place, is there?

And if space time does exist, it would extend indefinitely into infinity, so it ain't like you have a flat surface that you can throw a ball unto. Did Einstein think the universe was 2D? Makuta Makaveli (talk) 04:57, 4 September 2018 (UTC)

Spacetime is not 2D, but to visualize the effect of a massive object on spacetime, it is convenient to consider the effect only in two dimensions. That's why you often see pictorial representations such as this one. Once you understand what is being implied in 2 dimensions, you can mentally extrapolate that to the third spacial dimension, though it's rather difficult to represent in an image. Then if you also incorporate the time dimension, it becomes even harder to represent as an image, and we use things like animated light cones to show what's going on. 202.155.85.18 (talk) 05:12, 4 September 2018 (UTC)

Is warped spavetime the only explanation for gravity? It sounds beautiful, but then again there was never any nobel prize for it, and maybe for good reason. Makuta Makaveli (talk) 05:22, 4 September 2018 (UTC)

There are no good explanations for gravity at all. We only have good descriptions of its effects. We don't know what causes it anymore than we know why two like charges repel one another. From observing the way objects behave in response to gravitational fields we can confirm that general relativity is a very good description that predicts essentially all observations to within experimental error. 202.155.85.18 (talk) 05:31, 4 September 2018 (UTC)

Special relativity has also not earned a Nobel Prize. Does it mean that it is incorrect as well? Ruslik_Zero 20:50, 4 September 2018 (UTC)

Also, I don't understand why space is often looked at as if it were a physical entity.

In the words of Douglas Grossman, "Space is volume, nothing more. It's not a physical entity. It is an idea like distance or area. When you walk through the area of a doorway, do you bump into anything? No, because area is an idea, same as space. Space is nothing, physically. It has no mass or energy, although mass and energy can be found within it. Space itself is not a physical entity and has no properties of its own other than volume. It's an abstract idea we use to understand the arrangement and movement of matter and energy in our world. Only matter and energy exist physically."

"What about the expansion of the universe? Galaxies move apart from one another in every direction, thus more volume (space) appears between them as they do so, but believing space carries the galaxies with it as it 'expands' is a misconception. Space is not expanding, galaxies are just moving apart." Makuta Makaveli (talk) 05:38, 4 September 2018 (UTC)

As far as the assertion about the motion of galaxies, that's an easily testable alternative theory: if a distant galaxy is 1 billion light years away from us and moving away from us at 0.5c, then light emitted by it now should reach us in 1 billion years. But if the space between us and the galaxy is also expanding, it will take longer. The fact that it takes longer is one way we know that relativity is correct. This is well understood aspect of the nature of the universe and is applied in astronomy as Comoving and proper distances. 202.155.85.18 (talk) 05:43, 4 September 2018 (UTC)

If space was not physical, you could not observe it, move in it, measure it (distance and time), etc. See also the information about perfect vacuums. —PaleoNeonate – 08:03, 4 September 2018 (UTC)

We're moving in space right now. ←Baseball Bugs ^{What's up, Doc?} carrots→ 11:08, 4 September 2018 (UTC)

• Maybe, just maybe, general relativity is a bit more complex that the pop-science view of "mass warps spacetime". (It is also a bit more complex than "Einstein invented it all".) The fact that it did not get a Nobel prize is, let's say, not the best test of the correctness of a scientific theory; General_relativity#Consequences_of_Einstein's_theory has a lot of experimental tests without any less worse explanation. I dunno who this Douglas Grossman fellow is, but a paragraph of pop-sci from him is hardly a refutation of experimentally-validated theories. Tigraan^{Click here to contact me} 07:26, 4 September 2018 (UTC)

FWIW, a google search on the name doesn't yield any prominent results for anyone likely to be an authority on physics. {The poster formerly known as 87.81.230.195} 90.212.15.178 (talk) 10:53, 4 September 2018 (UTC)

The above quote seems to come from a comment on Quora by someone with the name quoted above [2] Nil Einne (talk) 12:55, 4 September 2018 (UTC)

Douglas Grossman may not be an authority on physics, but I like his definition so I chose it. if a distant galaxy is 1 billion light years away from us and moving away from us at 0.5c, then light emitted by it now should reach us in 1 billion years. But if the space between us and the galaxy is also expanding, it will take longer.

General relativity can't be the only way to explain this. PaleoNeonate said, If space was not physical, you could not observe it, move in it, measure it (distance and time), etc. This can be easily refuted. When you measure space, you are measuring nothing, uninhabited and matterless void. It's the same as measuring the invisible line around the earth called the Equator, which doesn't exist. As for moving space, there is nothing to move in the first place, and nothing to observe. Instead, you'd be observing and moving matter, which may or may not be invisible. Makuta Makaveli (talk) 17:29, 4 September 2018 (UTC)

General relativity is a set of equations and assumptions that purport to model the behavior of matter on a grand scale (on ordinary scales it reduces to simple Newtonian gravitation, and on quantum scales it breaks down completely). Scientists like the theory of general relativity because it not only provides an elegant explanation for cosmological observations, it has accurately predicted many new observations since its conception. There is no alternative to general relativity that makes better predictions. You can like or dislike how spacetime is described, but the math works out regardless. Perhaps you can describe more clearly what experimental or other observational result you think contradicts general relativity, or is better explained by something else. But you shouldn't put too much stock in verbal explanations seeming wonky to you - it's just a model, after all. The important part of the theory is that it can accurately predict what you will observe when you test the effects of gravity. Someguy1221 (talk) 22:40, 4 September 2018 (UTC)

Like a lot of things in physics, you can ignore the advanced theories if you don't measure quantities very precisely. So to shift the burden to the original poster: how accurately do you measure gravity, when you measure gravity? If the answer to this question is "I don't measure gravity," then you're categorically unqualified to have an opinion on the various advanced methods that others use to predict and measure gravity. Nimur (talk) 02:06, 5 September 2018 (UTC

My main issue is with how space and time are pictured in the General Relativity. Sure, it predicts and measures just fine, but are scientists sure that space time is responsible for gravity? Makuta Makaveli (talk) 02:20, 5 September 2018 (UTC)

Scientists are sure that the equations we commonly call "general relativity" are an accurate and precise mathematical model, and this mathematical model has explanatory power when we study gravity. Equations do not cause things like gravity - rather, equations can be used to explain things like gravity.

If you don't like these explanations, or if you don't understand them, that's okay. Major league ball players don't ask you to like or understand their methodology for picking batting orders in the mid-season; economists don't ask you to like or understand their theories about quantitative easing policy or its relationship to monetary inflation; physicists don't ask you to like or understand complicated mathematical models of gravity. These pursuits, to the extent practically possible, are meritocracies that are conducted by expert professional specialists; it takes a lot of years of dedicated work to develop the fundamental skills; and until you have established credibility in these fields by following well-established career-trajectories working toward the professional level, the experts don't really care what opinions you have about their work. You are free to critique advanced physics - or to complain that you don't understand it - but it will be about as productive as if you complain about the coaching strategy for a professional sports team. Your opinion carries no weight, and your critiques don't merit attention, because you aren't playing in the same league.

One does not begin a study of physics with generalizations of gravity; one does not embark on their ball-playing career as a starting pitcher for the Yankees.

To make my point more bluntly - if you want to understand general relativity, you begin by investing five or six years studying the easier parts of mathematical physics - usually by pursuing formal undergraduate college education culminating in a degree in mathematics or physics - and then you begin to study relativistic generalizations. If you think you can skip past those first five or six years of the easy stuff, you must be a super-genius whose superior mental acuity far exceeds that of the physicists whose work you are pretending not to understand.

Nimur (talk) 02:53, 5 September 2018 (UTC)

Piscis piscātor unus sunt? I'd like to talk with you sometime, Nimur. I'm sure the conversation would be intriguing. Makuta Makaveli (talk) 06:32, 5 September 2018 (UTC)

This is quantum mechanics, not relativity, but "empty space" is anything but: see Casmir effect, quantum foam, and related articles. It sounds to me like you have aesthetic objections to how relativity is commonly visualized. That's fine, but it doesn't change anything. The math makes certain predictions, every prediction that's been tested to date is correct, so we use it. If you don't like the visualizations, don't use them. As Someguy1221 stated, it's a model. All models are wrong; some are useful.

Fun fact: modern heliocentrism took a while to get off the ground (pun intended) in part because Copernicus was wrong about planetary orbits. He insisted they must be perfect circles, not ellipses, because circles are perfect shapes, and the heavenly spheres must only contain perfect shapes (following Plato, who stated the same). Since as we now know, planetary orbits are in fact ellipses, his published system involved all kinds of epicycles to make the orbits "correct", just like the Ptolemaic system it tried to replace. Hence, it was not any more elegant, and few people thought it had much merit. It took Kepler, working from Brahe's actual observations, to deduce that orbits were ellipses. This kind of metaphysical reasoning was really the norm for most of history. The Scientific Revolution was in large part about, "Hey, let's make predictions based on observation and test our predictions, instead of deciding how things must be and then looking for evidence to confirm it." Newton was quite troubled by gravity appearing to be some invisible force that caused action at a distance, but fortunately he published his theory anyway. The universe doesn't care what some apes on a tiny dirtball think about it. I feel similarly about the debates over interpretations of quantum mechanics. If we can't test it, it's irrelevant. Shut up and calculate. --47.146.63.87 (talk) 09:30, 5 September 2018 (UTC)

GR can be derived from first principles. Count Iblis (talk) 14:17, 5 September 2018 (UTC)

No more answers are needed, Nimur has already given a satisfactory one. Thank you, you all have been exceedingly helpful for this test. Makuta Makaveli (talk) 17:41, 5 September 2018 (UTC)

The Ptolemaic theory was actually better at predicting the planetary positions than Copernicus'. The elephant in the room, however, was the lunar theory. Although it predicted the position rather well, the size of the epicycle meant that there would be a huge increase in the moon's apparent size at its closest approach. Astronomers were well aware that the apparent diameter increased only by one part in seven - they knew the theory was wrong. 86.133.58.87 (talk) 19:18, 5 September 2018 (UTC)

Spider

What spider is this one, at least at the family or genus level? Spotted in my room, 3 cm in length (with legs). Possibly orb-weaver, but not sure. Brandmeister^talk 10:54, 4 September 2018 (UTC)

Where? Looks perhaps like one of the many grass spiders; the image is perplexing, doesn't seem to follow a proper arachnid body-plan→

Arachnid anatomy:
(1) four pairs of legs
(2) prosoma (cephalothorax)
(3) opisthosoma (abdomen)

2606:A000:1126:4CA:0:98F2:CFF6:1782 (talk) 17:31, 4 September 2018 (UTC) ... perhaps the abdomen is "missing"?

It's probably a male; they often have smaller, rather indistinct abdomens (lacking the egg producing organs that females need) which often don't show a clear break with the cephalothorax. The legs in the picture (the two-and-two on each side) reminds me of an orb weaver of some sort, especially the Argiope (spider) genus. --Jayron32 17:44, 4 September 2018 (UTC)