Wikipedia:Reference desk/Archives/Science/2020 April 29

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April 29

Planets

In the Planet article, it says that in order to be considered a planet, an astronomical body needs to be massive enough to be rounded by its own gravity. About how much mass is required for this? Is there some kind of "minimum mass" for a planet? 193.210.228.37 (talk) 11:43, 29 April 2020 (UTC)

This will depend on how strong the material is. If it is the very weak solid nitrogen, the smallest size would be much smaller than for an iron nickel asteroid. Graeme Bartlett (talk) 11:45, 29 April 2020 (UTC)

Here is an assessment in terms of radius. The radius is more useful for astronomers because it's easier to measure than mass (you need e.g. a satellite to measure mass). As expected the necessary radius depends a lot on the body's composition. 93.136.9.236 (talk) 15:30, 29 April 2020 (UTC)

Pluto is certainly round, but Tyson decided it wasn't a planet anymore, so it isn't. ←Baseball Bugs ^{What's up, Doc?} carrots→ 21:49, 29 April 2020 (UTC)

Because being round isn't the only qualifying factor to make something a planet. Tyson didn't decide anything, either. The International Astronomical Union decided on a definition. Tyson has been a proponent of said definition, but it wasn't his call. --OuroborosCobra (talk) 22:49, 29 April 2020 (UTC)

He championed it, so he gets the blame. ←Baseball Bugs ^{What's up, Doc?} carrots→ 03:57, 30 April 2020 (UTC)

That's not how this works. That's not how any this works. --OuroborosCobra (talk) 16:03, 30 April 2020 (UTC)

"Roundness" is not the only criterion. Pluto fails on the other tests for planetness. Or, to be more exact, if Pluto is a planet, then so are umpty-dozen other things in and around its orbit and in and around the asteroid belt. Which would make planet a less useful term. --Khajidha (talk) 17:36, 30 April 2020 (UTC)

How I Killed Pluto and Why It Had It Coming by Michael E. Brown is well worth reading. Mikenorton (talk) 17:53, 30 April 2020 (UTC)

Ceres with some more than 900 km and a mass of 9.5 × 1020 kg was the smallest celestial body thought to have been rounded by its own gravity. I think I read somewhere that another body with about 400 km could be also rather round and this would be probaly an example of minimum mass. But yes, mass alone is not all: a stony body covered with water ice will possibly get round faster than some irregular chunk of iron-nickel. 2003:F5:6F0A:C00:5CC0:1EE6:8417:F1F (talk) 20:17, 30 April 2020 (UTC) Marco PB

The self-styled experts changed the definitions. Pluto never changed. And Pluto will be around long after those who dissed it are gone. ←Baseball Bugs ^{What's up, Doc?} carrots→ 22:14, 30 April 2020 (UTC)

That's a very unscientific way of thinking. You do understand that the category "planet" is just a creation of the experts that is used to classify things so that we can understand them better? Also, experts had been debating Pluto's "planetness" basically since it was discovered.--Khajidha (talk) 22:31, 30 April 2020 (UTC)

And speaking of Ceres, when it was discovered in 1801, it was universally hailed as a newly-found planet. All decent science books from then on included Ceres along with Jupiter, Mars etc and all the other then-known planets. This situation obtained for almost 60 years (almost as long as Pluto was regarded as a planet), until it was reclassified as an asteroid after many similar-sized objects were found, and it dropped out of general consciousness so totally that most people these days have never even heard of it. That's unlikely to happen with Pluto, mainly because of all the hullabaloo after it was reclassified as a dwarf planet. I actually accuse most scientists of being closet astrologers whose equanimity was disturbed when they had to go back and recalculate all their horoscopes with Pluto left out. That's what this is really all about, mark my words. -- Jack of Oz ^{[pleasantries]} 23:47, 30 April 2020 (UTC)

I'm a supporter of Alan Stern's idea to call them "überplanets" ("main planets" sounds better to me). Pluto, Eris and Sedna are basically planet-sized and planet-shaped bodies that happen to be very far away from the Sun. Could've gone with that but that would mean avoiding a huge publicity grab... 89.172.8.118 (talk) 01:09, 1 May 2020 (UTC)

Baseball Bugs If you're interested, I strongly recommend this casual YouTube video from CGP Grey. Link here. --Puzzledvegetable^{Is it teatime already?} 00:00, 1 May 2020 (UTC)

What exactly does it mean for a photon to have an amplitude?

Given the extent to which photons cannot be described as classical waves, what exactly does it entail to measure the amplitude of one? As in, what are you physically measuring and called the 'amplitude', if the photon itself does not truly possess a 'height' the way a classical wave might. Apologies for any misconceptions inherent to the question itself. — Preceding unsigned comment added by Opossum421 (talk • contribs) 11:50, 29 April 2020 (UTC)

Amplitude in quantum mechanics refers to the level of probability of making that measurement at that value. See Probability amplitude (though that article like many at Wikipedia is probably too technical for someone unfamiliar with the field. Le sigh.) The basic way to think of the wave function is that it isn't a wave in space-space, it's a wave in probability space. Only the position wave function includes space-space in it, and even that isn't telling you where the particle is, it is telling you where the particle is likely to be if you were to try to interact with it. The particle isn't anywhere in particular until you interact with it, then it's wave function changes to a more narrow shape showing the increased probability that the particle is located where you interacted with it. There are lots of other wave functions, however, that do not have space or position in them, such as momentum or spin orientation or the like. If there was one thing about QM that most people get wrong (often because teachers either themselves don't get this, or don't make it explicit enough) is that quantum mechanics abandons the notion that a fundamental particle is an object in any sense we understand the term "object" to mean. Some properties of quantum particles are definite and well-defined, like electric charge and spin magnitude and things like that, but other properties (including position and momentum) are not well defined, meaning those values can only be described by giving the probability of finding the particle with that value for the measurement. If we graph all of those probabilities on a coordinate system, where the Y axis is defined as the probability of finding the particle with that value, and the amplitude is just the maximum probability of finding the particle with that value. The mathematics of the graph we draw obeys the mathematical rules of wave mechanics, which is why it is called a wave function. But again, it isn't a wave in the real world. It's a wave in probability space, which is a mathematical construct where the property being measured is plotted on some of the axes, and one of the axes is a probability. (This is a massive oversimplification, and ignores the difference between, for example Ψ and Ψ² and a WHOLE lot of messy math, but it captures the spirit, which is all we need here). I highly recommend a few channels on YouTube that explain this even better than I can through text are Science Asylum (Nick Lucid) and 3Blue1Brown (Grant Sanderson). Science Asylum does a fantastic job of explaining complex physics phenomena in a short, informative, and easy to digest way (pretty much the OPPOSITE of Wikipedia articles on the subject) while 3Blue1Brown covers complex mathematics in a slow, methodical, but still fantastically clear manner that also makes these things easy to understand. This video that Science Asylum did on the Wave Function is probably most germane to our discussion, but his entire series on QM would be useful. I don't have a specific 3Blue1Brown video to recommend on this direct topic, but he's done lot of videos the mathematics useful to understanding QM (such as this video on the uncertainty principle [1] which starts off his whole series on the Fourier transform, which is a mathematical tool with many wide-ranging uses, but which is SUPER important to understanding the mathematics of QM). I hope that helps some. --Jayron32 13:19, 29 April 2020 (UTC)

Like many simple questions in physics, there is a long and convoluted answer! To summarize shortly, whomever spoke of the photon's amplitude was being sloppy and imprecisely using terminology - and this sort of nonsense is very common amongst practicing physicists, because as a community, they've generally proven to themselves that they can be precise when they need to be, and they know that they don't usually need to apply that precision, because being excruciatingly correct all the time becomes very tiresome.

So - to the question: what is the amplitude of the photon?

To recite the rote-memorized answer, that would be a quite trivial question! Why, the amplitude of "the wave function", of course.

Now, the thing that's funny about quantum physics is that the books all speak in grandiose terms about the wave function; they have a special equation for the function; and they even have a special-purpose symbol, $\Psi$, which is exclusively reserved to represent the function. And if you read any book on the topic, the amplitude of $\Psi$ is a scalar; and it is an abstract quantity that can be used to predict the probability and the time-evolution of measuring some other physical observable. But what is it?

If you read a little deeper, and learn what the function is, you'll discover that it's actually unique to every single physical system. There are actually many different wave functions; the part that is common to all of them is that they must satisfy certain mathematical and physical requirements.

In the case of the quantum-mechanically-correct description of the photon, the actual equation that describes the wave function is not so surprising: it is derived from the very same relationships that describe the classical electromagnetic wave; and that wave is easily represented using the classical wave equation of conventional electrodynamics. That wave is a pair of coupled vector-quantities; the two components - a magnetic field and an electric field - have position and direction, but they have no extent.

By convention, we often simply work with the amplitude of the electric field and we ignore the amplitude of the magnetic field; but it doesn't really matter, because we can equally convert to calculate the amplitude of the magnetic field. Because the two fields are related by a very well-behaved governing-equation, we can easily switch between electric- and magnetic- field amplitude; this is simply a change of units, with a little extra-special mathematical care in the case the wave is propagating inside an imperfect material.

To make the equations for these amplitudes quantum-mechanically-correct, we just need to make sure that the time-evolution of the system abides by any quantized interactions; but in the case of the electromagnetic wave in a vacuum, there's no change from the classical case: the photon is the quantum particle, and its quantum mechanical wave function is the classical electromagnetic wave function.

The extra work to manipulate the equation so that it looks like the Schrödinger equation is really just a rearrangement of variables - and when you succeed in doing that, you've simply rearranged the same thing into a format that is particularly inconvenient for expressing macroscopic interactions between the photon and the outside world. But that form is useful for describing special cases in physics - things like photon-material interactions; or making statistical predictions about the probabilistic behaviors of individual photons; and so on. For those cases, the amplitude of $\Psi$ is used to predict the amplitude of E and B (the electric field and the magnetic field).

And of course, because the actual values of those field amplitudes are themselves a probabilistic attestation deduced from the amplitude of $\Psi$, we expect that $\Psi$ should evolve predictions that, over time, change in a manner that is statistically indistinguishable from the time-evolution of the amplitudes of E and B, in other words, the classical wave equation.

Nimur (talk) 13:27, 29 April 2020 (UTC)

Nimur's answer is also really good here, as it draws comparison to "classical" wave mechanics and quantum mechanics. I just want to point out that his analogy between the the classically defined EM wave equation and the quantum wave function is really useful here, but maybe not in the direction one thinks; for example, when one asks "what is waving" in the EM wave, we say "the electromagnetic field". This is similar to saying that the thing that is waving in an ocean wave is the ocean, except that the ocean is a real physical stuff we can pick up and touch and is an object. The electromagnetic field is not a stuff. Like all fields (classical or quantum) it is a mathematical construct. A field is just a set of numbers (which can be scalar, vector, or tensor) that we attach to space itself, describing a specific property that space has. The "manipulation of variables" and the other things Nimur talks about relating the quantum wave function to the EM wave itself are just a set of mathematical transformations. Just as you can do math to convert one function to another (for example, the way that the exponential function e^ix can be used to convert between circular motion and wave motion, there are also trivial mathematical tools we can use to convert between EM waves in the EM field to quantum wave functions in probability space. Such mathematical tools change our perspective on a phenomenon, but don't fundamentally change the phenomenon itself). So, when we say "what is waving" in an EM wave, it's the values we assign to the various points in space that we call the EM field, and when we say "what is waving" in the quantum wave function, it's the probability of the particle having the values in question. And because those functions are describing the same phenomenon from different perspectives (both describe light), there must be some mathematical tool to relate them to each other. --Jayron32 13:55, 29 April 2020 (UTC)

Thank you, Jayron. Your post has helped me to realize something: I am just assuming that everybody already knows what electric fields and magnetic fields are. Of course, if our readers are not intimately familiar, they can review those articles.

If I may coopt Jayron's terminology - and simplify by glossing some of the details - the "thing" that is "waving" is the Electric field (and the B-field, per our earlier discussion). The E-field is not "stuff." It is a set of numbers that tell us what force would be felt by a charged particle if it were at a specific place. Those numbers are what are waving up and down. If we had a way to measure those numbers, we could see them fluctuating in a more-or-less perfectly sinusoidal fashion. But the only way we can measure those numbers is to place a test-particle at some specific position, and watch how it moves.

The really tricky part is that if we actually put a charged particle there, the waving numbers that tell us what force the particle should feel would change because they would interact with the charged particle; it would have its own fields; and it would also be moving as the wave interacts with it. So these wave-equation representations are mathematical idealizations - they help us make useful predictions, and they only make helpfully-valid predictions when we consider statistically-large numbers of individual particles, so long as we are willing to ignore the effects of any individual particle.

It isn't necessarily obvious - great scientists became famous for finally realizing this very subtle detail! - but the E- and B- fields are deeply deeply related to the photon. Early physicists described electricity, and magnetism, and light; and for a lot of centuries, we thought of them as three separate things; but ... we now understand that all of them are actually the exact same thing under different conditions. Photons interact with E- and B- fields - but even more importantly, photons are actually made of E- and B- fields. There's nothing else inside of a photon except those fields - and those fields are not made of "stuff"! And if you're a real mathematical hot-shot with access to a good book, you can play some advanced vector-calculus-trickery to demonstrate that the E-field and the B-field are the exact same thing, too: they're not merely related or coupled fields - they're the same exact darned field. And this is the equally important bit, that's less-often shouted at students: if photons are made of E- and B- fields, then .... every E- or B- field you can conceive can be expressed as a photon. It might be a pathologically poorly-behaved photon - it might have a ludicrously useless wavelength; but ... there you have it. Photons-the-size-of-mountains, emitted by electric-wires-strung-between-peaks.

So if you're trying to figure out what "stuff" is "waving" when an electromagnetic wave ... "waves"... well, we can quickly find ourselves traveling down the rabbit-hole of physical definitions: what is "stuff"? Which physics-ese techno-jargon word corresponds to the plain English word "stuff"? (Matter? Mass? Momentum? Quantum state exclusivity?) And I am pretty sure our only conclusion will be that natural human languages are not really expressive enough to describe some of the physical realities unless we throw the weight of a lot of words at it.

Nimur (talk) 17:22, 29 April 2020 (UTC)

All of that being said, I really do recommend the OP watches the videos I recommended. Seeing someone explain something in a video format, with pictures and animations, can be a lot more enlightening than reading the same information. --Jayron32 18:15, 29 April 2020 (UTC)

The energy and momentum of a Photon which is the elementary particle of the electromagnetic field depend only on its frequency or inversely, its wavelength. Increasing the amplitude of a beam of light or radio wave doesn't create "stronger" or higher-amplitude photons, it just creates more of them. DroneB (talk) 21:39, 29 April 2020 (UTC)

Thank you tremendously folks, I hadn't anticipated such a thorough set of responses. To Jayron32's suggestion - I'm quite familiar with 3Blue1Brown and will surely venture down that particular rabbit hole along these lines, and have not heard of Science Asylum but will give it a proper go as well. I appreciate everyone's helpful explanations here. Opossum421 (talk) 11:12, 30 April 2020 (UTC)

Rooibus

Where can I buy a rooibus plant to grow in my garden?99.145.194.98 (talk) 19:42, 29 April 2020 (UTC)

Possibly you mean the Rooibus tea plant cultivated in South Africa. The American Herbal Products Association has a website that may help you locate sources and there is an Australian supplier. DroneB (talk) 21:22, 29 April 2020 (UTC)

Postage to and from Australia is very delayed at the moment due to limited international flights, so if you are in the USA, buy from USA. Graeme Bartlett (talk) 23:56, 29 April 2020 (UTC)

To import plants or seeds from abroad you need a phytosanitary certificate or a small lots permit, to make sure you are not bringing non-native pests or pathogens into the US. Please check USDA APHIS website for what documentation is necessary in your case, and how to apply for it properly. Best regards, Dr Dima (talk) 06:19, 30 April 2020 (UTC)

Googling [buy “Aspalathus linearis”|"Rooibos" seeds] produces several outlets.  --Lambiam 14:04, 30 April 2020 (UTC)

Try at your local plant nursery. 89.172.8.118 (talk) 19:00, 30 April 2020 (UTC)