Wikipedia:Reference desk/Archives/Science/2014 August 30

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August 30

Recycling

Is there an example of a recycling plant that employs destructive fractional distillation under a reducing hydrogen atmosphere? I know of examples that separately employ fractional distillation, and plasmification, but not one that combines both. Plasmic Physics (talk) 04:15, 30 August 2014 (UTC)

The ideal cases in mathematics, physics and chemistry

Does the ideal cases in mathematics, physics and chemistry are been always right? The ideal cases in mathematics, physics and chemistry are been always a regularity or a paradox?--Alex Sazonov (talk) 05:18, 30 August 2014 (UTC)

I think you're asking whether the theoretical answer is always the real-world solution. That would be more common in math, although there are also many wrong answers provided by math, along with the correct ones, such as negative square roots that don't apply to a real-world case. In science there's more often a difference between the theoretical and observed. For example, the observation of the universe expanding at an ever increasing rate was completely unexpected by theory. StuRat (talk) 05:27, 30 August 2014 (UTC)

What force(s) would be causing such acceleration? ←Baseball Bugs ^{What's up, Doc?} carrots→ 05:33, 30 August 2014 (UTC)

Bugs, see accelerating universe. Staecker (talk) 14:04, 30 August 2014 (UTC)

Thank you StuRat. I’m sorry for my next question, but I want to better understand you. Does the formulas of ideal cases in mathematics, physics and chemistry are been always right?--Alex Sazonov (talk) 05:46, 30 August 2014 (UTC)

In general in mathematics formulae are always exactly right, even when something is an approximation it is a correct approximation otherwise there is an error in the mathematics. In general in physics and chemistry everything is wrong because there is always something left out or the theory isn't absolutely certainly true of the real world. This is a problem of ontology and the difference between existence and truth in mathematics as opposed to physics or chemistry. Dmcq (talk) 07:02, 30 August 2014 (UTC)

Is mathematical scientific doctrine is not absolute in the sciences, that is, what the mathematical scientific doctrine does not provide the identity of theory and practice in the sciences, including the practice of scientific research?--Alex Sazonov (talk) 12:05, 30 August 2014 (UTC)

I think there are several different aspects here. But at the heart there is a serious philosophical debate. See The Unreasonable Effectiveness of Mathematics in the Natural Sciences. --Stephan Schulz (talk) 12:11, 30 August 2014 (UTC)

Thanks. Does the scientific knowledge of the world in mathematics is always absolute or not absolute? Does the mathematical of the cybernetics is been always right?--Alex Sazonov (talk) 12:35, 30 August 2014 (UTC)

Have you read and tried to understand the article pointed to by Stephen Schultz in the twenty minutes between him writing his reply and your response? Why do you expect anyone to be able to give you any better response than is already given? Dmcq (talk) 13:50, 30 August 2014 (UTC)

What practical and theoretical mathematics always had ambiguity? The mathematics always is been a much exact science!--Alex Sazonov (talk) 15:17, 30 August 2014 (UTC)

I think, Norbert Wiener always supposed that practical decisions in mathematics always had higher values than the theoretical decisions, as practical decisions in mathematics always explained something that is not able to explain the theoretical mathematics.--Alex Sazonov (talk) 15:55, 30 August 2014 (UTC)

The idealism concerned in the question is the conviction that scientific method must build objectively stated unambiguous theories that have reliable predictive power; it is satisfactory demonstration of predictions that distinguishes theories from hypotheses. The scenario for fulfilment of a prediction is the ideal case. In chemistry, formulae for reactions must assume that the ingredients are pure and in analytical concentrations; in physics, calculation of a two-body planetary orbit (Kepler) must assume that every other object in the Universe has zero gravity; in mathematics nothing exists unless it is designated and nothing designated may vary unless it is declared to vary in a more (Algebraic number) or less (Transcendental number) restricted way. Use of ideal cases

• is relevant for exposition and understanding of scientific theory
• is necessary to show the scope of applicability of a principle, accepting the "paradox" that the ideal cases are generally unachievable
• leads to amiable parody such as "Consider a Spherical cow in a vacuum...".

Idealized cases do not however relieve the intellectual from studying or the investigator from investigating more demanding real-world complexities, because hanging on to Naïve physics offers only the intellectual stagnation of Pope Urban VII confronting Galileo. The square root of -1 is formally an imaginary mathematical unit and far from being a "wrong answer" it is fundamental to Complex number calculations which have had serious practical applications since the 17th century (Tartaglia). "Absolute truth" is a commodity of belief systems that is inaccessible to scientific analysis, is a theme in philosophy that is accessible to scientists though not to science, is not yet claimed by responsible chemists or physicists, and is only ever delineated provisionally by mathematicians. 84.209.89.214 (talk) 15:58, 30 August 2014 (UTC)

Is identity in mathematics always been absolute? If A always is not been equal to B, is B always not been equal to A, or thats is not been right? I think, it always is been a much exact, it is been mathematics.--Alex Sazonov (talk) 17:30, 30 August 2014 (UTC)

Time does not enter into math unless it is deliberately introduced as a variable (often as t seconds). A and B do not exist in a mathematical proof until they are designated (invoked); expressions like A=B become absolutely true from the moment they are stated; an operation A+B can give a result C which is similarly true from the moment it is stated because the operator "+" has been defined earlier. Values that the mathematician assigns persist only as long as needed to complete a calculation; one may turn the page of a math textbook and then find A, B and C used differently. A few constants such as pi have unchangeable values. There is a particular meaning of Absolute value which is the distance from zero of a value but I assume you don't ask about that. 84.209.89.214 (talk) 18:40, 30 August 2014 (UTC)

I'm trying to prove that mathematics consists of identities and not of mathematical hypotheses have (had) no practical mathematical solution, I believe that all of mathematics is presented mathematical identities always have mathematical solutions, so I am a supporter of absolute mathematical identity as the absolute accuracy of mathematics.--Alex Sazonov (talk) 19:53, 30 August 2014 (UTC)

Sadly, you need to read Gödel's incompleteness theorems...and if you have the time and patience, Gödel, Escher, Bach by Douglas Hofstadter. Mathematics is (for sure) always going to be incomplete. There are mathematical statements out there that can never (even in principle) be either proved or disproved. SteveBaker (talk) 20:44, 30 August 2014 (UTC)

Umm, let's be a little careful here. The theorems say that no fixed formal theory, with appropriate technical stipulations, can answer all mathematical questions. They don't say that there's any particular statement that can never be proved or disproved by any theory. --Trovatore (talk) 08:01, 31 August 2014 (UTC)

I think that, a practical method of mathematical decision of a mathematical problem always had generates a theory of mathematics! Does it make sense to use in scientific knowledge the mathematical theories (hypotheses) which had no practical solutions?--Alex Sazonov (talk) 07:14, 31 August 2014 (UTC)

Exterminating virtual particles

I understand that virtual particles are very common in modern physics, but... my mind rebels against them. I mean, consider the Casimir effect. The plates are drawn together by the lack of virtual particles with certain frequencies that can't exist due to the conductive plates around them. It seems simple enough, except... suppose the plates weren't conductive, or were only mostly conductive. Then I'm supposed to believe that the vacuum is a sea full of an infinite variety of virtual particles, and out of all that mind-boggling density of imaginary stuff, the ones that measure the plates' conductivity are the ones that don't exist, even as "virtual" particles. Do I have that right? Whereas (as the article says) simply looking at the effect as a Van der Waals force, based on (I assume) the very clear uncertainty of the position and momentum of the real electrons in the metal plates, seems incredibly more straightforward.

Anyway, has a reputable authority tried to lay out a physics in which each and every proposed virtual particle has been exterminated from consideration, whether for mediating the Coulomb force or Hawking radiation or any of the dozen other things mentioned in virtual particle, relying only on honest-to-God particles? Wnt (talk) 17:46, 30 August 2014 (UTC)

This question is near the line between physics and metaphysics - Horror vacui (physics), The World (Descartes) (as we don't have an article specifically on the Cartesian Plenum), Vacuum energy and Dirac Sea might be useful further reading. The experimental observation for which we need to save the appearances is that particles interact with each other in a vacuum (a real vacuum that one can produce with a vacuum pump). The alternatives to virtual particles are the acceptance of action at a distance without any physical mediation, or the view that the vacuum isn't empty, but contains (an infinite amount) of a substance through which particles interact. All three have their metaphysical disadvantages, and all three give us theories that explain the real world. Tevildo (talk) 19:46, 30 August 2014 (UTC)

It is clear that virtual particles provide a useful framework for calculating a variety of very real phenomena. However, it is not necessarily the case that they really exist as such. Allow me to draw a very crude analogy. Suppose a small boat is sitting on a pond, and somewhere else on the pond you drop in a stone. This generates ripples on the pond that cause the boat to move. Now suppose you couldn't see the water ripple, instead all you could see was the passing stone and the bobbing boat. You might imagine that the stone was sending out invisible particles that were hitting the boat. In a way, virtual particles are a bit like that. Virtual particle interactions can also be interpreted as fluctuations in a hidden higher-dimensional structure of spacetime, sort of like ripples on a pond, but in a space that incorporates the fundamental forces and standard model particles as an extension of the properties of space itself. Essentially, one can consider virtual particles as a sort of accounting gimmick that allows us to describe the complex ways that the various forces perturb the universe. Whether you actually imagine that we live in a complex sea of virtual particles rippling in and out of existence, or rather choose to imagine that we live in a complex and dynamic higher dimensional spacetime is essentially a matter of interpretation. Like the various interpretation of quantum mechanics the different points of view are more about philosophical interpretation than useful prediction. Dragons flight (talk) 22:05, 30 August 2014 (UTC)

I suppose there are other cases of this; for example, the "holes" in semiconductors are like this. But if you have a semiconductor with one random atom missing, and you look at the localization of a "hole" that is adjacent to it, I assume it doesn't actually look like an anti-electron, because I'd expect the probability pattern of the hole to reach up and around the physical hole in the structure whereas the electron would have no interest in embracing it. I wonder if virtual particles can lead us astray the same way. For example, in the infamous black hole information paradox, we uncritically accept that "virtual particles" are bringing information from nowhere out of the hole. Only... what if this is more virtual particle BS? What if really the paradox can be explained by simply discovering that we're looking at the uncertainty of the position and momentum of the particles that were falling in before they hit the horizon, which allows for a chance they really never did? Or the odds that they did go in the singularity, but tunneled out again. Or ... something. I'm not a physicist and I'm not trying to propound a theory here, just feel like what I'm being fed tastes off. Wnt (talk) 15:29, 31 August 2014 (UTC)

The paradox - again, we're really still in metaphysics, although this issue is potentially amenable to experimental resolution - depends on the principle of quantum determinism, that Laplace's demon can put any system back together again, even if it falls into a black hole. This may not be true in the first place (which is a question of pure metaphysics), but, even if it is, the mechanism by which the wavefunctions of the black hole's source particles are recovered doesn't have to involve virtual particles. Without knowing what goes on at the singularity, we can't say definitely that the wavefunctions are "destroyed" and have to be "recreated". They could persist through the accretion and evaporation process, as you suggest. Until the physicists come up with a testable theory, all we can do is check the maths is correct and doesn't contradict observation. Tevildo (talk) 19:10, 31 August 2014 (UTC)

The original Hawking radiation paper derived the result nonperturbatively (without virtual particles). He only mentioned virtual particles as a handwavy informal picture of what's going on. It can certainly happen that no one knows any way to get a handle on a difficult problem except by some approximation method, and the result can have features that look like real physics but are actually artifacts of the approximation method. If the approximation involves virtual particles then you would be misled by virtual particles, in a sense. But those sorts of problems are unavoidable when you're doing original research. Professional particle physicists understand that the nonperturbative physics is what matters; I don't think they overvalue virtual particles the way pop-physics books do. -- BenRG (talk) 23:04, 31 August 2014 (UTC)

Hmmmm, to me it sounds as if Hawking was indeed saying something vaguely similar to what I was suggesting all along, from the first paper in 1975, the only difference being that his version was mathematical, meaningful and coherent. :) What I wonder, though, is if the "tunneling" going on in any way would imply that when matter is eaten, matter would outweigh antimatter in the radiation, i.e. that the notion of taking a mini black hole and stuffing it with a matter beam to convert it into energy might be too good to be true. Wnt (talk) 05:52, 1 September 2014 (UTC)

I'm not sure what you're saying, but there's no "tunneling". The Hawking radiation comes from outside the horizon. -- BenRG (talk) 22:05, 1 September 2014 (UTC)

Elevation and temperature

At what elevations do temperatures start to change significantly? 500m? 1000m? Etc — Preceding unsigned comment added by 90.192.117.124 (talk) 20:02, 30 August 2014 (UTC)

See Tropopause, Atmosphere of Earth, and (perhaps) Atmospheric temperature (although that last article isn't very good). 500 m and 1000 m are still comfortably within the troposphere - the tropopause (where temperature _stops_ changing significantly) is at about 10000 m. Tevildo (talk) 20:10, 30 August 2014 (UTC)

To answer your question literally, temperatures _start_ changing significantly at zero elevation. The temperature at the top of a medium-sized building (50 m / 150 ft) will be about 0.5 C lower than at ground level, which will be noticeable to most people. See lapse rate. Tevildo (talk) 20:35, 30 August 2014 (UTC)

You said elevation (i.e. height above sea level) and not altitude (i.e. height above local ground level). Assuming you really want to know about elevation related changes, then the surface elevation lapse rate is about 3 degrees C per km of elevation change in environments with slowly changing elevations. This is significantly less extreme than the about 6.5 degree C / km atmospheric lapse rate that one experiences from simply going up in altitude. The difference is related to the role of solar heating in setting the conditions at the ground surface. Dragons flight (talk) 21:27, 30 August 2014 (UTC)

A minor correction - altitude is also the height above sea level, which (unlike elevation) may be different from the height above ground level. Height above ground level is just "height" (or QFE). Tevildo (talk) 21:52, 30 August 2014 (UTC)

In my area of climate science, "altitude" is nearly always a synonym for "height above ground level" also known as the "absolute altitude". As far as I know, it is only people in aviation that insist in using "altitude" to generally mean height above sea level. Dragons flight (talk) 22:16, 30 August 2014 (UTC)

By way of evidence that "altitude" can be used to mean "elevation", I submit this. It'd be in England. --65.94.51.64 (talk) 05:50, 31 August 2014 (UTC)

I'd just submit altitude. --jpgordon^{::==( o )} 04:45, 2 September 2014 (UTC)