Wikipedia:Reference desk/Archives/Science/2018 April 6

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April 6

Fahrenheit's definition

The Fahrenheit articles states that "scale is now usually defined by two fixed points". Why 'usually'? Isn't there an official standard that defines it precisely? Is there another way of defining it, that would still make sense? --Doroletho (talk) 12:36, 6 April 2018 (UTC)

No, there are multiple ways it could be defined. Since the Fahrenheit scale is not usually used in a scientific context (even in the US where it is still used commonly) the rather imprecise method of defining it as a linear scale defined by the 32-212 points (freezing and boiling points of water at sea level pressure) is usually sufficient for common usage. However, there are other ways to define the scale; for example by pegging it to the more precisely defined Celsius or Kelvin scales. In that case, because the Kelvin is more precisely defined; a Fahrenheit scale pegged to the Kelvin definition will differ by a small fraction of a degree from one pegged to the freezing and boiling points of water. --Jayron32 12:42, 6 April 2018 (UTC)

I actually think our article is misleading. That may be the way Fahrenheit is defined in books or such, but in legal cases Fahrenheit is more likely to be defined based on Kelvin. (Rarely it may be defined as Celsius although that itself is likely to be defined based on Kelvin.) Of course you could still define it the traditional way too as a third option. Nil Einne (talk)

Again, it's what you mean by "usually". The need for a rigorously defined Fahrenheit temperature pegged to Kelvin is rare compared to how often it is used in a less rigorous context; hence the "usually" defined based on the freezing and boiling of water. --Jayron32 13:18, 6 April 2018 (UTC)

Well neither of us have provided any evidence for this. I did attempt to look before my first reply (well before any reply), but the US standards are incredibly confusing. But in any case, whether or not something is 'needed' often has little to do with how something is usually used. If you were to look at how Fahrenheit is actually defined in places like the US and UK where it is used, I think there's a fair chance that definition will ultimately come down to it being defined based on Kelvin; similar to the way the inch, pound, hour, etc are defined. Whether or not people think they should be defined, or people think or in reality there is a need for this definition is let me repeat for the last time, besides the point if the actual definition used, as show in the regulations etc is actually based on Kelvin. And let me repeat, what I said in my first reply, if it the definition actually used in the regulations etc is something else, then it's not reasonable to claim that some other definition must be the usual definition when there is another very common usual definition. (It's likely even most decent books will mention Kelvin too anyway.) Considering how rarely the temperature scale is used, if you can find evidence that most regulations or legal uses in the US, Canada or UK define Fahrenheit in the manner you claim is usual, then I will accept I'm wrong. The most I could find with brief mentions of the relation between Fahrenheit and Kelvin or Celsius but these were more explanations than real examples of definitions in the regulations (or case law). The hour (or other units of time) and for that matter celsius themselves are IMO decent comparitive examples here and IMO the article ledes themselves provide much better explanations of the complexities without making misleading claims about how something is 'usual' defined without evidence. (Although for your points, I don't think we even need to go that far. There's little practical difference between some sample metre and the actual modern definition of the metre for many purposes. I mean heck, we don't even need to go to a sample metre. A lot of produced measuring tapes, rules etc are accurate enough for many purposes. It doesn't mean to say I'm going to argue this ruler I bought from the Warehouse is the definition of a metre to me, even if it's the metre I normally use.) Nil Einne (talk) 04:56, 7 April 2018 (UTC)

Merits of logarithmic vs linear scales for temperature?

Usual linear scales for temperature (such as Celsius and Farenheit) have the drawback that they assume an "absolute zero". It would seem more logical to have a scale that approaches that "absolute zero" temperature asymptotically. On the other hand there are advantages in using a linear scale for temperature: for example thermometers are graduated linearly, so it seems that the expansion of liquids in terms of temperature follows a law that makes it simpler to graduate thermometers if a linear scale for temperature is used. What are the merits of linear vs logarithmic scales for temperature? Do they explain adequately why the choice was made to use linear scales? Do formulas involving temperature in physics become simpler or more complicated if one or the other is used? Thanks. Basemetal 17:51, 6 April 2018 (UTC)

I don't understand why the existence of absolute zero should be a "drawback".

The thermodynamic temperature can be defined in a number of ways, all of which are linear with respect to the others. Well, to the extent that they're well-defined at all — there are annoying bookkeeping issues no matter how you define it.

But certainly you could make a substitution U=log(T) or some such I just picked U because it's the next letter after T; in practice you'd have to find something else because U means internal energy, but most of the letters are already oversubscribed. Most formulas would become more complicated, I think. The difference between two temperatures is a good measure in a lot of contexts for how much thermal energy "wants" to flow from one to the other. You'd have to replace that by the difference between the exp(U) values. --Trovatore (talk) 18:21, 6 April 2018 (UTC)

Another self-quibble — you can't really write U=log(T), because the units don't work. It should be U=log(cT), where c is not the speed of light, but rather some constant with units of one over temperature. --Trovatore (talk) 21:23, 6 April 2018 (UTC)

Actually you could just write log(50K) = log(50) + log(K). The temperature in Rankine would be 90R, and its log is log(90)+ log(R). Note since K/R = 9/5, log(K) - log(R) = log(K/R) = log(9/5), which naturally will match the log gap between the two scales. I don't understand why tacking on "+ log(unit)" is so unknown in physics circles, because it is a very elementary way to do things. Wnt (talk) 00:03, 7 April 2018 (UTC)

Sure, formalistically you can do that, but it doesn't make any obvious sense. What is the logarithm of a Kelvin? If not a silly question, it's at least a silly-sounding question, notwithstanding the fact that you can use it formally in sufficiently circumscribed situations and make everything cancel out at the end. Now, plenty of interesting stuff has come out of silly-sounding questions, but I don't have high hopes for this one.

On a practical level, requiring transcendental functions to take dimensionless arguments is an excellent error check. If you want to add two things, they'd better have the same units, or at least be convertible to the same units. If you want to multiply or divide them, you do what you want, as long as the units come out to what you want in the end. And if you want to take the logarithm, or the exponential, or the sine or cosine, they'd better be unitless. You catch a whole bunch of mistakes that way, enough that natural units might not be a good way to work even if their values weren't so inconvenient compared to human-sized things. --Trovatore (talk) 03:52, 7 April 2018 (UTC)

I make no statement about the sine of a kelvin, but if you can multiply a number by a kelvin, why shouldn't you add the log of a kelvin? And people don't hold to your standard (e.g. pH). Wnt (talk) 10:16, 7 April 2018 (UTC)

most of the letters are already oversubscribed Indeed, they call that Overloading in computer science. Related: polysemy. SemanticMantis (talk) 00:39, 7 April 2018 (UTC)

• Linear temperature has some great advantages. For example, heat capacity is almost the same over a wide range, so heating water by one degree takes about as much energy if it is at 0 degrees or 80 degrees. Thermal expansion is mentioned above. More fundamentally, the Boltzmann constant and ideal gas constant relate the temperature directly to the kinetic energy per particle or per mole of particles (per degree of freedom). Twice as much temperature (in kelvin) means twice as much stored energy, or twice as much gas volume at a given pressure, or twice as much gas pressure at a given volume. Wnt (talk) 23:57, 6 April 2018 (UTC)
  • Well — sort of. The kinetic-energy formulation is OK for monatomic gases at sufficiently low pressure. For anything else you need to hem and haw and do bookkeeping tricks. And it doesn't work at all for spinglasses.
    The version I learned is that the temperature is the reciprocal of the derivative of entropy with respect to internal energy, with entropy defined as the logarithm of the quantum degeneracy. That's the formulation used by Kittel & Kroemer.
    It has its own bookkeeping problems — what exactly is "internal" energy?? I've never seen a philosophically satisfying demarcation between internal energy and the rest of energy. I know internal energy is supposed to be the "random" component of energy — but how do you tell which part is random? I'm not saying there isn't a philosophically satisfying demarcation; just that I've never seen it. Physicists usually don't worry about such things, or at least don't bother teaching them to undergrads, even at Caltech. --Trovatore (talk) 03:32, 7 April 2018 (UTC)

Wikipedia has an unusually readable article at internal energy, which explains that

$U(S,V,n)=const\cdot e^{\frac {S}{cn}}V^{\frac {-R}{c}}n^{\frac {R+c}{c}},$

where U is internal energy, S is entropy, V is volume, n is number of moles, c is the heat capacity of the substance, R is presumedly the ideal gas constant, and const is, apparently, some "arbitrary" constant (?). Here I suppose heat capacity is J/mol K, as is R, while S is J/K. Hence $T={\frac {\partial U}{\partial S}}={\frac {const}{cn}}\cdot e^{\frac {S}{cn}}V^{\frac {-R}{c}}n^{\frac {R+c}{c}}$. To me this just looks like U/cn -- which is to say, proportional to the internal energy. To be sure, I erred in some degree to say "kinetic energy" above because the potential energy of particles in cramped quarters, especially in non-gasses, would appear to be relevant also. Wnt (talk) 17:09, 8 April 2018 (UTC)

So first of all, if you look at the context, that formula is asserted only for ideal gases.

More to the point, it's not a definition of internal energy; it's an assertion about how internal energy varies with other things. Note that those other things themselves include quantities that are at least as hard to define as temperature itself (for example, heat capacity), so it is not particularly useful in explaining temperature as a concept. --Trovatore (talk) 21:44, 8 April 2018 (UTC)

The article says internal energy excludes energy from the overall kinetic energy of an object or from external fields. But admittedly that is not complete - overall angular momentum would need to be excluded also, I would think. I don't think many other non-random things can be on the list ... even if you have a vibrating iron bar in space, eventually the vibration should become atomic, so you might as well consider it as part of "temperature"? Hmmm... what if you can have an endothermic chemical reaction in a material whose equilibrium can shift for some reason? But by definition that means it really does change temperature, so chemical energy is excluded. I sort of see your point ... must be a longer list than I'd think. Wnt (talk) 11:45, 9 April 2018 (UTC)

Right. The larger point is that it's not philosophically satisfying for it to be a list at all — that makes it look like a bookkeeping trick. What is the underlying unifying concept? That seems to be very hard to isolate. Or, as I say, maybe it's been done to death, but no one bothered to tell me. --Trovatore (talk) 21:10, 9 April 2018 (UTC)

Seems kind of interesting because internal energy is a fundamental concept. Which implies that someone way smarter than I am might come up with a way to use that definition to separate "object" from "environment" and possibly understand the nature of space in the process. I'm vaguely reminded of how black holes can have mass, charge, and spin... another list, it would seem, and some of the same items. Wnt (talk) 00:24, 10 April 2018 (UTC)

Using logs would also give problems with Negative temperature. Well lets say more problems. ;-) Dmcq (talk) 11:17, 7 April 2018 (UTC)

God and the Big Bang

Please do not entertain this. Per the top of the page: "We don't answer requests for opinions, predictions or debate." TigraanClick here to contact me 11:58, 9 April 2018 (UTC)

Is the Big Bang proof that God exists? — Preceding unsigned comment added by Cookiemonster2018 (talk • contribs) 20:07, 6 April 2018 (UTC) Atheists would say no. Some theists and deists would say yes, others would say no. Ian.thomson (talk) 20:18, 6 April 2018 (UTC) First, define what "God" is. If you say, "God is the force that triggered the Big Bang" then the answer is "Yes". But it's a circular definition. ←Baseball Bugs What's up, Doc? carrots→ 20:43, 6 April 2018 (UTC) The big bang concept indicates that the Universe has a beginning, and was not eternally pre-existing. If the Universe always existed it would be incompatible with it being "created" by God. So a "big bang" start rules out that objection. Graeme Bartlett (talk) 00:14, 7 April 2018 (UTC) Anyone interested in this topic should read our article, Big Bang. There's some fascinating stuff there about what is required and entailed by Big Bang theory, as well as some commentary on religious perspectives. Of note, the idea was first conjectured by a Catholic priest. SemanticMantis (talk) 00:44, 7 April 2018 (UTC) In 1996, Jewish scholar and kabbalist Daniel C. Matt wrote a book called God & The Big Bang: Discovering Harmony Between Science and Spirituality. I attended a speech by Matt at that time and read the book, which I recommend to anyone interested in this topic. Cullen328 Let's discuss it 00:58, 7 April 2018 (UTC) No, it is not proof for or against in of itself. One cannot prove that it was or was not set in motion at the behest of a benevolent being, one can only prove that it definatively occured. In the same way as one cannot prove that the butterfly-effect which caused an exceptionally cold winter that contributed heavily to Napoleon's failure to conquer Russia, as being set in motion by God to preserve the present day geopolitical balance. Plasmic Physics (talk) 11:51, 7 April 2018 (UTC) It depends on how "God" is defined. ←Baseball Bugs What's up, Doc? carrots→ 15:17, 7 April 2018 (UTC) How can we mere mortals "define" God? Some things are beyond comprehension. 92.19.170.76 (talk) 16:30, 7 April 2018 (UTC) Bingo. ←Baseball Bugs What's up, Doc? carrots→ 17:41, 7 April 2018 (UTC) Not that it's really within the scope of the OP's question, but we can't give a comprehensive definition as we don't have a complete reference. However, we can derive an estimation from the core religious texts. This would make a definition at least partly subjective, because not all limitations, abilities, and capacities, etc. are explicitly stated and must be infered. Plasmic Physics (talk) 21:36, 7 April 2018 (UTC) Well, some things are beyond comprehension, but we should not retreat that fast. See god of the gaps. Of course, there is no way ever to disprove a truly omnipotent being, but we can determine if one is needed for explaining reality - and so far, the answer seems to be "no". Also, my suspicion is that historically "onmipotent" is a euphemism for "stronger than your Baal, or Astarte, nyah nyah nyah nyah nyah nyah...". --Stephan Schulz (talk) 10:26, 8 April 2018 (UTC) Technically, omnipotent doesn't mean most powerful, but instead having the power to do anything. In the sense as applied to God, 'anything' is limited by logic and reason, since God is said to be unable to sin, and it is is paradoxical nonsense for Him to create a boulder more heavy for Him to lift. Plasmic Physics (talk) 09:06, 9 April 2018 (UTC) Technically, omnipotent means "all powerful", and there's no reason to imagine that an all-powerful entity would be limited by anything, including logic and reason. ←Baseball Bugs What's up, Doc? carrots→ 12:00, 9 April 2018 (UTC) Indeed. Plasmic Physics (talk) 21:36, 7 April 2018 (UTC) This discussion is full of a lot of what seem like naive assumptions to me, such as that causality proceeds from past to future or that God creates a universe "at the beginning". The Copenhagen interpretation may appear to suggest, for example, that when the first person looked up at the stars (or otherwise "measured" them in his existence), their state was previously unobserved, so only then did they collapse to have specific positions. If God, then, is involved in the process that makes a person a person, God's influence in some fairly recent year of geologic time could determine the entire pre-history of the universe retroactively, regardless of whether it is closed or open; indeed, could actually determine whether it had a beginning Bang or not. Indeed, it seems conceivable that somehow only some supra-human phenomenon in the future is capable of putting things into a precise state, and that the state-vectors in current experiments collapse only because they become known to us and we only exist insofar as we will become known to ... whatever that turns out to be. Wnt (talk) 01:36, 9 April 2018 (UTC) I don't subscribe to the CI as it doesn't stand up to scrutiny. Bohr and Heisenberg must have forgotten about particle-wave duality when they came up with it. Since PWD is an established fact, no sytem is isolatable from its environment. Hence, any real system is under constant 'observation' by its environment. i.e. There must be some kind of correlation between the measure of environmental interaction and probability of wave function collapse. Frankly, I'm surprised to know that the correlation remains unidentified to date. Plasmic Physics (talk) 09:06, 9 April 2018 (UTC) The nature of the universe does not change. What changes is our understanding of it. ←Baseball Bugs What's up, Doc? carrots→ 12:01, 9 April 2018 (UTC)

Delivery of major uk government infrastructure projects.

Why is uk government now opening up the delivery of major infrastructure projects to private companies other than the infrastructure authority? Would the infrastructure authority still need to approve certain things during the project? 82.132.217.127 (talk) 21:44, 6 April 2018 (UTC)

Have a look at Public versus private: How to pick the best infrastructure finance option (Nov 2017) from the Institute for Government. Alansplodge (talk) 09:23, 8 April 2018 (UTC)