joigus

I would like to create a little room here for the wonderfully unexpected, beautiful,... (add your adjective) in Nature. Unexpected and/or beautiful could be interpreted as curious/spectacular, or similar. I mean to use these examples in order to keep the kids interested in Nature. The youngest ones get bored very easily. Examples could be: a rare animal, plant or protist, an almost unbelievably beautiful geological phenomenon, an amazingly complicated molecule that looks like a tinker-toy assembly, spectacular phenomena in water eddies and such. You get the idea. My getting-started examples: Glasswinged butterfly A family of butterflies that eat poisonous leaves when they're caterpillars and grow transparent wings. https://en.wikipedia.org/wiki/Greta_oto Rainbow Eucalyptus tree A species of tree that looks as if somebody had Photoshop-painted them. https://en.wikipedia.org/wiki/Eucalyptus_deglupta Maths are also welcome. Things that look paradoxical like 0.9999999... = 1 would be the idea. I'm sure people will enrich this with possibilities I'm not foreseeing.

Totally. +1

Touché.

Sanity is a mental condition. A platitude is an unnecessary (on account of being too obvious to be useful) statement. You really seem to have no clue, neither about what Eise is saying, nor about what you're saying yourself. Your sentences really are a challenge as to how many inconsistencies you can fit into them per word.

I agree with the nuance. In my case, it wasn't meant as an insult, by I understand how it might be construed as such. Words matter.

I'm glad you're back. Very interesting comments. It seems that the best scientists in history, the ones who guided the major breakthroughs, were people at crossroads between conservatism and revolution, between the practical and the abstract. I'm thinking of Kepler too. In his case, driven all his life by the desire to confirm Plato's ideas (conservative drive), but anchored to the experimental facts, which in that case embodied the change in paradigm. Anyway. Welcome back. I hope you're ready to roll.

Good point. +1 Well, from what I'm told there is descriptive linguistics and prescriptive linguistics. Prescriptive linguistics I think should be something like a set of recommendations with different degrees of emphasis on how much of a good expression a given one is if you want to sound like a well-read person, remove ambiguity, and so on. But some people go completely berserk with norms. I think we all know who we're talking about. The split-infinitive, hanging preposition, dangling participle crew.

I think you have a point that the OP's confusion comes from different defining conditions. I hadn't seen that. Evaporation would take place on the surface. Boiling would correspond to the situation when the water is heated (frequently it's from below). But evaporation, as generally understood, doesn't have to be an equilibrium situation: https://www.britannica.com/science/evaporation https://en.wikipedia.org/wiki/Evaporation The equilibrium situation (in my understanding) would correspond to equal amounts of molecules leaving the water than coming back. You need a closed container in general to get to that point. That's called evaporative equilibrium. But I suspect we call things differently. In order not to make the discussion more confusing, I would propose to try to sketch the two different scenarios that I think are mixed here and @studiot has suggested, by way of example: 1) A lake struck by a very hot Sun (mostly surface evaporation) 2) A cooking pot with water in it, taken to boiling point (bubbling more dominant and therefore more molecules escaping from within) And I would try to highlight the differences from there as clearly as possible, avoiding too fine points about equilibrium, stationary character, differences between kinetics and thermodynamics, etc. And would like to agree with @Daniel Waxman and share my part of the blame that we may have turned this discussion into something rather more obscure than need be. My experience tells me that insisting in what may only be terminological nuances can only bring more confusion.

Question: Do molecules below the surface of the liquid evaporate? Your answer: Water molecules below the water level can become gaseous. That explains the bubbling of water vapor through the surface of boiling water. I don't think that explains it, nor does it answer the OP question. Starting with: There is no such a thing as a "gaseous molecule". Bubbles are small domains of gaseous phase that form locally due to fluctuations (little variations of under-density, excess temperature, or both) which, by virtue of their lower density, and helped by convection, make it to the surface and are released, being much easier for them to break the surface tension than individual molecules. Any phase transition is governed by the formation of small subdomains of the final state. These subdomains appear and disappear constantly, but as the temperature approaches the boiling point or goes past it, they become more frequent, grow bigger, and last longer, thereby having more time to reach the surface and get released.

The square root of a complex number is more easily obtained in terms of absolute value and argument. Because number i (the imaginary unit) is 190º, and the square root of a complex number is: z=rtheta z1/2=r1/2theta/2 You would have i1/2=145º I hope that helps.

Maybe phosphorescence might be a useful alternative? Although phosphorescent molecules are considerably heavier than water molecules. It would change the time/energy scale of the problem. And they should be soluble in water at the given temperature. Agreed.

Here's a perhaps more intuitive way to explain why electricity cannot act as a substitute for gravity:

Which EM interaction would do that? Photons? Magnetostatics? Electrostatics? EM always vanishes at even moderately large distances. The picture of a supermassive black hole's interior as a nice habitable place has sent shivers down my spine. And your suggestion of sending physicists past the event horizon has reminded me of this line by Scottish comedian Danny Bhoy: "They say crocodiles can be faster than horses. I don't know how many horses it took to find that out."

So you're serious. (Just checking.)

Proving to whom?

Are you serious?

In other words, your theory must be falsifiable.

Just because you're a mechanical engineer it doesn't mean that you can't come up with an good idea. Actually, being an engineer you're in a better position to do so than many amateurs. But if you want to push your idea any further, you should be your first critic. Try to find things that could be wrong. Is energy conserved for a particle falling through the horizon? And angular momentum? Mmmm... really? Energy is not conserved in GR in the usual way. But for small test particles moving in a metric it must be. Can I make the fundamental invariant (proper time) go through the horizon continuously? Actually, the more there is of value in your idea, the more worth it it is to put it to the test for consistency. It's the best way to find possible modifications that might be needed. Or saving lots of time invested in an idea that's not worth pursuing. Saying that continuity, differentiability and injective character are essential in microphysics is no understatement. Discontinuities only appear in physics in the thermodynamic limit (phase transitions). Take some time to learn about the Lagrangian and Hamiltonian formalisms, and then Poisson brackets. They may look like gratuitous sophistication to some people, but they are very important in theoretical physics, and illuminate very important relationships. And then go through some primer on QFT. Enough to be going on with. The deep connection between symmetries and conservation laws, discrete symmetries, how they are different from continuous symmetries... And, above all:

You're right, that's what the OP said. But I think that's the wrong intuition about this problem. Internal molecular motions do not contribute significantly. I think it's mainly the CoM motion. Maybe they would contribute to the formation of bubbles... Or cavitation, as John said. I don't know. It's certainly conceivable. But I think even bubble formation would have more to do with collisions than internal oscillations.

etc. Ok. I don't know what the point about molecular vibration is in reference to the OP, but while I agree that molecules do vibrate whenever there is a temperature, these vibrations occur about the center of mass of the molecule and the way I see it that energy does not participate in the escape from the surface that evaporation implies. Well above the non-quantum range of temperatures (kBT>>hw) molecules have on average (1/2)kBT of energy per degree of freedom. For a molecule that has n internal DOF of oscillation, (n/2)kBT would go to excite it internally as an oscillator, but the remaining (3/2)kBT would go to increase the center of mass energy. Does that make sense? I must agree. +1

You couldn't be rightest. +1. Thank you.

Phonemes... Interesting. The Khoisan languages have most than any other family in the world. And Hawaiian, the least. The pattern of decreasing number of phonemes as you go West is thought to have to do with the spread of humanity. As a further curiosity, some Brahmin chants from Kerala seem to have many words with no known meaning, some people claim, which are repeated faithfully generation after generation. They've been compared to bird songs. Are those soothing words, conjuring words, trance-inducing words? Or no words at all? https://talkthetalkpodcast.com/110-brahmin-chant/ http://www.pbs.org/thestoryofindia/ask/answers_2.html#q3

Or a thank you present & letter. I'm sure some fish bully became history after that.

I mean loners, solitary BHs that have been ejected by the centrifugal potential barriers. There are bound to be many objects like that in the universe. Not only BHs. For those unfortunate wanderers, there is no accretion. Only a future of perpetual evaporation (if Hawking is right). OK. So I'm counting your answer as maybe there is, maybe there isn't. We know it must be anti-unitary because it's a consistency requirement both of quantum mechanics and quantum field theory. QM: The transition from state 1 to state 2 has an amplitude that is complex. Reversing time implies going from state 2 to 1 instead of 1 to 2, which requires complex conjugation. Proof in QFT (I will just reproduce the formulas that you can't see in the video below, by Sidney Coleman, the images are awful-quality): \[q\left(-t\right)=U_{T}^{\dagger}q\left(t\right)U_{T}\] \[p\left(-t\right)=U_{T}^{\dagger}p\left(t\right)U_{T}=-p\left(t\right)\] \[\left[q\left(0\right),p\left(0\right)\right]=i\] \[U_{T}^{\dagger}\left[q\left(0\right),p\left(0\right)\right]U_{T}=i\] \[\left[U_{T}^{\dagger}q\left(0\right)U_{T},U_{T}^{\dagger}p\left(0\right)U_{T}\right]=i\] \[\left[q\left(t\right),-p\left(t\right)\right]=i\] \[\left[q\left(t\right),p\left(t\right)\right]=-i\] Contradiction with canonical commutation rules. The intuitive argument that I've given you for QM is perhaps even more illuminating. Sidney Coleman, Lectures on QFT (Harvard). Lecture 7; 2' 02''-11' 57'': https://youtu.be/Y4W5qGbW-xg?list=PLhsb6tmzSpiwrZuDMyweABm7FShZu3YUv Version in PDF: http://fafnir.phyast.pitt.edu/py3765/Coleman-QFT.pdf (there are two paradoxes if you define time inversion as a unitary operator; the other one is for the Hamiltonian) Conclusion => Time inversion in QM or QFT must be implemented by an anti-unitary operator. Otherwise, you run into inconsistencies. I don't know what you've read into Weinberg, but it's either he or you wrong. I'm guessing you. Wrong again!! When you deal with a tiny particle in the presence of a black hole, you can write its Lagrangian and study its motion in the background geometry of the big object. How do you think one calculates the motion of Mercury and the anomalous precession of its perihelion? One completely ignores the distortion that Mercury itself produces. In that case, the proper time of the particle is a parameter to describe a geodesic in the background geometry. The proper time of the particles you're talking about is the parameter of a curve. Never mind that it's a "dimension". You really must study GR!!! I can give you another link for curves of particles in GR if you want. You really must study analytical mechanics and some classical field theory. Forget GR for now. You need lots of basic formalism. Energy conservation comes from Lagrangians through Noether's theorem when the action is invariant except for a total derivative (divergence in several dimensions). There is no conservation for the absolute value of the energy. If there were, I would be interested to know where it comes from. I really recommend you a primer in classical field theory. Lectures 1-5 from Sidney Coleman's course Physics 253a that I've linked are an excellent, if quick, one.

Very good and simple question. +1