joigus

OK. It took me a while to realize what you were trying to do (plus I've been busy.) I was missing some words and/or some data in the statement of your problem. I should have noticed that there must be a reason that you were given the volumes. For some reason I thought you were given the concentrations at equilibrium. It was a neutralization of two solutions with hydrolysis of the salt with initial concentrations and volumes specified, and you were given the k_a of the weak acid, right? I didn't know that. It seems you've solved it. I haven't checked the numbers in the quadratic eq. for the moles in equilibrium, but the method is correct. Plus it should give you a pH slightly above 7, so everything checks AFAICT.

Why? Something wrong with the logarithm? I may be getting this totally wrong, but what's the problem with [acid]=[base] and Henderson-Hasselbach? Most people are concerned with the murder of George Floyd now, which is only fair. So it seems that you're stuck with me, the chemical idiot of the lot. So, what's wrong with it?

Why? Something wrong with the logarithm? I may be missing something. Please, wait for the experts, I'm not one. In the meantime, maybe we both get lucky and you can find the key to your problem with my help, by discussing the basic concepts. If not, I'm sorry if I lead you into more confusion. I'm answering this because nobody else is reacting to your post so far and you seem to be in a bit of a hurry. Good luck! I meant "titration."

OK. I'm a bit hazy on this right now. But I think the key words you're looking for are Henderson-Hasselbach. Try to work it out, and if I'm not helping, maybe someone can provide better help. You must picture the tritation curve in your mind. It's what biologists call a sigmoid curve.

Yes, that's right. Time reversal in the equations of motion for a falling object just make it look like an escaping object by reversing the initial conditions for velocity. While the force term remains the same. Everything? I also think an invitation proffered to Leonard Susskind to the forum to give him a chance to actually say what he would actually say is in order.

What's the pka of propionic acid? You must know how weak it is, right?

Well, white is a charge. It's what in QCD plays the role of zero charge in electrodynamics. The complication with QCD, if you wish, is that there are more ways to obtain zero charge: red-antired, green-antigreen, blue-antiblue, red-green-blue, antired-antigreen-antiblue, and more complicated but higher order combinations. As Swansont said, color-anticolor are mesons (lighter particles that decay very quickly,) and RGB things are baryons (heavier particles like proton and neutron, some stable, some ephemeral.) OK. Let's call anti-something by crossing them out. Like G would be anti-green. You could hit a nucleus with something hard, like an energetic proton, or a meson, and kick off some GBR piece from it. But it wouldn't last long in that colored state. What remains in the nucleus (because the nucleus is white) would be anti-GBR = RR. They would start pulling from each other like crazy, so you would generate a lot of energy in gluon lines going from one to the other trying to "equilibrate the color imbalance" let's say (I'm not being very precise,) up to the point that antiparticle pairs would appear "closing the lines," and turning the colored particles that escape into white particles again. I can't find a useful diagram for you to picture it. Maybe tomorrow. Or maybe someone can provide it. The whole thing is even more complicated, because these colors are quantum numbers, so they're not even determined. They're constantly rotating in a space with three references R, G, B, but never quite being pure R, G or B. It's sort of like a dynamical rotation in the color space. Again, very imprecise, but I'm trying to explain as best I can. Swansont is totally right. A single quark would have to choose one color. But then again there are no "single quarks." Quarks in nucleons (protons and neutrons) are constantly rotating their colors by exchanging gluons, which are exchanging their colors among them!!! QCD is totally crazily complicated. Highly non-linear, which means even the interaction particles interact with each other. How do they do it? with other gluons that also interact with each other... Only quarks I can think of that were flying about with single colors must have been those that were doing so when the universe had a temperature TQCD (a very very high temperature.) It's crazily, crazily complicated. I hope it's clear that QCD colors are nothing like the ordinary concept of color!!!

AAMOF, you're totally right. I was imprecise to the point of being incorrect with "mix." It was a really bad word choice. You can mix them, yes. Gravity cannot escape the quantum nature, of course. I should have said gravity cannot be formulated as a quantum theory. A 3-body problem in which one of them is a photon is very simple. Even though with high speeds you must be careful, the photon wouldn't be very difficult to deal with. It's a 2-body Newtonian problem (which has an exact solution) plus a photon moving about. You can totally ignore the effect of the photon on the planets (I suppose you're assuming astronomical objects) and you could get fine details about the effects of the planets on the photon, which would be very small anyway.

Don't be sorry. It's OK. Confined particles are always white, yes. Well, quarks are perpetually changing color, with their gluons. It's not that confined particles are always white, it's more that aggregates of colored particles are always combine to white, and if you want to kick off a colored particle, it splits into white combinations again by creating particle-antiparticle pairs. It's the charges that balance out (or cancel out,) not the energies. Energies of quarks and gluons add up to the mass of the proton, neutron, etc. Exactly. If a particle is at x, there's no reason for it not to be somewhere else some time later. Charge is different. If a particle is white, it keeps being white or decays into red-antired, e.g. But then the products of decay immediately turn white again (because of confinement.) But you cannot have a particle with 1 unit of red charge turn into 2 red charge one second later. There are more differences. So that's why I told you not to take the analogy too seriously. In fact, there's no analogy at all. "Color" is just a name for a type of charge. You're very welcome. There's no reason why you can't get a reasonable understanding of QCD by reading popular science books or even some excellent books with some mathematics.

The resultant gravity field is the sum of the fields in Newtonian gravity, both for force fields or for potentials (superposition principle for Newtonian gravity.) It's a good approximation if the fields are not very strong. "Very strong" means that the Newtonian potential divided by c2 is << 1. In GR it's much more complicated (strong fields.) But even in the Newtonian case the resultant gravity field doesn't really solve the problem of motion if the three masses are comparable, as you are in the 3-body problem, which can only be approached numerically or perturbatively (by calculating incremental approximations from a simple particular solutions.) The reason is that any of the three bodies interact with the other two, and the equations cannot be separated. I'm not sure I'm answering your question, I'm trying incremental approximations to your question. I hope it adds something significant. I forgot: Mixing quantum mechanics and gravity is not possible as of today. Some people (Beckenstein, Hawking) have successfully combined both to do calculations, but it doesn't generalize very easily at all. Plus gravity generally is negligible in the very small world.

There are three colors in quantum chromodynamics (QCD). Colors don't cancel each other out. They cancel RGB = colorless. Or RG = anti-B, GB = anti-R, BR = anti-G. All observed QCD particles are colorless. Don't take the analogy too seriously. Frequencies of light are a continuum, while QCD "colors" are discrete observables. To make it even more puzzling, you can't actually observe them directly, due to confinement. Plus there is no simple "anti-red" fotons, while there are anti-red gluons in some sense x, y, z are very different from color charge. Charges are internal (non-space time) and conserved. x, y, z are not conserved. You can't word physics and make sense of it with poetic phrases. Especially quantum physics. You need higher mathematics. And very sophisticated experiments on the other side. There's no way around it. E.g., energy is not "a point," it's an abstract quantity that we define when systems don't single out any particular time (are time-symmetric.) Experiments take care of checking that our definitions, deductions, and inductions are correct. I applaud your enthusiasm to try to understand it all, but it's more complicated, and subtle, but equally mysterious and wonderful, or even more, than you try to suggest. I hope I don't bother you or diminish your enthusiasm about physics. Physics is really wonderful and helps you understand a lot about the world around you. But it takes time, dedication... Imagination in straight jacket, as Feynman said. I didn't say anything about spin, because Strange covered that pretty well. I just added some more info about QCD.

@Eise Now I really understand what you meant when you said, Let me ask you something. You don't think the Libet experiment settles the question, which I quite agree with. So here's my question: Is there any way you can conceive of that could settle it? Experimentally, I mean. Because otherwise, my next question will be: How is all this we've been discussing here in any way different from a battle of words?

I will just ignore all your contents, provided you eventually manage to find any. It's more... economic. I have no time for deliberate, self-indulging, obscenely pointless, and painstakingly --if ridiculously unskillfully-- worded idiocy. There's plenty of room for narcissistic lunacy on the internet. What brings you to this place of discussion and honest communication of evidence, make no mistake, is no mystery to most people here. Most, from what I'm starting to learn, are quite used to reasoning things out, self-informing/correcting and respectfully informing/correcting each other. You're pretty obvious to everybody. It's like entering a room where you're the only one naked. Put your clothes on!

Yes, that's true. It's a theorem. You can't argue with a theorem.

Are you an insectist-sexist? A very good point. I forgot interrelations.

I disagree. If only for the reason that genomic libraries as so immensely valuable. They may have toolkits that we lack. The challenge is to keep them under control. I know it's a tall order, but it's a must. Knowledge is too precious.

Ok. Just one question, though. Can't that be obtained also from the fact that the Newtonian approximation always ties you to some g00 that to first order must have a Newtonian interpretation and thus the maximum aging (or maximum proper time) principle is already implied by it? IOW, isn't it a matter of what axiomatic approach you take? As not all fields are amenable to weak field approx., what you say does seem more general and preferable from an axiomatic POV... On the other hand, you can always do a Taylor series expansion and the first order is one plus the Newton potential, according to the historical approach.

I don't understand. I quoted directly from your post before your last one. Yes, sorry. "That" is this: I never said that the whole point of thermodynamics is to model what a box of gas is going to do. That's what I thought you were pointing at. But thermodynamics is certainly powerful and sometimes you can predict behaviours in processes, define and measure coefficients, etc. Nevertheless, sometimes when I start reading through the forum I'm a bit tired and there's a danger for me to misinterpret. And I don't see criticism --of ideas-- as a bad thing. And as to the 'salt and pepper' I'm afraid I did it again. Now I understand what you meant, and that would be a good analogy for the runes IMO. You --unwillingly, of course-- had me looking for 'salt-and-pepper' idiom definitions at some point. LOL Here. That's what I said. Any comments, further qualifications or criticism welcome.

I've been thinking for like half a minute whether there could be any other reason than the Newtonian limit, but I can't find any other one.

What colour are Rube pills? How many do you take a day to feel this "good"?

The r12 convention tends to confuse me. I'd go with applying twice the right-hand rule. One for field/source and a second one for Lorentz force law: \[\boldsymbol{B}_{1}\sim\boldsymbol{\nabla}\times\boldsymbol{j}_{2}\] \[\boldsymbol{F}_{1}\sim\boldsymbol{j}_{1}\times\boldsymbol{B}_{1}\] The force on j1 is towards j2. Resp. for 2 <-> 1 I assume with Ghideon that there aren't, e.g. power sources that invert the current along AC or CG along either wire. Neither do I see how this is a speculation.

I never said that. Thermodynamics is about much more than that, of course. There are reversible processes, irreversible ones, and different interesting coefficients we've talked about before. But a gas is a good example to start talking about to illustrate its power and generality. I must confess, @studiot, that I wasn't following your arguments in this particular post as closely as I follow them in other posts, as I was following the OP's. And that's because the OP was rather lengthy already. I haven't been even able to follow all the details about the runes and the states based on them either --maybe lack of time and tiredness among other things. I thought I understood more or less what the OP was trying to do and tried to warn them as to what I called the "subtle misconceptions" in their approach. I thought it was an honest attempt at understanding the subtle concepts underlying the formalism. Any of your 'salt and pepper' explanations are welcome on my part. And even the ginger and lemon tea ones.

Nothing is pre-nothing here. It's gone full circle a few times already. But please keep going. I'm planning on getting myself a really good GR monograph by copying and pasting Markus' detailed explanations.

Exactly! Have you heard of Boltzmann brains? Well, I haven't shown you that your idea is wrong. I haven't shown you much, AAMOF. I've argued to you, I think, it's not plausible if you take it seriously to make a model of what a gas in a box is going to actually do. I've argued from general concepts derived from what I know. But there are qualifications to be made in cosmology. I would have to think about them deep and hard, or maybe have some expert in cosmology tell us what they think. The universe is not a boring place most of the time we are given to watch it because, in the case of the Earth, it's governed by fluxes of energy, coming in, and going out. Open systems like those are not Poincaré recurrences. They are the kind of systems that can hold something like life. There are very interesting models of systems which undergo self-organization under those conditions. But the universe is not like a closed box which thermalizes after some time. And I don't think the universe as a whole satisfies Poincaré recurrences. That's what I meant when I said, So if you don't like a universe that will thermally die, who knows, maybe that's not gonna happen and you (or some version of you in some far far away future or in some far far away cluster of the multiverse, is having that expectation fulfilled. Does that help? Maybe the universe repeats itself geometrically, by some periodicity condition. There may be many possibilities. They're going on. For example, some of the molecules I'm breathing now will be gasped by the last breathing creature that will live on Earth, and others were inhaled by the 1st breathing creature that lived on Earth. But I'm none the wiser. Yet, if the temperature goes up one degree, I will notice. Nice conversation.

Read it and liked it very much and +1-ed you accordingly. It's a very good illustration that concepts based on emergent quantities appear to point at agents that do not really exist. Got you! Causal relationships don't have to be between two different events. When emergence is involved, they typically are be between 1024 (micro)events and one event. Really? Why? Irrespective of your answer, that I'm pretty sure is going to be very interesting, you cannot ignore the social factor. Namely: that the way in which most people use the concept of free will is to justify other secondary concepts like "guilt," "punishment," and the like. Some among this hosts of derived concepts, like "responsibility," may be useful and constructive, but many are definitely not. As I said, I couldn't agree more on this. And the last point was brilliant. +1