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joigus

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Everything posted by joigus

  1. This is actually not very difficult to conceive in principle within the quantum formalism. Quite more difficult is to give a precise and detailed answer. As Eise has told you, a quantum particle, in some sense, sniffs around all of space time. When you see it in a mathematical formula printed on a paper, you see very clearly it doesn't look like the whim of a god. It does look like a precise mathematical pattern of evolution. Now, this evolution, in a quantum theory that includes special relativity, is very puzzling, among other things, in that it includes modes of propagation that are superluminal, subluminal, every which way. Those are called "virtual amplitudes", and they appear in the calculations, although they cannot be measured. They are called "off-shell". The basic reason for this is actually a peculiarity of relativistic kinematics. A real photon satisfies a condition or reality that has the form, \[k^{2}=0\] k is called 4-momentum, and codifies the direction in space-time in which the photon is moving. It's a combination of 4 numbers, the time component and the 3 spacial components: \[k^{2}=\left(k^{t}\right)^{2}-\left(k^{x}\right)^{2}-\left(k^{y}\right)^{2}-\left(k^{z}\right)^{2}\] So it could be negative, positive, or zero in general. Real photons are null. For real photons this quantity must be zero. But you can always decompose this "real" state as made up by the real components plus many other virtual ones, \[k^{2}=\left(k+p\right)^{2}\] These virtual ones have momentum ("direction") p, which is not physical, and in particular could be superluminal or subluminal: \[p^{2}>0\] \[p^{2}<0\] as long as they give you a real photon: \[0=k^{2}+p^{2}+2kp\] I haven't shown you the full-fledged argument in quantum field theory, which goes with amplitudes and so-called Dyson time-ordered formula, but a simplified version of it. It is by no means a foolproof explanation. But here's my question for you: Can you guarantee that the positions where the particle can or cannot land (the not-so-well-known partial reflection paradox is another interesting example) are not set in advance by all the components of the quantum state, including the virtual ones, that make up the Feynman propagation formula?
  2. Neither term would be precise in defining its properties. Dark matter is actually even weirder than transparent. Ordinary matter goes right through. It's not just transparent. Ghostly is more like it. Edit: But you're right that "transparent" is more suggestive of what it is. There's a tradition in the wording of physics. It's more like book-keeping than concept-suggesting.
  3. You're going a bit blurry here, in spite of my efforts to be concrete. Does philosophy make you uncomfortable? I sympathize (if not necessarily agree), but I can't do what you do. Philosophy always distracts me. +1. @Sensei is Boolean in nature.
  4. Your point is well taken. By "philosophies" (countable English noun) I mean each and every particular philosophical theory, irrespective of their merits, whatever criterion we use to measure those. By "philosophy" (uncountable English noun) I mean the activity itself, which more or less can be associated with the grouping together of all philosophical theories. The activity itself. I suppose you can do that without losing much specificity. It's true, e.g., that some people reject philosophy flat-out. Those would be the ones that subscribe to option 0. On the one hand, it's possible that they have considered each and every philosophical theory there is and reject them all but keep "hoping for the right one" (in that sense, they would reject all philosophies so far but wouldn't have given up yet on philosophy altogether). On the other hand, there's the possibility that these people, at some point, grow tired of looking for philosophical arguments and finally decide to give up on philosophy altogether. That goes to show that you're right in that a finer distinction could be made, so I admit that I'm simplifying a little bit. But I don't think that I'm overlooking any big demographics here by identifying all philosophies with philosophy in general. I'm subsuming people who don't like any philosophical theory at all into the group of people who just don't think philosophy should be paid much attention. Would it be good because it might be right or might it be right because it would be good? "Bad" or "good" are defined in a particular sense in the options for the poll. They are not described "for themselves". Good: useless/too arbitrary/self-serving... Bad: has something useful (interesting points to consider)
  5. I've missed that point. +1 I was so distracted with the equation itself, and then the OP completely changed the subject to gravity. It threw me off...
  6. I'm testing my first poll today. I've scanned for similar topics but wasn't able to find collocations "good philosophy" or "bad philosophy". Especially if your option is the third one, I'm very interested in your criteria, exceptions, and so on. Thank you very much.
  7. No can do. God may play dice, but that's too much of a stretch. Another brilliant logical point. +1
  8. So you were thinking about gravitational potentials from the get go, and you couldn't figure out that a plausible solution was k/x? Something doesn't add up here. This sounds a bit disingenuous... Is it gravity you want to talk about, instead of calculus?
  9. Thanks, @studiot. That was a pretty impressive informative answer. +1
  10. By inspection, y=0 is solution. Now, after a couple of tries, one gets the intuition that the solution is some kind of potential function, so let's try that out: \[y=kx^{p}\] then, \[y'=pkx^{p-1}\] \[y''=p\left(p-1\right)kx^{p-2}\] Substituting and finding condition for p and k: \[k^{2}p\left(p-1\right)x^{2p-2}=ak\left(2-p\right)x^{p-3}\] \[\Rightarrow p=-1\] \[2k^{2}=ak\Rightarrow\] \[k=0\] (the trivial solution we found by inspection) or: \[k=\frac{a}{2}\] with which, \[y=\frac{a}{2}x^{-1}\] Mind you, non-linear differential equations may have more families* of solutions. Check me for mistakes. * Typically, not families. Rather, isolated solutions. Edit 1: Please, ask me if you're interested in uniqueness.
  11. This is key, I think. There are several interpretations. They're not theories. The theory is quantum mechanics. You can bet that one is correct. Why it is correct being so mathematically ad hoc is another matter. That's where the different interpretations come up. IMO, the transactional interpretation is much more beautiful and parsimonious, although I must say I don't know it in detail. The one with empty amplitudes and occupied amplitudes is also more plausible IMO, even though it's somewhat ugly. The consistent histories approach is another one. As of today, I'm not aware that any of these have been finally confirmed or rejected experimentally or otherwise. There are claims in every which direction last time I looked, but I don't think there is unanimous thinking about that by any means. As we speak, more physicists are considering arguments about these interpretations, or maybe even other possible interpretations. Which means the problem is not settled. The elementary-particle-physicists' community favours the many-worlds interpretation, but that's all, as far as I understand. That's because their favourite toys (mainly the Wheeler-DeWitt eq.) are formulated within that framework. So it's a matter of heuristics and model-building, nothing else. And that's my two cents.
  12. Granite? Really? Would the granite parts be more eroded than the quartz veins? I've no idea really. I just want to learn more about rocks. And unfortunately I didn't have any geologist's kit with me.
  13. OK, then. Let me ask you a very technical question: What's with 2 and 3?
  14. The way I see it it was either Speculations or Nature.
  15. I've attached them here. The first one with the quartz-like veins was collected hereabouts: https://www.google.com/maps/@36.9992728,-7.89032,15357m/data=!3m1!1e3 And the obsidian/basalt looking one, hereabouts: https://www.google.com/maps/@37.9845133,-6.6169228,15156m/data=!3m1!1e3 I could be a little bit off in the second one. I do remember the terrain was ochre-red and the place was littered with many similar obsidian-looking rocks.
  16. Very interesting topic. (+1,+1) Thank you. If you don't mind, I will post a couple more pictures of rocks I collected in Spain and Portugal and be posting them here ASAP. One of them is very similar. Looks like a sedimentary rock that's been infiltrated by quartz. It's visibly more eroded in the "sedimentary body" and the "quartz" veins have resisted erosion much better, so it has some kind of ridges all around. The other looks to me like obsidian and rougher basalt arranged in layers, but I could be wrong. Is that possible?
  17. To my taste, those are very interesting philosophical-scientific questions I don't know the answer to. +1. I know it has been speculated that intelligence/conscience could be some kind of condition that's being seeded from a distant future or perhaps auxiliary dimensions. That we are simulations running on somebody else's computers. But, to me at least, that has the flavour of anthropocentrism again, of a Ptolemaic rather than Copernican perspective. I'm more of the opinion that conscience, whatever it is physically characterized by, is a condition that every once in a while in cosmic terms, appears in the universe. That we're not all that special even in respect to that. That there may even be other kinds of conscience than ours. So my line of thought is more along the lines of entanglement (correlated non-separability) and einselection (emergence of a special set of variables for that correlation) in quantum mechanics. For whatever reason, some physical systems become computers/register machines in relation to their environment. They "learn" to ignore the noise and develop handler variables for the environment as well as representation variables. Something like that. I hope it's clear and I hope it's not too out there. I think for something like conscience to evolve from a nebular chaos, it must have been universally inherent in all matter all along, and then something physical must be triggering it on over and over. And then I have suggested as a possibility that this 1+3 mapping of conscience may just be a characteristic of how conscience is formed rather that an inherent quality of the physical universe itself. But these are just speculations, admittedly. I don't know how we could do a gedanken experiment or more concrete hypothesis from that imprecise idea.
  18. I fully agree as far as I understand. That's why I said: "Have to do with" was not meant to imply causation, nor with a one-to-one mapping from ideas to patterns of neurons firing. The 1 is far too special. It shouldn't be there. But it is. But I tend to think that the 1 is in the mind and only in the mind.
  19. If you mean real gravitons, "free-flying gravitons" so to speak, that's out of the question. They should be what gravitational waves are made of, and GW are difficult enough to detect themselves. Let alone the quanta that (presumably) make them up. If you mean virtual gravitons, no virtual particle can be detected. They are un-physical or "off-shell" (they don't satisfy Einstein's mass-energy relation). For gravitons to be detected you would have to scatter them with massive particles* or other gravitons, and the cross section is so small, due to the smallness of the coupling at any reasonable energy that we wouldn't see anything. Besides, as Eise has pointed out, messenger particles, like photons, don't really have localization in the normal sense. This is a consequence of quantum field theory. In QFT, you cannot define a position operator. Because massive particles can move in a non-relativistic regime, you can approximately define position for them if they're in the non-relativistic regime. But photons and other gauge bosons cannot be considered as non-relativistic (except possibly the Z and W+, W- before they decay), so they cannot given position in any precise sense in QFT. *Actually, with anything that has energy.
  20. joigus

    Political Humor

    Good one! +1. True of all politicians. Only difference is who is more likely to get screwed.
  21. Most chemical reactions of interest take place at constant pressure. Irrespective of how general that assumption is, most chemistry books do consider P to be constant. If that's the case, even though partial pressures of the different components are changing: \[p_{i}=n_{i}\frac{RT}{V}\] because the moles are changing. And assuming the changes occur in quasi-static conditions, while every ni is changing, the total volume is not. Nor is the total pressure. So the total work is zero if the volume doesn't change. Maybe that has to do with what you mean by "the workflow that the gas performs to exist". Is that it? Are you picturing that the gas that's being formed does work in order to be formed? That's not the case if the volume is also constant. Mind you, there is no such a thing as "partial volumes". I hope that answers your question.
  22. I see. So it's a chemical reaction. Sorry. I should have read more carefully. I really don't understand this part of one of your sentences. I don't have a concept of "workflow that a gas performs to exist."
  23. I think you're confusing change in volume with change in amount of matter present in your system. Moles are a measure of the number of atomic participants in your system. Volume is very different. Please review your statement so that a proper answer can be given to what's troubling you. The system, such as you've defined it, is an open system (open to exchanges of both energy and matter).
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