joigus

Agreed. It doesn't have to be a sophisticated equation. The old quantum theory, eg, was a set of ideas with a crude mathematical formulation relating particle attributes like energy and momentum to wave-like properties like frequency and wavelength. Then came the Schrödinger equation, which is of course a more powerful version of these ideas. In physics and chemistry, at least, you can't even start to build anything without at least a crude mathematical statement.

Nice video explaining the whole thing:

I just use \[ (and the closing square brace) for centred (display) equations and \( (and its closing round brace) for inline maths. It seems to interact well with the MathJax "engine".

You mean, \[\int (f(x)+ dy/2)dx= \int f(x)dx+ \frac{1}{2}\int dydx\] \[ \frac{1}{2}\int dydx \] Yes you're right it looks like that, but it's not a double integral, as \( dy\left( x \right) = y'\left( x \right) dx \). But the whole point is OP mistakenly thought the second-order differential made a difference in the evaluation of the integral, while it doesn't.

\[\int (f(x)+ dy/2)dx= \int f(x)dx+ \frac{1}{2}\int dydx\] \[ \frac{1}{2}\int dydx \] Inline: \( dy\left( x \right) = y'\left( x \right) dx \).

Negative mass poses other problems: I'm not 100 % sure that you can't still play with these things in a speculative way by carefully distinguishing: 1) Active gravitational mass (as source of the gravitational field) 2) Passive gravitational mass (as reacting to a gravitational field) 3) Inertia And complicating the picture of how they interplay by introducing assumptions that extend the Bondi-Bonnor model. But negative mass is a completely different matter. Keep in mind that the Einstein relation between energy and momentum leaves you with, \[ E^{2} = \pm \sqrt{\boldsymbol{p}^2 + m^2 c^4 } \] Time orientation is on the plus minus determination of the square root, not on the sign of the mass.

Neutrinos hardly interact at all. As MigL said, how are they supposed to interact with macroscopic skyrmions? What's the mechanism? How do you focalise a beam of electron neutrinos so as to guarantee that they keep at a distance of a fraction of a nanometer from a lattice? Why should they invert their mass? And if they do, tachyonic quantum fields do not travel faster than light, and they do not have negative mass, but imaginary: https://en.wikipedia.org/wiki/Tachyonic_field (My emphasis.) I will also quote a sentence that I once heard Lenny Susskind: "Only crackpots think tachyons go faster than light"

Clarification: I meant that as per Holmes' claims; I did not mean that you were actually to blame. Sorry for being ambiguous. My distinct impression is that you always, at the very least, make constant efforts to support what you say on documents or arguments. Also, I tried to remind Holmes how their comments on L. Krauss are nothing short of a slur: "Krauss of all people?" "his shenanigans", and I quoted. Holmes is a bit enigmatic to me. I don't know where they're going. They've played a wildcard, and then dropped it, and then taken it again with a different value... I would like to know why. I'm kinda curious how one who's tasted the elixir of science can part ways with it and embrace the word that stands for anything. mess-posted with @iNow

Inspired by one of @beecee's previous posts: Here's a very interesting piece of interview in which Sagan explains my "semantic" point very eloquently, I think: I'll let Sagan do the talking and take a break from the conversation. Another thing. You've filed some ad-hominem-attack complaints here --If I'm not mistaken @iNow was to blame. iNow takes no prisoners, granted, but let's be fair...

I recommend you Susskind's Theoretical Minimum (Quantum Mechanics). You should have no problem following the main ideas and equations. Then his lectures on QFT to get an idea of what this renormalisation business is all about. I picture you as the ideal person for his approach: with a sound knowledge of physics but having fallen somewhat out of touch. The other lectures I provided are just to get a flavour of what the problems are. They're difficult for me too. I think the right way to tackle theoretical physics lectures is: I know I won't digest 100 % of this material. Let's see if I can understand the key ideas. And keep going. Things start clicking after a while. You probably know very well from your experience studying GR years ago. You can always forget about the equations for a while and concentrate on the words.

I think the question can be approached on a number of levels. For starters, quantum mechanics makes time a very special parameter. You need a distinguished time that goes hand in hand with a so-called Hamiltonian of the system (the energy operator). This Hamiltonian is also the mathematical operation that embodies time translation for the system. GR, on the contrary, has no special time. There is no preferred coordinate system in GR. If you have no special time, you have no special Hamiltonian, which means you have no special time-updating law for the state. So right from the start, the symmetries of GR don't bode well with the special needs of QM. This difficulty though, can be overcome AFAIK. One formalism that does it is the so-called Ashtekar variables, that allow you to include all the constraints of GR into a significant set of variables that are amenable to quantization. And they give you a Hamiltonian. But a lot of preliminary work is needed to get there. In any case, as @studiot suggests, the conceptual bases are quite different. Then there is the question of the perturbative structure of the theory, as @MigL pointed out. The theory is non-linear, has more field variables, and the loop calculations become intractable pretty soon. This, in and of itself, would not be catastrophic, as Yang-Mills fields (in the non-Abelian case, which is strong nuclear force) are also self-interacting and have a richer field-variable structure. But YM fields are far better-behaved than gravitation at short-distance (large-momenta) scales. The theory is free at short distances (large momenta), while gravity is just the opposite. Gravity, also, has no polarity and is thermodynamically exceptional. This bad large-momentum behaviour connects with what today is considered the ultimate reason why gravity is so unwieldy to a quantum treatment: the dimensions of the gravitational coupling constant. It is dimensionful (and badly so), as opposed to the dimensionless character of QED, QCD, and EW coupling constants. Renormalization crudely consists in decreeing a maximum momentum Λ for every scale that we wish to study, and then prove that the observables inferred from the quantum scattering amplitudes can be expanded as a sum of two parts, one that remains under control (finite), plus a logarithmically divergent one (scale independent). Now, you cannot do that with gravity. There are two technical ways to characterize this in words: 1) Gravity doesn't look like a scale-independent quantum field theory at large momenta 2) The large-energy spectrum of gravity is black-hole dominated Equivalence of both is discussed at: https://arxiv.org/pdf/0709.3555.pdf It's quite technical, in spite of the title, but enough words can be found there so that a crude idea of what goes on can be obtained. There is a last-ditch attempt in QFT to make quantum gravity renormalizable, and that's called asymptotic safety, initiated by Steven Weinberg, and it's based on hoping for a point in the phase space where this bad behaviour is saved by a so-called fixed point of the beta function (a function that monitors the renormalization behaviour when you shift the cutoff). But it takes a lot of guesswork and I don't know what the state of the art is at this point. Then comes supersymmetry. It's a big hope, because supersymmetry leads to much cancellation of infinities. New technologies have been developed in recent years, like calculations using the formalism of maximally-helicity-violating scattering amplitudes. It's a technology that involves massless gauge bosons, always leads to finite calculations, but is considerably more abstract, because it uses expansions of the amplitudes that cannot be understood as local quantities (at a point), and it involves twistors, which entails expanding space-time points into pairs of massless spin-1/2 wavefunctions (Weyl spinors). Two interesting lectures on the subject. The 1st one is more technical, but again, enough worded arguments are given so that one can get an idea of what goes on. Quantum gravity and its discontents (by Stanley Deser, 2010): Quantizing gravity and why it is difficult (Leonard Susskind, 2013):

No. I didn't talk about any theory of everything; I was talking about inflationary scenarios, which are falsifiable. Your explanation "god did it" is no explanation at all. I don't mind the term god, if explanatory mechanisms were provided. "God" is just a word. It doesn't bother me at all. You see? It's you who's interested in using god as a travesty for an explanation. I'm just calling you to task: Which god? How does this god operate? I don't need you to translate anything I say. It is intellectually dishonest to do so, and I would suggest you play by the rules. If you think my English is not up to par, ask me for clarification and I will oblige. You're playing semantic games because you're resting your whole case on an awe-inspiring traditional word that doesn't explain anything but is fraught with mystique. One is supposed to accept it only because of a cultural emotional baggage that we all share as a people. In fact, for centuries it has been forced on people. In a scientific theory, the whole structure would be completely the same even if you changed a key word by an arbitrary word. Example: "energy" by "mush": There is kinetic mush and potential mush. The sum of kinetic mush and potential mush is always conserved. Well, it is a bit strange that we call it "mush", but it doesn't affect at all the interrelations in the theory. On the contrary, take your first post on this thread and substitute "god" by "mush": Mush is that which brought the universe into existence, mush can be rationally inferred from that observation, it is a definition of mush. It is plain to see how ridiculous your thesis is. It doesn't prove anything, it's not falsifiable. In fact, it doesn't mean anything (much). I made no effort to rebut you because you made no argument. May I remind you that, is no argument. It's just your opinion. Translating my words to other words of your choice is also no argument.

I started out with similar books, although I wasn't fortunate enough to have such a big collection. I did use a general encyclopedia though. My getting-started science books were (translated to English) Tell me what it is, and Tell me how it works. There you could find many interesting facts and explanations, from will o' the wisps to rocket dynamics, or planetary motion. From there I went to Russell and Eistein. I prefer the internet, to be honest. The fact that you have to watch your step may actually be a good thing to develop your criteria.

"God did it" looks more like the blank sheet of paper that you've shown before, @Holmes. What god did it? Enki? Quetzalcoátl? How did he (or she, or it) do it? Why? You're playing semantic games. We now know something very much like the inflaton field explains structure formation in the universe. Why that happened and what this inflaton field is, etc is unknown. It explains planar large-scale structure, horizons problem, absence of monopoles... According to your "explanation", did god hate monopoles? The parametrics is by no means satisfactorily explained in the inflationary models. But, It must have had a very gentle slope and a very long time to evolve previous to the inflationary epoch. It must have had a very steep slope, dominated by friction, during the inflationary era. It must have bounced back in so-called re-heating. Those assumptions pretty damn well explain structure formation. Problem is, you need to assume parameters (those are the assumptions (axioms) that seem to bother you so much when they involve numbers and mathematical structure). Arguably, all physical theories are parametrizations in a context that we have very good reasons to believe is what physics looks like (a quantum field theory.) Did God like to play with scalar-field slopes? What's your explanation for planarity, horizon problem, and monopole absence? Answer: blank piece of paper. That's sarcasm.

There are many other possibilities for the emergence of "material quantities", whatever the definition of "material quantities" may be. You have not cared to define "material quantities" in any degree of precision. There may have been chaotic scenarios in which any clear-cut cause-and-effect sequence cannot be properly defined. There may be a limitless but finite causal structure for physical events, similar to the surface of a sphere, in which there is no point farther north of the north pole, while our intuitive grasp of reality demands to extend our framework of concepts "farther north". The example of hurricanes, that I proposed, was meant to illustrate that noticeable features may sometimes arise from a noisy background, without any particular macro or microscopic event serving as a valid cause of the whole thing. As to cosmology, current inflationary models do not suppose the pre-existence on any definite physical realm, although they use fundamental physical constants and, unfortunately, a number of free parameters. In those scenarios, there were just quantum fluctuations, which by their very definition are nothing like an atom, molecule or star; and there was also a simple mathematical function called the inflaton field. There wasn't even space time. That's part of the power of mathematical abstractions; they allow us to formulate less contingent scenarios than those you can conceive of with ordinary language. Even if at times they are somehow crude and leave something to be desired. Ordinary language is heavily constrained by the context in which it arose. Namely; to describe a world of rocks, and water, and fire, and plants, and animals. Concrete things. The very same things that --I can only surmise-- you perhaps mean by "material quantities". Quantum amplitudes, eg., just aren't material determinations in any sense that's familiar to us, evolved hunter-gatherers. They are beyond anything you, or I, or any human anywhere has a direct experience of. But the mathematics of them is clear, unambiguous, and useful --even though it's difficult to grasp--, and it leads to predictions about the material world --your material quantities, I suppose-- that has no parallel in anything philosophers and theologians may have concocted for centuries by sheer unassisted thought. Someone said that a philosopher is a person with a pen and a paper; while a scientist is a person with a pen, a paper, and a wastepaper basket. You really need a wastepaper basket for some of your ideas. I wasn't being facetious. I was dead serious when I said "I hope that helps". I still mean it. I hope that was clear. Is that any better?

Dear @Holmes, Previously you said that the universe must have an initial cause. How do you know the causal connections --whenever they occur-- do not respond to a pattern like a looping structure, with no beginning, and no end? About causeless things, an example: Hurricanes happen. But there is no way you can trace back the cause of the hurricane, or any significant cluster of causes. There just isn't a enunciable --let alone predictable-- series of events that caused it. I hope that helps.

I think this is clear based on the manifest whataboutism of the main argument. You see them as just creepy; I see them as an ancient lineage of animals that have been on this planet for hundreds of millions of years. So that's subjective. But in any case, how creepy something is should have no bearing on whether knowingly destroying it is justifiable. Phoenician tombs or Aztec monuments are creepy --they contain the rests of sacrificed people--, but they're invaluable; some people are creepy --e.g., people with bad hairpieces--, but they have the right to live, etc. As to the argument, I don't think this provides a solid basis for assessing whether an action is or is not justified or proportionate. It may be an argument for judging the degree of premeditation assuming the action has already been judged unethical, or unjustified, or disproportionate, or maybe just idle, on some other basis. It doesn't tell us anything about whether it's laudable or not. And pointing out that other actions are more culpable than the one we're defending doesn't make a good case. My personal opinion is that you should kill an animal only if it's a threat to your life, well being, etc. But maybe that's just me.

Duly noted.

"Nothing" is not a good semantic placeholder. Example: 1) Nothing is real (Nothingness is possible) 2) Nothing is real (no thing is real) (Completely different meanings) You have to mind your every step if you don't wanna fall into the use-mention fallacy. and other linguistic pitfalls. I didn't know this one. Even though I love American comedy. The nineties is my all-time favourite period. Especially: "This is the show, and we're not gonna change it." "Nothing happens on the show" --George Costanza

Thinking about nothing is good for nothing. Think nothing of it.

Dark energy is uniform by its very definition. The inverse square law is only valid for local clustering of energy-momentum, and it's an approximation. When you get close to sources of gravity, it's no longer valid. Example: Mercury's orbit around the Sun, for which the inverse-cube term's effects are sizeable at the time scale of centuries. No gravitational source that I know of has field exponentially-varying with distance. Systems dominated by gravity (all stars and black holes) are fundamentally out-of-equilibrium, due to negative heat capacities: They heat up when they lose energy into space, so they're thermally unstable. They don't "thermally die". The concept of heat death of the universe is a theoretical extrapolation that would apply to models of the universe other than the one we presently accept --and never to a standalone star, in any case. It doesn't apply to the present picture of the universe that emerges from cosmological observations AFAIK.

Australia plays in a different league when it comes to bugs. Most insects and arachnids won't harm you if you don't mess with them. I think it's gratuitously violent to kill animals just because it makes you feel more comfy. Take your picnic somewhere else is my advice. Similar reason why I oppose bullfighting, and hunting and fishing just for sport. We do enough damage as it is by destroying habitats at the rate we are. It's also a matter of growing up, IMO. Last time I killed a small animal at a place that's not in my home I was like ten. Stamping on an ant's nest would make me feel ridiculous today. The last time I stepped on a spider to feel manly in front of a girl I must have been something like that age too. But if I haven't convinced you, I suggest you extend your strategy to grizzly bears. Those can really disturb your picnic.

[sic] Here's how: Apparently you missed it the first time.

Please, get back in the box.

No. Counterexample: The Kardashians