joigus

This is not a conceptual problem for quantum mechanics. Then you just dissolve into vagueness: "it would be like", "a certain behavior", "would be like" three or four more times, "more or less energy" etc. Too vague to even make sense. And no, particles cannot exceed the speed of light, not even "in some cases." So-called virtual particles --if that's what you're refering to--, are not actual particles, they are modes of the quantum field that cannot be measured but must be included in the calculations.

It would be, not only presumptuous, but plain stupid for me to disagree with you. I'm keenly aware of this, yes. And I was for a while thinking about making due qualifications --retroviruses, that you mention, for which RNA goes to DNA, and prions, which I implied without mentioning them, and have to do more with folding or packaging of proteins of "chaperoning" as I understand. That's why I chose the prions as an (admittedly extreme) example of how the doings of the proteins more heavily determine what the brain ultimately looks like, does or doesn't do than the other way around. I introduced that example precisely because the OP was about the brain in particular. Francis Crick famously regretted having called this DNA-to-RNA-to-protein predominant flow of information a "dogma". Dogma is something accepted without question, while paradigm is just a typical example of a pattern. It is unfortunate that so many people use the word "paradigm" more pompously than it deserves, IMO. A paradigm is just a typical example of something. But you're totally right, of course. It's more complicated that that, with lots of feedback going on from the organ level to the molecular level, and back.

I was thinking the same thing: WTH are Calabi-Yau manifolds doing here? A picture is a picture is a picture...

You've had excellent responses already. You seem to be looking for a video though. Here's one just as a sample: Of course, as they've told you, it's not about the brain monitoring the process, but about regulatory sequences being activated/silenced, etc depending on the signaling going on. In order to understand all of this, you need to have a grasp of the paradigm of molecular biology: replication --> transcription --> translation from DNA to protein, which is almost always the case in bio. As an extreme case of the complete opposite happening (proteins acquired somewhere else determining the brain's behaviour), bad protein packaging can give you a brain going horribly wrong. Those are called spongiform encephalopathies.

Obviously. grav force/strong force is a dimensionless number, and represents a natural scale in Nature. Newtons OTOH are just some convenient units useful on the Earth for weighing bricks and such. My own favourite unit of force is the Jocular, and one Jocular is equal to 1020 N. Your coincidence has just vanished when expressed in Joculars. I concur with the other objections expressed, btw.

Good tip too. Thanks for the recommendations and welcome back.

Sorry you see it as though I wasn't trying to help. I was. I thought it was more urgent that you learn to handle dimensions than it was for you to handle vector addition. As an old professor of mine said, 'If you want to be able to write Chinese poetry, your first goal should be to be able to write Chinese'. I wish you best of luck with your Chinese poetry.

You said, This is not dimensionally consistent. All physical equalities must be dimensionally consistent. It can happen though that when a dimensional quantity is a universal constant, you can choose it to be one, and there is a dimensional reduction. AFAIK, the centimeter is not a universal constant.

How come you multiply force times distance to get a force? The result would have to be a work, energy, torque... (Never mind the mixed units, as you should convert cm to m.) This should be homework, right?

I sometimes wonder why people can't sense the imminent possibility that someone special is risking all their money on a Ponzi scheme. Nearly as life-threatening as bullets, when you think about it.

Sorry. I was editing and it came out by mistake. I'm working on a proper answer. Ok. Here's my answer. As @StringJunky said. You need enzymes, if you want to digest anything. If you have molecules that constitute cellular walls it makes a lot of sense that they be stable under a wide range of conditions. Eukaryotes use phospholipids as cellular walls, with the phosphoric group pointing out, and the fatty acid pointing in. I think there are good evolutionary reasons why no eukaryot would 'want' to evolve an enzyme that digests cellular membrane, as it is shared by all eukaryotes in the form of a double layer, like this: It would be like a suicide mechanism for all eukaryotes. Why do it? It's not because nature can't do it. Nature can, if it sets its non-mind to it. Think about N2. A sturdy molecule if there is one. Yet organisms have developed enzymes to break it. But why break down something that's the first chemical step to make you?

I don't think Gen Z people today can imagine what it was like. Daily life went on like none of that was happening though. Our parents and grandparents had seen much much worse.

Maybe. Or maybe just a tad less compelling. The Cold War was a crazy, crazy time. But I think that just substitutes the D in MAD for some sort of different acronym, like UD (unacceptable damage)?

I think nuclear power is a deterrent, not an actual tit-for-tat mechanism. This, I think, was well understood by the '60s by the likes of Robert McNamara and others. The MAD principle guarantees that. The actual tit-for-tat takes place on a whole different level once the MAD is guaranteed. It creates a fulcrum for other forces to operate, that's all. BTW, I also think "political scientist" is a contradiction in terms.

Very well explained here: https://en.wikipedia.org/wiki/Innumeracy_(book)

The more I think about superdeterminism, the more I think it's possible and, as Hanke said, untestable. Is it possible that back in a remote past of a preinflationary period lies the key to every happenstance in the universe? It's possible. It's a matter of plausibility perhaps. Occam's razor is sharp indeed. One should be, shouldn't one?

Aaah. I'm a stickler for precise terms. As if that was the problem with the present crossroads we're in. It's probably not. Revealed does have a religious sound to it though...

Ok. For the record, I think you're right that Genady's metric just describes flat spacetime, and that this argument that I'm giving is really clutching at straws. I was exposed to Schwarz's/Clairaut/Young theorem in the past and I remembered that if a function is not C2 (never mind the only non-continuous derivatives being the diagonal ones) the conditions of the theorem are no longer satisfied and it could happen that some devilish argument gives you a contradiction. I just don't know. Thereby my question "are you sure?" which I should have formulated more clearly. My intuition tells me that fxy and fyx could give you problems, but fxx and fxx is the same thing no matter what the continuity status is, because x is the same thing as x, as you rightly imply. Another part that makes me think that you're right even from the POV of a rigorous proof is that the distributions involved are Heaviside's, the delta, and its derivative. And those are extraordinarily well-behaved as long as you never integrate them against functions that don't fall to zero fast enough at infinity. All functions we use in physics fall to zero pretty fast, so no problem there. As to your question for me, if by "pathological" you mean "not continuous", it's not possible to have a composition of two functions, one continuous, and the other not, that gives you a continuous function. So my answer would be no. What does happen sometimes is that, trying to solve EFE, we get bad coordinate systems, and we must use singular coordinate transformations that mend the "singularities" that were never there in the first place. I do know that that's what happens with the Kruskal-Szekeres coordinates. After all, the composition of two singular transformations can restore continuity, exactly as 1/u (singular at u=0) with u=1/x (singular at x=0) becomes just x (continuous everywhere). It indeed is.

Oh, believe me, I did. One would think it's you who doesn't want to grasp the logic behind mine: Are you sure? Symmetry of partial derivatives is a consequence of continuity: https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives#Schwarz's_theorem Somewhere on the back of my mind I was trying to remember an argument that validates it. It might be something like this: https://en.wikipedia.org/wiki/Symmetry_of_second_derivatives#Distribution_theory_formulation But this is becoming farther and farther away from the OP with every post --and less and less interesting for everybody else, I suspect. Mm... Yes, you're right. Genady actually said it (if I understood correctly). That, as \( G_{\mu\nu}=8\pi G T_{\mu \nu} \), any \( G_{\mu \nu} \) obtained from the metric connection by means of the \( g_{\mu\nu} \) you give yourself can be used as the \( T_{\mu \nu} \) just after dividing by \( 8 \pi G \).

I hereby propose Godwin's second law. Namely:

Yes, it's flat space-time, almost everywhere. It seems obvious, doesn't it? A simple re-scaling of the variables takes you back to Minkowski. When I said "are you sure?" I meant that all the derivatives cancel. That there is total continuity. That "there is no problem", as you implied. This requires a calculation, and perhaps a little thought too. I'm getting, \[ g''_{zz}\left(z\right)=2H\left(z\right)+2z\delta\left(z\right)+12z²H\left(-z\right)-12z³\delta\left(-z\right) \] This is discontinuous because of the step function, not because of the delta terms, which have damping factors as I mentioned before. I had to do the calculation to actually see the step discontinuity. Has this discontinuity come from a sloppy parametrisation of empty space, or does it correspond to a weird distribution of matter at z=0? That's another question. I mention all this because, eg, a cone is flat space everywhere, except at a point where it has infinite curvature. That's why you must be careful and look at the topology, global properties, and so on. It seemed to me you were just blissfully saying it was flat space because a purely formal re-scaling does it. Does Genady's example answer Marcus' question then?

When you construct the Riemann tensor, second derivatives of the metric coefficients are involved, as you well know. As you didn't address my question (only half of it), I'll repeat: Those are certainly involved in the calculation of the Riemann tensor, aren't they?

No, it's ok. It was just me splitting hairs, as usual.

Are you sure? What is H'(z) and H''(z)? You might be right, and I wrong. You might be wrong, and I right. Or we both right or wrong, and not know. In any case, it's interesting.

Tunneling is about one particle going through a barrier a few angstroms thick --I'm thinking Josephson junctions and the like. Star Trek stuff is about sending 1025 atoms many miles away, and these atoms remembering who you where and what exactly you were thinking on the other side. Quite a feat in comparison. For the dark side of teleportation you might want to consider The Fly. Either the 1986 film, or perhaps the classic, 1958.