joigus

As to Ashtekar, Plebanski. It kind of boils down to successive changes of variables to get from a Lagrangian formulation to a Hamiltonian one, that's amenable to QM. The logical path is Palatini action -> Plebanski action -> Ashtekar Prime crash course (Lee Smolin, Perimeter Institute): https://pirsa.org/09070000 I do not properly distinguish between Lagrangian, Palatini, Plebanski, Ashtekar. Lagrangian is the focus. The rest are successive ways of reducing the number of "generalised coordinates" until the theory is really more user-friendly. A particularly illuminating step is when the curvature tensor is reduced to an expansion in a self-dual part and an anti-self-dual part. The content of Einstein's equations being that the anti-self-dual part is identically zero --something like that, I forget lots and lots of details.

Agreed. Extra-nice topic. The Bible on this: https://www.cambridge.org/core/books/spinors-and-spacetime/B66766D4755F13B98F95D0EB6DF26526 https://www.cambridge.org/core/books/spinors-and-spacetime/24388801C4B4BA419851FD4AF667A8F0 'Twistor' is another key word to look for in this concern. Twistors require masslessness, so it's a bit more of an adventurous approach. But very worth taking a look too.

https://en.wikipedia.org/wiki/Wave–particle_duality

Forces do appear in simplified contexts, if you want to call them that. https://en.wikipedia.org/wiki/Ehrenfest_theorem If you define your force as the gradient of the potential, -V'=F then the time rate of change of the space-average momentum of the wave is the space-average of the 'force'. So they are connected. Only in the average. As for classical systems the wave is sharply peaked around a central value, you get the familiar picture which you're trying to use to explain the more general picture. You don't understand quantum mechanics. That's (part of) your problem.

Energy only occurs in a theory that's invariant under time translations. This much we understood when Lagrangian and Hamiltonian mechanics became general enough, well-understood enough, that it became mathematically transparent why it should be so. In classical physics (both Newtonian and Einstenian) you can always widen your outlook so as to see your physics as happening in a background that is everywhere the same, and at all times the same (in Newtonian theory, absolute space; in SR, space-time). If your system doesn't conserve energy, you can always understand it in terms of it being part of a bigger system that does conserve energy. That's why energy is conserved in both theories. In GR, on the other hand, and very importantly, energy is something of a bit schizoid dual* concept that has to be connected through Einstein's field equations. Energy must always be exactly zero when you consider the energy term on the LHS of the equations, and the RHS of them. You have a sort of geometric energy, and a material-content energy, plus a vacuum energy that's conventionally placed on the LHS of the equations. All the energy terms must be counterbalanced. In order to incorporate the caveat in its very name, we could call it 'energy-like balancing scalar invariant' or something. I don't think the term would stick. Unfortunately, we're stuck with just 'energy'. In 'raw' quantum field theory (QFT, in flat space-time) you always have energy conservation for an isolated system, for reasons similar to those that make SR an energy-conserving theory. When you try to combine both (GR & QFT) the desire to asign 'reality' to energy and momentum becomes, if anything, even more unclear. Especially if you want to include the Big Bang in the picture. There you have several models where the 'creative work' is done by the vacuum --inflationary models--, where energy and momentum appear because of features of particular geometric models --CPT-invariant universe, conformal, cyclic, you name it. But, whatever the framework, energy and momentum's entering the scene must be accounted for, and it doesn't seem easy to do that by attaching to them any concept of 'hard reality'. By 'hard reality' meaning: They are something that is there, has always been there, and will always be there, 'from ever', forever, and for every observer or way of looking at it, or measuring it. Something has to give at certain critical points, and under certain symmetry demands. * It's actually even worse than dual. It's a triad: We have matter-content energy, geometric energy, and this vacuum-energy term that we can place either on the RHS or the LHS of the equations if we will.

Thanks for acknowledging it early. Word salad is not difficult to detect. Early detection system is important, and members are an essential part of it, IMO.

https://www.oxfordlearnersdictionaries.com/definition/english/pap_1?q=pap

You can use infographics in order to help understand a correctly formulated physical theory. You cannot formulate a physical theory correctly with just infographics. It's like trying to... It's like... Something like that.

I use, \( \frac{1-x}{2} \) for inline maths, and, \[ \frac{1-x}{2} \] for display maths. It always look fine: The first expression, \( \frac{1-x}{2} \), looks as you can see on this line. While the second expression looks like this: \[ \frac{1-x}{2} \] It does funny things like those you describe if I click some other website functions or refresh the page before committing my comment.

For some reason, I'm able to see how you're not able to see how the quantum and physical realms combine. Is one of the things you see something like the message "go see a doctor?" Really, get professional help.

Yes, it feels like wishful thinking, conspiracy discourse, mindless trashing of anything that comes from authoritative sources has become the norm. But to have videos promoting this stuff seems like too much.

I won't take any chances.

Food for MAGA nuts?

Thank you. Very interesting comments. Well, to tell you the truth, I'm more concerned about the sweeping statements that they're making about science as being a rigid system that stifles imagination than I am about the particular theory of Dr. Sheldrake. If his is a falsifiable theory, I'm OK with it.

I was looking for data on the Sudbury event that seems to have marked the end of the Late Heavy Bombardment and the start of the Mid Proterozoic and came across this very interesting website. https://craterexplorer.ca/home-2/ The Chicxulub is there, of course. I forgot to say. Any comments/criticism etc from experts are most welcome.

Yes, it is for reasons like this that I think they would be a better barometer. It doesn't rule out the possibility that minorities are being left out. That's why the general idea on which I suggested my rough definition of well-being of a society is based on a per-individual index. If individuals don't have to be spending every waking hour on trying to survive, I don't really care that much what they want to do with their time. For all I care they could all be philosophers. Does that make sense? Doesn't it stand to reason that societies where NGOs proliferate are necessarily societies where they are needed, and thereby unequal societies? Sounds like a truism to me.

Thank you. I think yours is much more detailed than mine, and more vulnerable to subjectively-driven manipulation, IMHO. Not necessarily by you, but certainly by vested interests. Remember I also said, The reason why I like something like this better is that every factor that contributes to what --to me-- is of paramount importance, is more impervious to number fiddling. Give you an example: You included NGOs in your index. Are all NGOs created equal? Do all NGOs evolve equally? I don't think so. There have been consistent claims that some NGOs can grow so big --perhaps even start so big-- that they end up becoming multinational enterprises, to the point of stiffling any progress in particularly weak countries. And there is a very transparent reason why this could be so: The last thing a very big enterprise with gargantuan financial needs would want is for their particular area of work eventually disappears. IOW, not to be needed anymore. I'm not saying that's a general rule, and I'm not naming names. I'm saying it's a reasonable concern. What I'm saying, IOW, is: Give me a parameter that directly tells me things are going better for the average individual, and I will believe your society is better off. That's why I took my cue from biology with the example of primary productivity. Does it come from plancton? Does it come from trees? It doesn't matter. Biology I trust, macroeconomics --and theoretical frameworks blatantly inspired by it--, I don't. I don't even totally, wholeheartedly, trust my own proposed index. And that's my two cents. As Markus, I'm no expert either.

In Newton's theory of gravitation, it is not. It is rather a field theory => gravitational field In Einstein's theory of gravitation, it is curvature of space-time. Although GR is peculiar, you still have sources (the momentum-energy density.) In pure geometry you don't have such a thing as "a source of geometry." People do call Einstein's famous G tensor "gravitational field," but its a peculiar geometric field.

Certainly not. But, as long as we're considering Newtonian physics, consider also this: To the extent that Newtonian physics is valid, inertial frames must exist within a reasonable degree of approximation. If they do, I can always go to an inertial frame where only those forces coming from fields and their identifiable sources are present. Now I go to a non-inertial frame of reference, and fictitious forces appear. That is, forces that in no manner can be identified with any physical sources by means of fields; forces that to all intents and purposes are kinematic in nature; ie, can be removed only with a reference re-labling. Now go to another non-inertial frame if you like. It's still incumbent upon you --the claimant that forces are real-- to explain why those forces are not present in an inertial frame, while they 'magically' seem to appear out of thin air in a non-inertial frame.

A locally inertial frame in GR is not an inertial frame in SR. It is a non-inertial frame. Just a particularly convenient one. As to Newtonian physics, if fictitious forces appear in whatever non-inertial frame with respect to any inertial frame, we must admit a class of forces that merit the name fictitious. Why? Galilean physics is classical physics, which is Galilean physics, whether the frame of reference be inertial or non-inertial. It's called 'Galilean' only because it takes a particularly simple form in inertial frames, and Galilean transformations tell you how to correlate your observations between any two of these particularly convenient frames of reference.

Actually, I am. That's what's painful. You say forces are real. MigL told you that in GR gravitational forces dissapear when you go to a locally inertial frame. After I understood you correctly --I hope-- I told you in Galilean physics forces that weren't there suddenly appear in a non-inertial frame --so-called fictitious forces. I repeat @MigL's question: In the second case, where was the non-existent force? It's precisely because I'm taking you dead-seriously that I ask you these questions. Otherwise, I wouldn't entertain this conversation.

No. We are discussing physics and reality. You say forces are 'real' for some reason that's only clear to you. You want to discuss non-inertial frames? OK. But mind you, forces then become --if anything-- even less 'real' than you claim. In an inertial frame you have F=ma. Now you go to a non-inertial frame and you have F'=F, and obtain F'=ma'-mA, where A is the acceleration between frames. So, if you want to preserve Newton's laws at least formally, you must write F'+mA=ma'. Ficticious forces mA appear in the new system. https://en.wikipedia.org/wiki/Fictitious_force Fictitious, huh? Ditto.

The last part, that I leave as a simple exercise, is to prove that indeed \( \boldsymbol{F}=-\frac{\partial V}{\partial\boldsymbol{x}} \) is a vector under rotations. So no, neither forces, nor accelerations, are frame-dependent in Galilean physics.

As is well known, acceleration is not frame-dependent in Galilean physics. Classes of inertial reference systems are related by Galilean transformations, which in their most general form are, \[ \boldsymbol{x}'=R\boldsymbol{x}-\boldsymbol{v}t+\boldsymbol{a} \] \( \boldsymbol{x}' \) being the coordinates of certain point P in a new reference frame, \( \boldsymbol{x} \), such coordinates but in some old reference frame, \( \boldsymbol{v} \), \( t \) the time in both frames, and \( R \) a fixed rotation. So, as to acceleration, \[ \frac{d^{2}\boldsymbol{x}'}{dt^{2}}=R\frac{d^{2}\boldsymbol{x}}{dt^{2}} \] So if the vector of force on the, say, LHS of Newton's equation of motion is a vector under fixed rotations, the equations remain consistent. Only a fixed rotation is applied to them. That's why in engineering problems you can choose your axes at will. Otherwise usual engineering procedures wouldn't be consistent. Now, the force --in the last analysis-- always comes from a potential energy. It is the gradient of a potential. But that's not enough: It must depend on differences of the coordinates, and be a scalar under rotations. All known cases comply with this --gravity, electromagnetism. Nuclear forces are more complicated, but I think we should agree nuclear forces are best treated quantum mechanically, and under the Lorentz group, not the Galilean group. Under those assumptions, the potential \( V \) must have the dependence, \[ V\left(\left\Vert \boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right\Vert \right) \] so that, \[ \left\Vert \boldsymbol{x}'_{i}-\boldsymbol{x}'_{j}\right\Vert =\left\Vert R\boldsymbol{x}_{i}-R\boldsymbol{x}_{j}-\boldsymbol{v}t+\boldsymbol{v}t-\boldsymbol{a}+\boldsymbol{a}\right\Vert =\left\Vert R\left(\boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right)\right\Vert =\left\Vert \boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right\Vert \] and so, as claimed, neither acceleration nor the law of force --in any fundamental case-- are frame-dependent. I forgot: \( \boldsymbol{v} \) is the velocity relating both inertial frames.

You're right about this Rupert Sheldrake person. What concerns me a bit more is how much attention pseudo-science like this --it's not just RS-- attracts. It's a concern having to do with social movements, and mass thinking, IYKWIM.