joigus

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.

I've just found a video on YT under the title "Exposing Scientific Dogmas - Banned TED Talk - Rupert Sheldrake". I'm constantly struggling over whether to say something or just shut up. This is one of the times when I just couldn't shut up. The video 'exposes' a series of dogmas that --apparently-- keep people's minds in a prison. For some mysterious reason dogmas #6 and #8 don't appear in the video. Unless they popped up at the end of the video, which I don't know. For some reason the algorithms 'thought' I would find this interesting. And they were right. I find some kinds of stupidity very interesting. So you don't have to watch the video, here's the low-down: Dogma #1: Nature is mechanical Dogma #2: Matter is unconscious Dogma #3: The laws of Nature are fixed Dogma #4: The total amount of matter & energy is always the same Dogma #5: Nature is purposeless Dogma #7: Memories are stored inside your brain as material traces Dogma #9: Psychic phenomena like telepathy are impossible Dogma #10: Mechanistic medicine is the only kind that works And here are my comments: Any thoughts --including, of course, disagreement--, further arguments, etc, most welcome.

As @Genady pointed out, force is frame-independent in classical mechanics --under the Galilean group. It's frame-nothing in GR, because force is not a thing in GR.

Weak neutral currents were first predicted, and then found in the laboratories at CERN. What difficulties?

I'd like to think your contribution here is just a wild imagination of mine, but probably bot.

Yes, that's something I've said at least a couple of times on these forums. I still think @MigL's example was brilliant. Why it --initially at least-- didn't have any effect on @martillo is beyond me. I liked your picture of "describe Idaho." What happens, the goings-on, happenstance, reality --if you will-- is a consequence of laws --some known, some unknown-- plus accidents. Quantum mechanics --among other theories-- has taught us that, even at the simplest level, accidents creep in, no matter how much we desire to control this "flow of details." Accidental is not incidental, it's an essential part of the brew.

It's mainstream physics. It's been done to death. It's been measured to great precision. Knock yourself out: https://en.wikipedia.org/wiki/Equivalence_principle

Agreed.

What force? There is no force. It has disappeared. A reference change and it's gone. That's the essence of GR.

@MigL wasn't talking about your force on the ball. He was talking about gravity. (My emphasis.) It weighed. Now it doesn't. Where's the force?

!!!

That's why I didn't say concepts like "force" or "interaction" are sterile. I said your concept of "real" is:

Not necessarily. The set of integers modulo 7 are numbers. And very useful ones at that. And there's nothing in their nature that even remotely suggests a line. They are quite independent from the concept of a point. Some numbers can be assimilated to topological and geometric concepts. But they don't have to. A line has no zero point. What is the origin of a geometric line? Geometry is one thing Topology is another And algebra, yet another Mathematicians love to play with these things. I'm sure @studiot and @wtf can tell you volumes about it. They go like: Can I drop this property and still get something interesting?

Then, a unicorn is real, as it is a real literary artifact used in story-telling. Which leads me to think that you've expanded your concept of what's real to the point of rendering it completely sterile.

How do you know these laws are real, and not a part of your theory? Are meridians and parallels real, or just a cartographic artifact?

Forces are not observables in quantum mechanics. Little wonder. "Force" is a very derived concept. How much force does a W boson exert on a neutron when it decays? Etc...

I brought it up because I know the theme of so-called detrimental genes that can be a blessing in disguise for the group has been the subject of extensive study and discussion in medical science / biology. Examples I can remember are sickle-cell anemia --which in its mild version protects you from malaria--, schizophrenia --which in its mild version is thought to have played a role in shamanism--, etc. I'm sure there are others. It could be the case for autism. I honestly don't know. That's a very good point. The brain is nothing but --it could be argued-- an organ evolved to map the world in certain ways. How it does that is subject to many variations. Some people count by projecting imaginary sounds in their minds, others do it by picturing images. It's even possible that there were some kind of 'maximum common divisor', so to speak, that affects us all, neurotypical or not. In that case J.B.S. Haldane's words "Now, my own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose" would be totally spot on as to what's given to us to know.

You haven't specified if this index is to be applied to ancient civilisations or modern ones. I concur with doubts expressed by @exchemist @Genady, and @Peterkin. Any definition you come up with is bound to meet criticism from almost any direction conceivable. You could try to formulate some kind of multi-index that takes into account factors such as, technological/scientific (functionality) artistic/spiritual/religious (symbolism) altruistic collaboration (solidarity) profit-focused collaboration (trade) If you think in terms of aspects that have played a role in defining 'civilisation' by anthropologists, historians, etc, you'll probably see that they're somehow or other included there. Examples: writing, accounting (technology), monumental architecture (symbolism and technology), etc. But there's plenty of room for ambiguity --eg, are old cosmogonies science or religion? This is where @Genady's comment on societies evolving becomes very relevant indeed. Or, I'm more inclined to try to work out a ratio very much inspired in biological definitions --like, eg, primary productivity-- that gives you an overall idea of what's going on in that direction, and to which a concept that most would agree underlies any reasonable definition of 'civilisation.' Such an index could go something like, #C:=(spare time)/(individual)x(day) Spare time being the time per day left over after having subtracted the time necessary for survival IOW, if a society has amazing technological capabilitites, but not enough time is left for people to dedicate to other activities than those essential for survival, then it's not civilised. Not enough, according to my index.

LOL. Beta decay = "when the neutron gives up the ghost" I understand 'ghostly' as 'interacting very weakly.'

By "fundamental" I mean resting on minimal/general assumptions, although I know how slippery that concept can be. Yes, theory of the mind --understanding that others have minds probably like we feel we ourselves have minds, and acting accordingly-- is one of the most important adaptive pressures that shaped the evolution of the human brain. I don't have the sources at hand to assert this, by I know from the reasoned arguments of many scientists of human evolution I've sampled through the years. I am in no doubt that there must be a reason why Nature has kept the genes that give us autism, which at first glance looks like just a cognitive impairment. Look closer and more can be seen. From my experience, from what I know from you, and others like you: Genuinely caring individuals, who suffer when they see conflict, generally devoid of manipulative intentions. Never foul players, sincerely concerned about problems, both human and technical, their own, and those of others. Hard workers, obsessive in a way that can be very productive, given the proper outlook, focus, and advise about how letting go when the time comes. Sometimes we're discussing something and we're being petty and narrow-minded. And here comes Markus Hanke and shines his light. All the pettiness is dissolved. The problem is re-focused to what the problem is. I guess that's why you lot are here for. Don't look now, but you activate us in a direction that --always in my experience, mind you-- usually is a good one.

Thanks, Phi. Now, what do you wish to discuss concerning neutrinos, @Vette888?

Right, but not news.

I couldn't agree more. For every bundle of sensory input we receive, we build models in our minds, filled with switches and state variables, or whatever you like to call them. Right now, in my mind, I picture @Genady's opinions and ideas, criteria, etc as --somewhat loosely-- some kind of a list with states of opinion, philosophical tenets and so on, that are perfectly defined as a series of 0s and 1s, so to speak. And you me, I'm sure. We work under such assumptions, and assign states, probabilities, etc to all these things. There is no fundamental reason why this should be true. What's more, even if it happens to prove itself useful to a certain degree, there's no fundamental reason why this process could be continued till the last least little consequence for everything we experience.