joigus

Ah, @studiot. Thank you. Whenever I'm reminded of this thread I wonder why nobody so far --including myself-- has dedicated a post to mathematical/geometrical beauty. Now you have. Thanks again.

I think this thread's gone to meet its maker. It's joined the choir invisible. If it wasn't nailed to the forums topics it would be pushing up the daisies. It is an ex-thread. ------------ Honestly. I see no promising science here. My summary: No. Monopoles are not dipoles for very much the same reason why monocles are not binoculars: two is not one. Gravity and electromagnetism are not the same. Radiation fields decrease with distance as (distance)-1; monopolar fields decrease with distance as (distance)-2; dipolar fields fall off as (distance)-3. That's another reason why they can be told apart. Beside the ones explained by myself and others. Each one varies with distance as the spatial gradient of the previous-order one. Plus EM doesn't satisfy the equivalence principle. Only repetition, and familiarity with it (the EP) makes you forget how incredibly surprising it is, how much different the world would be if EM and gravity were more like "different versions of the same thing," and how exceptional gravity is. The 1/r2 coincidence is but a mirage. Plus EM is scale-independent while gravity is scale-dependent. Plus charge is a relativistic invariant, while mass is not. Plus... And still I can't see what any of this has to do with number theory, which AFAIK has no relevance to physics,* as the question whether, say, the speed of light, or the mass of a body, or any other physical quantity is a rational or irrational number (or prime, or has any other number-recursion connection) doesn't really make sense, for the very simple reason that any of those are measured numbers, and inevitably go with a range of experimental precision. So any claim that you would want to make in terms of number theory would immediately be whitewashed by the fact that all physical quantities are cut off by virtue of experimental uncertainties. My feelings exactly. * Repeat: Number theory has no relevance to physics as both stand today. If it has, IMO, you should make a strong case why it does, if you think it does. There's nothing written in stone that says that number theory and physics will never be related in the future.

What I said is not my opinion; it's my informed opinion. I'm sorry, you're not making any sense at all to me. Let alone check with experimental data and known standard scientific theories.

No. I meant: That is, inertia and gravitational mass are very different things. and, So you can't define them as equal, which is what you said.

Ok. Sorry I hadn't read your comments when I gave you the previous reply. But here's an interesting point that shows clearly that you do not understand basic physics. Inertial mass (or simply inertia) is one thing, and gravitational mass is another --very different-- one. You cannot simply identify both in a definition. It is a salient experimental fact that both are exactly and universally proportional for all matter in the universe as far as we can tell. You can therefore identify them in the mathematics by choosing appropriate units.

I think you're trying to bite off much more than you can chew with the tools at hand here. Extinction phenomena are too complex for a simple idea coming from fundamental physics to do anything useful for us in the way of an explanatory mechanism. As to the physics, here's a rough list of some "concepts" you've sported here that are non-standard and demand a clear unambiguous definition in terms of things that can be measured: Proportionality cone Local gravity system Total gravity function Relativity of gravity (relativity with respect to what?) (The list is not meant to be complete.) If you cared to provide more details about those, maybe I and/or others would be able to provide more information about how your idea is probably wrong. As it stands, I can only tell you there's almost a 100 % chance that it's wrong.

Topic goes back to 2011...

I don't know what you've found, but it doesn't look like gravity at all. Starting with... it seems to violate the equivalence principle, it's not consistent with Cavendish's experiment... Although, to be fair, you haven't explained how your force depends on the masses (inertias) of the bodies. It seems to be an ill-conceived (or ill-explained) version of a magnetic effect. Any theory that purports to be the new theory of gravity must start with an explanation of the basics. And then you go on to explain the more subtle effects --dark matter, etc. as probably small corrections. I don't see that happening on this thread.

I think you put your finger on a fundamental confusion here. A field in physics is a mapping between a space (topological space, metric space) and a set of so-called field variables (vector, tensor, spinor, scalar...) while a field in algebra is a closed system of numbers.

Just curious: How do you coarse-grain time? What are the smaller grains to coarse over? You can coarse-grain a fractal landscape, but what are the bumps and dimples to average over in the case of time? And, as @studiot said, what does it all have to do with number theory? I still don't see it.

Yes. No. Yes. 66.6 % right as to the sheer number of assertions. And, as pointed out to you, 100 % wrong as to the logic. You could have a world in which e=mc2 (the world of special relativity), and it is conceivable that photons didn't couple to the gravitational field. So those are independent assertions.

Gravity would exist, but only as a continual bubbling of virtual states. Gravitons would pop up from the vacuum and die down without having found any real particle in their way. In terms of QFT, it would be only loop Feynman diagrams. Assuming a cogent theory of quantum gravity is found some day.

At several points on his lectures, Lenny Susskind makes a very emphatic case for that. I'm guessing it's in his book, The Theoretical Minimum? Any introductory book that explains to you that the most relevant thing about GR is equating geometry to energy-momentum, will do the job. Mass is not a central concept of GR, to put it mildly. I'm sorry I don't remember in what particular lecture he delves into that a little bit more, due to a question from the audience. But you should be alright if you follow his lectures on GR.

John Wheeler came up with this wonderful phrase to summarise what GR is about. But buzzwords can only get you so far. If you have a situation in which a small object moves in the vicinity of a stellar object that heavily distorts space-time around it, then it's fair to say that the star tells space-time around how to bend, while the relatively small stuff moving close is told how to move. However, consider the collision of two black holes. In that case, both the motion of the objects and the warping of space-time are very difficult to tell apart. For those cases, the only alternative is to appeal to the equations and have a computer solve them for you. The equations are highly non-linear, which means that ultimately it's impossible to express the warping as the sum of contributions of this and that piece of matter. Gravity itself gravitates. See my point? Another aspect I would like to point out is that mass is not the source of the gravitational field. It's energy-momentum that plays that role. The "mental operation" that you're proposing here, if I've understood you correctly, is to remove the sources and be left with an empty space-time, and then you ask yourself what shape does that space-time have. Well, think about this: Einstein's field equations have many solutions corresponding to an empty space-time. Gravitational waves are a particular example of solutions to the Einstein vacuum equations. So I guess my answer is: No, you can't figure out what space-time is like with nothing in it. Not a priori. You have to make a guess.

Whether torque is a vector or a pseudovector is a question that has nothing to do with energy being a scalar that comes from time-translation invariance. I'm not sure how relevant this is to the discussion, as I'm not sure of what's being discussed, and I cannot formulate what the claimed speculation is. This distinction vector/pseudovector has nothing to do with energy stemming from time-translation invariance. Noether's theorem is concerned with continuous symmetries, while the "pseudo" in "pseudovector" has to do with rotation-related vectors (angular momentum, torques, angular velocities) being perfect vectors with respect to rotations (also called SO(3), but behaving differently to normal vectors (position, velocity, etc.) with respect to so-called improper rotations; that are the product of rotations by inversions of coordinates. Normal vectors (SO(3) vectors; polar vectors being another name) change the sign of their components when we invert the sign of the coordinates. Pseudo-vectors do not, because they are really "external products of vectors". I hope that helps, but some parts of this thread sound like dadaist poetry to me. And I don't mean either Swansont of exchemist's contributions. I don't mean to be facetious. I really would like to understand what point is being made to be of any help at all.

Wouldn't you be satisfied with the regular lemmas and theorems, like L'Hôpital and such? Finding an N(epsilon) is a pain in the neck.

(My emphasis.) The question, of course, is how rare "exceedingly rare" actually is. I'm working on reading all the comments. I tend to agree with people who have pointed out that ants are interesting from many points of view and to many other organisms --Airbrush, Charon Y. Humans have been busy with ants probably for hundreds of thousands of years. The interest of hypothetical civilisations on us ants would have to be weighed against the Herculean task of overcoming the enormous difficulties of finding us in any useful way, as exchemist and swansont have implied. I don't know what that says about the argument Greene is trying to make. It's possible that the analogy does not efficiently bear out the point, even if the point is a good one.

Is what you want anywhere at the level of rigorousness as proving that, \[ \forall\varepsilon>0\:\exists N>0\:/\:x>N\Rightarrow\left|\left(1+2^{-x}\right)^{x}-1\right|<\varepsilon \] ?

Hi. I did not address the second question, because I figured you would solve it as soon as you applied yourself to it. Apparently you've solved the 1st one but are unsure of its validity? The first question is best addressed with assymptotics. Here's a sketch: \[\left(1+2^{-x}\right)^{x}\sim\left(1+2^{-x}\right)^{2^{x}x2^{-x}}\] Now, \[\left(1+2^{-x}\right)^{2^{x}}\sim e\] And, \[x2^{-x}\sim0\] So, \[\left(1+2^{-x}\right)^{x}\sim e^{0}=1\] Now, making it rigorous is another matter. In fact, I went dangerously off-bounds when I said \(x2^{-x}\sim0\), as you're not supposed to ever say anything is ∼0 in assymptotics.

Sorry. I did the derivative. You need the limit. The limit is of the kind 1^(infinity), which are solved by relating them to the definition of e=lim(1+f)^(1/f) if f-> 0 when x->infinity. The result is 1, if I'm not mistaken. I'll take another look tomorrow. Tell me what you get.

This is what you want: https://en.wikipedia.org/wiki/Logarithmic_differentiation#:~:text=In calculus%2C logarithmic differentiation or,rather than the function itself. Plus changing exponential bases: 2^(-x)=e^(-xln2)

Yes, Pinker's quote is what's in boldface. Pinker's adjectivation is unmistakable. They used atomic randomness as a random-number generator. You read the numbers of decay times and use those numbers as input for another variable that has biological relevance by setting this other variable to take those values. That's what I understand. I hope that helps answer the question, but some feedback would be very useful.

The Road to Reality is a very good book. Any recommendation from Genady is probably worth considering, OTOH. It's not a book to actually learn physics though. It's more of a whirlwind tour of the exciting topics of modern physics. As to popular books with emphasis on experiments, I recommend, Weinberg's The Discovery of Subatomic Particles. Then you can try the Feynman Lectures on Physics. If you want to learn physics in earnest, you probably can't do much better than Landau & Lifshitz's Course of Theoretical Physics. Encyclopedic (10 volumes.) A bit old, but will take you a long way in understanding the deepest principles of physics and how they're applied. There are many other books, I'm sure, and with a more modern focus. A good rule of thumb is: The more unassuming the title is, the more likely it will take you to the nuts and bolts. I think you get the idea. Although we could hardly be more off-topic.

This is no coincidence. The Laplace equation must monitor the spatial/vacuum factor of any physical equation worth its salt, as Einstein observed in his famous popular book on the theory of relativity. Physics does deal with many 3-dimensional problems, of course. When it comes to proposed generalisations of the standard model, it may even consider 26 dimensions. Why do you say that?

Yes, you're right. It's me who brought it up. I forget what it had to do with the primes, though. Or how the question surfaced. I'm no expert on number theory. You may be on to something when you say that differentiable functions of a complex variable may have to do with the prime-counting problem. A function being differentiable in a complex variable z=x+iy is a much more restrictive condition than the corresponding condition on a real-variable function. But in mathematics it's important to define anambiguously your concepts, and the state clearly what your assumptions are, and proving rigorously whatever you say about them. Sorry, I can't contribute much more at this point. I hope that was helpful.