joigus

Very interesting googling suggestion! I wasn't aware of this "extra dimension." The dream of cheap energy is too attractive, and it's bound to die hard. But I also agree with you that the internet plays an important part in keeping the dream alive --zombie-like.

This makes a lot of sense.

I very much agree with Eise on this one too. When I said deterring works to some extent, I meant for ordinary cases of breaking the law. Not for violent criminals. I lost some focus. For violent criminals I don't think deterrence is a factor. Nor is it positive to clump together people of a violent profile. I liked the video very much. Just one thing. When you say: I think you meant lose-lose. I don't think you want to conflate "lose" and "loose" when talking about criminals! I know it was an innocent typo, Eise, I hope you forgive me.

I meant "radiative" as in "radiative corrections" = "quantum corrections". In QFT, when you calculate any parameter like mass, charge, etc., you don't know what happens at very small length scales. So you have to assume that all possibilities quantum-mechanically possible, somehow, are there. Classically the gyromagnetic ratio is just 2: https://en.wikipedia.org/wiki/Gyromagnetic_ratio#For_a_classical_rotating_body Any deviations from this factor of 2 are purely quantum. Quantum electrodynamics owes much of its well-deserved prestige to the success of this calculation. The discrepancy with the classical factor of 2 is due to "radiative corrections", which means that you have to account for virtual particles contributing to these renormalised quantities. The mass, the g factor, even the charge, are affected by quantum corrections. If the salient suggestion of Fermilab and Brookhaven is that a fifth force is necessary to explain this anomaly, it must be because new gauge bosons have to be conjectured. That is, bosons other than photon, Z and W's, or gluons. IOW, bosons that are not contemplated by the standard model. That's what I meant by "new radiative modes." And I didn't mention curvature. That was @Prof Reza Sanaye.

Dear professor, I would very much enjoy that sitting with you and @MigL. Sometimes I have a feeling that you're intellectually honest, sincerely interested in knowledge, and perhaps just a little bit "spread too thin", if you take my meaning. I'm a bit "spread too thin" myself so... And you have a sense of humour, which is always a big plus. Take care, and keep an eye on radiative modes.

That's what I'm worried about. You proved some of its consequences if P=NP is true. IOW, it only means P=NP cannot be disproved --within your logical frame-- by reductio ad absurdum. But nothing else. That's called "begging the question." I'm not at the level of @Ghideon in these matters, I'm just telling you that you should be aware of this possible flaw. If you're aiming for the stars, you should point at them. I take it that your saying, was a joke. You may be on to something interesting after all. Even if it's not a proof of P=NP. I'll take a back sit and try to learn something.

Now, that's a very good question. And the kind of discussion that I wanted to entice here.

Seems like it was yesterday. Promise of jobs for physicists, a new era of almost limitless energy, and what not. The goose that laid the golden eggs died without a bang, and after months-long whimpers. And the world never recovered from it. Or did it? We lost a lot of our former innocence anyway. I did. Very interesting Nature article on it: Lessons from cold fusion, 30 years on https://www.nature.com/articles/d41586-019-01673-x Reflections welcome. Sorry that the topic is a bit old. It's not the anniversary that I'm interested in.

(My emphasis.) Curvature can be a 4-rank tensor (Riemann curvature tensor), a 2-rank tensor (Ricci curvature tensor), or a 0-rank tensor (curvature scalar). Watch out for 1-rank curvature tensors (vector fields); they're mean!! You took the words right out of my keyboard!

Sorry, next to total ignorant here. The Millennium Prize is on proving P=NP. I assume that's what you're aiming for: (My emphasis.) Isn't assuming P=NP kind of begging the question?

Now I understand! Those are cycling glasses, by the way.

I think that's because \( 1-1=0 \).

Rather: \[ \textrm{int}C\neq\textrm{Ø}\Rightarrow\textrm{if }x\in C\Rightarrow B_{\epsilon}\left(x\right)\subseteq C\Rightarrow\mu\left(C\right)\geq\mu\left(B_{\epsilon}\left(x\right)\right)>0 \]

This is the part I do not understand: And this is the part I do understand:

Deterring doesn't work 100% of the time. But it does in many cases. We need @Eise here. Wittgenstein or not.

Is it Lebesgue day today?

For the first one I would try the inverse direction; something like (as @mathematicsuggests), intC≠Ø⇒μ(C)≥0 Think open balls. I see you already have good help, so I'll leave it at that. Cheers.

Testing more stuff. \[ f\left(x\right)=\begin{cases} 1, & x\in\mathbb{Q}\\ -1, & x\in\mathbb{R}-\mathbb{Q} \end{cases} \] Testing more stuff. \[ \textrm{int}C\neq\textrm{Ø}\Rightarrow\textrm{if }x\in C\Rightarrow\in B_{\epsilon}\left(x\right)\subseteq C\Rightarrow\mu\left(C\right)\geq\mu\left(B_{\epsilon}\left(x\right)\right)>0 \]

Not hours; minutes. But many. Why? For all crackpots out there: https://www.gapingvoidart.com/

I think you have a point, @Sensei. I think what you're saying is "it's safer to interpolate a curve with three points than interpolating it with 2". Nobody would expect the results with anti-muons to be any different, though, because the standard model is CPT invariant. If anti-muons gave a disparate result... Now that would be a surprise! What I don't know is how difficult the experiments with taus would be. I'm guessing a lot more difficult, due to masses and lifetimes.

I'm more inclined to assess this as incontrovertible evidence of new physics beyond the standard model. But I'm reluctant to salute it as incontrovertible evidence of a "fifth force" just yet. For a fifth force to be there beyond any doubt, there would have to be evidence of new decay modes revealing brand-new gauge bosons, with new quantum numbers. But it is true that it's very difficult to conceive of a different gyromagnetic ratio of higher-generation leptons without anything dynamical being involved. The calculation of g-2 involves radiative corrections, essentially sums on all the gauge bosons "virtually flying around", and it's a dimensionless factor. If the gauge bosons are the same for different families, I see no reason why the gyromagnetic ratio should differ unless there are new radiative modes involved.

Yes, but that's not the point about matter-antimatter asymmetry. Call them what we may, the thing is there are considerably more electrons than their counterparts, and protons that their counterparts, and so on. There is an unbalance to one side, so to speak.

Beautifully put.

You need a mechanism that smooths out the universe to the presently known value, and does it at superluminal rates without violating causality in a local way. The way to do that is an expansion factor in cosmology consistent with GR. That's what inflationary models do. The fact that monopoles are swept out of sight is a bonus of inflationary models, rather than a robust argument, I think. The point being immediate generalisations of the standard model of particles physics (grand unification theories, aka GUTs) do predict these very heavy particles. So we can still pursue them (GUTs) while contemplating an explanation of why they (monopoles) aren't anywhere to be found. You need to study what the present models do in order to propose a wannabe cosmological model with any chance of being seriously considered. I hope that was helpful. I don't think a BEC will do the job, honest.

The rationale for the current inflationary model --as envisioned by Alan Guth, and developed by others--, is the need to explain certain observational facts: 1) The universe is large-scale homogeneous (this conflicts with causality: how did causally-separated regions equilibrate?) 2) The universe is extremely flat (why is it so stretched-out?) 3) Absence of heavy particles predicted by GUTs (monopoles) Your model should address these questions.