joigus

Beautiful. Thank you.

You're most welcome. Physics is the realm of common-sense wonder. Welcome to the forums.

A simulation is worth a thousand words:

\[\left(183.5\pm.5\right)\textrm{ cm}\] May I also insist on what they've told you before?: Talk to her. Make her smile. Don't mention height. Be sincere. Forget about pick-up lines. Whatever it is that's good in you, make it shine.

(My emphasis.) Merely? How did Newton and Galileo manage to get anything done?

It must have been sheer luck. Let's say I was just talking from hearlore. But you've made noises in the innermost recesses of my linguistic and mathematical mind and awaken the creatures that live in the gallery of my mathematical and linguistic monsters. Maybe another thread is in order.

Well, you're right. Maybe not always. In continuum mechanics that may not be the case. In field theory it certainly is.

Ditto.

Field variables always can be seen to "inhabit" a space of their own. In the case of the electromagnetic field this internal dimension is the angle along a circle. You can picture the EM field as an entity that, for every point in space time, is given by an angle in this internal dimension. That's why Kaluza and Klein were able to model the EM field as a curly dimension (circle) superimposed on every space-time point. Yes, you're right. But that happens after the measurement has taken place.

I couldn't agree more. X-posted with Tristan L. OK. Thanks for drawing my attention to right English. I'm always eager to learn about language. But how many of those Anglish speakers are knowledgeable enough to have a meaningful conversation about second-order logic? See my point? I'm sure a compromise is possible. Mathematics has nothing to do with empire-building, does it?

Your point is well taken, @Tristan L, but I think the topic is difficult enough in and of itself that facilitating communication to as wider readership as possible overrides every other need. You can't speak a language that only you understand. I was totally thrown off by "ownship" and "witcraft".

Oh, yes. But all this would fall under the category of the description of particular scenarios. If you want to be very specific, that's where Ockham's razor is not in its proper domain of validity. Remember what @Eise said: (My emphasis.) "Heuristic" refers to scientific hypotheses, thereby to general patterns, rules, or laws. One thing is "this happens to be here and going in that direction"; quite a different thing is trying to put forward a pattern according to which things that are here or there, going in this or that direction, behave.

They are. There is no mention to any particular space-time coordinate frame, so how could they depend on any of them? What is more, they have an internal symmetry. You can rotate in the electric-magnetic reference frame \( \boldsymbol{E}\), \( \boldsymbol{B}\) and the equations remain the same, which amounts to arbitrarily re-define part of the purely electric \( j \) as magnetic. Yes, it is the divergence of a curvature term, and thereby identically zero by the Bianchi identity. Please, give me some time to read your other points.

I think it's about at what level you wish to describe the theory. It is well understood that, e.g., Maxwell's equations are very simply formulated in a coordinate-free way as, \[dF=0\] \[d*F=j\] But it takes a considerable amount of time to explain to students what all of these symbols mean. Then again, in particularly "dirty" situations, it does no good to tackle the problem in such an all-encompassing, highfalutin way. And we're approaching the level at which everything I say is just my two cents.

The waves that are used in Bell's gedanken are completely un-polarised. The key to Bell's scenario is that entangled pairs of particles are described with fewer variables than those needed to describe two independent particles, so the particles are sharing some internal physical reality, so to speak. The reason for the angle 45º is a bit technical: It's the angle at which a certain projection of spin for a 2-state spin differs the most from two states that are perpendicular in ordinary 3-space. Keep in mind perpendicularity --orthogonality-- in the internal space is different from perpendicularity in ordinary 3-space. I don't see anything terribly obvious in any of that. But maybe it's just me.

I wouldn't put too much stock on that. Mechanism? Male insecurity, that's what this is all about.

Economy hasn't got all the answers. OTOH, if you just let the lazy mouse die, there's no lesson to be learnt either. I'm missing a third mouse in the story. One that's capable of foreseeing. The diligent mouse will strive just as hard when Nature stops delivering her goods.

The risks of auto correction.

I think this belongs in Spec elation.

Yes, that's one valid way to put it, IMO. In physics there are certain theoretical constructs, like the field, charge, couplings between different fields, etc. Takes considerable time to acquaint yourself with them, but once you do, you're completely won over by their power and generality. You need to let go of the old equipment: push, pull, levers, and so on. You can always go back to them, because sometimes it doesn't help to think about, (eg., an engineering problem) in terms of fields and elementary interactions. So if you're curious about magnetism and the like, you let go of the other stuff. It does no good.

Oh, boy. I'm sorry. I should have read you out. You are much more knowledgeable on this than I am. But your comments reinforce my impression that Gödel's theorem does not provide much in the way of a constructive process, even though the proof itself is constructive. I think what you mean is something like theorems in number theory, propositions on prime numbers, and the like, right? I simply don't know. I've never heard of any of those. That is a very good question. Maybe @wtf has something interesting to say about it.

Cohen's proof that it is undecidable whether there is a cardinality (number of elements) intermediate between that of \( \mathbb{N} \) and that of \( \mathbb{R} \). https://en.wikipedia.org/wiki/Continuum_hypothesis "Undecidable" is perhaps my colourful way of saying it. People seem to prefer the wording:

It's the other way around. We live in a DeSitter universe. So your proposal is against the observations. https://en.wikipedia.org/wiki/Accelerating_expansion_of_the_universe

My condolences, @MigL. I know how hard it is to say goodbye to a friend.

And what is speed? And what is change? Isn't time already implied there?