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In Millikan's oil drop experiment, when the oil droplets fell through the hole in the top plate, and passed through the ionised air, did only electrons get attached to the droplets? Or both the electrons and the cations? In my book, only electrons are shown as attached to the droplet. Why only electrons got stuck? Why not the positive ions as well? Or did they?

It's a good question. I suspect it is to do with speed of motion. The electrons ejected from the oxygen and nitrogen molecules are light and move fast compared to the molecular cations left behind, so they will tend to encounter the oil droplets more quickly and more often, I imagine.

If I tickle you, can you keep from laughing ? if you stick your finger down your throat, can you keep from throwing up ? Can you stop a sneeze, or touch a hot object and not recoil your hand ? Do you automatically yawn when you see someone else yawn? You are more 'hardwired' than you think.

"Should academic research establishments be political?" That's like asking "Should we support a crusade?" and not asking why...

I think this is quite tricky, at least for somebody as rusty as I am. 🙂 If it were not for the H bonding, I think one would expect the ortho- substituted nitro group to increase the acidity the most, being closer. The H bonding will, I should have thought, tend to weaken the acidity, by providing additional binding of the H atom. In orthonitrophenol the H bond setup is close to ideal, as it forms a 6 membered ring, so it can be a strong H-bond. So that could explain why the acidity is anomalously lower than the para version. In orthobenzoic acid however, you have 7 atoms jostling to form the H-bonded ring, which will bend it out of planar and may make the H bond weaker. So perhaps the H bonding effect is not strong enough to disturb the usual order of effectiveness of the electron-withdrawing group. But I have to say, this looks like one of those things in chemistry that can be rationalised either way after the event, but can't really be reliably predicted just from theory. All a bit hand-wavy. But maybe @John Cuthber will have something to add (or tell me I'm wrong).

To give a less mathematical response, it is the latter. For a QM entity to be in an exact place with an exact momentum is just not something that is even defined, in QM. The uncertainty is intrinsic to nature. From reading Carlo Rovelli's "Helgoland", it seems the "relational interpretation" of QM in effect denies that a QM entity even has any properties on a continuous basis. According to this view, all properties become manifest only in the course of interactions involving the QM system in question. In between interactions, it is not necessary to assume that it has any properties at all. The wave function (when the QM operator for a property is applied to it) tells you what range of values of the property the system may manifest when it interacts. Tying properties to interactions gets rid of the tiresome issue of "the observer", which has led all sorts of people astray over the years, even sometimes to the extent of speculating that QM gives a special place to conscious observers. This last is something that has spawned an entire industry of quantum woo (Deepak Chopra et.al.). But, on the contrary, any "observation" necessarily requires an interaction. It is the interaction that counts, not an act of observation. The further implication of this is that what we call "reality" is made up of the interactions going on all the time between QM entities. Which is not as crazy as it sounds. After all, something only provides evidence that it exists when it interacts with something else. Classically, we interpolate between interactions by assuming that objects possess properties with defined values all the time, in a continuous manner. But in QM it seems the only thing that unambiguously persists is the wave function, which represents the potential properties exhibited when an interaction "collapses" it. This, at least is my understanding. I find it elegant, as it seems to resolve a number of the paradoxes that QM throws up.

It applies to any pair of conjugate variables, so in QM it includes energy & time, and angular momentum & angular position as well. These variables don’t commute, so the order you do the operation matters. It’s inherent in QM i.e. it’s in the math. These variables are fourier transforms of each other. The observer effect is a distinct phenomenon edit: more detail here - https://www.forbes.com/sites/startswithabang/2017/08/12/ask-ethan-where-does-quantum-uncertainty-come-from/?sh=60c0a134794e

Right, that's why I propose the hyper sphere geometry. Our universe (the part we can perceive) would be the surface of the hyper sphere and the mass of dark matter would be located in the center of the hypersphere. Each body of matter in our universe would be equally distant from the center of the hyper sphere. A hand-wave is sadly the farthest I can go 😅

Dear Swansont, yesterday I just stumbled on the Scienceforums.net while doing some research. Honestly, I just discovered it. I was really amused by, actually, your comments and I had the impression that you had good understanding of physics. This is the reason why I posted my paper here. Elegance and symmetry are underlying principles of mathematics, group theory, ... Let me cite Paul Adrian Dirac: "What makes the theory of relativity so acceptable to physicists in spite of its going against the principle of simplicity is its great mathematical beauty. This is a quality which cannot be defined, any more than beauty in art can be defined, but which people who study mathematics usually have no difficulty in appreciating. The theory of relativity introduced mathematical beauty to an unprecedented extent into the description of Nature." Unfortunately, why it is more elegant - in most cases - to use tau instead of pi cannot be defined. A French croissant tastes imo better than a croissant from country y, but I would have great difficulties to explain why, it is difficult to define taste. (As a sidenote, with respect to tau, I may suggest you to read the Tau Manifesto: https://tauday.com/tau-manifesto).