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Just to add to what has already been said by other contributors here: 1. First and foremost, the notion of "gravitational potential" can only be defined in spacetimes that are stationary (more precisely: those which admit a time-like Killing vector field) and asymptotically flat. It cannot be generalised to more general spacetimes, which makes it useless so far as a general model for gravity is concerned 2. Gravitational potential itself is not an observable, only differences in potential can be observed and measured. This is because the potential has a gauge freedom, in that one can freely choose where the zero point is, without affecting the physics. The same is not true for the speed of light, hence the relation above is trivially and obviously wrong, since it equates two quantities that cannot physically and numerically be equal, on fundamental grounds. 3. A varying speed of light would constitute a violation of Lorentz invariance. This symmetry has been experimentally and extensively tested with modern equipment to extremely high precision, both here on Earth and in the vacuum of space - needless to say, no such violations have ever been found. Given the degree of precision of these tests, any variability in the speed of light can effectively be ruled out far beyond the usual 5 sigma threshold. 4. A variable speed of light would also break CPT symmetry, which underlies the Standard Model of Particle Physics. Since we continue to successfully use and test this model in particle accelerators on pretty much a daily basis, any variability in c can also effectively be ruled out on that ground. 5. Neither classical Maxwellian electrodynamics nor quantum electrodynamics allow for varying values of permittivity and permeability (in the same medium of course). Hence the notion of a varying speed of light is actually in direct contradiction to what we know about electrodynamics. 6. As has been pointed out on another recent thread, a scalar field theory such as this one is fundamentally incapable of capturing all required degrees of freedom of gravity; there is more to gravity than just time dilation! I could probably go on, but these are the points that immediately come to mind without thinking about the issue too much. I'll leave it at this.

One of the best little pieces of comic theatre of all time was based on this. Here is wikipedia, you may be able to find a ytube of it. https://en.wikipedia.org/wiki/Class_sketch Yes indeed it is quite long, so I do not find it suprising there are some contentious points. The author is rather dismissive of the use of auxiliary verbs in general and the verb to be in particular. He claims that the verb to be is unneccessary and has almost withered away. Not so. Consider the travels of Marco Polo to China, a jourrney that took several years. Had he been English, Marco might have said, "I'm going to go to China next week." As he left Italy he might have said "I'm going to China". Two years later he was still "going to China", he had not by then arrived. One thing he would not have said would be "I go to China". The action was "imperfect" as it occupied an extended length of time and was still in progress during other events that might be spoken about. Imperfect here means that it is not complete at the time of utterance. A perfect action is complete from start to finish. An imperfect one may never be completed for some reason. Two other gripes with the article. Firstly no mention is made of the difference between spoken and written language when comparing English to other languages. It is my belief that this difference is one of the key factors as most languages are largely phonetic, English being the glaring exception. So it is emminently possible to learn and know many words and the associated grammar in English but not to be able to say or recognise them when spoken. Even English speakers sometimes have this trouble. Take the letter a as in car or cat. The big difference in the pronunciation of the 'a' leads to two difference pronunciations of the word castle, which confuses many. Secondly the thesis that it was the influence of the Vikings who did away with the manyfold word endings. One wonders why they did also do this with old French. Or why the endings were still there in middle English a couple of centuries after the end of the Viking era.

Some of the latest posts in Speculations have led me to this attempt at clarification, because I see that some people are very confused when it comes to handling equalities. The point is their meaning. It's subtle, but it's not moot in general; although in some cases it may be. Not all equalities are the same. There are at least these variants: Definition (or substituting symbol or replacing symbol, etc.) Example: fine structure constant, \[\alpha\overset{{\scriptstyle \textrm{def}}}{=}\frac{e^{2}}{4\pi\epsilon_{0}\hbar c}\] Identity (or universal equivalence under known or specified set of previous rules that may be algebraic, geometric, etc.) Example: constriction between sine and cosine, \[\sin^{2}\theta+\cos^{2}\theta\equiv1\] Equation (proposed equivalence considered in relation to the finding of "solvers" or "solutions") Example: Pythagorean Theorem assumed true, solve for c2, given c1 and h, \[5^{2}=\left(c_{1}\right)^{2}+3^{2}\] Formula (proposed equivalence under non-universal, somehow hidden, or not necessarily specified assumptions) Example: Pythagorean Theorem, \[h^{2}\overset{\cdot}{=}\left(c_{1}\right)^{2}+\left(c_{2}\right)^{2}\] Some formulas can become equations once you give values to terms or supply additional information. And yes, sometimes the distinction between what is a formula and what an identity can be blurry, depending on how we look at the defining "valid rules." E.g., the constriction between sine and cosine can be seen as an identity if we take Euler's identities, \[\sin\theta\equiv\frac{e^{i\theta}-e^{-i\theta}}{2i}\] \[\cos\theta\equiv\frac{e^{i\theta}+e^{-i\theta}}{2}\] as the point of departure; or a formula, if we adopt Pythagoras' theorem plus geometrical definitions of sine and cosine. It may also depend on assumptions about curvature of space, etc. Needless to say, most people who use mathematics on a regular basis, don't need to be reminded of these distinctions, because they intuitively know what they're about. The danger is when people start playing with equalities (especially definitions, as I've seen) thinking they have a different value than they really do. Also needless to say, but better said, the symbols for eq., id., form., and def. are not intended for general use, but just to illustrate how confusing all this proves to be to many people.

From my area of math, the "definitional equality" is usually written as "x := ". For example: "Let f(x) := (x - 1)/(x + 1)".

I'm not very religious at all, so keep that in mind when considering my opinion. We are finding that more and more health problems are associated with stress. And prayer, like yoga, or meditation, can have a 'calming' effect on a person, and reduce levels of stress. I would imagine this works only if you believe that it is going to work. I myself used to get stress headaches, and I used to take acetaminophen with caffeine ( Tylenol Ultra ), then I convinced myself that it was actually the caffeine that dilated my brain's blood vessels, and stopped the headaches. Now I just make a large cup of coffee when I get one of those headaches, and I get relief, without having to take any acetaminophen. ( for some reason espresso doesn't seem to work, no matter how many I consume; maybe it's the Sambuca I add to it )

Certainly not unique to English. You mentioned Spanish: Acabar con/de/por Dar a/con Estar de/con/para/por I would just focus on the problematic word (belief) and the few instances in which it makes you stumble, find an appropriate pattern, paste it on your kitchen wall in a large font, stare at it every day during your morning coffee until it is drilled into your head. So, say, in the case of an opening sentence where you are doling “it” out: "I'm going to give you a piece of advice" or, "Let me give you some input" Just avoid the “companion”, pick something like: “Let me share with you a belief (of mine)” and stick with it like it is the best thing since sliced bread. And yes, “forget about the distinction between "belief" as countable and "belief" as uncountable.” My two cents.

Your question is about the shape of the universe itself. Here are a few of the top ideas: https://phys.org/news/2019-11-universe-rethink-cosmos.html

Nice link. +1. One of the first imprints of sea animals strolling (or maybe hurrying) ashore is in so-called* Track Central, Kalbarri National Park, Australia. Silurian sea scorpions of the genus Eurypterid seemed to follow in the footsteps of other arthropods, Kalbarria. http://www.dmp.wa.gov.au/Trace-fossils-of-the-Tumblagooda-1667.aspx It's by no means sure that Kalbarria were the first animals, but those are the first traces I know of. Wonderful PBS documentary Australia's First Four Billion Years. * Non-official name, AFAIK.

We can already invalidate Yanchilans theory as we have already tested different gravitational potentials for time dilation at different elevations. With precision atomic clocks. Even testing it a distance of one foot. The results agree with GRT. https://www.nist.gov/news-events/news/2010/09/nist-clock-experiment-demonstrates-your-head-older-your-feet This isn't the only experiment done at different elevations. I assisted at a University that also conducted similar experiments as part of the course curriculum. Though we used the coastal mountains of BC coast. It was pointless publishing the results. Nothing newsworthy or unexpected.

The issue that I see with this thread is that I'm proposing actual implementable changes. To the Police Unions and Hiring/training practices, for example. Then we start to work on the DAs who bring up unfair charges on minorities. Saying the problem is systemic ( your meaning CY ) means the whole justice system ( and more ) needs to change, from cops, all the way to the Supreme Court. And we both know that's not going to happen; so nothing will change. The higher up you go in the justice system, the more political it is. And with your polarized two party system, who would even propose such a change, and hope to get re-elected ? Myself, I don't see the point of self-flagellation, and saying "It's all whitey's or the system's fault, and not trying to do something about it. People are dying needlessly, and all I'm hearing is blaming, but no solutions.

I suspect it relates to the alleged instances of people time travelling without the benefit of physical mechanism. The example that comes to mind is of the two visitors to Versailles early in the 20th century who seemed to be transported back to an earlier period where the people they saw and the layout of the gardens matched (allegedly) the late 18th century. Wikipedia article. There is also a silent movie era newsreel (?) in which a member of the crowd appears to be using a mobile phone. All of the instances have simpler, more convincing, mundane explanations, but its a useful plot device for stories.

https://www.geol.umd.edu/~tholtz/G104/lectures/104land.html