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No, that is what is called the 'naturalistic fallacy', also known as 'one cannot derive an 'ought' from an 'is''. But your title is another question: "Does science provide a path to a meaningful life?". In a very basic sense, every person striving for something, whatever, leads a meaningful life. It could be even unethical. But leaving that aside, people derive their meaningful life from many things: successfully raising kids, getting rich or powerful, help other people, making beautiful woodworking (how do I get at this example? I wonder...), trying to improve on their moral stance, trying to understand the universe... Which is science. Personally I think science can lead in another way to meaningful life, not just because one finds it 'interesting' or for the usage of its results in technology. Understanding the universe and our place in it can be a spiritual experience. I even once heard something like that from a theology student: he found the essence of religion the realisation that we are just a dust corn in the universe. Of course I like the factual way, as science goes, much better than a theological 'understanding', based on fantasies or old mythologies. And last but not least (being very subjective now), I would plead for studying philosophy. Not freewheeling philosophy (that is fantasy not necessarily with gods or magic), but philosophy grounded as well in science as in our daily experience. The nice thing of philosophy is that it brings all together: it contains also the reflections on what facts, values, and a meaningful life are. So philosophy in this sense is the highest endeavor a human can do . So, I think this was my most subjective posting in this forum.

The Calvin and Hobbes take on DEI - one of the most succinct

Degeneracy pressure is not a 'force', but the result of two quantum mechanical principles. The Pauli Exclusion Principle, which says each Fermion is allowed only one quantum state, and must obey Fermi-Dirac statistics, as Genady mentions above. They cannot be 'stacked-up' in the same state as bosons, which obey Bose-Einstein statistics. The other is the Heisenberg Uncertainty Principle. If you put a box around an electron, and keep shrinking the box, its position is determined more and more accurately. Eventually you reach a point where its position is determined so accurately that its momentum could be so great as to exceed c ; a physical impossibility. Nature gets around this problem by forcing electrons to merge with protons, to form neutrons. As the neutron is 2000 more massive than an electron, it is capable of exceeding the electrons momentum by 2000 times before running into the velocity being equal to c problem. This is evidwnt in type 1A supernova where a white dwarf star takes enough material from a companion star, that electron degeneracy can no longer support it against gravity, and it collapses to a neutron star, which is supported by the much greater neutron degeneracy pressure. This is the analysiss Subraihmanyan Chandrasekhar performed in 1930, during his boat trip to England, to study under Sir A Eddington ( who ridiculed his work ), and which today we call the Chandrasekhar Limit for electron degeneracy of white dwarf stars ) about 1.4 solar masses ).

Weird. Ever since the forced dispossession of 700,000+ Palestinians in 1947-8, aka the Naqba, the native peoples of that region have offered a real simple suggestion. Stop stealing people's land and kicking them out of their homes and razing their olive and fruit groves and systematically brutalizing them while forcing them into small enclaves of poverty. Stop the endless cycles of reprisal and repression. Allow a two state solution. Stop calling people who want their homes back terrorists and vermin. Stop carpet bombing and killing innocent civilians in vengeful and vicious ratios up to 40:1 to your own losses and then shrugging it off as collateral damage while you blame the victims. Really not a big secret. I am delighted to hear that you support the Palestinians in their ongoing struggle to gain those rights!

https://www.telegraph.co.uk/obituaries/2024/04/19/daniel-dennett-philosopher-atheist-darwinist/ Daniel Dennett, the American philosopher, who has died aged 82, was, with Richard Dawkins, a leading proponent of Darwinism and one of the most virulent controversialists on the academic circuit. Dennett argued that everything has to be understood in terms of natural processes, and that terms such as “intelligence”, “free will”, “consciousness” “justice”, the “soul” or the “self” describe phenomena which can be explained in terms of physical processes and not the exercise of some disembodied or metaphysical power. How such processes operate he regarded as an empirical question, to be answered by looking at neuroanatomy – the engineering involved in brains. Darwinism, to Dennett, was the grand unifying principle that explains how the simplest of organisms developed into human beings who can theorise about the sorts of creatures we are. In Consciousness Explained (1991), he argued that the term “consciousness” merely describes “dispositions to behave” and the idea of the “self” was nothing more than a “narrative centre of gravity”. In Darwin’s Dangerous Idea (1995) he went further than any other philosopher or biologist in arguing that the whole of nature, including all individual human and social behaviour, is underpinned by a Darwinian “algorithm” – a single arithmetical, computational procedure. Borrowing Richard Dawkins’s notion of “memes” (“bytes” of transferable cultural ideas encompassing anything from a belief in God to an individual’s fashion tastes), Dennett argued that the Darwinian algorithm also explained, for example, the musical genius of JS Bach, whose brain “was exquisitely designed as a programme for composing music”. Dennett’s philosophy undercut any idea of teleology or “purposive” creation....

I agree. The political right and maga-class has been getting beyond ridiculous in ostracizing people who refuse to tow the party line and repeat the lies, casting out anyone deemed to be "others." It demands a level of purity nobody can ever maintain, and it's pretty sad that their views can't hold up to even remedial scrutiny.

Jester's license in Germany: Zölle = Trade Tariffs Klima ... = climate change(?) Massendeportationen (?) = Mass deportations And no, Annex-Ionen are no ions of annex, but annexations It is said jesters say the truth... And yes, I am very angry and very worried. WW2 is forgotten...

As some of you may already know, the SFN server hardware is currently located in the UK. I will quote from what was announced to the staff: “This year the UK government passed a bill called the Online Safety Act. A brief description of the Act is set out here, but the tl;dr of it is that there are now a set of laws in place in the UK that put a duty of care on operators of social media sites in order to make them accountable for the things that are posted on those sites, which could be harmful to children and other users. The focus in the media has mostly been around the larger sites like Facebook, but actually, the act is extremely broad” The upshot of this is that a modest operation like ours can’t be hosted in the UK on servers run by SFN; the requirements are too onerous and no individuals should be asked to take on the liability should someone find that weren’t compliant in some detail. It’s not enough to think we’re taking the right steps, and we don’t have lawyers on retainer to make sure of things. (Small UK bulletin board sites might be shuttering by the end of this week if their owners are aware of what’s going on) Shifting to a hosting option that avoids this is moving forward. This might end up being completely transparent to our members and visitors, but Murphy always seems to pop up and invoke their law, so there might be disruptions. We will keep you apprised as more information becomes available.

If Zelensky has no, or few, cards to play that is solely because Trump has chosen to betray him and side with the aggressor in this war. So it is pretty rich for Trump to tell Zelensky he has no cards, when it is Trump who has taken them away! I actually think this dust-up in the Oval Orifice was a manufactured publicity stunt by Vance and Trump to try to weaken Zelensky personally, in the hope he will stand aside and allow a more Russia-friendly leader to replace him. That has always been Putin's desire. Putin wants Ukraine to hold an election (preposterously, in the middle of a war with parts of the country under enemy occupation) which he can interfere with and cast doubt on. This can provide a pretext for a further invasion later on if the new leader is insufficiently subservient to Russia. The row was televised and no doubt carefully selected clips will now be circulated to depict Zelensky as ungrateful and unreasonable, when he has been fighting for the life of his country for the last three years, against a massively powerful foe. Trump has furthermore overturned the entire military posture of the USA since WW2 in the European theatre. He has wrecked the deterrent value of NATO, which has been the centrepiece of military strategy ever since WW2. This leaves Europe exposed to military conquest by Putin's revanchist Russia. It is absolutely plain now that Trump and Vance are Russian stooges, wanting to carve the world up into spheres of influence without regard to borders or law. It is also plain that they hate the EU deeply and want it to fail. What better way of achieving that than to neuter NATO and thereby encourage Russia to nibble off bits its eastern frontier, sapping its energy and resources? Meanwhile Vance and Musk try to destabilise it on the political front by encouraging far-right authoritarian movements. The USA is now, suddenly, the adversary of Europe, not its ally. "The West" is now dead. What we have now is the free democracies vs. the rest. Those comprise the EU, the UK, Canada, Australia, New Zealand, Japan and a few others. The USA is not a member of this group.

It's good, but it needs more accordion.

He’s Nazi. The salute, numerous anti-semitic remarks, promoting nazi apologists, appearing at an AfD campaignevent.

The Einstein tensor describes a certain aspect of overall spacetime curvature, in the sense that it determines the values of a certain combination of components of the Riemann tensor (it fixes 10 out of its 20 independent components). But unlike the Riemann tensor, it is not a complete description of the geometry of spacetime. Thus, the Einstein equations provide only a local constraint on the metric, but don’t determine it uniquely. Physically speaking, mass and energy have of course a gravitational effect, but neither appear as quantities in the source term of the field equations - there’s only the energy-momentum tensor field \(T_{\mu \nu}\). Here’s the thing with this - the Einstein equations are a purely local statement. So for example, if you wish to know the geometry of spacetime in vacuum outside some central body, the equation you are in fact solving is the vacuum equation \[G_{\mu \nu}=0\] which implies \[R_{\mu \nu}=0\] There is in the first instance no reference here to any source term, not even the energy-momentum tensor, because you are locally in a vacuum. During the process of solving these equations, you have to impose boundary conditions, one of which will be that sufficiently far from the central body the gravitational field asymptotically becomes Newtonian; it’s only through that boundary condition that mass makes an appearance at all. Only in the interior of your central body do you solve the full equations \[G_{\mu \nu}=\kappa T_{\mu \nu}\] wherein the energy-momentum tensor describes the overall distribution of energy density, momentum density, stresses, strains, and shear (note that “mass” is again not part of this). By solving this equation along with boundary conditions you can find the metric. You can work this backwards - you can start with a metric, and calculate the energy-momentum tensor. But here’s the thing: if the tensor comes out as zero, this does not mean that there’s no mass or energy somewhere around, it means only that the metric you started with describes a vacuum spacetime. If it’s not zero, you’re also out of luck, because the energy-momentum tensor alone is not a unique description of a classical system. Knowing its components tells you nothing about what physical form this system actually takes - two physically different systems in terms of internal structure, time evolution etc can in fact have the same energy-momentum tensor. That’s because this tensor is the conserved Noether current associated with time-translation invariance, so what it reflects are a system’s symmetries, but not necessarily or uniquely its physical structure. There’s no unique 1-to-1 correspondence between this tensor and a particular configuration of matter and energy, since all it contains are density distributions. IOW, a given matter-energy configuration will have a unique energy-momentum tensor associated with it, but the reverse is not true - any given energy-momentum tensor can correspond to more than one possible matter-energy configuration. Thus it is not useful to try and define matter-energy by starting with spacetime geometry. Yes, they are of course closely related, but the relationship is not just a trivial equality; there’s many subtleties to consider. A zero cosmological constant does not imply a static universe, only that expansion happens at a constant rate. Matter and antimatter have the same gravitational affects, they are not opposite in terms of curvature.

Uhhh, it only mentions one aspect that could be a liberal policy and that would be I mean, if trying to get folks equal rights results in autocracies, I would imagine that the democratic principles ain't that strong to begin with. Also I find it very interesting how that is phrased. Right-wing conservatives have worked very had to undermine democratic principles ranging from spreading blatant misinformation to incite culture and race wars, forming think tanks and societies that undermine checks and balances and putting anti-democratic forces into key positions, sowing mistrust into systems and also attempting the odd coups. And yet it is somehow liberal policies that caused all that? I mean come on, at least try to find Ockham's razor here. I will also note again that part of the autocratic playbook is to blame others for their actions. "Look what [they] make me do? Because of them I just had to overthrow democratic principles and build concentration camps. And taking away your rights is the only way to protect you from [them]." This has been best explored in fascism, where fascination with victimhood served as justification for the committed atrocities (and it is a common element in the identification of the rather diffuse characteristics of fascism). Also, how about I cite a few points from the book you mentioned and see if you can spot some overlap (BTW the book was published sometime around the first Trump administration): Why do we have something as stupid as the culture wars? Because some kind of enemy had to be found. And in recent times our lives have to be become so comfortable that folks decided to make up enemies and/or revive old tropes, such as immigrants. Again, there are no new ideas here.

The other day members of the EDL (English Defence League) came to our city to try and extend their campaign of racial violence and anti-immigrant slander in the wake of the Southport killings ten days ago. You may have read about this recent wave of violence across the UK, including a riot in Liverpool the other night where thugs burnt down a local community hub and library in Liverpool because some posts on social media had spread a lie that all the books in the childrens section of the library had been replaced by copies of the Koran - (they hadn’t). When they arrived in our city however, the EDL supporters got a surprise. They had intended to attack a Mercure Travel Lodge that was allegedly being used to house asylum seekers, but they found themselves outnumbered 4-1 by a well organised protective cordon of counter-protesters and local community leaders who were also protecting our local mosques and LGBT sites, and who successfully held the racists at bay until the police belatedly arrived to stop the EDL from setting fire to the Travel Lodge. https://www.bbc.co.uk/news/articles/cvgrrl0zlg5o The following day I met a female friend and lawyer on our local village green who said “Are you coming to the protest tomorrow ?” When I asked for details, she told me that the EDL were now planning to attack the premises and staff of law firms in our city centre who regularly assist asylum seekers (often on a pro bono basis). There is apparently a hit-list of such law firms circulating on far-right Telegram channels. https://www.bbc.co.uk/news/articles/c624r77gnm2o The Playboy of The Western World (1907) was the title of a play by the Irish playwright John Synge which tells the story of a braggart who falsely claims to have murdered his own father. It came to mind as a suitable epithet for Elon Musk - the CEO of SpaceX, Tesla and X (formerly Twitter) who has recently restored the X accounts of notorious UK hate speech trolls such as Tommy Robinson (EDL co-founder who recently fled the country), Katie Hopkins, and the violent misogynist Andrew Tate. https://www.independent.co.uk/space/elon-musk-tommy-robinson-prime-minister-southport-spacex-b2590114.html Within the last day or so, Elon Musk has put up incendiary posts on his X platform claiming that “Civil War in UK is now inevitable” and has also attacked our new PM Keir Starmer for disputing the accuracy of these irresponsible claims. According to Sky News, Elon Musk is now also planning to sue major companies for “Conspiring to withhold advertising revenue from X/Twitter” and causing it to miss out on billions of advertising revenue. https://news.sky.com/story/its-war-elon-musks-x-sues-companies-for-not-advertising-on-its-platform-13192318 The reality is that many large corporations stopped advertising on X after finding their adverts were being run in tandem with blatantly neo-Nazi and racist content - which happened as a direct result of Elon Musk gutting the staff at X, and removing most of the content moderation procedures that were formerly in place. The Playboy of The Western World” indeed ! - welcome to the land of consequences Elon.

The more physics one studies the more interconnected one realizes different theories get +1

True master of one-liners. The one about dating cracked me up!

I have a question too. We are a science forum, and only deal with the scientific ramifications of religion. Wouldn't Night FM be better served asking these questions of his pastor/priest/rabbi/iman/etc. ? I, for one, am getting tired of faith based questions on a scientific, evidence based forum. There are more appropriate places for these types of inquiries.

I would be careful to assume that everyone critical of Israeli actions have the same stance. I think most (though likely not all) are alright with targeting terrorist leaders. While there is an ethical argument regarding killing in general, there is an underlying assumption that eliminating those threats will overall lead to less deaths and misery as a whole. The issue (to me at least) is how many collateral deaths are acceptable. 9/11 led to a proliferation of conflict in which almost any number of civilian deaths were justified as retaliation. This specific attack seems to be more targeted (hence my question) and while innocents were injured, it seems to be me at least less bad than bombing centers were Hamas are holed up with civilians. Sure, one can argue that Hamas is to blame (and they are) for using civilians as protection. Conversely, I still there is a moral cost to make knowingly killing those civilians. These are not simple issues where you can just point to some original sin to justify all associated costs. Each action (again, on either side) has a moral cost. And I do think that it is dangerous to justify, without limits, actions of any one side, just because the other is worse. Conversely, if one think that is justified, one has also to accept that without limits, these action will include the indiscriminate destruction of lives. We know that Hamas is fine with that. But I don't think that Israel should stoop down to that level. The reason why there are more expectations to Israel are, similar to the US, they are supposed to be the good guys. I think interviews from the holocaust survivors provides much needed context, where they on the one hand see Israel as a refuge from persecution, yet at the same time see eerie similarities in the Palestinian plight. There are a lot of articles, following events like 9/11, as well as in Europe after surge of antisemitic and anti-Muslim sentiments. Of course they are not uniform, but I do think that their experience and insights are critical on multiple levels e.g., https://www.npr.org/sections/goatsandsoda/2024/01/30/1227849885/a-holocaust-survivor-identifies-with-the-pain-of-both-sides-in-the-israel-hamas-

I think it's unethical to use legislation to ban lab grown meat because rich people in the cattle and ag-community pay off and heavily pressure their congress people to do so (not due to any genuine health risks). Same for the treatment of nut milks bc the dairy industry doesn't like it.

This argument would hold more weight if we weren't witnesses to the lengths Israel has gone to in their cleansing efforts. Ever since its creation, Israeli policy has been to keep punching their neighbors in the face, then overreact when that neighbor punches back, hopefully gaining a little more territory in the process. It's Middle Eastern Jim Crow strategy, designed to oppress while subjugating. American conservatives taught them well, just keep your foot on their throats and tell everyone you have to keep kicking them or they'll hurt somebody.

As I was leaving the art museum, I got arrested for stealing a painting. I don't understand. Earlier when I asked the guide if I could take a picture, he said yes.

Just before this thread gets ditched, can I just ask how many of our transatlantic cousins are aware of this?

I completely agree with @TheVat. The idea of 'truth' makes no sense if we do nor relate to an objective reality. Our scientific theories are about something. And they can be wrong, or true, in their (limited) domain. The earth never was flat, we know that. A majority believing that is was (is) may have reasons to think so, but it is, and was never true. For me the expression 'my truth' makes no sense: the word 'truth' implies that it is claimed to be the case for everybody. We dis-cover reality. Maybe not as it is, but as a map of reality. If we behave according to the map, e.g. find our way to the Eiffel tower, and we get there, then the map was 'true'. There may be much left out from the map, but the map expresses at least some true aspects of reality. Science is not just a 'narrative', as many post-modernist philosopher liked to say.

This is the dominant definition of truth in the past century - that truth is by definition statements that correspond to an objectively determinable state of affairs in the world. The basic idea of the correspondence theory is that what we believe or say is true if it corresponds to the way things actually are – to the facts. This idea can be seen in various forms throughout the history of philosophy, but it really got serious traction with folks like G. E. Moore and Bertrand Russell. So you're in pretty good company, and I would say the correspondence theory has generally been adopted by scientists. 8 billion people may entertain myriad beliefs but those cannot gain the status of truth, or true statements, unless they correspond to objectively determined facts. E.g. "I see the light is red," is subjective, but "Anyone who measures the light finds its wavelength to be 650 nm," is true because it does not change due to variations in human perception, i.e. it corresponds to a fact external to a particular perceiver. Beliefs can change. "The earth is flat" was a belief that eventually was shown not to match the reality. So it was never true, because the earth has always been an oblate spheroid. The truth has not changed with respect to the earth, our beliefs have. Now our beliefs correspond better to the fact that the earth is round. But the truth was always what it was - in that sense, it is objective, because it doesn't "care" what we believe. The epistemological goal of humans is to improve our perceptions and measurements and inferences from them to get closer to the truth - the objective reality outside our heads. Were this not the case, no one would bother with science or philosophy and we would bow to chaos. To reiterate, there is no such thing as "my truth." Truth, by its definition at least since the Enlightenment era, is that the truth is out there in the world and not something that only corresponds to one person's belief system. I keep hammering on this because I see many people veering towards solipsism (as Moon mentioned) and the incoherent notions of personal truth or alternative facts. If it's personal, and only personal, then it's an opinion or a belief or a conjecture or a feeling. Not a truth.

My opinion of him went down considerably when I learned he has tried to rubbish philosophy: https://whyevolutionistrue.com/2014/05/20/pigliucci-pwns-neil-degrasse-tyson-smbc-teases-pigliucci/ He doesn't seem to understand that science is both rooted in philosophy and poses philosophical questions. So I suspect he's a bit shallow. I'm sure he knows his science but I would take anything he says about other matters with a pinch of salt.

A marine algae and a nitrogen fixing bacteria have officially teamed up and the bacteria has become a new organelle inside a marine algae. The teaming up of nitrogen fixing bacteria and plants Is not a new (Azolla carolinensis) is one but the bacteria is just in a communal relationship with the plant but this bacteria has actually become an organelle inside the algae cells much like mitochondria or chloroplasts in other cells, this new organelle has been dubbed Nitroplast. https://newscenter.lbl.gov/2024/04/17/scientists-discover-first-nitrogen-fixing-organelle/ I am remembering reading of another animal that has evolved something similar that allowed it live in anoxic water in the black sea. If I remember correctly it was a ctenophore, anyone remember this?

This is sad news. He was one of the great philosophers of our time. He belongs to one of the most science oriented philosophers and one of the most honest thinkers I have known during my philosophy study. He didn't spare anybody with too naive ideas, be it materialistic or dualistic, but he always was kind, never attacking people personally, but critical reflecting on their ideas. He was able to show that it is possible to have a theory of consciousness, without leaving a physicalist ontological stance. Many people thought that his book 'Consciousness Explained', should have been titled 'Consciousness Explained Away', but I certainly do not agree with that. Consciousness exists, but it can be explained. Same for free will. He could explain how a personal and societal relevant concept of free will can go perfectly together with determinism, where others keep sticking to either 'magical free will', or denying free will altogether. In his broader ideas, he was an atheist and humanist. I do not know much about his personal life, but at least I know he also knew how to enjoy the pleasant sides of life. Enjoyer of (red?) wine, making his own cidre, harvesting the apples himself. I remember I once saw a video, where he was sitting on his tractor. I think he lived a very fulfilled life. We should all be glad that he lived his life as he did. I will miss the many new ideas he could still have found, even in his higher age. A loss for the philosophical world and many other people who are, and might still be, inspired by his thinking.

A few things should be added to lay the foundation for further discussions. First gonochorism (the term to describe a sexual system where there are male and female members) does not always have to be linked to sexual dimorphism (the term to describe differences in appearance between male and females of a species). Sexual dimorphism is often a consequence of the respective reproductive strategies. Among hermaphroditic species, one can actually also distinguish between various forms. The one OP is thinking about is considered simultaneous hermaphroditism, i.e. all individuals producing sperm and eggs, but there are also species who are sequential hermaphrodites. I.e. producing egg or sperm at different points in their life. Studies trying to figure out fitness benefits have been investigating closely related species in which all three strategies are found, e.g. in certain worms. Here, it was found that the different species had different reproductive characteristics, that likely have benefits under different conditions. Generally, they found a trade-off between fecundity (how much they reproduce) and survival. Simultaneous hermaphrodites had the highest survival rate, but least fecundity (and smallest eggs, indicative of lower maternal investment), whereas the opposite was found for sequential hermaphrodites. The gonochoristic species was somewhere in-between. Taking that all together (survival rate, reproduction over total life cycle etc.) it seemed that the dichoristic species had overall the highest fitness. They had higher fecundity in the early stages of life cycle. They outperform simultaneous hermaphrodites, which have lower fecundity. While sequential hermaphrodites are more fecund, they are delayed until their female phase, and during the whole life cycle they are not able to compensate the early advantage. Essentially they are able to reach sexual maturity faster, likely as they only need to produce one form of gametes. The disadvantage of that gonochoristic species pay is that they produce males, that cost the same as females (as eggs) but do not directly contribute to future generations (the limiting factors are the eggs). Hermaphroditism is speculated to be a primary advantage when population densities are low and it is difficult to find a mate. There are also evolutionary developmental consideration. Transition from hermaphrodite to gonochoristic species is comparatively easy, as it could be reasonably executed by suppressing the development of one sexual function. Conversely, there are more steps involved in transition from gonochorism to hermaphroditism. I.e. once gonochorism outcompetes hermaphroditism in the evolutionary history of species, it is very unlikely that they hermaphroditism will develop, even if it became more advantageous.

Don’t be a jerk. The issue has been explained to you. The precaution of recalling the product is perfectly sensible as there is a risk, to immunocompromised users of the product, if to no one else.

I use it in the formal sense as defined in differential geometry, ie as a structure that allows you to meaningfully define the inner product of tangent vectors at points on the manifold, which in turn gives a meaningful notion of lengths, angles, areas and volumes. Yes. You need to be careful here - the Christoffel symbols and the connection are not the same thing. A connection allows you to relate tangent spaces at different points on the manifold to one another, ie it provides a notion of parallel transport. This is quite independent of any metric, which is to say you can meaningfully have a manifold that is endowed with a connection, but not a metric. The Christoffel symbols then give you the connection coefficients, ie they tell you what effects your connection has in a particular coordinate basis. They do this by describing what happens to basis vectors as you transport them between neighbouring points, which is something you can calculate from the metric and its derivatives. Without a metric you can still do parallel transport, but you can’t tell what happens to lengths and angles when you do it. Long story short - you can have a connection without a metric. See above. Having a different metric changes the Christoffel symbols (they are not tensors!), but not the connection. Ok, but in the context of physics (SR/GR) the term “metric” is most often used in the differential geometry sense. Physically speaking, equivalence then means a diffeomorphism, so that both metrics describe the same spacetime and thus physical situation. But here’s the thing - as explained above, you’re still on the same manifold endowed with the Levi-Civita connection. By changing the metric like this, you’re doing one of two things: 1. You’re describing a different spacetime, ie a different physical situation, since the two metrics aren’t related by any valid diffeomorphism; or 2. You’re describing the same physical situation, but the coordinates you are using no longer have the same physical meaning. I think what you are trying to do is (2). But the thing is that now measurements on your mathematical manifold (ie in the model) no longer correspond to measurements in the real world, so anything you calculate from this - eg the length of a world line - must first be mapped back into suitable physical coordinates to compare them to real-world measurements. Such a mathematical map may or may not exist, depending on the specifics of the setup. This will also change the form of physical laws, so all the various equations etc will be different for each choice of transformation you make. In either case, this creates a lot of additional work and confusion, for no discernible benefit. It would look for differences in the outcomes of experiments if you vary direction of relative motion, as mentioned previously. For example, if a uranium atom decays if you move it in one direction, but doesn’t decay if you move it at a 90° angle to that direction (everything else remains the same), then you have anisotropic space. This has nothing to do with conventions.

Anyway, it starts now here.

This morning I saw a video of a man who voted for Trump because he wanted to kill Obamacare but now he is angry because he is unemployed and realized the ACA he depends on for his healthcare is Obamacare. I never thought leopards would eat MY face, sobs woman who voted for the Leopards Eating Peoples Faces Party.

@Albert2024, @JosephDavid, and the other guy, Let's hammer it home again. At some point somebody among you will understand (one can only hope). No vacuum in QFT has external legs. The vacuum in QFT is made up of things that look like, This means, in a manner of speaking, that the amplitudes (infinitely many of them) go from nothing to nothing. The vacuum state gives zero as expected value for the number operator of each and every particle. That, people, is what we call a vacuum. And thereby the name. A vacuum ultimately has nothing in it, except for amplitudes of something appearing there, and swiftly disappearing, according to quantum rules (HUP). Vacuum = nothing. Doh! OTOH, In the diagramatics of QFT, the "vacuum" this "paper" seems to be talking about would look something like this, That is, it has external legs (real particles that go from \(t=-\infty\) to \(t=+\infty\). In the picture I've represented a triplet of SU(3). It could be an octet, or whatever. Maybe not even an irreducible rep. of SU(3). What have you. It would have ramifications displaying vacuum polarisation, and so on. The point is: This is no vacuum. These "atoms" are there, and they keep there. Do you understand? Do you? Really? Do you, at long last, understand? Precision tests of the standard model would have detected this background (rather than vacuum) long ago, because other particles would scatter off these "atoms" copiously (among other things they would have to be 1043 times more abundant than nucleons and electrons, and 1033 times more abundant than photons. So, presumably, your beloved paper has been turned down experimentally ages ago. Remember this comment, which you also chose to ignore?: Maybe it's another completely different SU(3) gauge group, with its own coupling constant and all. You tell me. I don't have to read the article, as per SFN rules. If my arguments are wrong or misplaced, then answer them, instead of cajoling each other with idle pleasantries and even idler reputation points, plus meaningless punishing -rep points, as @Mordred pointed out. And that will be all, unless you finally come up with real counter-arguments from physics. Bye.

No, it's not the accelerations at the start and finish of the journey that's responsible, but the acceleration in the middle corresponding to the travelling twin's turnaround. An interesting approach to the twin paradox is to consider not time dilation but Doppler shifts. While each twin is seen to be moving farther from the other, they appear redshifted, but while each twin is seen to be moving closer to the other, they appear blueshifted. However, the two twins do not see each other symmetrically. For the stay-at-home twin observing the travelling twin, the change from redshift to blueshift occurs after the light from the travelling twin's turnaround has reached the stay-at-home twin. But for the travelling twin observing the stay-at-home twin, the change from redshift to blueshift occurs immediately at the travelling twin's turnaround. Thus, the travelling twin sees the redshift and blueshift of the stay-at-home twin for equal times, whereas the stay-at-home twin sees the redshift of the travelling twin for a longer time than the blueshift.

Observed on my recent trip to Scotland:

If your intent is not merely to stir the pot as so many thousands of good little Chinese and Russian trolls are doing right now across the internet in a directed attempt to sow division and discord during a US presidential election, then you should clarify what discussion you wish to have here around this.

Avoiding threads with exchanges such as these

It’s not all that broad of a brush. White Christian Nationalists (White+Christian+Nationalist) is the intersection of three groups. It does not imply that all whites, or all Christians, are nationalists.

Sounds like the replies we hear like “all lives matter” in response to reminders that “black lives matter.” It ignores the underlying baseline and status quo where equality is very much not already present. Is mental health important for all? Of course! Are there reasons mental health might be harder for women? Of course! When’s the last time you had to accept 80 cents on the dollar for the same work? When’s the last time you got accused of being a DEI hire or slut shamed and accused of sleeping your way to the top even though you were twice as smart and worked twice as hard as everyone else? When’s the last time you had to question whether it was safe to be alone at a gathering where everyone else was a different gender from you? Yes, mental health for all is important, but not everyone is working from the same starting position. See also: Hatred and violence shown toward LGBTQ communities. There’s good reason we tend to focus more on mental health for them than middle aged entitled white men with a fluffy 401K. https://morganemichael.com/for-educators/middle-school-resources-grades-6-8/privilege-and-empathy-lesson-how-your-socio-economic-position-impacts-how-well-you-do/

I don’t know why people are surprised that Trump cheated death at his rally. Cheating is something he’s really good at.

Not missed out but it doesn't stand out as an option except in the sense that at small scale it would be the easiest to attempt using existing technologies. According the the Nuclear Devices for Planetary Defense link (included in the quote I used - KI being Kinetic Impactor) - 605 metric tons is a LOT of mass to launch, far beyond existing capabilities. And (if I understand it) high speed impacts shed a lot of energy as heat and explosively, not all will be delivered as changed momentum in line with the direction of the impact. Not necessarily a problem and possibly advantage if sideways deflection does it better. I still look at meteorite defense as a longer term challenge; yes one could be identified tomorrow but the odds favor not. In terms of odds a too ambitious "being prepared" program could look like waste - Note that this looks at risks from objects within the solar system - there remains the possibility, if very low likelihood, of large objects from outside the observable solar system.

Assume you and I are prehistoric people who have no idea the Earth is round. We are both at the equator, but separated from each other by a couple of thousand miles along it, and we decide to do an 'experiment'. We both head due North, and after several hundred miles of travel, we notice that our lateral distance has decreased considerably. The farther north we travel, the faster our lateral distance decreases, until finally, at a place with the signpost "North Pole", we crash into each other. So what do we conclude from our 'experiment' ? Some mysterious 'force' seems to be drawing us together, and this 'force' seems to act without any connection between us. Now all this is due to the fact that prehistoric peoples didn't know they were living on a curved surface. We present day people, know the Earth's surface is curved, so we don't come to such foolish conclusions. But what if it isn't just two dimensional surfaces that can be curved; what if both space and time comprise a manifold that can be 'warped' or curved by the configuration of the energy contained within it, whether that energy is in the form of mass, momentum, stress, or even pressure. It seems some of us are still foolish enough to make those assumptions, and wonder what is connecting the two bodies drawn toward each other, when the 'path' ( known as a geodesic ) is simply constrained to the 'lay' of the land ( known as a 4 dimensional space-time manifold )