joigus

Naked mole rats are not really rats, and they're not just any mammals: (Wikipedia) Sharks are also very resistant to tumours. I don't know what this has to do with beauty, but it does have a lot to do with the unexpected. Nature is truly amazing.

I hesitate to hesitate.

He's the only one who's objected to the beauty standards of this thread. But he didn't mention any wars...

As always, we should ask the beholder. https://en.wikipedia.org/wiki/Naked_mole-rat I think they are. But I'm no expert on beauty. Let's ask @MigL.

Are those naked mole-rats?

OK. I would like to make it up to you all for having posted that beautiful but non-legit picture. A real tepui (mount Roraima in Venezuela): https://en.wikipedia.org/wiki/Mount_Roraima The extraordinary plants of mount Roraima: https://www.bbc.co.uk/programmes/p00lx3pb Lack of nitrates in mount Roraima is due to heavy rain, that washes away all the nutrients. BTW, I strongly recommend BBC's The Private Life of Plants. Enjoy!

Well spotted, @Ghideon!! My bad. I didn't give it a second thought. You really have an inquisitive spirit. Keep it up, is all I can think of saying now. 😮

Oh boy, I didn't see those. You're right; they look human made...

Karsts are amazing. Experts will tell you more and better, but they basically consist of sedimentary rocks formed by many millions of years of deposition, made up of carbonate-rich substance from scheletons of marine animals; and later eroded by water. I suppose that those column-like features come from particular locations where the rock is less soluble in water for whatever reason. Differential erosion is the key. Very nice picture. You always post a picture you took yourself. That's even more valuable! Thanks. +1.

Roughly, @MigL's point was that every thought that you have is influenced by the history of how that thought was formed. Whether you like it or not, your thinking is influenced by the thinking of those that came before. Again roughly, @studiot's point was that even the most apparently obvious statements are presumably 'contaminated' by hidden assumptions. (I think) More arguments have cropped up, and I'm finding difficult to keep up with all of them, but what I can say for the time being is that I do not think the question of reality affects very much the activity of scientists. Perhaps it's just a matter of stance. Some scientists may believe that there is an ultimate reality to be discovered and described; others --most scientists today-- prefer to think that science is about elucidating in more and more detail how Nature works. Physical theories should be --and are-- the same and be used in the same way no matter what stance one adopts. Concepts like 'reality' are more of an --occasionally inspiring-- philosophical motif for some than the reflection of an actual professional commitment to a goal. And may I remind you 10 million light-years from any of them, both Frank Sinatra --the singer-- and a poached egg are the same: a pointlike particle of approximately the same mass.

Promised. But it'll take some time until I sort my ideas. The yolk was too tempting.

This morning I've had Kant for breakfast. It was noumenal! Brilliant.

Ignore my answer on thread "Four-vector" and follow this excellent tip by Markus. Studiot's recommendation looks fine. It's just that I'm not familiar with it. The simpler toys to play with are called "affine tensors". They do not depend on the point of space you're considering. Special Relativity is the place to start --> nothing depends on the location. Then make tensors depend on the point of space --> tensor analysis. You will become familiar with a monster called "the connection", and "the Riemann tensor" and everything else come from that "connection".

Tensor analysis. A very complete classic book of which affordable paperback editions exist: https://www.amazon.es/Tensors-Differential-Variational-Principles-Mathematics/dp/0486658406

(My emphasis) Interesting. But what are you going to do with all those diffeomorphisms? Differentiability is hard-wired into GR.

Sure, if you're interested. Let me PM you as soon as I have the time to write some words to explain what it's about. It would be quite off-topic and improper here.

LOL. That's a different bundle, and includes non-orientable surfaces. Very interesting stuff, and very relevant in gravitation, by the way. I did learn about those quite a bit. Yeah, I know who AJB is. It would be nice to have him around. I also miss @Markus Hanke, of course. I know he takes a peek sometimes. LOL. Thanks. I did manage to peer-review publish some of my speculations long ago! Not very noticeable though... or noticed perhaps. I do teach physics, but on another level.

Sorry, I misunderstood. It was Hume precisely who was there to open our eyes, wasn't he? Somehow I saw a colon there.

Most likely my mistake... Could you elaborate?

Yes, I'm a physicist by training, but I don't work as one. I only play one on social networks. Although I'm more up-to-date than quite a number of your average physicists out there. Through my years I've learnt to deeply mistrust the term 'real' and what it whispers to my ear, so to speak. I prefer less exalted terms, like 'objective'. To me, a lambda hyperon, which has a lifetime the order 10-13 s, is no less, no more real than a cloud, or a bee. It's very clear in my mind that it's more fundamental, simpler, less 'composite' than a cloud or a bee. But as doc said, at some point the word is not gonna cut it. Even for the cloud: Is it two clouds, or just one? A moment ago it wasn't there. Now it's come back at about the same position. Is it the same cloud? Well, yes. There's no guarantee that unification is possible. If it doesn't turn out that way, tough luck; but we must accept it. Somehow it seems hard to believe that the unification program will continue just up to a point, and then stop. I wouldn't invest too much on the concept of force. @MigL before proposed the more encompassing term 'interaction'. And @DrDon explained very clearly the limitations of such concept. The mathematics of physical theories is far less ambiguous in this respect. To me, whenever you have a system with coordinates X, another with coordinates Y, and and a coupling term involving X and Y, that's an interaction. It produces scattering, decay, etc. But again, words are very limited. Example: the cosmological constant: It is no doubt gravitational, but is it a force? An interaction perhaps? I don't think you can call it 'interaction' in any reasonable sense. I wasn't aware of this. I'll look it up. I find it very intellectually enticing. Thanks a lot. I'm very nearly philosophically illiterate. --Blush

I think the word we're all fumbling for here when we say 'reality' is in fact 'ontology'. One of the most important lessons of 20th-century physics is, I think, Nature doesn't care a great deal about our entities. I think @swansont, @MigL, @beecee, and myself; and perhaps most eloquently @DrDon have drawn arguments along these lines. Nature is probably connected all the way down to the most fundamental level. That's why such a thing as unification of physical laws is possible in the first place. But distinctions emerge. It is the business of physics to elucidate what connections/distinctions appear/disappear, and when (at what scale) they are relevant. Entities don't present themselves as 'solid' immovable categories; rather, as useful instruments for the scale of description given. Terms as bosonization (a fermion can be seen as a pair of bosons with a 'twist' between them), dualities (a strongly-coupled interaction in one region of space can be seen as a weakly-coupled one on the boundary of that region) etc., strongly suggest that any entities that we may propose are simply instrumental, and what emerges as really robust are physical principles, patterns, rather than 'things'. Lorentz invariance, locality, unitarity, symmetries and conservation laws. Those are the main characters in this play. Weinberg was a master at bringing out how they interplay. Einstein was one of the most brilliant theorists of all time, but this revolution caught him at a point in his life when he was already too set in his --ontological?-- ways. Weinberg was able to take home the lesson much more efficiently for what the 2nd half of the 20th century physics needed. Maybe nothing is, and everything emerges, in some kind of bootstrap mechanism of substantiation of entities in a grand cosmic scheme of which the building blocks are actually patterns and principles, and not things. --I'm getting blah, blah. I'm also glad that professor Lincoln has spent some time among us, be it ever so briefly.

Steven Weinberg was a great physicist. Einstein was too. Both have been highly influencial. But I think it's fair to say neither of them are very good at representing the "standard view" of their respective generations. Couldn't agree more. We're asymptotically going into meta-physics and epi-stemology.

I will have to insist on @Phi for All's point here. I thought I'd said something on this thread. I must have dreamed it. I do remember skimming through your initial post, pondering about saying something, then re-reading it, and then probably telling myself: "say what about what?"

Re-reading myself I realise I didn't explain at least a couple of technical terms, so I'm sorry. Horizons: Surfaces in space-time that separate regions of space-time that are inaccessible to observers on one side of those surfaces Renormalization: Treatment of a physical problem taking into account how it depends on the scale at which you study it Entropy: A variable that measures lost information; physical information that gets scrambled Gravity is peculiar on all of these accounts. Other 'forces' don't have horizons associated with them. They're not scale-dependent, like gravity is. This is the meaning of 'bad-behaved'. Other forces don't have an "intrinsic" entropy. Gravity is not so much a weak force as it is a scale-dependent force. That is, whether it's weak or strong depends a lot on the scale at which you look at it. It's actually the dominant force at scales that approach a Planck's length worth of distance. At stellar distances gravity becomes relevant again, but not because of scale-dependence. Rather, because gravity cannot be screened. Gravity also has a cosmologically-relevant component, which is the vacuum energy. Gravity is peculiar in many senses. So, whatever a force is --I'm with other users here that whether it really is this or that verges on metaphysical--, gravity is very different to the other bunch. It's the odd one out. I really hope that was helpful, but it's a difficult topic. Other users express themselves more eloquently than me. And welcome to the forums.

Wave functions of stationary states work pretty much as the density/current of a stationary fluid. Consider the flow lines of a fluid in a stationary flow state. At every point in the fluid, the velocity field is well defined, has a direction and a speed, even though nothing seems to be moving on the whole. More mathematically: If your stationary state is represented by wave function \( \psi_{n,l,m,s}\left(\boldsymbol{x},t\right)=e^{-iE_{n,l,m,s}t/\hbar}\Psi_{n,l,m,s}\left(\boldsymbol{x}\right) \), your 'cloud' of probability would be independent of the time-varying phase factor: \[ \varrho\left(\boldsymbol{x}\right)=\left|\Psi_{n,l,m,s}\left(\boldsymbol{x}\right)\right|^{2} \] The whole situation would be static, and yet, it would have an associated velocity field, which mathematically is given by the Fourier transform of the amplitude, \[ \hat{\psi}_{n,l,m,s}\left(\boldsymbol{p},t\right)=\frac{1}{\left(2\pi\hbar\right)^{3/2}}\int d^{3}xe^{i\boldsymbol{p}\cdot\boldsymbol{x}/\hbar}e^{-iE_{n,l,m,s}t/\hbar}\Psi_{n,l,m,s}\left(\boldsymbol{x}\right)=e^{-iE_{n,l,m,s}t/\hbar}\hat{\Psi}_{n,l,m,s}\left(\boldsymbol{p}\right) \] So the distribution in momenta doesn't depend on time either: \[ \varrho\left(\boldsymbol{p}\right)=\left|\hat{\Psi}_{n,l,m,s}\left(\boldsymbol{p}\right)\right|^{2} \] This is only valid for stationary states. I hope that answers your question. It's good to see you around.