joigus

You need a mechanism to explain why those excess neutrinos are there, and why they are decoupled from the rest of the matter. The attribute "relic" only says that they are remnant from the big bang. Nothing more. So what you said is a bit like saying "maybe the murderer is any old person, instead of that particular suspect" in a murder case. You see...

Was this of any help at all?

Plants react to light by means of certain chemicals like phototropins and such. They are a certain kind of proteins. That's how plants know in what direction to tilt when light comes from a very particular direction, as well as when to trigger growth, if I remember correctly. Maybe this is a topic more for the likes of @CharonY? Some animals have eyes that are only barely sensitive to light's direction and intensity, and not much else. Animals with more developed eyes, like most vertebrates, except a few which live underground or in complete darkness for some reason or another, have eyes that are a dioptric apparatus, which maps object points into image points consistently (preserving geometric relations for neighbouring points and therefore allowing the mapping of objects with spatial extension). (Dioptric is optical jargon for "lens". Catoptric is optical jargon for "mirror".) Plants have neither dioptric nor catoptric systems. So I suppose what I mean is, if we could say in some sense that a plant "sees" something, it would be a very different way of seeing than ours. Something like "hmm, there's light in that direction, let's tilt and grow". But light is what it is. As everybody's telling you: photons, quanta of the electromagnetic field.

There. +1 from me. I hadn't seen this. What good are algorithms? I think I've watched all of his online talks on YT, and the algorithm can't figure this out? My favourite Dennett tool is the intuition pump. It's the thought experiment of the philosophical world. He has a whole book devoted to this concept, as I'm sure you know.

You mean photon, not proton, right? Or is that your speculation, that light is made up of protons instead of photons? As I understand, the brain very heavily post-processes every signal that comes in to give you these "sensorially consistent" perceptions of pain, sound, spatial extension, colour, love and what have you. Other people more knowledgeable than me will elaborate on that, I'm sure.

Presentism? We tend to see ourselves as morally superior to our ancestors. If any of us had been born in, say, 70 AD, we probably would look upon slavery as a hard, but inevitable fact of life. It is only through undefatigable rational discourse that we get rid of these things. ¯\_(ツ)_/¯ And, again, the Bible has many levels, different addenda (Christianity), and reflects social reality in the Middle East through the major part of both the Bronze and the Iron Age, which is a quite long period of time. God is a human construct. It changes (its/his/her/their) view because people making it up change theirs about what "God thinks". Doesn't it make a lot more sense that way?

Absolutely agree.

In @iNow's last comment is the potential for your mind to finally put this matter to rest. Or... you can go back to Star Trek. Science fiction at least tries to give you an appearance of rationality.

Ok. I don't see how that can signify a directional derivative. I assume you mean a derivative with respect to a matrix when evaluated at a particular matrix value? I'm no one-trick pony, I'm very familiar with derivatives with respect to a matrix (something that only makes sense when the function to differentiate is diagonal in the chosen matrix variable, which yes, happens to be the case if you're differentiating with respect to the Hamiltonian itself, which is trivial, or any of the spectral projectors, which renders the corresponding eigenvalue times the projector). But what I'm absolutely sure of is that, provided the coefficients are finally evaluated as the corresponding numerical functions of the Hamiltonian eigenvalues \( \lambda_{j} \), their values can be no other than, \( e^{-it\lambda_{j}} \) The calculation produces, \[ U=\sum_{j=1}^{d}e^{-it\lambda_{j}}\left|j\right\rangle \left\langle j\right| \] (assuming \( \hbar=1 \). This is in keeping with the more general result of spectral analysis (for certain kind of operators, compact, etc) that, provided a certain observable \( Q \) admits the spectral expansion, \[ Q=\sum_{q\in\sigma\left(Q\right)}q\left|q\right\rangle \left\langle q\right| \] then, for "any" (again, "good enough"=compact) \( f\left( Q \right) \) we must have, \[ f\left(Q\right)=\sum_{q\in\sigma\left(Q\right)}f\left(q\right)\left|q\right\rangle \left\langle q\right| \] So the least I can say is that the notation is unnecessarily confusing. If those exponentials have the meaning of certain matrix directional derivatives and are expressed as \( e^{\lambda_j t} \), while evaluated as numbers they are \( e^{-i\lambda_j t} \) (as they surely are by the calculation you suggest I'm more familiar with), then that's notational mayhem, IMO. And I'm sorry this discussion is drifting farther and farther apart as per OP.

Matthew 19:23-26 American Standard Version (ASV) Apparently it's not advisable to be rich in any case.

I'm getting the impression that you are a Christian believer.

You forgot a -i in the exponent, Mordred. You are under arrest for violating unitarity. 🤣

God can't handle money.

Yeah, let's debate it. Calaprice, Alice (2000). The Expanded Quotable Einstein. Princeton: Princeton University Press, p. 217. Einstein Archives 59-797. End of debate. (my emphasis in bold-face) Exactly. Hawking famously played the same game.

You only get to develop some intuition after you've done a bunch of examples. Do you mean, \[ \sum_{n=1}^{\infty}\frac{n^{2}}{2^{n}} \]? If that's the series you're referring to, the quotient is a good way to go. You generally use comparison when your general term is easily related to a well-known convergent of divergent series, like the geometric series, the harmonic, etc. The root criterion I would try when I have a function of n raised to a function of n. But it's not an easy subject in which you can give a fixed recipe. Code: \[ \sum_{n=1}^{\infty}\frac{n^{2}}{2^{n}} \]

A neutron star is not an atom, IMHO. Swansont's answer gives you all you need to know.

This betrays a lack of understanding of what both coherence and entanglement actually mean. Please bear with me. Let us assume particles 1 and 2 are entangled in some way with respect to certain reference states \( \psi \) and \( \varphi \) of both identical-particle space of states. In your case, electrons. The state could be written without much loss of generality as, \[ \psi_{1}\varphi_{2}+\varphi_{1}\psi_{2} \] This can be phrased rather intuitively as "particle 1 could be in state \( \psi \) and particle 2 in state \( \varphi \), or particle 1 be in state \( \varphi \) and particle 2 in state \( \psi \). This is a typical situation of entanglement, and in a way it's akin to a superposition for particle 2 of states \( \varphi_{2} \) and \( \psi_{2} \), but in which the coefficients of the linear superposition, instead of complex numbers, are the (also complex) wave function components of particle 1, \( \psi_{1} \) and \( \varphi_{1} \). According to the formalism of quantum mechanics, the minutest interaction on particle 1 will introduce decoherence in the state as seen from the POV of particle 2, as \( \psi_{1} \) and \( \varphi_{1} \) of particle 1 will average over many mismatching phases, bringing about this lack of correlation between the complex coefficients accompanying \( \varphi_{2} \) and \( \psi_{2} \) that we know as decoherence. Therefore, entanglement guarantees decoherence as soon as interactions come into play, instead of precluding it, as you claim. In other words, you need to understand quantum mechanics.

Not central to what we're discussing, but this is a flawed explanation of why electrons --or neutrons for that matter-- cannot have zero kinetic energy. Quantum particles cannot have zero kinetic energy due to Heisenberg's uncertainty principle, not to Pauli's exclusion principle. So any fermions must always have some kinetic energy in any given reference frame. Never mind other identical fermions being around. This is called ground-state kinetic energy or zero-point KE, and it's the least KE any particle can have. Were fermions allowed to have 0 KE because x,p were not complementary (HUP for position and momentum), they could still be at different places and still PEP would not be violated. What fermions cannot ever do is be in the same quantum state with however much kinetic energy HUP allows them to have. Glueballs aren't either. Yet nobody says glueballs are neutron stars just because they're not bunches of atoms. Things are not only defined by what they're not. Tritium isotopes are not "tiny neutron stars" either. Degeneracy pressure is not electrostatic repulsion, and gravitation has nothing to do with gluons and other ephimeral QCD states going back and forth between nucleons, which is what makes nucleons stick together by QCD. It's a very different animal. Neutron stars do not undergo fission via beta decay, as nucleons do. They do not have magic numbers. They do not have the same scattering properties, they don't have a definite spin statistics. Merging of neutron stars is nothing like nuclear fusion... And so on. \(\sim\)1057 neutrons packed together by gravity against Pauli's exclusion principle is what we call a neutron star \(\sim\)102 neutrons+protons packed together by QCD virtual states against electrostatic repulsion is what we call a nucleus The difference in name is justified because the phenomenology, what makes them, and most everything else, is different enough that it merits a different name.

Nice! Yes I remember baboons depicted on a wall in Hatshepsut's tomb. But they're not the only ones, I think.

Who said it?

It's practiced nowhere, followed by no one, and you don't have to do anything to be a member. Doesn't have a point of view, knows not where he's going to isn't he a bit like you and me...?

(n,101-n) would almost do the job you need. But you need the powers of ten to be "out of step" and catch up every two steps, so to speak. If you want a simple recipe the simplest one I can think of is with the floor function: floor(m)=floor(n+p/q)=n where n is the integer part of rational number m and p/q<1 is the rational part you need to add to n to get m. Then, (n,10-C(n)) where C(n) := floor((n-1)/2) https://en.wikipedia.org/wiki/Floor_and_ceiling_functions A good thing about floor is that you have it built in in Mathematica, Wolfram, and the like. You probably can do this with trigonometric functions too.

Stability of a neutron star is due to balance between gravity and degeneracy pressure, rather than any kind of arrangement between QCD and QED, which is what gives stability to nuclei. Gravity, OTOH, plays no significant role in stability of nuclei. So a neutron star cannot be (sensibly) to be just a giant nucleus, IMO.

Yeah, it rings a bell: https://www.scienceforums.net/search/?q="MHV"&quick=1

And it's spilt over from there. Now it's about Netflix and the Bible.