@Slereah Well, that has units of mass. But it's not the "same kind" of mass as that of a quantum particle, or that of a classical particle, is it? You can define it, but you should be aware that you're choosing to imbue that quantity with a meaning that's not necessarily justified.
But I'm trying to beat the idea that there is Truth out of @Obliv. There are just models, just things that work well for some situations and less well for others. Using words like "particle" and "mass" and others for different things is a sneaky pitfall where you think that different models are talking about the "same things" when they might not. Ontology (what are things "really"?) is an unrewarding exercise.
@Obliv "Out there" implies models exist outside of our heads, and "truer" that truth is a one-dimensional "scale". But I already gave you lots of examples where "truer" models don't actually improve your handling and your predictions of situations where the "falser" models perform perfectly well.
@acuriousmind I would consider a model to be true if 1: it never fails (though there is no certainty that it will never fail) or 2: it follows from axioms
and I think it could be quantified in the sense that a model that predicts something 20% of the time is less true than one that predicts something 40% of the time
user218912
there is a new philosophy for scientists class we are recommended to take in my university.
@Obliv 1. Showing that it never fails will take you the entire lifetime of the universe. 2. That's an empty statement. Every model follows from axioms: Just take every statement of the model as an axiom.
@Danu I have been thinking of this, after digesting Aaronson's views on QM more and more. And I'm starting to think that ontology (which secretly means "classical", which the world is not) lost to epistemology in 1930 when Dirac published his QM textbook. OK, the date is loose, but still. Thoughts?
@Obliv But what's the point? What is the point of knowing that general relativity is "truer" if all you want to do is predict how long the stone you just threw upwards will come down? What is the point of having QED predict high energy scattering if all you want to know is how much energy your antenna will radiate?
@acuriousmind I don't think I said what I meant in 2: .. Okay, a model would be true if it was logically sound and was never imprecise due to the model's predictions as opposed to measurement device limitations.
@acuriousmind because if you keep following truer models , IMO you will eventually find a 'true' model under the definition I just gave. OR you hit a wall and have to start over from another angle but there's no way to justify whether you're on that path
@Obliv I'm not arguing against looking for the "best" model. I clearly said that I do not think you can order models along a one-dimensional scale where one end is "best" and the other is "worst".
@Danu why isn't there? I'm pretty sure SR is better than newtonian mechanics. If you don't think so, then why do we use it over newtonian mechanics for GPS?
@acuriousmind Because it's easier to do and the effects of SR are negligible. That doesn't mean it's something we should do though. What exactly are you using it for? If it's for locating the position of the ball then it's probably going to result in some error
@Obliv And that "error" is totally irrelevant for all practical purposes. Indeed, it doesn't mean we should do it, but (once again, perfect symmetry) it doesn't mean we shouldn't do it, either.
@acuriousmind It does mean we shouldn't do it if we want to find out the truth, though. I'm not majoring in physics so I can approximate the truth so that I can help develop human infrastructure
Some questions beckon imprecise answers anyway. Like if I asked what will happen if I throw a ball upwards. You don't need to invoke GR to answer that question with 100% truth
@Danu "We don't know everything" implies that there is something that in principle could be known in addition, which in turn implies the approximation isn't perfect. Words are tricky things ;)
So if $X$ is a metric space and $\{K_i\}$ is a countable number of compact sets such that $K_{i+1}\supset K_i$ and $\bigcup K_i=X$, then I conjecture any compact $C\subset X$ is contained in some $K_j$.
Hmm I'm looking into falsificationism, JTB & gettier problem to it and this got me thinking @acuriousmind do you think it'll be possible to logically prove that the universe is deterministic or non-deterministic? My first guess is that it isn't possible unless you find a deterministic theory..
@0celo7 I'm not sure what you want to tell me with that. However, I think I have a direct proof. Hint: For any cover $\bigcup_i U_i$, $\bigcup_j \bigcup_i (U_i \cap K_j)$ is still a cover.
@0celo7 Well, not really, but I'm always bad at predicting which part of proofs you find difficult. But you just use compactness of $C$ to choose a finite subcover, and then take the maximal $j$ on the $K_j$, in which $C$ then must be contained.
@SirCumference so a solid has an equation of state $\rho(p)=constant=p^0$, since no matter what the pressure is the density stays the same (I'm most familiar with the relativistic setting, where $\rho$ is the energy density is the mass density)
Everyone criticizing my work here has completely missed the point: the EPRG paradox is intended to be a straw man. Of course it doesn't actually work. The whole point of the talk is to explain why it doesn't work, because on the traditional pedagogy of quantum mechanics it seems like it should ...
@sirC it's the equation of state of an ideal gas. The other equation that the polytrope solution is pulled from is an equation of state of a polytropic fluid
spherically symmetrical, self-gravitating (whatever that means)
@SirCumference As used in stellar structure, "the equation of state" is the energy density as a function of pressure. The energy density is the thing that goes into Einstein's field equations, so given the equation of state, you can predict various things about the star. (like pressure as a function of r)
@SirCumference Well, for an incompressible soild, $\rho(p)=const.$. For degenerate fermions, $\rho(p)=p^{5/3}$ or something (I'd have to dig out my notes, sorry!). For an ideal gas, $\rho(p)=p$ or something (up to factors). All of those are of the form $\rho(p)=Kp^\gamma$. So it's very useful.
Actually, considering I was never taught a full physics course and had to learn it on my own (teacher was never in, he had to get leg surgery multiple times in the year), I'd say my thermodynamics knowledge is quite lacking.
@SirCumference but it's not 100% accurate, which is why in actual stellar research (No ocelot i do not know about not-so-stellar research) they, AFAIK, sometimes use piecewise polytropic fits
And as with everything in thermodynamics I'm "polytropic" is some name that Lord Kelvin or Maxwell gave something totally different in 1890 but which somehow still applies, but that's how I understand the term "polytropic equation of state" :)
> Thus, quasi-star envelopes are strongly convective, and their structures resemble $n = 3 (γ = 4/3)$ polytropes. The most accurate approach would be to model the envelope as a ‘loaded polytrope’ (Huntley & Saslaw 1975), with the black hole treated as a central point mass, but for $M_∗>>M_{BH}$ the standard Lane–Emden solutions suffice.
@0celo7 Yep. Learned about kinematics, but had to teach myself literally everything else for the SAT II.
Naturally, my knowledge on thermodynamics is limited.
@0celo7 Considering everything NeuroFuzzy said was completely overloading, and you were deliberately using only mathematics, I thought it was hopeless.
I never had that. I'm very bad at practical thermodynamics.
Well, if you want me to calculate how long it takes for a squiggle fry to cook all the way through, I can find a solution in Mathematica! But that's TOO practical.
@SirCumference I just read the wiki page lol. "Rather, this is simply a relation that expresses an assumption about the change of pressure with radius in terms of the change of density with radius, yielding a solution to the Lane–Emden equation."
On a side note, I was forced to take calculus for two years. Because my first teacher left in the beginning of the year and was never replaced, most of that class was just doodling.
The second year I actually learned some useful stuff.
@Obliv Technically, our teacher got replaced twice. Once by this lady who only taught us ship navigation, and the other was a priest when the class was turned into a Bible studies class
en.wikipedia.org/wiki/Polytrope end of first paragraph mentions "This relation need not be interpreted as an equation of state, although a gas following such an equation of state does produce a polytropic solution to the Lane–Emden equation" so
I'm not sure if you should use that solution or not
right now I am learning stat mech, gr, qft, and condensed matter. but I don't go to any of my lectures except qft so I have all day to learn these by myself.
Everyone criticizing my work here has completely missed the point: the EPRG paradox is intended to be a straw man. Of course it doesn't actually work. The whole point of the talk is to explain why it doesn't work, because on the traditional pedagogy of quantum mechanics it seems like it should ...
