That's not what I said at all, and your apparent unwillingness to accept that I am discussing here under the assumption GR is valid is starting to make me suspect you're trying to discredit my viewpoint as naïveté or something. OK, to make sure we're talking about the same devil, let's define...
@PeterDonis That's a nice overview, there, of the scope of TOV - but still, I would point to the use of the term "relativistic": it expressely refers to the free special-relativistic gas, in spite of a previous post in which you argue that this is justified due to the local Minkowskian character...
I believe you're attacking a strawman there: I referred to the first part of my post - the one that does not introduce a driving force; if you have trouble seeing it, just expand ## H, q, E ## in powers of ## \omega ## and kill off those terms higher than first-order: you will get the free...
The invariance in the problem is enforced by the connection, so we don't need worry about it; as for whether matter couples to the metric (i.e., gravitational potential) or to the curvature (i.e., gravitational field), that can be indicated by other classical models, like - again! - the Maxwell...
Well yeah, but what I said was that you get a free particle as the natural frequency of the harmonic osc. goes to zero; as for
I don't get it o_O - as you can see from the expression of the energy ## \displaystyle E(q_0,p_0,t) ##, it doesn't go to that of the harmonic osc. in that limit; if you...
Disclaim: TL;DR
No, it isn't my personal idea - it's my question, the reason why I posted this. You do not find suggestions of these possibilities on any of the papers I ref'd - and apparently on any other - simply because none of which I know of seems to have talked about those things...
My understanding of "free" is irrespective of the specific assumptions of the O-V paper - I'm basing myself on the general scheme of gauge theories as applied to physics. Gravity, like other gauge theories, is an expression of a symmetry of our equations: a "field strength", or "curvature"...
I'm not saying that it isn't - I'm asking whether it's not valid to ask whether the usual contribution of the gravitational potential (a.k.a. the metric) is incomplete, based on circumstantial evidence (cf. infra)
In my understanding, "free" means "uncoupled from", and this applies to all...
Disclaimer: to avoid giving the impression of speculative nature, I state the purpose of this thread is only to conflate known theory with my own understanding in a specific point and clarify where the disagreement lies; that is all.
TOV limit: since early research in black hole (BH) formation...
I mean as in a hierarchy: a harmonic oscillator goes to a free particle as the natural frequency ## \omega ## gets arbitrarily small (checks with intuition), but the driven oscillator doesn't go to the harmonic one as either the amplitude ## \lambda ## or the driving frequency ## \omega_d ##...
Some time ago I was playing with the oscillator when I noticed a few funny things. Consider first the 1D oscillator with Hamiltonian $$ \displaystyle H(q,p) = \frac{p^2}{2m} + \frac{m\omega^2}{2}q^2$$ whose solutions are $$ q(t) = q_0cos(\omega t) + \frac{p_0}{m\omega}sin(\omega t), p(t) = m...
Did you read my previous post? I just would like to make some drawings! But also, your comment is rather misguided: yeah, I suppose every hard sci-fi writer ever made extensive calculations regarding rocket engineering before their pens ever touched the manuscript; that certainly makes for an...
This discussion is not 'SciFi" based, the sci-fi aspect was only circumstantial motivation; if I ask a scientific question about the Periodic Table and mention in passing "oh, maybe I'll write a song about it", does it get bumped into the Folk Ballads subsection too?
I'm not asking you people...
Bah, why did this get moved? I only mentioned "I wanna use it in sci-fi", not "this is established sci-fi", as the rules require; if I want, I can talk about Special Relativity in my stories, even though SR is real physics, right? And I think this is also real - I believe nukes have been built...
Physicists are prolific children when it comes to playing with their computers, so I wouldn't be surprised at all if someone actually simulated crater formation or fallout hydrodynamics by now; but outta curiosity, on the former, have you ever seen some instance of non-circular crater in some...
Probably a silly question, but I'm curious because I wanna draw some hard sci-fi based on it: if I shoot a nuke "ballistically" (viz., think of firing a cannon at a mountainside), upon detonation, what would be the smoke's/plasma's (?) profile? I guess it wouldn't be the famous mushroom profile...
Well... that's an statement, alright. Meaning that, changing the numerical value of ħ never bears any difference in outcome for the same given problem, and people tested it explicitly? IDK if there exists some metastudy of this, because, even if we're talking about classical solutions used to...
Some motivation: It's relatively easy to postulate "supersymmetric theories" - e.g., you can build one by simply monkeying around with the harmonic oscillator H = p2+x2 and linear combinations of x and p using Grassmann numbers - that, AIU, is NOT what one usually refers to as SUSY, but...
It's relatively easy to postulate "supersymmetric theories" - e.g., you can build one by simply monkeying around with the harmonic oscillator H = p2+x2 and linear combinations of x and p using Grassmann numbers - that, AIU, is NOT what one usually refers to as SUSY, but regardless of the...
I do not see how it would solve the MP, since particle evolution is still governed by deterministic equations, but feel free to quote me the lit. on that one; you actually got me curious.
BTW, sorry to revive an old post, but since there appears to be experts on Bohmian mechanics here, I...
The only thing I claim is I don't know what the math that backs up this funride is. The stuff you posted I've already read about - the point is not what the theory is, but why it is interpreted the way it is; you see, in my small-minded world view there are two things that describe the universe...
OK, but this still doesn't tell me how Bohmian theory sits with the rest of physical theory; because, as I think everyone here agrees, the quantum potential is just something that one gets out of the wavefunction that is completely general, but, as soon one uses it to compute classical...
But that's what I'm trying to say: the important thing is the trajectories, which in this case are calculated from the assumption that the particles are under the influence of a potential V + Q0 (and not, as I argued from consistency, V + Q0 + Q1 + ...), because that's what the Bohmian...
As I see it, this seems to be the basis of the interpretation: as the S equation looks like the classical Hamilton-Jacobi equation with an additional potential term, if one stretches this likelihood to say that ∇S is actually the classical momentum of the particles, then one must consider the...
I understand the topic of QM interpretations is not much beloved around PF, but I find one odd enough thing regarding the pilot-wave formulation that strikes me as a fatal flaw: for suppose you have a Hamiltonian H0 = T + V0, a solution of which is given by Ψ0 = R0eiS0/ħ; so you use R0 and S0 to...
I figured as much; though
ψ(-a/2) = Acos(-ka/2) + Bsin(-ka/2) = Acos(ka/2) - Bsin(ka/2) = 0
ψ(a/2) = Acos(ka/2) + Bsin(ka/2) = 0
=> B = 0 (because symmetry, Fourier series, however you prefer) , cos(ka/2) = 0 <=> ka/2 = (2m+1)π/2
Like I said, it's some silly mistake; but whatever it is, it's...
Problem: The particle in a 1D box [0, a]
Eqs.: The general solution of the time-independent Schrödinger eq. may be written as ψ(x) = Acos(kx) + Bsin(kx), E = ħ2k2/2m. Imposing the boundary conditions ψ(0) = ψ(a) = 0 , we get immediately A = 0, ka = nπ (for any positive integer n). Using x' = x...
Thanks for the reply; but, in your own words, I don't think the no-go theorem would apply here because I asked about torsion in the G-bundle, not the frame bundle of GR (spacetime is still Minkowski). Also, SuSyQFT is not necessary, as this question is more fundamental. Another way of asking: if...