the proposed version of the pilot wave theory, the particle is guided bya combination of advanced and retarded waves.
Pilos-wave theory feels like a lost opportunity, when watching those videos with droplets on vibrating liquids (veritasium, worst example).
Along with the entaglement of quantum vacuum to bind gravity to entropy.
It is embarrassing to observe how rarely the vast literature on time’s arrow(See, e.g., [8, 9]) refers to the closely related issue of determinism.
Physicists sometimes avoid the very obvious contradictions and prefer formulaic bypasses.
inextricably linked
Well known to the folkls who do spherical navigation like Karapetoff and Somerfeld.
The hypothesis of linguistic relativity, also known as the Sapir–Whorf hypothesis /səˌpɪər ˈwɔːrf/, the Whorf hypothesis, or Whorfianism, is a principle suggesting that the structure of a language influences its speakers' worldview or cognition, and thus people's perceptions are relative to their spoken language.
https://en.wikipedia.org/wiki/Linguistic_relativity
link to Toki Pona as a conlang
Link to https://hypothes.is/a/6Znx6MiMEeu3ljcVBsKNOw We shape our tools and thereafter they shape us.
overall, the article proposes a way for massive collaboration in math, and explains the potential advantages which ultimately result from the inherent differences of human race and relativity (not the Einstein relativity, but the philosophical one which relates to the perspectives/angles of viewing the world in general): 1) the tendency of trying out different techniques to solve problems (assuming that we know exactly the same amount of knowledge), 2) the complementing nature of collective knowledge (if we know about different things), and 3) different strategies for approaching problems as people prefer and are good at different aspects of solving the same problem.
Different people have different characteristics when it comes to research. Some like to throw out ideas, others to criticize them, others to work out details, others to re-explain ideas in a different language, others to formulate different but related problems, others to step back from a big muddle of ideas and fashion some more coherent picture out of them, and so on. A hugely collaborative project would make it possible for people to specialize
mechanism 3: it is the difference that makes the human race flourish.
we don’t have to confine ourselves to a purely probabilistic argument: different people know different things, so the knowledge that a large group can bring to bear on a problem is significantly greater than the knowledge that one or two individuals will have. This is not just knowledge of different areas of mathematics, but also the rather harder to describe knowledge of particular little tricks that work well for certain types of subproblem, or the kind of expertise that might enable someone to say, “That idea that you thought was a bit speculative is rather similar to a technique used to solve such-and-such a problem, so it might well have a chance of working,” or “The lemma you suggested trying to prove is known to be false,” and so on—the type of thing that one can take weeks or months to discover if one is working on one’s own
mechanism 2: collective knowledge of a community is likely to better approximate reality; this applies especially to subjects like paleogeography; also related to relativity
d[V3(K−Λ3−3|E|2)]= 0.
One can check that (56) is the flow ofΣin(M\∂M,V−2g)by equidistantsurface
Transformar isso em observação sobre o significado físico do fluxo?
Note que esse fluxo implica numa escolha particular para o campo variacional. Seria interessante justificar essa escolha.
eachΦt(Σ0) := Σt,t∈[0,δ), is a compact almost properly embedded surface
Em outras palavras, a prpriedade de quase propriamente mergulhada é preservada ao longo do fluxo.
here exists a se-quence of initial data that satisfy all the hypothesis of item (i) and suchthat in the limit the equality in (3) is achieved. In this limit, the radius,the charge and the total mass of this sequence tend to zero.
A standard computation using the Gauss equation shows that∂f∂t(0,t′) =ddt|Σ0|g(t)(t′) =−∫Σ0(R−Ric(ν,ν))dμ=−4πχ(Σ0)−∫Σ0(Ric(ν,ν) +|A|2)dμ,where all geometric quantities are computed with respect tog(t′).
A computation in coordinates shows that the Ricci tensor ofhis given byRich(X,X) =−(1V∆gV)h(X,X),Rich(X,Z) = 0,Rich(Y,Z) =Ricg(Y,Z)−1V(HessgV)(Y,Z)
The structure of the metrichnear the singular set clearly implies thatgeodesics realizing the distance between a point inNand a component of∂Mmeets∂Morthogonally. The proof of this fact is essentially the sameas the proof of the Gauss’ Lemma.
$$ \begin{aligned} Q(t) & \equiv Q_{\nabla\phi}(\Sigma) := {1 \over 4\pi} \int_{\Sigma} \langle \nabla\phi, \nu \rangle d\sigma_g \\ %% & = {1 \over 4\pi} \int_{\Sigma} d\phi \cdot \nu d\sigma = {1 \over 4\pi} \int_{\Sigma} \frac{\partial\phi}{\partial\nu} d\sigma \end{aligned} $$
$$ \begin{aligned} \Longrightarrow \frac{dQ}{dt} = {1 \over 4\pi} \int_{\Sigma} \left[ d(\partial_t \phi) \cdot \nu + d\phi \cdot \partial_t \nu + d\phi \cdot \nu \frac{tr_{\Sigma} \partial_t g}{2} \right] d\sigma \end{aligned} $$
Tomando \( \alpha = 2 \), obtemos: $$ \begin{aligned}
the maximum principle above, yieldsSmin(t)≥Smin(0)1−2tmSmin(0)(5.3)for allt≥0 as long as the flow exists
Theorem 4.4Let(g(t),φ(t))solve(RH)αwithα(t)≡α >0. ThenSandSdefined as above satisfy thefollowing evolution equations∂∂tS=△S+ 2|Sij|2+ 2α|τgφ|2,∂∂tSij=△LSij+ 2ατgφ∇i∇jφ.(4.14)Proof.This follows directly by combining the evolution equations from Proposition4.2withthose from Proposition4.3.Remark.Note that in contrast to the evolution of Rc,R,∇φ⊗∇φand|∇φ|2the evolutionequations in Theorem4.4for the combinations Rc−α∇φ⊗∇φandR−α|∇φ|2donotdepend on the intrinsic curvature ofN.
Note que,
$$\alpha = 2 \Longrightarrow S = R - 2 |\nabla \phi|^2,$$
que é justamente a função que precisamos estimar (veja prova do corolário 5.2), no caso particular de um campo gradiente.
Haja visto que no na aproximação eletrostática do eletromagnetismo clássico, o campo elétrico (em domínios simplesmente conexos) é gerado por um potencial escalar, isso sugere que, pelo menos nessa aproximação particular, podemos utilizar esse fluxo \((RH)_{\alpha}\), tomando o pontical elétrico como dado inicial para o fluxo do calor para mapas harmônicos.
Essa ideia é inspirada nas ideias das seções 2 e 3, desse artigo do Benhard List, onde ele observa que soluções estáticas desse fluxo, com \(\alpha\) escolhido adequadamente, coincide com as soluções estáticas para a equação de Einstein no vácuo.
What we read, how we read, and why we read change how we think.
usingA−1=1det(A)adj(A)
the scalar curvatureRofds2is given byR= (1−u−2)Rρ+u−2n−1∑i,jR0ijij+ 2n−1∑i=1Rnini= (1−u−2)Rρ+u−2R0−2u−1∆ρu+ 2u−3∂u∂ρH0whereR0is the scalar curvature ofNwith respect tods20andRρis the scalar curvatureof Σρwith the induced metric.
Let Σ0be a compact strictly convex hypersurface inRn,Xbe the position vector ofa point on Σ0, and letNbe the unit outward normal of Σ0atX. Let Σrbe the convexhypersurface described byY=X+rN, withr≥0. The Euclidean space outside Σ0canbe represented by(Σ0×(0,∞),dr2+gr)wheregris the induced metric on Σr. Consider the following initial value problem(2.1)2H0∂u∂r= 2u2∆ru+ (u−u3)Rron Σ0×[0,∞)u(x,0) =u0(x)whereu0(x)>0 is a smooth function on Σ0,H0andRrare the mean curvature and scalarcurvature of Σrrespectively, and ∆ris the Laplacian operator on Σr.
Note que de agora em diante o autor se detém a estudar esse caso particular, onde estão inteiramente determinadas as geometrias intrínseca e extrínseca das folhas do semi cilindro, obtido folheando-se pelas paralelas o exterior da hipersuperfície estritamente convexa dada a priori.
Given a functionRonN, we want to find the equation forusuch that(1.2)ds2=u2dρ2+gρhas scalar curvatureR.
O papel da aplicação \( u: N \longrightarrow \mathbb{R} \) é distorcer as fibras do semi cilindro \( N \), por dilatações e torções, deixando a geometria intrínseca das folhas invariante, de tal forma que o resultado seja um semi cilindro com a curvatura escalar prescrita \( \mathcal{R} \).
Let Σ be a smooth compact manifold without boundary with dimensionn−1 and letN= [a,∞)×Σ equipped with a Riemannian metric of the form(1.1)ds20=dρ2+gρfor a point (ρ,x)∈N. Heregρis the induced metric on Σρwhich is the level surfaceρ=constant
Isso significa que a construção a seguir é feita a partir de um semi cilindro em que a geometria das folhas é dada a priori.
Esse artigo não trata da construção desse semi cilindro inicial.
However, this re-scaling of the space and time coordinates is in fact the result of Einstein ignoring the principle of the constancy of the speed of light by applying the usual vectorial velocity addition and then subsequently trying to compensate for this error by making a further error and changing the given length and time definitions (see my page regarding the Speed of Light).
if the corresponding distances are identical in both systems, then the delay times will also be identical and there won't be any difference in the clock readings afterwards
An all-star international team of astrophysicists used an exquisitely sensitive, $1.1 billion set of twin instruments known as the Laser Interferometer Gravitational-wave Observatory, or LIGO, to detect a gravitational wave generated by the collision of two black holes 1.3 billion light-years from Earth.
https://www.ligo.caltech.edu/news/ligo20160211<br> http://www.ligo.org/
Lemma 2.3.(2.1) has a unique solutionufor allrwhich satisfies the estimates in Lemma2.2.
Let Σ0be a smooth compact strictly convex hypersurface inRn. Letrbe the distance function from Σ0. Then the metric on the exteriorNof Σ0is given bydr2+gr, wheregris the induced metric on Σr, which is the hypersurface with distancerfrom Σ0. The functionuwith prescribed scalar curvatureR= 0 is given by2H0∂u∂r= 2u2∆ru+ (u−u3)RrwhereH0is the mean curvature of Σr,Rris the scalar curvature of ΣrandR0is the scalarcurvature of Σrwith the induced metric fromRnand ∆ris the Laplacian on Σr.
If the space doctor’s ideas were wrong, your phone wouldn’t be able to tell where it was.
If all of the space boats travel at the same velocity and the same distance from the Earth's surface, the time shift of the on-board clock due to relativity would be the same. The difference between the clocks would be almost the same. How would the trouble appear?
θ dμ ≥ p 16 π | Σ |
Qual a relação dessa desigualdade com a dita desigualdade de Penrose Riemanniana provada por Huisken-Ilmanen e Bray?
GIBBONS-PENROSE INEQUALITY
Qual a relação dessa desigualdade com a dita desigualdade de Penrose Riemanniana provada por Huisken-Ilmanen e Bray?
"the correct perception"-which would mean "the adequate expression of an object in the subject"-is a contradictory impossibility. For between two absolutely different spheres, as between subject and object, there is no causality, no correctness, and no expression; there is, at most, an aesthetic relation:
No absolute truth, all subjective and relative. Reality much more complex
For the truth is, Socrates, that you, who pretend to be engaged in the pursuit of truth, are appealing now to the popular and vulgar notions of right, which are not natural, but only conventional
Right and wrong are convention
appears to be seeml
Unconcerned with morality. Relativity.