Recent content by anuttarasammyak

Thanks you all for good teachings. I add would add a rough hand drawing explaining the event.

From "general theory of relativity" by Dirac, as for Einstein pseudotensor, (32.3) where ##\mathcal{L}=\sqrt{}\ L## with (26.3) , we got the formula for Schwartzshild coordinates and metric given by (18.6) and integrated in volume outside the Schwartzshild surface, r > 2m as (31.4) I did it...

From the graph in ＃7, we observe for |x| >> 1 only n=1 term survives so it is sinusoidal between -1 and 1. From the graph in #3 , for 1<x<2, S_100 shows vibration. It suggests a toughness of showing a convergence. I have no good idea to solve it.

Once, I calculated the integral of the Einstein energy–momentum pseudotensor for a Schwarzschild black hole in the region outside the Schwarzschild surface and obtained the value m, corresponding to the mass of the black hole. Performing the same calculation for a Kerr black hole would be quite...

Order does not matter for real number inner products. However, in (c), $$<u|v> = <v|u>^*$$a conjugate complex.

Train Fall Paradox A train is running on a long bridge over a river. A series of bombs planted on the bridge by terrorists explode simultaneously, and the bridge collapses into dust in an instant. The train falls while keeping its cars in a horizontal line and hits the river. All the cars...

##x^2-3x+3>1## ##x<1,2<x## for these area $$ \sum_{n=1}^\infty |\sigma_n| < \sum_{n=1}^\infty \frac{1}{n^p} ,p>1$$ so the sum converges. Therefore we may pay our effort for ## 1 < x < 2 ## PS

FYI please share the plot of the sum as function of x which I ordered to ChatGPT.

I do not expect that learnig Hilbert space give you a direct answer to your question, but you may become familiar with mathematics of infinite dimension space with it. Though I have no objection, In a view-point, 1 dimension space {x} corresponds to uncountable infinite dimension space in QM...

We are familiar with countable infinite dimension Hilbert space in QM. You may be able to get some hint for your problem from it.

Thank you @PeterDonis. I should be somewhat satisfied to know that studies are going on.

In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A##...

The first term has dimension of T^-1 though it should be non dimensional. You should investigate its derivation.

The author explains the figures saying "the point of view of S(or S′)". Therefore, there is a possibility that readers may misunderstand these figures as referring to the same event.　A pair of lightnings which are simultateous in S and not so in S' and another pair of lightnings which are...

I see. “The moving inertial frame against the original IFR” would eliminate those cases.