3.4 Electric fields and potentials of point charges

Posted on March 18, 2023 by rpflee

A First Course in String Theory

(a) Show that for time-independent fields, the Maxwell equation $\displaystyle{T_{0ij}=0}$ implies that $\displaystyle{\partial_i E_j - \partial_j E_i = 0}$ . Explain why this condition is satisfied by the ansatz $\displaystyle{\vec E = - \nabla \Phi}$ .

~~~

Eq. (3.23):

$\displaystyle{ \begin{aligned} T_{\mu \lambda \nu} &= \partial_\lambda F_{\mu \nu} + \partial_\mu F_{\nu \lambda} + \partial_\nu F_{\lambda \mu} \\ \end{aligned}}$

…

$\displaystyle{ \begin{aligned} &\vec E \\ &= - \nabla \Phi \\ &= - \left( \partial_x, \partial_y, \partial_z \right) \Phi \\ \end{aligned}}$

$\displaystyle{ \begin{aligned} &\partial_i E_j - \partial_j E_i \\ &= \partial_i \partial_j \Phi - \partial_j \partial_i \Phi \\ \end{aligned}}$

— Me@2023-03-18 11:08:24 AM

Debugging quantum concepts

Posted on March 17, 2023 by rpflee

Reality is a superposition of eigenstates. Even if we use the pilot-wave formalism, in which a particle has definite position or momentum, the pilot wave itself is in a superposition.

— Me@2012-04-16 2:27:20 PM

Physics reality is NOT a superposition of eigenstates. If physics reality was a superposition of eigenstates, there would have never been any interference patterns.

For an experimental setup, what is in a superposition is the quantum state, which is a tool for deducing probabilities of different potential measurement results.

“A quantum state is a superposition of eigenstates” just means nothing more than that we need to use individual probabilities of the eigenstates to calculate the probabilities.

A quantum state, which is represented by a wave function, is logical, mathematical, conceptual, and linguistic in nature. A quantum state is NOT physical. A quantum state is NOT reality. A quantum state is NOT directly corresponding to a physical reality (aka observable events, measurement results, etc.)

A quantum state is NOT even corresponding to a probability directly. (If a quantum state was a probability, there would have never been the phenomenon of interference.) Instead, a quantum state is corresponding to a probability amplitude, which is used for calculating probabilities.

— Me@2023-03-16 09:57:07 AM

Computing Note, 5

Posted on March 15, 2023 by rpflee

21[.]07[.]2002 

From Personal Computer[s] to Personal Robots 

27[.]07[.]2002 

optical fibers

In the beginning of the optical fiber research, 
there were a lot of difficulties. But I thought if 
[I succeeded], the research payoff would be huge, 
because it could create a whole new world. 
"Mingpao Monthly"

        By the Father of Optical Fibers 

19[.]08[.]2002

Make Robot as inexpensive and as useful as 
Personal Computer -- Personal Robot

Corsair Vengeance RGB Pro

Posted on March 13, 2023 by rpflee

你有「婚前性」的話，一定不會從一而終。

如果你宣稱，你的「婚前性」對象，由始至現在至未來，只有一位，亦只會有一位的話，那樣，你在一開始時，為何不先與其結婚？

第二，數字不是零或一的話，就不知是多少。

第三，可以前的話，就可以外。

— Me@2023-03-12 10:28:29 AM

MangoHud

Posted on March 7, 2023 by rpflee

A Vulkan and OpenGL overlay for monitoring FPS, temperatures, CPU/GPU load and more.

vram
ram
swap
gpu_temp
cpu_temp
gpu_power
cpu_power

— Me@2023-03-07 09:14:51 AM

Ex 2.1-2 Particle in a Box

Posted on March 5, 2023 by rpflee

Quantum Methods with Mathematica

Reproduce Figure 2.1-1 …

~~~

phi[n_, x_] := Sin[n Pi x]

p[n_] := Plot[phi[n,x],{x,0,1}]

GraphicsColumn[{p[1], p[2], p[3]}]

— Me@2023-03-03 01:30:46 PM

Intermediate states

Posted on March 2, 2023 by rpflee

What happens in the interval between the initial and final states of the interaction process?

What happens in between is everything and nothing. There is no privileged clearcut answer what happened that would be physically meaningful. It’s really the very basic point of quantum mechanics that only results of measurements are physically meaningful facts or observables; all other data are fictitious or uncertain. By the very definition of your problem, no measurement took place in the intermediate states which means that no sharp answers to any questions were generated, no answers or values became real or privileged or facts.

…

But unlike classical physics, quantum mechanics says that not only the probabilities of each history matter. All the relative phases matter, too.

— answered Jan 9, 2021 at 16:10

— Luboš Motl

— Physics StackExchange

2023.03.02 Thursday ACHK

Copyleft 7

Posted on March 1, 2023 by rpflee

What stands in the way becomes the way.

— Marcus Aurelius

capitalize on

~ 用之以謀利

~ 利用

copyleft

~ 敵為己用

~ 幽默利用

~ 反利用

~ 草船借箭

— Me@2023-03-01 01:22:15 PM

Physics Town

continues

Monthly Archives: March 2023