Universal wave function, 20

Posted on July 21, 2018 by rpflee

The physical (synthetic) universal wave function logically cannot be found by any local observers.

The definition of “universe” is “all the things”. So there is no outside.

A global observer has to be outside the universe.

However, a mathematical (analytic) universal function is possible.

It applies to theoretical/model universe, which can be used to develop interpretations of quantum mechanics and successively approximate the physical universe.

— Me@2012-04-16

The fault of optimism

Posted on July 18, 2018 by rpflee

The illusion of peace

The seemingly rational world is rendered by exceptional good parents.

The seemingly peaceful time is provided by exceptional expense of defense.

— Me@2011.08.19

神的旨意 2.2

Posted on July 18, 2018 by rpflee

這段改編自 2010 年 4 月 18 日的對話。

合情合理，自圓其說的，就有機會真；無情無理，自相矛盾的，則必定為假。

又例如，如果現在神明顯靈在你面前，你怎樣判斷，那真的是「神明」？

「祂」既可能其實是「邪靈」，亦可能只是你自己的幻覺而已。

假設，現在神明顯靈，向你（甲）頒下旨意：

神：你必須殺害無辜，將來死後，才可以上天堂；否則，我會罰你下地獄。

甲：我不想作惡。

神：那不是你想不想的問題。你必須奉行神的旨意。

甲：但是，為什麼要我殺害無辜呢？

神：我是神，而你只是人。神的心思，凡人不一定能夠理解。所以，作為凡人的你，應該心存謙卑，完全信任你的神，奉行神的旨意。

甲：不合理呀！

如果要殺害無辜，才可上天堂，而不殺害無辜，會被罰落地獄的話，那代表著，你天堂的居民，都是壞人；而你地獄的居民，反而是善人。

那樣，你的所謂「天堂」，根本是我的地獄。而你雖然自封為「神」，卻根本是我的「魔」。

— Me@2018-07-16 07:51:33 PM

Chain Rule of Differentiation

Posted on July 15, 2018 by rpflee

Consider the curve $y = f(x)$ .

$\displaystyle{\frac{d}{dx}}$ is an operator, meaning “the slope of the tangent of”. So the expression $\displaystyle{\frac{dy}{dx}}$ , meaning $\displaystyle{\frac{d}{dx} (y)}$ , is not a fraction.

In order words, it means the slope of the tangent of the curve $y = f(x)$ at a point, such as point $A$ in the graph.

d_2018_07_15__21_31_32_PM_

The symbol $dx$ has no relation with the symbol $\displaystyle{\frac{dy}{dx}}$ . It means $\Delta x$ as shown in the graph. In other words,

$dx = \Delta x$

The symbol $dy$ also has no relation with the symbol $\displaystyle{\frac{dy}{dx}}$ . It means the vertical distance between the current point $A(x_0, y_0)$ , where $y_0 = f(x_0)$ , and the point $C$ on the tangent line $y = mx + c$ , where $m$ is the slope of the tangent line. In other words,

$dy = m~dx$

$\displaystyle{dy = \left[ \left( \frac{d}{dx} \right) y \right] dx}$

The relationship of $\Delta y$ and $dy$ is that

$\displaystyle{\Delta y = \frac{dy}{dx} \Delta x + \text{higher order terms}}$

$\displaystyle{\Delta y = \frac{dy}{dx} dx + \text{higher order terms}}$

$\Delta y = dy + \text{higher order terms}$

Similarly, for functions of 2 variables:

$\displaystyle{\Delta f(x,y) = \frac{\partial f}{\partial x} \Delta x + \frac{\partial f}{\partial y} \Delta y + \text{higher order terms}}$

$\displaystyle{df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy}$

For functions of 3 variables:

$\displaystyle{df = \frac{\partial f}{\partial x} dx + \frac{\partial f}{\partial y} dy + \frac{\partial f}{\partial z} dz}$

$\displaystyle{\frac{df}{dt} = \frac{\partial f}{\partial x} \frac{dx}{dt} + \frac{\partial f}{\partial y}\frac{dy}{dt} + \frac{\partial f}{\partial z}\frac{dz}{dt}}$

— Me@2018-07-15 09:30:29 PM

Problem 14.4b2

Posted on July 14, 2018 by rpflee

Closed string degeneracies | A First Course in String Theory

(b) State the values of $\alpha' M^2$ and give the separate degeneracies of bosons and fermions for the first five mass levels of the type IIA closed superstrings. Would the answer have the different for type IIB?

~~~

Type IIB closed superstrings

Equation (14.85)

$(NS+, NS+), (NS+, R-), (R-, NS+), (R-, R-)$

— Me@2015.09.16 06:08 AM: Should be the same. But I am not sure whether I have missed something.

$f_{NS+}(x) = 8 + 128 \, x + 1152 \, x^{2} + 7680 \, x^{3} + 42112 \, x^{4} + ...$

$f_{R-}(x) = 8 + 128 x + 1152 x^{2} + 7680 x^{3} + 42112 x^{4} + ...$

$f_{NS-}(x) = \frac{1}{\sqrt{x}} + 36 \sqrt{x} + 402 x^{\frac{3}{2}} + 3064 x^{\frac{5}{2}} + ...$

$f_{R+}(x) = 8 + 128 x + 1152 x^{2} + 7680 x^{3} + 42112 x^{4} + ...$

— Me@2018-07-14 09:41:10 PM

Pointer state

Posted on July 3, 2018 by rpflee

Eigenstates 3

In quantum Darwinism and similar theories, pointer states are quantum states that are less perturbed by decoherence than other states, and are the quantum equivalents of the classical states of the system after decoherence has occurred through interaction with the environment.

— Wikipedia on Pointer state

In calculation, if a quantum state is in a superposition, that superposition is a superposition of eigenstates.

However, real superposition does not just includes states that make macroscopic senses.

That is the major mistake of the many-worlds interpretation of quantum mechanics.

— Me@2017-12-30 10:24 AM

— Me@2018-07-03 07:24 PM

Mirror selves, 5.2

Posted on July 2, 2018 by rpflee

Anatta 3.3 | 無我 3.3

You fight for existence, for being alive.

However, your existence is not “yours”.

The existence of you, is not your property.

The existence of you, is a property of the group you are in.

The existence of you, is a property of other people.

To meaningfully say the statement “I exist”, you have to specify you exist with respect to whom.

To exist, you have to specify to exist in which people’s world.

— Me@2018-05-22 7:43 AM

Physics Town

continues

Monthly Archives: July 2018