SecretLabs (SE Branch)

5:22 AM

room topic changed to SecretLabs (SE Branch): The Labs, where the ideas are organised. Occassional attempt at modelling of a variety of phenomenon here. Always remember: Ideas mix. For MathJax see meta.stackexchange.com/a/220976. WARNING: May contain Eldritch and Lovecraftian ideas that can drive a person insane (no tags)

room topic changed to SecretLabs (SE Branch): The Labs, where the ideas are organised. Occassional attempt at modelling of a variety of phenomenon here. Always remember: Ideas Mix. For MathJax see meta.stackexchange.com/a/220976. WARNING: May contain Eldritch and Lovecraftian ideas that can drive a person insane (no tags)

Secret

5:47 AM

Past projects:

in The h Bar, Sep 2 '16 at 5:37, by Secret

(Extension) Maybe I can actually implement this chores I am suffering from into an actual quantum experiment. Suppose I have 3 qubits: A,B and C. A is prepared in some known state $\lvert \psi\rangle$. B and C are initially undetermined. Now wired B and C in a way such that the resulting eigenstate of of B is determined by the eigenstate taken by C, and the eigenstate of C is determined by that of B.

in The h Bar, Sep 2 '16 at 5:40, by Secret

Now place a measurement device M (maybe a polariser, a magnetic field, I am not sure) between A and C, and A and B respectively. Now wired the measurement device in a way such that whether C is being measured or B is being measured first is determined by the state A. Now prepare A in the superposition $\frac{1}{\sqrt{2}}(\lvert 1\rangle + \lvert 0\rangle)$, calculate the final probability of all possibel outcomes of B and C and (B and C).

in The h Bar, Sep 4 '16 at 16:05, by Secret

Dealing with maths like an architect: In general, given a ugly mathematical object $M$, you want it to become $N$. Therefore your tools are the various axioms and theorems. Use your tools to massage $M$ into $N$

in The h Bar, Sep 17 '16 at 7:16, by Secret

For me, I like to derive formulae for a variety of scifi and fantasy scenarios. This is why I rarely find out of reach ideas and proposals absurd, such as momentum being a 2 order tensor, disciontinous worldlines, nonlinear time, discontinous spacetime, infinite heat sinks, subzero flames etc. etc. etc.

Discontinuous worldlines

in The h Bar, Sep 17 '16 at 7:20, by Secret

Secret

6:06 AM

in The h Bar, Oct 15 '16 at 21:39, by Shing

This question may be a bit dumb, but what exactly is the problem with a path-dependent potential? I am not quite sure about this one, I think besides it will be a mutlivalued function, maybe things are just too complicated if you are dealing with a path dependent potential.

in The h Bar, Oct 15 '16 at 21:44, by Secret

It basically will mean that the value of $\Phi$ will be determined by the set of points in a path in some kind of state space. I think Feymann path integrals has a similar logic

in The h Bar, Oct 15 '16 at 21:43, by DanielSank

@Secret What does a path dependent potential mean?

in The h Bar, Oct 15 '16 at 21:47, by Secret

NB googling "path dependent potentials" found a bunch of interesting papers related to feymann integral stuff. I am guessing such potential is the norm in QFT

Path dependent potentials

in The h Bar, Nov 17 '16 at 7:14, by Secret

For base b, $\{nx_b: n\in [(1_b)_{10},(10_b)_{10}]\}$
$$(b-1)_b=(b-1)_b*0+(0_b+(b-1)_b)$$
$$(b-1)_b*n=(b-1)_b*(n-1)+(n_b+(b-n)_b)$$

where $(b-n)_b=0_b$ for $n=(10_b)_{10}$

I think the reason why it works (at least for integers, not sure how to prove it for arbitrary bases) is because the symbols from the base are elements of $(\mathbb{Z}/b,+)$. Therefore, for each succesor in base b, the unit digit is always the final symbol in that base, which can be decomposed into the sum of first and last digit in that base

in The h Bar, Nov 17 '16 at 7:20, by Secret

@SirCumference This is the reason why the digits of 9n add up to 9. In fact, it applies to all base

Q: Dependent Worldlines

I am currently studying Special Relativity and I have the following question: Let us first take the (Minkowski) spacetime diagram in the figure. Consider a causal macrostate $X$ with horizon time $\tau_2$, consisting of path microstates $x(t)$ with initial state $x(0)$. Let us also consider the ...

in The h Bar, Nov 23 '16 at 7:05, by Secret

Right now, during the waiting period. I am working on my driver license revision (which is SOOO BORING thus I am not often seen doing it) and also my various personal science* and scifi^ projects that is sparked due to my curiosity:
*1. Division by zero and zero term algebras
^2. Negative mass properties
^3. The mathematical formulation of a tensorial momentum
^4. Time travel modelling with malleable histories
*5. Quantum mechanics revision and preparation to QFT
*6. Topology
*7. Abstract algebra (currently at group theory)

in The h Bar, Dec 18 '16 at 9:10, by Kenshin

is it possible to derive creation and annialation operators?

in The h Bar, Dec 18 '16 at 9:11, by Kenshin

for a general hamiltonian?

in The h Bar, Dec 18 '16 at 11:14, by Secret

\begin{align}
H & = -\frac{1}{2}\frac{\partial^2}{\partial x^2 } + x^4\\
H & = \frac{1}{2}i^2\frac{\partial^2}{\partial x^2 } + x^4\\
H & = \frac{1}{2}i^2\frac{\partial^2}{\partial x^2 } -i^2 x^4\\
H & = i^2\left(\frac{1}{2}\frac{\partial^2}{\partial x^2 } - x^4\right)\\
H & = i^2\left(\frac{1}{\sqrt{2}}\frac{\partial}{\partial x } - x^2\right)\left(\frac{1}{\sqrt{2}}\frac{\partial}{\partial x } + x^2\right)+\frac{1}{\sqrt{2}}[\frac{\partial}{\partial x},x^2]\\
H & = i^2\left(\frac{1}{\sqrt{2}}\frac{\partial}{\partial x } - x^2\right)\left(\frac{1}{\sqrt{2}}\frac{\partial}{\partial x } + x^…

in The h Bar, Dec 18 '16 at 11:15, by Secret

at least for this factorisation, you cannot get the ladder operated state to be eigenstates of the hamitonian

in The h Bar, Dec 18 '16 at 11:32, by ACuriousMind

@Secret I'm pretty sure ladder operators are all but useless for most potentials. Sure, you can define the operators that map $\lvert n\rangle\mapsto \lvert n\pm 1\rangle$, but they aren't of much use in the general case

Nature of CTC experimental proposal

Experimental procedures:
1. Find or create a wormhole. This wormhole has both mouths "comoving" as they are both in the present.
2. Set up the experimental setup as shown in the diagram.
3. Subject anything except photodiode 2 and the mouth labelled past mouth under a sufficiently strong gravitational potential (This can be done relatively easily by having these components located on the surface of the earth, and the mouth labelled future mouth placed in near earth orbit. A time dilation in the order of seconds is more than enough for the experiment)

The blocker is used to mimic the grandfather paradox (Duplicate at the past mouth, which should be the future version of the original laser pulse, should vanishes when the blocker is raised)

Note: Quantum version not included. Calculations needed to ensure I am not talking nonsense

Squared limits

in Mathematics, Jun 13 '16 at 13:42, by Secret

Hey guys, I have a question concerning limits that I am not sure how to make it narrow enough so it can fit MSE question guidelines:

I am interested in finding a function $f(x)$ such that its limit

$$\lim_{x\rightarrow 0} f(x)$$

Is hard to compute using known rules of limits, but

$$\left(\lim_{x\rightarrow 0} f(x)\right)^2$$

will allow the limit to be simplified into two bits

$$\lim_{x\rightarrow 0} g(x)+\lim_{x\rightarrow 0} h(x)$$

where the limits of $g(x)$ and $h(x)$ are easy to compute, thus allowing the original limit to be determined by taking the square root of this limit?

Squared RPS magma

in Mathematics, Oct 15 '16 at 19:31, by Secret

in Mathematics, Oct 15 '16 at 20:27, by arctic tern

you seem to have a symmetric bilinear map $\phi:\Bbb Z_3\times\Bbb Z_3\to\Bbb Z_3$ satisfying the two properties $\phi(a,b)\in\{a,b\}$ and $\phi(\phi(a,a),a)=\phi(a,a)$.

Yablo paradox and grandfather paradox, relation?

in Mathematics, Nov 28 '16 at 2:19, by Secret

[scifi context?] Actually, I suspect Yablo paradox can be used as a proof pathway to show that the liar paradox is inconsistent, because the liar paradox seemed to act like the yablo paradox except with all statement equal to itself as a requirement of self rerential.

Meanwhile, the grandfather paradox can be modelled with a logical structure that it reverses its truth value after a fixed period T, thus the Yablo paradox can be applied to that context by imposing a period T as the delay it takes before the S_n+1 th statement appear, hence reversing the truth value of all previous statements.

Patterns in multiplication of two polynomials

Integral symmetries

Cauchy Riemann theorem like analogues in reals:

$$\frac{d^n}{dx^n}f=\lambda\int^{(m)}fdx$$

(where $f=\sin, \cos,e^x$ (possibly more?),$\lambda \in \mathbb{R}$)

For example

$$\int x^n \sin x e^x dx$$
Consider

$(uv)''=u''v+2u'v'+uv''$

Plug $u=\sin x$, $v=e^x$. Then

$(uv)''=-uv+2u'v+uv$

Note how the antisymmetry of $\sin x$ wrt the functional $()''$ results in cancellation. Hence

$(uv)''=2u'v$

Now it is easy to check that $\cos x$ is also antisymmetric wrt $()''$ thus we could have start with $u' =\sin x\implies u = -\cos x$. Hence