The h Bar

0celo7

12:04 AM

Star Wars was good.

TanMath

@0537 with the same name?

vzn

@TanMath what prj is that? QM biology related? have been blogging quite a bit last mo myself, lots of CS related news, busy holidays...

TanMath

@vzn yep

Sir Cumference

1:19 AM

@HDE226868 Bit random, isn't it?

0537

1:35 AM

@SirCumference What lecture are you on?

Sir Cumference

@0537 Hyperbolic functions

It's actually damn interesting

Ya'll said calc would suck

0537

I didn't say that.

Sir Cumference

Er, not you, but others

0celo7

1:46 AM

It does suck

Hyperbolic functions: trig functions with imaginary arguments

Not very interesting

Sir Cumference

2:00 AM

That actually sounds amazing

@0celo7 Ya get to combine math in weird ways

Dunno how it sounds boring to you

no_choice99

hello there

Sir Cumference

Howdy

no_choice99

I'm here for the GR night talk

where's FendersLesPaul

and 0celo

Sir Cumference

Ping him

Secret

2:18 AM

@Bass I see. Then it seems M being coordinate independent will be a good sign for being a geometric object based on what you said

@Slereah I think then tensors over the reals or complex will be a sub(forgot term) of the definition you given, since the reals and complex numbers form a topology (with the neighbourhood defined using cauchy sequences), and tensors are built from these vector spaces, endowed with the topology of the reals and complexes

I think I will use both views when reading physics papers in the future, or deriving things, because from my experience, geometric objects usua…

Slereah

2:30 AM

It's not like you need that many functions for physics

Polynomials, trigonometric, hyperbolic, exponentials, logs, gamma, bessel

That's about it

no_choice99

hermite

legendre

and sum of powers

Slereah

Those are both polynomials

no_choice99

true

Slereah

I've seen weirder functions but that's pretty rare

no_choice99

yeah in statistical mech i remember some weird ones

a g(z) function

defined as an integral of something i think

Slereah

2:42 AM

You get mathieu functions and spheroidal wavefunctions in weird coordinate systems

Oh right, I almost forgot the spherical harmonics

no_choice99

and green functions , dirac delta's

Slereah

Dirac isn't a function :V

no_choice99

close enough :)

AngusTheMan

3:37 AM

what does the C in C*-algebra stand for? can't find anything :/

Stan Shunpike

@Slereah hey!

Slereah

That's me

Complex maybe?

Stan Shunpike

Question: can all of newtons laws be derived from the principle of least action or just the second?

Slereah

The action reaction thing stems from conservation of momentum

which stems from translation symmetry

Stan Shunpike

6:30 AM

Hello

I am confused about the Dirac equation. Whenever I read about it on Wikipedia, I never see it written using a Hamiltonian operator like the Schrödinger equation does. Why is that?

dmckee

6:49 AM

As usually exhibited the Dirac and Klein-Gorden equations are for free particles. In other words, they are the kinetic part of the Hamiltonian. If you need to put them in a potential you just add it in.

Slereah

amazon.com/Linear-Operators-Hilbert-Graduate-Mathematics/dp/…

>$100

>:|

You can write Klein Gordon and Dirac as Hamiltonians

The Klein Gordon and Dirac equations are useful to get the Schwinger Dyson equation, though

Stan Shunpike

#mylibraryhaseverything

@dmckee I see. Hmm. So it's convention. Okay thanks. It's interesting the Dirac equation has $\Box$ as the operator where sas the Schrödinger equation has the time derivative on the opposite side of the momentum operator.

Slereah

Just use the usual quantization procedure to find the Hamiltonian for Klein Gordon and Dirac

$H = \dot \phi \pi - \mathcal{L}$

For Klein Gordon that's $H = \int d^3x \frac{1}{2}(\pi^2 + (\nabla \phi)^2 + m^2 \phi^2)$

Slereah

7:19 AM

(you can show that it's $\approx \int \hbar N dk)$

Hitesh Pathak

Is there anyone who knows how newton established his third law of reaction

Can it br demonstrated without using second law however using the first law

I am here to discuss how one can assign mass in dynamics

Slereah

The third law basically states that momentum is conserved in a closed system

If you have a system of two objects acting on each others, then it states that $F_1 + F_2 = 0 = \dot p_1 + \dot p_2 = \frac{d(p_1 + p_2)}{dt}$

Secret

9:09 AM

Hi guys, another weird question:
This question is inspired from a table tennis lesson when the instructor send the ball one after the other with seemly random velocity, rotation and angle of inclination.

While it is true that the trajectory of the ball is random, one can still send it back to the other side of the table as long one have the paddle position near where the ball is expected to land and then hit it by swinging the paddle towards the ball

This lesson caused me to recall some of the things I learnt about weather forecasting and chaotic systems, such as how to people who newly e…

Secret

Basically, all of this jumble of memory recall due to that table tennis caused me to wonder about one thing:

Is there any examples of physical systems that are (I am not sure if that's the correct term) so random that regardless on what spatial or time scale you are in (i.e. no matter how narrow you set the scale) that it does not display any recognisable pattern

i.e. is the exists a physical system that is analogous to weather prediction, but no matter how small you made the time window, the system still behave in a truly random fashion with no decernible pattern?

(As a rough analogy, the system I am wondering about will be analogous to as if hypothetically there is a table tennis ball having some weird trajectory such that you cannot predict where it land thus you will always miss it (as otherwise for any conceivable trajectory of a table tennis ball, one can always hit it back to the other side of the table by position the paddle at just the right region of space and window of
opportunity)

Slereah

What does "no discernable pattern" mean

Is that just a uniform distribution

Secret

I think, the first step is that the system is aperiodic at all scales, and (perhaps?) it is non deterministic at all scales (that is, given any model M that tried to model this system, no matter how narrow the time window or how small the region of space, the system always evolve in some way outside the prediction by the model)

(I am actually not sure if that's even a scientific thing...)

(A rough analogy is something that is random at all scale, and does not get any more predictable no matter how much you zoom in, unlike a wave packet where if you take a shot enough time interval, you ca…

Slereah

Look up brownian process maybe

I dunno

Secret

It is as if there's a table tennis ball trajectory that even the most predictable step that can ensure the ball to be hit back to the other side (positioning of the paddle so that it is right in the path of the ball) is simply not possible because the window of opportunity has a size of zero

hmm, let me chcekc that out...

Slereah

9:24 AM

Although brownian process depend on the previous step

Lévy process

In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random and independent, and statistically identical over different time intervals of the same length. A Lévy process may thus be viewed as the continuous-time analog of a random walk. The most well known examples of Lévy processes are Brownian motion and the Poisson process. Aside from Brownian motion with drift, all other proper Lévy processes have discontinuous paths. ��2...

Secret

9:38 AM

Btw
Found something interesting when reading the brownian motion and levy process wikipedias
https://en.wikipedia.org/wiki/Singular_perturbation

The first thought that came to mind after skim read it is "it is an example where approximation=/=true+negligible terms"

0celo7

1:35 PM

@Slereah Send me the money and I'll get you the $25 MyCopy

John Duffield

@SirCumference : I left a comment.

John Duffield

1:56 PM

@Slereah : well it isn't me. My answers aren't wrong. And nor was Einstein, Minkowski, Maxwell etc. The evidence isn't wrong either. Don't blame me if guys like Bosoneando have such utter conviction that what they've been taught is right, that they'll downvote anything that challenges it. Instead of following the references.

@SirCumference : no, you aren't the first to realize it.

0celo7

2:58 PM

@JohnDuffield Pretty sure Einstein was wrong. And don't even get me started on Maxwell.

Slereah

3:34 PM

"men are trying bring in the fallen angels through CERN, thereby breaking the barrier set by God to the other dimension and realm. This is doom."

Finally

(Hail Satan)

0celo7

Is the salty Satan around