The h Bar

enumaris

12:29 AM

oh dear

offers for FTE is much more complicated than offer at Contractor loool

@ACuriousMind apparently I transferred my cold to you through the internet

parvin

1:20 AM

hi.

I know that in lever and fulcrum, in a special condition we need to use less Force than usual.
But what I want to know is that does using less force mean spending less energy?

@JakeRose I want to know if we use lever for a robot it leads to using less ENERGY, meaning, less electrical power

danielunderwood

2:10 AM

@enumaris I warned you about those internet-transmitted sicknesses!

enumaris

2:58 AM

@danielunderwood lol, u been busy at work or something? Don't see you around much anymore

dmckee

@JohnRennie "since the genre didn't exist when I was a young adult." I believe they were called "mammoth operas"...

Though, I admit that things had moved on to hot, new bronze-age technologies in my day.

ZeroTheHero

3:25 AM

@DanielSank right... simple enough: there a MathJax plugin for GitHub that works so smoothly i managed to install it and make it work at the first trial.

Anonymous

3:42 AM

@parvin You asked the question on the main site just a couple of minutes ago (so I removed it). Just be a little patient! :) See my previous rant on this. And now that makes me hope that I don't come across as an old grumpy mod these days... :P

DanielSank

@ZeroTheHero Very good.

Anonymous

73

A: Is anti-matter matter going backwards in time?

To the best of my knowledge, most physicists don't believe that antimatter is actually matter moving backwards in time. It's not even entirely clear what would it really mean to move backwards in time, from the popular viewpoint. If I'm remembering correctly, this idea all comes from a story tha...

Leaky Nun

4:38 AM

6 hours ago, by Jake Rose

@LeakyNun https://physics.stackexchange.com/questions/391/is-anti-matter-matter-going-back‌wards-in-time

@Blue you're sniped by 6 hours :P

Anonymous

4:57 AM

@LeakyNun Uh oh. :)

John Rennie

5:25 AM

@dmckee I meant the young adult genre didn't exist in my time :-)

Rumplestillskin

6:35 AM

Hi there all! Is anyone familiar with Doppler shift for navigation? I just read about it and I'm not entirely sure I understand!!

John Rennie

Doppler shift for navigation?

Rumplestillskin

As is using doppler shift from a signal from an earth orbiting satellite to determine your posiiton

position on Earth

John Rennie

Ah. No, sorry, it isn't something I've ever studied.

It should be well documented through since it's been used for 50 years :-)

Rumplestillskin

@JohnRennie no problem! I actually understand what is going on in principle. I am just really confused by one particular point which I am misunderstanding or reading too much in to!

Leaky Nun

7:26 AM

what do I see if I look outside from inside a black hole?

user2723984

just for fun I'm trying to simulate a planet orbiting the Sun in MATLAB using simply the differential equations for a classical particle in a central potential and solving them with ode45

but my planet's orbit just decays, it gets smaller and smaller and it crashes into the Sun

is it something I can solve or it's just a too naif numerical approach?

oh for some reason ode23 works much better

Leaky Nun

7:43 AM

?

user301074

@LeakyNun You're stationary in the interior of the black hole or in free-fall?

Leaky Nun

idk

user301074

Probably you will see the ingoing Light-rays from the outside of the black-hole

Leaky Nun

but infinite time would pass outside before even a nanosecond passes inside right

then what would I see one second later

John Rennie

7:59 AM

@user2723984 that's a common problem if you use a simple integrator. It's because a simple integrator does not conserve energy.

user301074

I don't know your math/physics Level, but here's a penrose diagram of the situation i.stack.imgur.com/XUokp.gif

John Rennie

@user2723984 You'd have to use a ridiculously small step size to get a reliable orbit. The way round this is to use a symplectic integrator instead:

Symplectic integrator

In mathematics, a symplectic integrator (SI) is a numerical integration scheme for Hamiltonian systems. Symplectic integrators form the subclass of geometric integrators which, by definition, are canonical transformations. They are widely used in nonlinear dynamics, molecular dynamics, discrete element methods, accelerator physics, plasma physics, quantum physics, and celestial mechanics. == Introduction == Symplectic integrators are designed for the numerical solution of Hamilton's equations, which read p ˙ ...

user301074

The light-rays are freezed (how you stated) just for an infalling observer from the ouside of the black-hole

John Rennie

@LeakyNun You can see the universe outside the event horizon but it looks a bit odd. Actually calculating what you see is rather complicated.

I think there are web sites that show calculated images of what the view from inside the black hole looks like.

user301074

outside*

John Rennie

8:03 AM

@LeakyNun have a read through this:

11

Q: What would be the view like from inside a black hole looking towards the event horizon?

Ignoring the fact that we would be torn apart by gravitational gradient and assuming we get some time to make some observations before hitting singularity, what would we see looking towards the event horizon or in any other direction away from the singularity?

user2723984

@JohnRennie we used symplectic integrators in a course in numerical physics because of the same problem, though the problem was much less noticeable, here it's noticeable already in 2 orbits

I remember something about the Verlet algorithm

well maybe I'll review it, can't hurt, thanks

Slereah

morning

John Rennie

@user2723984 I found exactly the same thing when I wrote my first orbit calculator as an enthusiastic but underinformed young student :-)

user2723984

I thought about that, but google didn't tell me that straight away so I thought that maybe there was another problem, silently hoping not to have to look at symplectic integrators again

the word symplectic scares me

John Rennie

@user2723984 :-) Verlet integrators are pretty straightforward.

1

Q: MATLAB: Verlet Algorithm -

Below is my code for the Verlet function, to be called from my main script. % verlet.m % uses the verlet step algorithm to integrate the simple harmonic % oscillator. % stepsize h, for a second-order ODE function vout = verlet(vinverletx,h,params) % vin is the particle vector (xn,yn) x0 = vin...

algorithm matlab verlet-integration

user2723984

8:16 AM

I'm trying to simulate Mercury's orbit both with Newton's law and General Relativity in the weak field approximation

tired of calculating Christoffel symbols by hand

user301074

Nice

PiKindOfGuy

Hi

user301074

Heyo

Leaky Nun

8:43 AM

> But the failure of binocular vision is merely a limitation of beings who have evolved in flat spacetime. Trinocular vision would work fine. The three-eyed ape at right, drawn by my daughter Wildrose, would have no problem leaping from tree to tree in a highly curved spacetime.

w0t

user2723984

8:54 AM

this is useful, it's making me understand that I understood nothing of general relativity. The geodesic equation is $\ddot{\gamma}^i + \Gamma^{i}_{jk}\dot{\gamma}^j\dot{\gamma}^k=0$, all the derivatives are wrt proper time, is it correct that then $\gamma^0$ represents the time for an observer that sees the planet having some nonzero initial condition $\gamma^i, \dot{\gamma}^i$ at proper time 0?

Slereah

$\gamma^0(\tau)$ represents the time in the coordinate system chosen at the proper time $\tau$

user2723984

what do you mean "coordinate system chosen"?

Slereah

the coordinate system you're working in

user2723984

I don't think I understand, suppose I want to find the trajectory of a planet, and I have some initial position and velocity of the planet with respect to the Sun. Then I'm an observer stationary with respect to the Sun and $\gamma^0(\tau)$ is the time coordinate for me

if I wanted to plot position as a function of time for me I would plot $(\gamma^0(\tau), \gamma^i(\tau))$

is this right?

user301074

You're working with weak-field limit, then time dilation is negligible i.e. $\frac{d(\gamma^0)}{d(\tau)}$ approach $1$

user2723984

9:03 AM

yes, but I was wondering what initial condition should I impose to $\gamma^0$, and I realized I don't really understand what it represents

John Rennie

$\gamma$ is a funny symbol to use for the position in spacetime. Why not just $\mathbf x$?

user301074

^

user2723984

uhm yes we used $\gamma$ in the lectures to note curves, we usually use this symbol and really the trajectory is $x(\gamma(\tau))$ for some chart $x$ but it's just clumsy newbie notation

user301074

$\gamma^0$ represents the time coordinate, if you want write position as a function of $\gamma^0$ set $\gamma^i = (\frac{d(\gamma^i)}{d(\gamma^0)}) d(\gamma^0)$

John Rennie

@user2723984 in GR we don't normally think of things evolving in time because time is just a choice of some coordinate system. Typically a geodesic is a curve $\mathbf x(\tau)$ where $\tau$ parametrises the curve. $\tau$ may or may not have a physical meaning.

For a timelike curve $\tau$ is normally taken to be the proper time of the observer following that trajectory, but for a null geodesic $\tau$ has no physical meaning ( guess this also applies to spaelike curves).

So first you choose your coordinates, which in this case I guess will be the Schwarzschild coordinates $(t, r, \theta, \phi)$ then the geodesic equations tell you how the values of $t$, $r$, $\theta$ and $\phi$ evolve with $\tau$.

user2723984

9:17 AM

@Zober $\gamma^i = \frac{d\gamma^i}{d\gamma^0}d\gamma^0$ ? What is $d\gamma^0$?

John Rennie

So $\mathbf x(0)$ would just be the position you start from.

user2723984

@JohnRennie I have no problem setting the spatial parts of $\mathbf{x}(0)$ and $\dot{\mathbf{x}}(0)$, but I'm confused about the time part. In the weak field approximation I would guess it's $x^0(0)=0, \dot{x}^0(0)=1$

John Rennie

$x^0$ is just the time shown on a clock held by the observer watching from infinity. Just set $x^0(0)$ to zero i.e. reset your stopwatch at the moment you start following the orbit.

user301074

I mean't (there's a $d$ in the front, sry for the error): $d(\gamma^i) = (\frac{d(\gamma^i)}{d(\gamma^0)}) d(\gamma^0)$ and $d(\gamma^0)$ represents the infinitesimal change in $\gamma^0$, how i said before, $\gamma^0$ represents the time coordinate, then $d(\gamma^0)$ is the infinitesimal change in time

user2723984

Ah, MATLAB just shows me a bunch of NaN if I set $x^0(0)=0$ lol

@Zober so I can find the position of the body at the time $t$ from my frame as $x^i(t)=\int_0^t d\tau \frac{d\gamma^i}{d\gamma^0}\gamma^0$ ?

but that seems to just give me $\gamma^i$ back

user301074

9:41 AM

ye, just write $x^i(t)=\int_0^t \frac{dx^i}{d(\tau)} d\tau$ and use the geodesic equation to find $x^i$ that you obtained from $\ddot{x}^i + \Gamma^{i}_{jk}\dot{x}^j\dot{x}^k=0$

user301074

i have to confess that im getting very confuse with that gamma's and x's notations

user2723984

I must be missing something huge in what you're saying, $x^i(t)=\int_0^t d\tau \frac{dx^i}{d\tau}$ is just like the fundamental theorem of calculus

I'm more confused than you

let's drop the gammas altogether: I set up some variables $x^i, i=0,1,2,3$ and the Christoffel symbols for the weak field, I made MATLAB solve the equations and I set $x^i(0), \dot{x}^i(0), i=1,2,3$ at some initial positions and velocities, and $x^0(0)=0, \dot{x}^0(0)=1$

now, MATLAB spits out some NaN unless I put an $x^0(0)\neq 0$, like $0.1$, but then I get nonsensical results, most importantly that $x^0(\tau)$ is pretty much constant

I just want to know if the problem is in the code or if I completely misunderstood the physics, I think $x^0(\tau)$ should be approximately equal to $\tau$

John Rennie

@user2723984 Yes $x^0(\tau) \approx \tau$ in the weak field.

user2723984

ok, then I must've screwed up the code

I'll stop monopolizing the chat now, sorry

thank you for the help :)

John Rennie

$\dot{x}^0(0) = 1$ only if your object starts out stationary (in your chosen coordinates).

In general $\dot{x}^0(0) = \gamma$, where I'm using the conventional notation that $\gamma$ is the Lorentz factor.

(in the weak field approximation $\dot{x}^0(\tau) \approx 1$ for any $\tau$)

@user2723984 this is exactly the sort of thing the chat is used for, so no need to stop!

user2723984

9:55 AM

@JohnRennie yes I just realized it, I tried to change it to gamma but it's so close to 1 it really shouldn't matter

ok :) just tell me if it becomes too much

John Rennie

If you're talking about physics there is no too much.

user2723984

I think the worst problem is that $x^(0)=0$ produces NaN, it really should not

John Rennie

Indeed it should not ...

user2723984

well I'm talking about things that are probably obvious and not really interesting to many more advanced users, I just worry about that :)

Slereah

NaN is generally a bad sign

user2723984

10:03 AM

Ah! I have no words

OdeToVectoerField was messing with the order of the variables

I inputed x0,x,y,z and it spit out x,x0,y,z for some reason

Slereah

heh

user2723984

it still doesn't work, but now in less horrible ways

I was initializing $x^1(0)=0$, directly into the Sun

no wonder it gave NaNs

Slereah

TO THE SUN!

user301074

What spatial coordinate-system are you using?

user2723984

Cartesian, I'm using the metric $$ \left( 1+\frac{2\phi}{c^2}\right)dt^2 -\left( 1-\frac{2\phi}{c^2}\right)(dx^2+dy^2+dz^2)$$

John Rennie

10:08 AM

@user2723984 wouldn't polar coordinates be easier?

user2723984

where $\phi=-\frac{GM}{\sqrt{x^2+y^2+z^2}}$

John Rennie

Also I'm 99% certain the sign of the term in $\phi$ should be the same in both brackets.

user2723984

@JohnRennie no I don't think so, the minus arises then approximating the $(1-\frac{2M}{r})^{-1}$ in the Schwartzschild metric

John Rennie

Ah, oops, yes you've expanded the ()^-1

user2723984

and would polar coordinates change much? I would just have the same thing with $dr^2$ instead of $dx^2+dy^2+dz^2$ and an angular part

John Rennie

10:12 AM

Polar coordinates would feel more intuitive to me. But I guess it makes no difference to the calculation.

user2723984

yes, they are more intuitive, thing is, I already calculated the Christoffel symbols for this one haha

well I verified they were right comparing with a solution of an exercise sheet so I'm fairly sure of them

John Rennie

Ah yes, the joys of calculating Christoffel symbols.

Slereah

eh it's mostly alright

even by hand, if symmetric enough

user2723984

I'm glad the universe is torsion free

Slereah

Or is it

though even with torsion, GR is mostly simple

Since almost every matter source is torsion free

unless you're doing spinor fields you're fine

user2723984

10:19 AM

I'm struggling enough already with the vanilla torsion free weak field metric for the moment

and spinor fields in flat spacetime

Slereah

the horrible part comes if the connection isn't metric

dun dun duuun

John Rennie

If we demand that the universe be torsion free is that an extortionate demand?

Slereah

womp womp

although

Torsion doesn't actually affect geodesics

so it's not extremely problematic

for that task, anyway

since ${\Gamma^a}_{bc} u^b u^c$ only requires the symmetric parts

user2723984

halleluja

Slereah

that is a circle

There are better algorithms to do circles

John Rennie

10:28 AM

That looks a bit eccentric to me :-)

user2723984

natural units screwed me, $x^0(0)=c\gamma$

well it's an ellipse

why should it be a circle?

John Rennie

Shouldn't it be precessing?

user2723984

it's only one orbit

now I'll try multiple orbits

John Rennie

You'll need to make it pretty eccentric to see precession on timescales of a few orbits

user2723984

and it iiiiis....

not precessing

trying more eccentric

ok I'm not sure if it's precessing or if it's just an error of the numerical algorithm, which is not symplectic. I'll try to use Verlet

John Rennie

10:31 AM

Bear in mind that the precession of Mercury is 44 arcseconds per century, which is techically known as bugger all.

Slereah

just make the sun bigger

or make the orbit closer

user2723984

this is not precessing, this is a numerical problem

Slereah

indeed it isn't

user301074

thonk

user2723984

well this looks more like it, turns out matlab has a symplectic integrator ready to go

still crashes into the sun though

John Rennie

10:45 AM

@user2723984 that's OK, we've got plenty more astronauts

2

user2723984

nope, still numerical, it precesses with Newton too

Slereah

It might be some rounding errors accumulating

user2723984

11:15 AM

yeah, I think this task is beyond me. I can use a symplectic integrator for Newton but I have no idea where to start with Einstein

oh well, I tried

user129412

12:28 PM

Does anyone here (from the top of their head) remember how the size of a superconducting gap depends on perpendicular magnetic field, for a type 1 superconductor? Away from the critical field lets say.

Slereah

'fraid not

danielunderwood

12:52 PM

@enumaris yeah I started a new job and I'm still getting used to the schedule. It's like they want me to actually show up and work!

Slereah

1:16 PM

Damn the man!

danielunderwood

Yeah work would be a lot easier if I didn't have to do stuff

and didn't have to go places

Slereah

that's why you should work for the government

danielunderwood

1:33 PM

Suddenly I like doing things and going places

Slereah

2:36 PM

"This art of epsilon management, once mastered, is not terribly difficult – it basically requires one to mentally keep track of which quantities are “small”, “very small”, “very very small”, and so forth"

"In addition to the usual analytical interpretations, we can also interpret the concept of a limit as a voting system, in which the natural numbers n are the voters, which are each voting for a real number $x_n$, and the limit $\lim x_n$ is the elected “winner” emerging from all of these votes."

Don't blame me, I voted for Kodo

"In the voting theory interpretation given earlier, this means that we abandon the pretense that the election is going to be “fair”; some voters (or groups of voters) are going to be treated differently than others, due to some arbitrary choices made in designing the voting system. (This is the first hint that the axiom of choice will be involved.) "

Nooooooo

danielunderwood

"voting theory"

Mathematicians want to do everything, huh?

Anonymous

3:09 PM

@danielunderwood They're a nosy bunch. ;)

Anonymous

@danielunderwood Oh wow. Data science job? Or software?

Physics Meta

3:23 PM

-2

Q: Don't agree with the votes to close the question "Why is the MKS unit of time the same as the CGS unit?"

I don't agree with the vote to close the question "Why is the MKS unit of time the same as the CGS unit?". The question is, when Giorgi proposed to replace the CGS system, could he alternatively have chosen to replace the unit of time instead of the unit of mass. The answer is "no", because Giorg...

discussion

VARUN.N RAO

3:36 PM

Guys I need some quick help in delayed quantum choice eraser, is there anyone who knows something about it?

Anonymous

4:14 PM

@VARUN.NRAO Don't ask about asking, just ask.

danielunderwood

4:30 PM

@Blue well it's partially data engineering, but hopefully I'll get a chance to do data sciencey things at some point

Anonymous

@danielunderwood Nice!

enumaris

@danielunderwood data engineering...mmmhm

enumaris

4:55 PM

welp, gave my current comp a chance to match the offer...seems like it's unlikely...D:

John Rennie

5:05 PM

@enumaris you've had a job offer?

enumaris

indeed

John Rennie

A job you want?

enumaris

Yeah, everything's pretty good about that job except the commute

John Rennie

Cool :-)

enumaris

But I'm not unhappy at my current job or anything, it's just I am on a 1 year contract so it's time for negotiations. It seems like my current company is unlikely to match the offer tho.

I'm pretty impressed w/ myself tho, Data Scientist to Senior Data Scientist in 10 months :D

John Rennie

5:08 PM

With a permanent job I've advise against asking your current employer to match an offer, but when you're on a temporary contract that doesn't apply. Is the new job also contract, or permanent?

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