The h Bar

6:36 AM

it's a bunch of geodesics

well, curves in general

It is also a foliation

2 hours later…

8:53 AM

Riddle me this : Is the construction of a clock in GR affected by the same curvature issues no matter what the mechanism is?

If I have the mirror clock that counts the number of reflected light pulses by assuming a given distance, or if I have an atomic clock that counts the number of crests of an emitted wave, are they both affected in the same way by local curvature that can rescale the distances?

Does it always rely on some length scale

if the clocks were affected differently one of them wouldn't be a clock, would it?

since then the two "clocks" obviously measure different things

Yes, but also no real clock actually measures proper time

So I will probably let that problem slide

I just want estimations of the size of the problme

also on a conformal point of view, is there a mass associated to a clock's mechanism?

Defining a length scale

I guess a mass does define some time scale, from the hyperbola of momenta in the light cone

Perlick also defines clocks using light rays and massive particles

9:12 AM

I suppose you need very flat clocks near a black hole. ;) The tidal force at 112 km from a 3 solar mass BH is strong enough to break a 1 m bar of A36 structural steel in freefall.

I used Andrew Steane's semi-Newtonian solution: physics.stackexchange.com/a/631427/123208

9:37 AM

The name of structures is always a little confusing because they are named precisely after what symmetries they break

I think the mass setting a scale for the metric is exactly what EPS was using?

check out those big mass hyperbolas

10:04 AM

JPL use TDB for ephemeris calculations. "TDB was to tick uniformly in a reference frame comoving with the barycenter of the Solar System ... located outside all of the relevant gravity wells". en.wikipedia.org/wiki/… Accurate conversion between TDB and Terrestrial Time (based on TAI) is a bit messy, because you need to know where all the major solar system gravity sources are.

For precision work inside the Solar System, we use TDB or TCB. For details of the conversion between Earth-based TAI and TDB see section 2.3 of The JPL Planetary and Lunar Ephemerides DE440 and DE441, Ryan S. Park et al (2021). — PM 2Ring Sep 28 at 1:00

If we had an atomic clock network on Mars, converting between Mars atomic time and Earth atomic time, with picosecond precision, would be tricky!

How else will we synchronize our packets for martian internet

It's gonna have quite some lag

I wonder what the EFEs look like if you split them into every possible GR structure

@Slereah 3 minute ping, unplayable :(

Since the conformal structure cares not for mass but the volume structure does, and GR should have some interest in the SET's mass, maybe there is something interesting going on there

Live interaction with Mars would be too painful. Mirroring can cover the lag for a lot of net use, though.

We'll also need a relay satellite or two, to cover the times when the line between Earth & Mars passes too close to the Sun, which will increase the lag even more.

Just use copper wires I say

Q: Question still closed after several edits

10:41 AM

That's using a 10 day time step, with my Sage Horizons script at the end of this answer: astronomy.stackexchange.com/a/49955/16685

2 hours later…

schn

12:17 PM

Could someone kindly explain why the CO2 molecule only has two rotational degrees of freedom (DOF) whereas methane has three? I would assume any molecule can rotate around the x, y and z-axes, which would amount to three DOFs.

schn

12:29 PM

This answer helped: chemistry.stackexchange.com/a/49653

Physics Meta

1:26 PM

This question was closed. Based on the comments I found that people misunderstood/didn't understand the question so I simplified the description at the end and also posted several replies to the comments. But it still isn't opened.

support

Feynman_00

1:52 PM

Given a matrix Lie group say $SO(n)$, its elements are matrices. Then, does a representation map such matrices into... Matrices (well, linear maps)?

sure

Feynman_00

I mean, I still have to deal with this things but what do you get by representing a matrix with a matrix?

I would understand if I had rotation as abstract objects that can be represented by a matrix

2:14 PM

@Feynman_00 well, you can get n-dimesnional rotations acting on stuff that isn't n-dimensional vectors!

note that nothing forces a representation map of e.g. 3-dimensional rotations to go to linear operators on a 3-dimensional vector space

The determinant representation is pretty useful, for example.

Feynman_00

2:31 PM

@ACuriousMind :O

This helps

Though I guess if this is SO(n), not O(n), then the determinant is not so terribly useful after all.

a physicist might be more appreciative of the tensor representations $(\mathbb{R}^3)^{\otimes n}$, anyway :P

Or maybe other exterior powers?

yeah but for 3d that's not a very nice example either because the second power is just 3d again

granted.

1 hour later…

Nihar Karve

3:43 PM

Called it: chat.stackexchange.com/transcript/71?m=59297438#59297438

2 hours later…

Physics Meta

5:18 PM

Q: Where are my bookmarks?

It seems that there is no tab "bookmarks" anymore in the activity section of the profile. Are all my bookmarks gone? Will they come back? If not, can the bookmarks be recovered? Will the same happen to the "following" tab? There I save interesting questions/ answers and it would be problematic if...

bug bookmarks

2 hours later…

7:10 PM

Is there a way to show that having some particle of mass $m$ sets up a time scale on a spacetime

Looking at the clock building but they don't seem to talk about mass much

1 hour later…