The h Bar

8:20 AM

morgen

8:56 AM

I love this comment:

You are at the trailhead of the long journey that every student of quantum physics takes. We all started at the trailhead, and we all started with similar doubts. Eventually, after becoming experts, we realize that there really is something here that we don't understand, but it's much more subtle than we thought at first. Nature has given us a wealth of clues, and quantum theory is currently the best way we have to encode all of those clues. We base our language and intuition on quantum theory because it's the best foundation we currently have, not because we think no mysteries are left. — Chiral Anomaly 15 hours ago

Slereah

9:54 AM

I had another idea for an article on my site I wouldn't finish

But I forget what that was

I'm pretty sure it was something already in The Book

Ah yes

measurements in GR

Secret

11:32 AM

The environemtalism of infinity:

When settlers cut forest to make way of pasture, only to find the pasture to dry and rendered unusuable due to the lack of forest protection. Instead of recognising the root cause, economic forces propel them to cut more forest as a short term solution. This is a never-ending process that tries to reach from below the solution itself, but it never reached
This emptiness produced by the failure of understanding the nature of infinity means at the completion of this process, all forests are being cut down, and the solution too dissolved with it.

The completed infinity of forest cutting is the absence of forest, but seen from below, it is an indefinitely receding line of forest with a growing land area of pasture
Infinity is a contradictory existence, but lacking the knowledge of its completion, all you see is a hope that is rendered false because our world is finite and hence the process will end

The settlers are hence, short sighted, they only see the illusion of potential infinity in a finite world

But the actual infinity, should they see it, is really finite. Had they realised that they will stop cutting down the forests

PM 2Ring

@Secret From this post, and your previous one about anarchism, I think you would enjoy reading Jared Diamond, in particular Guns, Germs, and Steel and Collapse.

@Secret Not necessarily. Consider what happened on Easter Island. They obviously noticed they were depleting the trees, but they persisted in cutting them down. Diamond discusses this briefly in Guns, Germs, and Steel, and analyzes the decline of Easter Island in depth in Collapse.

yuvraj singh

11:47 AM

@PM2Ring hi will you help in one concept

Secret

Hmm, I should add that into my reading list

will definitely help me to understand more about green anarchism

PM 2Ring

That's an extreme example, because they were fairly isolated on an island. But there are other less extreme examples of society collapse through resource exhaustion. Eg, the pueblo dwellers in the south of what's now the USA. They got to the stage where they had to travel many miles just to get firewood.

@yuvrajsingh Maybe. ;) What's your question?

@Secret Definitely. Especially in GG&S, Diamond explores the differences between peoples who practiced settled agriculture vs nomadic hunter-gatherers, and why the former came to dominate the planet.

Physics Meta

0

Q: heat of vaporization

I have a question about my Physics Stack Exchange post: Quality of Vapour - Thermodynamics What is heat of vaporization. What is it formula. How it can be related to heat.

discussion

yuvraj singh

12:07 PM

@PM2Ring i was reading question on geometrical optics ,and i read of one of the question physics.stackexchange.com/questions/465219/… her is the link i have read the answer but it look.incomplete to me ,first you read and ping ,then i will ask my query

@PM2Ring are you interested in answering.

PM 2Ring

@yuvrajsingh That answer looks complete to me (although it did have a typo, which I just fixed).

He didn't give the complete solution to the question because it's a homework question. But he gave a good way for the OP to think about such questions, so he can find the solution himself.

@yuvrajsingh What is your query?

bolbteppa

12:35 PM

Carroll NYT Quantum piece: "Even Physicists Don’t Understand Quantum Mechanics - Worse, they don’t seem to want to understand it."

These kinds of passages are actually kind of unbelievable:
"In the 1950s the physicist David Bohm, egged on by Einstein, proposed an ingenious way of augmenting traditional quantum theory in order to solve the measurement problem. Werner Heisenberg, one of the pioneers of quantum mechanics, responded by labeling the theory “a superfluous ideological superstructure,” and Bohm’s former mentor Robert Oppenheimer huffed, “If we cannot disprove Bohm, then we must agree to ignore him.”"

I don't know why pretty much every popular QM piece has to include this noble outsider vs. rigid establishmentarian nonsense

Slereah

12:54 PM

More exciting

Slereah

1:38 PM

Hm

it's hard to think about measurements in GR

I'm gonna need to prove some things and assume some others i think

like we can't really have proper distance measurements without assuming that the variation of the metric in a small neighbourhood (on the scale of what we can do) is small enough to be below experimental error I think?

Like obviously at a sufficiently small scale that is true, but I don't know if you can show that this scale happens to be superior to our own scale of measurements

and you can probably make some inequalities wrt the energy to show that it must be bounded to something, but then you'd have to know about the energy of our own world, which seems that it would require the ability to make measurements first

bolbteppa

Never really heard about GR measurement issues tbh

Ryan Unger

physicists don't think about the real issues

Slereah

It's not a super hot issue but Reichenbach talks about it a fair bit

The thing is like

Given a set of measurements on your spacetime

How can you narrow it down to a small subset of the space of all metrics (local to your little coordinate patch, 'course)

Because the interpretation of the measurements themselves require some assumptions on the metric

You can probably do it alright if you assume that it's all alright for the metric being $\approx$ minkowski at our human scale

Which is probably true but I think would be hard to prove from first principles

Or like with minimal assumptions

Like you always have a discrete set of measurements for a start

I don't think you can really narrow down metrics very effectively from discrete points without some rather big assumptions

And that's only for metrics within a small neighbourhood of the experiment. Global properties are another matter

Like I think a common assumption is just that if, for experiments on some small scale, you have $g \approx \eta$ up to experimental error, then the metric is going to be closer to $\eta$ at smaller scales

I think there are probably ways to make up counterexamples with the metric varying a lot at very small scales but the measurement being about the same since it's going to be integrated over that

PM 2Ring

2:09 PM

Right. Eg, you can have a chaotic spacetime foam at the Planck scale, as long as that chaos averages out at larger scales. Similarly, if you're a plumber analyzing the behaviour of water in a building's pipes you can ignore Brownian motion and molecules, and just treat the water as a classical continuous fluid.

Slereah

yeah

though I'm not sure that like

If you perform an experiment at human scale and one at plank scale

Can one be flat within experimental error and the other not be???

Not sure

It's pretty hard to think about a very general argument because things can get pretty weird if you assume a completely generic spacetime even at small scales

Obviously you can make a lot of good arguments given enough assumptions, but I'm not sure what would be the minimal amount of assumptions you could get away with

PM 2Ring

I expect spacetime to get messy down at the Planck scale, like the Loop Quantum Gravity people believe, but who really knows without a proper theory of Quantum Gravity?

Slereah

Though I think you'd basically have to assume the topology of an experimental-scale neighbourhood to be roughly $D^4$, because if you allow random handles and singularities things are going to be intractable

Otherwise you could have suddenly a wormhole appearing between any two points and making your distance arbitrarily small!

Oh also

You know what's a great opportunity here?

Use that one experiment showing that on a scale of a few km, the geometry of space is roughly euclidian

Performed in the 19th century

By measurements between 3 mountains

PM 2Ring

Pragmatically, GR is hard, so when doing actual calculations we try to make things as simple as we can get away with. ;) It's hard enough modeling the interaction of 2 well-behaved stellar mass black holes. Trying to look at stuff near the Planck scale, with possible wormholes etc popping up would not be fun.

Slereah

Oh even without going that far it's hard

Like just the assumptions of initial conditions around stars

You can have decent ones for isolated stars, but what kind of initial conditions can you get for binary systems of stars?

PM 2Ring

2:26 PM

Sure. So on the large scale you can proceed by cutting up your spacetime into chunks. Use Schwarzschild or Kerr on chunks where applicable, and use Minkowski on the flattish chunks. If a flattish chunk isn't flat enough, recursively cut it up until it is flat enough.

It's hard to say because there are also like

Interactions

Big binary systems can have gravitational waves shenanigans going on

Possibly very important for compact star collisions, even

and of course you usually have fairly limited data from astronomical data

It's not like you have an interferometer laid out every meter around the star

PM 2Ring

@Slereah As usual, you start with a Newtonian approximation. And then use a good integrators with small timesteps, and lots of digits of precision. :)

Slereah

Well assuming that it is Newtonian is a fairly big assumption, is my point!

PM 2Ring

@Slereah Well, sure. And bound to be crazily wrong near black holes. But it's just a starting point, like an initial approximation when you're trying to solve an equation. Adding GR perturbations on top of a Newtonian estimation is perfectly fine for NASA to calculate spacecraft trajectories. It may be a bit trickier if you're trying to set up a space station orbiting in a binary neutron star system. ;)

Slereah

2:39 PM

Hm

I'm trying to think of like

some ways to make the metric unique up to some freedoms

I'm thinking of like

Make a triangulation of the spacetime around, with the metric having discrete values

Based on instrument precision

PM 2Ring

@NovaliumCompany Ok. Firstly, you aren't going to get much of a field happening with those electrodes. You need something more plate-like. But I guess you'd expect to see some tiny movement.

Slereah

I think given specific enough assumptions, you'd get a unique (or at least restricted set of) metrics for measurements

ie : given a set of $n$ measurements with $\Delta x$ precision

and then the relation between the set of metrics v. the discretized metric is some equivalence class

PM 2Ring

Secondly, I think you need to use less TiO2 goop, and you need to disperse it into the baby oil in the cell, not have it sitting there as a separate lump.

Slereah

I mean for a start, if you have a set of discretized metrics over a finite space, the space of all metrics will be finite to begin with

Large but finite

PM 2Ring

@Slereah That sounds reasonable.

Slereah

2:45 PM

yeah it's probably a decent idea

If somewhat harsh to work out

PM 2Ring

If spacetime can have arbitrarily stupid metrics at the scales we can observe, then we should have seen some evidence of that by now. But the people looking for defects, like cosmic strings, or primordial black holes, have seen nothing.

Novalium Company

@PM2Ring How to disperse it so it's not like a separate lump?

Slereah

@PM2Ring Space is big yo

I can probably do the equivalence class by considering a bunch of observers sprinkled throughout spacetime taking measurements of a certain precision

Like have a bunch of timelike geodesics exchanging light signals to measure the response time

And also angles

Those are all alright things to measure without too much worrying

Also I can assume that their (measured) distance between respective observers is fixed because that's something you can do IRL

Well, maybe

i need to work this out

PM 2Ring

@Slereah True. And even the people who model black hole accretion disks and even mergers don't try to make their maps too detailed. They don't mind if there are various patches labelled "Here be dragons" as long as they can get reasonable predictions that match observations at a distance.

Slereah

And maybe using that, I can see what kind of metrics I can narrow things down given a) a set of measurements and b) a set of assumptions on the underlying spacetime

Like I think you can reduce things quite a lot if you assume the metric to be analytic

Analytic and some condition on the... microscopic variation of the metric

Then it would just be some small neighbourhood in the space of all metrics I think

PM 2Ring

3:02 PM

@NovaliumCompany I don't know. Try with a few drops of goop, and add baby oil to it & mix. How well does your liquid soap mix with the baby oil?

Slereah

Bounded variation metric, mb

Novalium Company

@PM2Ring No idea

Slereah

I think you can probably make up some condition by comparing the total variation of the metric and the scale of measurement

I guess it's basically trying to find the link between theoretical GR and experimental GR :p

PM 2Ring

@NovaliumCompany Part of the function of the surfactant is to allow the TiO2 suspension to mix with the oil. So it needs to mix well with the TiO2 suspension, but it also needs to mix well with the oil.

Novalium Company

@PM2Ring Got it.

Slereah

3:09 PM

Also another annoying thing

You have to assume that the devices you use are small enough to ignore any possible effect

Have your atomic clock and interferometer equipment and computer memory in a device small enough that we can roughly expect everything to be about Euclidian

or at least something you can sweep in under experimental error

ie : your device has multiple sensors for light signals to be in communication with other observers, but you have to assume that the distance between any two such sensors is about constant

PM 2Ring

@Slereah It's like with an atlas of the Earth. You want each flat map to be a reasonable approximation of the territory, so if there are large deviations from flatness in a region you need to use lots of small maps. But if the region is a prairie you can get away with a larger map.

Slereah

yeah but at least in classical things you can expect the geometry to be about constant!

Although of course

The same problems also apply

just in different ways

ie how do you know that the ruler you use hasn't dilated due to various effects between two measurements

Reichenbach's point was of course that to cut out the madness, you define the measurement as the ruler

and don't worry about the theory until you work out the details

But then all the hard work becomes how you relate the measurements to the theory

It's basically the old problem of "how do you know that your ruler hasn't dilated due to heat and how do you know the temperature because your thermometer is a heat sink"

PM 2Ring

@Slereah You don't really have any other option. Of course, your ruler is actually a lightbeam and a clock. And then you "just" have the problem of synchronizing your observers clocks. But Einstein has told us how to do that in a reasonably sensible way for observers at rest wrt each other. And if that's unsatisfactory we can use Reichenbach's more general scheme.

Slereah

even with that it remains hard, alas

And that's not even thinking about weirder issues :p

PM 2Ring

Even the issue of the impossibility of measuring the one-way speed of light is bad enough.

Slereah

3:23 PM

that too

I can think of like a dozen arguments as to why GR would be basically impossible to do any decent predictions for

at least as it is

there's a whole bunch of underlying assumptions to GR

1) Spacetime isn't required to be globally hyperbolic so that unknown data can enter the system at any point in time
2) Lack of ability to determine proper initial data given a finite number of measurements
3) Several metrics can fit the same measurements as proper time measurements are define by integrals
4) Measuring apparatus themselves affected by the geometry of spacetime
5) Measuring apparatus themselves *affecting* the geometry of spacetime

it's all terrible

I can think of some more but they're mostly variations on those issues and generic measurement problems

Oh and of course you can't really synchronize the observer properly due to the evolution of $g_{00}$

bolbteppa

3:50 PM

Just let every measurement take place in Minkowski space where none of this matters and don't go so small that QM started affecting things right

Slereah

Oh do you mean becoming an ENGINEER

I mean I guess you can let the observers exchange their synchronization in the light signals

but of course we don't know how long that takes

I guess what I'm basically getting from those observers is a triangulation of the spacetime, with every edge being a light signal

And then the game is to guess some bounds for the distances from the informations of those signals

Novalium Company

4:41 PM

@PM2Ring I just checked, the liquid soap mixes very good with the baby oil and TiO2. Can you please repeat what I can try to do? Also, the TiO2 particles and liquid soap seem to kinda float in the baby oil, they don't sink. I guess that's how epaper displays keep their image even when no power is applied.

Slereah

I should try to work out that business in 2D

Assuming global hyperbolicity it's just 3 functions to work out rather simply

also everything conformal assuming some small neighbourhood

Slereah

5:22 PM

I think a decent counterexample for the approximation of the metric from measurements is $$ds^2 = -(2A + A\sin(\omega t)) dt^2 + dx^2$$

Hm

Need to work out how that proper time would be

Slereah

5:35 PM

We do have that $$\int_{a}^b \sin(\omega t) dt = -\frac{1}{\omega} [\cos(\omega b) - \cos(\omega a)] \in [-\frac{2}{\omega}, \frac{2}{\omega}]$$

For a high enough frequency it is arbitrarily close to zero

PM 2Ring

@NovaliumCompany How fine is your TiO2 powder? If you mix a small amount of the dry powder into oil do you get a milky suspension, or do the particles quickly settle? I'm getting the feeling that the water may be the main problem here, preventing proper mixing and encouraging the TiO2 to clump together. OTOH, I guess we need some water in order to get a charge on the particles when the NaOH is added to them...

Slereah

Hm

Is there a nice smooth periodic function which is always $> 0$

and arbitrarily high

Wait no that won't help

I guess it's more a function where the integral is arbitrarily close to zero at large scales but can be fairly arbitrarily high at small scale

I guess it would be more a function that is mostly very flat with occasionally very high peaks

Maybe just stringing along very tall bump functions

but widely spaced

Novalium Company

7:26 PM

@PM2Ring I put some plain TiO2 particles (not charged, no water) in just baby oil and I shook it up a bit. Some of the particles spread out like stars and some formed a ball (I'm not sure if the ball was there at the beginning or got formed by the submersion). It didn't look like milk, more like the dark sky full of stars. The particles settle down by gravity quite slowly. I can try to put a solution of TiO2, H2O and NaOH in baby oil and see how it looks?

PM 2Ring

@NovaliumCompany Sounds good. Maybe mix a small amount of detergent or liquid soap into the oil first.

Novalium Company

@PM2Ring Oks

@PM2Ring Should the solution of TiO2, H2O and NaOH look like wet dirt? Or more on the liquid side? (Like attempt 1 or attempt 2 at the video)

PM 2Ring

7:44 PM

@NovaliumCompany I really don't know. I suspect you need to keep the water content to a minimum.

Novalium Company

@PM2Ring Ok

grE

8:09 PM

Hello. The total angular momentum operator can be interpreted as the quadratic casimir of sl(2), up to a proportionality constant. This quadratic casimir commutes with sl(2)-action, where sl(2) acts as e= (1/h) (J_x + i J_y), h = (2/h) (J_z), f = (1/h) (J_x - iJ_y). I should be able to make a statement like 'thus the total angular momentum is preserved under X', what is X though?

Like, sl(2) action preserves the total angular momentum, but what physical notion does this action correspond to?

grE

9:04 PM

I mean, I am happy to say the total angular momentum is preserved by the sl(2)-action, but I imagine I can say something about how sl(2) actually alters the spin in the x,y,z directions

grE

10:09 PM

Anyone :)

ACuriousMind

@grE It's $\mathfrak{su}(2)$, not $\mathfrak{sl}(2)$, and the physical statement is that total angular momentum is unchanged by rotations.

grE

I meant sl(2,C) (and sl(2,R) and su(2) both complexify to sl(2,C), so it's equivalent right?)

ACuriousMind

Well...it means that the linear complex representations of all of these are equivalent

But the rotation algebra is still very much $\mathfrak{su}(2) \cong \mathfrak{so}(3)$.

grE

I mean that sl(2,R) and su(2) are both real Lie algebras that are R-forms of the complex lie algebra sl(2,C)

Although I guess I see what you're getting at, given the lifts to different Lie groups

ACuriousMind

That is correct, but angular momentum really lives in $\mathfrak{so}(3)$ as that is the algebra of the rotation group. The reason why you can instead talk about $\mathfrak{sl}(2,\mathbb{C})$ is that quantum mechanically we care about the complex representations, which are the same for a complexified algebra and its real forms.

grE

10:16 PM

Thank you

ACuriousMind

I'll happily admit I'm nitpicking if this is completely beside the point you were trying to make, though ;)

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