04:00 - 20:0020:00 - 00:00

4:22 AM
>
This is the danger of much pseudo-philosophizing: If you don't define your terms carefully, all statements can be true or false depending on how you interpret them!
And giving an example is not a definition, it is at best something that can guide you to one
It is good to finally know for once what is pseudophilosophy. I always have trouble figuring out what is not philosophy
Now I knew at least half of the reasons why people cannot understand my stuff
@M.N.Raia I think the laws of physics is itself a very vague term. Let's say there is some force that varies with time and we cannot find any dependence on some regularity that explains this variation. Do we said the law has changed, or it is just what the law is
If a phenomena involve a change all of a sudden for a known experiment, it can be due to other environmental factors or regularities we don't account for, or it could mean the laws have a time dependence and hence "mutable"

Hey @JohnRennie , would you mind looking at this question

4:38 AM
@NoahJ.Standerson hi :-)

4:59 AM
@NoahJ.Standerson it can be helpful to think of the field as acting on individual electrons in a wire, and this often helps you understand what is going on. However this can be misleading.
For example suppose I make a toroidal transformer with the primary toroid inside a secondary, so the cross section looks something like this:
When I pass an AC current through the primary it creates a field inside the primary i.e. the shaded area here:
But in a toroidal coil there is no field outside the coil i.e. the current in the primary does not create any magnetic field at the secondary coil. Even so an EMF is induced in the secondary.
So in this case you cannot understand the induction by considering a magnetic field acting on electrons in the secondary because there is no magnetic field at the secondary.

@JohnRennie , Oh yes. Thats correct. So is there even any theoretical way of understanding the electromagnetic induction?

To be honest I have never thought about it. Since Maxwell's equations give the right answers I've always just used them without attempting intuitive explanations for what is going on.
It is an interesting point now I think about it.

1 hour later…
6:24 AM
Wow. This is one hell of an experiment. At first thought he was doing magic.

7:13 AM

7:39 AM
For a fun philosophy time you can try reading EINFÜHRUNG IN DIE GRUNSTRUKTUREN DER THEORETISCHEN PHYSIK
Or "A New Foundation of Physical Theories", for a more English version
"Deutung des Begriffs "physikalische Theorie" und axiomatische Grundlegung der Hilbertraumstruktur der Quantenmechanik durch Hauptsätze des Messens"
Ludwig wasn't fucking around with his titles

8:28 AM
what is the policy on similar answers lol

1 hour later…
9:53 AM
I am now thinking on, how would a quantum field of observers affect other quantum fields.
Possibly a "hole" in an observer field could make deterministic states again non-deterministic. It would be an "anti-measurement".
Without interaction.

What is an observer field

I'm just chilling. It's raining here. I'm not that good in what you are talking about

@Slereah A quantum field. It relates to the QM observer as the EM field relates to the photon.

Observers are not a specific field

photons are not a specific field

9:57 AM
They certainly are.
Observers in quantum theory are denoted by states
not fields

Does wave have velocity? Or is it speed?

This is why I am thinking on this weird idea. It came into my mind after I've woke up today morning.

It think book has ambiguity here
it must be speed
or how do you predict wave velocity?

@Slereah No, photons are the quanta of the EM field. Around a permanent magnet, there are no photons. Only the field.

not i know what is difference of speed and velocity

10:01 AM
In general a wave has two velocities - a phase velocity and a group velocity. In many cases the two velocities are the same.
It's a velocity because it is determined by the wave vector, which as the name suggests is a vector so it has a direction.
@Stupidquestioninc velocity is a vector and has a magnitude and a direction. Speed is the magnitude of a velocity so speed doesn't have a direction.

10:30 AM
@peterh-ReinstateMonica what do you understand by “quanta of the EM field”?

11:19 AM
4

> "A New Foundation of Physical Theories", for a more English version
I have checked the preview pages and it so far looks good, will try to find a library to get it or to order one (30 something is within range considering I have not bought many books)
the section on reality seemed to answer some of the questions generated from my recent pondering on how physics models it

I was actually here to bring some much more positive news: Ryan Unger has published his first paper, in collaboration with none other than Shing-Tung Yau! Congratulations to him! arxiv.org/abs/2009.12618
11

wow a small world
so two people I kinda knew more or at least met in person have made a string theory paper huh

kudos

11:31 AM
The paper is on the non-existence of metrics of positive scalar curvature for a certain class of manifolds

Who's Ryan Unger, that name sounds familiar for some reason?

He's transitioned beyond us mere mortals

ah, fair play

@Danu it's hard when they grow up ;')

Definitely brought back some interesting memories...

11:41 AM
@JohnRennie sorry I meant note not not. Thanks for idea. I am beginner so I am kinda curious about it.

11:51 AM
@Stupidquestioninc Wikipedia has nice animations showing the two types of wave velocity

Matter waves and the dispersion relation results in phase velocity differing from group velocity? It's been a few months since I've done atomic physics, feels like I've forgotten something basic as to why they might differ lol

2 hours later…
1:27 PM
@Danu Thanks for sharing the great news!

2:18 PM
Data science, anybody?

I work in data science
I'd rather not get any more

2:32 PM
0

Imagine a horse is tethered to a cart. According to Newton's third law, when the horse pulls on the cart, the cart will also pull backwards on the horse. Since the two objects are attached together, they are technically the same object, and they cannot accelerate. This doesn't make any sense. In ...

@JohnRennie I was thinking about closing as a duplicate like you did, but I think the questions are slightly different
The proposed duplicate is asking about how a single object moves; i.e. it is misunderstanding the fact that Newton's third law describes force acting on different objects
However the above question recognizes this. The OP is just forgetting about friction. Their misunderstanding doesn't lie in Newton's third law, but rather just about what other forces are at play.

@Slereah those are some mind blowing numbers

1 hour later…
3:36 PM
I've seen ever larger numbers
My mind isn't easily blown

3:50 PM
Ryan publishing his first paper with a fields medalist is pretty incredible imho

@Danu Could you please remove that
@ACuriousMind mb you could do it
actually just the reference to my old username w/e

@RyanUnger I can do that, yes

thx
how are you?

I've removed the reference but it's not that hard to make the connection if one searches the chat transcript

yeah I know

3:53 PM
@RyanUnger pretty good, though probably not wrote-my-first-paper good ;)

I'm too busy preparing for the qualifying exam
I finally know the quadratic formula

Hey @RyanUnger

hah, nothing can stop you then

@Slereah hi

All math is just generalization of the quadratic formula, really

3:55 PM
@ACuriousMind i know certain people irl have read pretty much everything I've written here
really weird actually

I can't remember Ryan, were you working on your masters or PhD?

I'm sure there's an $\infty$-topos encoding the logic of the quadratic formula :P

@ACuriousMind I'm guessing you don't need to go that far, even
a regular topos would probably do it

So what is the paper by Sir Ryan Unger, if I may ask?

@JMac phd

3:56 PM
What's the PhD going to be?
Still the positive mass theorem?

lol.

@RyanUnger That's a lot of reading...at least they cared enough about you to do that? :P

@ACuriousMind I don't think it was meant in a good way
But I've only been confronted once about something I wrote

I feared it might not be :/

@RyanUnger Nice, that's gotta be a fun mix of exciting and stressful.

3:57 PM
a bit weird

@TerryBollinger we partially prove a conjecture of Schoen--Yau and when combined with some recent work it's completely proved
recent work by Chodosh--Li
@Slereah we mention the PMT in this paper but I do want to actually write a paper about the PMT

Ryan, is there an online title? A Google Scholar search on your name is... um... not helpful!

it's the last paper by R. Unger on arxiv
the other ones being another R. Unger, I assume

I guess so

4:04 PM
@RyanUnger congrats

thx

@Slereah well, the others are all about group theory and don't involve any geometry, that'd be a radical change in his opinions on algebra :P

Ah, got it:

@ACuriousMind people can change

@ACuriousMind Maybe he has diverse interests

4:06 PM
For some reason you don't show up on Google Scholar yet. A lot of papillomavirus papers though

@RyanUnger sure, but this particular change would really have surprised me

I'm organizing a seminar and the first speaker is a number theorist
Maybe I really have changed

whoa

it's not a number theory seminar
the second speaker will be someone more reasonable don't worry

Like an ISIS militant?

4:09 PM
is ISIS still around

to some degree, yes

so the number theorist is the one with weird interests, gotcha :P
I mean, weird for a number theorist

it's a seminar for ppl in my cohort
well, research areas

ah, free-for-all style?

we did it last year and it was a big success
gonna try to get more technical this year, might be a disaster we'll see

4:10 PM
Depends on the audience

probably hard to get anything substantial across but interesting to see what others are doing or maybe see connection to one's own work

it's true but I want one person to continue trying to compute a Fukaya category, for example

it's been a rough year, though
Maybe he wasn't focused on Fukaya categories the whole time

More nonsense describing things string theorists found using basic calculus!

I was about to say it's abstract nonsense but that one looks pretty concrete.

4:20 PM
there's no Fukaya category in the sky

is bolbteppa still on about string theory

He certainly is

yes, not all people change :P

all of Princeton knows who he is

What person? That is just a common expression to talk about things that are not concrete.

4:23 PM
the dirac belt guy
variable speed of light
etc

I also highly doubt any string theorists "found" this using "basic calculus" - the A-model in which they occur was found by Witten and mirror symmetry has been very mathematical pretty much from the start

I'm sure I don't know any such person

@RyanUnger you're allowed to talk about people but you still have to be nice to them :P

IIRC you're not even allowed to mention banned individuals

4:24 PM
Say 5 nice things about J.

Wasn't Duffield banned for a century?

Not yet

Has it been that long?

@RyanUnger A guy from Munich also keeps on talking about variable speed of light.

He actually recently came back
but didn't stick around

4:25 PM
@RyanUnger time is very strange in 2020

Variable speed of light was the original idea for GR, IIRC
it was the idea that inspired the metric tensor
I'm not sure if you could describe modern GR by variable speed of light, though

I would fail my generals exam if I said that

Might be doable but it seems tricky to define everything
Especially wrt diffeomorphism invariance

We are big believers in establishment science here

"diffeomorphism invariance" ::eye twitches::

4:27 PM
General covariance
if you prefer

Yeah this is why I don't talk to physicists

better for sanity, certainly

A variable speed of light is probably an insane idea, it would probably end up modifying absolutely everything, it's like saying the speed of interactions depends on some field to propagate interactions where the interaction of this field propagating the interaction must also vary and on and on down a barrel of monkeys

It's kind of how the Pauli-Fierz theory works, though?
The gravitational field interacts with the EM field
although that's different from "The fundamental speed of light varies"

"The A-model arose in formal physics from considerations of superstring-propagation on Calabi-Yau spaces" this can be done with basic calculus
https://ncatlab.org/nlab/show/A-model

4:31 PM
the main problem is that it's not clear what we would gain from such a formulation - like, sure, we also have Lorentz ether theory as an alternative to the geometric formulation of SR

@ACuriousMind It would make J. happy

@bolbteppa you can't even formulate what a Calabi-Yau space is in "basic calculus"
but no one is excited about LET compared to SR because SR works fine

@ACuriousMind, about Witten's volume formula again:)... he computes the integral $\int e^{-S(A)}dA$ over flat connections mod gauge group.

Read a bit about general relativity recently, and decided pretty soon that setting the speed of light to 1 is actually a really good idea.

So I think this is the one you said is easier to compute compared to $\int e^{iS(A)/h}dA$, which is oscillatory. But there is also a formula for the latter which gives an exact expansion in terms of critical points of S(A), this is due to Duistermaat and Heckman I believe. I wonder if I can use that to get a different volume formula. or even the same. I am not sure what is the link between dimension of representations with critical points of the action.

4:33 PM
@ACuriousMind I'm sure there's still fans of it
@ThomasKlimpel It's mostly done for practicality
You're supposed to put the $c$'s back in for measurements afterward

But setting c to 1 really makes things easier, because many tensor become symmetric by doing so. And it makes complete sense to use the same units for space and time.

Yeah trying to throw the extra dimensions into complicated Calabi-Yau's does introduce formal questions you can't be blase about and you enter the place where results can be found that can't be found by basic methods, but give it time :p
@RyanUnger welcome to the establishment

Do you get to disappear cranks once you're part of the establishment?

Science hasn't reached Handmaid's Tale levels yet

Like so

4:43 PM
@RyanUnger, most impressive, your group completed the proof of the Liouville theorem! (I realized I'm waaay behind on this conversation, but that is intriguing and impressive.)
Hmm, even by exact paper title there's no bib for your article in Google Scholar yet (so yes I'm lazy). Granted it's only 3 days, but I'm still a bit surprised.

give it time

Yep, it's just that I've seen other papers cycle though a lot faster.

is the paper itself published yet?
Or is it just the prepublication

Looks prepub at arxiv.

@ACuriousMind huh? Ricci flat Kahler manifold
@Slereah it's been submitted, I have no further information

4:51 PM
Maybe that's why then

neither of these words is something I'd consider part of "basic calculus", but then again I don't really know what 'calculus' exactly is supposed to be, either :P

usually arxiv's get in pretty quickly, maybe it just takes longer without a journal

calculus is anything that could reasonably be seen in a harvard math 55 class

that certainly includes Yau's theorem although perhaps not all the details

4:53 PM
Algebraic geometry done with analysis tools like in that Griffiths Harris book is basically just calculus at the end of the day
The multivariable complex analysis kind of calculus!

Are we gonna claim that after set theory and category theory, all math is based on calculus?

No, algebra isn't calculus, topology isn't necessarily, algebraic geometry done the modern way isn't etc

@juliensurel Witten's computation of the partition function is exact, it doesn't contain any approximation - that's the power of two dimensions here. So I'm not sure why you're looking at different ways to compute the path integral here?
sure you could try to compute it approximatively or by some series expansion but why are you trying to?

I'm not sure "calculus" is the proper term for this really
When I think calculus I think $\mathbb{R}^n$
Not ideal for global manifold things

@ACuriousMind, I was just curious about the relationship between the two formulas, but now I also realized the alternate formula is only for torus actions not any gauge group action... but thanks anyway.

@RyanUnger I s'ppose

@Danu It seems that rather it was written in collaboration with one other than Shing-Tung Yau.

found the logician^

6:00 PM
Oh boy
Gunther Ludwig wrote an actual epistemologist axiomatization of QM
it's gonna be weird
with pretheories and whatnot

6:24 PM
"In fact, the basic concepts such as observable, ensemble, state, or yes-no measurement, employed in the "usual" interpretation of quantum mechanics, are themselves not explainable by known pretheories."
"Whenever we speak of single microsystems, we cannot simply display them as one would display a cup on a table."
No microsystems in the night sky

Some of this conversation reads so oddly to me, in no small part because I can only conceive of mathematicians as biological versions of AI systems... and in such systems, there is only approximation (labels) and calculations (programs attached to such labels.
Thus this (Cauchy?) statement: "Calculus is the computation process ... but useless by itself; it can only function in the context of a complete number field" has for me, alas, no quantifiable meaning; it is instead an inverted statement about the reliability of the calculation process, stated in terms of what calculation makes possible at some unrealistic and completely unreachable (both mentally and physically) limit.
That is, it is really a badly stated assertion about self-consistency of the calculation method across multiple scales of resolution, with the infinite (and thus impossible) sum of which approximates this peculiar concept labeled (and thus always approximate) by the phrase "complete" number field. What am I missing here?

6:47 PM
"A typical feature of all these theories is the objectivating manner of description. This. fact was before quantum mechanics perceived as so fundamental that many physicists rejected quantum mechanics since it no longer presents an objectivating description of microsystems."

@TerryBollinger Cauchy's statement should not be read in the context of modern mathematics where we essentially mean the "computational parts" of elementary real analysis by 'calculus'. Cauchy was one of the first mathematicians to demand a certain kind of rigor and in this context, "calculus" was probably the sort of (unrigorous) computations everyone was doing without making sure they made rigorous sense (e.g. in terms of limits being well-defined, series converging, etc)

@RyanUnger Who, me?

I read this in more modern language as "It's useless to try to compute limits without having defined what a complete field is and what convergence means"

@ThomasKlimpel : you might like to read things like this: einsteinpapers.press.princeton.edu/vol7-trans/… : “Second, this consequence shows that the law of the constancy of the speed of light no longer holds, according to the general theory of relativity, in spaces that have gravitational fields. As a simple geometric consideration shows, the curvature of light rays occurs only in spaces where the speed of light is spatially variable”.

@Slereah is objectivating just very intense objecting?
also, why is there a sentence in there that's just "This."

7:01 PM
@ACuriousMind I think it's the epistemologist way of saying that if you measure an object in a state then it has that property?
Not sure
I'm only up to chapter 2
He has yet to say what the hell objectivating is

@Slereah that would be what every other source I know calls "realist" :P

Well, we'll see!
Epistemologists are a weird bunch
Hm, I'm not sure he really describes it in this book
it might be in his other books

@Slereah perhaps he means "reification"?

Ugh
The reference he gives is to his untranslated german book so it's hard to find something
@ACuriousMind you're germany

@JohnDuffield Well, Einstein wrote this (in January 1920) long after he had published his general theory of relativity. So I don't think that he would object to setting c = 1.

7:11 PM
How would you translate "objectivating" in German
From what I can gather it's the idea that measurements and the physical state of a system are directly related
but he doesn't seem to define it anywhere precisely

I would guess it's a bad translation of objektivieren, for which a better translation (at least its common meaning) would be "objectivize"

The German book talks of $\mathfrak{objektivierende Beschreibungsweise}$
(objektivierende Beschreibungsweise)

@ThomasKlimpel : you should read this too: einsteinpapers.press.princeton.edu/vol4-trans/144 “On the other hand I am of the view that the principle of the constancy of the velocity of light can be maintained only insofar as one restricts oneself to spatio-temporal regions of constant gravitational potential”. That was in 1912.

Let's see

guess I guessed right

7:16 PM
Like Slereah said, the variable speed of light was the original idea for GR. That changed after Einstein died. See this: en.wikipedia.org/wiki/…

@ACuriousMind was ist das

@Slereah "The preparation procedure $a$ produces physical objects with different properties with the frequency of the different properties described by the measure $m_a$. The detection procedure detects the properties, but only imperfectly. There is no influence of the preparation procedure on the detection procedure other than via the objective properties. This is called the objectivizing method of description."

hm

I'm afraid it doesn't make total sense to me in the original German either :P

I guess I'll have to scour other papers to find a proper definition

7:22 PM
Thomas: see einsteinpapers.press.princeton.edu/vol4-trans/271 for an example from 1915: “the writer of these lines is of the opinion that the theory of relativity is still in need of generalization, in the sense that the principle of the constancy of the velocity of light is to be abandoned”. Note though that c=1 isn't actually wrong, it's just telling the story from the local observer's perspective rather than from the God's eye perspective.

"As Hanson outlines, ‘seeing’ is not a physical process, the formation of the retinal image, but is a ‘theory-laden’ enterprise"
it gets a bit abstract

well, it's not wrong - see all the strange optical illusions that can arise because our brains do all sorts of weird stuff instead of rendering the image "as is" (whatever that would mean)

John Duffield is back
It's like I'm back in high school

I think they mean that in an even more abstract way

and certainly we also tend to interpret what we see in terms of what we expect to see even outside of the subconscious pre-processing of the brain

7:26 PM
objectivation seems to be a notion common enough that most papers don't feel like they have to define it
But not common enough that I can find a definition specific to that domain

@JohnDuffield "Note though that c=1 isn't actually wrong, it's just telling the story from the local observer's perspective rather than from the God's eye perspective." Is that your opinion, or Einstein's?

"The concept of objectivation goes back to Kant"

@ThomasKlimpel : It's my opinion, but it's also other people's opinion. See for example math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/…. I don't think I can give you an Einstein quote for "God's eye perspective".'

ah, I think it basically means "all observers see the same things"

@ThomasKlimpel Don't get dragged into irrelevant textual exegesis when the root confusion is that when you say "c=1" or "the speed of light varies" in a GR context as we understand it today you have to define a bit more carefully what you mean by "c" (one-way speed of light, local speed of light, round trip speed of light, ...). It's the local speed of light that is still constant in GR and most confusion around this arises from people leaving out the qualifiers.

7:33 PM
ie there are objective things that can be measured by all

good lord has this chat not moved past c=1
some things really never change

@RyanUnger you picked a bad day to return :P

@RyanUnger You said the forbidden name

it's true

@Slereah that still sounds to me as if I'd more commonly call that position "(objective) realist"

7:35 PM
@ACuriousMind maybe, although apparently it's an older (and more general) idea

@ACuriousMind right well never underestimate my desire to procrastinate learning algebra

what sort of algebra?

I guess the fact that Kant wrote about it is why everyone assumes readers know it
Kant might as well be philosophy Newton

learn = remember enough to not be completely embarrassed
finite groups, modules, Galois theory
basic stuff but hard for me :(

I don't recall that particular concept from our stint with Kant in school, but maybe my memory is bad or you actually have to have read the whole thing instead of the cliff notes :P

7:38 PM
Kant wrote a bunch

@RyanUnger I think I've forgotten everything about Galois theory

Evarix le Galois

I mean, I could vaguely tell you stuff about it but not a single hard theorem

all I know is the Galois group of x^3 - 2
heopfully that will be enough

I'd rather not read the critique of pure reason so I'll just assume I got it
I don't want to critique pure reason, it seems fine

7:42 PM

I'm even on board with insanity

Thomas: he used the phrase "global observer".

oh god how do I get equations to work

Mathjax
31

As a workaround while this request is pending, there exist several client-side workarounds that can be used to enable LaTeX rendering in chat, including: ChatJax, a set of bookmarklets by robjohn to enable dynamic MathJax support in chat. Commonly used in the Mathematics chat room. An altern...

or go there directly

yeah I'm trying
I do have the bookmarks somewhere
$\int f$

7:46 PM
@ThomasKlimpel re the comment from ACuriousMind, this is worth a read: arxiv.org/abs/0705.4507. Magueijo and Moffat talk about the tautology. That's where an observer uses the local motion of light to define his metres and his seconds, and then uses them to measure the local motion of light. Hence he always measures the local motion of light to be the same.

This is stretching it even for me, why is
$$- \int dx dy dz c_{\alpha}(x) (\frac{\delta^2 \mathcal{G}(x)}{\delta \Lambda^{\gamma}(z) \delta \Lambda^{\beta}(y)} ) \overline{c}^{\gamma}(z) \overline{c}^{\beta}(y) = - \frac{1}{2} \int dx dy c_{\alpha}(x) (\frac{\delta \mathcal{G}(x)}{\delta \Lambda^{\delta}(y) } ) f^{\delta}_{\beta \gamma} \overline{c}^{\gamma}(z) \overline{c}^{\beta}(y)$$
where $c^{\alpha}$ are ghosts, $\mathcal{G}(x)$ is some gauge-fixing function.
Look at how second derivatives magically become first derivatives!

@ACuriousMind The reason why I recently read a bit about general relativity was to better understand whether one could make sense of a statement claiming that Planck's constant h always stays constant. I am not claiming that I would understand that question much better now.

@bolbteppa for stuff that huge, remember to use double dollar signs
ie $$- \int dx dy dz c_{\alpha}(x) (\frac{\delta^2 \mathcal{G}(x)}{\delta \Lambda^{\gamma}(z) \delta \Lambda^{\beta}(y)} ) \overline{c}^{\gamma}(z) \overline{c}^{\beta}(y) = - \frac{1}{2} \int dx dy c_{\alpha}(x) (\frac{\delta \mathcal{G}(x)}{\delta \Lambda^{\delta}(y) } ) f^{\delta}_{\beta \gamma} \overline{c}^{\gamma}(z) \overline{c}^{\beta}(y)$$

whoa @RyanUnger's back
how's life?

who are you?

7:48 PM
...

@RyanUnger didn't get a degree in feelings, certainly

@SirCumference I'm ok. I don't know why I'm here
@Slereah he just has to answer the question

Wait I don't think it's bad actually

@ThomasKlimpel Strictly speaking, you can only meaningfully talk about changes in dimensionless constants, cf. physics.stackexchange.com/q/78684/50583. So it's meaningless to argue about the constancy of $c$ or $\hbar$, you need to talk about things like the fine-structure constant

It looked like they were doing $\delta \Lambda^a(w) \delta \Lambda^b(z) = \frac{2}{ \delta(z - w) f^c_{ab}} \Lambda^c(z)$ inside partial derivatives :/

7:54 PM
@ThomasKlimpel as far as I know conservation of energy and E=hf mean Planck's constant stays constant. Einstein said “an atom absorbs or emits light at a frequency which is dependent on the potential of the gravitational field in which it is situated“. When the ascending photon ascends, its E=hf energy does not reduce, and nor does its frequency f.
My understanding is that the fine structure constant varies with gravitational potential. The Parker Solar Probe was going to test this, but they cancelled that experiment.

But with respect to c, as long as no unit for measuring time is specified, I guess I have all the freedom in the world to set c=1. For $\hbar$, it is less clear to me whether I have freedom or not. If the unit of time and the unit of energy is fixed, then the unit of $\hbar$ would be fixed too. But then, is the statement of conservation of energy still meaningful in general relativity. If yes, then I cannot just freely monkey around with the unit of energy.

@ThomasKlimpel GR does not in general have conservation of energy because energy is only conserved in time-invariant dynamics (cf. Noether's theorem).
and you are still free to choose a unit of energy even when it's conserved
there are also different ways to think about what we mean when we write something like $\hbar = 1$.

04:00 - 20:0020:00 - 00:00