8:00 PM
And also I was quoting myself (in real time)
So I could just copy paste:

"In physicsstackexchange were okay with the above quote ... And even if brought to our attention ... It okay!"
Is the essence of what ur saying?
Also QM was taught in year 2 in my unversity and Im sure there are those with year 1

@MoreAnonymous you still haven't pointed out how 'discontinuity and non-unitarity of measurement' even apply to this derivation

I feel I have done so many times (in fact Im not sure why you feel otherwise) ... I feel Acuriousmind can represent my position better than I have ...
Maybe he is more suitable
And you should ask him the very same question

@MoreAnonymous A counter-anecdote: I learnt QM in my 4th semester (so 2nd year) where this exact derivation of M-T time-energy uncertainty was presented. I didn't see anything wrong with it then, and it did not lead me or my peers (that I know of) to unfounded conclusions.

@bolbteppa I’d actually agree on this: the derivation is very much predicated on unitary time evolution. But that’s exactly the context in which it is relevant

Whatever is causing confusion, I feel strongly it is not, or at least not mostly, this particular derivation or the lack of giant CAUTION signs around it

8:06 PM
@ACuriousMind I feel you and your peers were more than us mere mortals plus ... I feel your saying the average opinion I have encountered is a statistical fluke ... which is a posssiblility but still an improbability

So to complain about it not addressing the case of non-unitary evolution is to complain that it’s answering a different question than the one you want

@MoreAnonymous We were of flesh and blood and caffeine as you are.

@ACuriousMind I used to think the same of Einstein :P ...
Also are u of the opinion what Ive encountered is a statisical fluke or not?

@MoreAnonymous No, I'm well aware there's a lot of confusion around this. We just disagree as to what's causing it.

@Semiclassical if I understand you right I agree, I have no problem with that, my question is really though - how does non-unitary time evolution even relate to this discussion
I think we talked about non-unitary Hamiltonians or Non-Hermitian QM on here before done by respectable people

8:09 PM
Hi o/
I'm a student and am a bit confused on the conservation of energy.

hey there

@ACuriousMind Can we agree we can minimise the damage by adding a few lines (maybe putting an edit in bold so those who want to read that section can?)
???
Even if not minimise we can lessen/
?

@MoreAnonymous You're free to suggest an edit, but as I said I do not think that what you want that answer to say is at all relevant to the specific question it is answering.

@JMac I left a comment ages ago ... But it didnt get answered let alone upvoted
And I lost patience and asked a question

8:11 PM
@MoreAnonymous Well then clearly your concern doesn't seem to reflect the rest of the community. Not much else you can do there.

So take a runner for example. We can see energy transfer from place to place. Sun → Grass → Cow → Runner. But once the runner starts running, where does the energy go? Obviously the runner is using energy to run (this is known because they cant run forever), but the energy doesn't seem to transfer anywhere.

@JBis friction with the ground + movement of the earth (imperceptible since its mass is so large compared to the runner)

@JBis The air, the ground, body heat, sounds. It basically "dissipates".

@JMac nope Acuriousmind is under the opinion that people of the community are unaware (if not misuing) this derivcatoin and hence it involves the whole community

@ACuriousMind so you are negligibly slowing or speeding the earths spin?

8:13 PM
@JBis Among other things (heating the ground and air through friction, etc.), yes

Hmmm.
Ok so what about mass → energy and energy → mass. Isn't energy lossed/gained there as well as matter, breaking both the conservation of energy and conservation of mass laws?

@JMac Also it is highly intimidating to think you are right when your against a 90 upvoted question (I mean if u do then ur on crackpot level) ... And a user like me shouldnt have to pay the price of downvotes on a seperate question regarding some legtimate (doubts) ...
I feel physics stackexchange has let me down ...
:(((

@JBis 1. There is no "conservation of mass". 2. $E=mc^2$.

In special relativity, energy and momentum are constrained by $E^2 - \mathbf{p}^2 = m^2$

Oh

8:18 PM
Also @ACuriousMind will you be willing to continue our discussion where I make the case a few more lines can really minimize the damage?? (I can wait if ur teaching) ... Or ...

> The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy,

@MoreAnonymous Welcome to the internet, things are going to let you down. Doesn't mean that you just to change things to fit the way you want to see them, when others in the community don't seem to agree. I'm not saying you're necessarily wrong or anything, but adding disclaimers to answers because you find something misleading isn't the correct approach on SE.

@MoreAnonymous he's basically just quoting a section from Griffiths QM book, I really don't understand what the problem is with the derivation apart from hand-waving worries that 'continuity' and 'unitarity' somehow don't apply because ... (coupled with hand-waving worries about unnamed alternative interpretations maybe disagreeing)

@JBis What about it? For most classical systems, assuming that all mass remains as mass and all energy remains as energy is fine, and in that case both are independently conserved in a closed system.

8:21 PM
@JMac I suspect if an answer doesnt enlighten the user to what physical case it is relevant in then its not really a great answer ... I mean if you scroll up you can see other chat users making the case for this derivation in cases it clearly doesnt apply to ... In which case "you" is the wrong word ....

@MoreAnonymous I'm sorry. But I feel I have said all that I can say (multiple times, in fact). I have explained why I think your question is problematic even if your underlying confusion is earnest and legitimate, and I have explained why I think josh's answer is a good answer to the question it is written as an answer to. You seem to have different expectations of what an answer here is supposed to do, and that is fine, but I simply do not agree.

Hmmm ... Oh well ... thank you for being clear on this and atleast letting me making a case for otherwise ...

@JMac So are there exceptions?

@MoreAnonymous Well, your suspicions don't really align with how this site works... The answer clearly provided some information that others found useful, hence it was well received. You don't get to add things to it just because you didn't personally receive it as well. This site would turn into a mess that way, and that's basically my only point.

8:24 PM
@bolbteppa ... maybe if acuriousmind if up for it he can convince you why "(my) underlying confusion is earnest and legitimate"

I fear if I say "measurement is a black box" one more time the ghost of von Neumann will appear and bludgeon me to death with a giant ket.

@MoreAnonymous it's fine to be confused about the derivation and to have concerns things don't apply, that's basically the whole point of studying physics is to question things until you're convinced, but honestly you have ignored multiple direct questions from me written in multiple ways asking you to directly point out why your concerns are even relevant and you haven't done that yet

(More seriously, I'm just tired)

@JMac You keep saying "you" and I would agree with you if it were just me (I feel above 50% of the users have my misgivings) .... Acuriousmind seems to agree my experience is not a statistical fluke ...
@bolbteppa I feel like youve ignored my direct answers (I notice I use the wording feel)

8:26 PM
@JBis To just the conservation of energy, there are kind of exceptions; but not really. Mass and energy are treated as equivalent. As far as energy conservation in introductory physics classes are concerned though, you typically assume mass and energy are separate and don't convert between each other

I mean you link some of them to acuriousmind ....

Ok thanks for the help, I'm sure I'll need more soon
:)

There is an arrow on the left of each post, click and then see the "permalink" thing, send me that link to even one direct answer

8:28 PM
@MoreAnonymous I would call that a dodge haha
I'm going to make a bold claim that I can also permalink my response to that post :p

@MoreAnonymous Still not really my point. My point is that just because you and possibly some others find some issues with the answer, doesn't mean that you should substantially change what someone else's answer is saying. It's just not how this site is supposed to work. The community works together, but it's not like we're a wiki. People have their usernames attached to the posts, so changing content of others is best left alone.

@JMac So your okay with above 50% of users misinterpreting and then misusing the answer ???
If you say yes ... we will reach an agreement instanansously

I'll let you in on something: There are upvoted answers on this site that are flat-out wrong! Yet we do not delete them because that is not how we do things here: If it is an attempt to answer the question, it will be judged by votes. If the wrong stuff gets upvoted, that is a failure of the community, but not a failure we would remedy through edits or deletion.

@MoreAnonymous I have no control how others chose to use information they get online, so yes, I'm fine with it. People can misinterpret any answer on this site if they want to.

@JMac And your okay with it being above 50% as well?? Im quite saddened to hear that ...

8:34 PM
@MoreAnonymous I linked about 7 posts of yours above where you asked questions, not one of those things I linked is an answer to even one of my direct questions about why non-unitarity of measurements even matters to the unitary evolution described by Heisenberg's equations used in the time-energy derivation, it's comparing apples and oranges and you still haven't explained why it's an apples to apples comparison

I only use question marks due to sheer disbelif
@bolbteppa honestly my argument seemed to make sense to Semiclassical and Acuriousmind who (I feel) engaged with me ... And they all had access to typing (as do you) ...
I suspectr it would take alot of effort for you to even see why I said what I said ... let alone ever sympathise with it ... And hence I advise you should ask those who understood me ... I am far too exhausted right now and mentally fatigued ... and Now after witnessing the brazen "its okay" policy Im questioning the frequency I'll visit the site (let alone the chatroom)
@JMac @ACuriousMind ... I suspect the real reason stackexchange has the elitist sterotype is becasue perhaps the intellectually elite have given up on this system ...

@MoreAnonymous I'm so aware of the fact that you're hinging on the hope you at least convinced someone of your concerns that earlier I already pointed out you used an apparent understanding on other users part to claim that "the measurement problem implied that the Heisenberg equations sometimes did not apply" chat.stackexchange.com/transcript/message/51657961#51657961 which is absurd, this is not a good way to gain an understanding of the topic you asked for help with tbh
You're actually disagreeing with a section from a Griffith's book and trying to blame the site for Griffith's explanation of time-energy at this stage

Yes ... Maybe at this point I am too mentally fatigued to understand why you disagree (without the use of non sequitors) ... And hence I 'll be leaving the chat soon ... I apologise for not being able to have the intellect or the perseverance to convince you ... But others might ...

No worries, you don't even have to convince me of anything, just asking you to explain your how concerns are even relevant to the derivation

@MoreAnonymous What? What does the elite giving up on the site have to do with "elitist stereotypes"? Wouldn't you expect the opposite correlation if anything? Also, I don't go around looking up other opinions of Physics SE, so I can't even speak of this elitist stereotype you speak of.

8:48 PM
Anyway I'll be dropping of for the chat .. Let me just add this is the first time I feel let down by physicsstackexchange .... I feel upto this point it has been a gr8 experience (in fact I feel emotioinally run down becasue it has been so gr8) ... Atleast my doubts were clarified in the end albeit in an unusual way

I'm sorry a virtual quote from a section of a Griffith's QM book being the top up-voted answer has upset you so much, take heart that people tend not to like Griffiths' books :p

Man trying to think of schemes for measuring distances properly in GR is hard
I can't even assume that the distance won't increase by more than $ct$ with time because space expansion can 100% do that

@Slereah curveball - the measuring device isn't even a rigid body and so can't even be trusted beyond a certain accuracy

@bolbteppa Well i'm using light signals here

@Slereah Wait until you get to measurement stacks!

8:52 PM
but of course, also consider this : the gravitational field will change the frequency of the atomic transition
Since that adds another potential to the Dirac equation
I mean that one I choose to ignore because come on
I just assume that my measuring device is some perfect device full of lasers, light detectors, clocks, memory and computing units that is exactly a point

I'm always just assuming you do measurements in a locally inertial frame where everything's fine

The current problem is the ideal case : consider some 2D spacetime $(\mathbb{R}^2, g)$, with $g = \Omega^2(x,t) (-dt^2 + dx^2)$
It is foliated by timelike curves, which are observers
At every point in time, each observers emits two light signals (one forward, one backward)

@JMac (only since you guys pinged) ... Nope I use the word intellectually elite ... And I feel your doing what the user below was doing
@bolbteppa it wasnt the quote ... it was the price I had to pay to learn if anything ... Esp for a site which is supposed to enable "learning" ... I suspect you do not take my advise of asking semiclascial or acuriousone seriously ... Because of this "price"

each light signal encodes informations about its observer of origin, what proper time it was emitted at, etc
Given all this, can one observer reconstruct the entire metric?
@bolbteppa That's the easy way, of course
But that's making pretty large assumptions
Even worse, unstated assumptions!
It's pretty hard to do because even just making sure that all observers are synchronized isn't trivial

@MoreAnonymous I literally don't understand how your response relates to our conversation. I when I said "elite" I also meant "intellectually elite" just like you had said.

8:58 PM
If I assume everyone synchronized at some Cauchy surface $t = 0$ I think it should be easier

@MoreAnonymous come on haha this is getting hilarious, asking me to ask other people whether they understood you and asking them to reiterate back to me their understanding of your point, even though I have already literally given an example where you got people to say things that you interpreted as validating a beyond absurd claim? Is this for real?

Although of course
Here's another problem
HORIZONS!
What if some light signals never arrive to you???
Hopefully I can at least reconstruct the metric in some neighbourhood

@Slereah You could say you'd stay in the dark about them.

Indeed I can

@JMac Are you saying the IQ points of this "intellectual elite" is so much that they wont make sense to the people wo misunderstand (in this case more than 50%) ... atleast I for one am an outlier on that one

9:00 PM
why can't we just live in Minkowski space, really

@MoreAnonymous 'the intellectually elite have given up on this site'... 'alternative interpretations'... 'quantum equations of motion can fail sometimes'... I mean, there is a way to describe statements like these...

@MoreAnonymous I have to say that nothing you've said pertaining to "elites" made any sense to me either.

@MoreAnonymous Not even slightly... wtf? You said that stackexchange has an "elitist stereotype" because "intellectually elite have given up on this system", and it's very unclear to me how that follows.

(I thought I was in the elite, until today...)

I mean
Things are hard enough in Minkowski space

9:03 PM
@bolbteppa it must be pretty easy to convince yourself that the others are "validating a beyond absurd claim" ... Rather than think ur being absurd ... I feel they arent taking a side because they dont wanna ... Maybe someother price

The elite live in Minkowski space

@ACuriousMind yes and i never said you did

I'm not even sure how easy it is to reconstruct synchronization for accelerated objects
Because the usual synchronization is basically just a Lorentz transform of the foliation
But once it's non-linear
Anything goes

@Slereah can we not just pretend we do? :P
I mean, sure precession of mercury is gonna be off a bit, but otherwise, what'd be the difference? :P

@ACuriousMind Can't go back to the garden of eden, I'm afraid

9:05 PM
@JMac to me its pretty clear in this case Im refering to those who get that context of that derivation as intellectually elite ... I feel they enough points to make a difference .. But maybe thats where Im wrong ... And the "elitist sterotype" prevails in this case because the elites do not wanna make the effort?
To correct the idiotsw (like me) ... From idiocy

Why wouldn't you listen to the intellectual elite, really
Sounds like they know what they're talking about

@MoreAnonymous are you saying I am being absurd in asking you to simply state (or even re-state) your concerns about a topic, rather than taking the easy way out and asking other people to state your opinion for you

@MoreAnonymous I'm having increasing difficulty following you... so I'm gonna head out and get a coffee because this doesn't seem to be going anywhere

@Slereah I did listen to them and hence gotan answer finally ... But Im not sure everyone else with this problem (more than 50%) would be willing to pay this "price"

@ACuriousMind The thing is that the parameter of the Reichenbach synchronization, $t = t_1 + \varepsilon (t_2 - t_1)$, is basically the "tilt" of the Cauchy surface

9:08 PM
@bolbteppa I dont care about the opinions of Lee Smolin or Lubos Molts I care about the arguments they make

So I'm pretty scared that for a generic Cauchy surface it's gonna be some awful function

@JMac Agreed Im gonna go for sleep though

But the hard part is making sure that the synchronized points are spacelike separated, at least

@Slereah but why can't you take the easy way out since GR reduces to SR locally

@bolbteppa Well that's the thing
how locally?
(I mean I know that in real life that's obviously true at human scale)
But it's one of those things where like...

9:10 PM
@bolbteppa also in this case I feel they understood my arguement and will not misrepresent it ... In fact they will do my concerns better justice ...

I like to show the general case to show that the approximation is valid

@MoreAnonymous are you sure they weren't just saying it's understandable for someone to have legitimate questions about a derivation and nothing more beyond that, seems like a big stretch to assume other people got your point when you can't even quote a single passage where you made this point after directly being asked to do so
Rather than making a gigantic presumptuous assumption about other people, it's probably safer to just re-state your point or even just post a link to where you made this point
At this stage, I'm going to say you can't

I agree with JMac that this doesn't seem to be going anywhere useful and would ask everyone to drop the topic for now.

Okay, last thing: lol

And of course
If we're just assuming physics as is
No point in doing any research

9:16 PM
@bolbteppa No I precisely feel even though you hear people say "on this point I agree with him on this point"... "I'm disappointed that the answer doesn't address the question I wish the OP had asked." ... Also acuriousone personally pinging you and telling you that this derivation does not have imply the physical situaiton you think it does ... You have convinced me (and perhaps not only me) it is not worth the trouble
Sorry I just read your comment acuriousmind ... I was amidst typing the above comment

@MoreAnonymous super last thing, really quick, I think you read the "I'm disappointed that the answer doesn't address the question I wish the OP had asked." sentence unironically, I think you need to re-read that one
@Slereah have you got any links to these issues with GR measurements (that don't involve crazy global GR)?

@bolbteppa As mentionned, the only extensive treatment I know on the topic is Reichenbach

But like, even a popular article on the issues with GR measurements related to these topics

There might be others in the more philosophical-oriented GR books like maybe some of Malament or Earman's stuff, but I can't think of any rn
Well today i found this, for instance :

I have no idea how high the sarcasm level you think in this chat is ... But I disagree because u have also "I'm allowed to be wrong :)" ... Where he admits the position he took was wrong and only got to know the answer because of a user like me ...

9:24 PM
It's pretty hard to work out in GR because there are so many things that can go wrong

This is all probably part of the GPS relativity (engineering :p) literature

Well I think in the actual literature they just assume that earth is ~ a kerr metric
They don't go building an interferometer every meter of space

9:48 PM
They see that the earth looks about round and don't go start thinking "Maybe it only looks round because of the geometry of space!!!"
(it's by the way kind of what Reichenbach discusses)
the how can you know what the geometry of space is without too many assumptions

@bolbteppa ... I feel I should try to clarify my stance with you .However, I am already of the impression that it will take more than this one chat session ... Are you up for it?

@Slereah ...have you become some kind of GR flat earther?

@ACuriousMind Not so far!

@MoreAnonymous sure

@Slereah if I'm sure r/earthisflat would love whatever u've done :P

9:52 PM
I mean even assuming weird geometry it still has to be diffeomorphic to a sphere :p
Although it could be a cube I suppose

Alright Lemme see where the disagreement comes from?

Synchronized atomic clocks ftw

Do u disagree that the measurement (naively) cannot be represented by a unitary transformation?
@bolbteppa

I don't know what it means to represent measurement as a transformation tbh

Part of the issue is assuming that measurements are a transformation on the wavefunction
I'm not sure that's a good argument to make
although of course it's a bit weird because quantum probabilities aren't Kolmogorov probabilities

9:58 PM
You should find this post enlightening on why whatever the measurement is why people are not comfortable saying that the measurement is a unitary operation
3

It is said, that when measured, a quantum system undergoes "wave function collapse", which is a non-unitary transformation. Why? The wave function is $\Psi = \alpha \left|0\right\rangle + \beta \left|1\right\rangle$ where $\left|\alpha\right|^2 + \left|\beta\right|^2 = 1$ The probabilities...

A measurement is an interaction between a measuring apparatus which is (quasi-)classical and a quantum system
You can model this, it's in Landau's QM section 7, I don't want to quote the whole thing, but this wave function collapsing business is pretty straightforward there without all the woo

(the physic stackexchange post mentioned above)

A measurement of a state from the subspace of the Hilbert space $H_1$ by an observer of the Hilbert space $H_2$ is an evolution of the form $$|\psi_1 \rangle \otimes |\psi_2 \rangle \to \sum_{\alpha} c_\alpha |\psi_{1,\alpha} \rangle \otimes |\psi_{2,\alpha} \rangle$$

That question is basically modelling measurement as a projection without even considering the measuring apparatus etc

This is all extremely unitary
Of course the observer doesn't see it this way because he too is part of the system

10:01 PM
Okay if thats your interpretation of quantum mechanics you have to answer why is the apparatus (quasi-)classical sytem and another quantum system ... Why does it fail to make model it as 2 quantum system ... you have to answer why the experimental apparatus is special?

The experimental apparatus isn't special at all
cf above
It's just another ray in a subspace of the Hilbert space

@MoreAnonymous check out section 7 of the book I just referenced, it goes into this, but basically the theory as it stands was constructed for this to be this way, to end up with eigenvalues as the measurements, the wave function collapse is just a consequence of linearity

yes .. but bolbteppa is of the opinion its k to say the appartus is (quasi-)classical

@Slereah That aside is crucial. You've described measurement as seen "from the outside" by some observer who hasn't interacted yet with either the system or the measurement apparatus.

@Slereah ^

10:03 PM
I mean it's like saying if you turn a pen on its side it shrinks because you see it become smaller :V

@bolbteppa I do not doubt the result of this modelling ... I'm asking why you are allowed to do it in the first place
?

Measurements are actually readings of the apparatus

Why not just use one quantum sytem to "measure" another?

@MoreAnonymous Quasiclassical just means that the apparatus has macroscopic "pointer states" that the experimenter can in turn "measure" by just looking at it.

You can describe apparatus as quantum systems
It's less pleasant but it has been done

10:05 PM
We're going in circles, again, because this is just decoherence/von Neumann measurement scheme mentioned waaaay earlier.

But then you have to make sure you're comfortable of yourself being in a superposition of reading one number and reading another
@ACuriousMind Well as I said
I wanted to talk Navier-Stokes but no
Everyone wants the quantum

@Slereah Unfortunately, I'm not fluent in fluid dynamics :P

Oh neither am I
But it seemed more pleasant than another rehash of the usual quantum conversation

@bolbteppa Im guessing u believe that decoherence solves the measurement problem entirely but not even Wojciech H. Zurek takes this extreme position

@Slereah I am increasingly inclined to agree

10:07 PM
I've taken 3 or 4 courses specifically about fluids, and my understanding of the N-S equations is very limited. That stuff is pretty wild when you dig into it.

So you'd say it's turbulent? ;)

@ACuriousMind @Slereah Its either this or reform the answer!! :P .... So I dont have make the world a better place :P

There are plenty of books you can read on the topic of quantum shenanigans
Streater and Jammer are two good ones
Jammer is actually pretty good because it opens with an actual definition of what a physical theory is

@bolbteppa I'm also curious of your solution to Wigner's friend (thought experiment)

@MoreAnonymous No, it's me asking you and @bolbteppa to take this to another room if you really want to continue this discussion. We've been talking about this for hours now and there has been little evidence of progress, and other people seem to tire of it, too.

10:10 PM
I dont think I have enough points to even open a chatroom and I know if that relevant since I havent done so in the past ....
:P

Just read section 7 of that book basically, I don't have any extra insight

hmmm ... k ... I'll have to take time and get back to you ... It will take some time esp since I am messed up for office tomorrow
Must sleeeep
Feel free to ask the question "does de-coherence alone solve the measurment problem?" till then

@Slereah What is a fluid but a special case of quantum stat mech :p

@bolbteppa Well that's the thing!
From what I hear, there is currently no derivation of Navier Stokes from a stat mech system
that's pretty strange

Right, there's no full quantum non-equilibrium stat mech yet
It's just incredible how hard CM, EM, GR, QM,QFT, SUSY, SUGRA and strings are that there's no time to do stat mech and fluids etc properly

10:24 PM
I think you vastly underestimate how many people are working on things like fluid dynamics vs. strings/SUGRA there

Well fluid mechanics is certainly more lucrative
The oil companies don't extract so many superstrings

haha

Just doing CM is already hard enough if you do it weirdly enough :V
I'm still trying to write that article about how to do CM without using numbers or functions

Yeah
That Spivak mechanics book in terms of bundles for example

It's not easy because the author of that book didn't group the axioms at all
that too
or doing CM as a one dimensional field theory!
There's so much weird CM problems that nobody talks about
like those non-collision Painlevé singularities
and that's just a 5 body problem
Did you know that there's a classical system of infinitely many balls which, due to their collisions with each other, will just exit to infinity in finite time
You have infinitely many balls in your space at $t$ and zero balls at $t + 1$
there's a whole bunch of weird systems like that if you can extract an infinite amount of energy from your system

10:38 PM
CM can't even guarantee unique solutions to the equations of motion (cf. Norton's dome)

Well those cases are also like that actually
because they are time-reversible
you can have an empty space and then have it filled with infinitely many balls!
hopefully this won't happen to us

"False vacuum collpase" got nothing on this

Well of course GR has the equivalent problem

The universe doesn't end in fire or a soup of entropy, just balls.

Norton's dome is a thought experiment that exhibits a non-deterministic system within the bounds of Newtonian mechanics. It was devised by John D. Norton and first discussed in his 2003 paper "Causation as Folk Science". Norton's dome problem can be regarded as a problem in physics, mathematics, or philosophy. It poses interesting philosophical questions about the concepts of causality, determinism, and probability theory. The model consists of an idealized particle initially sitting motionless at the apex of an idealized radially symmetrical frictionless dome described by the equation...

10:40 PM
ie nothing prevents our spacetime from just having a random missing point from which cakes pop out

'While many criticisms have been made of Norton's thought experiment, such as it being a violation of the principle of Lipschitz continuity (the force that appears in Newton's second law is not a Lipschitz continuous function of the particle's trajectory -- this allows evasion of the local uniqueness theorem for solutions of ordinary differential equations)...'
Interesting
Lipschitz in the proof of existence for ode's ftw

Sure, if you can sucessfully argue that your forces are Lipschitz then you evade Norton's dome. The problem is that "Forces are Lipschitz" is not a particularly natural assumption
Especially given that the shape of the dome isn't really exceptional. It's hard to explain why a smooth parabola is an acceptable idealized dome but Norton's shape wouldn't be
@Slereah the cake is a lie

The balls problem in GR
The balls problem in GR is a bit different though because you can't really have objects from infinity
Well, you can, with AdS space
but it's rarer :p

11:26 PM
Hey is there any mod I can ask/plead if its okay to use a big list question?
*question tag

11:40 PM
Also @bolbteppa u might like this post:
https://www.math.columbia.edu/~woit/wordpress/?p=10533

@MoreAnonymous make sure to read this rebuttal to it haha

@bolbteppa i'll have to think about lubos's response but Woit has also shown better understanding of the finer points of string theory than lubos (and its on the internet too) :P
In this whole Woit versus Lubos (sterotypical sheldon)
To be fair Id be willing to put them both on the same stage for the purpose of reality entertainment than science