@SirCumference the winner will be the next google. Ad revenue will clearly follow whomever dominates in AI prediction of user preferences.
@Relativisticcucumber isn't that just factorisation of common term, and that common term cannot be zero, and so it can be just divided throughout?
@Obliv Everything up to A=D is correct. Why did you relate B to A? That expression is not matching value and derivative, but rather, you tried to match the entire function. That's just wrong.
@SirCumference history is littered with unscrupulous first mover winners who shamelessly pushed nascent tech out to the public, and then later refined them to "good enough" status.
@Obliv I think you just mean that you want to consider differential equations where you may have a disturbance that roughly looks like it is propagating. However, that is a doomed approach, because Slereah already showed you many cases of wave equations that has dispersion, that the shapes of the disturbances change and spread out as it propagates. Those don't necessarily have nice looking wave equations. The space of those DE is too big.
@DannyuNDos I'm not sure why you would be narrowing the category down to just Buddhists, but I think you are just trying to be clear about which group is being referred to.
Actually, this chat is not at all filtering enough. When miao miao was moderating another place full-time, the convo is a lot more filtered. Sadly, it was a chat for popularising science and science news, and so the level of discourse is a lot lower. But it is still remarkable for the filtering of toxic behaviour, particularly because miao miao was very hands-on for that.
that's kinda wrapped up in what I meant by "quality", too, though.
I know you get extremely miffed to put it mildly by a certain user, but putting that aside, it's been very high level and polite. you don't see that often these days
Consider a vertical circular motion from the top of a circle with constant radius, at which the initial angle is zero, and the max angle is 90 degrees. Can you conceptualize the fact that the normal force at each moment is not equal to the gravity component of the inward direction (its radial component) because the ball "hovers" around each infinitesimal point, similar to how it would hover if it slips an infinite staircase?
@qwerty oh, im not actually miffed. There are a few users, not just one. But other than the peddlers of falsehoods, of course the discussions tend to be much better. Scientists tend to be nice in general.
@naturallyInconsistent phys.SE also has amateurs, and students at different levels as well (even if there's the problem solving room to divert some of the traffic).
@naturallyInconsistent haha yeah I have that in my zotero
thanks
I did remember that the form of the maxwell equations are different (it's in Jackson) and I think that it can be put down to the dimensions not being all the same, unlike when you change units in most other applications.
well, that's the case for Gaussian vs SI - I haven't double checked the other systems
@naturallyInconsistent ok - imagine you had the result that you had different constants in your equations depending on if you measured length in metres or feet
i havent had the time to think it through deeply but i'm fairly sure this is the reason ti was singled out in whatever I read
I need to work through my thoughts on general covariance etc first
The thing is that you expected to have different numerical values and different constants when you change between length units; so why should one be confused by similar things happening when one changes electromagnetic units?
one which probably said something different but different in what way, who knows
@naturallyInconsistent I think (I'm really just guessing here) it's because the factors of pi for example are unitless. so you would have expected whatever other units you use in an equation to be valid, but that's not the case
that's a bit different to the "usual" case where your constants have units
so their values change when you have different units
On reflection the "form" is the same, but nonetheless it is a point which seems akin to picking natural units
where you mess with dimensions as well as just a shift and/or rescaling
@qwerty I'm not sure what it is you are expressing right now. But consider a function such that you could naturally express in terms of energy $E=hf=\hslash\omega$, in frequency, in angular frequency, or by reciprocals, in times (periods), it should be clear that having different constants with or without units, is really materially unimportant.
the point is here h is unusually assumed to have some units. what might be weird if you hadn't encountered something like natural units or cgs before is if instead you had something like E = 1× f and expecting to be able to sub in SI, since 1 has no attached units.
there isn't a "material difference" but it was probably pointed out in a text where the author expected the student hadn't encountered natural units
Yes, if you are used to nicer units and then have to downgrade to unnatural units, then you will keep having to second guess if you have missed out some annoying constants.
It is not so much that the constants bring with them units; the units are actually for our own mental health. Part of why people argued endlessly about Gaußian units is precisely because there were incompatible ones in use, and then that causes all kinds of confusion; confusion that is absolutely missing in SI precisely because we gave them different names.
But shifting arbitrarily is not the usual step in units. We tend to have privileged zeroes and respect them. Temperature is the exception that proves the rule.
susskind is saying that the graph between mass^2 and angular momentum of composite particles, along with some properties of Feynman diagrams about quark scattering, led them to think that quarks were connected by strings
but they ditched this idea becuz they cud never get it to work. but later, someone thought they cud get it to work for quantum gravity instead
@JohnRennie yes, he did mention an analogy with magnetic field lines!
the early version of this idea is really weird. it's like they're taking Feynman diagrams literally, but also theyre not allowed take it literally becuz theyre doing quantum mechanics
The idea of extra dimensions was already well established as an explanation of the existence of local gauge symmetries, so the idea of compactified dimensions in string theory seemed very reasonable.
It wasn't something that originated from string theory.
My point is that physicists are not fools. No-one thought hey string theory seems cool but we need to invent lots of new things to explain away its weirder features.
4D is special in all sorts of ways, and it seems plausible that there would be some mechanism for a space of arbitrary dimension to evolve into an "effectively" 4D manifold.
next question. if string theory put the constraint at 10D, but simultaneously also showed that 6 of those have to be small (unobservable at our scales), our credence of it would shoot up just the same, wouldn't it?
In topology, and here I'm being vague because I know next to nothing about it, low dimensions are simple because there are very few degree of freedom and high dimensions are simple because there are lots of degrees of freedom. Three spatial dimensions are the uneasy middle ground where there is enough freedom to make things complicated but not enough to make them simple.
@RyderRude But isn't that the same as showing there must be four and only four macroscopic dimensions?
@SirCumference They've invested billions of dollars into this garbage and they have to find a way to get their promised return on investment before the bubble pops; the first big analysts have already started saying the possible returns don't justify the massive investments and so the pressure is on.
I think it's pretty obvious that < 4D intelligent life like us couldn't exist. The question is could you prove in > 4D intelligent life couldn't exist?
@JohnRennie The anthropic explanation isn't that 4d is special but that because we exist in 3d and 4d we only understand how to ask the interesting questions in those dimensions ;)
my point is... If we allow the former two observations to shoot up our credence, but the last observation to not lower our credence, we are being unscientific. we are using an experimental test solely as a means to shoot our credence
so the last observation is against string theory, in the sense of Popper
@RyderRude I think your argument is specious because it is based on a choice of premises that may or may not be correct. My position would be that there is something fundamental we do not yet understand about the dimensionality of spacetime.
More precisely we simply don't know enough to start making arguments about whether the fact string theory requires 10 dimensions makes it physically suspect or not.
@ACuriousMind I can see you're taking this discussion as seriously as it deserves! :-)
@JohnRennie i can list my two premises : 1. String theory predicitng the macroscopic dimensions at 3 would have boosted our credence. 2. No scientific test should only allow us to boost our credence
@RyderRude (1) is trivially true. I'd also like string theory to cure cancer and bring world peace but I am not about to rule it out because it hasn't done that (yet :-).
It is entirely possible that GR is an effective theory not a fundamental one. We simply don't know. There have been lots of arguments along these lines though no convincing ones so far.
@JohnRennie I mean most people would say that GR can't be fundamental because it's not quantum, right? The position that "quantum gravity" does not exist in any form and GR is already fundamental is definitely fringe, if it even exists.
Going back to before you were born I heard the argument: "QMers say GR isn't compatible with QM so GR must be changed" "GRers say QM isn't compatible with GR so QM must be changed" I suspect the latter view is well over to the fringe end of the spectrum but who knows?
@JohnRennie Does anyone actually hold the idea that one of the two is fully correct and the other just has to be changed? I think most people are looking for a synthesis theory of QG where you have standard QFT/QM and GR as different limits
@ACuriousMind It goes all the way back to Gauss IIRC
Like talking about little flat people wasn't invented by Flatland
I know Hinton talked about them in 1880 at least
@ACuriousMind The semiclassical gravity people
Pretty fringe indeed
> A piece of paper on a smooth table affords a ready image of a two-dimensional existence. If we suppose the being represented by the piece of paper to have no knowledge of the thickness by which he projects above the surface of the table, it is obvious that he can have no knowledge of objects of a similar description, except by the contact with their edges. His body and the objects in his world have a thickness of which however, he has no consciousness. Since the direction stretching up from the table is unknown to him he will think of the objects of his world as extending in two dimension…
i also came across this physics.stackexchange.com/a/70987 thread yesterday which says that String theory may predict similar things as QFT when it comes so scattering
but leads on reproducing other predictions of QFT
because string theory only talks about scattering so far
also, the big problem isn't that string theory is perturbative. even if we had the non perturbative summation, it wouldn't suddenly start predicting things about non-scattering processes
the big problem is that the parent theory is missing. the general theory from which you r supposed to derive the S-matrix
but i haven't seen these criticisms raised in talks. no one is focusing on that it's a scattering-only theory
@SillyGoose You can set up the question you want to answer differently and then you get different answers to that question :P
1. You can take the position that the EFE are a constraint on Lorentzian manifolds, and ask for manifolds which fulfill the EFE for some $T$
2. You can have the manifold fixed and stress-energy and metric data on a Cauchy surface fixed and use the EFE to solve for their time evolution
3. You can not care about the global character of spacetime at all and just conceive of the EFE as a local differential equation you solve in some neighbourhood of interest
and probably more
only the first position is really "solving for spacetimes" (mathematicians call such manifolds that are solutions to the vacuum $T=0$ Einstein manifolds) as I would naively understand the phrase
@ACuriousMind do you happen to know the difference between a probability density function and a probability distribution?
We did some modelling using Gaussian and Poisson distributions but I thought probability density functions had continuous variables and distributions had discrete, so Gaussian should be a density not a distribution?
@Obliv 1. Why do you claim it's used more often? 2. The question doesn't really make sense, one a is discrete probability distribution the other is continuous
so given $\bar{N} \approx \mu$ which you calculate from your data collection, you can then guesstimate the associated probability of there being $N$ counts of something
@Obliv there is something more to the interpretation. it is probability that there are N counts of something that is expected to occur at a rate of $\mu$ on average
I think this is correct. Distribution might refer to the cumulative distribution, and the density, (in the absolutely continuous case) might refer to the derivative of it. This also makes sense if we look at the various "convergence" notions: "almost surely", "convergence in probability" and "convergence in distribution".
The last one being convergence in cumulative distribution function
e.g. something is expected to happen 3 times on average in a given time. then Poisson gives u the probability that it happens N times in the given time @Obliv
@nickbros123 the thing is that while statisticians may distinguish the terms that way, if a physicist hands you a "probability distribution" 10 times out of 10 what they give you is a density function :P
@Obliv by definition of this distribution, $\mu$ or $\lambda$ is the expected count. The formula for standard deviation is then sometjing u can compute
it means that, if mu is large, then a Gaussian with mean =mu and sigma = root(mu) looks approximately like the Poisson with mean =mu (and sigma =root(mu) ofc) @Obliv
the Gaussian has two independent parameters, i think. standard deviation and mean
E is the placeholder for $\int_{\text{whole domain}} (\text{insert ur function here})f_X(x)dx$, or in this case $\sum_{i=0}^{\infty}(\text{insert function of i here})P(i) $
$\delta$s are perfectly fine objects both in mathematics and physics, just, as with everything, the mathematicians have a different kind of understanding of them. See for instance this answer of mine for a discussion of whether this should be of concern
@RyderRude yh, the thing that physicists do all the time! if u have a point mass density, say $pm(x)=1/3$ if $x=1,2,3$ and $0$ elsewhere, u can write the density function as $\sum_{i=1}^3 1/3 \delta(x-1)+1/3\delta(x-2)+1/3 \delta(x-3) $
@ACuriousMind unlike @fqq , miao miao can also give a CDF~
@Obliv I think that is a clear typo in the paper. When $\mu$ is small, the naïve definition of the Poisson distribution's probability distribution function is perfectly fine, as only the first few terms would be appreciably different from zero. But when $\mu$ is large, that naïve definition become cumbersome to compute, and so we always use the much easier to compute Gaußian to approximate the Poisson.
actually now that i come to think of it, I can thnk of perhaps one use case of this "dirac delta" trick. Suppose we have a random variable that is "discrete" $X$ and a random variable that is continuous $Y$, and we are told theyre independent. I think it would be a correct thing to take the dirac delta version of the mass density of X and multiply it with the density function of $Y$ to get the joint probability density of the new 2 variable distribution
@ACuriousMind Is this similar to how one proves things for general norms or measures, and when a finite case comes up, one uses the counting-measure? I have seen theorems like Hoelder inequality and Cauchy Schwartz where this is done
@Obliv i now understand the view u were aiming for. $P(i)$ can be thought of as linear maps on the space of $f(i)$, such that $P(i) (f(i)) = \sum P(i) f(i)$
in this way $E(f(i))$ is just applying $P(i)$ to $f(i)$
but i haven't seen books use this formulation. QM uses a similar idea to formulate expectation values
well it is said that the vacuum of afree QFT is maximally entangled
so i am wondering how one woudl conceive of measuring this in real life
Also isn't stuff like tomography for reconstructing the actual state based on measurable quantities. so what about doing some sort of tomography to reconstruct "the vacuum state"
the vacuum being entangled does not even make sense by the standard definition since the 0-particle space (which is the vacuum) is not a tensor product of other obvious state spaces
It is unclear because such statements would not be made in QM. we'd say at some time initial state $\psi_0$ evolves into a, say, definite state $\sigma$
or we would say if we measure $\psi_0$ with some measuring device corresponding to an observable $O$, then...
