@RyanUnger I know why it makes sense to use affine parameters for geodesic curves. But I am wondering if there is an "affine parametrization" for random curves, too. The reason I am asking is the statement by J. Been in his book saying "the concept of an affine parameter is extended from geodesics to all C^1 curves".
PS: this is done regarding the introduction/definition for "generalized affine parameters"
If the plates of a capacitor are joined together by a conducting wire, then its capacitance will become infinity as distance between the plates reach 0 or will it become 0 because it can no longer hold charge?
@JohnRennie Oh, I see, beg your pardon then. The reason for that questions is that I was looking for better explanations of Warp Drive spacetimes and then your name poped up kkkk. But the expecific question (if you want to look) about Warp Drive spacetime is:
I - The Warp Drive metric:
The Warp Drive is a geometry in a spacetime $(\mathcal{M},g)$ given (in geometrized coordinates $c=G=1$) by the following metric tensor:
$$ ds^{2} = -dt^{2}+ (dx-v_{s}f(r_{s})dt)^{2}+dx^{2}+dy^{2}+dz^{2} \tag{1}$$
The basic interpretation is: suppose that we have a ...
But another point of physics which I struggling is given by the paper wrote by M J Pfenning and L H Ford "unphysical nature of warp drives". It seems that the generation of the warp bubble is much like to "enter a black hole". Concerning this another question is: to use a warp drive an spaceship which generates the curved metric must to pass the outer wall<inner wall and the reach the center of the bubble?
Where does Ampere's law actually derive from? Wikipedia briefly mentions that Maxwell derived it using principles of fluid dynamics, but that's so vague that it doesn't even help me find it in his paper.
Does anyone know if Griffiths or Jackson (or any other book) has an explanation of this? Or is it just an entirely empirically justified law like Faraday's?
I know that the Maxwell equations are usually the explanation for all electromagnetic phenomena, but I would like to know why those are valid, if there is any reason for them.
I have a question of which I'm not sure it warrants opening one on the main page. It's about the Josephson effect. I've learned two interpretations of it; one is that the superconductors on either side of the junction have a finite overlap between their wavefunctions, allowing Cooper pairs to tunnel. The other is that Andreev bound states allow transferring Cooper pairs across the junction depending on the transparency of the junction and the number of channels.
Is the ABS picture simply a more refined one of the first one, or are they separate processes?
If I connect two capacitor with capacitance C1 and C2 with charge Q1 and Q2, with opposite plates joined together will total capacitence be $ C_1+C_2 $ or $ \dfrac{1}{\dfrac{1}{C_1} + \dfrac{1}{c_2} } $
@JohnRennie
I think it should be the latter as they are in series but the answer is the former.
@user541396 I'd have to see the question as it isn't clear to me what is being asked. It looks like two capacitors in series, in which case the answer is $1/C = 1/C_1 + 1/C_2$
@RyanUnger In the dupe target there's a link to a good article by Greg Egan. He cheats a bit, by just examining a Rindler horizon in flat spacetime, but it's still worth reading, IMHO.
@PM2Ring the Rindler horizon is an excellent way to understand what a coordinate singularity like the event horizon looks like. One day I must get round to writing an article explained the relationshp between the two.
@JohnRennie Ok, but it's not just low quality. It's persistent deliberate posting of non-orthodox material, even after being told numerous times that his opinions clash with the mainstream understanding of general relativity.
@RyanUnger JD's version of Einstein's version. :) But as John Rennie just said, even old Albert himself didn't have a flawless grasp of GR. But that's quite understandable. It takes a while for new paradigms to properly settle into the landscape.
And while Einstein surely had some great physics intuition he was by no means perfect. His antagonistic attitude towards QM may have been somewhat useful in the very early days, keeping guys like Bohr on their toes, but in later years it effectively sidelined Einstein. But I guess that didn't bother him much, since he was focusing on trying to unify gravity with the other forces...
My own theory, for which I have absolutely no proof, is that Einstein suffered a crisis of confidence as theoretical physics got too mathematical for him, and he deliberately isolated himself by working in an area where there was no competition.
Perhaps. Let's not forget that he introduced some pretty far-out mathematics into physics with GR. Although he wouldn't have been able to do that if not for the help of Minkowski.
But I guess the kind of maths needed for QM & particle physics is of a different character. Eg, someone might find differential geometry quite natural, but have difficulties with group theory stuff.
I think he managed to get a good grasp of differential geometry, mostly learned from Marcel Grossmann, but I think his maths pretty much stopped there.
Quantum field theory started very early on. Remarkably early really. OK it was in a crude state before renormalisation was understood, but the basic ideas were there.
@RyanUnger I think you underestimate the sophistication because you have a good grasp of the maths involved. It seems hard to me. I'm not claiming to be ona par with Einstein, but I suspect it would have seemed hard to him as well.
The text here is largely recycled from your website, meaning you're still looking for ways to use this site to get more eyes on your content. That is not a good faith use of this site. — called2voyage ♦Jul 1 at 19:57
... but, that said, if the point is on External Website A and External Website A is just pseudoscience, then copy-pasting from it is still not appropriate, and it does have the promotional-content aggravant
If you're feeling unusually bored try Googling for his name along with his alter ego farsight. You'll find complaints about him going back years on all sorts of different forums.
re the einstein topic... think he had very deep intuition alongside his math prowess that few physicists had. he seemed to anticipate some kuhnian ideas even as living them out/ epitomizing them himself. yes he became an isolated figure at end of his life. there are rare cases where scientists are vindicated long after they die & think einstein will eventually be put in this category along with eg Bohm. there are further surprises in store in 21st century physics, its not "finished" yet...
also, einstein was on the trail of some particular realist-flavored ideas that are starting to actually play out for those attuned to subtle shifts in overall physics directions. it seems that physics moved on without him without examining his ideas that carefully, and suspect mainstream physicists are not exactly aware of the "leads" he was pursuing. it looks like some has been overlooked/ forgotten in the sands of time...
have read some books on the topic. einstein had a close personal relationship with Godel at the end of his life. at the very end it looks like einstein wasnt working on much at all. his groundbreaking appointment to the IAS was something of a bust wrt "productive output/ discoveries" so to speak.
The point is that a mathematical model is just a mathematical model. It stands or falls by its predictions, and if it makes the correct predictions it's a good model.
It's tempting to take the model as illustrating some fundamental reality, but that isn't the job of a model.
einstein said differently in ways than what you are asserting. some of this cuts to philosophy of science which he had strong expressed opinions on. yes, some of his ideas are now regarded as minority-to-fringe pov(s).
If you formulate a model based on hydrodynamics that gives the same predictions then it's a perfectly good model. Does that mean the underlying reality is hydrodynamic? Well maybe, but just because the model works doesn't mean it reflects any reality.
the hydrodynamic model is seeing a resurgence and there will be new interpretations/ interpretations, theyre already starting to appear/ emerge. new physics isnt built in a day. lets recall the kuhnian like quote of Planck re new theories, do you recall?
If you formulated a model based on hydrodynamics and it worked better e.g. allowed calculations in regimes where GR is too complicated to calculate then it would be a better model. If it doesn't then it's just another model.
new models are created all the time in physics to replace old models. but its a (usually) gradual process that some dont recognize much in their own lifetimes. it helps to study the basic history of the field. it helps to realize everything taught in college textbooks can and does change over time.
@vzn it's exceedingly rare that a fundamentally new model displaces an established model. Generally new models are developments of existing models not complete reformulations.
And the old models usually remain accurate within their domain of applicability. We don't stop teaching Newtonian mechanics because we know it fails at velocities near $c$.
Most of what is written in old textbooks is still perfectly applicable and indeed still taught to first year undergrads.
If there is a revolution in cosmology due my guess is that it will be when we realise GR is an emergent theory i.e. a limit of some deeper underlying theory.
But it's hard to see that a hydrodynamic approach is going to offer that.
More likely a hydrodynamic model would also be an emergent theory, just as regular hydrodynamics emerges from interactions between atoms and molecules.
re new models of hydrodynamics for GR: honestly am a bit shocked you bring up the analogy, dont recall seeing you do so anywhere before. lets agree there are deep mysteries in GR wrt eg black hole behavior and wouldnt it be a bit naive to think that standard modern theory will calculate the correct answers?
it seems that few physicists would argue we completely understand black hole dynamics and there is much current research on the topic to work out the exact details. yes the general outlines are well known. same with big bang. and dark matter + energy are widely recognized massive open questions/ problems of the field that current theoretical frameworks seem incapable of answering. add GR + QM unification. these are not controversial statements.
Suppose you heat water to 100°C and then add extra heat slowly enough that the rate of surface evaporation matches the rate of heat input. Isn't that boiling? Heat is being added and it's producing steam. But there aren't any bubbles.
But I'd guess a thermodynamics textbook will mean boiling to be when the liquid reaches the boiling point and extra heat causes the liquid-vapour transition.
@JohnRennie To be fair, I prefer using "boil" to refer to actual bubbling evaporation; and just use evaporation in the general sense. The word "boil" is pretty well associated with bubbles (like the noun form).
but nowadays it can just mean regular evaporation; which kinda kills off some of it's utility
I remember when the Pons/Fleischmann cold fusion fuss kicked off people were saying be careful when you do the experiment as the amount of energy released can be dangerous.
Which of the following must be true for adiabatic processes?
$C_\mathrm{V} = C_\mathrm{p}$
$\Delta H = 0$
$\Delta U = 0$
$\Delta S = 0$
$q = 0$
(Source: Chemistry GRE)
The answer is $q = 0$. From what I can find, an adiabatic process is when there is no transfer of heat,...
reddit.com/r/IAmA/comments/cl4boe/… This is hilarious IMO. Guy is trying to promote his "algorithm" for sustainable energy; when it just looks like he did basic energy calculations like everyone else, and didn't even get it peer reviewed.
@Semiclassical I wrote down everything I did based on notes I'm rebuilding. If you have the possibility, could you add an answer to me? At the moment I have to leave the station and I hope you will excuse me. Thank you for your interest. See you later. Greetings.
@enumaris I would say yes. The neuromorphic architectures are inherently parallel. An example of this would memory retrieval in humans, it takes milliseconds to search, but then the retrieval is Petabytes of equivalent data.
GPUs are massively parallel, but they take a lot of power. most GPUs have a "deep sleep" cycle as they are designed for graphics, and effectively produce data at 60Hz. If you want to keep them running, you need to take turns with the cores.
I have a key word recognition circuit that works on 2nW. that's the measured current. "Hey Siri" takes... who knows how much power when you include the network and everything else.
Honestly, I do not know. In the analog networks we used, there was only one way to "learn". The STDP algorithms were tied to the physics of the injection of the electrons on the floating-gates.
But STDP is unsupervised learning right? How did you include the supervised part - to actually tell the network "this is the word 'siri'" or some such?
I have a MATLAB program that takes an input and hten generates the initial weights.
VMMs are different than silicon neurons, but solve the same problem.
BTW, I have found that neural networks failed about 10% of the time for the "rat in a maze" scenario. There's a lot of open research. We know barely anything about the brain
So the basic idea is look at neuronal activations when different things are being said, and if activations for neurons associated with the keyword shows up you kinda infer that the keyword was said?
so basically the STDP gives you clustering of "utterances" and then you just check which "cluster" your utterance most likely belongs to at inference time?
yes. BTW, excitation neurons are often fewer than inhibition neurons in these systems; however, in biology, it seems to be opposite. I only mention that because although the systems seem to operate on the generally same premise, they do seem to be a tad bit different.
Prof. Hasler is currently working through this with the neuroFPAAs and rats. I don't know the details.
yeah, so, in the networks, there are some that apply excitation to the next dendrite input, and some that calm the input. It keeps your system from getting a feed-forward loop. biology seems to do that too
I think that's kinda equivalent to having a negative weight on that synapse...hmmm but I guess I just assumed the weights were positive due to my internal conception of the network
yeah I think everything I read just assumes you can have negative weights represent the inhibatory synapses and the positive weights are excitory...but I just assumed everything was positive lol
On of the ways to do "negative weights" was just have leak paths. The neuMOS work by SHIBATA and OHMI in the 80s/90s did that. I have no idea when the idea of a negative weight was added instead of just leakage. Sarpeshkar's work at CalTech and Bohem (currently active in this field at Standford) both used negative weights.
If you are geographically located in the USA, there's a few lectures you probably could sneak into
I - The Warp Drive metric:
The Warp Drive is a geometry in a spacetime $(\mathcal{M},g)$ given (in geometrized coordinates $c=G=1$) by the following metric tensor:
$$ ds^{2} = -dt^{2}+ (dx-v_{s}f(r_{s})dt)^{2}+dx^{2}+dy^{2}+dz^{2} \tag{1}$$
The basic interpretation is: suppose that we have a ...
I know that the Maxwell equations are usually the explanation for all electromagnetic phenomena, but I would like to know why those are valid, if there is any reason for them.
Which of the following must be true for adiabatic processes?
$C_\mathrm{V} = C_\mathrm{p}$
$\Delta H = 0$
$\Delta U = 0$
$\Delta S = 0$
$q = 0$
(Source: Chemistry GRE)
The answer is $q = 0$. From what I can find, an adiabatic process is when there is no transfer of heat,...
Starting from two equations:
$$
\mathbf{E}=-\boldsymbol{\nabla} \varphi-\frac{\partial\mathbf{A}}{\partial t}, \qquad
\mathbf{B} = \boldsymbol{\nabla} \times \mathbf{A}$$
and are valid the Maxwell-Proca's equations:
\begin{equation}
\begin{cases}
\boldsymbol{\nabla} \cdot \mathbf{B}=0\\
\bold...
