These are eigenfunctions of Laplacian on the hyperbolas (so-called conal functions) and the Mma code produces unexpected oscillations at near some otherwise unremarkable points... I m looking for alternates to Mma...
@ZeroTheHero currently kind of on hold to see exactly what parameter ranges we will care about
It's likely that we will be close enough to the Laguerre case that we can use those solutions as seeds without any instabilities arising
Though as always that last bit remains to be seen
It also seems that we are partially shifting our attention back to the Bessel case, a flat coaxial waveguide (of physics.stackexchange.com/questions/371031 'fame'), but now with a finite confining potential on both sides
Which, as you can imagine, is thrilling news. What better ways to spend one's time than solving the wavefunction matching equations from a Beesel J + Y combination to a Bessel K and a Bessel I on either side?
With the added challenge that it's all technical challenge with no real intellectual advance but it's still (only just) niche enough that there are no pre-built solutions 😒
@rob deleted posts are definitely going to be a challenge.
I can see that they're there but I don't think I can get at their scores or tags
I can get the absolute number of open, upvoted hw posts, but it's unlikely that SEDE will provide data on the fraction of hw-tagged posts those represent
"In special relativity the possibility of synchronizing distant clocks so as to obtaina global coordinate time was proved by Weyl [15] in a fundamental and unfor-tunately overlooked proof."
Take a globally hyperbolic topologically trivial spacetime $M \cong \mathbb{R} \times \Sigma$, $\Sigma \cong \mathbb{R}^{(n-1)}$. Given $p, q \in M$, such that there exists a future-directed null geodesic $\ell$ between $p$ and $q$, is this equivalent to the condition that $p \nearrow q$, ie $p \...
We've all seen them: short comments saying
Related: http://physics.stackexchange.com/..., and links therein.
Also, we've all seen bunches of useful links to closely-related questions on the Linked sidebar over on the right, which are a very useful way to navigate the site. Also, you know what...
If spacetime do have some kind of frame rate, it will mean the poncaire transformations are somehow, discrete in time
and time will be quantised
which... I don't think that the question of the quantisation of time has a conclusion yet
Actually I wonder...
Since we knew how nonlinear optics can knot light in all sorts of ways to the point that torus like momentum (I forgot the actual name of that term in the twisted light article) can be observed, I wonder if the extent of knotting place a limit on how discrete spacetime can go
Background and Question
So I ask this question: Validity of the derivation of time-energy uncertainty principle?
Where I'm thinking about joshphysics's answer: What is $\Delta t$ in the time-energy uncertainty principle?
And the gist of what I get is (from the answers and the chatroom) within ...
@MoreAnonymous Well, there's no rule (AFAIK), but generally it is considered courtesy to ask the author first before migrating stuff from chat to the main site. That's because we tend to follow higher stricter standards when writing answers (or questions) on the main site, compared to informal discussions in chat.
@Secret It's hard to reconcile a frame rate with the relativity of simultaneity. My frames are not your frames, they're Lorentz transformed.
@Secret Maybe I'm misunderstanding your point (or vice versa). There isn't a single universal set of time slices. Stuff that occurs in one of my time frames is by definition simultaneous in my reference frame, but that one time slice of mine will intersect a bunch of your time slices if we have any nonzero relative velocity.
Sorry about the triple ping. Stupid autocorrect...
Oh, ok. So was I. Focusing on time dilation makes it seem like that (if we have a relative speed) the only issue is that I think your frame rate is slower than mine, and vice versa. But it's worse than that, because space & time are combined.
As you have said, there are no universal time slides (and it is even worse for some crazy spacetimes where you cannot even foilate spacetimes into hyperspace slides like these). Notice how the rate of blinking as the time slide of one of the moving observers scroll past A B C in that order. I am suspecting time dilation will have already govern that rate of blinking
It is less clear, what framerate means. If we think of it like the FPS in games, it means spacetime itself somehow comes in slides like movies, so... are we end up having another time coordinate?
I guess, maybe I should ask you, what do you think framerate means since we already have space and time meshed together by the speed of light, and hence time and space are already relative between observers?
@Secret I'm just attempting to use the most naive idea of a framerate, that I think the OP of that question is using. Presumably they know about time dilation, but they don't realise that space & time get kind of mixed together.
yeah, if I interpret the OP correctly, he is arguing that spacetime has a framerate of c, the speed of light. Since speed of light is the only invariant speed in relativity, to assign a framerate to that will be like saying there is some extra time coordinate which is invariant to lorentz transformation. Otherwise I don't know how you can have a notion of framerate that is not already redundant due to time dilation and length contraction should capture most of the context of signal speeds
Problem of two time physics is that most dynamics become unpredictable due to hyperbolic solutions to equations of motion so presumably the OP have not thought of that direction
"These hyperplanes are called horizontal hyperplanes, and in the language of gauge theories they define a connection: the simultaneity connection[7]. If this connection is integrable, i.e. its curvature vanishes, the distribution of horizontal hyperplanes is integrable and gives rise to a spacetime foliation through spacelike hypersurfaces: the hypersurfaces of simultaneity."
@Secret If you start adding time dimensions like that, you have to keep adding them, so you get an infinite number of them. That's... a little messy. ;) But an English philosopher investigated it mid last century. See en.wikipedia.org/wiki/An_Experiment_with_Time I think you'd enjoy that book. It was quite popular in certain circles, for several decades.
That philosophy of time had fell out of fashion though, given how people just focus on illusion camp, emergent camp, block universe, growing block and presentism
Anyway, assuming a naive framerate model can avoid the complications of time travel and two time dynamics (by having that other dimension to not be time, but some other physical parameter and its associated symmetry group), then we can end up with an interesting cosmology that can predict variable speed of light in different regions of the universe. I am however not ready to investigate on that yet, as there are still other things in logic I tried to make sense
Yup and this shapiro delay is something that one of the recent quantum gravity experiment proposal try to account for by swapping the masses to ensure the delay balances out
You keep running into the same structures, no matter how you transform the problem, so you get caught up studying the "backstage" mechanisms underlying the isomorphisms.
QFT is a special case of quantum theory, but with a more systematic way of constructing observables. The same postulates governing measurement in quantum theory are also present in QFT, and they're not "hidden" at all. Not even sure what "hidden" would mean. Maybe the author is thinking of QFT in terms of scattering (as though that were its only application) or even perturbation theory. That view of QFT has been the source of all kinds of strange statements, and it does indeed "hide" some things that would otherwise be pretty obvious. — Chiral Anomaly34 mins ago
Background
So I am reading the following here (Blog: Not Even Wrong, Blog post: Not So Spooky Action at a Distance, Commenter: vmarko)
"The collapse postulate is also present in QFT, only hidden inside the LSZ formula. But if you are against using the collapse postulate to describe measureme...
This idea that the rules of QM somehow break during measurement is ridiculous, I think the buzzword about non-unitarity during measurement is behind all this
Here is measurement: we begin with a quantum system described by a normalized wave function $\Psi(x)$ and an apparatus described by a normalized quasi-classical wave function $\Phi_n(y)$ where $n$ is the n'th possible 'reading' of the apparatus. Before we take any reading the whole system is described by a wave function $\psi(x,y) = \Psi(x) \Phi_0(y)$ (where we know the $\Phi_0(y)$ reading) which is separable because the apparatus and quantum system are independent.
After measuring, i.e. as the wave function of the combined system evolves under the Schrodinger equation for this total system, we find a new wave function which is no longer a product of wave functions at first glance, however we can expand it in a basis of states of the apparatus $\sum_n A_n(x) \Phi_n(y)$ and NOW because the apparatus is quasi-classical we know it can only be in one of the $\Phi_n(y)$ states whose eigenvalue is the measurement,
so we have found a new function $A_n(x)$ which is proportional to the true wave function of the quantum system after measurement (but it's not correctly normalized since it has to be normalized only for the total system wave function), so you see how the classical nature of the apparatus 'collapses' the sum onto only one of the possibilities, where is the magic here...
I'm saying, if you did that whole scenario above with two quantum systems, the 'collapse' of that sum would never occur and we would never be able to measure, it is the inherent classical nature of the apparatus and the fact we know it has to have a measured value that we know it can only be in one of those eigenstates and so the sum 'collapses'
@bolbteppa where is the experimentalist going wrong then? You still have to explain why can't he replicate the experiment ...Please dont say clumsy hands
Here it is the existence of classical mechanics that causes 'instantaneous wave-function collapse' from $\sum_n A_n(x) \Phi_n(y)$ to some $A_m(x) \Phi_m(y)$
If we didn't have a classical experimenter, after the experiment goes on we would still only have a sum $\sum_n A_n(x) \Phi_n(y)$ and no collapse and so no way to do experiments
Which of the eigenstates is it going to collapse onto, more likely the one with more probability... How do we know which has what probability, Schrodinger equation which respects the symmetries and boundary conditions of that system tells us!
@MoreAnonymous you tell me why we need to talk about non-unitary operators in being able to say that after measurement we can expand the total wave function in a basis of apparatus eigenstates and then use the classical nature of the apparatus to realize this expansion is actually only one term in the sum
Like we're talking about an interacting system interacting during some period of measurement, the idea a wave function simply projects randomly onto one of it's basis eigenstates in a vacuum is ridiculous
I mean this is kinda the problem ... we use the eigenvalue equation ... But don't mention which hermitian operator ... In fact it can't be a hermitian operator like $xp + px$ ... Blah blah blah
@bolbteppa I feel you can write an answer to my question along the lines: the intial conditions of the measuring apparatus are not the same ... But that sounds more like chaos theory :/
If your referring to chaos theory its that I can have the same intial condition (with slight difference) and in one it will go to the extreme right and the other it will go to the extreme left
Chaos theory is about like initial conditions on ODE's leading to crazy outcomes with slight variations right, QM is saying you can't even define ODE's which have well-defined paths, different beasts
@MoreAnonymous you should read section 7 of this book if you want more details on measurements in QM, one interesting point is it makes an argument that might explain the difference between past and present :p
Paths don't exist, all of classical mechanics fails, probability now governs things
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== Description ==
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sigh...
example of hard to determine quackery that even I have trouble figuring out it is quack as there are enough people opening centres with journals to study it
this post truth business is making everything but mathematics and physics hard to fact check
So the Hydrogen atom, we can measure the spectrum, the whole thing is time-independent non-relativistically and we get answers, not sure how this is relevant
What does "If I have the same intial configuration (apparatus + system) then (your) Cophenghen says I should get the same final result" mean, Copenhagen says you will get random final results
That doesn't conflict with the total energy being conserved, I gave an example above where it is conserved and this still goes on, and you call this example trolling haha
I think you misunderstand Noether's theorem, you can still have dynamics in classical mechanics, things changing in the system, but the overall energy is still conserved