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12:34 AM
@DavidZ & other mods, if this one gets deleted, please make sure it's converted to a comment instead
A: Why not use the magnetic scalar potential?

JERROLD FRANKLINI didn't see your question until just now. The magnetic scalar potential can be very useful, and is too often dismissed witout much consideration. I treat and use it in some detail in my textbook https://www.amazon.com/Classical-Electromagnetism-Jerrold-Franklin/dp/0805387331?ie=UTF8&kyeywords=...

@EmilioPisanty See also physics.stackexchange.com/a/268747
spking of QM+GR, ambitious/ wild conjectural framework
> If we perturb the state a little bit, how does the emergent geometry change? (Answer: space curves in response to emergent mass/energy, in a way reminiscent of Einstein’s equation in general relativity.)
12:54 AM
hello everyone
1:40 AM
1 hour later…
2:54 AM
yet ;)
@skillpatrol I killed one, I know they're real
3:35 AM
Get some spray @0celo7
3:49 AM
@skillpatrol no money
2 hours later…
5:26 AM
Nice day!
6:10 AM
What does mean the "OP"?
Original Poster
(of the question)
@skillpatrol Thanks a lot!
7:07 AM
@vzn : "...we’re building on ideas that have come before. The idea that spacetime geometry is related to entanglement..." Tsk. Einstein explained why light beams curved. General relativity is the best-tested theory we've got. Gravity is nothing to do with entanglement.
2 hours later…
8:40 AM
for those of you wondering if a time operator exists in non-relativistic quantum mechanics ;-)
\o @yuggib
@skillpatrol o/
@EmilioPisanty OK; that would have been better indicated by a flag (for future reference)
9:16 AM
Anyone around?
Hello! You wouldn't happen to know much/anything about cosmology would you? The deceleration parameter in particular.
@JohnRennie (In case you're around...)
@NoahP Sorry, I know nothing about that.
Bummer! No worries
@yuggib There are lots of questions on this very topic at PSE, on a footnote.
9:32 AM
This is talking about ultra-weak time operators.
9:44 AM
@NoahP Hi Noah
Just the man I was looking for! @JohnRennie
A universe with just dark energy has the de Sitter geometry
You've lost me there
The scale factor varies with time as $a(t) = e^{Ht}$ where $H$ is the Hubble constant.
So the universe expands exponentially with time.
A de Sitter universe is a cosmological solution to the Einstein field equations of general relativity, named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to correspond to dark energy in our universe or the inflaton field in the early universe. According to the models of inflation and current observations of the accelerating universe, the concordance models of physical cosmology are converging on a consistent model where our universe was best described as a de Sitter...
Okay, which would fit with what I said in the question?
9:48 AM
You would get $q_0 = -\Omega_\Lambda$ yes.
But i think your focus on things like the deceleration parameter is not helping you.
I'm going on a week long physics course next week around this, and have been given a set of questions to research
There are lots of ways to try and get a handle on an FLRW geometry, and the deceleration parameter is just one such handle, and I'm not convinced it's a partyicularly useful one.
I don't have to submit them, but I want to try and understand & be able to answer them all
@MAFIA36790 the questions on PSE are about mistaking time derivatives with an operator
OK, I guess if you've been given the problems to do you don't have a lot of choice in the matter.
9:50 AM
not much on the topic of time operators are they are explained there ;-P
@yuggib yup.
But really I would focus on understanding the form of a(t) and how it depends on various things.
@JohnRennie The questions seem to move on to that from now, for example:
Just asking, although beyond my scope, what did they mean by ultra-weak @yuggib?
Suppose the universe is spatially flat, and at some point was dominated by a fluid with a stiff equation of state $p=\rho c^2$
Then, solve the continuity equation for $\rho$ and obtain the scaling of $\rho$ with respect to the scale factor, a
@JohnRennie I'll probably be posting a couple more questions today
9:53 AM
That should keep you busy for a while :-)
Have you seen:
and the answers from Pulsar that I link to?
Q: How does the Hubble parameter change with the age of the universe?

John RennieHow does the Hubble parameter change with the age of the universe? This question was posted recently, and I had almost finished writing an answer when the question was deleted. Since it's a shame to waste the effort here's the answer anyway. Maybe this can be one of the canonical answers sugges...

There is lots of useful stuff there, and the Living Reviews article you linked is also quite helpful.
I'll have a look now, thanks for all your help
I'm in and out today, so I may not be able to respond immediately but if you ping me here I'll see it eventually.
@MAFIA36790 it is a ultra weak notion of time operator, based on how the canonical commutation relation with the hamiltonian is intended
Are you going to delete that last question now you have the answer?
(a time operator is one that noncommutes canonically with the hamiltonian, in a way that energy time uncertainty is satisfied)
9:55 AM
Should I answer it myself, delete it, or wait?
Well I can post an answer if you want, but it's kind of a one liner.
@yuggib Thanks for that.
@MAFIA36790 anyways the "hierarchy" of time operators, from ultra-strong to ultra-weak is explained inside the paper ;-)
@JohnRennie I'm just reluctant to delete it as it would be helpful to show my research next week
@NoahP There's certainly no obligation to delete it. It might be interewsting to see if anyone else answers.
9:57 AM
@yuggib Can't resist myself to read the paper; but yeh it's beyond my scope for now T__T
Whether asking other people counts as research is somewhat debatable :-)
@JohnRennie Okay, I'll leave it be for the time being then. I'm sure it'll be joined by more questions later. And I'd agree with you there, but plenty of research has been conducted beforehand! These concepts are a little difficult to grasp for a 17 year old who hasn't yet been taught beyond A-Level
(If you're in the US, Projectile motion is one topic I did this year, should give context), and has only been taught differentiation using the chain, product, and quotient rules - no implicit integration or anythinng
It didn't like that as one long message @JohnRennie
I have to say that the FLRW metric is a bit advanced to be teaching 17 year olds. You wouldn't normally do it until the later years of a Physics degree. Anyhow, good luck with it :-)
Yeah, this is all stuff I'm doing outside school, no help from my teachers within - the course is being taught by a University professor, and is intended to push I think. Thought it would be useful considering I'm applying to Oxford. Thanks!
@NoahP Re Oxford, for the admission, you just need to pass with high marks their admission exam which would be based on Physics and Maths if you are considering for majoring in Physics. The questions are not hard, in any way, but the problems are very lengthy though. Maths is comparatively easier.
10:06 AM
@MAFIA36790 Yeah, I'm going on a two week holiday near the beach soon, so plan on doing lots of past PAT papers, as well as BPhO papers. And it is Physics I'm applying for.
Thanks for the advice though! :)
@NoahP Olympiad questions are of numerical taste; but the admission exam would consist both of numerical and conceptual question although of varying numbers every year.
@MAFIA36790 Apparently theyve taken out the longer questions as of last year, so it's much less wordy
I doubt the entrance exam would be asking you about general relativity. I went to Cambridge not Oxford, but as I recall the exam was basically A /S level physics. It's just that the questions were more taxing than the A level.
10:19 AM
@JohnRennie That's my understanding of it too, but everything else, including my EPQ (If you remember all the black hole stuff a while back) will hopefully help in the interview stage