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6:32 AM
I've heard people say that there are fundamental constants in the universe that if they weren't what they are, nothing would have existed. My question is if the constants were a little different, wouldn't that generate a different type of a universe that works with those constants?
 
 
3 hours later…
9:07 AM
@NovaliumCompany The point of these people is usually that the stability of matter and bound systems in general depends on the relative value of these constants to each other
If you just change one, it's easy to get universes where no atoms are stable, so yes, you get a "different universe", but it's just proton soup or something like that.
 
ACM would you like to help me with some symmetry argument in Magnetostatics? If you are not busy at your office
 
9:22 AM
@Knight not convinced by my argument then? :-)
 
9:38 AM
moved
 
@ACuriousMind How do you know it's just a soup of protons. Maybe it's a universe with laws and systems we can't imagine.
 
@NovaliumCompany The premise here is that the laws stay the same, and just a constant changes
 
@ACuriousMind wut?
 
@NovaliumCompany When people say "if the fundmental constants were different", they really mean that just the constants change, and not the physical laws in which these constants appear.
 
@ACuriousMind Aaalrighty theen
My guess would be that universes with different constants will not necessarily equal to a proton soup.
 
9:54 AM
@JohnRennie No sir, you were busy that’s why I came here. Is it possible that I don’t get convinced by you?
You don’t have faith on me 😭😭
 
$m = E/c^2$ so basically, what my weight machine is measuring when I step on it is the energy (kinetic and potential) stored in my body?
mass is energy
can we then conclude that all matter is just energy?
 
 
2 hours later…
12:12 PM
@JohnRennie hi.
 
@YuvrajSingh... hi :-)
 
What is the speed of current, as I switch one a circuit.
How much time will it take a electron to complete a circle.
 
Let's use an analogy. Suppose you replace your electrons flowing through wires with water flowing through pipes.
 
So you have a pump instead of a battery, and you replace the switch by a valve.
 
12:15 PM
Ok
 
So you close the valve and start your pump, then you open the valve and see how fast the water in the pipes starts moving.
Before you open the valve the water pressure on the far side of the valve is zero, because with the valve closed the pump cannot exert any force on the waer.
 
OK far side which has no water?
 
The pipes are always full of water, just like the wires in a circuit are always full of lectrons.
 
Remember that a battery doesn't create electrons, it just sucks them in at the cathode and pushes them out of the anode, just like a water pump sucks in water at one side and pumps it out of the other side.
 
12:18 PM
Yes yes!
 
So your valve always has water on both sides, it's just that with the valve closed there is a pressure on one side of the valve but zero pressure on the other side.
Then when you flick open the valve the pressure jumps to whatever the pump pressure is. This produces a pressure wave that travels through the water in the pipes.
The water in the pipes stays at zero pressure until the pressure wave reaches it, and only then does it feel a force that makes it start moving.
And this pressure wave moves at the speed of sound in water.
(the speed of sound in water is about 1.5 km/sec)
 
So imagine you have a 1.5km long tube of water, and you suddenly open a valve at one end. The water at the other end won't start moving until one second has passed i.e. not until the pressure wave from the open valve reaches it.
The surprising thing is that an electric current behaves in exactly the same way.
 
The only difference is that the "speed of sound" for the electrons is around 0.1 to 0.5 times the speed of light.
 
12:24 PM
Relative permittivity is also defined as "the ratio of the capitance of a capacitor with dielectric between the plates to that without dielectrics"
Please explain this statement
 
So when you close the switch this raises the voltage immediately after the switch, and that voltage wave travels along the wire at 0.1 to 0.5c.
 
This isn't just theory, I remember doing an experiment at school to actually measure this speed.
 
Wwow! Please share how you had done it
 
12:26 PM
We took a long reel of wire, connected a pulse generator to one end and measured the delay in the pulse reaching the end of the wire.
 
Pulse generator?
A voltage source?
 
@YuvrajSingh... this was back in the 1970s, so the equipment we used would be outdated now. If you Google I'm sure you can find descriptions of how to do the experiment with modern technology.
@RafaelNadal hi
@RafaelNadal Do you know the equation for the capacitance of a parallel plate capacitor?
 
@JohnRennie ok, but that would be speed of voltage is that same to speed of an electron
 
12:31 PM
@YuvrajSingh... go back to my water analogy. The pressure wave travels at the speed of sound in water, but the water itself moves far more slowly.
 
It's just the same in circuits. The (average) speed of the electrons is the drift velocity and it's really slow. A few millimeters per second usually.
But the voltage wave travels at getting on for the speed of light.
 
@JohnRennie we all know that a single electron can, t complete a circle?
 
@RafaelNadal the equation is given here. It is:
where k is the relative permittivity.
@RafaelNadal OK so far?
 
OK one more question how do we calculate speed of sound in different medium.
@JohnRennie
 
12:37 PM
@YuvrajSingh... the speed of sound is related to the bulk modulus, so if you want to calculate it from scratch you need to calculate the bulk modulus, presumably from the properties of single atoms. But that's really hard.
 
I now one one formula that is v = root gamma B/rho
@JohnRennie
 
@YuvrajSingh... that sounds like the equation for the speed of sound in air, v = sqrt(γP/ρ)
 
Yes That p only be B
 
where P is the gas pressure and γ is the adiabatic constant.
 
From PV^gamma =constant.
 
12:42 PM
In a liquid the speed of sound is v = sqrt(B/ρ) where now B is the bulk modulus. In both cases ρ is the density.
 
In a solid it's a bit more complicated because you also need to take the shear modulus into account. See:
37
A: Why does sound travel faster in iron than mercury even though mercury has a higher density?

John RennieThe speed of sound in a liquid is given by: $$ v = \sqrt{\frac{K}{\rho}} $$ where $K$ is the bulk modulus and $\rho$ is the density. The bulk modulus of mercury is $2.85 \times 10^{10}$ Pa and the density is $13534$ kg/m$^3$, so the equation gives $v = 1451$ m/sec. The speed of sound in solids...

 
Young modulus too right?
@JohnRennie
 
I can never remember which modulus is which, but I think it's the shear modulus not the Youngs modulus.
The Young's modulus describes stretching doesn't it?
So that is different from the shear modulus.
I need to go now. I won't be back later today but I'll be around tomorrow as usual.
 
Yes I am sorry it is G*
@JohnRennie bye sir have a nice day!
 
12:48 PM
Bye :-)
 
1:23 PM
Hello gents
So the EPS method to measure the metric tensor is all fine and good
But it seems to be LIES
They argue that affine structures are equivalent if the metric is the same up to a constant factor
but that's not generally the case
It's mostly the case, but there's some counterexamples
Famously Minkowski space has the same affine structure as (A)dS space
 
1:39 PM
John sir will not come back until tomorrow
I need help, we have a uniform surface current $\mathbf K$ flowing in the $xy$ plane. It is given that the current flows in positive x axis direction.
What informations can I get about the magnetic field? By Maxwells Law $$\nabla \times \mathbf B = \mu_0 \mathbf K$$
 
@Slereah What exactly do you mean by "affine structure" there?
 
I actually mean projective structure
Although also somehow true of the affine structure
Projective structure is for two spacetimes $(M,g)$, $(M,g')$, then if $\nabla_{\dot{\gamma}} \dot{\gamma} = 0$, $\nabla'_{\dot{\gamma}} \dot{\gamma} = 0$
The change preserves geodesics
and the structure is the equivalence class $[g]$
 
I see
 
It's a nice structure to have, because if you're not sure your clock measures proper time, you can still get a spacetime's projective/affine/conformal structure
The metric structure you do need a proper clock, though
Though how to prove that an atomic clock measures proper time, though!
or at least verify that it works out, if we assume it
The GR people think that the light clock is so great, but the light clock is only as good as your standard object for distance, which also depends on QM
 
@Slereah Is that really a problem? The postulate "clocks measure proper time along their worldlines" seems easy to test - e.g. send a clock along a well-known worldline, then compare the clock's elapsed time with your prediction for the proper time along that worldline.
 
1:52 PM
Someone please help me with that symmetry problem of Magnetostatics
 
@ACuriousMind How do you predict the proper time along that worldline?
 
@Slereah Ah, you're talking about doing this without knowledge of the metric or assuming the EFE hold. right?
 
@ACuriousMind Yes indeed!
That's the point of the EPS construction, btw
it holds for any metric theory of gravity without too many assumptions about the geometry
Although it does require you to use only geodesics, which is a pretty big assumption I'd say!
 
I think the common view on how to test GR is the other way around - we test a combination of EFE/"clocks measure arc-length" by assuming the EFE hold, compute the metric, derive predictions for e.g. time dilation along specific worldlines from that and then compare the measurements of the clocks to these predictions
 
Yeah it usually works, but it's kind of like
Having to pre-assume some of the geometry is a HUGE assumption, and it's hard to put down precisely in rigorous terms
although then again, the EPS method has its own flaws
ie it's in the test field limit, and to actually get the metric, you need an infinite number of geodesics
which isn't really "the test field limit"
So I'm trying to get something in between
ie some measurements (not infinitely many), some assumptions about the spacetime geometry
 
2:03 PM
@Slereah I feel like this objection only works if you believe that claims like "Spacetime is a Lorentzian manifold" are ontological claims and not just mathematical tooling to produce the correct predictions.
 
Well there's a reason all that stuff I unearthed is in philosophy books :p
I had to buy a bunch because many of them aren't even on libgen
I know the real calculations are "It's just the Schwarzschild metric with some perturbations over it"
and that works fine
From a rigorous perspective though, there's a lot of unstated assumptions
ie we do a lot of measurements for GR stuff with the assumptions of Euclidian space
although there is a bit of overlap between the philosophy and experimental aspects
some of the authors are both in philosophy and experimental GR books
ie Perlick is in both
 
2:40 PM
Now, anybody interested in talking about the symmetry argument with me? I can explain myself quite elaborately and clearly now. I have asked it twice and I know doing it again is no good but believe me this is the last time I’m asking.
 
 
1 hour later…
dsm
3:41 PM
0
Q: Better way to find the intertwiner for equivalent representations

dsmI've just found the intertwiner for the fundamental and $P_1(\mathbb{C}^2)$ representations of $\mathfrak{su}(2)$, but I did it by inspection. For notation info about the $(\pi_\ell,P_\ell(\mathbb{C}^2))$ representations of $\mathfrak{su}(2)$, see my post here. Finding the intertwiner $\phi:P_1(\...

@ACuriousMind @Slereah if either of you fine folks are feeling like adding some exciting representation theory to your day
 
3:58 PM
@dsm If you already know that the two representations are isomorphic and just want to write down the/an intertwiner, it seems much easier to me to use the spectral theorem - pick one of the $S_i$, find eigenbases in both reps for it, and then the intertwiner must map the basis vectors with the same eigenvalues to each other.
 
Is mass just energy? I mean, $m = \frac{E}{c^2}$
a kilogram is a measurement of energy?
 
Usually one does it the other way around - particle masses are commonly measured in electron volt, which is a unit of energy.
 
dsm
@ACuriousMind I see I see. What if we don't know they are isomorphic, and just trying to prove they are equivalent with no prior knowledge? Restricting us from pulling out spectral theorem artillery
 
@dsm Usually you should have something like a classification by values for Casimirs for the representations, so to figure out isomorphy, you'd compute the values of the Casimirs
 
@ACuriousMind If mass is just energy, wouldn't that imply that something heavy has a lot of energy (potential and/or kinetic)?
How does uranium have so much energy and yet I suppose is not that heavy
 
4:06 PM
@NovaliumCompany Mass energy is neither potential nor kinetic, and uranium does not "have more energy" than other substances, it is just particularly well-suited to releasing that energy via fission.
 
So a uranium atom is striked with a neutron which causes an imbalance and therefore a collapse that released a lot of energy plus 2 (or 3) other neutrons to kickstart an exponential explosion?
 
dsm
@ACuriousMind Alright, I currently know nothing about universal enveloping algebras, but now you've given me something to look into
 
@NovaliumCompany Not necessarily an explosion, but a self-sustaining chain reaction (with enriched uranium, it is only U-235 that is so easily fissile)
 
@ACuriousMind "Mass energy is neither potential nor kinetic" what do you mean?
 
@NovaliumCompany An electron at rest in the absence of fields has mass, and hence mass-energy, but that energy is neither kinetic nor potential.
Since the electron has no substructure we know of, this is also not potential binding energy from its constituents.
Also, who ever drew that diagram does not understand how Venn diagrams work :P
 
4:25 PM
I took it from here www.physicsoftheuniverse.com lol
anways gottago
 
I tend to classify mass energy as potential
It tends to work out in the usual definitions of potential energy
 
4:52 PM
@ACuriousMind hi, actually we measure mass as inertia, when we measure mass of an electron what do we actually measure?
Or we say electron has certain mass what does it define, what is the meaning of mass of an electron.
 
@YuvrajSingh... It's not different from any other mass, just more difficult to measure. See Wikipedia for specific ways to measure it.
 
5:07 PM
Electron mass is usually measured by considering the curve of an electron in an EM field
 
Freeman Dyson :(
He really lived long!
 
5:23 PM
In honor of Dyson I would recommend everybody read and comment in here on his famous The Radiation Theories of Tomonaga, Schwinger, and Feynman paper which set up qft, e.g. adding the electromagnetic mass around eq. 21 is a bit shocking
 
Wow that's a cool paper^
 
I recommend reading Schwinger's paper on his own formalism for QFT
Which is also nice
The quantized action formalism
 
@bolbteppa I don't quite understand the part of the paper in which it talks about the surfaces of the field being infinitely close together and satisfying the differential equation
specifically, what does this really mean? "Equation (9) can be solved explicitly. For this purpose it is convenient
to introduce a one-parameter family of space-like surfaces filling the whole
of space-time, so that one and only one member σ(x) of the family passes
through any given point x. Let σ0, σ1, σ2, . . . be a sequence of surfaces of
the family, starting with σ0 and proceeding in small steps steadily into the
past."
so he's stacking space-like surfaces?
I don't really understand why though..
why does he require one and only one member $\sigma(x)$ of the family to pass through any given point $x$?
 
5:44 PM
I think each $\sigma$ is just the space part of space-time, one for each instant of time, and you integrate in a way that ensures time-ordering is satisfied?
 
@bolbteppa What is the mathematical background needed for that? I only know up to Vector Calculus
 
You would need to be ready for a course in quantum field theory
 
So it means that I cannot understand it. What else can I do ?
 
Read these
The Course of Theoretical Physics is a ten-volume series of books covering theoretical physics that was initiated by Lev Landau and written in collaboration with his student Evgeny Lifshitz starting in the late 1930s. It is said that Landau composed much of the series in his head while in an NKVD prison in 1938-1939. However, almost all of the actual writing of the early volumes was done by Lifshitz, giving rise to the witticism, "not a word of Landau and not a thought of Lifshitz". The first eight volumes were finished in the 1950s, written in Russian and translated into English in the late 1950s...
 
6:00 PM
No I meant how can I honor Mr. Dyson if I’m unable to understand that paper and couldn’t comment.
 
6:51 PM
@Knight you can honor him by understanding one sentence of the paper. No need to learn it all at once :)
 
 
3 hours later…
9:45 PM
Man, just realized 1970 is as far away as 2070
That's nuts
 

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