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1:30 AM
neither, if you're in a superposition of non-degenerate energy eigenstates @DIRAC1930
 
 
2 hours later…
3:18 AM
Why is inferiority complex a bad thing in an individual?
How to deal with it?!
How can you change your identities which are decided by accident or birth?
How much of life is a choice of an indivitual
and how do you define individuality of someone?
Good Morning everyone btw!
 
@RewCie Because you are undervaluing yourself?
@RewCie Self conviction
@RewCie I think you will find determinism (not to be confused with fatalism) interesting
Hey all! I was wondering if any GR expert could help me?

If we assume isotropy and homogeneity then we get the FLRW metric upto a constant (cosmological constant). Is there any counter argument why this constant cannot be a property of the stress energy tensor?
 
4:23 AM
@MoreAnonymous How will you justify a IC Patient underevaulating himself?
@MoreAnonymous Self conviction sounds more like a Unique Selling Proposition for a business....
 
4:45 AM
@MoreAnonymous determinism sounds more like a belief than a proved theory...
 
 
2 hours later…
6:46 AM
@MoreAnonymous The CC can be treated either as a curvature term, in which case we write it on the left side, or as a vacuum energy, in which case we write it on the right side and add it to the SE tensor.
The two are mathematically equivalent. Traditionally it tends to be treated as a curvature, but now that we have discovered dark energy I guess that would be added to the SE tensor.
 
7:13 AM
@DIRAC1930 You may find the Bloch sphere helpful. "The points on the surface of the sphere correspond to the pure states of the system, whereas the interior points correspond to the mixed states".
 
 
2 hours later…
8:44 AM
@JohnRennie But like if I have a fluid stress energy tensor for hyrogen and one for helium. How do we their cosmological constant will be the same?
@RewCie It's more a consequence of having the laws of physics formulated as initial value problems
*How do we know their cc will be the same
 
@MoreAnonymous The SE tensor is the sum of the SE tensors from all the components present. So for example with a mixture of hydrogen and helium you can split the SE tensor into a contribution due to the hydrogen and a contribution due to the helium.
 
@JohnRennie So this is what I meant
If we assume isotropy and homogeneity then we get the FLRW metric up to a constant (cosmological constant). Let's say I have $2$ isotropic and homogenous universes one with hydrogen and another with helium. Will they have the same cosmological constant?
 
If you have dark energy as well you add this so your SE tensor now has three components.
 
I was typing the question :P
 
The CC is separate from the matter density. Hydrogen, helium or any other matter will never result in a SE tensor that contains a cosmological constant.
To get a CC contribution you need a form of energy with an unusual equation of state, i.e. you need dark energy or something like it.
 
8:59 AM
@JohnRennie Would u be kind enough to look at 7 latexed pages and tell me where I'm going wrong?
I think its a property of the material
 
I can look ...
 
honestly
Email?
 
Can you convert it to a pdf and upload it to swarchive.ratsauce.co.uk/.uploads
That's my upload server.
 
Oh wow! okay its already a pdf
Can u confirm u got it?
Can u delete this image^ ?
It says my name :p
Wouldnt remain anonymous
Thanks
 
Oops :-(
 
9:02 AM
No worries
It's a low energy limit result
And kinda heuristic
 
I can't see how that's going to work.
 
Which part?
Or equation?
 
A component that acts like a CC has to have an energy density that is independent of the scale factor i.e. as the universe expands the energy density remains constant. This is equivalent to having a negative pressure.
I find it hard to see how any scattering process is going to satisfy this requirement.
 
Yes ... but in classical mechanics u only measure potential energy difference
@JohnRennie See equation 19 or 20
 
I can't help I'm afraid, I'm not familiar with approaching GR through an action principle.
 
9:08 AM
Welp
 
But I think you'd need an interaction force that was independent of distance to get a cc from the interparticle potential.
 
@JohnRennie Proof of claim>
?
 
You need the energy density to be independent of the particle density. Suppose you have N particles per cubic metre and take the pairwise sums to get the interaction energy. Call this V.
 
From the action perspective you would need a constant in the action and that's like towards the end Equation 28
 
Now double the size of your cube and the interaction energy has to increase to 8V to keep the energy density constant.
Hmm, I'd have to reach for a pen and paper to see what this meant for the interaction potential, and I don't have time for that right now.
 
9:12 AM
@JohnRennie I dont see why equation 19 wouldn't satisfy this?
 
Maybe it does. I can't comment.
 
@JohnRennie No worries
@Slereah is it coincidental you just pop up with the mention of GR in the chatroom or you got some cool alert bot setup? :P
 
9:43 AM
@MoreAnonymous I pop up often
I just don't comment if it's about a topic I don't know about
 
10:09 AM
@Slereah I see ... By the way we were talking about a more updates version of what I sent u btw
 
10:27 AM
@ACuriousMind what the hell is a (-1)-category
oh wait I think (-1)-truncation is for 0-categories
 
10:45 AM
@Slereah I have no idea
 
I guess it's like the $(-1)$-simplexes
 
 
3 hours later…
1:35 PM
What constraints are we maximizing the entropy for in the grand canonical ensemble?
One is that all the probabilities add to 1
But I'm confused about energy
I cant constrain energy to be a constant otherwise nothing would happen right?
As in, it would be like the reservoir and box were isolated
 
1:49 PM
Hi, anyone here?
 
Do you know the answer to my question?
 
No I don't sorry
 
2:32 PM
Can anyone help me with a question about thermodynamics?
 
" Don't ask about asking, just ask."
 
Since entropy is a state function that means that regardless how we reach from state A to state B (for a given system) entropy will be the same S_B - S_A
But if the process to reach state B from A is reversible then the entropy change is zero
and if it is irrever. then its bigger then zero
so this is a contradiction
So what's the correct thing to say or think about?
 
3:09 PM
Can someone tell me what the constraints are and why?
What exactly are we measuring in statistical physics?
Averages I assume?
So is the average energy of system A being conserved (where system B is the reservoir) an axiom?
 
3:28 PM
from wikipedia: "The thermodynamic variables of the grand canonical ensemble are chemical potential (symbol: µ) and absolute temperature (symbol: T). The ensemble is also dependent on mechanical variables such as volume (symbol: V) which influence the nature of the system's internal states. This ensemble is therefore sometimes called the µVT ensemble, as each of these three quantities are constants of the ensemble."
so fixed chemical potential, absolute temperature, and volume
in particular this means that the total number of particles and the system energy are not constrained and can fluctuate
(by contrast, the canonical ensemble assumes a fixed number of particles and the microcanonical ensemble further assumes a fixed energy.)
(Hence why wikipedia also denotes the microcanonical/canonical/grand canonical ensembles as the NVE, NVT, and µVT ensembles respectively.)
in short: read the wikipedia page
 
3:45 PM
That's not really an answer at all to my question
In short: read my question
 
you asked for the constraints. chemical potential, absolute temperature, and volume are the constraints.
 
But you don't use those as conserved charges of the system
 
sure you do.
 
How?
 

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