5:04 AM
@JohnRennie !

3 hours later…
7:48 AM
So the question is
What does the real Klein-Gordon Hilbert space look like
You have the big Fock space that is too big, it contains the theories for all kinds of weird vacuum states that can't be reach from the zero one
After applying superselection, what does the Hilbert space look like?
(also I guess the Fock space has all kinds of KG theories for all possible masses or something)
how does one whittle it down and to what
The usual KG Hilbert space can't contain any of those infinite particle states (that can't be reached from the $C^*$ algebra), it can't contain states that aren't on the mass shell or in the wrong time direction
what does that leave

@Slereah isn't it just the space generated by finitely many creation operators on the vacuum?
essentially the GNS construction for the algebra of observables

@ACuriousMind I mean obviously
But
what is it

I'm not sure what sort of answer you expect to that question

It's like saying $\mathbb{N}$ is the space generated by adding infinitely many $1$
idk, a structure?
A quotient space?
a... functor???
From the space of $C^*$ algebras to Hilbert spaces
I guess it is something to do with the GNS construction
Maybe it's just the Fock space except with finite number of particles and each wave function inside is on the mass shell?
though that seems to be tough to get a basis out of that

8:09 AM
how would there be states in the Fock space that are off the mass shell? The creation operators only create on-shell states, don't they?

well yes, that is what I am saying

ah, okay, you made it sound like it was a condition that selected a subspace or something, no worries then

I am wondering if there is a basis of such a Fock space
It is apparently countable, but what is it

start with the basis for the 1-particle space, which is countable (e.g. use Hermite polynomials in momentum or whatever) and the basis of the full Hilbert space is just that + the basis for the 2-particle space as tensoring the 1-particle space with itself + the basis for the 3-particle space etc.
this is still countable because you've started with a countable basis and the n in n-particle space is also countable - a countable collection of countable things is still countable

Yes, but the full Fock space isn't
But you can't have infinitely many particles, but you can have arbitrarily many
It's countable in that way, but what the basis actually is sounds non-trivial
Does the creation operator form a basis?
But then if that was true, $(1,1,1,1, \ldots)$ would be a state too I think?

8:40 AM
@Slereah I think you might be confused about what the "full Fock space" is
remember that in the infinite case, there's a difference between the direct sum and the direct product
the Fock space is already defined in a way that infinitely many particles aren't allowed
(or if you don't define it that way, then you should :P)

I mean yes, but
I mean
A superposition of every possible number of particles
that was the Haag example, IIRC?

the Fock space is built as the direct sum of the n-particle spaces. "direct sum" means any given element only has finitely many non-zero contributions from the individual n-particle spaces

Hm
then what was that example?
I guess $(1, 1, \ldots)$ may not be a normalizable state, in the product of the Fock space
But why was he using it?
I'm at the office so I can't check the book right now I'm afraid
Also if that state is already forbidden, that means that the (projective) Fock space is already pretty non-trivial

9:14 AM
Hello!
Can I ask if a free-body diagram needs to have a representation for frictional force for every applied force?

9:29 AM
you can ask that, sure :P
but whether your FBD needs that depends on what you're drawing it for
these diagrams are not ends in themselves, they are a means to solve some specific problem - sometimes you'll be interested in friction forces, sometimes you won't be

1 hour later…
10:49 AM
Good morning/evening! I am planning to drop a magnet into a copper tube to make luminiscent LEDs as an experiment. I wanted to know would the flux/change in flux depend on the cross-sectional area of the copper tube.
In other words if a magnet is falling into a tube would pipes with bigger area make bigger emf or smaller ones?
I do know that the faradays formula says emf = NASinthetha * dB/dt so can we use that and say theres a direct propotionality?

0- 60km/h in 282 secs. This is the data from speedometer app of train. What is its acceleration?
.212 km/h per second?

I mean just divide for the average acceleration?
That's 60.000m/(3600s * 282s)
About $0.059m/s^2$

.06 m/s^2
Ya! Didn’t click in my head
.2 km/ min^2

12:00 PM
0

I have edited some posts of mine and others which are older than a year, including modifying some tags, but I do not get the badge. How exactly do you get it? Does it has to be precisely inactive for 6 months?

@ACuriousMind Wait. I thought you need to include almost all forces involved. Since there is an applied force, I thought you also need to include the frictional force

12:11 PM
@Slereah is the train very slow with 1cm/s^2 ?
I mean 6cm/s/s

Things with people in tend to have slow accelerations
To avoid passengers feeling it
also trains usually have a very long straight path to take so they can afford slow acceleration

0-100 in 410 sec. So it means even with slow acceleration train can achieve a speed of 100 km/h ?
Is timing of 400 secs right?

I'm not a train expert
If that's the data you got, that's the data you got
I can't judge whether it's correct or not
It seems reasonable to me

what kind of train are you talking about? seems reasonable for a slow train

I am travelling in a train from tapri to Nizamuddin New Delhi

12:27 PM
Real life performance is affected by many things, in general trains tend to go slower and accelerate than the maximum they can do. 0-100 in 410s sounds slow but reasonable
if it's a medium/long distance train with not too many stops, acceleration does not matter too much

09020 - Hw Bandra Spl runs from Haridwar Jn to Ghaziabad, 7 days of the week. The 09020 mail express train departs from Haridwar Jn at 01:30 hrs and arrives at Ghaziabad at 05:59 hrs. The total running duration of 09020 train is 4hr 29min, stopping at 7 stations during the journey.

I mean typically a train will run for several hours
200 seconds to accelerate is peanuts

@Slereah what?

If a train takes 3 minutes to accelerate to full speed it is not very important for the total travel time

@Slereah 7 minutes!

12:33 PM
Whatever
For a 3 hours trip it's pretty unimportant
Plus rough acceleration is not pleasant
Also if the acceleration reached 8G people start to die

@Slereah how? For 3 hours straight slow acceleration is a good deal or everybody will get tired

@Slereah I don't think that's a factor, there's a big gap between what trains actually do and unpleasant acceleration I think. Your other argument is more important, it doesn't really matter for multi-hour trips

@fqq I don't even like car acceleration

maximum speed is usually the limiting factor
@Slereah yes but train acceleration is much much less than cars anyway

12:37 PM
a good thing

yes

Also I'm guessing that accelerating a train is probably harder than a car, on a technical level

Sure is. I can accelerate a car easily, but when I try to accelerate a train the police gets involved

@Slereah yes! Or it will get derailed !

I mean, there's usually people running around in a train at any given moment, so I'm not sure there's technical considerations here so much as "we don't want people to stumble and fall" considerations :P

12:38 PM
Acceleration an electron is much easier

Lots of inertia

@ACuriousMind Tell that to bus drivers

@Slereah different situation in that there's a much stronger expectation that you're either sitting or holding on to something in a bus

@ACuriousMind yeah! I think slow acceleration is good. Less tired and happy passengers

@ACuriousMind I'm not sure you're aware of the realities of riding the bus

12:40 PM
@cOnnectOrTR12 I'm not sure what acceleration has to do with tiredness

@Slereah in the before-times when I physically went to work like some sort of caveperson, I took the bus every day :P

Then you may know that not everyone is lucky enough to have even a bar to hold onto

busses that full happen really rarely here

I mean dizziness
But no

12:42 PM
and if they're that full there's not that much room to fall on your face anyway, so where's the problem? :P

@ACuriousMind It depends on your ethical beliefs regarding personal space
Some people do not enjoy having strangers smash into them

Some people don’t like the armpits of others
But helpless they are

@Slereah which is probably one of the reasons why, where ACM is, the public transport is more adequate to the number of people and the buses are not that full

@Slereah sure, I'm just being facetious :P

the famed German sense of humour

12:47 PM
@Slereah but I think slow acceleration de acceleration avoids derailment and soothes passengers

You'll have to ask train people if you want to know more I'm afraid

@Slereah good comedy is much easier to import than good public transport

I'm sure the engineering SE doesn't lack those nerds

Mar 7 '16 at 18:53, by ACuriousMind
@0celo7 How many Germans do you need to screw in a lightbulb? One. We're efficient and don't have a sense of humor.

The only German comedian I know is Henning Wehn and apparently Germans are not aware of him

12:55 PM
Theoretically a continuous system is made up of a continuously infinite number of particles and a continuous spectrum 'fock space' is able to handle that as bizarre as it is, it's just not clear that this needs to be excluded in general

@bolbteppa Do you remember what Haag's example was for a state that coudn't be reached from the vacuum state in the KG Fock space

No, something something anharmonic oscillator maybe

@Slereah yes, he was funny so they sent him over to the UK
@Slereah something like thermal states? but yes, they're not in the direct sum of n-particle states

I would buy that $(1, 1, 1, \ldots)$ isn't a real state since it's (maybe?) not with finite norm, but otoh the Fock space is in momentum basis so this makes everything harder to think about

@Slereah I mean, why would you know people who make jokes in German? You're not gonna get them anyway (either due to the language barrier or to due lacking the societal/political context)
I don't know a single French comedian, either

1:00 PM
Some jokes transcent language barriers!

@Slereah thermal states solve the normalisation issue

@ACuriousMind Do you know these guys

@ACuriousMind Wait. I thought you need to include almost all forces involved. Since there is an applied force, I thought you also need to include the frictional force

and they are (I think) in the direct product of n-particle states, but not in the direct sum

I'll check this when I get home
I miss the pandemic, I could check my Haag at home

1:03 PM
@Slereah unfortunately, yes

I also know this classic

one of these things where I have no idea what people in the '80 were thinking
@soupless As I said, what you want to include in your drawing depends on what you want to do with it
sometimes you want to neglect friction, sometimes you don't, there's no hard rule for that

Possibly @ACuriousMind

@Slereah that's Swiss, not German :P

the famous Swiss sauerkraut

1:07 PM
@ACuriousMind Okay, thank you very much

@Slereah I have no idea what that's trying to sell me

@ACuriousMind The fine culture of Germany

1 hour later…
2:29 PM
0

3 hours later…
5:23 PM
@ACuriousMind are trains slow because of slow acceleration or because of low top speed?

I don't understand the question
I wouldn't exactly call trains slow, some of them reach speeds of 300 km/h and higher - what exactly are you comparing them to when calling them "slow"?

Trains in foreign compared to India
Top speed 118

then I still don't understand the question - if you're talking about the top speed, how could it possibly be the "slow acceleration" and not the low top speed that's the reason?

If the acceleration of train is high with low top speed is that what you call slow or fast

6:00 PM
@ACuriousMind do you get it?

4 hours later…
9:52 PM
@Semiclassical is the reason you take the C (particle-antiparticle conjugate) to be the Hermitian conjugate because the annihilation operator is the is the Hermitian conjugate of the corresponding creation operator?

@cOnnectOrTR12 you can call them whatever you want