The h Bar

Secret

00:32

sciencedaily.com/releases/2016/07/160718133218.htm

Prepare an ensemble of identically prepared photon pair states, measure thrm to get interference information. Group all of them together to get the hologram formed by the wavefunction of a single photon

Will read the paper in more detail to see how they carry this out

Secret

[Something else about inteepretarions] We define the wavefunction as something that contains all the information we can learn about the quantum state. After reading the PSE answers about probability in quantum

mechanics, I am tempted to think that a hermitian operator $\hat{M }$ kind of filter out the probability amplitude that corresponds to the information of the observable $m$ only, which then, when the overlap of that with the wavefunction is computed via the inner product $\langle \psi \lvert \hat{M} \rvert \psi \rangle$

with give the sum of all values of $m$ weighted by the amplitude squared (i.e probability), thus giving the expectation value as expected. However there is an obvious question to ask. We knew that

while there are a lot of observables are noncommutative, there are some that are. This means there exists some state $\lvert K \rangle such that it is both an eigenvector of two observables $\hat{A}, \hat{B}$. Then

the interpretation of hermitian operators "filtering" out relevant information from the wavefunction will be challenging in this special case: Suppose I have the ket $\lvert K \rangle$, does it mean that it contains information of both $a$ and $b$...? In that case we cannot really say a hermitian operator $\hat{A}$ filter out information of $a$ only from the wavefunction, as the above ket also contains information of $b$

Perhaps one way to look at it is similar to the mathematical phenomenon of some equation of motion having multiple solutions at some positions in phase space, it might just happened that under a certain basis, the state vector that corresponds to some observable $a$ happened to have the same form as $b$

And since it is true for one basis, it is true for all bases as eigenvectors of linear operators are independent of basis. So maybe, if we insist on the filtering interpretation, there are actually two $\lvert K\rangle$ that look the same but contains diffetent information of the wavefunction that corresponds to the quantum state it started with. An

alternate way to think about this issue is that most filters are not perfect (because they are linear hermitian operators, there are only so many possible states they can act on and not give the same state vector), therefore when a hermitian operator $\hat{A}$ is trying to filter information of $a$ it is more common that the filtered result will contain information of, say, $b$. This will then explain noncommutativity

But even then, there is still an interpretational issue on that:

Sir Cumference

01:08

@HDE226868 I give up.

@0celo7 Search for knowledge.

I've spoken with graduate students fluent in QM, yet they were giving the same definition for i that I originally gave.

They were just as surprised when I brought up the problems you showed me with the definition.

Secret

Because any state vector is linear, they can be linear combinations of other state vectors, which may contains eigenvectors corresponds to some hermitian operator. Then assuming we have the filtering information interpeetation above, we will need to deal with the issue of how can information of $a$ (say position) be added to information of $b$ (say spin projected at the z axis) to give information of a completely unrelated $c$ (say the mass of a particle)

If the above interpretation is the correct one (which I doubt it) it will imply information has a weird property that they are linear, they give different physical qualities when arranged in certain ways

and then, one may come to the conclusion that all the physical things like charge, momentum etc might be nothing but a result of different ways these information overlap with each other. And in the macroscopic scale, decoherence (may be one of thr things that) ensure we only ever observed one of the many, with some probability

Unless there's an experimental way to probe this interpretarion about information, I don't think the filtering interpretation I had make sense

Therefore, either information has such weird properties, or that the filtering interpretation is wrong, thus meaning that quantum probabilities and logic cannot simply be treated in the same way (with some modification such as linearity and superposition) of claasical probability in the notion of that propositions filter out relevant elements from the set (except that by definition it just happened that a vector space is a type of set)

Or put it more directly, quantum probabilities cannot be thought of as some form of venn diagram

0celo7

01:48

Who do you think will read that?

skill patrol

02:02

Shog9

Sir Cumference

02:12

Okay I'm reading about degenerate gases and energy levels, so I need to know

Is energy discrete or continuous?

The whole "energy level" thing makes it sound discrete

0celo7

depends

Sir Cumference

on?

0celo7

your system

Sir Cumference

oh my god i'm tired

All right, say we're in a neutron star

0celo7

I know nothing about those

AFAIK they have no practical purpose

Sir Cumference

02:19

Okay, give me an example of a system where energy is discrete

@0celo7 They're the epitome of awesomeness

0celo7

@SirCumference harmonic oscillator

Sir Cumference

Why is energy discrete there?

0celo7

I'm not a physicist

Sir Cumference

What are you then?

0celo7

doing homework

Sir Cumference

02:22

Oh crud, I didn't realize I was talking to you

I didn't check the username...

@0celo7 Anyway, on the chat?

0celo7

you're dumb

Sir Cumference

Perhaps

right now i'm tired tho

You know, it's funny how many people say "Schrödinger's cat is an example of quantum mechanical effects"

When really it was made to ridicule QM

Schrödinger would be rolling in his grave

0celo7

It was made to ridicule an interpretation of QM

Sir Cumference

@0celo7 And yet people are talking about how great of an example it is for QM effects

Most of them think it was made to support that interpretation of QM

0celo7

Oh, but you're smarter than them, I see

Sir Cumference

02:35

I just looked up the history

I feel like it got bastardized

0celo7

very clever

Sir Cumference

>_>

You're being sarcastic...stop being sarcastic...

0celo7

I don't know why you would thing I'm being sarcastic

Did you look up some dirty pictures yet

Sir Cumference

Yeah in other news

Here's a picture of a dog

0celo7

what about it

Sir Cumference

02:40

It's the beauty of photoshop

0celo7

what

Sir Cumference

Do you not see the human smile?

0celo7

Sure, so?

My dog smiles

Sir Cumference

I hope not like that

0celo7

Exactly like that

Sir Cumference

02:42

Jesus christ get it exorcized

0celo7

no

Sir Cumference

yes

0celo7

you're Jewish, what do you know about that

Sir Cumference

I know that face isn't holy

You're christian I assume, you should be worried

0celo7

Don't assume

Sir Cumference

02:44

Okay religion do you believe in (if any)

0celo7

it makes an ass out of you and me, but mostly you.

Sir Cumference

You know what happens when you assume, you make a you out of ass and me

0celo7

@SirCumference I worship the Nine Divines.

Sir Cumference

@0celo7 Ok

I can't really respond to that

0celo7

Depends, do you support Talos?

Sir Cumference

02:45

"Support"?

0celo7

Infidel!

Sir Cumference

Wat

At least you don't worship pokemon like half the people I know

You realize how many people are obsessed with Pokemon go?

0celo7

No.

I need to show that $L(f)\cdot L(g)=L(f\times g)$...

Sir Cumference

Well a pokemon appeared in Central park, there was a riot

Pokemon Go - Vaporeon stampede Central Park, NYC

►

0celo7

never heard of "Pokemon"

Sir Cumference

02:47

Wallets stolen, people stabbed

@0celo7 That's a rock worth living under

0celo7

It's called having a job

Sir Cumference

I don't see why that means you've never heard of pokemon

0celo7

Me neither

Sir Cumference

Right...

You see the wikipedia vandalism that google cached?

This here is why I don't trust Wikipedia

0celo7

There's a Vaporeon near me

By the university gym

Sir Cumference

02:51

Nice knowing you

Prepare for a stampede

0celo7

People in the south are civilized

Unlike the ghetto north

HAH

Sir Cumference

@0celo7 History says otherwise >_>

skill patrol

Excuse me? <_<

0celo7

Solved the problem

Sir Cumference

With lotsa blood...

Speaking of which, I'd get out of there if there's a vaporeon

0celo7

02:54

@SirCumference The North started the war

Sir Cumference

You wanna go?

breaks wine bottle

bleeds to death

0celo7

oh please

skill patrol

:runs:

0celo7

I have German warrior blood

also American weapon fondness

skill patrol

Says you.

0celo7

02:57

which part do you doubt

skill patrol

as he rus...

0celo7

what

lucas

I hope (wish) you are not a German.

0celo7

@lucas based on your behavior, the feeling is mutual

assuming that means I might be related to you

user218912

03:18

lolwut roger penrose authored a book with deepak chopra? amazon.com/Consciousness-Universe-Quantum-Physics-Evolution/dp/…

user218912

that's ridiculous

user218912

if you don't understand why that's retarded watch this youtube.com/watch?v=tZXewVWUKAM

user218912

"consciousness is defined as a superposition of possibilities"

Secret

en.m.wikipedia.org/wiki/Spinor

0celo7

Penrose is insane @3750

Secret

03:24

I wonder, if spinors are a linear way to track the topologies of special orthogonal groups...?

user218912

@0celo7 how do you know?

Secret

given their path dependence that depends on only two nonequivalent rotational classes

0celo7

@3750 he's gone into old physicist mode

Secret

which is related to the topology of the rotational group being not simply connected (i need to check whether SO(n) is also mot simply connected later...)

0celo7

SO(n) is not simply connected for $n>2$.

Secret

03:46

Ok, so it seems we are fine (for now)

> Lorentz transformations include 3-dimensional rotations as well as boosts. A boost transfers to a frame of reference with a different velocity, and is mathematically like a rotation into time.

(the above quoted block of text is unrelated to the spin discussion)

I wonder, since lorentz boost mathematically act like a rotation in spacetime, surely there is a way to measure the rapidity, maybe it is tan (v)...?

We can directly see a rotational angle (by measuring how much something is spatially displaced by a rotation). Do similar notions for direct measurement of rapidity exist...?

> Additionally, the assumption (known as microcausality) that spacelike separated fields either commute or anticommute can be made only for relativistic theories with a time direction.

Might need to ask Acuriousmind later on why microcausality means spacelike separated fields can only be of the form $[/phi_1, /phi_2]=/pm 1$

Obliv

04:06

@0celo7 do you study all day or something?

0celo7

@Oblivno

John Rennie

05:18

Ah, erm, yes, my latest badge. Erm, perhaps I shouldn't be too proud of this one :-)

physics.stackexchange.com/help/badges/1332/…

skill patrol

Congrats, I guess.

:-)

Are you the first? @JohnRennie

John Rennie

Yes, though I'm not boasting about it. The (gold) badge of shame :-)

Secret

05:57

en.m.wikipedia.org/wiki/Spin_(physics) I might need to revise again why spin of a particle is always aligned with magnetic moment of a particle

Also if spin basically describe the topology of SO(n) and in 3+1 spacetime, lorentz invariance result in spacelike separated field operators to tranform in a symmetric or antisymmetric way, then how is one of the two classes of action of SO(3) being assigned to what field operator.

KNP

@0celo7 what's wrong with it?

Secret

For example, why do field operators that creates something with lepton number 1, charge -1, $mass m_e$ (i.e. Electron) will have a SO(3) topology that is of the class that corresponds to "rotations by 4$\pi$"...?

I might get my answer when I revise how the value of spin of particles are calculated, such as the Higgs, the photon etc.

skill patrol

06:35

Hi @JohnDuffield

John Duffield

@Skill patrol: hi. I thought I'd look in while I wait for the wife to bring me my morning cup of tea.

Ah, here it is. I am English you know.

skill patrol

Yes, I know :-)

What kind of tea? @JohnDuffield

John Duffield

Not as obviously English as some. You won't be getting too many toodle pips from me.

@skillpatrol : Tetley!

skill patrol

Golly good :D

Enjoy your Tetley.

Hi @lucas

lucas

Hi

Nice day!

@skillpatrol

John Duffield

06:44

@skillpatrol : would you believe it, I have to go already.

skill patrol

:-)

user116211

23

A: Mathematician trying to learn string theory

Many string theorists would like to know more algebraic geometry. There are a few of us who know algebraic geometry at a pretty high level (not me) but many more who would like to learn more and feel it would help with their research but find the literature very difficult. I think the optimal sol...

user116211

I think the optimal solution would be to find such a string theorist and agree that you will teach them algebraic geometry if they will teach you string theory.

user116211

07:22

Holy Lord!

user116211

Bourbaki did write a treatise on Algebraic Geometry!!

user116211

90

A: Did Bourbaki write a text on algebraic geometry?

Wrong! Here is Bourbaki document on algebraic geometry, taken from the now available Master's Archives: click on Autres rédactions, then on Chap.I Théorie globale élémentaire (91 p.) This preliminary draft was apparently written (according to a penciled annotation on the first page) for Bourb...

Noah P

08:19

Morning all (In england anyway)

lucas

09:17

What does mean the "PTSD"?

Noah P

Post traumatic stress disorder?

lucas

Thanks! This means he/she has had an accident?

Noah P

Anything can cause PTSD; Common among soldiers, in accidents, victims of abuse

Slereah

also internet bloggers

Noah P

Go on..?

Slereah

09:28

Oh a lot of internet people pretend to have PTSD

lucas

Well!

Slereah

When something makes them upset

Noah P

fair enoug

lucas

@NoahP Is English your native language?

Noah P

Yeah

lucas

09:31

May you please teach me some short phrases for thanking.

Noah P

Typically I'd say:

Thanks!

Cheers

Or put thanks a lot, not many variations

lucas

I want to use them for those people that post me answer or comment.

Noah P

Thanks or thanks a lot

lucas

But I need more, because someone said me duplicate phrases aren't nice.

I always say: Thank you.

Noah P

I cant really think of anymore, with saying thanks it doesn't really matter about repeating yourself

I do it all the time

lucas

09:35

But sometimes more than one comment posted to me.

Noah P

There's no need to thank them all

lucas

Shouldn't I answer all comments?

I think this make the poster uncomfortable.

Noah P

I woudlnt expect a thanks for a comment

lucas

OK. Thank you very much! :-)

Noah P

No worries! :)

user116211

09:41

Something is weirdo here:

user116211

1

A: Kepler Orbits: Small Perturbations->Elliptical Orbits

MAFIA36790 thought it was inappropriate for a person (myself) with PTSD to ask people on the internet not to be abusive to them (as I did in the original post and he/she removed) so I abandoned this question immediately since honestly I think I ought to be able to ask people to not be abusive to ...

user116211

Weirder fact is that it got a upvote too ;P

user116211

I've left a comment though:

user116211

I really don't know why you are doing all these. I removed an unnecessary part of your question; we have Be nice policy on SE; so you don't have to explicitly mention that. I'm not bullying you in any way. The comment was generated from the review as it didn't answer the original question. Also, if you have any grievance, you can post it Meta Physics SE. — MAFIA36790 21 mins ago

Noah P

It's got a downvote and a flag now too

user116211

09:44

she seems to be adamant, though.

lucas

He looks like be a boy.

Noah P

In any case, the question is not the place to discuss the issue

user116211

@NoahP yes.

Noah P

Though im wary to point that out, so flagged it for a mod

@MAFIA36790 If I was trying to find the temporal dependence of a variable, a, would that be da/dt?

user116211

@NoahP Think so.

Noah P

09:52

So I've got $a=a(t)$

And I want the temporal dependence of that

I know the initial condition is $a(t=0)=0$

So I'm looking for $\dot{a}$?

@MAFIA36790

user116211

@NoahP I'm not sure then; if they want the derivative. Because you said you have the function of a in terms of t.

Noah P

Yeah, but there's also $\dot{a}$'s all over the place

I'm solving the Friedmann equation

user116211

@NoahP Don't know about that; Is it a differential equation?

Noah P

user116211

If yes, then solve it for $a$; then use the initial condition to get the temporal dependence.

user116211

10:01

@NoahP I can google ;P

Noah P

How would I do that exactly?

user116211

@NoahP Show me your work then.

Noah P

I've got $k=0$ and $\rho=Ca^{-6}$, where $C$ is a constant from integration, not the speedy $c$

So $(\frac{\dot{a}}{a})^2=\frac{8\pi G C}{3a^6}+\frac{\Lambda c^2}{3}$

you suggest solving for $a$?

user116211

@NoahP No time to go through the wiki article; if $a$ is a function of $t$ and you have got the initial conditions, solve it then using integration.

Noah P

I could marry you for pointing that out

user116211

10:09

@NoahP ;D

Noah P

I've got some maths to crunch then

user116211

@NoahP: One advice from me; learn how to solve differential equations and hence integration; they are easy; you can easily self-teach yourself.

Noah P

Ok, will do - Actually solving them is a new concept to me

user116211

@NoahP solving means solving the differential equation which means integration ;)

lucas

Do these symbols have different meanings? :-) ;-) :D ;D :P ;P :/ ;/ :| ;| , etc.

Noah P

10:12

Ugh

Can i integrate $\dot{a}^2$?

user116211

@NoahP of course?

Noah P

I don't need to get rid of the $^2$ somehow?

user116211

I'm busy right now; would be back within an hour.

Noah P

Okay @MAFIA36790

skill patrol

@lucas when you use " ; " it means you are winking your eye.

lucas

10:22

And what does that mean?

skill patrol

A wink usually means you are joking.

lucas

Well! What about "D" and "P"?

skill patrol

The first one is a smile, and the second one is sticking out your tongue.

lucas

And have especial meanings?

skill patrol

Nah

They are what you would call body language

lucas

10:27

Thanks very much! You are so patient with me.

skill patrol

on the net

np = no problem

etc

Noah P

10:40

@JohnRennie I need you

$(\frac{da/dt}{a})^2=\frac{8\pi G C}{3a^6}+\frac{\Lambda c^2}{3}$, where $a=a(t)$, and $a(t=0)=0$.

Anyone got any ideas how to solve this for $a$?

Well, solve it - I think for a, but this question states for the "temporal dependence of $a$"

lucas

10:57

I have passed differential equations some years ago and I have forgotten that completely. I am not sure, but maybe this help that differentiate both side of the equation with respect to the t for getting rid of power of 2.

Noah P

Is that not just going to get me further from the answer if I need to get rid of the derivatives?

Slereah

@NoahP Multiplying by $a^4$ might help

$$a^2 (\frac{da}{dt})^2=\frac{8\pi G C}{3a^2}+\frac{\Lambda c^2}{3}$$

lucas

@NoahP Sorry, as I said I have forgotten. It was a suggestion.

Noah P

@Slereah Don't you need $a^4$ next to $\Lambda$ then? @Slereah

@lucas No worries"

Slereah

Then you can do $y(t) = a^3(t) \to \dot y(t) = 2a^2 \dot a ...$

Nah I have no idea

Noah P

11:01

Im lost

Slereah

Try "Polyanin A.D., Zaitsev V.E. Handbook of exact solutions for ordinary differential equations"

It's a good place when you're lost on ODEs

Noah P

It looks horrific

Slereah

Math reference books all are

but sometimes you gotta jump in

Noah P

I certainly can't do that on an empty stomach, so it's gonna have to wait a bit

Slereah

I'd say if you have to solve shit regularly

You need that book

The integral book

And the function book

Noah P

11:12

:(

0

Q: Solving the Friedmann Equation

Through substituting for values of $\rho$ and $k$, I have: $H^2=(\frac{\dot{a}}{a})^2=\frac{8\pi G C}{3a^4} + \frac{\Lambda c^2}{3}$ $a=a(t)$, and $a(t=0)=0$. Note that $C$ is a constant of integration, introduced from the substitution to eliminate $\rho$ - it is not the same as $c$. I'm not re...

cosmology

Might make this all a bit easier. I'm off for lunch now, back in a bit

user116211

11:44

@NoahP You asked it at Physics? Why? It would be closed as in the present form, it is surely off-topic.

user116211

@NoahP Better ask it as Math SE.

user116211

Oh... it's already closed.

Jim

@MAFIA36790 why would a question about finding the temporal dependence of the scale factor be off-topic for physics?

user116211

@Jim Because it's homework based question.

Jim

@MAFIA36790 homework based questions are not off-topic by default. They merely need to be worded properly. The question has potential so long as it isn't asked like "Show me what to do"

user116211

11:50

I'm seeing there are two Friedmann equations.

user116211

@Jim Sure, they can be.

Jim

also, it's funny that people immediately turn to john rennie for cosmology. He is the top user in the tag, but I'd wager he's top in every tag because he answer probably 33% of all questions asked. What people should do is turn to the top users with high score/answer ratios

highest would appear to be ted bunn, then pulsar. Lubos doesn't count because his presence on chat and the site in general is too unreliable

user116211

Still think the question is more competent for Maths SE.

0celo7

Is "Ingvild Lorentzen" a chick or a dude?

Jim

chick

user116211

11:55

@Jim nods

Jim

ingvild sounds like a chick name

Noah P

Hi, Maths SE aren't much help as they say its a physics equation - hence why I put it here

It's currently got 2 re-open votes, and I explained my reasons in a comment

@MAFIA36790 @Jim

@Jim John Rennie was the one who replied to me first on here, hence the mention

Jim

John Rennie. It's good to know he's consistent. First responder to questions both on the main site and in chat

Noah P

Do you think there is a chance it'll be re-opened?

Jim

yes, there's a chance

Noah P

12:06

Ok

#:)

user116211

@NoahP: Is $\omega$ a function of $t\;?$

Jim

you could help it along if you edit it to ask more about the concepts of what you are doing and less about the specific mathematical method of doing it

user116211

i.e. $p = \omega(t)\rho\;?$

Noah P

No, its not a function of t

Jim

@MAFIA36790 sometimes but not always

Noah P

12:07

It's not in this case

$\omega$ is a constant

Jim

usually it isn't a function of time. But I've seen cases where the observational data has shown it to change slightly through history

Noah P

Ah ok

user116211

@Jim Then it could have been converted to single linear second order differential equation.

Noah P

I haven't considered the second Friedmann equation for acceleration, which is precisely that

user116211

You could have add the two. By suitable choice of the parameter; that could be made to Riccati equation.

Noah P

12:09

That isn't going to look nice probably, but I'll come back to you with it in a sec

Jim

yeah, you kinda need it. Otherwise, it'd be possible to claim that at late times $a$ approaches a linear function of $t$

user116211

The rest would be easier then.

Noah P

Ok, I get:

$\frac{\ddot{a}}{a}=\frac{-16 \pi GC}{3a^6}+\frac{\Lambda c^2}{3}$

Jim

now take a look at the late times, when $a$ should grow very large

Noah P

Is it not important that $a(t=0)=0$?

Jim

12:14

$\frac{\dot a}{a}\to C$ and $\frac{\ddot a}{a}\to C^2$

Noah P

Youve lost me there, how do they tend to that?

Jim

@NoahP it is if you define it that way. Makes the early times messier.

Noah P

I have to define it that way

Jim

@NoahP if $a$ grows large, $\frac{1}{a^n}$ drops off to zero

Noah P

Ok

Jim

12:16

$C$ is a random constant

Noah P

Not random, but yes

Jim

no, I'm using it to signify "approaches a constant value"

Noah P

There is already a $C$ in the equation

Are you talking about the same one

Jim

no

Noah P

ahhh ok

Jim

12:19

from that relation, it's easy to see that at late times, $a(t)\to e^{Ht}$

Noah P

Where $H=\frac{\dot{a}}{a}$?

Jim

yup

Noah P

And this all considers that $a(t=0)=0$?

Thats pretty crucial

Jim

at early times, it's a bit more complex

Noah P

Ok

Jim

12:21

but you could start with $a(t)=F(t)e^{Ht}$

Noah P

$F$?

0celo7

Since when do you know about cosmology, Jim?

Jim

@NoahP random unknown function

@0celo7 since I'm a cosmologist

Noah P

@0celo7 @Jim meow

@Jim Okay

Jim

I did my degree on early-universe cosmology

0celo7

12:24

@Jim How do extended objects move in GR? Do you have a good reference?

Jim

@0celo7 extended objects? Is this more about your metal sheet metric?

0celo7

Metal sheet metric? Whut?

Do you have me confused for @Slereah

Jim

... there's a chance I'm thinking about someone else

nevertheless, it might be useful to clarify your question

Slereah

You can treat extended objects as families of geodesics

With constant distance between them

Jim

okay, but how extended is extended?

0celo7

12:35

@Slereah Can you prove that $\mathrm{GL}(n)$ has two connected components

@Jim extended enough for your mom :)

Slereah

I can prove at least two connected components

Jim

@0celo7 okay, but the extension I'm sure my mom would be fine with is probably still treatable as a point in GR. Let's face it, less than a foot is hardly worth mentioning

Slereah

40

Q: How many connected components does $\mathrm{GL}_n(\mathbb R)$ have?

I've noticed that $\mathrm{GL}_n(\mathbb R)$ is not a connected space, because if it were $\det(\mathrm{GL}_n(\mathbb R))$ (where $\det$ is the function ascribing to each $n\times n$ matrix its determinant) would be a connected space too, since $\det$ is a continuous function. But $\det(\mathrm{G...

general-topology matrices lie-groups

0celo7

@KNP It's not even continuous

Jim

@0celo7 Ah, you want to know math. Ask someone else. I'm a cosmologist that was formerly an engineer. I know the cosmology concepts very well and how to perform the math I might be called on to use, but I never studied the pure mathematics. Math terminology and identities get me every time

0celo7

12:42

What

I'm asking him an unrelated question

Jim

Ok, then my go-to reference for anything GR is Carroll. Beyond that, I have no standard reference; I just look it up as I need it

koolman

12:56

In figure a how to find pressure at pallet of mercury
And the air is present in column 20 cm

Sorry the picture which is uploaded is inverted

please help

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