The h Bar

6:51 AM

@ACuriousMind Plenty of experiments you can do!

7:43 AM

$e=mc^4$

7:53 AM

Oh no, a musician just burst in through the door confidently twirling a treble clef.

8:06 AM

All those symbols and he didn't include the dagger $\dagger$

Faded Giant

Most mathematical symbols have a size of only a few mm, and they usually consist of ink on paper. Hard to fight with that.

The size only depends on the font size

you can make them as big as you want

$$\Huge{\dagger}$$

$\Huge{\pi}$

$\Tiny{\pi}$

Laplace–Beltrami operator

8:31 AM

For any twice-differentiable real-valued function f defined on Euclidean space Rn, the Laplace operator (also known as the Laplacian) takes f to the divergence of its gradient vector field, which is the sum of the n second derivatives of f with respect to each vector of an orthonormal basis for Rn. In the field of differential geometry, this operator is generalized to operate on functions defined on submanifolds in Euclidean space and, even more generally, on Riemannian and pseudo-Riemannian manifolds. This more general operator goes by the name Laplace–Beltrami operator, after Pierre-Simon Laplace...

11:08 AM

2 messages deleted

@Slereah Ones I can do without access to a black hole?

Drop a ball

Entirely quantum gravity experiment

The ball is entirely made of quantum matter

fair, I guess

Also there were some fairly underwhelming quantum experiments done in the 70's, just to rule out some of the dumbest theories

Basically torsion balance plus superposition experiments

Dropping a ball may not sound like much but just replicating this will rule out most of the crank theories :p

Crank theories want the truth of the cosmos but they care little for balls

I wonder if there's an actual derivation for ball dropping in string theory

I guess you can do it with a very heavy open string and a light open string

And then look at the $\mathbb{\hbar}, G \to 0$ limits

Is there even a relativistic point particle derivation of a ball dropping?

@bolbteppa Sure

There's a whole theory of particles dropping in classical gravity

The Heisenberg-Newton equation I think it's called

Don't know if there is for the source particle also being a wavefunction, though

11:20 AM

Technically, a ball dropping in Newtonian mechanics is not even a purely mechanics problem, modelling it as a rigid body in a potential $V(x)$ of gravity and a velocity dependent friction is an approximation, so...

Schrodinger-Newton

Here's a question

Wheeler–DeWitt equation

The Wheeler–DeWitt equation is a field equation. It is part of a theory that attempts to combine mathematically the ideas of quantum mechanics and general relativity, a step towards a theory of quantum gravity. In this approach, time plays a role different from what it does in non-relativistic quantum mechanics, leading to the so-called 'problem of time'. More specifically, the equation describes the quantum version of the Hamiltonian constraint using metric variables. Its commutation relations with the diffeomorphism constraints generate the Bergman–Komar "group" (which is the diffeomorphism...

\begin{eqnarray}
i\hbar \frac{\partial \Psi}{\partial t} &=& - \frac{\hbar^2}{2m} \Delta \Psi + V \Psi + m \Phi \Psi\\
\Delta \Phi &=& 4 \pi G m |\Psi|^2
\end{eqnarray}

That's the one

They try to say that $H |\psi > = 0$ is the WDW equation and implies timelessness, but the exact same thing happens in the Klein-Gordon equation and nobody says that's a timeless system

Yeah I never really got the timelessness argument

11:25 AM

It just looks completely wrong unless I'm missing something (likely/definitely)

I guess technically it is true, but that's only because the time dependance is hidden in $H$ itself

$H=0$ onshell is a generic feature of time-reparametrization invariant Hamiltonian systems

Yeah

It's nothing to do with "timelessness" because it's not guaranteed that the evolution variable of the Hamiltonian is "time" at all

A lot of physicists kind of jump to that conclusion, though

as if it's physically meaningful

11:32 AM

"The Hamiltonian is a constraint (characteristic of most relativistic systems)... $H |\psi> =0$... leading to the so-called 'problem of time'" it looks like this is what they're saying, which is the exact same thing you get quantizing a relativistic point particle, but you get the KG equation from this procedure which is absolutely not timeless :p

Q: Discussion about bounties as charity

I'm guessing the whole problem of time idea maybe started in olden times before constraint theory was very advanced?

Physics Meta

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I have recently asked a few critical and non localized questions which have not been answered (properly/completely unanswered). Is there a provision that I can ask for someone else with an appreciably high reputation to place a bounty? Can it be implemented as a feature for those who are new to ...

discussion support feature-request

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I'd say it's a real issue, but it's just a fact that Dirac's constraint stuff applied to a relativistic point particle leads to $i \frac{\partial }{\partial \tau} \psi = \hat{H} \psi = 0$ for $\hat{H} = (-\partial^2 + m^2)$ i.e. the Klein-Gordon equation, so the 'problem of time' exists here too

It's an issue but I don't know if the issue is time

More of a gauge issue

11:44 AM

Well they seem to claim it's a time issue?

The wiki says "Unlike ordinary quantum field theory or quantum mechanics, the Hamiltonian is a first class constraint on physical states." which is just completely wrong given the example I just gave

I think Slereah is right that this is either older than - or was at least done first by people not familiar with - proper/modern Hamiltonian mechanics

And once the foundational texts of a subject go on at length about such a problem, it's hard to get people new to the field to do it right instead of just taking over their old arguments :P (especially since Hamiltonian mechanics at this level is still not something you can expect most physicists to be familiar with)

The Wheeler-DeWitt Equation - Renate Loll

I'm just not sure, it's hard to believe they are all misunderstanding it, especially in texts where they set up constrained quantization in a GR context (harder than the usual stuff), e.g. this 2010 one which makes the timeless argument

►

Dunno

Seem to talk about it around minute 26 here

Maybe it's just the terminology by now

"Problem of time" just describes the fact that $H\Psi = 0$

and nothing further

More Anonymous

12:06 PM

@Slereah Sorry to disturb your conversation but do you know how to do asymptotics with the line element?

I do not

More Anonymous

But is it a thing?

Well I'm not sure but it seems like the KG thing above is saying the proper time derivative is zero, and here for some reason they really take the time $t$ derivative, not the $\tau$ derivative. So qft has a problem of 'proper time' while GR has a problem of time apparently, the former is ignored, the latter a deep philosophical thing apparently, hmm

Even though they make seem like it's a $\tau$ derivative arising from reparametrization invariance in the wiki, so not even sure about this

But the time in Wheeler-De Witt is also the proper time

It's the time of the selected foliation

I guess it's tough to have proper opinions on it because there aren't a lot of solved cases for canonical quantization

A good start is knowing why the KG equation does not suffer from the problem of time, but I can't find any source even indicating it is relevance yet

12:18 PM

that's because it's not a problem :P

I think Carlip has some exact solutions?

For $2+1$-gravity

At least as close to it as you can get

Since the phase space can be reduced a lot for $2+1$

The video cites this as an authoritative source talking about it as a real problem, around (3.2.7) they seem to indicate the $t$ is $t$ and not $\tau$

Do they mean the lack of derivatives in $t$

Bc that is also a thing in EM

They seem to take a $t$ derivative, not a $\tau$ one

The wiki Hamiltonian depends on $t,x,y,z$ so this just makes no sense...

I'm guessing the wiki version probably doesn't take great care of doing everything properly

Hm

Where would there be a proper version of that

Ncatlab doesn't seem to have a page for it

Thiemann has a whole chapter on the problem of time

12:25 PM

I think roughly that Dirac, DeWitt and then that Feynman book are the real first steps in quantum gravity

Quantum gravity took a while to be popular because a lot of the people who cared about GR didn't care about QM :p

Bloody Einstein

DeWitt talks about some 30's Rosenfeld calculation as well, hmm

there were a bunch of early attempts

going as far back as 1917 IIRC?

But then that's what you do

When you have a new theory that can be generalized to whatever field, you throw all the fields at it

1:53 PM

In a LQG book of all places:
"$H = 0$... More precisely, the hamiltonian is proportional to the constraint $H \approx C$. This should not be a real surprise, since the hamiltonian generates evolution in the evolution parameter in the action, namely in $\tau$, but a change in $\tau$ is pure gauge, and in the hamiltonian formalism the generator of a gauge transformation vanishes (weakly).
This does not mean in any sense that the dynamics is "frozen", or other similar absurdities that one sometimes reads. The dynamics of this system is the one described by the Newton equation above. The vanish…

2:10 PM

Rovelli calls $C \psi = 0$ for $C$ a constraint the WDW equation, then gives examples where $C$ involves space and time derivatives exactly as in the KG example above, in a chapter called 'physics without time' where he seems to imply that the issue is we never specified which of the variables are time or space (i.e. like covariance lets you ignore which is which) as if this is the issue, not the frozen time stuff...

Yeah this is pretty much it I guess

He says things like "Notice that the construction does not ever require us to mention the word “time”or to refer to a "time variable""and " this equation [$C\psi = 0$] is precisely the Schrodinger equation for the parametrized form of the Newtonian systems"

So "all the examples considered admit a Newtonian formulation where the time variable is used as in-dependent evolution variable. However, general relativity comes already formulated in this language, and there is no general way of selecting one of its variables and interpreting it as "the time variable". General relativity asks us to describe the world in terms of relative evolution of partial observables rather than in terms of evolution of degrees of freedom in time" is the timeless physics

i.e. even Klein-Gordon equation is timeless in this boring sense

Yeah

What are even the spooky ghosts for GR

2:59 PM

"A local function $f$ is weakly zero if it vanishes when one pulls it back to the stationary surface."

One can never just do what a physicist does, always have to justify it with a pullback or a bundle or something :p

3:32 PM

If someone did a physics book properly it would be like 90% pullbacks

and lifts

3:44 PM

map by jinglebells :P

ronak jain

4:36 PM

Hi everyone

Faded Giant

4:59 PM

@JingleBells nice observer bias

user434058

5:42 PM

@Slereah IMO, a trident shape $\psi$ would be way more useful than the weird curvy $\zeta$. Just sayin'...

@FadedGiant wat do you mean?

7:10 PM

It's really cool how we actually understand evolutionary algorithms and we can simulate them on computers but we can't achieve anything substantial because real biology has the advantage of playing around with atoms and molecules, and our computers don't have the computational power to do that.

I have a theory about the human brain. I'm pretty sure I'm not the first one to think about this (of course lol) but here it is: I think that the human brain, thoughts and everything that happens inside is all a function of the environment. Our brains are the depended variable and the environment, the independent. When I try to prove my free will, the thought of doing that has been sparked by the writing of this message, which has been sparked by watching youtube videos and so on.

I am reading Feynman, a bit confused by

spin

I thought before a measurement speaking of a spin up or down makes little sense

The environment essentially changes itself, we don't change the environment. We physically change it, but not because we chose to do so, but because we perceived something from the environment that sparked the thought of doing something that changed the environment.

but Feynman keeps saying spin up

I am probably the wrong one

can some one be kind enough to teach me?

So I see the environment as its own separate entity (it's outputs based on randomness or some form of higher-dimensional intelligence) that essentially uses our brains to alter itself.

why Feynman says spin up and down like it is a classical object?

7:18 PM

IDEA: the chatroom should have a button "Ask" that allows you to ask your question and pins it somewhere so two or three people don't talk over each other like me and Shing

You can measure spins up and down along a specific direction

ie you have $\sigma_x$, $\sigma_y$ and $\sigma_z$

And they have + and - eigenvalues

@JingleBells You're just describing some form of determinism, no?

@Shing Quantum states can have definite values for some quantities prior to measurement, they just don't have to

You'll have to be a bit more specific about what Feynman writes and what problem you have with it for us to say anything more

7:38 PM

@ACuriousMind I am a bit confused by the ferromagnetism part. what you said have helped me a lot already, thanks. but I am still not sure if a spin can "rotate" itself via some interaction (quantumly)?

@Slereah yes, I was confused why Feynman talking about spin as if they are classical objects. btw, is there a quantitive explanation for ferromagnetism in this modern age?

ps: vol III, ch4 Identical Particles

@ACuriousMind Well, somewhat, I guess. It's more of a flowchart between a brain and the environment. But determinism on the quantum level is clearly not the case (as far as I know).

I call my model - "The causality of the environment-brain loop". Omg I sound so smart

Following my logic of the environment being the center of everything, and not the human brain, the question of general AI becomes "How do we build the right environment" rather than "How do we build the right brain model". Btw I have no idea what I'm talking about but just thoughts...

it's 11PM I have an excuse