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15:02
@nickbros123 I think they are just looking for the Klein-Gordon equation
you're not expected to write down the square root and derive the Dirac equation here
@RyderRude I don't know what you mean by "in GR, the observed time would depend on the dynamical field"
what is "observed time"
the problem that there is no universal time coordinate occurs already in SR
The time that the clock of the experiment would measure would depend on the dynamical metric
what experiment?
Of the quantum gravity experiment
Where the theory is relevant
why is there a clock there?
I mean that the parameter of unitary evolution is getting entangled with the dynamic field
English usage of "entangled"
We compute unitary evolution wrt to a paramter that is supposed to be the observed time of the clock
15:08
what clock
This parameter is getting entangled with the dynamic field that the quantum theory is describing
There's always a clock in GR experiments
nothing in the formalism relates the parameter intrinsically to any specific clock
Are you claiming that gravity violates unitarity?
@ACuriousMind the clock that we wud use to test the predictions of the theory
15:08
if you're saying that the time coordinate we use should be the time coordinate of some observer, that's true
but that's not quantum
when you solve the classical Cauchy problem in GR you're also starting with initial condition w.r.t to some time coordinate
and then you evolve those w.r.t that time coordinate
Yeah, that is true. But the time of the observer depends on the dynamic field across his worldline
why aren't you worried there that whatever you think goes wrong in the quanutm case also goes wrong there
@RyderRude peek gang: arxiv.org/abs/2104.03253
@Amit I don't think it is useful to randomly throw papers into the conversation just because they share a few buzzwords
@ACuriousMind in case of GR, we can just solve euelr langrange equation in some meaningless co ordinate. The proper time of the worldline can b calculated after we have already obtained the solution
In case of quantum, the dynamical eqn is the schrodinger eqn, which relies on the observes time
15:10
but that's not what we do
when people solve GR in practice they solve it as a Cauchy problem
i.e. give initial conditions and evolve
@ACuriousMind You are very correct, I'm sorry, I don't like to throw papers at anyone
This is weird. How can one know the time before we have solved for the metric
Oh i think i got it
either you think there is a fundamental problem with the notion of initial value problems in GR, and then this problem is both classical and quantum or there is no problem here
But not really :P
@RyderRude the point is that the evolution equations don't care whether the time is "real" or not
15:13
Ooh so they just solve it wrt meaningless time
And the real time can b calculated later
the parameter $t$ in the evolution equations is just that, a parameter. It doesn't have to be tied to a worldline - in fact, it never is because the time coordinate covers a whole patch of spacetime, after all, not just a single worldline
After we have the metric
and once you have the result, you know how to change coordinates and translate that result into the proper time of some observers if you need to
@ACuriousMind ok so this time-co ordinate has nothing to do with the metric we just solved for. Its just a parameter
Or does this time parameter agree with the metric?
I don't know what that means
there are infinitely many possible time coordinates for a given metric
it's just any coordinate whose direction is time-like
15:16
But i thought we were supposed to label it using proper time
label what
proper time is not a coordinate
I think you have misunderstood the nature of proper time
Ok i dont mean we need to label the entire spacetime using proper time
I just mean we label just the observer's worldline using proper time
And we can possibly switch to co-ordinates where the observer's wordline is a co-ordinate axis
Is this possible to do
So the proper spacetime is NOT a co-ordinate for the entire spacetime. But it can merely be chosen to be the time labels of our time-axis
If we choose our time axis to be the observer's worldline
Ok I think this gotta be valid. Becuz worldline is timelike and is infinitely long
I think it's only correct as a time axis for things that happen at distance zero from whoever is measuring that time, it is very limited in its use isn't it
Yeah, i need only that to be true
The rest co-ordinates can be meaningless
My point is that, in case of QM, the unitary evolution eqn must have THIS time as its parameter. So it wud depend on the dynamics. In the case of classical mech, we cud solve the eqn wrt ANY TIME
But in qm, we describe some observer's experiment. So we gotta use this specific time parameter for qm equations
@RyderRude worldlines are not necessarily infinitely long :P
15:26
. Imagine a family of astronauts :)
The generations continue the worldline
Lets just idealise for discussion
this was not a practical objection
you can have cases where some worldlines just terminate after finite proper time
Oh did u mean singularities
yes and no
I'm not sure what you mean when you say "THIS time", by symmetry, every time coordinate is the proper time of a certain reference frame? Isn't it?
but anyway it doesn't matter
15:28
$$\Delta{t}^2-\Delta{x}^2 = \Delta{\tau}^2 \implies \Delta{t}^2 = \Delta{\tau}^2-\Delta{x}^2$$
@Amit ye, but u gotta use the observer's time for QM equations. The observer who is doing the experiment
I don't know who "the observer" is in QM
the Schrödinger equation does not involve observers
and observers don't observe the time evolution of states, they observe the outcomes of measurements
Ok let's imagine u trying to test ur theory. U start with an initial condition. On paper, u predict the probbailistic outcome after a finite time. Then u run ur clock. At ur prediction time, u collapse
But ur predictions come out wrong becuz ur theory used the wrong time
ah I have an error in sign there
@RyderRude why did I use the wrong time?
of course if I did the computation in any coordinate system other than my own comoving one, I first need to transform the results into that one
in particular I need to transform the spacetime coordinates I used in my computation into my comoving ones
15:31
Should have used the other metric signature
but again there is nothing quantum about this
classical physics is also about observation :P
Ok so the procedure is the exact same as in GR
U compute unitary evolution wrt meaningless time
it's not meaningless!
It's just not some specific proper time of some observer
Yeah
So after u have ur solution, u also get ur physical time.
And then u transform to physical time
but that's just how time and space in relativity work - they're relative
the whole point is that we construct the theory in a way where we can switch between different coordinate descriptions without having to re-derive everything
15:34
But my problem is that, in the case of quantum theory, ur solution in terms of the "usless" time would not provide u information about ur physical time
In case of GR, ur solution includes a definite metric field
Thay gives u information bout ur physical time
In qm, u just got a wavefunction wrt useless time
And the metric is probabilistic!
the experimenter usually does not evolve themselves
we're outside of what we measure
That is a very good point
The observer exists in a classical metric. It's not probabilistic
like, you can't say "we're doing a quantum measurement" and then just evolve yourself and your measurement apparatus unitarily
Becuz if the observer's metric had meaningful quantum effects, the observer wudnt even be alive
that's not how measurements work
15:37
So the metric is probabilistic only for the experiment
Ok i think this solves it
But it also means that quantum experiments are only defined when the observer exists in a classical spacetime
So quantum mechanics sort of needs classical conditions to be meaningful
I guess we'll have to live with this :)
It would be very weird to talk about experiments if the observer is dead
That's talking interpretations again isn't it... not all interpretations accept that there is a real distinction between "classical" and "quantum" conditions
Yeah, but how do we define the time of unitary evolution without assuming a classical background time for the experiment to be performed? @Amit
The unitary evolution needs a definite parameter. The parameter isnt probabilistic
what is a classical background time? is time a classical quantity? I'm not sure that's a widely accepted view
Yeah u r right @Amit
But i dont see any solution
The parameter time doesn't need to relate to the metric at all
It's just a coordinate
15:43
"Smooth operator... smooth operator...."
U have general covariance, it works with any time coordinate
@Slereah that's a good viewpoint. But the problem is that schrodinger equation isnt form invariant under arbitrary transformation of time co-ordinate
Qg theories are
So for unitary evolution, we cant have a meaningless parameter
General covariance is prztty high up on qg list of priorities
15:45
@Slereah like, string theory?
hello, i am wondering about a quote in carroll. it says "the lorentz group includes not only boosts and rotations, but discrete reversals of the time direction as well as parity transformation.....what we really want is the set of continuous transformations (those connected smoothly to the identity)..." i am trying to unpack this statement. first, I dont understand why there is a specification that the time translation is discrete [...]
[...] and second i do not understand why we need to eliminate these from being possible transformations? i know that parity should be eliminated since it does not leave physics invariant, but why is the time reversal a problem?
Sure
Ok but string theory so far only talks about scattering @Slereah
To deal with this problm, string theory wud need to talk about finite time evolution
It may be true that the involvement of time in QM is not done quite correctly... maybe that's how we ended up with the reverse time direction of anti particles (as far as the formalism goes apparently, I don't know if many take that seriously as a physical fact)
There's also covariant LQG which just gets rid of schrodinger equation.
Idk what the hell covariant lqg is describing
It's some foams. But idk about probabilities
15:48
@Relativisticcucumber He says that the reversal is discrete. I think it just means that there is no inherent thing in GR that prevents you from looking at the "lower half" of light cones, or in other words, the EFE are AFAIK completely time symmetric
@Relativisticcucumber It's a problem when you want to assign a direction to time... the continuous transformations prevent you from flipping the time direction, but technically I don't remember exactly how (something to do with the fact that the invariant interval can't pass through the null value continuously I think)
You can flip the time direction but that is part of another connected component of the reparametrization group
@Relativisticcucumber "discrete " as opposed to "continuous" - there's just "reverse the time direction" and "don't reverse the time direction", but not "do an infinitesimal reversal of the time direction"
to answer your question of why you only want the continuous transformations I'd need more context
16:08
@Amit it's a very outdated formalism :P
Really? I thought it pops out of looking at the QFT expressions... but I don't know it first hand
@Amit another terrible misinterpretation of a straightforward technical fact
the technical meaning is CPT symmetry, and no, it doesn't imply that antiparticles are particles from the future
although it does mean that it is consistent to believe that
but there is a difference between a particular ontological interpretation being consistent with the formalism and the formalism actually directly stating something
@ACuriousMind okay i will provide more context tomorrow i am falling asleep sadly
@Slereah i will think about this tomorrow as well
@ACuriousMind i dont even get this as an interpretation of CPT theorem. Isnt CPT theorem just : The Hamiltonian commutes with the CPT operator?
How is that interpretation still popping out :P
It's unclear to me how serious Wheeler was when he proposed the one-electron universe but CPT + equal amount of particles and antiparticles would make it consistent
@RyderRude well, CPT means that a particle going forwards in time with some handedness behaves exactly the same as its anti-particle going backwards in time with the reverse handedness
so if you're silly (and we forget about handedness for a moment because people don't understand what it is anyway :P) you can technically use that to interpret all "particles + antiparticles going forwards in time" instead as "particles going forwards in time + particles going backwards in time"
because by CPT symmetry the physics of these two situations are the same
16:16
For whatever reason, time is not a "regular" observable in QM, I am wondering whether this can be easily justified
@Amit what's there to justify
it's not a "regular observable" in classical mechanics, either
just a parameter in the evolution equations
it's not a function on phase space
@ACuriousMind except for some stupid toy models :P
But in any case, time cant be an observable for just some specific models @Amit
@ACuriousMind i think there is a weird case like $P^2+X$. We were discussing it long ago
The momentum operator for example, corresponds to a position derivative (and vice versa). The Hamiltonian operator corresponds to a time derivative... but time isn't an observable (as opposed to position and momentum). Now this is proper nonsensical meta observation probably lol. But just from these shallow facts, I think a weird asymmetry is apparent
16:24
@Amit Ok i have a really nice way to interpret that analogy
Please sir go on
@Amit it's not a weird asymmetry
you can make it perfectly symmetric (make the theory "generally covariant")
Both time and space can exist as parameters of wavefunction. It is important to distinguish between parameters of wavefunction and arguments of wavefunction
@ACuriousMind Which would mean I would have an operator that corresponds to the time observable?
Time cant be an argument of wavefunction
16:27
@Amit the symmetric version just isn't, in general, useful
Space can be a parameter of the space translation schrodinger eqn
you just add a coordinate $t$ to phase space
but then in Hamiltonian terms your theory becomes constrained - the constraint is just what was the time evolution equation before that - and just everything gets more complicated for no reason
Does this mean that something like $\hat{T}$ will be a time observable proportional to $\frac{\partial}{\partial{E}}$ ?
the point is less that it's impossible to make time a phase space coordinate or operator and more that there's no useful way to do that
@Amit see, that's what doesn't work
when the spectrum of the Hamiltonian is discrete, something like $\partial_E$ makes no sense
Doesn't work in the sense that we don't know how to write anything physical as a function of $E$?
16:30
it's all a lot more complicated and ultimately pointless
@Amit no, doesn't work as in it's nonsense
doesn't mean anything
lol
I was just pondering, could the laws of thermodynamics be different inside a black hole...
I think that any direction that can shed light on $W\tau\phi$ is time is interesting, but if you say this direction is nonsense in that regard, I take your word for it :)
time is what clocks measure
I don't find it any more interesting than space
You don't think that time may have some real quantum properties? In space we know what it means, that a particle can be in superposition in space but we never consider this situation across time
16:33
I think this stuff also conflicts with GR. Becuz the schrodigner eqn isnt form invariant under arbitrary transformstions of the time-parameter. If one is using the schrodinger eqn one must use physical time determined by the metric
So then we get into conflicts we just discussed
U wud need the experimenter's time to be classical for the parameter of schrodinger eqn to be defined
Then it all works out
@Amit I don't know why I have to say this so often lately but I'm really pretty satisfied with the physics we've already got
You can make the Schrodinger equation invariant under reparametrization
If that tickles you
then it becomes a gauge theory
I just said that :P
just used "constrained" instead of "gauge"
I didn't read
Yeah, u can do that for sure @Slereah
But the main problm is the the parameter has to be definite at least. It cant work with a peobabilistic metric
So the experimenter's time needs to be classical
16:36
@ACuriousMind Satisfied doesn't necessarily implies that you don't find room for improvement / advancement though :) I think what we have is lovely as well
As I said, the metric doesn't change the time coordinate
Okay i got u now
@Amit No, what I mean is that I really don't see any necessity to believe QM is somehow "incomplete"
@Slereah i will need 2 think of another problm :P
I don't know what "time may have some real quantum properties" is even supposed to mean
16:37
A grain of time.
what situation can QM currently not deal with that you think could be dealt with better if we answered that question?
Exactly @ACuriousMind it would be impossible to test experimentally. Cuz no experimenter can exist in non-classical time
But idk. For personal satisfaction, i guess a theorist wud look for such a "deep" theory
@ACuriousMind Ah, indeed there is no reason to assume it's incomplete. But this business about time for example, wouldn't necessarily fundamentally change QM, I would find it interesting enough if it would just allow us to draw new conclusions / predictions from QM as it is without changing it fundamentally...
as I said there are already formulations that treat time and space on equal footing
they're just ugly
but they're there
and there are good reasons for why they're ugly
@ACuriousMind Mind your manners
16:40
Is there a "famous" example of such?
Polysymplectic QM
@Amit I'm not sure what you mean by an example
Covariant lqg
It has quantum time too
Example of a formulation...
no, LQG is another different theory
it has nothing to do with what I'm talking about at all
16:41
But to test it, they say that they need to first construct a classical time using it
CDT has discrete time IIRC
I'm just saying that there is a general procedure to turn any (classical or quantum) Hamiltonian theory into an equivalent theory that has time as a coordinate
and causal sets
@ACuriousMind yeah, then u get constraints. But u still dont get quantum time
I describe the procedure for instance in this answer
it's just a boring technical thing, and the resulting theory is more annoying to deal with than what you started with in most cases
16:43
Covariant lqg has quantum time. But they say they need to construct classical time using it before they can predict scattering
@RyderRude I have no idea what "quantum time" means
when you quantize this constrained, generally covariant theory, you of course get an operator corresponding to time in the pre-constrained Hilbert space
but the time operator isn't gauge-invariant so it doesn't become an observable
which is how this evades Pauli's theorem
@ACuriousMind I mean time becomes probabilistic. So the fundamental version of the theory doesnt make any prediction becuz time of experiment isnt defined
There are some theories that try to do this
why would time be undefined
I don't think what you're talking about has anything to do with what I'm talking about
Like covariant lqg
16:45
do you have a citation for what you're talking about
@ACuriousMind yeah. U r talking about standard theories formulated in an ugly way
@Slereah yeah. I shall get it
6
Q: Is Loop quantum gravity an unadulterated quantisation of general relativity, or does it have additional assumptions?

Ryder RudeI was reading this Phys.SE answer written by user346. At the end of point 3, they say they've only made a change of canonical variables from the ADM formalism to get the Ashtekar formalism. Then point no. 4 is about applying the standard Dirac quantisation on this theory. We end up with a Hilbert...

It's in the 4th point of the first answer I think
They talk about constructing a classical background
:63279371 Pirates of the Lagrangiean?
6
A: Does Loop Quantum Gravity predict general relativity in semi-classical Limit?

Prof. LegolasovThe confusion arises because there are essentially two different approaches to the LQG dynamics in the literature. The canonical approach pioneered by Thiemann is to define the matrix elements of the Hamiltonian constraint operator acting on spin networks, and then postulate the kernel of that o...

This other link is about an LQG theory that is known to reproduce GR
not seeing anything about probabilistic time
They talk about superposing the lqg foam to construct classical spacetime @Slereah
So I thought the spin foam had probabilistic time
16:50
does it
why would you think that :P
I shall quote the part :P
@Amit I'll put that on the next play list.
It is not clear how the semi-classical limit of LQG works (and if it works at all). Currently, we do not even know two-point functions that would be somehow computed on semi-classical backgrounds.
Isn't spin foam for the spatial part of GR for a start
16:52
No no
Thats usual LQG
Covariant lqg goes full crazy
I think you just have already some sort of idea how you want physics to work in your head and you're always interpreting the stuff you hear in terms of how it can be made to fit that idea instead of paying close attention to what people are actually saying
Lol
I swear there are two camps of lqg. The whole point of covariant lqg is to have a time foam too :P
The other alternative is also ok: forget what people are saying and write down your own theory :)
U can read about covariant lqg. It's not my confirmation bias :P
@Amit lol
But, is it mainstream?
16:54
Hopefully, im capable to write my crazy theory someday
Even if its wrong :P
@user4539917 it is one of the two mainstream camps of lqg
U can read about it on the wiki main page of lqg. The two camps r in the intro
Will do.
But lqg itself isnt mainstream, yes :P
Later, then :-)
@Slereah @ACuriousMind Was I wrong on my interpretation of covariant lqg
I do not know enough about LQG to say for certain but it doesn't sound like what I think is going on there
and to be honest I don't care about LQG enough to find out
16:59
U r right that I have merely read a few articles about this theory
I cud b wrong :P
looking at spin foam models I am not quite getting "probabilistic time"
It would probably require some more explanations :p
Oh yeah. If time isnt definite, how can there be a probbailistic interpretation!
I should've said non-definite time
Very nice drawing
So u cant have a definite parameter for unitary evolution, thats it
In fact, covariant lqg isnt based on any previously known quantisation technique
So it makes sense that theres no schrodinger eqn
So covariant LQG dynamics don't evolve wrt time?
17:06
It just describes a foam as the "ontological" thing
There's no time. All that is obtained in the classical limit
It's hard to do physics without time evolution
And that's where u begin to make predictions
After taking the classical limit
The only plus of this theory is that it is known to reproduce GR
But its not based on canonical quantisation. So thats a minus
The other lqg camp is based on canonical quantisation. But its not proved to reproduce gr
Becuz the other lqg camp allows for an imaginary metric, imaginary distances, etc :P
So it has problems reproducing GR despite being based on canonical quantisation
It's all string manipulation isn't it, not a lot of physics without falsifiable predictions ^_^
Foam-manipulation :)
^_-
17:14
Strings are actually the rivals here :P
I dont yet buy either of these theories tho
Very unlikely anyone cud invent QG before experimental input
We do have some experimental input but I think since the current problematic observations are in astronomy it's a bit difficult to work with in comparison with controlled experiments
Yeah, and the dark matter stuff seems to b more related to classical GR than QG. It is generally believed that Standard Model + Effective Field GR describe everything until Plnack scale.
I don't know, if it's real new matter it can also be a particle physics thing
Yeah, but then it is expected 2 b matter that doesnt interact with electromagnetic field. Its not directly relates to QG
Y does my message get copied twice when i edit it
17:30
Maybe because you are logged in to the chat on several devices
Either way it's a bug, even if you are
@Amit @Slereah @ACuriousMind Is it common for people with phds to write new fundamental theories?
I'd expect everyone is creating their stuff
most physicsts don't even work near what you call fundamental theories
Oh yeah
most of them just write about the physics of hot dogs or something like that
Not everyone have an insatiable need to disturb the status quo
17:37
even in theoretical physics a lot of people will just do a boring thesis
Just study a particular case or something
People should be doing it just for fun tbh
Writing a fundamental theory
I advise you learn it first
Yeah lol
I mean..other physicists who have learned it
honestly I think by quantity there are more crackpots than physicists writing fundamental theories
it's much easier to do when you're not constrained by logic the establishment
Thats true. I just think actual physicists should try this often too. It'd be wrong, but for fun, it's good
17:40
why do you think they "should" do it?
presumably those who find it fun already do it
I mean physicists have this apetite for invention
@ACuriousMind yeah
but most aren't the kind of specialists that understand what is actually necessary here on a technical level and realize they aren't gonna make any actual progress there
part of being an expert is knowing what you can't do
if you're trying to make new theories before you know the old ones I have some suspiscions it will not go well
I dont expect it to go well even after learning it
@RyderRude so what? they do invent stuff! but in their chosen specialty
17:42
Lol
you really need to let go of this undertone that "fundamental" physics is somehow more valuable or real than what the vast majority does
The point is that u just do it for urself. Doesnt matter if its a bad theory
Even u urself dont have to believe in it
U just do it for the hell of it
Not that i'll try it before learning previous stuff tho
But my main point is that u urself dont have to believe in it either
Just do it as a fun DIY idk :P
@ACuriousMind i agree. Most time should be spent on useful progress
what
that's not what I'm saying
I'm saying that most people disagree with you that trying to randomly come up with fundamental physical theories is "fun"
Again, there's only so much you can do without experimental input... I think a lot of the motivation for rewriting physics simply comes from how temporally close we still are to all the latest revolutions in physics. There may be a slight illusion that these kind of things can happen more often than they really can... and again, that involves often ignoring the lack of the necessary experimental input
and that your claim that this is fun because of "invention" implies all the other forms of doing physics are somehow lesser or devoid of invention
17:46
There's infinitely many things you can do without experiments
No. In fact, that other stuff is more valuable than what im suggesting
I didn't talk about anything being "useful"
just let people do what they choose to do
@Slereah Yes, but experience shows that they mostly don't lead to new fundamental discoveries doesn't it
That never bothers me
@Slereah Yeah it shouldn't bother you if you have reasonable expectations, not everyone does
17:50
Hello to contributors of this chat, I add these references for my username user142929 of MathOverflow if you want to read (my attempts to get relations) about arithmetic billiards and prime numbers: you can to search in the browser of MathOverflow the key words arithmetic billiard, Goldbach conjecture, chirality, gnomon. Good afternoon physicists.
You're trying to relate billiard balls and prime numbers?
they are obviously related
here's one right there
Yes, just an attempt @Amit I imagine prime numbers as the shape L.
Ah! Thanks @Slereah don't know how I missed that one
17:53
Numbers have shape?
Ok i got something about this but its long shot
Pi shows up in number of collisions of blocks due to conservation of energy/momentum stuff
Just a moment and I add a reference from MathOverflow and a draw from this post @Amit
And u can then relate pi to number theory stuff
There's connections with primes
I imagine prime numbers as the figures F1, F2 or F3 from imgur.com/a/TlmdwHi that is one of attached file for my post Arithmetic billiards, prime numbers and the Goldbach conjecture this mathoverflow.net/questions/429420/… @ACuriousMind
It appears like an illegitimate use of a SE question
17:56
@user250478 I see. Please don't ping me about this anymore.
I'm sorry if I bother you.
Good afternoon.
@Relativisticcucumber I don't know

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