@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
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
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
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
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
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
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
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
That's talking interpretations again isn't it... not all interpretations accept that there is a real distinction between "classical" and "quantum" conditions
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?
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)
@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)
@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
@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
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
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
Both time and space can exist as parameters of wavefunction. It is important to distinguish between parameters of wavefunction and arguments of wavefunction
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
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 :)
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
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
@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
@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...
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
@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
@ACuriousMind I mean time becomes probabilistic. So the fundamental version of the theory doesnt make any prediction becuz time of experiment isnt defined
I 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...
The 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
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.
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
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.
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
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
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.
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